Find the volume of the rectangular prism.
The volume is cm?

8 cm
5 cm
9 cm

The rate charged per hour by the first mechanic = $105,

And the rate charged per hour by the second mechanic = $110.

Use the concept of ratio defined as:

A ratio indicates how many times one number contains another number. The ratio of two numbers is written as x: y, which is equivalent to x/y.

Where x and y are individual amounts of two quantities.

And, the Total quantity gives after combining as x + y.

Given that,

Two mechanics worked on a car.

The first mechanic worked for 10 hours.

The second mechanic worked for 5 hours.

Together, they charged a total of $1600.

The sum of the two rates charged per hour is $215.

Assume that,

The rate charged per hour by the first mechanic is = x dollars,

The rate charged per hour by the second mechanic is = y dollars.

The first mechanic worked for 10 hours,

The total amount earned by the first mechanic would be 10 times their hourly rate = 10x dollars.

Similarly,

The second mechanic worked for 5 hours,

The total amount earned by the second mechanic would be 5 times their hourly rate =  5y dollars.

Set up two equations based on the given information:

The first equation is the sum of the two rates, which is,

x + y = 215  ......(i)

The second equation is the total amount earned by both mechanics,

10x + 5y = 1600  .....(ii)

Use substitution to find the values of x and y:

From the first equation, we can express x in terms of y as,

x = 215 - y

Substitute this value of x into the second equation:

10(215 - y) + 5y = 1600

Expanding the equation, we get,

2150 - 10y + 5y = 1600

Combining like terms, we have:

-5y = 1600 - 2150

-5y = -550

Dividing both sides of the equation by -5, we get:

y = 110

Now that we have the value of y,

Substitute it back into the first equation to find x:

x + 110 = 215

Subtract 110 from both sides, and we get:

x = 105

Hence,

The rate charged per hour by the first mechanic is $105, &  the rate charged per hour by the second mechanic is $110.

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The bottom of the ladder is now 96 feet closer to the house compared to its initial position.

To solve this problem, we can use the concept of similar triangles. Let's denote the distance between the bottom of the ladder and the base of the wall as x (in feet). We are given the following information:

Initial ladder position:

Top of the ladder is 16 feet above the ground.

Bottom of the ladder is 12 feet away from the base of the wall.

New ladder position:

Top of the ladder is 18 feet above the ground.

Since the triangles formed by the ladder, the ground, and the wall are similar, we can set up a proportion to find the new distance between the bottom of the ladder and the base of the wall.

Using the initial position of the ladder:

(16 ft) / (x + 12 ft) = (18 ft) / (x)

Cross-multiplying:

16 ft * x = 18 ft * (x + 12 ft)

Expanding:

16x = 18x + 216 ft

Moving the terms involving x to one side:

16x - 18x = 216 ft

Simplifying:

-2x = 216 ft

Dividing by -2:

x = -108 ft

Since distance cannot be negative, we discard the negative solution. The distance between the bottom of the ladder and the base of the wall is 108 ft.

Now, to find how much closer to the house the bottom of the ladder is, we can subtract the initial distance (12 ft) from the new distance (108 ft):

108 ft - 12 ft = 96 ft

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Answer:

1 . x 3 +  3 x 2 y  +  3 x y 2  +  y 3

2. x 3 -  3 x 2  y  +  3 x y 2  -  y 3

3. a + b

4 . a - b

Step-by-step explanation:

Hope this answer helps you :)

Have a great day

Mark brainliest

Answer:

[tex]t \le 6[/tex] min

Step-by-step explanation:

The time to do 25 problems should take less than (or equal to) the 150 minutes available.

[tex]25t \le 150\\t \le 6[/tex]

Answer:

x = 5/7

Step-by-step explanation:

Here, we want to get the value of x

Firstly, according to indices;

(a^m)^n = a^(m * n) = a^mn

Also;

a^m * a*n = a^(m + n)

a^0 = 1 (any number raised to zero as its power is 1)

And lastly;

a^m divided by a^n = a^(m-n)

So using these we can have;

7^4x = 7^( 2 + 3)/7^3x

7^4x = 7^5/7^3x

7^4x = 7^(5-3x)

Since we have the same bases, we have to equate the powers

4x = 5-3x

4x + 3x = 5

7x = 5

x = 5/7

Answer:

-1.3+2 that is point A to find ir

Answer:

[tex] \large{ \tt{❃ \: STEP- BY - STEP \: EXPLANATION}} : [/tex]

[tex] \large{ \tt{❁ \: LET'S \: START}} : [/tex]

[tex] \boxed{ \large{ \bf{❀ \: y -y _{1} = \frac{y_{2} - y_{1} }{x_{2} - x_{1}} (x - x_{1)}}}}[/tex]

- Plug the values :

[tex] \large{ \bf{⇢ \: y - ( - 1) = \frac{4 - ( - 1)}{ - 7 - 4}(x - 4) }}[/tex]

[tex] \large{ \bf{⇢y + 1 = \frac{4 + 1}{ - 11} (x - 4)}}[/tex]

[tex] \large{ \bf{⇢ \: y + 1 = - \frac{5}{11} (x - 4)}}[/tex]

[tex] \large{ \bf{⇢y + 1 = - \frac{5}{11}x + \frac{20}{11} }}[/tex]

[tex] \large{ \bf{⇢y + 1 = \frac{ - 5x + 20}{11} }}[/tex]

[tex] \large{ \bf{⇢11(y + 1) = - 5x + 20}}[/tex]

[tex] \large{ \bf{⇢11y + 11 = - 5x + 20}}[/tex]

[tex] \large{ \bf{⇢5x + 11y + 11 - 20 = 0}}[/tex]

[tex] ⇢ \boxed{\large{ \bold{\bf{5x + 11y - 9 = 0}}}}[/tex]

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Answer:

64 times

Step-by-step explanation:

There are 4 sessions of 15 minutes in an hour. Meaning that a person would vape 4 times in an hour. 4 * 16 = 64. A person vapes 64 times in 16 hours. o-o dont vape kids.

Answer and Step-by-step explanation:

We are given the ratio of 1 vape every 15 minutes. We need to convert the time to hours, then multiply the hours by 16.

1 : 15

We know that there are 60 minutes in 1 hour, so we need to multiply 15 by 4 to get 60.

15 × 4 = 60

We also need to multiply 1 by 4, so that the result will be a multiple of the beginning number and so that we didn't get random numbers from somewhere.

1 × 4 = 4

Now we have the ratio 4 : 60, which means that the person vapes 4 times every 60 minutes, or every hour. But since we turned the minutes into an hour, this turns the 60 into a 1.    4 : 1

Now, we have to multiply 4 and 1 by 16 to get the amount of vapes done in 16 hours.

4 × 16 = 64

1 × 16 = 16

So, we have the ratio 64 : 16

This means that the person smokes 64 times in the 16 hours.

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[tex]\huge{ \mathfrak{  \underline{ Answer} \:  \:  ✓ }}[/tex]

Figure - 1 :

The given triangles are similar, so their corresponding sides will be proportional.

Let the missing side be x

_____________________________

Figure - 2 :

The given figure is a Cylinder :

[tex] \large \boxed{ \mathrm{volume = \pi {r}^{2}h }}[/tex]

_____________________________

[tex]\mathrm{☠ \: TeeNForeveR \: ☠}[/tex]

Answer:

[tex]\text{First number: }-10, \\\text{Second number: }-4[/tex]

Step-by-step explanation:

We can write the following system of equations:

Let the first number be [tex]f[/tex] and the second number be [tex]s[/tex]:

[tex]\begin{cases}f+6=s, \\2f-4=6s\end{cases}[/tex]

Solving, we get:

[tex]\int\limits^a_b {x} \, dx \begin{cases}f+6=s, \\2f-4=6s\end{cases},\\2f-4=6(f+6),\\2f-4=6f+36,\\-40=4f,\\f=\boxed{-10}[/tex]

Solving for [tex]s[/tex]:

[tex]f+6=s,\\-10+6=s,\\s=\boxed{-4}[/tex]

Answer:

x = 10

Step-by-step explanation:

We know that in a parallelogram base angles are supplementary angle (add up to 180°)

Given that;

∠U = 9x + 15

∠V = 6x + 15

we can say that:

∠U + ∠V = 180°

(9x + 15) + (6x + 15) = 180

Combining like terms we get;

15x + 30 = 180°

15x = 180 - 30

15x = 150

x = 150/15

x = 10

Hope this helps!

