The diagram below represents the measurements of Jennie’s yard. The yard’s width is x feet shorter than its length. If the area of the yard is 540 square feet, how many feet shorter than the length is the width?

The Diagram Below Represents The Measurements Of Jennies Yard. The Yards Width Is X Feet Shorter Than

Answers

Answer 1

Answer: The width is 12 feet shorter than the length.

Step-by-step explanation:

The area of a rectangle can be calculated with this formula:

[tex]A=lw[/tex]

Where "l" is the lenght and "w" is the width of the rectangle.

 We know that lenght of Jennie's yard is 30 feet, the width is [tex](30-x)ft[/tex] and the area is 540 square feet. Then:

[tex]l=30\\w=(30-x)\\A=540[/tex]

Substitute these values into the formula and then solve for "x":

[tex]A=lw\\\\540=30(30-x)\\\\540=900-30x\\\\30x=900-540\\\\x=\frac{360}{30}\\\\x=12[/tex]

Therefore, the width is 12 feet shorter than the length.

Answer 2

Answer:

C

Step-by-step explanation:

got it on edge


Related Questions

How do you answer a, b and c, answers and also how you worked it out

Answers

We can either convert to standard form first or convert to a common multiplier, kinda like a common denominator.  The latter makes more sense if they wanted the result in scientific notation, but let's do it that way anyway.

a)

4.5 × 10⁴ + 3.8  × 10³ = 45 × 10³ + 3.8  × 10³ = 48.8× 10³ = 48,800

Answer:  48,800

b)

4.5 × 10⁴ - 3.8  × 10³ = 45 × 10³ - 3.8  × 10³ = 41.2× 10³ = 41,200

Answer:  41,200

c)

7.2 × 10⁻³ + 6.3  × 10⁻² = 7.2 × 10⁻³ + 63  × 10⁻³ = 70.2 × 10⁻³

       = 7.02 × 10⁻² = 0.0702

Answer: 0.0702

What value of x is in the solution set of 3(x – 4) = 5x + 2?
-10

Answers

Answer:

x = - 7

Step-by-step explanation:

Given

3(x - 4) = 5x + 2 ← distribute left side

3x - 12 = 5x + 2 ( subtract 5x from both sides )

- 2x - 12 = 2 ( add 12 to both sides )

- 2x = 14 ( divide both sides by - 2 )

x = - 7

Write the slope-intercept form of the line that passes through the point (1, 0) and is parallel to x - y = 7. T

Answers

Answer:

y = x -1

Step-by-step explanation:

x - y = 7

We need to put this in slope intercept form to find the  slope.

Add y to each side

x-y+y =7+y

x = y+7

Subtract 7 from each side

x-7 = y+7-7

x-7 = y

The slope is 1  since it is in the form y = mx+b

We have a slope 1 and an point (1,0)

We can use point slope form to make an equation

y-y1 = m(x-x1)

y-0 = 1(x-1)

y = x -1

This is in slope intercept form

If f(x)=2x^2+1, what is f(x) when x=3?

Answers

Answer:

19

Step-by-step explanation:

Plug in x = 3 into the function

f(x)=2x^2+1

f(x)=2(3)^2+1

f(x)=18+1

f(x)=19

The answer is:

f(3) = 19

Work/explanation:

To evaluate this function, plug in 3 for x:

[tex]\sf{f(x)=2x^2+1}[/tex]

[tex]\sf{f(3)=2(3)^2+1}[/tex]

[tex]\sf{f(3)=2\times9+1}[/tex]

Then, according to PEMDAS, we multiply:

[tex]\sf{f(3)=18+1}[/tex]

[tex]\sf{f(3)=19}[/tex]

Therefore, when x = 3, the function evaluates to 19.

Which is the graph of x-y=1?

Answers

Answer:

In graph

Step-by-step explanation:

First put it in Slope -Intercept form.

then graph the y- intercept first.

After that it's rise over run so think 1/1

up 1 over one.

