Answer:
259.8 square feet
Step-by-step explanation:
What is the area of a regular hexagon with sides that measure 10 feet and an
apothem that measures 8.66 feet?
The formula to solve the above question is given as:
Area = (3√3 s²)/ 2 where
s is the length of a side of the regular hexagon
Area of this Hexagon is calculated as:
= (3√3 × 10²)/2
= 3√3 × 100/2
= 259.80762114 square feet
Approximately = 259.8 square feet
The area of the regular hexagon = 259.8 square feet
10) You use a technical support company for your computer. The company bills you at a rate of $10 per month and $35 per hour for phone support.
a. Identify the fixed cost (the constant).
b. Identify the independent variable (x).
c. Identify the dependent variable (y).
d. Write an equation that describes the situation above.
e. If you were billed $97.50 for last month, how many hours of phone support did you need? Show all work.
Answer:
a) 10
b) Number of hours of phone support (per month).
c) Total bill (per month).
d) y = 35x + 10
e) 2.5 hours
Step-by-step explanation:
The company bills you at a rate of:
$10 per month$35 per hourPart aThe fixed cost (the constant) is the cost per month ⇒ $10.
Part bThe independent variable is the variable that is not affected by any other variables.
Therefore, the independent value (variable x) is the number of hours of phone support per month.
Part cA dependent variable is the variable that is affected by the other variable.
Therefore, the dependent value (variable y) is the total bill (in dollars) per month.
Part dThe equation that describes the given situation is:
[tex]y = 35x + 10[/tex]Part eTo calculate how many hours of phone support was needed for a bill of $97.50, substitute y = 97.5 into the equation from part d and solve for x.
[tex]\implies 35x+10=97.5[/tex]
[tex]\implies 35x+10-10=97.5-10[/tex]
[tex]\implies 35x=87.5[/tex]
[tex]\implies \dfrac{35x}{35}=\dfrac{87.5}{35}[/tex]
[tex]\implies x=2.5[/tex]
Therefore, 2.5 hours of phone support was needed last month.
Write 108:96 in the form 1:n.
Answer:
it will be [tex]1:\frac{8}{9}[/tex]What percentage of the class voted for Maria?
more geometry stuff pls help
Answer:
[tex]y=\sqrt{10}[/tex]
Step-by-step explanation:
Using the geometric mean theorem, [tex]y=\sqrt{(2)(5)}=\sqrt{10}[/tex].
(Simplify: 7a + 6 - 3 - 2
Use the number line to find the difference of-3(-1.5).
Answer:
=4.5
Step-by-step explanation:
the rule is
positive - negative changes to positive + positive so
3- (-1.5) changes to 3 + 1.5 which equals 4.5
What is an equation of the line that passes through the point (-5,7) and is parallel to the line x-5y=15?
Answer: An equation of a line that is parallel to another line has the same slope as the original line. The slope of a line can be found by rearranging the equation of the line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept (the point at which the line crosses the y-axis).
To find the equation of a line that is parallel to the line x - 5y = 15 and passes through the point (-5,7), we can first rearrange the equation of the original line in slope-intercept form:
x - 5y = 15
y = (1/5)x - 3
The slope of this line is (1/5). To find an equation of a line that is parallel to this line and passes through the point (-5,7), we can use the point-slope form of a line:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope of the line.
Substituting in the values given in the question, we get:
y - 7 = (1/5)(x - (-5))
y - 7 = (1/5)x + 1
y = (1/5)x + 1 + 7
y = (1/5)x + 8
Therefore, the equation of the line that is parallel to the line x - 5y = 15 and passes through the point (-5,7) is y = (1/5)x + 8.
Step-by-step explanation:
What will be the minimum value of the expression 3x² 6x 6?
The minimum value of the expression 3x² + 6x + 6 is 3.
Therefore the answer is 3.
A quadratic mathematical expression contains a variable of highest degree of 2 and it is of the general form ax² + bx + c, where a, b and c are constants.
Minimum value of a quadratic equation of form ax² + bx + c is when
x = -b/ 2a
Then minimum value is
a( -b/ 2a )² + b( -b/ 2a ) + c
= (b²a + -2ab² + 4a²c)/ 4a²
= ( - b² + 4ac)/ 4a
= c - b²/4a
In the expression 3x² + 6x + 6, a = 3, b =6 and c = 6. So minimum value is
= 6 - 6²/ (4×3)
= 3
--The question is incomplete, answering to the question below--
"What will be the minimum value of the expression 3x² + 6x + 6?"
