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3 years ago

Find the inverse of the linear function y=1/2x+3.

Mathematics

2 answers:

Anni [7]3 years ago

7 0

Answer:

2(x-3) = y

Step-by-step explanation:

y = 1/2 x +3

To find the inverse, exchange x and y and then solve for y

Exchange x and y

x = 1/2y +3

Then solve for 3

Subtract 3 from each side

x-3 = 1/2 y -3+3

x-3 = 1/2 y

Multiply each side by 2

2 (x-3) = 1/2 *2 y

2(x-3) = y

This is the inverse

Natasha_Volkova [10]3 years ago

6 0

Interchange the variables:

x = 1/2y + 3

Solve for y:

Subtract 3 from each side:

x-3 = 1/2y

Multiply both sides by 2:

2x-6 = y

Rewrite the equation with y on the left side:

y = 2x-6

Replace y with f^-1(x):

f^-1(x) = 2x-6

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. Three types of shirts sold at a store cost $9.00, $11.00, and $12.50. One day, the store sells a total of 23 shirts and makes

lbvjy [14]

Answer:

X + 3y = 23

9x + 36y = 243

11 shirts sold at $9.0 per shirt, 4 shirts sold at $11 per shirt and 8 shirts sold at $12.5 per shirt

Step-by-step explanation:

-----Since we are told to assume that the number of shirts sold for $9.00 each is x, that of $11.00 is y and also that of $12.50 is z.

9x + 11y + 12.5z = 243

9x + 11y + 12.5(2y) = 243

9x + 36y = 243_______ equation 1

----- The statement also read that One day, the store sells a total of 23 shirts and makes $243 on the sales. TWICE AS MANY SHIRTS WERE SOLD FOR $12.50 THAN WERE SOLD FOR $11.00

Z = 2y

x + y + z = 23

X + y + 2y = 23

X + 3y = 23_____ equation 2

Now multiply the above by 9 to have this equation's "x" sharing the same coefficient with that of equation 1

9x + 27 = 207 will be the new one___equation 3

-----Subtract equation 3 from 1 and we have

9x + 36y = 243____ equation 1

9x + 27y = 207____ equation 3

9y = 36

Y = 4

-----Substitute y = 4 in equation 2

X + 3y = 23

X + 4(3) = 23

X + 12 = 23

X = 23 - 12

X = 11

-----Remember that x + y + z = 23

11 + 4 + z = 23

15 + z = 23

Z = 23 - 15

Z = 8.

So therefore, x =11 shirts, y = 4 shirts and z = 8 shirts

4 0

3 years ago

A rectangular park of length 60 m breadth 50 m encloses w volleyball court of length 18 m and breadth 10 m. Find the area of the

Zanzabum

Given

A rectangular park of length 60 m breadth 50 m encloses with volleyball court of length 18 m and breadth 10 m.

To find:

The area of the park excluding the court at the rate of Rs 110 per square meter.

Solution:

Area of a rectangle is:

$Area=length \times breadth$

Area of whole park is:

$A_1=60 \times 50$

$A_1=3000$

Area of volleyball court is:

$A_2=18 \times 10$

$A_2=180$

Now, the area of the park excluding the court is:

$A=A_1-A_2$

$A=3000-180$

$A=2820$

Therefore, the area of the park excluding the court is 2820 square meter.

4 0

3 years ago

The waiting time to ride a roller coaster is 20 minutes when 150 people are in line. How long is the waiting time when 240 peopl

laiz [17]

Answer: The waiting time will be 32 minutes when 240 people in line.

Step-by-step explanation:

Let us assume that the waiting time is directly proportional to the number of people in the queue.

Equation of direct proportion between variables x and y : $\dfrac{x_1}{y_1}=\dfrac{x_2}{y_2}$

Put $x_1=20,\ y_1=150,\ y_2=150$ to find $x_2$ .

$\dfrac{20}{150}=\dfrac{x_2}{240}\\\\\Rightarrow\ x_2=\dfrac{20}{150}\times240\\\\\Rightarrow\ x_2=32$

Hence, the waiting time will be 32 minutes when 240 people in line.

3 0

3 years ago

Read 2 more answers

12351 rounded to the nearest hundred explain how you rounded

Nataly_w [17]

$\bf 12,\underline{351}\impliedby \textit{3 hundreds, and 51 units, let's round that}
\\\\\\
\begin{array}{llll}
300----- 50-----400\\
\qquad \qquad \uparrow\qquad \qquad \qquad \uparrow \\

\begin{array}{llll}
anything\ here\\
rounds\ up\ to\\
300
\end{array}\quad
\begin{array}{llll}
anything\ here\\
rounds\ up\ to\\
400
\end{array}
\end{array}
\\\\\\
\textit{therefore, the hundreds value of 300, the 51 tips it over to 400}
\\\\\\
12,\underline{400}$

3 0

3 years ago

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A local petting zoo allows visitors to feed the goats food pellets. The petting zoo starts the month with 525.25 pounds of food

Alisiya [41]

I’m sorry, I wish I knew this one and I would help

6 0

3 years ago

Read 2 more answers