Translate the algebraic expression 7(8j+4+9j) to a verbal expression.

Answer:

[tex]m\angle BAD=73^o[/tex]

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Find the value of x

Let

O ----> the center of the circle

we know that

Triangle BOC≅Triangle COD

[tex]m\angle BOC=arc\ BC[/tex] ----> by central angle

[tex]m\angle COD=arc\ CD[/tex] ----> by central angle

[tex]m\angle BOC=m\angle COD[/tex]

therefore

[tex]arc\ BC=arc\ CD[/tex]

substitute the given values

[tex](9x-53)^o=(2x+45)^o[/tex]

solve for x

[tex]9x-2x=45+53\\7x=98\\x=14[/tex]

step 2

Find the measure of angle BAD

we know that

The inscribed angle is half that of the arc it comprises.

so

[tex]m\angle BAD=\frac{1}{2} [arc\ BC+arc\ CD][/tex]

[tex]arc\ BC=9(14)-53=73^o[/tex]

[tex]arc\ CD=2(14)+45=73^o[/tex]

substitute

[tex]m\angle BAD=\frac{1}{2} [73^o+73^o]=73^o[/tex]

The measure of mBAD is 73⁰

Given the following expression

mBC = (9x-53) and mCD = (2x + 45)

From the given diagram, both arcs are equal, hence

9x - 53 = 2x +45

7x = 98

x = 14

Get the measure of arc BC

arcBC = 9x - 53

arcBC = 9(14)-53

arcBC = 73 degrees

The measure of mBAD = 1/2(73+73) = 73 degrees

Hence the measure of mBAD is 73⁰

Learn more on geometry here; https://brainly.com/question/24375372

I can't see it you have to put it closer to the screen it is scratchy

Answer: Step 3: [tex]3x>3[/tex] (Subtraction).

Step-by-step explanation:

1- Given the inequality shown in the problem, Zareen should solve it as following:

2-Subtract 4x from both sides:

[tex]7x + 5-4x > 4x + 2 -4x\\3x+5>2[/tex]

(Zareen did this step correctly)

3- Subtract 5 from both sides:

[tex]3x + 5-5 > 2-5\\3x>-3[/tex]

(As you can see, Zareen made a mistake in Step 3, because the subtraction is actually  [tex]2-5=-3[/tex])

4- Divide both sides by 3, then:

[tex]\frac{3x}{3}>\frac{-3}{3}\\\\x>-1[/tex]

Zareen's mistake occurred in Step 2, where she incorrectly subtracted terms that did not simplify the inequality properly. She should have subtracted 4x from both sides and then divided by 3 to isolate x and solve correctly, which would have given x > -1.

Zareen made her mistake in Step 2 of solving the inequality

7x + 5 > 4x + 2.

In this step, she should have subtracted 4x from both sides of the inequality to isolate the variable term (x) on one side. This would have resulted in

3x + 5 > 2,

which she correctly simplified to

3x > -3

after subtracting 5 from both sides. Following the order of operations to the end, she would then divide both sides by 3 to find x > -1. However, the provided solution incorrectly states that the second step of just subtracting 3x resulted in the term 5 > 2, which is not relevant to the inequality manipulation and does not follow the correct algebraic steps to solve the inequality. The correct sequence would respect the operations to eliminate terms and simplify the algebra.

Answer:

Step-by-step explanation:

The formulas for the areas of a rectangle and a parallelogram are actually the same; both involve length and width.  

It may be easier to understand this if you draw a rectangle of width w with a drawing of a parallelogram of width underneath.  The parallelogram's ends appear slanted; they are neither vertical nor horizontal.  However, so long as you measure the length of the rectangle horizontally, all measurements are equal to each other as well as equal to the length of the rectangle.

Hence the calculated areas will be one and the same.

Area formula of a rectangle to find the area formula of parallelogram, the length of the rectangle should be used as the height of the parallelogram.

Area of rectangle is the product of the length of the rectangle and the width of the rectangle. It can be given as,

[tex]A=a\times b[/tex]

Here, [tex]a[/tex] is the length rectangle and [tex]b[/tex] is the width of the rectangle.

Given information-

The area formula of parallelogram has to find using the area formula of rectangle.

Parallelogram is a closed shaped quadrilateral polygon in which opposite sides is equal and parallel and opposite angles are equal.

The shape of the parallelogram is attached below.

