Find the area of the polygon.
2 cm
3 cm
1 cm
3 cm
4 cm

The exponent for the expression, 5 × 5 × 5 × 5 × 5, would be expressed as: [tex]5^5[/tex].

An exponent can be defined as the power to which the base is to b e raised.

For example, a × a × a can be expressed in  exponent form as a³.

In the same vein, given the expression, 5 × 5 × 5 × 5 × 5, we would expressed this in exponent form as: [tex]5^5[/tex].

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[tex]y= 6x -4~~~~~~...(i)\\\\y = 5x -3~~~~~~...(ii)\\\\\text{From (i) and (ii):}\\\\~~~~~6x -4 = 5x -3\\\\\implies 6x -5x = -3 + 4\\\\\implies x = 1\\\\\text{Substitute x = 1 in equation (i):}\\\\y = 6(1) -4 = 2\\\\\text{Hence,}~ (x,y) = (1,2)[/tex]

Answer:

there are 75 colors of each candy

Step-by-step explanation:

300÷4=75

The ratio of the area of sector abc to the area of sector dbe is 4/3

For sector abc, we have:

Angle = x

Radius  = 2r

For sector dbe, we have:

Angle = 3x

Radius = r

The area of a sector is:

[tex]Area =\frac{\theta}{360}* \pi r^2[/tex]

So, we have:

[tex]ABC =\frac{x}{360}* \pi (2r)^2[/tex]

Evaluate

[tex]ABC =\frac{x* \pi r^2}{90}[/tex]

For DBE, we have:

[tex]DBE =\frac{3x}{360}* \pi (r)^2[/tex]

Evaluate

[tex]DBE =\frac{x}{120}* \pi r^2[/tex]

The ratio of both areas is:

[tex]Ratio = \frac{x}{90}* \pi r^2 : \frac{x}{120}* \pi r^2[/tex]

Cancel out the common factors

[tex]Ratio = \frac{1}{90} : \frac{1}{120}[/tex]

Express as fraction

[tex]Ratio = \frac{120}{90}[/tex]

Divide

[tex]Ratio = \frac{4}{3}[/tex]

Hence, the ratio of the area of sector abc to the area of sector dbe is 4/3

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4/3

its the answer edmentum

Answer:

As a fraction:

x | y

________

|

7/3 | 2

3 | 4

11/3 | 6

13/3 | 8

As a mixed fraction:

x | y

________

|

2 ⅓ | 2

3 | 4

3 ⅔ | 6

4 ⅓ | 8

As a decimal:

x | y

___________

|

2.33.. | 2

3 | 4

3.66.. | 6

4.33.. | 8

You should start with x values since the y values will be easier to plot. x's will not be easy to represent.

For example:

x | y

________

|

0 | -5

1 | -2

2 | 1

3 | 4

4 | 7

5 | 10

Answer:

[tex]\sf 59 \frac{17}{20} \: in^3[/tex]

Step-by-step explanation:

Regular-size box of crackers

Dimensions:  [tex]\sf 2 \frac{1}{4} \: in \times 9 \frac{1}{2}\:in \times 14\: in[/tex]

Snack-size box of crackers

Volume = [tex]\sf \frac{1}{5}[/tex] of the volume of a regular-size box

To calculate the volume of the snack-size box of crackers, calculate the volume of the regular-size box then multiply it by [tex]\sf \frac{1}{5}[/tex].

[tex]\begin{aligned}\textsf{Volume of a rectangular prism} & = \textsf{width x length x height}\\\\\implies \textsf{Volume of regular-size box} & = \sf 9 \frac{1}{2} \times 14 \times 2 \frac{1}{4}\\\\& = \sf \dfrac{19}{2} \times 14 \times \dfrac{9}{4}\\\\& = \sf \dfrac{19 \times 14 \times 9}{2 \times 4}\\\\& = \sf \dfrac{1197}{4}\: in^3\end{aligned}[/tex]

[tex]\begin{aligned}\implies \textsf{Volume of snack-size box} & = \sf \dfrac{1}{5} \times \textsf{volume of regular-size box}\\\\& = \sf \dfrac{1}{5} \times \dfrac{1197}{4}\\\\& = \sf \dfrac{1 \times 1197}{5 \times 4}\\\\& = \sf \dfrac{1197}{20}\\\\& = \sf 59 \dfrac{17}{20}\: in^3\end{aligned}[/tex]

Therefore, the volume of the snack-size box is [tex]\sf 59 \frac{17}{20} \: in^3[/tex]

Answer:

x = 2

Step-by-step explanation:

This is a 45-45-90 special right triangle. The legs in this triangle are equal and the hypotenuse is leg multiplied with √2. Refer to the picture at the bottom.

