Answer:
it's "c" or the third option
9. Expand :
(i) (3x - 4y + 5z)² (ii) (2a-5b-4c)²
(iii)
(5x + 3y)³
(iv) (6a - 7b)³
What is the value of x? (HINT: find the sum of the
interior angles of the pentagon first)
Answer:
(2x+10°) + (x°) +(2x-20°) = 540°
540 is the sum angle of the polygon
collect like terms
2x+x+2x+10°-20°=540°
5x-10°=540°
5x=540°+10°
5x=550°
x=550°/5
x=110°
(2(110)+10)+(110)+(2(110)-20)=540°
Geometry Questions....need help pls
This given figure carries onto themself at 360, 180, and 60 degrees respectively.
What does carrying a figure onto itself mean?If a rotation between 0° and 360° around the center of a figure in the plane may map the figure onto itself, the figure possesses rotational symmetry. From its starting point, the figure can be rotated and mapped onto itself. The symmetry is of order 4. As a result, the figure displays both rotational and line symmetry.
Given three figures those figures have rotational symmetry from their center point. The fixed point that the rotation revolves around in a figure or object with rotational symmetry is referred to as the center of rotation.
for figure 1
figure 1 does not have rotational symmetry on any given angles thus, its rotational symmetry would be 1 since it carries onto itself at 360°.
for figure 2
figure 2 has rotational symmetry at 180°. thus, its rotational symmetry would be 2 since it carries onto itself at 180° and 360°.
for figure 3
figure 3 has rotational symmetry at 60, 120, 180, and 240. thus, its rotational symmetry would be 6 since it carries onto itself at 60, 120, 180, 240, and 360°.
therefore, the given figures have 1, 2, and 6 rotational symmetry.
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2x-(x+5)=-1
Solve for x.
Answer:
x=4
Step-by-step explanation:
2x-(x+5)=-1
Solve for x
Distribute the minus sign
2x-x-5=-1
Combine like terms
x -5 = -1
Add 5 to each side
x-5+5 = -1+5
x=4
[tex]2x-(x+5)=-1[/tex]
Distribute negative sign:
[tex]2x+-1(x+5)=-1[/tex]
[tex]2x+-x+-5=-1[/tex]
Combine Like Terms:
[tex](2x+-x)+(-5)=-11[/tex]
[tex]x-5=-1[/tex]
Add 5 to both sides:
[tex]x-5+5=-1+5[/tex]
[tex]\fbox{x = 4}[/tex]
1. Cameron ran 3 miles in 24 minutes. Identify the equivalent ratio that represents Cameron's run. *
The equivalent ratio that represents Cameron's run is 1 : 8
Equivalent Ration:
In mathematics, the definition of equivalence ratio says: The equality of two ratios is also called a ratio. Front and follow have different values, but reducing them to their simplest form gives the same value.
For example, to find out if 2:3 and 16:24 are equivalent ratios, we need to reduce both ratios to their simplest form. The HCF of 2 and 3 is 1, so 2:3 is already in the simplest form. The HCF for 16 and 24 is 8. Divide these two numbers by 8 to get the reduced form. This means (16÷8):(24÷8) = 2:3. It's clear that 2:3 and 16:24 are the same value, equivalent ratios.
Based on the question :
Cameron ran 3 miles in 24 minutes.
Now,
Therefore we can say that :
Cameron ran 1 miles in 8 minutes;
Therefore, the equivalent ration is 1 : 8.
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In the figure, JKLM-EFGH. Complete the following table,
type your answer
Value of x
Value of y
Scale factor of JKLM to EFGH
type your answer.
type your answer
Value of z
type your answer.
The values of x , y and z are 80,2,110 respectively from the given figure where JKLM ~ EFGH
What is Quadrilateral ?
Quadrilateral can be defined as the type of the polygon in which it contains four sides.
Given ,
JKLM ~ EFGH
Since , JKLM ~ EFGH
3/30 = 11/z
z = 30*11/3
z =110
3 / 30 = 8/ x
3 * x = 8 * 30
x = 80
3 / 30 = y/ 20
y = 20 * 3 / 30
y = 2
Hence the values of x , y and z are 80,2,110 respectively.