According to the property of proportions,

Product of means = Product of extremes

So, simply we did cross multiplication.

Step-by-step explanation:

56/3 is the answer. Refer to the attachment for the solution. :)

Answer:

x = 12, x = 7

Step-by-step explanation:

The 2 legs of the triangle are congruent, both 2x + 7, then

2x + 7 + 2x + 7 + x + 11 = 85 ← equation for perimeter

5x + 25 = 85 ( subtract 25 from both sides )

5x = 60 ( divide both sides by 5 )

x = 12

-----------------------------------------------------------

Opposite sides are congruent, then

2(2x) + 2(5x + 3) = 104 ← distribute and simplify both sides

4x + 10x + 6 = 104

14x + 6 = 104 ( subtract 6 from both sides )

14x = 98 ( divide both sides by 14 )

x = 7

Answer:

x=12 x=7 yup thank me later

Answer:

a. y= f(x-1)

Step-by-step explanation:

___________

Answer:

the first one

Step-by-step explanation:

To find the answer we want to find the volume of each rectangular prism

Which ever prism has an exact volume of 98 is the correct answer

( note that volume of a rectangular prism = length times width times height )

For the first answer choice

4 * 3.5 * 7 = 98

We get an outcome of 98, which means that the first one could possibly be the correct answer however lets find the volume of the rest of the prisms just to be safe.

For the second one

6.25 * 7 * 2 = 87.5

87.5 ≠ 98 therefore the second choice is not correct

For the third one

3 * 6.5 * 5 = 97.5

97.5 ≠ 98 therefore the third choice is not correct

For the fourth one

7.5 * 1 * 14 = 105

105 ≠ 98 therefore the fourth choice is not correct

So we can conclude that the first answer choice is correct

Answer:

14

Step-by-step explanation:

The equation to find slope is [tex]\frac{y_{2} -y_{1}}{x_{2}-x_{1}}[/tex]. You plug in the values to get [tex]\frac{8-(-20)}{5-3}[/tex]. This simplifies to [tex]\frac{28}{2}[/tex], which is 14.

Answer:

x = 0.1854 and x = -16.1854

Step-by-step explanation:

refer to photo

Answer:

B. four less than three times a number

Answer:

40 %

Step-by-step explanation:

the difference between cost and selling price:

91 - 65 = 26

Find the percentage:

26/65 = 0.4 --> 40%

Markup = 40%

Hope this answer helps you :)

Have a great day

Mark brainliest

Answer:

D

Step-by-step explanation:

The very first thing you have to realize is that the temperature goes further down the minus scale which means that only A and D can be correct. That's because time in this question is positive.

So if you just try the first value (x = 3), you will get

-3/2 * 3 = -9/2 which would mean that you would add -4 1/2 onto - 10 which is much larger than - 10

A: is not the answer.

-2/3 * 3 - 10 = -6/3 - 10 = -2 - 10 = - 12

That is the answer you should get. The answer is D.

Answer:

61.2

Step-by-step explanation:

base=6

height=10

Area of parellelogram=base x height

=6x 10.2

=61.2 sq.ft

MARK ME BRAINLIEST THANKS MY ANSWER PLEASE

Answer:

8 meters per second

Step-by-step explanation:

We can divide meters by seconds to get his average speed in meters per second. -- 640 m / 80s = 8 m/sec (meters per second). We can also figure out his average speed in minutes by multiplying 8 by 60 (because there are 60 seconds in a minute), 8 * 60 = 480 m/min (meters per minute).

Answer:

8m/s

Step-by-step explanation:

Speed is equal the distance upon time.

640/80

so speed is equal to 8m/s

Answer:

Step-by-step explanation:

Answer:

The answer is B

Step-by-step explanation:

Answer:

1,456 crates needed

Step-by-step explanation:

oranges = 133,952

crate capacity = 92

133,952 / 92 = 1,456 crates needed

Answer:

x=9

Step-by-step explanation:

−4(2x+5)+5x−1= −48

-8x-20+5x-1=-48

-3x-21=-48

-3x=-27

x=-27/-3

x=9

Answer:

D.17

Step-by-step explanation:

Answer:

1/100

Step-by-step explanation:

P(4 then 7) = 1/10 x 1/10