Answer:
To solve this problem, we need to set the equation of the line and the equation of the given curve equal to each other and then solve for x. Once we find the value of x, we can substitute it back into either equation to find the corresponding y-coordinate. Here are the steps:
1. Set the equations equal to each other:
4 - 2x = 1
2. Solve for x:
4 - 2x - 1 = 0
3 - 2x = 0
3 = 2x
x = 3/2
2. Substitute x back into either equation to find y:
y = 4 - 2(3/2)
y = 1
Therefore, the point where the graph of y=4-2x crosses the line y=1 is at (3/2, 1).
I NEED HELP ON THIS ASAP!!! IT'S DUE TONIGHT
Because the distances XY and X'Y' are different, we can conclude that the rotation is incorrect (it shouldn't affect the lengths of the sides).
How to determine if the rotation is correct or not?Let's look at the original triangle, we can see that the distance between the vertices X (2, 5) and Y (10, 9) is:
Distance = √( (2 - 10)² + (5 - 9)²)
Distance = 8.94
The distance between the corresponding vertices in the second triangle X' (0, 1) and Y' (3, 9) is:
D = √( (0 - 3)² + (1 - 9)²) = 8.54
So that distance changed, which means that the shape of the triangle is now different, so the rotation is not done correctly.
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Follow this link to view Jamie’s work. Critique Jamie’s work by explaining the reasonableness of the scenario and the accuracy of the two parts of the graph he described . For any portion of Jamie’s response in which he has made an error, provide and explain an alternative response.
To enhance Jamie’s explanation, describe both sections of the piecewise function using linear equations. Include any limits to the domain.
Using the graph,
The 1st statement is true as we can see from the graph the runner starts at origin 0 and till it reaches the point (12,1) it grows steadily as the graph is steep and increasing as we move forward.
This 2nd statement is also true as we can see in the graph that the 2nd runner's graph is a lot steeper than the 1st runner & stops at a point (20,2).
Define graph?An organised representation of the data is all that the graph is. It facilitates our understanding of the facts. Data is the term used to describe the numerical information obtained through observation.
In the first statement:
It says that the runner begins the race & runs at a steady pace for 1 minute.
This statement is true as we can see from the graph the runner starts at origin 0 and till it reaches the point (12,1) it grows steadily as the graph is steep and increasing as we move forward.
Now in the 2nd statement it says, another runner runs from point (12,1) and runs at a steady but faster pace for 1 minute.
This statement is also true as we can see in the graph that the 2nd runner's graph is a lot steeper than the 1st runner.
So, the 2nd runner is going faster than the 1st and we can see that the 2nd runner stops at a point (20,2).
That shows the 2nd runner also ran for 1 minute.
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Can someone please answer these questions and explain how you got them
Answer:a) r >= -20
b) -10 <= x, or x >=-10
c) q<= 5
Step-by-step explanation:
a)-11r >=220
-11r/-11 >= 220/-11
r>=-20
b) -8<=-7+x/10
-8+7<=x/10
-1 <=x/10
-10 <=x
c) -1-6(5q-2)>=-139
-1 -30q +12 >= -139
-30q+12-1>=-139
-30q+11>=-139
-30q >= -139-11
-30q>= -151
-30q/-30 >= -151/-31
q <= 5,
u will notice the sign has changed from >= to <= it is coz when the negative signs erase themselves.
my neighborhood is full of one-way streets. to drive from my house to the grocery store, i have to go 1 block south, then 1 block east, then 5 blocks north, then 2 blocks east. each block is of a mile. how much shorter would my trip be if i could fly like a bird?
if you could fly like a bird, your trip would be approximately 3.9 miles shorter than the route you currently have to take (9 - 5.1 = 3.9).
If you were able to fly like a bird, you could take a direct path from your house to the grocery store, which would be shorter than the route you currently have to take.
By looking at the given directions, we can see that you have to travel a total of 1+1+5+2=9 blocks, with each block being a mile long, so your total distance traveled is 9 miles.