Answer:

CCCCCCCCCCCCC

Step-by-step explanation:

Find the area of the hexagon to the nearest tenth.

Answers

D. 37.8 square meters

A=1/2ap
A=1/2(4.2)(3•6)
A=1/2(4.2)(18)
A=37.8

“a” stands for the apothem
“p” stands for the perimeter

which is the graph of the inequality? 3y - 9x ≥ 9

Answers

The inequality 3y - 9x ≥ 9, you can start by rearranging it into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. Now, you can graph the line y = 3x + 3. When graphing the inequality, you will shade the region above the line, which represents the solutions to the inequality 3y - 9x ≥ 9.

To graph the inequality 3y - 9x ≥ 9, you can start by rearranging it into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

3y - 9x ≥ 9

3y ≥ 9x + 9

y ≥ 3x + 3

Now, you can graph the line y = 3x + 3.

When graphing the inequality, you will shade the region above the line. The shading represents the solutions to the inequality 3y - 9x ≥ 9.

Here's how you can graph it:

Plot the y-intercept at y = 3 on the y-axis.Use the slope m = 3 to find another point. For example, move up 3 units and to the right 1 unit from the y-intercept, and plot another point.Draw a solid line through these two points.

Which of the following is not a solution to the system of linear equations below?
5y = 3x+15
6x = 10y– 30
A. (5,6)
B. (–15, 12)
C. (0,3)
D. (-10,-3)

Answers

Answer:

B. (-15, 12)

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}5y=3x+15&\text{subtract 3x from both sides}\\6x=10y-30&\text{subtract 10y from both sides}\end{array}\right\\\left\{\begin{array}{ccc}-3x+5y=15\\6x-10y=-30&\text{divide both sides by 2}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-3x+5y=15\\3x-5y=-15\end{array}\right}\\.\qquad0=0\qquad\bold{TRUE}\\\\\bold{Infinitely\ many\ solutions}\\\\5y=3x+15\qquad\text{divide both sides by 5}\\\\y=\dfrac{3}{5}x+3\qquad(*)\\\\\text{Put the coordinates of the points to the equation (*)}[/tex]

[tex]A.\ (5,\ 6)\\\\6=\dfrac{3}{5}(5)+3\\\\6=3+3\\\\6=6\qquad\bold{CORRECT}\\\\B.\ (-15,\ 12)\\\\12=\dfrac{3}{5}(-15)+3\\\\12=(3)(-3)+3\\\\12=-9+3\\\\12=-6\qquad\bold{FALSE}\\\\C.\ (0,\ 3)\\\\3=\dfrac{3}{5}(0)+3\\\\3=0+3\\\\3=3\qquad\bold{CORRECT}\\\\D.\ (-10,\ -3)\\\\-3=\dfrac{3}{5}(-10)+3\\\\-3=(3)(-2)+3\\\\-3=-6+3\\\\-3=-3\qquad\bold{CORRECT}[/tex]

Which of the following equations represents a line that is perpendicular to
y = -2x+4 and passes through the point, (4, 2)?

Answers

Answer:

[tex]\large\boxed{y=\dfrac{1}{2}x}[/tex]

Step-by-step explanation:

[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\===============================[/tex]

[tex]\text{We have the equation:}\ y=-2x+4\to m_1=-2.\\\\\text{Therefore}\ m_2=-\dfrac{1}{-2}=\dfrac{1}{2}.\\\\\text{We have the equation:}\ y=\dfrac{1}{2}x+b.\\\\\text{Put the coordinate of the point (4, 2) to the equation:}\\\\2=\dfrac{1}{2}(4)+b\\\\2=2+b\qquad\text{subtract 2 from both sides}\\\\0=b\to b=0.\\\\\text{Finally:}\\\\y=\dfrac{1}{2}x[/tex]

20 POINTS
WILL MARK BRAINLIEST
The last two pictures are to question two.

Answers

Answer:

The total surface area of the solid is 702 cm² ⇒ answer B

The true statements are m∠WYX = 46° and  m∠YWX = 63° ⇒ 1st and 2nd answers

Step-by-step explanation:

* Lets explain the solid figure

- It has one rectangular base of dimensions 10 cm and 14 cm

- It has 4 rectangular side faces , two of dimensions 6 cm and 10 cm

 and another two of dimensions 6 cm and 14 cm

- It has 4 triangular faces , two of base 10 cm and height 12 cm and

 another two of base 14 cm and height 11 cm

- The total surface area of the solid is the sum of the area of the 9 faces

* Lets find the area of all the faces

# Area of the base

∵ The base is a rectangle

∵ Area of the rectangle = length × width

∵ Length = 14 cm and width = 10 cm

∴ Area of the base = 14 × 10 = 140 cm²

# Area of the four rectangular faces

∵ Length = 10 cm  and width = 6 cm

∴ The area of the face with dimensions 10 , 6 = 10 × 6 = 60 cm²

∵ Length = 14 cm  and width = 6 cm

∴ The area of the face with dimensions 14 , 6 = 14 × 6 = 84 cm²

# Area of the four triangular faces

∵ Area of a triangle = 1/2 × base × height

∵ The base = 10 cm and the height = 12 cm

∴ The area of the face = 1/2 × 10 × 12 = 60 cm²

∵ The base = 14 cm and the height = 11 cm

∴ The area of the face = 1/2 × 14 × 11 = 77 cm²

∵ The total surface area of the solid = the sum of the areas of 9 faces

∴ TSA = 140 + 2 × 60 + 2 × 84 + 2 × 60 + 2 × 77

∴ TSA = 140 + 120 + 168 + 120 + 154 = 702 cm²

* The total surface area of the solid is 702 cm²

* Lets solve the 2nd part

- WXY is a scalene triangle

- m∠WXY is 71°

- The two sides of the triangle WY and XY exceeded

- The ray WY and the ray XY intersect each other at point Y and

  formed vertically opposite angles with measure 46°

∵ Ray WY intersect ray XY at point Y

m∠WYX = 46°

- In Δ WYX

∵ m∠WXY = 71° ⇒ given

∵ m∠WYX = 46° ⇒ proved

∵ The sum of the measures of the interior angles of a triangle is 180°

∴ m∠YWX + m∠WXY + m∠WYX = 180°

∴ m∠YWX + 71° + 46° = 180

∴ m∠YWX + 117° = 180° ⇒ subtract 117 from both sides

m∠YWX = 63°

Lets check the true statements

# m∠WYX = 46° ⇒ true

# m∠YWX = 63° ⇒ true

# m∠WXY = 46° ⇒ not true

# m∠YWX = 46° ⇒ not true

# m∠WYX = 134° ⇒ not true

* The true statements are m∠WYX = 46° and  m∠YWX = 63°

Evaluate: 6 x (-2) + 1 - 3

Answers

Answer:

-14

Step-by-step explanation:

Follow PEMDAS, then the left -> right rule.

PEMDAS =

Parenthesis

Exponent (& roots)

Multiplication

Division

Addition

Subtraction

First, multiply 6 with -2:

6 x -2 = -12

Next, add 1, then subtract 3.

-12 + 1 = -11

-11 - 3 = -14

-14 is your answer.

~

Answer:

-14

Step-by-step explanation:

Order of operations

PEMDAS

Parenthesis

Exponent

Multiply

Divide

Add

Subtract

Do parenthesis first.

6*(-2)=-12

-12+1-3

Add and subtract the numbers from left to right to find the answer.

-12+1-3

-12+1=-11

-11-3=-14

-14 is the correct answer.

I hope this helps you, and have a wonderful day!