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The annual cost of Randall coverage is 4900. The college pays 62% of the cost. How much is Devi red from his biweekly paycheck for medical insurance?
$1862 is Devi red from his biweekly paycheck for medical insurance
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
The annual cost of Randall coverage is 4900.
The college pays 62% of the cost.
We need to find How much is Devi red from his biweekly paycheck for medical insurance
Let us convert 62% to decimal value by dividing with 100
62/100=0.62
Now multiply 0.62 with 4900
0.62×4900
3038
Now subtract 3038 from 4900
4900-3038
1862
Hence, $1862 is Devi red from his biweekly paycheck for medical insurance
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Complete the table for an object that goes 3/4 miles in 6 minutes.
Write any fraction as follows: 1/2 for one half
The speed of Ana is in miles per hour 7.5mph
By dividing the distance Ana covered by the amount of time she spent running, one may calculate her speed in miles per hour. Since the question asks for the speed to be calculated in miles per hour, an hour rather than a minute would be utilized as the unit of time.
Speed = distance ÷ time
Distance = 3/4
Time = 1/10
Speed = 3/4 ÷ 1/10
Speed = 3/4 x 10 = 15/2 miles per hour
or, 7.5mph
Divide the distance Ana covered by the time she ran to get her speed.
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The question is incomplete
Ana runs 3/4 mile in 6 minutes or 1/10 hour. Assuming she runs at a constant rate, what is her speed, in miles per hour
What is the area of right triangle with base 10 cm and height 5 cm?
Answer:25cm
Step-by-step explanation:area of triangle=1/2 × base× height
=1/2×10×5
= 25cm^2
distance of -6,8 and 1,7
Answer:
d ≈ 7.07 units
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (- 6, 8 ) and (x₂, y₂ ) = (1, 7 )
d = [tex]\sqrt{((1-(-6))^2+(7-8)^2}[/tex]
= [tex]\sqrt{(1+6)^2+(-1)^2}[/tex]
= [tex]\sqrt{7^2+1}[/tex]
= [tex]\sqrt{49+1}[/tex]
= [tex]\sqrt{50}[/tex]
≈ 7.07 units ( to 2 decimal places )
Can you make a triangle with 3 different length sides?
Yes, you can make a triangle with three different length sides.
1. Draw three lines of different lengths on a piece of paper.
2. Connect the ends of the lines to form a triangle.
3. The triangle will have three different length sides. The lengths of the sides depend on the lengths of the three lines you drew.
4. To make sure the triangle is valid, use the triangle inequality theorem. This theorem states that the sum of any two sides of a triangle must be greater than the third side.
5. Measure each side of the triangle with a ruler and add them together.
6. Compare the sum of the two sides to the third side. If they are not equal or greater, adjust the lines to create a valid triangle.
7. Once the triangle is valid, it will be a triangle with three different length sides.
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Is x2 4x 4 a perfect square trinomial?
x² + 4x + 4, this is a perfect square trinomial, which is expressed as
(x + 2)²
What is trinomial?Trinomials are algebraic formulas that include three dissimilar terms, therefore the name "trinomial."
An algebraic expression called a trinomial contains three terms that are non-zero. Trinomial expression illustrations: The trinomial x + y + z has three variables: x, y, and z.
A trinomial is formed when three monomials are added together or subtracted from one another. A quadratic trinomial has the following form: ax² + bx + c, where a, b, and c are real, non-zero values.
Given that,
x² + 4x + 4
= (x)² + 2(2x) + 4
= (x)² + 2(x)(2) + 2²
This is similar to a² + 2ab + b² = (a + b)²
so, we can write:
= (x + 2)²
= (x + 2) (x + 2)
so, this is a perfect square trinomial.