If you could fly like a bird, you could take a straight-line path from your house to the grocery store, which would be the hypotenuse of a right triangle with sides of 1 block and 5 blocks. Using the Pythagorean theorem, we can calculate that the distance of the hypotenuse would be the square root of[tex](1^2 + 5^2)[/tex] = square root of 26, which is approximately 5.
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Help me out please, thanks !! <3
Answer:
A
Step-by-step explanation:
because I took the test
Answer: I think it's a. 84 cubic units
Hope it helped : D
Use the vectors u = (7, 2) and v = (-2, 4) to find the indicated quantity.
3u•V
State whether the result is a vector or a scalar.
The answer is 3u•v = 3(-6) = -18. So, the result is a Scalar
What do you mean by Scalar and Vectar quantity?In physics, a scalar quantity is a physical quantity that has only magnitude, but no direction. Examples of scalar quantities include mass, time, temperature, energy, and distance. Scalar quantities are represented by a single numerical value, and they can be added, subtracted, multiplied, and divided like regular numbers.
On the other hand, a vector quantity is a physical quantity that has both magnitude and direction. Examples of vector quantities include displacement, velocity, acceleration, force, and momentum. Vector quantities are represented by a magnitude (the size or amount of the quantity) and a direction (the orientation of the quantity in space), and they are usually written as boldface letters or with an arrow above them. Unlike scalar quantities, vector quantities cannot be added, subtracted, multiplied, or divided like regular numbers. Instead, they must be combined using vector operations such as vector addition, dot product, and cross product.
The dot product of two vectors u and v is defined as:
u•v = (u1 * v1) + (u2 * v2)
where u1 and u2 are the components of vector u, and v1 and v2 are the components of vector v.
Using this formula, we can calculate:
u•v = (7 * -2) + (2 * 4) = -14 + 8 = -6
So, 3u•v = 3(-6) = -18.
Therefore, the result is a scalar.
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EASYY!!!
Take a factor out of each square root:
We can write √a⁵ as √a⁴ × a.Therefore, a factor out of each square root of √a⁵ = a²√a.
What is factor?A factor in mathematics is an algebraic expression or number that divides another expression or number without producing a residue.
For instance, 1, 2, 3, 4, 6, and 12 are factors of 12 because they can divide 12 equally.
Then, using the property of square roots that √ab = √a × √b, we can simplify this to:
√a⁴ × a = (√a²)² × √a = a²√a
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quadratic equation y=(x+4)²+3
The graph of the quadratic function is plotted, in which Vertex (h,k) = (-4,3).
Explain about the quadratic function:In mathematics, a quadratic equation is one with degree 2, which means that its maximum exponent is 2. A quadratic has the formula y = ax2 + bx + c, where a, b, and c are all numbers and a cannot be zero.
Given quadratic function:
y = (x+4)²+3
Now, the equation in vertex form is:
y = a(x - h)² + k
(h,k) are the vertex.
On comparing:
a = 1, h = -4, and k = 3
Vertex (h,k) = (-4,3)
Decide on a number of points along the parabola, making sure to get points on each side of the parabola and replacing x with both positive and negative numbers.
The ideal mirror image is: y = (x+4)²+3
x = 0, y = 19
x = 1, y = 28
x = 2, y = 39
x = -4, y = 3
Plot the vertex together with the points you choose. With the vertex serving as the minimum point, draw a parabola (curve) it through points.
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Complete question:
Given quadratic equation y=(x+4)²+3. Plot the graph.
Kayla, Tony, and Danielle kept track of their communications over a week. The data collected is represented in this display.
Which questions can be answered from this display?
After answering the presented question, we can conclude that Kayla had expression the most conversations on Wednesday, with eight.
what is expression ?An expression in mathematics is a collection of representations, digits, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a combination of the two can be used as an expression. Mathematical operators include addition, subtraction, rapid spread, division, and exponentiation. Expressions are often used in arithmetic, mathematics, and form. They are employed in the representation of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.
Tony had the most communications over the week, with a total of 33.
Danielle had the fewest communications over the week, with a total of 16.