Which function has an inverse that is also a function?
{(-1, -2), (0, 4), (1,3), (5, 14), (7,4)}
{(-1,2), (0, 4), (1,5), (5, 4), (7, 2)}
{(-1, 3), (0, 4), (1, 14), (5, 6), (7, 2)}
{(-1, 4), (0, 4), (1, 2), (5,3), (7, 1);

Answers

The third one is correct. A function does not repeat x values. So if it asks the inverse you would have to see if the y values repeat. The third choice is the only one that has non repeating y values.
Final answer:

A function has an inverse that is also a function if each element of the function's range corresponds to exactly one element of the function's domain, a concept known as the horizontal line test. In the given options, the second function (with points {(-1,2), (0, 4), (1,5), (5, 4), (7, 2)}) meets this criterion.

Explanation:

In mathematics, a function has an inverse that is also a function if each element of the function's range corresponds to exactly one element of the function's domain. This concept is also known as the horizontal line test. If any horizontal line intersects the graph of the function exactly once, then the function has an inverse that is also a function.

In this question, you are provided with four sets of points representing four possible functions. Upon examination, you can observe that the second function, represented by points {(-1,2), (0, 4), (1,5), (5, 4), (7, 2)}, meets the criteria of the horizontal line test. Each y-value in this function is unique, meaning that each element of the range corresponds to exactly one element of the domain, making its inverse a function as well.

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What are the solutions of this system of equations?
The first three steps in determining the solution set of the
system of equations algebraically are shown.
y = x2 - x-3
y=-3x + 5
(-2, -1) and (4, 17)
(-2, 11) and (4, -7)
(2, -1) and (-4, 17)
(2, 11) and (-4,-7)
Step
1
2
Equation
x– X-3 = -3x +5
0 = x² + 2x - 8
0 = (x-2)(x+4)
3

Answers

Answer:

Option C is correct.

Step-by-step explanation:

y = x^2-x-3     eq(1)

y = -3x + 5      eq(2)

We can solve by substituting the value of y in eq(2) in the eq(1)

-3x+5 = x^2-x-3

x^2-x+3x-3-5=0

x^2+2x-8=0

Now factorizing the above equation

x^2+4x-2x-8=0

x(x+4)-2(x+4)=0

(x-2)(x+4)=0

(x-2)=0 and (x+4)=0

x=2 and x=-4

Now finding the value of y by placing value of x in the above eq(2)

put x =2

y = -3x + 5

y = -3(2) + 5

y = -6+5

y = -1

Now, put x = -4

y = -3x + 5

y = -3(-4) + 5

y = 12+5

y =17

so, when x=2, y =-1 and x=-4 y=17

(2,-1) and (-4,17) is the solution.

So, Option C is correct.

Answer: Third Option

(2, -1) and (-4, 17)

Step-by-step explanation:

We have the following system of equations:

[tex]y = x^2 - x-3[/tex]

[tex]y=-3x + 5[/tex]

We have the first three steps to solve the system.

[tex]x^2- x-3 = -3x +5[/tex]   equal both equations

[tex]0 = x^2 + 2x - 8[/tex]      Simplify and equalize to zero

[tex]0 = (x-2)(x+4)[/tex]     Factorize

Then note that the equation is equal to zero when [tex]x = 2[/tex] or [tex]x = -4[/tex]

Now substitute the values of x in either of the two situations to obtain the value of the variable y.

[tex]y=-3(2) + 5[/tex]

[tex]y=-6 + 5[/tex]

[tex]y=-1[/tex]

First solution: (2, -1)

[tex]y=-3(-4) + 5[/tex]

[tex]y=12 + 5[/tex]

[tex]y=17[/tex]

Second solution: (-4, 17)

The answer is the third option

What is the following difference?

Answers

Answer:

29 square root 5.

Step-by-step explanation:

You must simplify the surds to subtract them.

ANSWER

[tex]29 \sqrt{5} [/tex]

EXPLANATION

The given radical expression is

[tex]11 \sqrt{45} - 4 \sqrt{5} [/tex]

We remove the perfect squares to get:

[tex]11 \sqrt{9 \times 5} - 4 \sqrt{5} [/tex]

Split the square root sign to obtain:

[tex]11 \sqrt{9} \times \sqrt{5} - 4 \sqrt{5} [/tex]

We simplify further to get:

[tex]11 \times 3 \sqrt{5} - 4 \sqrt{5} [/tex]

[tex]33 \sqrt{5} - 4 \sqrt{5}[/tex]

This simplifies to

[tex]29 \sqrt{5} [/tex]

In The Diagram △ ABC≅ △ECD. Which statement is true?


A.) Angle BCA ≅ Angle ECD

B.)Angle CAB ≅ Angle ECD

C.)BC≅ED


D.)AB≅CE

Answers

Answer:

The correct option is D.

Step-by-step explanation:

Given information: △ABC≅△ECD.

The corresponding parts of congruent triangles are congruent.

The congruent angles are :

[tex]\angle A\cong \angle E[/tex]

[tex]\angle B\cong \angle C[/tex]

[tex]\angle C\cong \angle D[/tex]

[tex]\triangle BCA\cong \triangle CDE[/tex]

Option A is incorrect.

[tex]\triangle CAB\cong \triangle DEC[/tex]

Option B is incorrect.

The congruent sides are :

[tex]BC\cong CD[/tex]

Option C is incorrect.

[tex]AC\cong ED[/tex]

[tex]AB\cong EC[/tex]

It can also written as

[tex]AB\cong CE[/tex]             [tex][\because EC=CE,\text{Reflective Property}][/tex]

Therefore the correct option is D.

Final answer:

The correct statement is BC ≅ ED.

Explanation:

The correct statement is BC ≅ ED.

Since △ABC ≅ △ECD, the corresponding sides and angles of the triangles are congruent.

Therefore, we can conclude that BC ≅ ED.

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WHAT IS ANOTHER WAY TO WRITE 6%

Answers

Answer:

3/50 or 0.06

Step-by-step explanation:

6/100=3/50

6/100=0.06

Answer:

0.06

Step-by-step explanation:

What is the measure of angle AFE? 79 81 91 99

Answers

Answer:

AFE = 99°

Step-by-step explanation:

Correct on E2020

Answer:  [tex]99^{\circ}[/tex]

Step-by-step explanation:

In the given picture , we have a hexagon having all its exterior angles.

We know that the sum of all exterior angles is [tex]360^{\circ}[/tex].

Let x be measure of [tex]\angle{AFE}[/tex]

Then , the exterior angle to  [tex]\angle{AFE}=180^{\circ}-x[/tex]

Then According to the given figure , we have

[tex]62^{\circ}+44^{\circ}+70^{\circ}+60^{\circ}+43^{\circ}+180^{\circ}-x=360^{\circ}\\\\\Rightarrow\ 459^{\circ}-x=360^{\circ}\\\\\Rightarrow\ x=459^{\circ}-360^{\circ}\\\\\Rightarrow\ x=99^{\circ}[/tex]

Hence, the measure of [tex]\angle{AFE}=99^{\circ}[/tex]

can someone help me please

Answers

For this case we must indicate an expression equivalent to:

[tex]x + 2 + [4x- \frac {x ^ 2 + 6x + 8} {x + 4}][/tex]

If we factor the quadratic expression, we must find two numbers that when multiplied give as result 8, and when summed give as result 6. These numbers are 4 and 2. Then:

[tex]x ^ 2 + 6x + 8 = (x + 2) (x + 4)[/tex]

Rewriting the expression:

[tex]x + 2 + [4x- \frac {(x + 2) (x + 4)} {(x + 4)}] =[/tex]

Simplifying common terms we have:

[tex]x + 2 + [4x- (x + 2)] =[/tex]

Taking into account that:

[tex]- * + = -\\x + 2 + 4x-x-2 =\\x-x + 2-2 + 4x =\\4x[/tex]

ANswer:

4x

In general, how does the growth of y = 3x compare to the growth of y = 3x?

Answers

Final answer:

The growth of y = 3x is identical to itself as it's the same function. The growth in y = 3x represents consistent linear growth, with a steady increase of the dependent variable as the independent variable increases. In an exponential function, the growth rate increases over time, unlike the consistent slope of a linear function.

Explanation:

The question seems to contain a typo and asks how the growth of y = 3x compares to the growth of itself, y = 3x. Since this is the same function, their growth rates are identical. To provide a meaningful comparison, let's consider an inverse relationship such as y = k/x versus an exponential relationship such as y = 3x. In the case of the inverse relationship, as x increases, y decreases; the growth rate is negative. In contrast, for the exponential function y = 3x, as the independent variable x increases, the dependent variable y increases exponentially, and the rate at which y grows also increases over time. For example, if x represents time and y represents a population, in exponential growth like that of bacteria under ideal conditions, the population increases significantly with each generation.

Graphs are an essential tool in displaying data and unveiling patterns. In a graph of y = 3x, also referred to as a line graph, you would find that the slope, which describes the growth rate, is consistent along the entire line. Here, the slope of the line is 3, indicating a consistent growth rate, where y increases by 3 units for every 1 unit increase in x. This consistent slope is representative of linear growth, differing from exponential growth where the growth rate increases as the value rises.

Final answer:

The original question likely contains a typo, comparing y = 3x to itself. Assuming the comparison was intended to be between a linear and an exponential function, a linear growth rate is constant as seen in y = 3x, whereas an exponential growth rate increases over time and is proportional to the value of the variable, as would be seen in y = [tex]3^x.[/tex]

Explanation:

The question seems to have a typo since it compares y = 3x to the same expression y = 3x. Assuming the comparison should be between two different types of functions, such as linear and exponential, we can provide a general explanation of how growth rates differ between linear and exponential functions.

For a linear function like y = 3x, the growth is consistent. That means for every unit increase in x, y increases by 3 units. This represents a constant rate of change. In contrast, with an exponential function, such as y =[tex]3^x[/tex], the rate of growth is proportional to the current value. In other words, as x increases, the value of y grows at an ever-increasing rate, which is characteristic of exponential growth.

A good example is in the growth of bacteria which can reproduce at an exponential rate, leading to a much faster increase compared to linear growth, as more bacteria contribute to the population each generation. Similarly, economies can grow exponentially, with the growth applied to an also growing base value, resulting in a curve that steepens over time.

2. At a temperature of 20°C the common amoeba reproduces by
splitting in half every 24 hours. If we start with a single amoeba
how many will there be after (a) 8 days, (b) 16 days?​

Answers

Step-by-step explanation:

Each day it splits in half. You wouldn't multiply by 2, for you would have to go, day 1 = 1 amoeba

day 2 = 3 amoebas (because you have the previous amoeba plus the starting one)

You would continue like this until you get day 8 and 16.

Final answer:

Amoebas reproduce by splitting in half every 24 hours. To calculate the number of amoebas after a certain period of time, use the exponential growth formula. After 8 days, there will be 256 amoebas, and after 16 days, there will be 65,536 amoebas.

Explanation:

To determine the number of amoebas after a certain period of time, we need to use the exponential growth formula. In this case, amoebas reproduce by splitting in half every 24 hours. So, if we start with one amoeba, after 24 hours, there will be two amoebae (2¹). After 48 hours, there will be four amoebas (2²) and so on.

For (a) 8 days, we need to calculate the number of 24-hour periods in 8 days. There are 8 days x 24 hours/day = 192 hours. So, we divide 192 by 24 to get the number of 24-hour periods, which is 8. Therefore, after 8 days, there will be 2⁸ = 256 amoebas.

For (b) 16 days, we repeat the same calculations. There are 16 days x 24 hours/day = 384 hours. Dividing 384 by 24 gives us 16 24-hour periods. Therefore, after 16 days, there will be 2¹⁶ = 65,536 amoebas.