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BRAINLY GRANTED FOR CORRECT ANS PLEASE HELP
P (X)= [tex]x^3+4 x^2-3x+2[/tex] moreover, [tex]\frac{P(x)}{x - 1} = x^{2} + 5x +2[/tex] as a result, the actual claim is [tex]$p(x)=(x-1)\left(x^2+5 x+2\right)+\frac{4}{x-1}$[/tex]
How do you find the probability equation?The likelihood of an event occurring is determined by probability: P(A) = f / N. Probability and odds are related, but probability is necessary for odds to exist. Prior to calculating the likelihood that an event will occur, probability is required.
The steps listed below can be used to determine an event's likelihood: Step 1: Identify an event that has only one outcome. Step 2: Compile a list of all potential outcomes, including any positive ones. Step 3: Subtract the number of favourable outcomes from the total number of outcomes that are feasible. The probability of A or B is equal to p(A or B) = p(A) + p(B) if occurrences A and B are mutually exclusive (B). A probability is a number that expresses the possibility or likelihood that a specific event will take place.
Therefore the correct answer is option A ) [tex]$p(x)=(x-1)\left(x^2+5 x+2\right)+\frac{4}{x-1}$[/tex]
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. The length of one line segment is 9cm and the length of a parallel line segment is 3cm. What scale factor would you need to use to map the first line segment onto the second line
semgment?
O 9/3=3
O 9x3=27
O 3/9=0.33
O 9/9=1
Scale factor required to map the first line segment onto second line segment is 3/9=0.33
What is scale factor?The scale factor is the ratio of the length of the image to the length of the pre-image.
In this case, we're looking for the that would map the first line segment (length 9cm) onto the second line segment (length 3cm).
To find the scale factor, we can divide the length of the image by the length of the pre-image:
scale factor = length of image / length of pre-image
In this case:
[tex]ScaleFactor=\frac{Length Of Image}{Length Of Pre-image}[/tex]
[tex]scale factor = 3cm / 9cm = 1/3=0.033[/tex]
So the scale factor to map the first line segment onto the second line segment is 1/3.
It means the 1st line is 3 times longer than the second one.
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can someone help me find two true statements!
1. In a triangle line parallel to one side will divides other two sides in the same ratio
2. 8/x = 12/18
x = 12
How do you find a linear equation from two points?Finding the slope between two points on a line and solving for the y-intercept in the slope-intercept equation y=mx+b allows us to formulate an equation for that line.
A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. (b).
Because (0,y) is the location where the line crosses the y-axis, the value of y when x is 0 is referred to as the y-intercept.
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which set of ordered pairs below is a function?
The first and the third set of order pairs is a function.
What is function?
A set of ordered pairs that contain only unique ordered pairs with unique x coordinates is referred to as a function. A function is defined by an equation that generates a set of ordered pairs.
Consider, the given set of order pairs,
I - {(3, 3), (6, 1), (2, 3)}
II - {(4, 7), (2, 8), (4, 2)}
III - {(9, 6), (3, 1), (7, 3)}
We have check which set of ordered pairs above is a function.
Since, a function is a set of ordered pairs in which no two different ordered pairs have the same x -coordinate.
In the given order pairs the second order pair contain same x - coordinate.
So, the second order pair is not a function.
Hence, the first and the third set of order pairs is a function.
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A town has a population of 4000 and grows at 2% every year. To the nearest year, how long will it be until the population will reach 4500?
=========================================================
Work Shown:
x = number of years
y = population
y = 4000*1.02^x
4500 = 4000*1.02^x
4500/4000 = 1.02^x
1.125 = 1.02^x
log(1.125) = log(1.02^x)
log(1.125) = x*log(1.02)
x = log(1.125)/log(1.02)
x = 5.94784893412128
Rounding to the nearest year, it takes about 6 years for the population to reach 4500 people.
---------------
Check:
Plug in x = 5
y = 4000*1.02^x
y = 4000*1.02^5
y = 4416.3232128
y = 4416
We come up a bit short. Now try x = 6
y = 4000*1.02^x
y = 4000*1.02^6
y = 4504.649677056
y = 4505
We go a bit over the target, but it's better to go over rather than come up short.