One leg is x, the second leg is x and hypotenuse x√2.

[tex]x \sqrt{2} = 2 \sqrt{2} \\\\\text{Divide both sides with } \sqrt{2} \text{ to isolate } x.\\\frac{x \sqrt{2}}{\sqrt{2}} = \frac{2 \sqrt{2}}{\sqrt{2}}\\\\x = 2[/tex]

The statement: "Kiley bought a platter for $ 19 and several matching bowls that were $ 8 each. What is the cost before tax?" shows discrete graph.

A discrete graph is one with scattered points. They may or may not show a direction or trend. They don't have data in between the points already given.

Here only first option shows a graph with scattered point.

Thus, the statement: "Kiley bought a platter for $ 19 and several matching bowls that were $ 8 each. What is the cost before tax?" shows discrete graph.

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Step-by-step explanation:

Here is the solution...hope it helps:)

The possible dimension of the third side is 10 units.

A right triangle is a triangle that has three sides known as the opposite, adjacent and hypotenuse. The hypotenuse is the longest sides of the triangle. The opposite side is the side that faces an angle. The adjacent side is the third side.

If two side lengths are given, the third side can be determined using the Pythagoras theorem.

√a² + b ² = c

√6² + 8² = √36 + 64 = 10 units

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The sequence whose first term is - 4 and defined recursively by the formula f(n + 1) = f(n) + 3 have the element - 1 as the next term. (Correct choice: B)

In mathematics, sequences are sets whose elements observe at least a condition, which is represented by a recursion formula in this question:

f(n + 1) = f(n) + 3

Thus, the following term of the sequence is:

f(2) = f(1) + 3

f(2) = - 4 + 3

f(2) = - 1

The sequence whose first term is - 4 and defined recursively by the formula f(n + 1) = f(n) + 3 have the element - 1 as the next term. (Correct choice: B)

The statement is poorly formatted and reports typing mistakes. Correct statement is:

A sequence is defined recursively by the formula f(n + 1) = f(n) + 3. The first term of the sequence is - 4. What is the next term in the sequence? a) - 7, b) - 1, c) 1, d) 7

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The average rate of change for this function for the interval from x = 1

to x = 3 will be 8. Therefore option B is correct.

Let the thing that is changing be y and the thing with which the rate is being compared is x, then we have the average rate of change of y as x changes as:

[tex]\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

where when

[tex]x = x_1, y = y_1\\and \\x = x_2, y = y_2[/tex]

The average rate of change can be calculated as;

From x=1 to x=3,

y = 2 and y = 18

Therefore, based on the table, when:

[tex]x_1 = 1 y_1 = 2 \\and \\x_2 = 3, y_2 = 18[/tex]

Then:

[tex]\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]\text{Average rate} = \dfrac{18 - 2}{3-1}\\\\\text{Average rate} = \dfrac{16}{2}\\\\\text{Average rate} = 8[/tex]

Therefore option B is correct.

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Answer:

height = 18m

Step-by-step explanation:

cone volume = 3183.96 m³

1/3 πr²h = 3183.96

1/3×3.14×13×13×h = 3183.96

h = 3183.96×3/13×13×3.14

h = 9551.88/530.66

h = 18

A ratio shows us the number of times a number contains another number. Caitlin is right.

A ratio shows us the number of times a number contains another number.

The ratio of the ages of Mandy and Sandy is 2:5. Therefore, the ratio will be,

M/S = 2/5

M = 2S/5

After 8 years, their ages will be in the ratio 1:2, therefore,

(M+8)/(S+8) = 1/2

2M + 16 = S + 8

2M - S = -16 + 8

Substitute the value of M,

2(2S/5) - S = -8

-0.2S = -8

S = 40

Now, if we substitute the value of S in the first ratio,

M/S = 2/5

M/40 = 2/5

M = 16

Now, if we take the difference in their ages the difference will be 24(40-16).