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How do you determine area?
Answer:
You multiply one side and then the other. Basically doing hxw
20 h(x)=−x 2 8x20, determine the average rate of change of the function over the interval 0 ≤ x ≤ 5
The average rate of change of the function h(x) = -x² + 8x over the interval 0 ≤ x ≤ 5 is 3.
What is the average rate of change?
The Average Rate of Change function is defined as the average rate at which one quantity is changing with respect to something else changing. In simple terms, an average rate of change function is a process that calculates the amount of change in one item divided by the corresponding amount of change in another.
To find the average rate of change of a function over an interval, we need to find the difference in the function values at the endpoints of the interval, divided by the difference in the x-values of the endpoints.
In this case, the function is h(x) = -x² + 8x, the interval is 0 ≤ x ≤ 5, and we want to find the average rate of change over that interval.
So, we can use the following formula:
Average rate of change = (h(5) - h(0)) / (5 - 0)
Now we have to substitute the values into the equation:
h(5) = -5^2 + 85 = -25 + 40 = 15
h(0) = -0^2 + 80 = 0
Average rate of change = (15 - 0) / 5 = 3
Hence, The average rate of change of the function h(x) = -x² + 8x over the interval 0 ≤ x ≤ 5 is 3.
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WILL GIVE BRAINLIEST PLEASE HELP
The following triangular prism has a base that is a right triangle.
A. Draw or describe the net of this triangular prism. Make sure to include the dimensions of each part of the net.
B. Use your net to calculate the surface area of the prism.
A. The net of a triangular prism is a flattened version of the prism that shows all the faces of the prism.
The prism's base is a right triangle with a base of 3 units and a height of 4 units. The prism is six units tall. The net of the triangular prism would look like a rectangle with a length of 3 units and a width of 4 units. On top of this rectangle, there would be two smaller triangles, each with a base of 3 units and a height of 6 units.
B. To calculate the surface area of the prism, we need to add the area of all the faces.
The base of the prism is a right triangle with an area of (1/2) (3 units) (4 units) = 6 square units.
The two triangular faces have an area of (1/2) (3 units) (6 units) = 9 square units each.
The rectangular face has an area of (3 units) (6 units) = 18 square units.
So, the total surface area of the prism is:
6 square units (base) + 9 square units (triangular face) + 9 square units (triangular face) + 18 square units (rectangular face) = 42 square units.
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A band wants to enter a contest that requires traveling expenses. They need at least $1,150 to cover all of the expenses. They have already saved $700. They are selling shirts with a profit of $7. 00 per shirt to earn the remaining money Part Which inequality represents the minimum number of shirts, n, the band must sell to earn the remaining money 1, 150
the number of shirts has to be an integer (you can not sell "part" of a shirt) n >= 65
They need at least $1,150
They have already saved $700
They are selling shirts with a profit of $7.00 per shirt
If they sell n number of shirts, they will earn n times $7.00
Since they have already 700, they will earn a total of 700 + 7n
If this quantity has to be equal or greater to 1,150, we can write:
1150 <= 700 + 7n
if we solve this inequality for n:
1150 <= 700 + 7n
1150 - 700 <= 7n
450 <= 7n
450/7 <= n
64.28 <= n
Since the number of shirts has to be an integer (you can not sell "part" of a shirt)
n >= 65
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Today you ran seven-eighths of a mile. Yesterday you ran three-fourths of a mile. How much farther did you run today?
You ran 1/8 of miles more today than yesterday.
What is Subtraction?Subtraction can be done for any numbers or algebraic expressions. It is the process of taking out certain value from a given amount of number.
Miles you ran yesterday is three fourths of a mile.
Let 1 mile be M.
Miles you ran yesterday = 3/4 M
Today you ran seven-eighths of a mile.
Miles you ran today = 7/8 M
Difference of miles = 7/8 M - 3/4 M
3/4 is same as 6/8.
Difference of miles = 7/8 M - 6/8M
= 1/8 M
Hence you ran 1/8 of miles more than yesterday.
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How do you find the shorter leg of a 30 60 90 triangle?
The short leg of a 30-60-90 triangle is 1/2 the length of the hypotenuse. 30-60-90 triangle is the half of an equilateral triangle.
Right triangles with 30-60-90 interior angles are called special right triangles.
A 30-60-90-degree triangle is a special right triangle and its side lengths are always consistent with each other. The ratio of the sides follows the 30-60-90 triangle ratio: 1: 2: [tex]\sqrt{3}[/tex] .