The area of the rectangle is the base time height. It can be given as,

[tex]A_r=l\times h[/tex]

In case of a parallelogram the height of the parallelogram is not equal to the side of it.

The area of the parallelogram is still given as the area of rectangle which is base time height, with new height.

Thus for the attached figure of parallelogram the area of it can be given as,

[tex]A_p=l\times h[/tex]

Hence, The area formula of a rectangle to find the area formula of a parallelogram, the length of the rectangle should be used as the height of the parallelogram.

Learn more about the area of rectangle here;

https://brainly.com/question/11202023

Answer: The answer is 90.

Step-by-step explanation:

Answer:

30 ft^2

Step-by-step explanation:

Area of square = 12 x 12 = 144

Area of circle = 3.14 x 6^3 = 3.14 x 36 = 113.04

So area of the remaining board = 144 - 113.04 = 30.96

Answer: 30 ft^2

The whole steps are;

collect the like terms

4x - x = 9 + 6

Add or subtract the like terms

3x = 15

Divide both sides by the coefficient of 3

x = 15/3

From the information given, we have that the expression is;

4x -6=x +9

collect the like terms, we get;

4x - x = 9 + 6

Add or subtract the like terms, we get;

3x = 15

Divide both sides by the coefficient of 3. we get;

x = 15/3

Divide the values

x = 5

Learn more about algebraic expressions at: https://brainly.com/question/4344214

#SPJ6

Answer:

[tex]y^2=-8x[/tex]

Step-by-step explanation:

The directrix intersects the x-axis at point (2,0). Points (-2,0) and (2,0) are symmetric about the origin, so the vertex of the parabola is placed at the origin (0,0).

The parameter p of the parabola is the distance from the focus to the directrix, thus p=4.

The branches of the parabola go in negative direction of x-axis, because the focus lies to the left from the vertex.

The equation of the parabola is

[tex](y-0)^2=-2\cdot 4\cdot (x-0),\\ \\y^2=-8x.[/tex]

Answer:

commutative because you can add or subtract in any order

Answer: OPTION C

Step-by-step explanation:

To solve the exercise you must descompose the number 648 into its prime factors, as you can see below:

[tex]648=2*2*2*3*3*3*3[/tex]

You can rewrite the above as following:

[tex]648=2^3*3^4[/tex]

Then:

[tex]\sqrt{648}=\sqrt{2^3*3^4}[/tex]

Therefore, as you can see, the value of  a and b are the following:

[tex]a=3,b=4[/tex]

Answer:

The correct answer option is C. a=3, b=4.

Step-by-step explanation:

We are given the following expression and we need to determine whether which of the values of [tex]a[/tex] and [tex]b[/tex] should be used to make the equation true:

[tex] \sqrt { 648 } = \sqrt { 2 ^ a \times 3 ^ b } [/tex]

A. a=3, b=2:

[tex] \sqrt { 2 ^ 3 \times 3 ^ 2 } = \sqrt { 72 } [/tex]

B.  a=2, b=3:

[tex] \sqrt { 2 ^ 2 \times 3 ^ 3 } = \sqrt { 108 } [/tex]

C. a=3, b=4 :

[tex] \sqrt { 2 ^ 3 \times 3 ^ 4 } = \sqrt { 648 } [/tex]

D. a=4, b=3:

[tex] \sqrt { 2 ^ 4 \times 3 ^ 3 } = \sqrt { 432 } [/tex]

Therefore, the correct answer option is C. a=3, b=4.

Answer:

B and D

Step-by-step explanation:

A difference of squares has the form a² - b²

4p² - 9 = (2p)² - 3² ← is a difference of squares

q² - 36 = q² - 6² ← is a difference of squares

Answer:

answer:

4p²-9 and q²-36 as it is in the form of x²-y²

Answer:

[tex]\begin{array}{c|c}x&y\\-2&13\\-1&9\\0&5\\1&1\\2&-3\end{array}[/tex]

Step-by-step explanation:

Put x = -2, x = -1, ... , x = 2 to the equation of the function y = -4x + 5 and calculate the values of y:

for x = -2

y = -4(-2) + 5 = 8 + 5 = 13

for x = -1

y = -4(-1) + 5 = 4 + 5 = 9

for x = 0

y = -4(0) + 5 = 0 + 5 = 5

for x = 1

y = -4(1) + 5 = -4 + 5 = 1

for x = 2

y = -4(2) + 5 = -8 + 5 = -3

Just put the values given for x in the equation to find y

-4(-2)+5=13

-4(-1)+5=9

-4(0)+5=5

-4(1)+5=1

-4(2)+5=-3

Answer: The required value of x is 12 units.