Since the difference is 24, we can conclude that Caitlin is right.

Hence, Caitlin is right.

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The solution to the question is:

c is 6 = [tex]\sqrt{a^{2} + b^{2} -2abcosC }[/tex]

b is 5 = [tex]\sqrt{a^{2} + c^{2} -2accosB }[/tex]

cosB is 2 = [tex]\frac{a^{2} + c^{2} - b^{2} }{2ac}[/tex]

a is 4 = [tex]\sqrt{b^{2} + c^{2} -2bccosA }[/tex]

cosA is 3 = [tex]\frac{b^{2} + c^{2} -a^{2} }{2bc}[/tex]

cosC is 1 = [tex]\frac{b^{2} + a^{2} - c^{2} }{2ab}[/tex]

it is used to relate the three sides of a triangle with the angle facing one of its sides.

The square of the side facing the included angle is equal to the some of the squares of the other sides and the product of twice the other two sides and the cosine of the included angle.

Analysis:

If c is the side facing the included angle C, then

[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] -2ab cos C-----------------1

then c =  [tex]\sqrt{a^{2} + b^{2} -2abcosC }[/tex]

if b is the side facing the included angle B, then

[tex]b^{2}[/tex] = [tex]a^{2}[/tex] + [tex]c^{2}[/tex] -2accosB-----------------2

b =  [tex]\sqrt{a^{2} + c^{2} -2accosB }[/tex]

from equation 2, make cosB the subject of equation

2ac cosB =  [tex]a^{2}[/tex] +  [tex]c^{2}[/tex] - [tex]b^{2}[/tex]

cosB =  [tex]\frac{a^{2} + c^{2} - b^{2} }{2ac}[/tex]

if a is the side facing the included angle A, then

[tex]a^{2}[/tex] = [tex]b^{2}[/tex] + [tex]c^{2}[/tex] -2bccosA--------------------3

a =  [tex]\sqrt{b^{2} + c^{2} -2bccosA }[/tex]

from equation 3, making cosA subject of the equation

2bcosA =  [tex]b^{2}[/tex] +  [tex]c^{2}[/tex]  - [tex]a^{2}[/tex]

cosA =  [tex]\frac{b^{2} + c^{2} -a^{2} }{2bc}[/tex]

from equation 1, making cos C the subject

2abcosC =  [tex]b^{2}[/tex] + [tex]a^{2}[/tex] -  [tex]c^{2}[/tex]

cos C =  [tex]\frac{b^{2} + a^{2} - c^{2} }{2ab}[/tex]

In conclusion,

c is 6 = [tex]\sqrt{a^{2} + b^{2} -2abcosC }[/tex]

b is 5 = [tex]\sqrt{a^{2} + c^{2} -2accosB }[/tex]

cosB is 2 = [tex]\frac{a^{2} + c^{2} - b^{2} }{2ac}[/tex]

a is 4 = [tex]\sqrt{b^{2} + c^{2} -2bccosA }[/tex]

cosA is 3 = [tex]\frac{b^{2} + c^{2} -a^{2} }{2bc}[/tex]

cosC is 1 = [tex]\frac{b^{2} + a^{2} - c^{2} }{2ab}[/tex]

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Answer:

Step-by-step explanation:

Formula

The sin(A) =  opposite / hypotenuse

Givens

Opposite = CB = 11

Hypotenuse = AB = 61

Solution

Sin(A) = 11/61

Sin(A) = 0.1803

Answer

Sin(A) = 11/61

Sin(A) = 0.1803

The scale factor of the dilation of line segment BA is 1/5.

An equation is an expression that shows the relationship between two or more numbers and variables.

Dilation is the increase or decrease in the size of a figure.

From the diagram:

scale factor of BA = AC / CA' = 4 / (4 + 16) = 1/5

The scale factor of the dilation of line segment BA is 1/5.

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Answer:

B

Step-by-step explanation:

I do believe

Answer:

$48

30/10 is equal to 3/1, 16 x 3 equals to 48.

Answer:$48

Step-by-step explanation:

$30/10p = $3 per person

3x6=18

18+30=48

Answer:

Can't see the problem. Send a picture of it.

Answer:

-3 ,-2 ,-1, 0

Step-by-step explanation:

x is the smallest integer then, x+x+1+x+2+x+2=-6
4x+6= -6   4x=-12 x= -3 so the integers are..

