Two teachers, Mr. Meehan and Mrs. Chipps, decide to buy compasses and rulers for their classrooms. Mrs. Chipps buys 30 compasses and 50 rulers for $95. Mr. Meehan buys 40 of each for $116. What are the individual costs of the compasses and rulers that were purchased? Explanation Please

Answer:

21

Step-by-step explanation:

140*0.15 is 21

Answer:

21

Step-by-step explanation:

Answer:

The solution is too long. So, I included them in the explanation

Step-by-step explanation:

This question has missing details. However, I've corrected each question before solving them

Required: Determine the inverse

1:

[tex]f(x) = 25x - 18[/tex]

Replace f(x) with y

[tex]y = 25x - 18[/tex]

Swap y & x

[tex]x = 25y - 18[/tex]

[tex]x + 18 = 25y - 18 + 18[/tex]

[tex]x + 18 = 25y[/tex]

Divide through by 25

[tex]\frac{x + 18}{25} = y[/tex]

[tex]y = \frac{x + 18}{25}[/tex]

Replace y with f'(x)

[tex]f'(x) = \frac{x + 18}{25}[/tex]

2. [tex]g(x) = \frac{12x - 1}{7}[/tex]

Replace g(x) with y

[tex]y = \frac{12x - 1}{7}[/tex]

Swap y & x

[tex]x = \frac{12y - 1}{7}[/tex]

[tex]7x = 12y - 1[/tex]

Add 1 to both sides

[tex]7x +1 = 12y - 1 + 1[/tex]

[tex]7x +1 = 12y[/tex]

Make y the subject

[tex]y = \frac{7x + 1}{12}[/tex]

[tex]g'(x) = \frac{7x + 1}{12}[/tex]

3: [tex]h(x) = -\frac{9x}{4} - \frac{1}{3}[/tex]

Replace h(x) with y

[tex]y = -\frac{9x}{4} - \frac{1}{3}[/tex]

Swap y & x

[tex]x = -\frac{9y}{4} - \frac{1}{3}[/tex]

Add [tex]\frac{1}{3}[/tex] to both sides

[tex]x + \frac{1}{3}= -\frac{9y}{4} - \frac{1}{3} + \frac{1}{3}[/tex]

[tex]x + \frac{1}{3}= -\frac{9y}{4}[/tex]

Multiply through by -4

[tex]-4(x + \frac{1}{3})= -4(-\frac{9y}{4})[/tex]

[tex]-4x - \frac{4}{3}= 9y[/tex]

Divide through by 9

[tex](-4x - \frac{4}{3})/9= y[/tex]

[tex]-4x * \frac{1}{9} - \frac{4}{3} * \frac{1}{9} = y[/tex]

[tex]\frac{-4x}{9} - \frac{4}{27}= y[/tex]

[tex]y = \frac{-4x}{9} - \frac{4}{27}[/tex]

[tex]h'(x) = \frac{-4x}{9} - \frac{4}{27}[/tex]

4:

[tex]f(x) = x^9[/tex]

Replace f(x) with y

[tex]y = x^9[/tex]

Swap y with x

[tex]x = y^9[/tex]

Take 9th root

[tex]x^{\frac{1}{9}} = y[/tex]

[tex]y = x^{\frac{1}{9}}[/tex]

Replace y with f'(x)

[tex]f'(x) = x^{\frac{1}{9}}[/tex]

5:

[tex]f(a) = a^3 + 8[/tex]

Replace f(a) with y

[tex]y = a^3 + 8[/tex]

Swap a with y

[tex]a = y^3 + 8[/tex]

Subtract 8

[tex]a - 8 = y^3 + 8 - 8[/tex]

[tex]a - 8 = y^3[/tex]

Take cube root

[tex]\sqrt[3]{a-8} = y[/tex]

[tex]y = \sqrt[3]{a-8}[/tex]

Replace y with f'(a)