Step-by-step explanation:  Given that the figure A is a scale image of figure B.

We are to find the value of x.

Since figure A is the scale image of figure B, so both the figures are similar to each other.

Also, the corresponding sides of the similar figures are proportional, so we get

[tex]\dfrac{30}{25}=\dfrac{x}{10}\\\\\\\Rightarrow\dfrac{6}{5}=\dfrac{x}{10}\\\\\\\Rightarrow x=5x=60\\\\\Rightarrow x=\dfrac{60}{5}\\\\\Rightarrow x=12.[/tex]

Thus, the required value of x is 12 units.

Answer:

x=12 units

Step-by-step explanation:

Answer:

Part 7) Option C. The approximate perimeter of the patio is [tex]54\ ft[/tex]

Part 8) Option G. [tex]3\ floats[/tex]

Part 9) [tex]150.72\ minutes[/tex]

Step-by-step explanation:

Part 7) we know that

The perimeter of the figure is equal to the circumference of the larger half circle plus the circumference of the smaller half circle plus two times the length of 8 ft

step 1

Find the circumference of the larger half circle

The circumference of the larger half circle is

[tex]C=\pi r[/tex]

we have

[tex]r=8+2=10\ ft[/tex]

substitute

[tex]C=\pi(10)[/tex]

[tex]C=10\pi\ ft[/tex]

step 2

Find the circumference of the smaller half circle

The circumference of the smaller half circle is

[tex]C=\pi r[/tex]

we have

[tex]r=2\ ft[/tex]

substitute

[tex]C=\pi(2)[/tex]

[tex]C=2\pi\ ft[/tex]

step 3

Find the perimeter of the figure

[tex]10\pi\ ft+2\pi\ ft+2(8)\ ft=(12\pi+16)\ ft[/tex]

assume [tex]\pi=3.14[/tex]

so

[tex](12(3.14)+16)=53.68=54\ ft[/tex]

Part 8) we know tat

The area of a circle is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]A=28.26\ ft^{2}[/tex]

assume [tex]\pi=3.14[/tex]

substitute the values and solve for r

[tex]28.26=(3.14)r^{2}[/tex]

[tex]r^{2}=28.26/(3.14)[/tex]

[tex]r^{2}=9[/tex]

[tex]r=3\ ft[/tex]

Find the diameter D

[tex]D=2r=2(3)=6\ ft[/tex]

Divide the width of the pool by the diameter of the floats

so

[tex]\frac{18}{6}=3\ floats[/tex]

Part 9)

step 1

Find the circumference of one coaster

The circumference of circle is

[tex]C=2\pi r[/tex]

we have

[tex]r=1.5\ in[/tex]

assume [tex]\pi=3.14[/tex]

substitute

[tex]C=2(3.14)(1.5)=9.42\ in[/tex]

step 2

Find the circumference of 48 coasters

so

[tex]48(9.42)=452.16\ in[/tex]

step 3

we know that

The laser cut woods at the rate of 3 inches per minute

By proportion find how many minutes will it take to cut out 48 coasters

[tex]\frac{3}{1}\frac{inches}{minute} =\frac{452.16}{x}\frac{inches}{minutes}\\ \\x=452.16/3\\ \\x=150.72\ minutes[/tex]

Answer: The answer is (3,0).

Step-by-step explanation: We know this because we have to move the positive 5, 2 to the left. Then we have to do the -5 up 5. After you do that you get (3,0). Hope this helps!

Point P is translated by 2 units to the left and 5 units to the upward direction. Then the coordinate of the point P' is (3, 0).

It simply means that the point is being shifted from [tex]\rm (x_1, y_1)[/tex] to [tex]\rm (x_2, y_2)[/tex] in a cartesian coordinate.

Given

The point P' is the image of point P (5,-5) under a translation by 2 units to the left and 5 units up.

Then the position of the point P' will be.

Point P is translated by 2  to the left is the negative x-axis. Then coordinate of point P will be

[tex](5 - 2, -5)\\\\(3, -5)[/tex]

Point P is translated by 5  to the upward is the positive y-axis. Then coordinate of point P will be

[tex](3, -5 + 5)\\\\(3, 0)[/tex]

Then, the coordinate of the point P' is (3, 0).