This confirms the answer is approximately 6 years.
the swim team trains 4 days every week. Mon, Tues, and Thurs, the swim tea spends 1/2h in the gym followed by 1 1/4 in the pool. On Saturday there is no gym work but double the swim team time. how many hours per week does the team train?
The number of hours that the team trains per week is 17 hours.
How to illustrate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
Since the swim tea spends 1/2h in the gym followed by 1 1/4 in the pool. On Saturday there is no gym work but double the swim team time. The number of hours will be:
( 1 1/4 + 1/2 + 2 1/2) × 4
= 4.25 × 4
= 17 hours.
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I
Student council is selling personal pan pizzas to raise money for a field trip. They
make a profit of $1. 50 for each pizza they sell. If they already have $235, what is the
minimum number of pizzas must they sell in order to have at least $300?|
The minimum number of pizzas must they sell in order to have at least $300 is 44.
What is the profit?
The profit is defined as the amount gained by selling a product, and it should be more than the cost price of the product. In other words, the profit is a gain obtained from any business activities.
The student council needs to raise $300 - $235 = $65 to reach their goal.
They make a profit of $1.50 for each pizza they sell.
so they need to sell $65 / $1.50 = 43.333 pizzas to reach their goal.
As you cannot sell a fractional number of pizzas, they need to sell at least 44 pizzas to raise enough money for the field trip.
Hence, the minimum number of pizzas must they sell in order to have at least $300 is 44.
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Carolina is mowing lawns for a summer job.for every mowing job,she charges an initial fee plus $6 for each hour of work.her total fee for a 4-hour job,for instance is $32
The function Formula is, f(t) = 6t + 8.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The collection of values that could result in a function's outputs is known as the co-domain.
Given:
Carolina charges an initial fee plus $6 for each hour of work
Her total fee for a 4-hour job = $32
So, if she work for 't' hours then linear equation will be of the form
f(t) = mt + b
Here m is the constant rate = 6
Now we plug in the values and find out b, m=6
f(t) = mt + b
32 = 6(4) + b
32= 24 + b
8 = b
So, the function is f(t) = 6 t+8.
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3. The difference between the digits in a two-digit numeral is 3. The units’ digit is twice the tens’ digit. Find the numeral.
Answer:
36
Step-by-step explanation:
let the number be 10x+y
x - y = 3 (eq 1)
given: y = 2x (eq 2)
putting 2 in 1
x - 2x = 3
-x = 3 (we can ignore the negative sign for now because we only need to find the absolute value)
y = 6
number is 36
If a coin is tossed 4 times, the odds of it coming up either heads every time or tails every time are 1:7.
What is the probability the coin comes up all heads or all tails after 4 tosses?
The probability the coin comes up all heads or all tails after 4 tosses is 12.5%.
What is probability?Probability refers to the ratio, chance, likelihood, or odds that an expected outcome is achieved when there are many possible outcomes.
Probability is a fractional value, especially when the odds of the occurrence of the expected event are not 100% uncertain or certain.
In this case, probability lies between zero and one.
Odds of a coin coming up either heads or tails every time = 1:7
The sum of ratios = 8 (1 + 7)
Thus, the probability of the coin coming up with all heads or all tails = 12.5% (1/8 x 100)
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Stefanie has 18 grams of 20% sugar syrup and john 30 of 25% what is the concentration in the new mixture
The concentration in the new mixture will be 11.1 grams.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
Stefanie has 18 grams of 20% sugar syrup.
And, john has 30 grams of 25%.
Here,
Stefanie has 18 grams of 20% sugar syrup.
Hence, The amount of sugar = 18 × 0.2
= 3.6 grams
And, john has 30 grams of 25%.
Hence, The amount of sugar = 30 × 0.25
= 7.5 grams
Thus, The concentration in the new mixture = 3.6 + 7.5 grams
= 11.1 grams
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Mario has 3/4 cups of chocolate chips needs 1/3 cup to make a batch of cookies how many batches can Mario make if he uses all of his chocolate chips
In the given equation, Mario can make 2.25 batches of cookies using all of his chocolate chips.
