Consider parallel lines cut by a transversal.
Parallel lines q and s are cut by transversal r. On line q where it intersects line r, 4 angles are created. Labeled clockwise, from uppercase left: angle 1, angle 2, angle 4, angle 3. On line s where it intersects line r, 4 angles are created. Labeled clockwise, from uppercase left: angle 5, angle 6, angle 8, angle 7.

Explain which theorems, definitions, or combinations of both can be used to prove that alternate exterior angles are congruent.

Answer: [tex]\frac{r^9}{r^3} = r^{9-3} = r^6[/tex]

We subtract the exponents when dividing terms with the same base.

The general rule is [tex]\frac{a^b}{a^c} = a^{b-c}[/tex]

Hii!

___________________________________________________________

[tex]\rightsquigarrow\circ\boldsymbol{Answer}\circ\leftharpoonup[/tex]

r^6

[tex]\rightsquigarrow\circ\boldsymbol{Explanation}\circ\leftharpoonup[/tex]

To simplify this we need to use the division property of exponents:

[tex]\large\boxed{\mathtt{\frac{x^m}{x^n} =x^{m-n}}}[/tex]. So if we divide two numbers with the same base, we subtract their exponents.

Let's apply this rule here.

[tex]\twoheadrightarrow\sf r^9\div r^3[/tex].

[tex]\bullet[/tex] Since these two numbers have the same base, we subtract their exponents

[tex]\twoheadrightarrow\sf r^6[/tex]

[tex]\bullet[/tex] Great job! We found the answer

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Hope that this helped! Best wishes.

[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]

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The length of BC , AC and AD is 4 , 10 , 14.

Length is the distance between two points , It is measured in cm , m , km etc.

It is asked to calculate the length of BC , AC , AD

For BC

Point B is on point 0 and Point C is on point 4.

BC=|b−c|

BC=|0−4|

BC=4

For AC

Point A is on point -6 and Point C is on point 4.

AC=|a−c|

AC=|-6−4|

AC= 10

For AD

For AC

Point A is on point -6 and Point D is on point 8.

AD=|a−c|

AD=|-6−8|

AD= 14

Therefore the length of BC , AC and AD is 4 , 10 , 14.

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Answer:

Step-by-step explanation:

Answer:

62.5 copies per minute

Step-by-step explanation:

Note that the word "per" means divide.  So, a rate of change in "copies per minute", means a number of copies divided by a number of minutes

If the copy machine can make 250 copies in 4 minutes, then the number of copies is 250 copies, and the number of minutes is 4 minutes:

[tex]\text{rate of change in copies per minute}=\dfrac{\text{number of copies}}{\text{number of minutes}}[/tex]

[tex]\text{rate of change in copies per minute}=\dfrac{\text{250 copies}}{\text{4 minutes}}[/tex]

[tex]\text{rate of change in copies per minute}=62.5\dfrac{\text{copies}}{\text{minute}}[/tex]

1. 5:15 = 1/3
scale factor is 1/3going from bigger to smaller

2. 2/8 = 1/4

14 x 1/4 = 3.5

X = 3.5

The correct answer will be option D which is the value of D will be [tex]\left[\begin{array}{cc}-6&11&\\-5&9\\\end{array}\right][/tex]

A matrix, which is used to represent a mathematical object or an attribute of one, is a rectangular array or table containing numbers, symbols, or expressions that are organized in rows and columns.

The value of D will be calculated by multiplying the matrix if we get a unit matrix that will be the answer.

[tex]=\left[\begin{array}{cc}-9&-11&\\5&-6\\\end{array}\right]\times \left[\begin{array}{cc}-6&11&\\-5&9\\\end{array}\right] \\\\\\=\left[\begin{array}{cc}(-54+55)&(99-99)&\\-(-30+30)&(55-54)\\\end{array}\right]\\\\\\=\left[\begin{array}{cc}1&0&\\0&1\\\end{array}\right][/tex]

Therefore the correct answer will be option D which is the value of D will be [tex]\left[\begin{array}{cc}-6&11&\\-5&9\\\end{array}\right][/tex]

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Answer:

please mark me as brainlest

Answer:

12

Step-by-step explanation:

Input interpretation: triangle | vertex coordinates (-3, 5) | (-3, 2) | (1, 2) | perimeter

Result: 12

Properties of Triangle:

The value of a is 72.74.

