What is the slope of the line shown below?
10+
5
(9, 1)
o A. -
OB.
OC
10
15
(-3,-7) 5
10
O
D.
WIN

Answer:

Reflect over the y-axis, vertically stretch by a factor of 3, and then shift down 1 unit

Step-by-step explanation:

The general form of the straight line equation is, y = m·x + c

Where;

m = The slope

c = The y-intercept

The parent function is, f(x) = x

The slope of the parent function, m₁ = 1

The y-intercept of the parent function, c₁ = 0

The x-intercept of the parent function = 0

The equation of the given function g(x) is derived as follows;

Two points on the line g(x) are (-2, 5) and (1, -4)

The slope of g(x), m₂ = (-4 - 5)/(1 - (-2)) = -3

The equation of g(x) is therefore;

y - 5 = -3 × (x - (-2)) = -3·x - 6

∴ y = -3·x - 6 + 5 = -3·x - 1

y = -3·x - 1

The slope of the given function, m₂ = -3

The y-intercept of the given function, c₂ = -1

The x-intercept of the function = -1

We have that a reflection of (x, y) across the y-axis gives (-x, y)

Therefore, the function g(x) is a reflection of f(x) across the y-axis

The slope of g(x) = -3 × The slope of f(x), therefore, g(x) is obtained by a vertical stretch of of f(x) by a factor of 3

The y-intercept of g(x) is lower than the y-intercept of g(x) by -1, therefore, f(x) is shifted down vertically by 1 unit to obtain g(x)

Therefore, the sequence of transformation that can be used to obtain g(x) from the parent function f(x) are;

Reflect over the y-axis, vertically stretch by a factor of 3, and then shift down 1 unit

Answer:

62

Step-by-step explanation:

A polynomial f(x) divided by (x - a) has remainder f(a)

f(x) = 9x² - 4x - 7 is divided by (x - 3) , then remainder is

f(3) = 9(3)² - 4(3) - 7 = 9(9) - 12 - 7 = 81 - 19 = 62

Answer:

(x+3)(x+4)(x-4)

x+2 and x-3 are not factors but x-4 is

Step-by-step explanation:

let's factor it :)

x^3 + 3x^2 - 16x -48

first we will factor this:

x^3 + 3x^2

x^2(x + 3)

then factor the second part :

- 16x - 48

-16(x + 3)

so now,

x^2(x + 3) - 16(x + 3)

factor out x+3

(x+3)(x^2 - 16)

factor x^2 - 16

(x+3)(x+4)(x-4)

Answer:

Job B

Step-by-step explanation:

If we calculate her salary after 10 years

For job A:

it would be 40,000+10,000=$50,000

For job B:

it would be $75,562.3749

Answer:

The height of the pyramid is 6 cm.

Step-by-step explanation:

The volume of a square pyramid is given by:

[tex] V = \frac{1}{3}A_{b}h = 72 cm^{3} [/tex]

Where:

[tex]A_{b}[/tex]: is the area of the base

h: is the height

Since the base edge length is equal to the height, the area of the base is:

[tex]A_{b} = l^{2} = h^{2} [/tex]

Hence, the height is:

[tex] 72 cm^{3} = \frac{1}{3}A_{b}h = \frac{1}{3}h^{2}h [/tex]

[tex] h = (3*72 cm^{3})^{1/3} = 6 cm [/tex]

Therefore, the height of the pyramid is 6 cm.

I hope it helps you!          

Answer:

The expression "Keep body and soul together" is an idiom, a well-known phrase or collection of words that together mean something distinctly.

Answer:

5x

Step-by-step explanation:

3x+2x

Combine like terms

x(3+2)

x(5)

5x

Answer:

5x

Step-by-step explanation:

3x + 2x

Step 1 :- Calculate like terms by adding their coefficient.

Step 2 :- Combine like terms.

Step 3 :- Multiply ; 5 times x.

Answer:

608

Step-by-step explanation:

32 x 19

= 32 x ( 10 + 9 )

= 320 + 288

= 608

Answer:

4

Step-by-step explanation:

B = (6,5)              C = (6,9)

√(x2 - x1)² + (y2 - y1)²

√(6 - 6)² + (9 - 5)²

√(0)² + (4)²

√16

= 4

Answer:

The formulas are functionally the same, but 'n' (the sample size) is used instead of 'N' (the population size).

Step-by-step explanation:

The sample mean is the average value for a set of observations which is derived from a population. While the population mean is the average value for the entire set of observation belonging to a particular study of interest.

The set of observation belonging to a population is denoted by 'N' ; while the sample size is denoted as 'n' :

The mean formula is written thus :

Population mean = Σx / N

Sample mean = Σx / n

Where, x = set of values.

Answer:

B

Step-by-step explanation:

r=3 in

h=8 in

Volume of funnel

[tex]V=\frac{1}{3}\pi r^2h\\=\frac{1}{3} \times 3.14 \times 3^2 \times 8\\=75.36 in.^3\\time ~taken~to~drip out=\frac{75.36}{15}\\\approx 5.02~minutes.[/tex]

Answer:

5.02 is right

Step-by-step explanation:

i hope this helps

Answer:

Hence 48 outfits can Bill create with the clothes he purchased.

Step-by-step explanation:

Now the given are,

8 shirts,

4 pairs of shorts,

2 pairs of pants.

Here we have to find the outfits can Bill create with the clothes he purchased:

8 * (4+2) = 48.