Kayla and Tony had the most conversations on Monday, with each having nine.
On Thursday, Tony communicated 7 times.
Danielle communicated 16 times during the week.
Kayla had the most conversations on Wednesday, with eight.
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Answer:
Step-by-step explanation:
Hello! I just did the quiz and this was the correct answer!
Solve the following quadratic equation for all values of x in simplest form
9(x^2 −10)−3= 7
Answer: To solve the quadratic equation, we can start by simplifying the left side of the equation:
9(x^2 −10)−3 = 7
9x^2 - 90 - 3 = 7
9x^2 - 93 = 7
Next, we can isolate the x^2 term by adding 93 to both sides:
9x^2 = 100
Finally, we can solve for x by taking the square root of both sides and considering both the positive and negative square roots:
x = ±√(100/9)
x = ±(10/3)
Therefore, the solutions to the quadratic equation are:
x = 10/3 or x = -10/3.
Step-by-step explanation:
Answer: x=10/3
Step-by-step explanation:
9(x^2-10)-3=7
=>9(x^2-10)=7+3
=>x^2-10=10/9
=>x^2=10/9+10
=>x^2=100/9
=>x=10/3
what is the volume of this right rectangular prism
anter your answer in the box
ft3
The volume of the right rectangular prism with dimensions length = 7 feet, width = 2 feet, and height = 3.5 feet is 49 cubic feet.
What is volume ?
Volume is a physical quantity that refers to the amount of space occupied by an object or a substance. In mathematical terms, volume can be defined as the measure of the three-dimensional space enclosed by a closed surface or shape.
It is usually expressed in cubic units such as cubic meters, cubic feet, or cubic centimeters, depending on the system of measurement being used.
the length of the prism is 7 feet, the width is 2 feet, and the height is 3.5 feet.
Volume = Length x Width x Height
Volume = 7 ft x 2 ft x 3.5 ft
Volume = 49 cubic feet
So, the volume of the right rectangular prism with dimensions length = 7 feet, width = 2 feet, and height = 3.5 feet is 49 cubic feet.
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Help me please. Today I have to turn this in.
what information can be inferred (deduced) from the graphs you created? can you predict what the graphs would look like if you had polled 100 people? be specific in your explanations- this answer should be 6 thoughtful sentences long.
The information inferred from the graphs includes the overall trend, frequency of responses, and distribution of data, and predicting what the graphs would look like if we polled 100 people depends on factors such as sample population, question being asked, and range of possible responses.
From the graphs created, we can infer several things such as the overall trend, frequency of responses, and distribution of the data. For instance, if the graphs depict a bell-shaped curve, we can conclude that the responses were normally distributed, and that most people fell within the average range of responses. Conversely, if the graphs show a skewed distribution, it can indicate that a particular response was more common among the participants. We can also deduce from the graphs which response was the most popular and which was the least popular.
As for predicting what the graphs would look like if we polled 100 people, it would depend on various factors such as the sample population, the question being asked, and the range of possible responses. However, we can assume that with a larger sample size, the graphs would provide a more accurate representation of the population as a whole, and the distribution of responses would be more normal.
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The price of a laptop was marked 80 percent off because it had a cracked screen. If the resulted in a savings of $600, what is the value of x in the table above?
Answer:
$750
Step-by-step explanation:
.8x = $600, so x = $750
Mrs Sweet has 8 different milk chocolates and 9 different plain chocolates.
-
Her daughter chooses one of the milk chocolates.
Her son then chooses one of the plain chocolates.
Mrs Sweet then chooses one of the remaining chocolates.
Work out how many different combinations of three chocolates they can choose.
There are 1008 different combinations of three chocolates that they can choose.
What is a combination?
Combination is a way of selecting objects from a larger set, where the order of the selected objects does not matter.
There are three separate choices to be made, so we need to multiply the number of choices for each step.
First, the daughter chooses one of the 8 milk chocolates. She has 8 options.
Next, the son chooses one of the 9 plain chocolates. He has 9 options.