Considering the definition of equation, the equation that represents the statement "Two times a number x increased by 8 is 20" is: 2x + 8= 20

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.

The unknown values represents the number (or numbers), if any, that make the equality true. This unknown number is the solution of the equation.

Considering that:

the equation that represents the statement "Two times a number x increased by 8 is 20" is:

2x + 8= 20

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The equation for the statement "two times a number x increased by 8 is 20" is 2x+8=20.

The given statement is two times a number x increased by 8 is 20.

We need to write the equation to represent this statement.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Now, two times a number x=2x

Increased by 8 is 20=2x+8=20

Hence, the equation for the statement "two times a number x increased by 8 is 20" is 2x+8=20.

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Answer:

The answer is (0.5, 0)

Step-by-step explanation:

[tex]-3x^3 +12x^2 -15x +6\\\\=-3(x^3 -4x^2 +5x-2)\\\\=-3(x^3 -2x^2-2x^2 +4x+x-2)\\\\=-3\textbf{[} x^2(x-2) -2x(x-2)+ (x-2)\textbf{]}\\\\=-3(x-2)(x^2 -2x +1)\\\\=-3(x-2)(x-1)^2[/tex]

A. Distance between A and B is: 5 units.

B. Triangle ABC is not an equilateral triangle because only two of its sides are equal.

An equilateral triangle has three sides that have the same length.

Given the vertices with their coordinate points as:

A (-3, 2)

B (-6, -2)

C (0, -2)

Use the distance formula, [tex]d =\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex], to find AB, BC, and AC:

AB = √[(−6−(−3))² + (−2−2)²]

AB = √25

AB = 5 units

BC = √[(−6−0)² + (−2−(−2))²]

BC = √36

BC = 6 units

AC = √[(−3−0)² + (2−(−2))²]

AC = 25

AC = 5 units

Only two of the sides of the triangle, AB and AC, are equal. Therefore, it is not an equilateral triangle.

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The function f(x) = 2|x – 2| + 6 has a vertex at (2, 6) option second is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function that has vertex at (2, 6)

The options are:

f(x) = 2|x – 2| – 6

f(x) = 2|x – 2| + 6

f(x) = 2|x + 2| + 6

f(x) = 2|x + 2| – 6

As we know the vertex form of a quadratic function is given by:

f(x) = a(x - h)² + k

Similarly, mod function  can be expressed as:

m(x) = a|x - h| + k

Here (h, k) is the vertex of a function.

In the function:

f(x) = 2|x – 2| + 6

The vertex of the function is (2, 6)

Thus, the function f(x) = 2|x – 2| + 6 has a vertex at (2, 6) option second is correct.

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Answer:

y=-3/10x+1/2

use the coordinates to find the gradient (m)then substitute it in this formula y=mx+c

find c by substituting one of the coordinate

Answer: The ten thousand digit is 6.  And the millions digit is 4. So the answer is 10.

The true statement is the cost of steak at grocery store 1 is $0.75 less per pound than at grocery store 2.

In store 1, the cost of 1 pound of steak is $6.75.

Cost of 1 pound of steak in store 2 is 15 /2 = $7.50

Difference in the cost : $7.50 - $6.75 = $0.75

Here is the complete question:

The equation y = 6.75x models the cost, in dollars, to purchase x pounds of steak at grocery store 1. This table shows the cost to buy different weights of steak at grocery store 2.

Cost of Steak at Grocery Store 2

Weight (pounds) Cost

2..........................$15.00

3..........................$22.50

5......................... $37.50

9......................... $67.50

Which statement is true?

answer choices

The cost of steak at grocery store 1 is $0.75 less per pound than at grocery store 2.

The cost of steak at grocery store 1 is $0.75 more per pound than at grocery store 2.

The cost of steak at grocery store 1 is $0.50 less per pound than at grocery store 2.

The cost of steak at grocery store 1 is $0.50 more per pound than at grocery store 2. R

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]5x-y=-7\implies 5x-y+7=0 \\\\\\ \stackrel{\stackrel{m}{\downarrow }}{5} x+7=y\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so a line perpendicular to that one above will have a slope of

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{5\implies \cfrac{5}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{5}}}[/tex]