Find (f + g)(x).
(f + g)(x) =

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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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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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:

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:

x=9

y=?

36= 1/2(x*y)

36 *2 = 2* 1/2 (9*y)

72 = 9*y

72/9= 9*y/9

8=y

The other number is 8.

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:

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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Answer:

x = -16

y = 20

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 ❞

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: [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)

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:

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

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:

infinite or if where using whole numbers

y≥25

Hope This Helps!!!

Answer:

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

Option C).

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!

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:

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

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:

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

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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Answer:

Step-by-step explanation:

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.

By using the given graph, we will see that:

Here we have a graph of function G(x), and we want to evaluate it in different values of x.

To do that, we need to look at the interval where the lines are defined. An open dot means that the endpoint does not belong to the interval, while the closed dot means that the endpoint belongs.

First, G(0).

If you look at the graph, when x = 0 we have a closed dot on the bottom line. That is the line that we need to look to do this evaluation, there we can see that when x = 0, we have G(0) = -5.

Then we have x = 2.999.

Notice that x < 3.

And the second line (the one at y = -3) is on the interval (0, 3].

Then x = 2.999 is included on that interval, it means that:

G(2.999) = -3.

Now we have x = 0.0001

Again, notice that the second line is on the interval (0, 3]

Because 3 > 0.0001 > 0, then:

0.0001 ∈ (0, 3]

From that, we conclude that:

G(0.0001) = -3

Finally:

G(3).

Again, 3 belongs to the interval (0, 3]

Then we use the second line again.

G(3) = -3

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Answer:

G(0) = -5

G(0.0001) = -3

G(2.999) = -3

G(3) = -3

Step-by-step explanation:

Answer:

14 will be the answer...

Step-by-step explanation:

6 13/28 = 6

8 3/32 = 8

6 + 8 = 14