The function f(x) is shown in this graph.
The function g(x) = -6x + 3.
-5
Compare the slopes and y-intercepts.

The parent function y=1/x²

If a function f(x) is shifted horizontally by k units the parent function f(x) becomes f(x+ k) where k>0

Here, the parent function y=1/x²

Add 3 to x in the denominator as the graph is shifted to left 3.

and, Add 1 to the fraction, because the graph is shifted up 1 unit.

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Answer:

Boys = 605

Girls = 675

Step-by-step explanation:

Let x be the number of boys in school.

So, girls = (x+70)

Total no. of students = 1280

x + x + 70 = 1280

2x + 70 = 1280

2x = 1280 - 70

2x = 1210

x = 1210/2

x = 605

Hence, no. of boys = 605

no. of girls = 605 + 70 = 675

Answer:

Step-by-step explanation:

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

Term refers to each variable or constant separated by a mathematical operator.

Coefficient refers to the numberic part of variable or a constant number present in an expression.

[tex]\qquad \tt \rightarrow \: 12a - 10b + 6[/tex]

[tex] \large\textsf{Terms :} [/tex]

[tex] \texttt{coefficient = 5} [/tex]

[tex] \texttt{coefficient = -8 } [/tex]

[tex] \texttt{coefficient = 20} [/tex]

[tex] \texttt{coefficient = 6} [/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Peter's gross pay will be 1820.9.He put in 32 hours of work two weeks ago, and the tip money came to $1587.30.

Before taxes, benefits, and other payroll deductions are taken out of an employee's paycheck, that amount is known as their gross pay.

Given data;

Peter earn per hour = 7.30

Gratuities = 7 %

Given condition;

No of hour person work = 32

Gratitutes = 1587.30

Let the gross pay will be x;

x = gratuities + no of hoy\ur work × money earned per hour;

x =  1587.30 + 32 × 7.30

x = 1820.9

Hence,Peter's gross pay will be 1820.9.

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The trigonometric ratios shows that the cos M is 4/5.

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  The greatest side of a right triangle is called hypotenuse. And, the other two sides are called cathetus or legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.

The Pythagorean Theorem says: [tex]hypothenuse^2=(leg_1)^2+(leg_2)^2[/tex] . And the main trigonometric ratios are: sin [tex]\alpha[/tex],  cos [tex]\alpha[/tex] and tan [tex]\alpha[/tex], where:

[tex]sin \alpha =\frac{opposite\;leg}{hypotenuse} \\ \\ cos \alpha =\frac{adjacent\;leg}{hypotenuse} \\ \\ tan \alpha =\frac{opposite\;leg}{adjacent\;leg}[/tex]

For finding the cos M, firstly, you should find the side MN from Pythagorean Theorem.

[tex]hypothenuse^2=(leg_1)^2+(leg_2)^2\\ \\\ 30^2=18^2+(MN)^2\\ \\ 900=324+(MN)^2\\ \\(MN)}^2=900-324\\ \\ (MN)^2=576\\ \\ MN=24[/tex]

If MN=24, the cos M will be

[tex]cosM =\frac{adjacent\;leg}{hypotenuse} =\frac{24}{30} =\frac{4}{5}[/tex]

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Answer:

y = -3x + 1

Step-by-step explanation:

The line crosses the y-axis at 1. This is called the y-intercept. This is the number you fill in for c in the form of the equation given.

You can pick any two points on the line to calculate the slope. But you can actually SEE the slope without having to calculate it when you have the graph to look at. See the line crossing the y-axis at 1. Look for another point (that has nice whole number coordinates) there is one DOWN3 and OVER1. If you notice, the next point is also DOWN3 and OVER1.

DOWN3 and OVER1 is the slope -3/1, which is equal to -3.

Fill in -3 in place of the m in the equation.

y = -3x + 1

Done!

Answer:

y = -3x + 1

Step-by-step explanation:

The equation of a line in slope/intercept form is y = mx + c where m is the slope and c the y-intercept(ie the value of y when x =0)

The slope can be found by taking any two points on the line,  (x1, y1) and (x2,y2) and computing (y2-y1)/(x2-x1)

If you look at the line 2 points on the line are P(2,-5) and (0,1)

Slope = (-5-1)/(2-0) = -3

The y-intercept is the y-value at which the line intersects the y-axis ie at x = 0 and you can see that this is 1

Therefore equation is
y = -3x + 1

You can check to see if this is correct by plugging in some other value of x and seeing if the correct y value corresponds to the equation y-value

For example, in the graph we see that at x = 1, y = -2

Indeed -3(1) + 1 = -3 + 1 = -2 also

Answer:

One possible answer is:  2.25p + 2.25b + 2.25s

Another possible answer:  2.25(p + b + s)

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

Explanation:

Each item costs $2.25 per box, so,

Add up those subtotals to get the grand total

2.25p + 2.25b + 2.25s

is one possible answer

What we can do is factor out the common 2.25 using the distributive rule in reverse.

Another possible answer is:  2.25(p + b + s)

Step-by-step explanation:

The are two angles ie. 45 and 80 than find the third angle

80 will be vertically opposite and alternative angle to a

Answer:

Just think of which number, when you multiply it with 20 will give you -8

and then you multiply that number with -4 to get y. Hope it helps!

Answer:

infinite or if where using whole numbers

y≥25

Hope This Helps!!!

An equation that models the height of the ball as a function of time t is; h(t) = -16t² + 40t + 3. The maximum height that the ball will reach is 28 ft

We are given the equation for the vertical velocity model as;

h = -16t² + vt + s

Where;

v = velocity

s = starting height

h = ending height

t = time

A) From the question, we have;

v = 40 ft/s

s = 3 ft

Thus, the equation is;

h = -16t² + 40t + 3

B) To find the time that the ball reaches its maximum height, we will equate the height equation to zero and find the roots. Thus;

-16t² + 40t + 3 = 0

Using an online quadratic equation calculator gives;

t = 2.573 s

C) The maximum height that the ball will reach is;

h'(t) = -32t + 40

At h'(t) = 0;

-32t + 40 = 0

32t = 40

Thus;

t = 1.25 s

Max height = -16(1.25)² + 40(1.25) + 3

Max height = 28 ft

D) The height of the ball after 2 seconds is;

h(2) = -16(2)² + 40(2) + 3

h(2) = 19 ft

E) Time for the ball to hit the ground is;

T = 2 * 2.573

T = 5.146 s

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26 potters will be required to make 169 pots in 4 days.

Given: 11 potters can make 143 pots in 8 days.

Step 1:

1 potter makes  143 pots in 8 × 11 days.

1 potter can make 1 pot in

(8 × 11)/143 days.

Step 2:

Let the number of potters required be x, then

x potters can make 1 pot in (8 × 11)/( 143 × x) days

x potters can make 169 pots in (8 × 11 × 169)/(143 × x ) days

Step 3:

The number of days given is 4. Hence equating the above equation to 4.

(8 × 11 × 169)/(143 × x ) = 4

Step 4:

Solve for x

14872/(143x) = 4

572x = 14872

x = 14872/572

x = 26

Thus, 26 potters will be required to make 169 pots in 4 days.

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Answer:

x = -16

y = 20

Step-by-step explanation:

Answer:

Three linear equations that has a unique solution (1,2,-1) are:-

x+ y+ z =2

2x + y + 3z = 1

x+ 2y+ z  = 4

Step-by-step explanation:

Linear equations in three variables:-

If a, b, c and r are real numbers (and if a, b, and c are not all equal to 0)

then ax + by + cz = r is called a linear equation in three variables. (The

“three variables” are the x, the y, and the z.)

The numbers a, b, and c are called the coefficients of the equation. The

number r is called the constant of the equation.

so from from above explanation we can write 3 linear equations with three variables as.

x+ y+ z =2

2x + y + 3z = 1

x+ 2y+ z  = 4

Now to check if the given point (1,2,-1) is solution or not  these equations must satisfy this point,

x+ y+ z =2

1+ 2- 1 = 2

   2= 2

2x + y + 3z = 1

2×1 +2 - 3×1 = 1

     1=1

x+ 2y+ z  = 4,

1+ 2×2 -1 = 4

    4=4  

therefore all three equations satisfies the given point

hence these are the three linear equation having point (1,2, -1) as the unique solution

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The value of the variable x = 6 and y = 5. Then the position vector of P will be 6i + 5j.

The equation of line is given as

y = mx + c

Where m is the slope and c is the y-intercept.

PQRS is a parallelogram. the position vector of Q R and S are 5i +7j, -3i-8j and -4i-6j.

Then the point of Q, R, and S will be (5, 7), (-3, -8), and (-4, -6).

