On a blueprint, a rectangular room 14 feet by 12 feet has a semicircular sitting area attached with a diameter of 12 feet.
(a) What is the total area of the room and the sitting area? Show your work. (2 points)
Click or tap here to enter text.
(b) What is the perimeter of the room (including the sitting area)? Show your work. (2 points)
Answers
Answer:
a) [tex]A=224.55\ ft^2[/tex]
b) [tex]P = 58.85\ ft[/tex]
Step-by-step explanation:
a) The area of a rectangle is calculated as the product of its length by its width.
[tex]A = lw[/tex]
Then the area of the rectangular room is:
[tex]A = 14 * 12\\\\A = 168\ ft ^ 2[/tex]
The area of a semicircle is[tex]A = \frac{1}{2}\pi r ^ 2[/tex]
We know that the diameter is 12 feet, then the radius is:
[tex]r = \frac{12}{2} = 6\\\\r = 6\ ft[/tex]
[tex]A = \frac{1}{2}\pi(6) ^ 2\\\\A = 56. 55 ft ^ 2[/tex]
Finally, the total area is:
[tex]A=56. 55\ ft ^ 2+168\ ft ^ 2[/tex]
[tex]A=224.55\ ft^2[/tex]
b) The perimeter of a rectangle is:
[tex]P = 2l + 2w[/tex]
The perimeter of a semi-circle is:
[tex]P = 0.5 * 2\pi r[/tex]
In this case r = 6
Since the semi-circle is attached to one of the sides of the room and its diameter is 12 feet, you cannot add one of the sides of rectangle that measures 12 feet to the perimeter (Observe the figure attached, which is not drawn to scale).Then the perimeter is:
[tex]P = (12 + 2 * 14)+(0.5 * 2\pi (6))\\\\P = 58.85\ ft[/tex]
Related Questions
Hamill finds the measure of x to be 90. He justified his work by writing “ all exterior angles of a polygon are found by 360/n. Which of the following statements explain why his answer is incorrect
Answers
Answer:
the polygon is not regular and the 360/n formula is only applies to regular polygons
Step-by-step explanation:
Let f(x) = x − 3 and g(x) = x + 11.Find f(x) ⋅ g(x)
Answers
For this case we have the following functions:
[tex]f (x) = x-3\\g (x) = x + 11[/tex]
We must find the product of the functions:
[tex]f (x) * g (x) = (x-3) (x + 11)[/tex]
We apply distributive property, which states:
[tex](a + b) (c + d) = ac + ad + bc + bd[/tex]
So:
[tex]f (x) * g (x) = x ^ 2 + 11x-3x-33 = x ^ 2 + 8x-33[/tex]
Answer:
[tex]x ^ 2 + 8x-33[/tex]
Answer: [tex]f(x).g(x)=x^2+8x-33.[/tex]
Step-by-step explanation: We are given the following two functions ;
[tex]f(x)=x-3,~~~~~~~~g(x)=x+11.[/tex]
We are to find the value of [tex]f(x).g(x).[/tex]
To find the required expression, we need to multiply the expressions for both the functions f(x) and g(x).
therefore, we get
[tex]f(x).g(x)\\\\=(x-3).(x+11)\\\\=x(x+11)-3(x+11)\\\\=x^2+11x-3x-33\\\\=x^2+8x-33.[/tex]
Thus, [tex]f(x).g(x)=x^2+8x-33.[/tex]
Among 1501 respondents to a survey, 20% said that there is no solid evidence to support global warming. Use a 0.01 significance level to test the claim that less than 25% of the population believes that there is no solid evidence of global warming. State the final conclusion. A. There is not sufficient evidence to support the claim that less than 25% of the population believes that there is no solid evidence to support global warming. B. There is sufficient evidence to support the claim that less than 25% of the population believes that there is no solid evidence to support global warming. C. There is sufficient evidence to support the claim. D. There is sufficient evidence to support the claim that more than 25% of the population believes that there is no solid evidence to support global warming.
Answers
Answer:
B. There is sufficient evidence to support the claim that less than 25% of the population believes that there is no solid evidence to support global warming.