More about the translation of the point link is given below.

https://brainly.com/question/19127095

Answer:

The answer will depend on the units used for 17299986438377. If the number is in dollars, then the answer is 17300000000000.

Step-by-step explanation:

Answer:

20,000,000,000,000

Step-by-step explanation:

take the number right before the number your rounding and if its 5^ add 1 to your number if not, you dont add anything. convert all numbers before your number to 0

Answer:

x = 2

Step-by-step explanation:

The volume of this prism is half the volume of it as a rectangular prism. The volume is listed as 30. The rectangular prism would be 60. Volume is found by multipyling base, height and width.

The base is 10 and the width is 3.

Divide 60 by 10 and by 3.

60/10 = 6

6/3 = 2

This means the height x is 2.

Answer:

B. (4,12)

Step-by-step explanation:

The process is really easy, all you have to do is substitute the numbers of the ordered pairs into the equations.

So like for A. (-5,8)

Putting this into the equation would look like this,

10 * -5 + 2 * 8 The -5 being substituted for the x and the 8 for the y.

This equation equals to -34, not 64.

3 * -5 - 4 * 8 = -47

not equal to -36, so A is eliminated.

For B. (4,12)

10 * 4 + 2 * 12 = 64

3* 4 - 4 * 12 = -36

These equal to both of the given equations.

For C. (2, 10)

10 * 2 + 2 * 10= 40

3 * 2 - 4 * 10 = -34

These are not equal to the given answers of these equations, C is eliminated.

And D. (-3,11)

10 * -3 + 2 * 11 = -8

3 * -3 - 4 * 11 = -53

These are not equal to the given answers of these equations, D is eliminated.

So the only pair that have made both equations true is B.(4,12)

Answer:

Step-by-step explanation:

4

Answer:

Answer is B on e2020. (4)

Step-by-step explanation:

The answer is C. $15,600

The yearly pay for Leeann will be $15600. The correct option is C.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Leeann works 20 hours per week and makes $15 per hour. The yearly pay will be calculated as below:-

There are 52 weeks in a year then the total number of hours in a year will be:-

Total hours = 52 x 20 = 1040 hours

Yearly income = 1040 x 15 = $15600

Therefore, the yearly pay for Leeann will be $15600. The correct option is C.

To know more about an expression follow

https://brainly.com/question/13094635

#SPJ2

QUESTION 1

Recall the mnemonics; SOH

[tex]\sin L =\frac{Opposite}{Hypotenuse}[/tex]

[tex]\sin L =\frac{12}{13}[/tex]

QUESTION 2

Recall the mnemonics; CAH

[tex]\cos L =\frac{Adjacent}{Hypotenuse}[/tex]

[tex]\sin L =\frac{5}{13}[/tex]

QUESTION 3

Recall the mnemonics; TOA

[tex]\tan M =\frac{Opposite}{Adjacent}[/tex]

[tex]\tan M =\frac{5}{12}[/tex]

QUESTION 4

[tex]\sin M =\frac{Opposite}{Hypotenuse}[/tex]

[tex]\sin M =\frac{5}{13}[/tex]

QUESTION 5

a) From the Pythagoras Theorem,

[tex]AC^2+AB^2=BC^2[/tex]

[tex]AC^2+4^2=5^2[/tex]

[tex]AC^2+16=25[/tex]

[tex]AC^2=25-16[/tex]

[tex]AC^2=9[/tex]

[tex]AC=\sqrt{9}[/tex]

[tex]AC=3yd[/tex]

b) Using the cosine ratio,

[tex]\cos (m\angle B)=\frac{4}{5}[/tex]

Take the inverse cosine of both sides;

[tex] m\angle B=\cos ^{-1}(\frac{4}{5})[/tex]

[tex] m\angle B=36.86[/tex]

[tex]\therefore m\angle B=36.9\degree[/tex] to the nearest tenth.

c) [tex]m\angle B +m\angle C=90\degree[/tex]

[tex]\Rightarrow 36.9\degree +m\angle C=90\degree[/tex]

[tex]\Rightarrow m\angle C=90\degree-36.9\degree[/tex]

[tex]\Rightarrow m\angle C=53.1\degree[/tex]