Bill can create 64 outfits with the clothes he purchased

The given parameters are:

[tex]Shirt = 8[/tex]

[tex]Shorts = 4[/tex]

[tex]Pant = 2[/tex]

Bill can only select one of each cloth, at a time.

So, the number of outfits is the product of the number of shirts, shorts and the pants.

So, we have:

[tex]n = Shirt \times Shorts \times Pant[/tex]

This gives

[tex]n = 8 \times 4 \times 2[/tex]

Evaluate the product

[tex]n = 64[/tex]

Hence, Bill can create 64 outfits

Read more about counting and selection at:

https://brainly.com/question/4658834

Answer: We know that for any circle with radius r the formula for the area and circumference of the circle is given as: Area of circle=πr². ... Hence, to describe the relationship between the area of a circle and its circumference. The Area of circle is 1/2 times the radius times the circumference.

Step-by-step explanation:

Answer:

-4/5

Step-by-step explanation:

sin theta = opp/ hyp

sin theta = -3 /5

Using the Pythagorean theorem

opp ^2 + adj ^2 = hyp ^2

(-3) ^2 + adj ^2 = 5^2

9+ adj ^2 = 25

adj ^2 = 25 - 9

adj ^2 = 16

Taking the square root of each side

adj = ±4

Since we are in the 3rd quadrant  sin and cos are both negative so adj must be negative

adj = -4

cos theta = adj / hyp

cos theta = -4/5

Answer:

126 5p coins

Step-by-step explanation:

Because there are three unknowns, you would need to have three equations. (1p=x, 2p=y, 3p=z). The three equations are: x+y+z=630, (2/5)*630=y, and 2z=x. Now we know that y=252. x+252+z=630, x+z=378, replace x with 2z (from last equation) to get 3z=378, so z=126.

Answer:

true

Step-by-step explanation:

it's a z shaped angle and angels on s straight line sum to 180⁰

hope this helps

Step-by-step explanation:

180 - 37 = x angles on a straight line

x = 40

180 - 40 = y angles on a straight line

y = 140

180 - 140 = z angles om a straight line

z = 40

Answer:

5 meters traveled in distance.

Step-by-step explanation:

Since we are finding the distance of a frog traveling ? distance in 25 mins, we can substitute t for 25. If we do, 0.2 x 25 = 5, d = 5.

Hope this helps!

Step-by-step explanation:

7+3+2+1+13+8+1+5+14+11+15= 80(total scores)

number of scores is 11, then divide 80 by 11

ans=7.27

Answer:

36 dollars

Step-by-step explanation:

We need to think backwards to solve this question.

(8 - 2) x 2 = 12

(12 - 2) x 2 = 20

(20 - 2) x 2 = 36

Step-by-step explanation:

For the 1st picture,

The 2nd option is the answer.

Let say we have

[tex] a_{3}[/tex]

Replace it into the recursive formula.

[tex] a_{3} = a_{3 - 2} + (a) _{3 - 1}[/tex]

We are given a,1 and a,2 so the 3rd terms has to be

[tex]2[/tex]

So the second option is the answer.

For the second picture, a geometric sequence is a group of terms that has the same ratio between each consecutively.

Infinite means going on forever

The fourth option is the answer.

Answer:

1,1,2,3,5

part #2 none are exactly correct... the terms go on forever, so 1 &2 are out...

the "difference" is definitely not the same, so three is out..

4 is the closest, but the ratio is not the same, there is a trend in the ratio..

this is the Fibonacci sequence, and the ratio trends toward the "golden ratio" ( φ -phi) but never is exactly φ because φ is irrational

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

The sum of measure of exterior angles is equal to 360

5x-20+2x+5+x+15+x = 360 add like terms

9x = 360 divide both sides by 9

x = 40

Answer:

a (26+10)-2 =34

b (34+42)-42 = 34

c ( 39+40)-45 =34

d (52+25)-43 =34

e(25+22)-13 =34

f (47+11)-24 =34

g(59+19)-35 =34

h (71 +7)-44= 34

solved

Answer:

The polynomial simplifies to an expression that is a  

quadratic  trinomial  with a degree of  2 .

Step-by-step explanation:

trial and error

Answer:

Have a great rest of your day :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

x = length of screen

x-4 = width of screen

x² + (x-4)² = 20²

x² + (x²-8x+16) = 400

2x² - 8x - 384 =  0

x² - 4x - 192  = 0

use the quadratic formula to solve for x

x = [4 ± √(4²-4·1(-192))]/[2·1]

= [4 ± √784]/2

= 4 ±  28]/2

= 16, -12

-12 is an extraneous solution, so x = 16 inches.

:::::

Exponents need to be marked with a ^. For example, (x-4)² can be written (x-4)^2.

Answer:

x = 16

Step-by-step explanation:

The answer above is correct.

Answer:

A and E are correct congruence statements.

Answer:

A E

Step-by-step explanation:

Answer:  Choice B)  [tex]\frac{y}{x} = \frac{2}{3}[/tex]

This is the same as saying  y/x = 2/3

Or I suppose you could say "y over x = two-thirds".

===============================================

Explanation:

Recall that slope is rise over run

slope = rise/run

The rise being the change in y, while the run is the change in x.

So we could informally think of it as slope = y/x

-----------

Since we're told that it "has a rise of 2 and run of 3", this means slope = 2/3.

The slope is both y/x and also 2/3.

Equating the two expressions leads us to y/x = 2/3. This is why choice B is the final answer.

-----------

Side notes:

Answer:

B

Step-by-step explanation:

(-_-)