Step-by-step explanation:
The following information has been availed;
n = 1501
sample proportion = 20% = 0.2
Level of significance = 0.01 = 1%
We are required to test the claim that less than 25% of the population believes that there is no solid evidence of global warming. In mathematical notation this claim can be written as;
p < 0.25, where p is the population proportion. From this information, we can formulate the following set of hypotheses;
H0: p ≥ 0.25
Ha: p < 0.25 (claim). This will be a left-tailed test.
The test statistic for hypothesis on population proportions is z, defined by the formula;
[tex]z=\frac{sampleproportion-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]
where p is the population proportion under the null hypothesis, that is p = 0.25.
Using the given information , the test statistic becomes;
[tex]z=\frac{0.2-0.25}{\sqrt{\frac{0.25(1-0.25)}{1501} }}=-4.4736[/tex]
The next step is to compute the p-value in our left-tailed test;
p-value = P(Z < -4.4736) = 0
Our p-value is less than the level of significance and thus we reject the null hypothesis in favor of the alternative hypothesis which is also our claim. The final conclusion is thus;
There is sufficient evidence to support the claim that less than 25% of the population believes that there is no solid evidence to support global warming.
At an elementary school, the fourth-grade class is planning a field trip to the science center. The roster shows 113 students who will attend the event. School-district rules specify that there must be one adult chaperone for every 10 students.
Which equations correctly represent this situation, where c is the number of chaperones?
Select all that apply.
10c=113
113=c10
10=c113
c=113(10)
c=11310
Answers
Answer:
10c=113
113=c10
Step-by-step explanation:
Either is same. For multiplication, even though you flip it, it is same.
Answer:
10c=113
113=c10
c=113/10
Step-by-step explanation:
What are the coordinates of the endpoints of the mid segment for ABC that is parallel to Bc?
ANSWER ASAP PLEASE !!
Answers
Answer:
(4,2) and (8,2)
Step-by-step explanation:
The mid segment unites the middle of two sides of a triangle. In this case, the question wants us to have it parallel to BC, so it has to unite the middle of AB to the middle of AC.
The use of the clear grid in this case makes that we don't have to use any angle calculation.
If you start from point B, you'll need to go 6 units to the right and 8 units up to meet with A. That means the center point is located 3 units right and 4 units high from point B... so, we have point (4,2).
Starting from C, we do a similar calculation. you need to go 2 units to the left and 8 units up... so the mid-point is 1 unit to the left and 4 units up... so (8,2).
WILL GIVE BRAINLIST, RIGHT ANSWERS ONLY
Shiri is planting a 4-foot flower border around the edge of her yard. she drew this diagram to show how it should look.
what is the area of the flower border?
Answers
Answer:
384
Step-by-step explanation:
Answer:
They answer 256 because you will multiply the border four times (4x4x4x4) to get the perimeter of border.
Please explain your answer. THX!!!
Answers
Answer:
1) cos (3x)
2) [tex]\frac{-(1-\sqrt{3})^{2}}{2}[/tex]
Step-by-step explanation:
Given expression:
cos(7x)cos(4x)+sin(7x)sin(4x)
By using the trigonometric identity
cos(a)cos(b) + sin(a)sin(b) = cos(a-b)
we have:
cos(7x)cos(4x)+sin(7x)sin(4x) = cos(7x - 4x)
= cos(3x)!
part 2:
tan (-π/12)
by using property tan(-x)= - tan(x)
=-tan(π/12)
= - tan(π/6 / 2)
Using tan(x/2) = [tex]\sqrt{\frac{1 - cos(x)}{1+cos(x)} }[/tex]
= - [tex]\sqrt{\frac{1 - cos(pi/6)}{1+cos(pi/6)} }[/tex]
cos π/6 = [tex]\frac{\sqrt{3} }{2}[/tex]
= -[tex]\sqrt{\frac{1-\frac{\sqrt{3} }{2} }{1+\frac{\sqrt{3} }{2} } }[/tex]
= - [tex]\sqrt{7-4\sqrt{3} }[/tex]
= - 2+[tex]\sqrt{3}[/tex]
= [tex]-\frac{(1-\sqrt{3}) ^{2} }{2}[/tex]
!
If cos x = sin(20 + x)° and 0° < x < 90°, the value of x is
Answers
Answer:
x=35
Step-by-step explanation:
ANSWER
x=35°
EXPLANATION
We want to find the value of x, when
[tex] \cos(x) = \sin(20 + x) \degree[/tex]
and 0°<x<90°
Recall that the sine and cosine are complementary trigonometric ratios.