[tex]f'(a) = \sqrt[3]{a-8}[/tex]

6:

[tex]g(a) = a^2 + 8a- 7[/tex]

Replace g(a) with y

[tex]y = a^2 + 8a - 7[/tex]

Swap positions of y and a

[tex]a = y^2 + 8y - 7[/tex]

[tex]y^2 + 8y - 7 - a = 0[/tex]

Solve using quadratic formula:

[tex]y = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex]

[tex]a = 1[/tex] ; [tex]b = 8[/tex]; [tex]c = -7 - a[/tex]

[tex]y = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex] becomes

[tex]y = \frac{-8 \±\sqrt{8^2 - 4 * 1 * (-7-a)}}{2 * 1}[/tex]

[tex]y = \frac{-8 \±\sqrt{64 + 28 + 4a}}{2 * 1}[/tex]

[tex]y = \frac{-8 \±\sqrt{92 + 4a}}{2 * 1}[/tex]

[tex]y = \frac{-8 \±\sqrt{92 + 4a}}{2 }[/tex]

Factorize

[tex]y = \frac{-8 \±\sqrt{4(23 + a)}}{2 }[/tex]

[tex]y = \frac{-8 \±2\sqrt{(23 + a)}}{2 }[/tex]

[tex]y = -4 \±\sqrt{(23 + a)}[/tex]

[tex]g'(a) = -4 \±\sqrt{(23 + a)}[/tex]

7:

[tex]f(b) = (b + 6)(b - 2)[/tex]

Replace f(b) with y

[tex]y = (b + 6)(b - 2)[/tex]

Swap y and b

[tex]b = (y + 6)(y - 2)[/tex]

Open Brackets

[tex]b = y^2 + 6y - 2y - 12[/tex]

[tex]b = y^2 + 4y - 12[/tex]

[tex]y^2 + 4y - 12 - b = 0[/tex]

Solve using quadratic formula:

[tex]y = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex]

[tex]a = 1[/tex] ; [tex]b = 4[/tex]; [tex]c = -12 - b[/tex]

[tex]y = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex] becomes

[tex]y = \frac{-4\±\sqrt{4^2 - 4 * 1 * (-12-b)}}{2*1}[/tex]

[tex]y = \frac{-4\±\sqrt{4^2 - 4 *(-12-b)}}{2}[/tex]

Factorize:

[tex]y = \frac{-4\±\sqrt{4(4 - (-12-b))}}{2}[/tex]

[tex]y = \frac{-4\±2\sqrt{(4 - (-12-b))}}{2}[/tex]

[tex]y = \frac{-4\±2\sqrt{(4 +12+b)}}{2}[/tex]

[tex]y = \frac{-4\±2\sqrt{16+b}}{2}[/tex]

[tex]y = -2\±\sqrt{16+b}[/tex]

Replace y with f'(b)

[tex]f'(b) = -2\±\sqrt{16+b}[/tex]

8:

[tex]h(x) = \frac{2x+17}{3x+1}[/tex]

Replace h(x) with y

[tex]y = \frac{2x+17}{3x+1}[/tex]

Swap x and y

[tex]x = \frac{2y+17}{3y+1}[/tex]

Cross Multiply

[tex](3y + 1)x = 2y + 17[/tex]

[tex]3yx + x = 2y + 17[/tex]

Subtract x from both sides:

[tex]3yx + x -x= 2y + 17-x[/tex]

[tex]3yx = 2y + 17-x[/tex]

Subtract 2y from both sides

[tex]3yx-2y =17-x[/tex]

Factorize:

[tex]y(3x-2) =17-x[/tex]

Make y the subject

[tex]y = \frac{17 - x}{3x - 2}[/tex]

Replace y with h'(x)

[tex]h'(x) = \frac{17 - x}{3x - 2}[/tex]

9:

[tex]h(c) = \sqrt{2c + 2}[/tex]