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Tomas is making trail mix using granola and walnuts. He can spend a total of $12 on the ingredients. He buys 3 pounds of granola that costs $2.00 per pound. The walnuts cost $6 per pound. He uses the equation to represent the total cost, where x represents the number of pounds of granola and y represents the number of pounds of walnuts. He solves the equation for y, the number of pounds of walnuts he can buy.

Answer- B Tomas added 6 to both sides of the equation instead of subtracting 6.
just took the test

Answers

Final answer:

Tomas should subtract 2x from both sides of the equation, not add 6.

Explanation:

In the given question, Tomas is buying granola and walnuts and he can spend a total of $12 on the ingredients.

He buys 3 pounds of granola that costs $2.00 per pound, and the walnuts cost $6 per pound.

The equation he uses to represent the total cost is: y = 12 - 2x, where x represents the number of pounds of granola and y represents the number of pounds of walnuts.

To solve the equation for y, Tomas should subtract 2x from both sides, not add.

This will give the correct equation for the number of pounds of walnuts he can buy.

Therefore, the correct equation is: y = 12 - 2x.

Which of the following is an even function?
f(x) = |x|
f(x) = x3 – 1
f(x) = –3x

Answers

Answer:

f(x) = |x|

Step-by-step explanation:

Only f(x) = |x| is an even function.  If you evaluate this function at x = 3, for example, the result is 3; if at x = -3, the result is still 3.  That's a hallmark of even functions.

Answer:

f(x) = |x|

Step-by-step explanation:

If we keep -x in place of x and it does not effect the given function, then it is even function. i.e. f(-x) = f(x).

and, If we put -x in place of x then the resultant function will get negative of the first function, then it is odd function. i.e. f(-x) = -f(x).

1. f(x) = |x|

Put x = -x ,then

f(-x) = |-x| = |x| = f(x)

Hence, f(x) is even function.

2.f(x) = x³ - 1

Put x = -x, then

f(-x) = (-x)³ - 1

      = -x³ - 1 = -f(x)

Hence, this function is odd.

3. f(x) = -3x

Put x = -x

then, f(-x) = -3(-x)

                = 3x = -f(x)

Hence, the given function is odd function.

Thus, only f(x) = |x| is even function.

Polygon A is 4 times smaller than polygon B. If one side of polygon B measures 20 inches, what does the matching side of polygon A measure?

Answers

So polygon B measures 20 and polygon A is four times smaller than you would divide that 20 by for and get 5 for your answer:)
Final answer:

A matching side of Polygon A measures 5 inches if it is 4 times smaller than a side of Polygon B that measures 20 inches.

Explanation:

If Polygon A is 4 times smaller than Polygon B, and a side of Polygon B measures 20 inches, then the matching side of Polygon A measures 5 inches. This is because when an object is said to be 'x times smaller' than another, you divide the original size by 'x' to find the new size. Therefore, the matching side length of Polygon A would be 20 inches ÷ 4 = 5 inches.

Example related to area comparison between two squares: Marta has a square with a side length of 4 inches. She has another square with side lengths that are twice as long. The side length of the larger square would be 4 inches x 2 = 8 inches. Since the area of a square is the side length squared, the area of the larger square would be 8 inches x 8 inches = 64 square inches, which is 4 times the area of the smaller square (16 square inches).

In what form is the following linear equation written?
y=9x + 2

A. Standard
B. Rise-run
C. Point-slope
D. Slope-intercept

Answers

Answer:

D

Step-by-step explanation:

ax+by=c is standard form

point slope form is y-y1=m(x-x1)

slope-intercept form is y=mx+b

rise-run is not a form for a linear equation

rise/run equals slope though

So anyways y=9x+2 is comparable to the form y=mx+b

So it is in slope-intercept form

Answer:slope-intercept

Step-by-step explanation:

What is the greatest common factor of 37 and 88

Answers

Answer:

The Greatest Common factor is 1.

Step-by-step explanation:

You can't reduce the numbers anymore.