Hence cos x = sin (90-x)
Our equation now, becomes;
[tex] \sin(90 - x) \degree= \sin(20 + x) \degree[/tex]
We now equate the argument to get,
[tex]90 - x=20 + x[/tex]
Group similar terms to obtain:
[tex]90 - 20 = x + x[/tex]
[tex]70 = 2x[/tex]
This implies that,
[tex]x = 35 \degree[/tex]
Determine the equation of the line for the given information: Two points on the line are (0, 4) and (7, 18). Use the points to first determine the slope and y-intercept. Then write the equation of the line
Answers
Answer:
y = 2x + 4
slope: 2
y-intercept: (0,4)
Step-by-step explanation:
to find the slope and y-intercept of the two points, we can use the following formula:
y2 - y1/ x2 - x1 = slope
to solve, we plug in the values into the equation
we will treat (0,4) as x1, y1 and (7,18) as x2, y2
y2 - y1 = 18 - 4 = 14
x2 - x1 = 7 - 0 = 7
14/7 is the slope, but we can simplify as 14/7 is equal to 2
so the slope is 2 (can also be said as 2/1)
we can now put the following slope into slope-intercept form (y=mx+b)
y = 2x + b < b is the slope, we so we need to solve for b
looking at our points (0,4) and (7,18), we see that we have the y-intercept, as the y-intercept has the x-coordinate 0, and any y-coordinate. the y-intercept is (0,4)
but if we dont have the y-intercept that easily, we can plug in any coordinate that we are given into the equation and solve for b. for this example, ill use (0,4) to plug into the equation
4 = 2(0) + b
4 = b
the y-intercept is 4
the final equation would be the following:
y = 2x + 4
The equation of the line that passes through two points (0, 4) and (7, 18) is y = 2x + 4.
To determine the equation of the line using the given information, we first need to find the slope and y-intercept. The slope of a line can be calculated using the formula:
slope (m) = (change in y-coordinates) / (change in x-coordinates)
Using the points (0, 4) and (7, 18), we can calculate the slope:
slope (m) = (18 - 4) / (7 - 0) = 14 / 7 = 2
So, the slope of the line is 2.
Next, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. To find the y-intercept, we can substitute one of the points into the equation and solve for b.
Using the point (0, 4):
4 = 2(0) + b
b = 4
Therefore, the y-intercept (b) is 4.
Finally, we can write the equation of the line:
y = 2x + 4
To learn more about the slope;
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Which of the following mapping diagrams does not represent a function?
Answers
Answer:
C cannot represent a function
Step-by-step explanation:
For every income (the left column) can have only one outcome (the right column).
Each constituent of one set, such as Set (A), is transferred to a particular member of another set (B), such as Set (B). Then the correct option is C.
What is a function?A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.
Just one function, also known as an input feature function, was among the most prevalent forms of functions. We will also study the opposite of this function here.
Thus, the correct option is C.
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9 min left please help
Answers
the answer for this question is 20 x cube by 5
For this case, we must simplify the following expression:
[tex]\sqrt [3] {\frac {4x} {5}}[/tex]
For this, we follow the steps below:
We rewrite the expression as:
[tex]\frac {\sqrt [3] {4x}} {\sqrt [3] {5}}[/tex]
We multiply by:
[tex]\frac {(\sqrt [3] {5}) ^ 2} {(\sqrt [3] {5}) ^ 2}\\\frac {\sqrt [3] {4x}} {\sqrt [3] {5}} * \frac {(\sqrt [3] {5}) ^ 2} {(\sqrt [3] {5}) ^ 2} =[/tex]
We have by definition of multiplication of powers of equal base that:
[tex]a ^ m * a ^ n = a ^ {m + n}[/tex]
So:
[tex]\\\frac {\sqrt [3] {4x} * (\sqrt [3] {5}) ^ 2} {\sqrt [3] {5}) ^ 3} =\\\frac {\sqrt [3] {4x} * (\sqrt [3] {5}) ^ 2} {5} =[/tex]
We know that:
[tex](\sqrt [3] {5}) ^ 2 = \sqrt [3] {5 ^ 2}[/tex]
So, we have:
[tex]\frac {\sqrt [3] {4x} * \sqrt [3] {5 ^ 2}} {5} =\\\frac {\sqrt [3] {4x} * \sqrt [3] {25}} {5} =\\\frac {\sqrt [3] {100x}} {5}[/tex]
Answer:
Option c
What is the slope of the line?