Finally, Mrs. Sweet chooses one of the remaining 14 chocolates (8 milk and 9 plain chocolates have already been chosen). She has 14 options.
To find the total number of combinations, we multiply the number of choices for each step:
8 x 9 x 14 = 1008
Therefore, there are 1008 different combinations of three chocolates that they can choose.
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what is the mean mode and median of 5,5,5,6,9
Answer:
Mode: 5
Mean: 6
Median: 5
Step-by-step explanation:
- The mean is the sum of the data divided by the number of data points.
- The mode is the data point that appears most frequently.
- The median is the middle value in the sorted data set.
In the given cone, the radius OC is 5 cm long. Find the volume and the total surface area of the cone if m∠BCO=42°. Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
i would say 45cm
3. A man earns # 140 000 per annum. He is allowed a tax free pay of # 30 000. If he pays 25 kobo in the naira as tax on his taxable income, how much has he left as disposable income?
4. A discount of 15% is allowed on an article. If a customer received N600.00, find the actual amount paid on the article.
the man has #112,500 left as disposable income after paying taxes.
the actual amount paid on the article after the 15% discount is N600.00.
How to calculate the disposable income?To calculate the disposable income of the man, we first need to determine his taxable income.
Taxable income = Annual income - Tax-free pay
Taxable income = #140,000 - #30,000 = #110,000
Next, we need to calculate the tax he has to pay on his taxable income.
Tax = Tax rate x Taxable income
Note that the tax rate is given in kobo, so we need to convert it to naira.
1 naira = 100 kobo, so 25 kobo = 0.25 naira
Tax = 0.25 x #110,000 = #27,500
Finally, we can calculate the disposable income by subtracting the tax from the annual income.
Disposable income = Annual income - Tax
Disposable income = #140,000 - #27,500 = #112,500
Therefore, the man has #112,500 left as disposable income after paying taxes.
4.If the discount allowed on an article is 15%, it means that the customer will pay only 85% of the original price of the article after the discount is applied.
Let the original price of the article be P.
Then, the amount paid by the customer after the 15% discount is 85% of the original price:
Amount paid = 0.85P
We know that the customer received N600.00.
So, we can set up an equation:
0.85P = N600.00
Solving for P, we get:
P = N600.00 / 0.85
P = N705.88 (rounded to two decimal places)
Therefore, the actual amount paid on the article after the 15% discount is N600.00.
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The number of tickets sold each day for an upcoming performance of Handel's Messiah is given by N=-0.3x^2+9x+13, where x is the number of days since the concert was first announced. When will daily ticket sales peak and how many tickets will be sold that day?
Question content area bottom
Part 1
Ticket sales will peak ?
days after the concert was first announced.
Part 2
The number of tickets sold on that day will be ?
(Round to the nearest integer as needed.)
To find when the daily ticket sales will peak, we need to find the maximum value of the quadratic equation [tex]N &= -0.3x^2+9x+13[/tex].
How to calculate no. of ticket solds and peak ticket sales?
Part 1:
The maximum value of a quadratic equation of the form [tex]y &= ax^2 + bx + c[/tex] occurs at [tex]x = \frac{-b}{2a}[/tex]. So in our case, the peak day will be at:
[tex]x &= \frac{-9}{2(-0.3)} = 15[/tex]
Therefore, the peak will be reached 15 days after the concert was first announced.
Part 2:
To find the number of tickets sold on that day, we substitute x=15 into the equation [tex]N &= -0.3x^2+9x+13[/tex]:
[tex]N &= -0.3(15)^2 + 9(15) + 13 = 67[/tex]
So the number of tickets sold on the day of the peak will be 67.
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A football coach orders one hoodie or one long sleeve performance shirt for each of his 45 players. Each hoodie costs $60 and each long sleeve performance shirt costs $45. The entire order totaled $2,400.
For a total of $2,400, the coach purchased 30 hoodies and 15 long sleeve shirts. A hoodie costs $60 and a long sleeve shirt is $45.