QUESTION 6

a)  using the sine ratio,

[tex]\sin(51\degree)=\frac{DE}{18}[/tex]

[tex]DE=18\sin(51\degree)[/tex]

[tex]DE=13.99[/tex]

[tex]\therefore DE=14.0yd[/tex] to the nearest tenth.

b) Using the cosine ratio,

[tex]\cos (51\degree)=\frac{EF}{18}[/tex]

[tex]EF=18\cos (51\degree)[/tex]

[tex]EF=11.3yd[/tex] to the nearest tenth.

c) [tex]m\angle D+ m\angle F=90\degree[/tex]

[tex]\Rightarrow m\angle D + 51\degree=90\degree[/tex]

[tex]\Rightarrow m\angle D=90\degree-51\degree[/tex]

[tex]\Rightarrow m\angle D=39\degree[/tex]

QUESTION 7

a) Using the Pythagoras Theorem;

[tex]lG^2+GH^2=lH^2[/tex]

[tex]l15^2+GH^2=17^2[/tex]

[tex]225+GH^2=289[/tex]

[tex]GH^2=289-225[/tex]

[tex]GH^2=64[/tex]

[tex]GH=\sqrt{64}[/tex]

[tex]GH=8km[/tex]

b) Using the sine ratio,

[tex]\sin(m\angle H)=\frac{15}{17}[/tex]

[tex]m\angle H=\sin^{-1}(\frac{15}{17})[/tex]

[tex]m\angle H=61.9\degree[/tex]

c) [tex]m\angle l + m\angle H=90\degree[/tex]

[tex]m\angle l +61.9\degree=90\degree[/tex]

[tex]m\angle l =90\degree-61.9\degree [/tex]

[tex]m\angle l =28.1\degree [/tex]

QUESTION 8

We plot the points as shown in the diagram.

QUESTION 9

From the diagram, the side lengths XY and YZ can be obtained by counting the boxes. Each box is 1 unit.

This implies that;

XY =3 units

YZ=5 units.

We use Pythagoras Theorem, to obtain XZ.

This implies that;

[tex]XZ^2=XY^2+YZ^2[/tex]

[tex]XZ^2=3^2+5^2[/tex]

[tex]XZ^2=9+25[/tex]

[tex]XZ^2=34[/tex]

[tex]XZ=\sqrt{34}[/tex] units

QUESTION 10.

a) Using the tangent ratio;

[tex]\tan(m\angle X)=\frac{5}{3}[/tex]

[tex]m\angle X=\tan^[-1}(\frac{5}{3})[/tex]

[tex]m\angle X=59.0\degree[/tex]

b) [tex]m\angle Z+m\angle X=90\degree[/tex]

[tex]m\angle Z+59.0\degree=90\degree[/tex]

[tex]m\angle Z=90\degree-59.0\degree[/tex]

[tex]m\angle Z=31.0\degree[/tex]

QUESTION 11

a) Triangle BCD is shown in the attachment.

The length of side DC=|3-2|=1 unit

The length of side DB=|4-3|=1 unit

Using Pythagoras Theorem;

[tex]BC^2=DC^2+DB^2[/tex]

[tex]BC^2=1^2+1^2[/tex]

[tex]BC^2=1+1[/tex]

[tex]BC^2=2[/tex]

[tex]BC=\sqrt{2}[/tex]

b) DB is perpendicular to DC, therefore m<D=90 degrees.

The length of DB is equal the length of DC.

This implies that;

m<C=m<B=45 degrees.

QUESTION 12

[tex]\sin 30\degree=\frac{1}{2}[/tex]

QUESTION 13

[tex]\cos 30\degree=\frac{\sqrt{3} }{2}[/tex]

QUESTION 14

[tex]\tan 30\degree =\frac{\sqrt{3} }{3}[/tex]

QUESTION 15

[tex]\tan 45\degree =1[/tex]

QUESTION 16

[tex]\cos 45\degree =\frac{\sqrt{2} }{2}[/tex]

QUESTION 17

[tex]\tan 45\degree =1[/tex]

Answer:

7r < 4

Step-by-step explanation:

First step: add +21 to both sides.

Second Step: Add +35r to both sides

Third Step: Simplify bringing it to 7r > 4

Mark brainliest if you can thanks!

if you multiply 10.4x5x8 it equals 416 millimeters

Step-by-step explanation:

Since the formula of a rectangular prism is when we multiply length times width times height, or 10.4 * 5* 8.