The greatest common factor of 37 and 88 is 1 .

What is greatest common factor ?

The greatest common factor of two or more integers, which are not all zero, is the largest positive integer that equally divides each of the integers. The greatest common factor of two numbers say x and y is represented as gcf(x,y) .

How to calculate the greatest common factor of the two numbers ?

The two numbers given are 37 and 88 .

There is no common divisors of 37 and 88 except 1 .

Thus the greatest common factor, of numbers -

gcf(37,88) = 1

Therefore, the greatest common factor of 37 and 88 is 1 .

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the line passing through point (0, 0) and parallel to the line whose equation is 3x + 2y - 6 = 0


Answers

Answer: y= -3/2x

Explanation:

3x+ 2y- 6

→ 2y= -3x+ 6

→ y= -3/2x+ 3

Parallel to y= ax+ b is to have the same slope (ax) and have a different y- intercept.

For this equation, y= -3/2x + 3, it is y= -3/2x because the line has to pass through point (0,0).

(0,3)(2,0) you can use desmos to find all your graph answers

Nancy sold cosmetics products on a commission if her total sale for the month were 2000 and her rate of commission was 7.5% what was the amount of her commission

Answers

Answer:

The amount of her commission= 150

Step-by-step explanation:

Sale price = 2000

Rate of commission = 7.5%

Amount of commission =?

Formula:

Commission_amount = sale price * commission_percentage / 100

Now put the values in the formula.

Commission_amount=2000*7.5/100

Commission_amount=150.

Thus the amount of her commission is 150....

Find the value of the function sin
7pi/2

Answers

Answer:

The answer is D: -1.00

Step-by-step explanation:

I just took the test on edg 2020 and got it correct

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The required value of the given trigonometric ratio is - 1.

Hence option D is correct.

Use the concept of trigonometric ratio defined as:

Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain all trigonometric functions' values.

The trigonometric ratios of an acute angle supplied are the ratios of the sides of a right-angled triangle with respect to that angle.

The given trigonometric ratio is,

[tex]\text{sin}(\dfrac{7\pi}{2})[/tex]

Since we can write the expression of radian as,

[tex]\dfrac{7\pi}{2} = 3\pi + \dfrac{\pi}{2}[/tex]

Then,

[tex]\text{sin}(\dfrac{7\pi}{2}) = \text{sin}(3\pi + \dfrac{\pi}{2})[/tex]

Since we know that,

sin(3π + θ) = -sinθ

Therefore,

[tex]\text{sin}(3\pi + \dfrac{\pi}{2}) = -\text{sin}(\dfrac{\pi}{2})[/tex]

Ans we also know sin(π/2) = 1

So,

[tex]\text{sin}(\dfrac{7\pi}{2}) = -1.00[/tex]

Hence, the required value of the given trigonometric ratio is - 1 which is option D.

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A 34-m tall building casts a shadow. The distance from the top of the building to the tip of the shadow is 37m. Find the length of the shadow. If necessary, round your answer to the nearest tenth.

Answers

Answer:  14.6

Step-by-step explanation:

Draw a right triangle such that the building is perpendicular to the ground (which is where the shadow is cast).

Use Pythagorean Theorem to find the length of the shadow (x):

x² + 34² = 37²

x²          = 37² - 34²

x²          = 213

√x²       = √213

x          = 14.59

-5 is a(n)
help please asap

Answers

Answer:

B

Step-by-step explanation:

It is rational because it is terminal (meaning it ends and doesn't go on forever) it is also under 0 because it is negative. It is an integer because it is not a fraction or decimal.

Final answer:

-5 is an integer, a category of whole numbers that includes positive, negative, and zero. Specifically, -5 is a negative integer.

Explanation:

The number -5 in mathematics is classified as an integer. An integer is any whole number found on the number line that can either be positive, negative, or zero. Therefore, the number -5, being a whole number and negative, fits into the category of integers. -5 is also an example of a negative integer.

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