Let x represent the number of hoodies ordered and y represent the number of long sleeve shirts ordered. To describe the provided data, we may construct the following system of two equations:
x + y = 45 (because there are 45 players) (since there are 45 players)
60x + 45y = 2400 (the total cost of the order) (the total cost of the order)
We may determine that x = 30 and y = 15 by solving for x and y. As a result, the coach placed orders for 15 long sleeve jerseys and 30 hoodies. We can confirm that the total price is $2400: (30 x $60) + (15 x $45) = $1800 + $675 = $2400
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Find the lateral area of the pyramid
Answer:
The lateral surface area of the given square-based pyramid is 74 in².
Step-by-step explanation:
The lateral surface area of a three-dimensional object is the total surface area excluding the area of the base(s), so the total area of the "sides".
Therefore, the lateral surface area of a square-based pyramid is the sum of the area of the four triangular sides.
The area of a triangle is half the product of its base and height.
Therefore, the formula for the lateral surface area (L.S.A.) of a square-based pyramid is:
[tex]\boxed{\begin{minipage}{6 cm}\underline{L.S.A. of a square-based pyramid}\\\\$\sf L.S.A.= 2 \cdot s \cdot \ell$\\\\where:\\ \phantom{ww}$\bullet$ $s$ is the base length. \\ \phantom{ww}$\bullet$ $\ell$ is the slant height.\\\end{minipage}}[/tex]
From inspection of the given diagram:
[tex]\ell = \sf 7.4\;in[/tex][tex]s=\sf 5\;in[/tex]Substitute the given values into the formula to calculate the L.S.A. of the given square-based pyramid:
[tex]\begin{aligned}\implies \sf L.S.A.&=\sf 2 \cdot 5 \; in \cdot 7.4 \; in\\&=\sf 10 \; in \cdot 7.4 \; in\\&=\sf 74 \; in^2\end{aligned}[/tex]
Therefore, the lateral surface area is 74 in².
The lateral area of the pyramid is approximately 74square inches.
What defines a pyramid's horizontal side?
The triangular faces of the pyramid that converge at the apex are known as the lateral faces. These are the four triangles that encircle the square base in the provided net. As a result, the entire area of the four triangles makes up the pyramid's lateral surface area.
According to the given information:To find the lateral area of a pyramid, we need to find the sum of the areas of all the triangular faces except for the base. The lateral area formula for a pyramid is given by:Lateral area = 0.5 × Perimeter of base × Slant height where the slant height is the height of each triangular face.
First, let's find the perimeter of the base. Since the base is a square with a side length of 5.1 inches, its perimeter is:
Perimeter of base = 4 × Side length = 4 × 5.1 in = 20.4
In Next,
let's find the slant height. We can use the Pythagorean theorem to find the slant height of each triangular face.
The slant height is the hypotenuse of a right triangle with one leg equal to half the base length (since the base is a square) and the other leg equal to the height of the pyramid.
Half the base length = 5.1 in / 2 = 2.55
In Using the Pythagorean theorem, we get:Slant height = √(2.55² + 7²) ≈ 7.45 In Finally,
we can use the lateral area formula to find the lateral area of the pyramid:
Lateral area = 0.5 × Perimeter of base × Slant height= 0.5 × 20.4 in × 7.45 in≈ 76.02 in²
Therefore, the lateral area of the pyramid is approximately 76.02 square inches. Which is near to 74
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suppose you are conducting a hypothesis test to determine if a new marketing campaign increases sales for a particular product. what are the two types of errors you might make in conducting this test? (select all that apply)
The two types of errors you might make in conducting hypothesis test is type I error occurs when we conclude that the new marketing campaign does not increase sales when it actually does, This would lead to missed opportunities for increased sales and revenue for the company. Type II error occurs when we conclude that the new marketing campaign does not increase sales when it actually does, This would lead to missed opportunities for increased sales and revenue for the company. So, the correct option is A) and D).
Type I error is also known as a "false positive" error, where we reject the null hypothesis (i.e., conclude that the marketing campaign does increase sales) when it is actually false (i.e., the campaign does not have an effect on sales). This would lead to missed opportunities for increased sales and revenue for the company.