5*8 = 40, and 10.4*40 = 416. (0.4*40 = 16 and 10*40 is 400, so you add them up)

That means that you answer is 416 Millimeters

Answer:

x=7     x=-5

Step-by-step explanation:

x^2 – 2x – 35 = 0

Factor

What 2 numbers multiply to -35 and add to -2

-7*5 = -35

-7+5 = -2

(x-7) (x+5) =0

Using the zero product property

x-7 =0       x+5=0

x-7+7=0+7      x+5-5=0-5

x=7     x=-5

2/x-9

is the answer to this problem

Answer:

2/x−9

Step-by-step explanation:

Write it out just the way you read it, then follow the order of operations.

The “Order of Operations” (P-E-MD-AS … or … B-O-DM-AS) tells us that quotient (division) comes before less (subtraction) so:

How do you represent “the quotient of two and (a number) X” ?

The quotient of 2 divided by X is (2÷X) or (2/X) or 2

What is nine less than that quotient?

subtract 9 from your choice of the previous representations, for example:

2/x−9

I believe the answer is A)

Answer:

A

Step-by-step explanation:

81.2 * 0.45 = 36.54

Answer:

Step-by-step explanation:

There are several words that might well fit this sentence:

"supplemental"

"entrepreneural"

"earned"

Answer:

Finding the mean from the line plot is a matter of finding the average. My rationale for my answer is written below:

Step-by-step explanation:

1.) Add all numbers together - 0+1+2... = 136

2.) Divide by the amount of numbers given - 136/17 = 8.

3.) 8 is your final answer.

Answer:

The answer is 8.5

Step-by-step explanation:

first you add up all the numbers which is 136 then divide it by how many numbers you have which is 16. 136/16= which is 8.5

PLS MARK BRAINLIEST

Answer:

x = 9

Step-by-step explanation:

Given that,

coordinate 1  = (-6,10)

coordinate 2 = (12,-2)

Find the slope of line which contain above coordinates

Formula to use

[tex]m=\frac{y2 - y1}{x2-x1}[/tex]

m = [tex]\frac{-2-10}{12+6}[/tex]

m  = -2/3

Find the equation of the line

Formula to use

y = mx + c

where m is the slope =  -2/3

           c is the y intercept

Using coordinate (-6,10)

Plug in the formula

10 = -2/3(-6) + c

10 = 4 + c

c = 10-4

c = 6

So, the equation will be

y = -2/3x + 6

Find the x-intercept

we know that the x-intercept is the value of x when the value of y is equal to zero

so substitute y with 0 in the equation

when y = 0

0 = -2/3x + 6

2/3x = 6

x = 6(3/2)

x = 9

Answer:

x = 9 is the x-intercept.

Step-by-step explanation:

We have given the coordinates (-6,10) and (12,-2).

We have to find the  x-intercept of the line containing these points.

First we find the slope m by using these points.

We know that m = (y₂-y₁)/(x₂-x₁)

m = -2/3

The general form of the equation of line is :

y = mx + c

Where c is the y intercept.

Using the first coordinate to find c .

10 = (-2/3)(-6) +c

c = 6

So, the required equation is :

y = (-2/3)x+6

We have to find the x-intercept.

For this we put y=0

(-2/3)x+6 = 0

2/3 x = 6

x  = 6(3/2)

x = 9 is the x-intercept.

Answer:

∠1

Step-by-step explanation:

The external angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠1 is an exterior angle and ∠' s 2 and 3 are the opposite interior angles.

Hence

∠2 + ∠3 = ∠1

The measure of angle 1 is equal to the sum of the measures of angles 2 and 3.

The sum of the measures of angles 2 and 3 is equal to the measure of exterior angle B, which is angle 1.

This relationship is described by the exterior angle theorem, which states that the measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.

So, we have:

[tex]\[ \text{Angle 1} = \text{Angle 2} + \text{Angle 3} \][/tex]

Therefore, the measure of angle 1 is equal to the sum of the measures of angles 2 and 3.

The probable question may be:

In the given figure, the sum of the measures of angles 2 and 3 is equal to the measure of which angle?

Answer:

$321.75

Step-by-step explanation:

The total area of the carpet needed is 9(11) = 99 sq yards.  If costs $3.25 per yard, so we pay..

$3.25(99) = $321.75