How to find the given equation?First, you can find out how many total cups of chocolate chips Mario has by multiplying the number of cups per unit (3/4) by the number of units (1).
[tex]3/4 cups * 1 = 3/4 cups\\[/tex]
Then you can divide the total amount of chocolate chips Mario has by the amount of chocolate chips needed per batch:
[tex]3/4 cups / 1/3 cup/batch = 3/4 cups * 3/1 cup/batch = 9/4 cups/batch[/tex]
Finally, you can convert this to a whole number by dividing both the numerator and denominator by their greatest common factor, which is 1:
[tex]9/4 cups/batch = (9/1) / (4/1) = 9/4 = 2.25 batches[/tex]
Mario can make 2.25 batches of cookies using all of his chocolate chips.
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Donna reads 56 chapters of a book in 7 hours. What is her rate in chapters per hour?
Answer:
To find what her rate for how many chapters she reads per hour, you want to find out what times 7 gives you 56, or you can simply divide:
56/7 = 8
Donna reads 8 pages per hour.
Step-by-step explanation:
Hope it helps! =D
Sergio purchased 4 items for $1.50 each. Sales tax was 8.25%. What was the total price?
please explain if you can, thxs!
Answer:
6.495.Step-by-step explanation:
The total cost of the items before tax was $1.50 * 4 = $<<1.54=6>>6.
The sales tax was $6 * 8.25% = $<<68.25*.01=0.495>>0.495.
So the total price was $6 + $0.495 = $<<6+0.495=6.495>>6.495.
What is the value of x?
3/4(x−8)= −1/2
Answers:
x = -26/3
x = 10
x = 22/3
the value of x would be 22/3 after simplification.
What is simplification?The acts or process of simplifying something such that it is simpler to accomplish or understand, or the item that is the consequence of such simplifying: The group offers suggestions on how to make trade procedures simpler. In mathematics, we generally use the PEMDAS method to simplify the values.
Given, the equation in the form of x is 3/4(x−8)= −1/2
For the value of x
3/4(x−8)= −1/2
multiply by 4 on both sides
3(x - 8) = -2
divide by 3 into both the sides
x - 8 = -2/3
add 8 on both sides
x = -2/3 + 8
x = 22/3
therefore, the value of x for the given equation 3/4(x−8)= −1/2 is 22/3.
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Which milk product will have approximately 15.36 grams of milk fat in an 80-gram serving?(Heavy Cream: 36.7%, Light Cream 19.2%, Whole Milk 3.5%, Low-Fat Milk 1.5%, Skim Milk 0.05%)
The Light cream with 19.2% content will have 15.36g of milk.
What are percentages?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”
Given here Light cream as 19.2% of 80g
∴ 0.192×80=15.36g
Hence, The Light cream with 19.2% content will have 15.36g of milk.
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prove that (4x-5)2 -5x(3x-8) is a positive for all values of x
To prove that (4x - 5)^2 - 5x(3x - 8) is positive for all values of x, we can start by expanding the expression:
(4x - 5)^2 - 5x(3x - 8) = 16x^2 - 40x + 25 - 15x^2 + 40x = -14x^2 + 80x - 25
Now, we can complete the square to find that this expression is always positive:
-14x^2 + 80x - 25 = (-14x^2 + 80x) - 25
= (-14x^2 + 80x + (80/2)^2 - (80/2)^2) - 25
= (-14x + 40)^2 - 25 - 40^2 + 40^2
= 15^2 - 25
= (15 - 5)(15 + 5)
= 10(20)
= 200
Since this expression is equal to 200, which is a positive number, we can conclude that (4x - 5)^2 - 5x(3x - 8) is positive for all values of x.
3 ratios equivalent to 6/18
Answer:
Step-by-step explanation:
divide them both by 2
which is 3/ 9
divide them both by 3
whic is 2/6
and finally divide them both by 6
which is 1/3
you can multiply them both by an number as well
take care