Probability is the study of likeliness of an event to happen.

It is given that

The mean [tex]\rm \mu[/tex] of the distribution is 70

Standard deviation [tex]\rm \sigma[/tex]  is 2

p( x<a) = 0.9147

a = ?

From Z table

For p ( p < 0.9147) , z = 1.37

[tex]\rm Z = \dfrac { X - \mu}{ \sigma}[/tex]

[tex]\rm \rm 1.37 = \dfrac { a - 70}{ 2}[/tex]

a = 70+ 2*1.37

a = 72.74

Therefore the value of a is 72.74.

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Answer:

D. Intersecting lines.

Step-by-step explanation:

The lines are intersecting each other.

The reason it is not perpendicular lines is because perpendicular lines have 90° angles.

Hope this helps!

If not, I am sorry.

Answer:

a) a=17/16, b=3/8     (17/16, 3/8)

b) x=12/17, y=25/17     (12/17, 25/17)

Step-by-step explanation:

I attached the work for solving the equations with substitution method... Sorry it took a bit of time and this would've been easier if the question's asking for elimination lol

The marginal distribution of tenure in counts who owns a home is 76, while those who rent a home is 40.

The addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.

For the given data the table can be made as shown below. The marginal distribution of tenure in counts can be calculated as,

Owns home = 71 + 5 = 76

Rents home = 13 + 27 = 40

Hence, The marginal distribution of tenure in counts who owns a home is 76, while those who rent a home is 40.

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Mrs. Phillips needs to buy 8 packs of floor boards

In contrast to a square, a rectangle is a planar figure having four equal neighboring sides, four straight sides, and four right angles. An enclosed 2-D form called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposing sides. A rectangle has two dimensions—length and width—because it is a two-dimensional form. The rectangle's longer side is its length, while its shorter side is its breadth.

As per the figure attached Mrs. Phillips floor plan can divided into two rectangles

The area of rectangle is as follow:

Area = length(l) x Width(w)

Area of part 1 will be:

A = 6 x 2 = 12 m²

Area of part 2 will be :

a = 3 x 2 = 6 m²

Total area of floor = A + a

Total area of floor = 12 + 6

Total area of floor = 18 m²

Given one pack of floor boards will cover 2.5 m².

So total pack of floor block needed will be as follow:

Total pack of floor block = Total area of floor/Area covered by one pack of floor boards

Total pack of floor block = 18/2.5

Total pack of floor block = 7.2 packs ≈ 8 packs

Hence Mrs. Phillips needs to buy 8 packs of floor boards

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The true statement is the circle has the radius equal to 7.

The general equation for a circle is (x-h)² + (y-k)² = r², where ( h, k ) is the center and r is the radius.

As, standard form of equation of circle is

(x-h)² + (y-k)² = r²

At origin, equation of circle will be

(0-h)² + (0-k)² = r²

r² = x² + y²

Now, The line intersects the circle at (0,7)

r² = 0² + 7²

r² =49

r=7.

Hence, the circle has the radius equal to 7.

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Step-by-step explanation:

sin(theta)=4/7

cos(theta)=√1-sin²theta

=√1-(4/7)²

=√1-16/49

=√(49-16)/49

= √33/49

=(√33)/7

Answer:

35/100

Step-by-step explanation:

You have to find how many juniors there are, so if you add 13, 20, and 2 you get 35. For the denominator you have to find the total number of students, so just add all of the numbers together to get 100. So there is a 35/100 chance that a randomly selected student is a junior.

Answer: 7/20

Step-by-step explanation:

The number of chicken dish is 131 dishes while the number of lobster dishes is 119 dishes

Let

Since it cost $40 per dish for chicken dish, the total cost of chicken dish is 40x.

Also, since it cost $70 per dish for lobster dish, the total cost of lobster dish is 70y

So, the total cost of dish is T = 40x + 70y

Also, we know that the total cost of dish is $13,570.

So, 40x + 70y = 13570  (1)

Also, there are going to be 250 guest at the dinner and thus 250 dishes.