Type II error is also known as a "false negative" error, where we fail to reject the null hypothesis (i.e., conclude that the marketing campaign does not increase sales) when it is actually false (i.e., the campaign does have an effect on sales). This would also lead to missed opportunities for increased sales and revenue for the company.
Therefore, it is important to choose an appropriate significance level (alpha) and calculate the power of the test to minimize the risk of both types of errors in a hypothesis test. The correct answers are (A) and (D).
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--The given question is incomplete, the complete question is given
"Suppose you are conducting a hypothesis test to determine if a new marketing campaign increases sales for a particular product. What are the two types of errors you might make in conducting this test? (select all that apply)
a) A type I error occurs when we conclude that the new marketing campaign does not increase sales when it actually does. This would lead to missed opportunities for increased sales and revenue for the company.
b) A type II error occurs when we conclude that the new marketing campaign increases sales when it actually does not. This would lead to wasted resources on the marketing campaign and potentially lost sales if the company shifts resources away from a successful strategy.
c) A type I error occurs when we conclude that the new marketing campaign increases sales when it actually does not. This would lead to wasted resources on the marketing campaign and potentially lost sales if the company shifts resources away from a successful strategy.
d) A type II error occurs when we conclude that the new marketing campaign does not increase sales when it actually does. This would lead to missed opportunities for increased sales and revenue for the company."--
s varies directly as t, and = 8 when = 16. Find the constant of variation and write a direct variation equation relating s and t. Then find t when = 16. (Write answers in decimal form.)
constant of variation:
direct variation equation:
when s=16, t=
The constant of variation and write a direct variation equation relating s and t direct variation s= (1/2)t and t=32.
What is direct variation?Direct Variation is that in which there is a relationship between two variables in which one is a constant multiple of the other. For example, when one variable changes the other also changes, then they are said to be in proportion. If y is directly proportional to x then the equation is of the form y = k x (where k is a constant).
Given that,
s varies directly as t
i.e. s∝ t
⇒s= kt [ where k is the variational constant] -------------(1)
Given that s=8 when t= 16
putting these values in equation (1) we get,
8= k× 16
k= 8/16
k= 1/2
so, s= (1/2)t
If s= 16 then t= 16×2=32
Hence, s= (1/2)t and t=32
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how to slove totla suface area of triangle
To find the area of a triangle, the correct formula is Area = (base x height) / 2.
A triangle is a 2-dimensional shape with three sides and three angles. It does not have a total surface area like a 3-dimensional shape such as a cube or a sphere.
However, you can find the area of a triangle using the following formula:
Area = (base x height) / 2
where "base" refers to the length of one of the sides of the triangle, and "height" refers to the perpendicular distance from the base to the opposite vertex.
Once you have calculated the area of the triangle, you can use this value to find other quantities such as the perimeter or the length of other sides using various formulas.
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A maze and walkway with the same total area of 5,616 square yards has a walkway that is one yard wide. What are the dimensions of this maze?
The total width of the maze is 51.5+2=53.5 yards and the total length of the maze is 105 yards.
What is an Equations?Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
The total area of the maze and walkway is equal to the area of the maze plus the area of the walkway. The area of the walkway is equal to the length of the maze plus twice its width since the walkway is one yard wide on both sides of the maze.
Let x be the width of the maze. So, (x+2) is the width of the maze and walkway, and (2x+2) is the length of the maze and walkway.
length×width=area
(2x+2)(x+2)=5616
2x²+6x+4=5616
2x²+6x=5612
Write in the form x2+bx=d by dividing both sides by 2:
x²+3x=2806
Complete the square by adding (23)2=2.25 to each side:
x²+3x+2.25=2806+2.25
(x+1.5)²=2808.25
Take the square root of both sides:
x+ 1.5 = ±√2808.25
x = −1.5±√2808.25
x ≈ −54.5 or x ≈ 51.5
A negative solution does not make sense so we take x≈51.5.
Hence, the total width of the maze is 51.5+2=53.5 yards and the total length of the maze is
2(51.5)+2
= 105 yards.