Answers
Answer:
7/4
Step-by-step explanation:
up seven, right four
7/4. Go up seven, right 4
0.000000057 in scientific notation would be:
Answers
Answer:
[tex]\large\boxed{0.000000057=5.7\cdot10^{-8}}[/tex]
Step-by-step explanation:
[tex]\text{Scientific notation:}\\\\a\cdot10^k\\\\\text{where}\ 1\leq a<10\ \text{and}\ k\in\mathbb{Z}\\-------------------------\\\\0\underbrace{.00000005}_{8\rightarrow}7=5.7\cdot10^{-8}[/tex]
If you move the comma several places to the right, the exponent at 10 is negative.
If you move the comma several places to the left, the exponent at 10 is positive.
The temperature in Oslo was −20∘C at midday. At 4 pm, the temperature rose 3∘C, and then dropped 8∘C at 8 pm. Anyone Help me out? Because im not sure with with the rising by 3 degrees C part, because I think that it is - 20 + 3 which = -23 or -17 im not sure please help me out
Answers
You are on the right track: - 20 + 3 = - 17 but do not forget about "dropped 8°C"
-20 + 3= -17
You are correct.
Janelle is making a poster. She cuts a triangle out of poster board. What is the area of the poster board that she has left?
Answers
The poster is a parallelogram, and it's area is:
A = bh
A = 20 x 10
A = 200 in.^2
Note: ^2 after in. means squared for area.
The area of the triangle that Janelle cut out of the poster board is:
A = 1/2bh
A = 1/2 x 10 x 9
A = 90/2
A = 45 in.^2
The area of the poster board that she has left is: 200 - 45 = 155 in.^2
Answer: 155 in.
The area of the poster board that she has left is,
⇒ 155 in²
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Now, The area of the parallelogram is,
⇒ Area of Parallelogram:
A= base × height
A= 20 in × 10 in
A= 200 in²
And, Area of Triangle:
A= 1/2 base * height
A= 1/2 (10 in)(9 in)
A= 1/2 (90)
A= 45 in²
Thus, The Area of Poster Left is,
A= Parallelogram Area - Triangle Area
A= 200 in² - 45 in²
A= 155 in²
Thus, 155 in² is the area of the poster board she has left.
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What is the median of 23 2 5 14 25 36 27 42 12 8 7 23 29 28 11 20 31 8 36
Answers
Answer:
23
Step-by-step explanation:
The median is the number in the middle of the data once it is organized from least to greatest, so that is what we must do first.
[tex]2,5,7,8,8,11,12,14,20,23,23,25,27,28,29,31,36,36,42[/tex]
There are 19 numbers, that means that the 10th value will be the number in the middle
This means that the median is 23
What is the completely factored form of x^4+8^2-9?
Answers
Answer: wads
Step-by-step explanation:wasd
Answer:
Is that equation typed correctly?
For one thing, that second term should (probably) be 8x^2.
Step-by-step explanation:
what could tara have written as the result from step 2?
Answers
Answer: (x-30)^2=4
Step-by-step explanation:
helppp 20 POINTS ANSWER FAST
Answers
Answer:
x=2.4
Step-by-step explanation:
We can take the ratios and solve for the unknown side
AE ED
----- = ---------
JN MN
Substituting in
1 3
----- = ---------
.8 x
Using cross products
1x = 3*.8
1x = 2.4
x = 2.4
A group of randomly selected members of Mothers' Club were asked how many kids they have. The table below shows the results A group of randomly selected members of Mothers' Club were asked how many kids they have. The table below shows the results of the survey. There are 120120120 members in Mothers' Club. Number of kids Number of mothers 111 999 222 666 3+3+3, plus 555 Based on the data, what is the most reasonable estimate for the number of Mothers' Club members who have fewer than 222 kids?the survey. There are 120120120 members in Mothers' Club. Number of kids Number of mothers 111 999 222 666 3+3+3, plus 555 Based on the data, what is the most reasonable estimate for the number of Mothers' Club members who have fewer than 222 kids?