So, the total number of dishes is x + y = 250

So, x + y = 250 (2)

So, the equations of the linear system are

40x + 70y = 13570  (1)

x + y = 250 (2)

Since

40x + 70y = 13570  (1)

x + y = 250 (2)

From (2), x = 250 - y

Substituting x into (1), we have

40x + 70y = 13570  (1)

40(250 - y) + 70y = 13570  (1)

10000 - 40y + 70y = 13570  

30y = 13570 - 10000

30y = 3570

y = 3570/30

y = 119

Substituting y = 119 into x, we have

x = 250 - y

x = 250 - 119

x = 131

Therefore, the number of chicken dish is 131 dishes while the number of lobster dishes is 119 dishes

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Answer:

multiply 2×3 to get 6and then multiply 6×4 to get 24

Answer:

Multiply 3 × 4 to get 12 and then multiply 12 × 2.

Multiply 2 × 3 to get 6 and then multiply 6 × 4.

Explanation:

Original Answer : 2 × 3 × 4 = 24

1) 12 × 6 = 72

2) 6 × 12 = 72

3) 12 × 2 = 24

4) 6 × 4 = 24

5) 6 × 12 = 72

Hence, only option 3 and 4 is correct.

The total hours joe spent watching TV each day for two weeks is 12 1/2 hours

Total hours spent watching TV for two weeks = Number of hours × days

= (0 × 1) + (1/4 × 1) + (1/2 × 1) + (3/4 × 3) + (1 × 3) + (1 1/4 × 4) + (1 1/2 × 1)

= 0 + 1/4 + 1/2 + 9/4 + 3 + 5 + 3/2

= 8 + (1+2+9+6) / 4

= 8 + 18/4

= 8 + 4 2/4

= 8 + 4 1/2

= 12 1/2 hours

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If f(x)=-3x-5 and g(x)=4x-2, then the value of (f-g)(x) is -7x-3.

The given functions are f(x)=-3x-5 and g(x)=4x-2.

We need to find the value of (f-g)(x)

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

Now, (f-g)(x)=f(x)-g(x)=(-3x-5)-(4x-2)

= -3x-5-4x+2 = (-3x-4x)+(-5 + 2)

= -7x-3

Therefore, the value of  (f-g) (x) is -7x-3.

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Answer:

1 55

2 455

3554

Step-by-step explanation:

nfn

Answer:

how?

Please Attach Figure so someone can Solve...

Step-by-step explanation:

Answer: 128

Step-by-step explanation:

[tex]4^3 = 4*4*4 = 16*4 = 64[/tex]

[tex]8^2 = 8*8 = 64[/tex]

[tex]64+64 = 128[/tex]

[tex]12^2+9^2=x^2\\144+81=x^2\\x^2=225\\x=15[/tex]

The missing blanks have been filled.

A function is a mathematical statement used to relate a dependent and an independent variable.

It is given that

Total time taken to hike is 8 hours

Let the time taken in hours is represented by t

and the elevation is represented by h

Every hour, the hikers gain 250 feet in elevation.

The independent variable is t , time taken to hike , in hours .

The dependent variable is h , increased elevation in feet or elevation the hikers have gained .

A possible verbal description is Elevation at any given time equals 250 times the time taken to hike.

The equation h = 250 t corresponds to the relationship.

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Answer:

The sea lion dives 24 feet.

Step-by-step explanation:

A seal (S) dives 15 feet.

A sea lion (SL) dives 6 feet less than 2 times the seal's dive.  That can be expressed as:

SL = 2S -6

Since we know S = 15, we can say:

SL = 2*(15) - 6

SL = 24 feet

The sea lion dives 24 feet.

Assessing the regression model on data other than the sample data that was used to generate the model is known as cross-validation

From the question, we have the following highlights:

When the sample data is not used in a regression model, then the term is known as cross-validation.

Hence, the term that completes blank is cross-validation

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Answer:

240

Step-by-step explanation:

Using the straight line formula; y=mx+c, take two points, for example, (4, 80) and (5, 100)

m=change in y/change in x, so;

m=(100-80)/(5-4)= 20

Take point (4, 80)

80=20×4 + c

80-80=c=0

so y=20x

y=20×12=240

In the triangle ABC, the length of the line segment SA=3 ft ( 3rd option).

In triangle ABC,

According to the triangle proportionality theory, we know that if a triangle has a line segment parallel to one of its sides, the line segment splits the other sides correspondingly.

Hence,

SA/SB=CT/BT

⇒SA/10=2.7/9

⇒SA=(2.7*10)/9

⇒SA=3

So, the length of SA is 3 ft.

Therefore the 3rd option is correct.

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