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Hunter loves riding Ferris wheels and roller coasters. While visiting the Hancock County Fair, he first went on the Ferris wheel 1 time and the roller coaster 2 times, using a total of 15 tickets. Then, after taking a break and having a snack, Hunter went on the Ferris wheel 5 times and the roller coaster 4 times, using a total of 39 tickets. How many tickets does it take to ride each attraction?
Answer:
54
Step-by-step explanation:
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The equation y 5 15x represents the dollar amount a football team earns as a function of the number of tickets sold for its end-of-season banquet. The table shows the budget balance as the team pays for table rentals.a.What is the rate of change for the money earned by the football team? What does this represent?b.What is the rate of change of the budget balance? What does this represent?c.If one table seats 8 guests, does the football team earn more from ticket sales or spend more on table rentals? Explain.
Answer:
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Step-by-step explanation:
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Which expressions are completely factored? Select each correct answer.
Responses
12a^3+8a=4(3a^3+2a)
24a^4+18=6(4a^4+3)
16a^5−20a^3=4a^3(4a^2−5)
30a^6−24a^2=3a^2(10a^4−8)
According to the given expression some are shortlisted factored expressions are [tex]4(3a^3 + 2a) for 12a^3 + 8a , 6(4a^4 + 3) for 24a^4 + 18, 4a^3(4a^2 - 5) for 16a^5 - 20a^3.[/tex]
Explain expressions?Expressions in mathematics are numerical, variable, and operation combinations that are used to indicate a quantity or a relationship between values.
One or more variables or numbers are combined with one additional operation to form an expression. An illustration of an expression is X + 1.
The completely factored expressions are:
[tex]4(3a^3 + 2a) for 12a^3 + 8a\\\6(4a^4 + 3) for 24a^4 + 184a^3(4a^2 - 5) for 16a^5 - 20a^3[/tex]
So the correct answers are:
[tex]12a^3+8a=4(3a^3+2a)24a^4+18=6(4a^4+3)16a^5−20a^3=4a^3(4a^2−5)[/tex]
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Divide. 4×10^2 4×10^1
After dividing the given expression 4×10²/4×10¹, we have the resultant answer which is 10.
What is an expression?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.
Algebraic expressions contain both numbers and variables in terms, separated by operators, whereas mathematical expressions only contain numbers and operators.
So, we have the expression:
= 4×10²/4×10¹
Now, solve as follows:
= 4×10²/4×10¹
= 4×100/4×10
= 400/40
= 10/1
= 10
Therefore, after dividing the given expression 4×10²/4×10¹, we have the resultant answer which is 10.
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Mrs. Kelley is teaching a 5th grade class. She is standing 6 meters in front of Gabrielle. Leslie is sitting to Gabrielle's right. If Leslie and Mrs. Kelley are 7 meters apart, how far apart are Gabrielle and Leslie? If necessary, round to the nearest tenth.
Gabrielle and Leslie are approximately 9.2 meters apart, rounded to the nearest tenth, given that Mrs. Kelley is standing 6 meters in front of Gabrielle and Leslie and Mrs. Kelley and Leslie are 7 meters apart.
Where M represents Mrs. Kelley, G represents Gabrielle, and L represents Leslie.
We can see that a right triangle is formed by Gabrielle, Mrs. Kelley, and the distance between Gabrielle and Leslie. We can use the Pythagorean theorem to find the missing side:
[tex]c^2 = a^2 + b^2[/tex]
where c is the distance between Gabrielle and Leslie, a is 6 meters (the distance between Mrs. Kelley and Gabrielle), and b is the distance between Mrs. Kelley and Leslie (which is equal to 7 meters).
Substituting the values, we get:
[tex]c^2 = 6^2 + 7^2[/tex]
[tex]c^2[/tex] = 36 + 49
[tex]c^2[/tex] = 85
Taking the square root of both sides, we get:
c ≈ 9.2
Therefore, Gabrielle and Leslie are approximately 9.2 meters apart, rounded to the nearest tenth.
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