Short side (opposite the 30° angle) = x
Hypotenuse (opposite the 90° angle) = 2x
Long side (opposite the 60° angle) = x√3
30-60-90 Triangle Theorem:
These three properties can be examined by the 30-60-90 triangle theorem and are unique to these special right triangles:
The hypotenuse (the triangle's longest side) is twice the length of the short leg.The length of the longer leg is the√3 times of the shorter leg.If we know the length of any one side of a 30-60-90 triangle, we can find the missing side lengths.Read more about the right triangle :
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The top-notch middle school had athletes from all the grades playing on a sports team. 6th grade 7th grade 8th grade basketball 2 4 7 baseball 1 6 5 soccer 7 4 4 football 8 15 10 explain what the ratio 5:73 represents. the ratio 5:73 represents the ratio of 8th grade baseball players to total athletes. the ratio 5:73 represents the ratio of 7th grade football players to total athletes. the ratio 5:73 represents the ratio of total athletes to 7th grade football players. the ratio 5:73 represents the ratio of 6th grade athletes to total athletes.
The ratio 5:73 represents the ratio of 8th grade baseball players to total athletes.
What is ratio?In mathematics, a ratio is a comparison of two or more numbers that demonstrates how large one number is relative to the other. The divisor or number that is dividing is known as the consequent, while the dividend or number being divided is known as the antecedent. A ratio divides two numbers to compare them.
Given that the Total number of athletes are 2+4+7+1+6+5+7+4+4+8+15+10
= 73
Ratio of 5:73 represent the athletes in a particular grade with specific games to total number of athletes in the school.
There are on one event is where 5 athletes are, that is 8th grade baseball players.
So the correct answer is The ratio 5:73 represents the ratio of 8th grade baseball players to total athletes.
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The surface area of a sphere with the radius r is 4 pi r^2. Including the area of its circular base, what is the total surface area of a hemisphere with the radius 6 cm? Express your answer in terms of pi.
The total surface area of the hemisphere is 108 pi cm^2.
Surface area is the amount of space covering the outside of a three-dimensional shape. We calculate the surface area for three dimensional objects. The surface area of a 3-D object is not same as its volume.
The surface area of a sphere with the radius r is 4 pi r^2
The surface area of a hemisphere with the radius r = 2 pi r^2 + pi r^2
where pi r^2 represents the area of the circular base of the hemisphere of radius r.
The surface area of a hemisphere sphere with the radius r is 3 pi r^2
For radius r=6cm
TSA of the hemisphere is 3 pi (6x6) cm^2
TSA = 108 pi cm^2
108 pi cm^2 is the total surface area of a hemisphere with the radius 6 cm.
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Is 16x2 40x 25 a perfect square trinomial?
No, 16x2 40x 25 is not a perfect square trinomial.
What is perfect squares?Perfect squares are numbers that are the result of multiplying a number by itself. Examples of perfect squares include 4, 9, 16, 25, 36, and 49. Perfect squares are also known as "square numbers" or "whole numbers." Perfect squares are not just limited to whole numbers; some decimals and fractions can also be perfect squares.
A perfect square trinomial is an expression of the form a2 + 2ab + b2, where a and b are constants. 16x2 40x 25 does not fit this form, and is therefore not a perfect square trinomial.
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What is a sine ratio of an acute angle?
The sine of an acute angle in a right triangle is the ratio of the angle of the triangle to the opposite side of the hypotenuse.
Trigonometric ratios:
Trigonometric ratios are the ratios of the lengths of the sides of a triangle. These ratios in trigonometry relate the aspect ratio of a right triangle to each angle. A basic trigonometric ratio is the ratio of sin, cos, and tan, or the ratio of sin, cos, and tangent. Other important trigonometric ratios cosec, sec, and cot can be derived from sin, cos, and tan, respectively.
Acute Sine Ratio:
The tangent function examines the ratio of his two legs of a right triangle. You can also use the ratio of leg length divided by hypotenuse length.
In a right triangle, each angle has an opposite side and an adjacent side. And there is always a hypotenuse. On the opposite side and the hypotenuse we are dealing with the sine ratio. The sine of an angle is the ratio of the length of the opposite side divided by the length of the hypotenuse. In a right triangle, the sine of an angle is the ratio of the length of the opposite side divided by the length of the hypotenuse.
Let's examine some properties of the sine ratio using the Pythagorean theorem. For a right triangle, let the lengths of the triangle be a, b, and c. where a is the length of the other side of A and b is the length of the other side of B.
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A test has a mean of 75 with a standard deviation of 5. Which of the following scores is within one standard deviation of the mean
The score interval that is within one standard deviation of the mean is
(70 , 80).
What is standard deviation?
The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean of the collection.
Some of the properties of the standard deviation are:
1. It cannot be negative
2. It is only employed to calculate the spread or dispersion around a data set's mean
3. It displays the degree of deviation from the mean value
4. The larger the spread, the more standard deviation, with data of about the same mean.
Given,
The mean of the test μ = 75
The standard deviation σ = 5
We are asked to find the scores within one standard deviation of the mean.
This means that the scores should be in the interval ( μ - σ , μ + σ )
μ - σ = 75 - 5 =70
μ + σ = 75 + 5 = 80
Therefore the scores should be in the interval = ( 70,80), which is within one standard deviation of the mean.
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On the way home, Mark rode the first six miles of the trip in 30 minutes to stop at the ice cream shop. What was his speed in miles per hour
The speed of Mark riding the bike is 16 miles/hour. If you know how far something has travelled and how long it took to get there, you can calculate its average speed. Speed is calculated as follows: speed = distance * time.
What are time, distance, and speed?Speed tells us how quickly or slowly an object is moving. While distance, as the name suggests, refers to the amount of space between two points, time refers to the period of time separating two events.
Given,
Distance travelled= 6 miles
time taken = 30 minute =0.5 hour
[tex]speed = distance/time\\speed=8/0.5\\speed= 16 miles/hour[/tex]
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column A
1. 4.08÷4=N
2. 2.25÷1.5=N
3. 106.26÷4.2=N
4. 71.46÷0.2=N
5. 3.015÷15=N
Column B
A 25.3
B 357.3
C 0.201
D 1.5
E 1.02
with solution plss
Column A and B matching the results with the operations
4.08÷4=1.02 (N=1.02) A2.25÷1.5=1.5 (N=1.5) D106.26÷4.2=25.3 (N=25.3) A71.46÷0.2=357.3 (N=357.3) B3.015÷15=0.201 (N=0.201) COn a assembly line, 2 parts can be made per minute. There are 8 parts already made. To determine how many more minutes (x) it will take to make y total parts, the equation y=2x + 8 is written. What is the description of a solution to this problem?
The description for the problem involving the linear function is given as follows:
The time it will take to make a total of 20 parts is of 6 minutes.
How to interpret this problem in the context of a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change.b is the y-intercept, representing the initial value.In this problem, the function is defined as follows:
y = 2x + 8.
In which the variables are given as follows:
x is the time in minutes.y is the number of pieces made.Hence the time needed to make 20 pieces is given as follows:
20 = 2x + 8
2x = 12
x = 12/2
x = 6 minutes.
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Can someone help me please? Picture attached
Answer:
Step-by-step explanation:
A^2 + B^2 = C^2
12^2 + B^2 = 18^2
144 + B^2 = 324
Subtract 144 from both sides
B^2 = 324 - 144
B^2 = 180
[tex]\sqrt{180}[/tex] = 13.416
B^2 = 13.4
Evaluate the integral by reversing the order of integration.
2
0
6
11ex2 dx dy
3y
When we reverse the integration and evaluation orders, we obtain: [tex]\frac{c}{2}-1[/tex]
What is integration?In mathematics, an integral lends numerical values to functions to represent concepts like volume, area, and displacement that result from combining infinitesimally small amounts of data. Integration is the action of locating integrals.
So, we have:
[tex]$$\int_0^1 \int_x^z e^{\frac{x}{y}} d y d x$$\\[/tex]
Here: [tex]z=\sqrt{x}[/tex]
Next, reverse the sequence:
[tex]$$\int_0^1 \int_m^y e^{\frac{x}{y}} d y d x$$ $m=y^2$$$\\\\\begin{aligned}\\& \int_{=0}^1\left(e^{\frac{x}{y}} y\right) \| \begin{array}{l}y \\y^2\end{array} d y \\& \int_{=0}^1(e y)-\left(e^y y\right) d y\end{aligned}$$[/tex]
The following section uses integration by parts,
[tex]$$\begin{aligned}& \mathbf{u}=\mathbf{y}, \\& d v=e^y\end{aligned}$$$$\mathrm{d} u=1$$$$v=e^y$$$$\begin{aligned}& =\left(\left(\frac{e y^2}{2}\right)-\left(y e^y\right)\right)||_0^1+\int_0^1 e^y d y \\& = \\& =\frac{e}{2}-e+e-1=\frac{e}{2}-1\end{aligned}$$[/tex]
Therefore, when we reverse the integration and evaluation orders, we obtain: [tex]\frac{c}{2}-1[/tex]
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Correct question:
Evaluate the integral by reversing the order of integration.
8 0 2 3ex4 dx dy 3 y
4. What function represents an absolute value that has a vertex at (-7,-10)?
a. |y-7|-10 3
b. |y+7|+10
c. |y+7|-10
d. -|y+7|+10
More than one applies to the slope.
How is the absolute value function calculated?The non-negative value of a real number x without regard to its sign is known as its absolute value or modulus in mathematics and is indicated by the symbol |x|. Specifically, display style |x|=x and |x|=-x for positive and negative numbers, respectively, and display style |0|=0 for zero.
The slope of the parent function from any point to the vertex is either 1 or -1. The points in the issue are (-2, 3), and (–1, 0)
The slope is m = 0 - 3 / (-1 - (-2)) between the two sites.
m = 3
It is steeper than one.
As a result, a scale factor other than 1 has been used to dilate the graph.
The complete question is : The graph of an absolute value function has a vertex at (–2, 3) and passes through the point (–1, 0). Using transformations of the parent function, has the graph been dilated by a scale factor other than 1? Explain.
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I am stuck on this question and i honestly am stuck and do not know what to do.
The basic parts of a circle include its diameter, circumference, radius, arc, chord, tangent, tangent, section, and segment.
What is Circle radius?the surface or circumference of a circle, ball, and other object measured in a straight line The radius and diameter of a circle are equal. The length of such a line. whatever radiating or radial component. A circle's chord is the line segment that connects any two locations on the circle's circumference. It should be remembered that a circle's diameter is defined as the lengthiest chord that runs across the center of the circle.
Here,
given
The letter "C" should be in the center.
radius=r=AC=CB
Diameter=d=2r=AB.
Therefore , the solution to the given problem of circle comes out to be ,the basic parts of a circle include its diameter, circumference, radius, arc, chord, tangent, tangent, sector, and segment.
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PLEASE HELP!!! I need these answers for Geometry.
Answer: x=(y+9)5−32 simplified
Step-by-step explanation:
The length of one diagonal of a rhombus is 4 times the length of the other diagonal. Write an expression that represents the perimeter of the rhombus. Let d be the length of the shorter diagonal.
The expression that represents the perimeter of the rhombus is 2d√17
How to determine the expression that represents the perimeter of the rhombus?
From the question, we have the following parameters that can be used in our computation:
The length of one diagonal of a rhombus is 4 times the length of the other diagonal.
This means that
Length 1 = 4 * Length 2
From the question, we have
Let d be the length of the shorter diagonal.
This means that
Length 1 = 4d
Length 2 = d
The perimeter of the rhombus from the diagonals is calculated as
P = 2√(Length 1² + Length 2²)
Substitute the known values in the above equation, so, we have the following representation
P = 2√((4d)² + d²)
Evaluate the exponents
P = 2√(16d² + d²)
So, we have
P = 2√(17d²)
Evaluate the exponents
P = 2d√17
Hence, the perimeter is 2d√17
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Decrease 520 by 60%.
Answer:
208
Step-by-step explanation:
60 percent of 520 is 312
520 subtract 312 is 208
Answer:
208
Step-by-step explanation:
(520)-60% of 520
(520)-3×104
520-312
=208
Hope it helps you
PLS RATE AS BRAINLIEST ANSWER
Which expressions are equivalent to (1/3x+2x−5/3x)−(−1/3x+5) ?
Select all correct expressions.
Responses
−4x+5+3x
negative 4 x plus 5 plus 3 x
5−x
5 minus x
x−5
x minus 5
4x−5−3x
Answer:
Both x - 5, and 4x-5-3x are equivalent to (1/3x+2x−5/3x)−(−1/3x+5)
Step-by-step explanation:
Let's reorganize the given expression:
(1/3x+2x−5/3x)−(−1/3x+5)
1/3x+2x−5/3x + 1/3x-5 [Expand the parentheses]
2/3x+2x−5/3x -5 [Combine like terms]
-3/3x+2x -5
-x + 2x - 5
x - 5 One of the equivalent expressions
The option 4x-5-3x also reduces to x - 5