Let the point P be (x, y).

We know that the slope of the line QS and PQ will be same and line is passing through (-3, -8).

y = 1.444x + C

-8 = 1.444 (-3) + C

C = -3.667

Then the equation will be

y = 1.444x – 3.667  …1

The slope of the line PQ and RS will be same and line is passing through (5, 7).

y = -2x + D

7 = -2 (5) + D

D = 17

Then the equation will be

y = -2x + 17  …2

By solving equation 1 and 2, we have

x = 6 and y = 5

Then the position vector of P will be

⇒ 6i + 5j

The graph is given below.

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Answer:

The area is 16 inches squared and the perimeter is also 16 inches

Step-by-step explanation:

To find the area, you must multiply the length by the width. Since this is a square, you have to multiply one adjacent side by the other. For perimeter, you can either multiply one side by 4 or add all 4 sides.

Answer:

14 will be the answer...

Step-by-step explanation:

6 13/28 = 6

8 3/32 = 8

6 + 8 = 14

Answer:

x=6

Step-by-step explanation:

check the scale factor by the fraction 10/5

after/before

it simplifies to 2 meaning that the second triangle is two times the size of the first

then take 3 fron segment AB to the similar segment DE and times it by the scale factor(2)

2×3=6

Answer:

6

Step-by-step explanation:

since AC = 5. and DF = 2(5) = 10

FW = 2(4)=8 DE= 2(3) = 6

therefore x = 6

Option C).

Answer:

1

Step-by-step explanation:

Could this be a tricky question? See the point:

Though it's inlikely that the first 240 people have only 10 years. Don't take this answer very seriously

Answer:

2nd and third option

Step-by-step explanation:

The second option just combines the 6.5p and the 0.01p on the right side to obtain 6.49p. The third option just multiplies both sides by 100.

Answer:

Part A -  2/5 of a dollar

Part B - It shows that 10 pounds of cabbage cost $4

Step-by-step explanation:

If 5 pounds cost $2 then 1 pound costs 2/5 of a dollar.

(10,4) - 10 is the x-axis which is pounds and 4 is the y-axis which is $. So 10 pounds cost $4.

Answer:

(3,3) (-1,-3), you just have to look at the coordinates

The volume of the pyramid is 2496 cu.m.

A pyramid is a three dimensional structure which has a polygon base and  in general triangular faces which join at the top .

It is given that

A pyramid [tex]\rm frustum[/tex] has a 4 m by 4 m square top

Height = 12 m

Base = 20 m

The volume of a square pyramid with a  [tex]\rm frustum[/tex] is given by

V = (1/2) * ( Area of base + Area of  [tex]\rm frustum[/tex] ) * height of the  [tex]\rm frustum[/tex] from the base

V = 0.5 * ( 20 *20 + 4*4 ) * 12

V = 2496 cu.m

The volume of the pyramid is 2496 cu.m.

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Answer: [tex]g(x) = 3^{x-6}[/tex]

Step-by-step explanation:

Think about it like doing

x - 6 = 0

x = 6

That is how you know that it will be shifted 6 units right (how you can tell the difference between right and left shift)

To me, Benjamin should use graph A to show the decrease in temperature. It would be best for Benjamin to use this graph for his presentation because the temperature decrease in this graph

The graphs that complete the question are added as an attachment

From the attached graph, we have the following highlights:

The above means that graph B is a misleading graph

Hence, Benjamin should use graph A for his report

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option  (B) is correct the graph second represents the line that is perpendicular to the line y = 4x - 2

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

The question is incomplete:

The complete question is:

Consider the equation y = 4x - 2 Which graph shows a line that is perpendicular to the line defined by the given equation?

Please refer to the attached picture.

The given line:

y = 4x - 2

The slope of the line M = 4

The slope of the line which is perpendicular to the above line:

m = -1/4 = -0.25

The graph second has a slope of -0.25

[tex]\rm y\ -2\ =\ \dfrac{\left(2-0.5\right)}{-4-2}\left(x+4\right)[/tex]

y - 2 = -0.25x - 1

y = -0.25x + 1

m = -0.25

Thus, the graph second represents the line that is perpendicular to the line y = 4x - 2 option  (B) is correct.

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Answer: C

Step-by-step explanation:

Answer:

the answer will be 36

Step-by-step explanation:

if you divide 24 by 8 it will be 3 so then you multiply 12 times 3 and it's 36