find the value of A , B and C from the following figure​

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]

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]

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

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

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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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

The name of the national road that follows the eastern coastline of South Africa is the N2.

The N2 is a national road in South Africa that starts at Cape Town and goes towards the eastern part of South Africa.

It passes though Port Elizabeth, East London, Durban, and Richard's Bay which are all cities on the eastern side of South Africa and are along the coastline.

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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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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 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:

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

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

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

well, we know the discount is 4975 - 3781 = 1194.

if we take 4975 to be the 100%, what is 1194 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 4975 & 100\\ 1194& x \end{array} \implies \cfrac{4975}{1194}~~=~~\cfrac{100}{x}\implies \cfrac{26}{6}=\cfrac{100}{x} \\\\\\ 26x = 600\implies x=\cfrac{600}{26}\implies x\approx 23.08[/tex]

Answer:

0.76

Step-by-step explanation:

4975 × 0.76 = 3781

the discount percent given is .76%

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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Answer:

there are 75 colors of each candy

Step-by-step explanation:

300÷4=75

Answer:

Use given values of h and j, and find the value of k:

The equation is now:

Find the value of g when h is 2 and j is 3:

Correct choice is D

Answer:

D. 144

Step-by-step explanation:

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

Step-by-step explanation:

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

[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:

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 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:

ELA

Step-by-step explanation:

you add ela to a bonus points

Answer:

PLA + ELA = 90

Step-by-step explanation:

lol

Answer:

x=2

9+2=11

6+2=8

8x11+88

Step-by-step explanation:

Answer:

$43 + $6l

Step-by-step explanation:

Hello!

She spends $43 and bus several $6 laces.

We don't know how many she buys, but we know that we can represent that number using l.

That means she spends $43 + $6l.

The algebraic expression is $43 + $6l.

We can determine the price if we know the number of laces she buys. We can simply plug in the number of laces she bought, and we can plug it in for l in the equation.

Answer:

43= 6(x)

Explanation:

43 is the total,  and each of them are 6$ each. X is the variable that we don't know.

Answer:

The answer is (0.5, 0)

Step-by-step explanation:

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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