Replace h(c) with y

[tex]y = \sqrt{2c + 2}[/tex]

Swap positions of y and c

[tex]c = \sqrt{2y + 2}[/tex]

Square both sides

[tex]c^2 = 2y + 2[/tex]

Subtract 2 from both sides

[tex]c^2 - 2= 2y[/tex]

Make y the subject

[tex]y = \frac{c^2 - 2}{2}[/tex]

[tex]h'(c) = \frac{c^2 - 2}{2}[/tex]

10:

[tex]f(x) = \frac{x + 10}{9x - 1}[/tex]

Replace f(x) with y

[tex]y = \frac{x + 10}{9x - 1}[/tex]

Swap positions of x and y

[tex]x = \frac{y + 10}{9y - 1}[/tex]

Cross Multiply

[tex]x(9y - 1) = y + 10[/tex]

[tex]9xy - x = y + 10[/tex]

Subtract y from both sides

[tex]9xy - y - x = y - y+ 10[/tex]

[tex]9xy - y - x = 10[/tex]

Add x to both sides

[tex]9xy - y - x + x= 10 + x[/tex]

[tex]9xy - y = 10 + x[/tex]

Factorize

[tex]y(9x - 1) = 10 + x[/tex]

Make y the subject

[tex]y = \frac{10 + x}{9x - 1}[/tex]

Replace y with f'(x)

[tex]f'(x) = \frac{10 + x}{9x -1}[/tex]

Answer:1.--63 dollars

6 months-108

1 year=216

Step-by-step explanation:18 times 6 is 108 and 108 times 2 is 216

Answer:

y = 2x + 1

Step-by-step explanation:

With parallel lines, the slope is always the same, only the y-intercept changes.

y = mx + b

m = slope

b = y-intercept

?????????????????????

Answer: 600

Step-by-step explanation:

I just took the test

Answer:

B. -1

Step-by-step explanation:

STEP 1: Simplify 3x+2(x−9).

[tex]5x-18=8x+x-14[/tex]

STEP 2: Add 8x and x.

[tex]5x-18=9x=-14[/tex]

STEP 3: Move all terms containing x to the left side of the equation.

[tex]-4x-18=-14[/tex]

STEP 3: Move all terms not containing x to the right side of the equation.

[tex]-4x=4[/tex]

STEP 4: Divide each term by −4 and simplify.

[tex]x=-1[/tex]

Answer:

m(x) = 5 + 100x

Step-by-step explanation:

Let m(x) be the balance of the account after x months.

m(x) = 5 + 100x

Answer:

look below.

Step-by-step explanation:

as z= 7

3z -3

3(7) -3 =21-3 =18

Answer:

hi

Step-by-step explanation:

[tex]\text {Hello! Let's Solve this Problem!}[/tex]

[tex]\text {\underline {The First Step is to Add 4}}[/tex]

[tex]\text {3x-4+4=14+4}[/tex]

[tex]\text {3x=18}[/tex]

[tex]\text {\underline {The Final Step is to Divide 3}}[/tex]

[tex]\text {3x/3=18/3}[/tex]

[tex]\text {Your Answer Would Be:}[/tex]

[tex]\Huge\boxed {x=6}[/tex]

[tex]\text {Best of Luck!}[/tex]

[tex]\huge\text{$x=\boxed{6}$}[/tex]

We can solve for the variable [tex]x[/tex] by isolating it on one side of the equals sign.

Start by adding [tex]4[/tex] to both sides to cancel out the [tex]-4[/tex] on the left side of the equation.

[tex]\begin{aligned}3x-4+4&=14+4\\3x&=18\end{aligned}[/tex]

Now divide both sides of the equation by [tex]3[/tex] since [tex]3x[/tex] is the same as [tex]3*x[/tex] and we want to isolate [tex]x[/tex], keeping in mind that anything multiplied by [tex]1[/tex] is itself.