Answers
Answer:
54
Step-by-step explanation:
Estimate=Population size × Sample proportion
population size = 120
sample proportion = (9)/(9+6+5) = 9/20 (check on Cymath as a resource)
estimate = 120 x 9/20 = 54
The estimation will be 54 for the number of mothers.
What is estimation?The estimation is the approximated results of anything it can be the possibility or probability of any event to happen or any number to come.
Estimate=Population size × Sample proportion
population size = 120
sample proportion = (9)/(9+6+5) = 9/20 (check on Cymath as a resource)
Estimate = 120 x 9/20 = 54
Hence estimation will be 54 for the number of mothers.
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Which of the following is equivalent to the radical expression below, when the denominator has been rationalized and X >_ 5?
Answers
Answer:
Option D is correct.
Step-by-step explanation:
[tex]\frac{10}{\sqrt{x}-\sqrt{x-5}}\\[/tex] We need to rationalize this term and find the answer.
To rationalize the term we multiply and divide the above expression by [tex]\sqrt{x}+\sqrt{x-5}[/tex]
Solving:
[tex]\frac{10}{\sqrt{x}-\sqrt{x-5}}\\=\frac{10}{\sqrt{x}-\sqrt{x-5}} * \frac{\sqrt{x}+\sqrt{x-5}}{\sqrt{x}+\sqrt{x-5}} \\Multiplying\\=\frac{10*(\sqrt{x}+\sqrt{x-5})}{\sqrt{x}-\sqrt{x-5}*\sqrt{x}+\sqrt{x-5}}\\=\frac{10*(\sqrt{x}+\sqrt{x-5})}{(\sqrt{x})^2-(\sqrt{x-5})^2}\\=\frac{10*(\sqrt{x}+\sqrt{x-5})}{x-(x-5)}\\=\frac{10*(\sqrt{x}+\sqrt{x-5})}{x-x+5)}\\=\frac{10*(\sqrt{x}+\sqrt{x-5})}{5}\\=2*(\sqrt{x}+\sqrt{x-5})[/tex]
So, Option D is correct.
Answer:
The correct option is D) [tex]2\left(\sqrt{x}+\sqrt{x-5}\right)[/tex].
Step-by-step explanation:
Consider the provided radical expression.
[tex]\frac{10}{\sqrt{x}-\sqrt{x-5}}[/tex]
Multiply by the conjugate [tex]\frac{\sqrt{x}+\sqrt{x-5}}{\sqrt{x}+\sqrt{x-5}}[/tex]
[tex]\frac{10\left(\sqrt{x}+\sqrt{x-5}\right)}{\left(\sqrt{x}-\sqrt{x-5}\right)\left(\sqrt{x}+\sqrt{x-5}\right)}[/tex]
[tex]\frac{10\left(\sqrt{x}+\sqrt{x-5}\right)}{\left(x-(x-5))}[/tex]
[tex]\frac{10\left(\sqrt{x}+\sqrt{x-5}\right)}{5}[/tex]
[tex]2\left(\sqrt{x}+\sqrt{x-5}\right)[/tex]
Hence, the correct option is D) [tex]2\left(\sqrt{x}+\sqrt{x-5}\right)[/tex].
What number must you add to complete the square x^2+2x=9
Answers
Answer:
+ 1
Step-by-step explanation:
Given
x² + 2x = 9
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(1)x + 1² = 9 + 1²
(x + 1)² = 10
Answer:x =(-2-√-32)/-2=1+2i√ 2 = 1.0000-2.8284i
x =(-2+√-32)/-2=1-2i√ 2 = 1.0000+2.8284
Step-by-step explanation:
Adam calculates his annual commission, y, using the model y = 0.28x, where x represents his total sales for the year. What is the meaning of the x-intercept in the model?
Answers
Answer:
The x intercept is where Adam made 0 commission for x number of sales.
Step-by-step explanation:
The x intercept is where the line crosses the x axis. It has a point (a,0) where y=0. In this model y is Adams total commission and x is his total sales. The x intercept is where Adam made 0 commission for x number of sales.
If WXYZ is a square, which statements must be true? Check all that apply
Answers
Answer:
True statements are,
A, B, D, E , and F
Step-by-step explanation:
Properties of a square
1) All sides are equal
2) All angles are equal to 90°
3) Opposite sides are parallel
A. WXYZ is a parallelogram
True (property 3)
B. <W is right angle
True (Property 2)
C. WXYZ is a trapezoid
False
D. WX ≅ XY
True (Property 1)
E. <W congruent to <Y
True (Property 1)
F. <W is supplementary to <Y
True (Property 2)
True statements are,
A, B, D, E , and F
Answer: A. WXYZ is a parallelogram
B. [tex]\angle{W}[/tex] is a right angle.
D. [tex]\overline{WX}\cong\overline{XY}[/tex]
E. [tex]\angle{W}\cong\angle{Y}[/tex]
F. [tex]\angle{W}[/tex] is supplementary to [tex]\angle{Y}[/tex].
Step-by-step explanation:
Given: WXYZ is a square.
A. A square is a parallelogram because its opposite sides are equal.
B. [tex]\angle{W}[/tex] is a right angle , since all the interior angles in a square area right angle.
C. A trapezoid has two equal parallel sides and two non-parallel sides.
But square has opposite sides parallel , therefore WXYZ is not a trapezoid.
D. Since all the sides of a square are congruent to each other , therefore
[tex]\overline{WX}\cong\overline{XY}[/tex]
E. Since all the angles of a square are congruent to each other , therefore
[tex]\angle{W}\cong\angle{Y}[/tex]
F. Since , all the interior angles in a square area right angle.
Thus, [tex]\angle{W}+\angle{Y}=90^{\circ}+90^{\circ}=180^{\circ}[/tex]
Hence, [tex]\angle{W}[/tex] is supplementary to [tex]\angle{Y}[/tex].
Solve this system of linear equation. Supérate the x- and y-values with a comma. 2x+4y=-48 4x-9y=57
Answers
Answer:
(x,y) = (-6.12,-11.76)
Step-by-step explanation:
2x+4y=-48 => eq(i)
4x-9y=57 => eq(ii)
We need to solve these equations simultaneously to find the values of x and y.
Multiplying eq(i) with 2 and subtracting both equations
4x + 16y = -96
4x - 9y = 57
- + -
__________
25 y = -153
y = -153/25
y = -6.12
Putting value of y in eq(i)
2x + 4(-6.12) = - 48
2x - 24.48 = -48
2x = -48 + 24.48
2x = -23.52
x= -23.52/2
x= -11.76
So, values of x and y are -6.12 and -11.76
(x,y) = (-6.12,-11.76)
The solution to the system of linear equations is [tex]\(x = -6\) and \(y = -9\).[/tex]
Let's solve the system of linear equations:
[tex]1. \(2x + 4y = -48\)\\2. \(4x - 9y = 57\)[/tex]
We can use the substitution or elimination method. I'll use the elimination method here:
Multiply the first equation by 2 to make the coefficients of [tex]\(x\)[/tex]in both equations the same:
[tex]1. \(4x + 8y = -96\)\\2. \(4x - 9y = 57\)[/tex]
Now, subtract the second equation from the first to eliminate [tex]\(x\):[/tex]
[tex]\((4x + 8y) - (4x - 9y) = -96 - 57\)[/tex]
Simplify:
[tex]\(17y = -153\)[/tex]
Now, solve for \(y\):
[tex]\(y = -\frac{153}{17} = -9\)[/tex]
Now that we have \(y\), substitute it back into one of the original equations. I'll use the first equation:
[tex]\(2x + 4(-9) = -48\)[/tex]
Simplify:
[tex]\(2x - 36 = -48\)[/tex]
Add 36 to both sides:
[tex]\(2x = -12\)[/tex]
Divide by 2:
[tex]\(x = -6\)[/tex]
So, the solution to the system of linear equations is [tex]\(x = -6\) and \(y = -9\).[/tex]
If a bakery produces 520 fried pies during an 8 hour shift, what is the production rate per hour of fried pies?
A) 60
B) 65
C) 70
D) 75
Answers
Answer:
B
Step-by-step explanation: divide 520 by 8 and you get 65
Answer: is B 65
Step-by-step explanation:
520 divided by 8
=65 per hour
Answer:
B. 65
Step-by-step explanation:
You have to average it out.
520÷8=65
Help please ill appreciate it
Answers
Answer:
I = 0.5
Answer
B
Step-by-step explanation:
When R = 20, plug in R
I = 10/R
I = 10/20
I = 1/2
I = 0.5
Answer
B
If y = 5x − 4, which of the following sets represents possible inputs and outputs of the function, represented as ordered pairs?
{(0, −4), (2, 6), (4, 20)}
{(0, −4), (2, 6), (4, 16)}
{(0, 4), (2, 6), (4, 16)}
{(0, 4), (2, −6), (4, 20)}
Answers
ANSWER
{(0, −4), (2, 6), (4, 16)}
EXPLANATION
The given function is
[tex]y = 5x - 4[/tex]
when x=0,
y=5(0)-4
y=-4
(0,-4)
When x=2,
y=5(2)-4
y=6
(2,6)
When x=4
y=5(4)-4
y=16
(4,16)
The correct choice is
{(0, −4), (2, 6), (4, 16)}
Answer:
{(0, −4), (2, 6), (4, 16)}
Step-by-step explanation:
Since, in an order pair the first value represents the input value and second value represents the output value,
i.e. (a, b) is an order pair ⇒ a = input, b = output,
Here, the given function,
[tex]y = 5x - 4[/tex]
(i) For the relation {(0, −4), (2, 6), (4, 20)},
At ( 4, 20), y = 5(4) - 4 = 20 - 4 = 16 ( false ),
(ii) For the relation {(0, −4), (2, 6), (4, 16)},
At (0, −4), y = 5(0) - 4 = -4 ( true ),
At (2, 6), y = 5(2) - 4 = 10 - 4 = 6 ( true ),
At ( 4, 16), y = 5(4) - 4 = 20 - 4 = 16 ( true ),
(iii) For the relation {(0, 4), (2, 6), (4, 20)},
At (0, 4), y = 5(0) - 4 = -4 ( false ),
(iv) For the relation {(0, 4), (2, −6), (4, 20)}
At (2, -6), y = 5(2) - 4 = 6 ( false ),
Hence, (ii) represents possible inputs and outputs of the function.
Find the solution set for this inequality: -3x -12> 8x+ 21
Answers
-3x - 12 > 8x + 21
Step 1: Combine like terms
x's go with x's (-3x and 8x). To do this add 3x to both sides
(-3x + 3x) - 12 > (8x + 3x) + 21
-12 > 11x + 21
Normal numbers go with normal numbers (-12 and 21). To do this subtract 21 to both sides
(-12 - 21) > 11x + (21 - 21)
-33 > 11x
Step 2: Isolate x by dividing 11 to both sides
-33/11 > 11x / 11
-3 > x
Hope this helped!
Answer:
[tex]x\:<\:-3[/tex]
Step-by-step explanation:
The given inequality is:
[tex]-3x-12\:>\:8x+21[/tex]
We group similar terms to obtain:
[tex]-12-21\:>\:8x+3x[/tex]
Combine the similar terms to obtain:
[tex]-33\:>\:11x[/tex]
Divide both sides by 11;
[tex]-3\:>\:x[/tex]
Or
[tex]x\:<\:-3[/tex]
Let f(x)=x^2+5x-8. What is the average rate of change from x = 2 to x = 6? Enter the answer in the box ___
please show the work and answer
Answers
Answer:
13
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Here [ a, b ] = [2, 6 ]
f(b) = f(6) = 6² + 5(6) - 8 = 36 + 30 - 8 = 58
f(a) = f(2) = 2² + 5(2) - 8 = 4 + 10 - 8 = 6
Hence
average rate of change = [tex]\frac{58-6}{6-2}[/tex] = [tex]\frac{52}{4}[/tex] = 13
Final answer:
The average rate of change of the function f(x) = x^2 + 5x - 8 from x = 2 to x = 6 is calculated to be 13.
Explanation:
The average rate of change of a function f(x) from x = a to x = b is found by the formula Δf / Δx = (f(b) - f(a)) / (b - a). In this case, we have f(x) = x^2 + 5x - 8, and we want to find the average rate of change from x = 2 to x = 6.
Calculate f(2) = 2^2 + 5(2) - 8 = 4 + 10 - 8 = 6.Calculate f(6) = 6^2 + 5(6) - 8 = 36 + 30 - 8 = 58.Apply the average rate of change formula: (f(6) - f(2)) / (6 - 2) = (58 - 6) / (4) = 52 / 4 = 13.Therefore, the average rate of change of the function from x = 2 to x = 6 is 13.