[tex]\begin{aligned}3x&=18\\3*x&=18\\3*x\div3&=18\div3\\x*3\div3&=18\div3\\x*1&=6\\x&=\boxed{6}\end{aligned}[/tex]

The ratio of the number of eggs in three boxes to the total number of eggs is 1: 15 in its simplest terms.

Suppose the real measurements were "a" and "b". Then their ratio will be formed as;

[tex]\dfrac{a}{b} = \dfrac{p \times x}{q \times x} = \dfrac{p}{q}[/tex]

where is a common factor (not 1)? This shows that to get the real measurements from the given ratio, we need to assume to have some factor possibly canceled from both the numerator and the denominator.

Thus, a = px, b = qx

We have given that farmer 30 boxes of eggs. and there are 6 eggs in each box.

Thus, we know that the total number of eggs is the same as the number of eggs given in 30 boxes.

Hence, the ratio will be;

2: 30,

then divide both sides by 2 ;

1: 15

Therefore, the ratio of the number of eggs in three boxes to the total number of eggs is 1: 15 in its simplest terms.

Learn more about ratios here:

brainly.com/question/186659

#SPJ2

Answer: 19.3

Step-by-step explanation:

Answer:

I think its C (I think..im doing the test so ill tell u if its right or wrong)

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Blake should not include the outlier because it overstates the effect of rainfall on temperature.

Answer:

900 cubic inches.

Step-by-step explanation:

Given the following data

Volume of right circular cone = 300in³

We know that the volume of a right circular cone is given by the formula;

[tex] V = \frac{1}{3} \pi r^{2}h[/tex]

Where;

The volume of a right circular cylinder is given by the formula;

[tex] V = \pi r^{2}h[/tex]

Thus, multiplying the volume of the right circular cone by 3 would give us the volume of the right circular cylinder.

[tex] V = \frac{1}{3} \pi r^{2}h * 3[/tex]

Substituting into the equation, we have;

V = 300 * 3

V = 900in³

Therefore, the volume of a right cylinder that has the same base and height as the cone is 900 cubic inches.

Answer:

x = by + 3b

Step-by-step explanation:

I hope this helps ya!

Answer:

-31 F = -35 C

-45 C = -49 F

-40 C = -40 F

City Y is coldest

Fahrenheit to Celsius conversion (°F to °C)

okay???i guess sooooo??

Answer:

for question two: 12

for question four: 1/3

for question six: 25.75 (rounded to two decimal places)

Answer:

5/14

Step-by-step explanation:

5 + 9 = 14- so our denominator is 14

Theres 5 milk chocolates, so the probability is 5/14

I hope this helped, please mark Brainliest, thank you !!

Answer:

Step-by-step explanation:

t22 = a + (n- 1)d

t22 = 3 + 21*4

t22 = 3 + 84

t22 = 87

Answer:

The answer is False 9/12 simplified equals 3/4

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

Answer

I think you meant to wtite

80.4/d = 0.0804

the answer is d = 1000 or 10^3

Step-by-step explanation:

Answer:

2/5 mile

Step-by-step explanation:

Let's give the total distance the variable x.

1/4x = 1/10

x = 4/10

x = 2/5

Answer:

( -8 , 3 )  8 Down 3 Across

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

x = -1/9

Step-by-step explanation:

[tex]\frac{18}{x} = -2[/tex] multiply by 1/18 to cancel out

[tex]x = -2(\frac{1}{18} )\\x = -\frac{2}{18} \\x = -\frac{1}{9}[/tex]

Hey there!

18/x = -2

Multiply both sides by x

-2x = 18

Divide both of your sides by -2

-2x/-2 = 18/-2

Cancel out: -2x/-2 because it gives you 1

Keep: 18/-2 because it helps us solve for our answer

x = 18/-2

18/-2 = 18 divided by -2 ➡️ -9

Thus your answer is: x = -9 ✅

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

Answer:

x = -2

Step-by-step explanation: