a(3x - 8) = b - 18x

Find the value of a

find the value of b

Explain how the value of a and b you got makes the equation true

A wading pool is being filled with water from a garden hose at a rate of

6 gallons per minute. If the pool already contains 80 gallons of water and can hold 152 gallons, and it will take 12 minutes for the pool to overflow.

In this scenario, we have a wading pool being filled with water from a garden hose at a constant rate of 6 gallons per minute. The pool already contains 80 gallons of water, and its maximum capacity is 152 gallons. We want to find out how long it will take for the pool to overflow.

Let's use "t" as the variable representing time in minutes. After "t" minutes, the amount of water in the pool will be the initial 80 gallons plus the additional water being filled by the hose at a rate of 6 gallons per minute. We can express this mathematically as:

Amount of water in the pool after "t" minutes = 80 gallons + 6 gallons/minute * "t" minutes

Now, we want to find out when the pool will overflow. The pool's capacity is 152 gallons, so we set up an equation to represent this:

Amount of water in the pool after "t" minutes = 152 gallons

Substituting the earlier expression for the amount of water in the pool after "t" minutes:

80 gallons + 6 gallons/minute * "t" minutes = 152 gallons

Now, we have an equation to model the scenario: "80 + 6t = 152".

To find the time "t" it takes for the pool to overflow, we need to solve this equation for "t."

To solve for "t," we need to find the value of "t" that satisfies the equation we derived earlier:

80 + 6t = 152

To isolate "t," we'll perform the following steps:

Subtract 80 from both sides to move the constant term to one side of the equation.

80 + 6t - 80 = 152 - 80

This simplifies to:

6t = 72

Divide both sides by 6 to solve for "t."

t = 72 / 6

t = 12

So, it will take 12 minutes for the pool to overflow.

In summary, we have a wading pool being filled with water at a rate of 6 gallons per minute, and we want to know when it will overflow, given its current water level of 80 gallons and a maximum capacity of 152 gallons. The equation "80 + 6t = 152" models this situation, with "t" representing the time in minutes. Solving this equation will give us the time it takes for the pool to overflow.

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Answer:

b4

Step-by-step explanation:

Answer:

28 days

Step-by-step explanation:

Answer:

Step-by-step explanation:

x=5

Answer:

x is 5.

Step-by-step explanation:

X varies directly with y, so we can use the equation x = yk (with k standing for the constant of variation) to find what the constant is. Substitute 3 for x and 15 for y

3 = 15k

Now divide both sides by 15.

3/15 = k

3/15 simplifies to 1/5.

1/5 = k

Now that we know the constant, then what we need to do is find 1/5 of 25 to get x.

1/5(25) = x

Multiply 1/5 by 25 to get 5.

5 = x

The problem is solved.

X will be 5 in this scenario.

Answer:

128

Step-by-step explanation:

Sum of interior angles of a 4 sided quadrilateral is 360.

90 + 90 + 52 + x = 360

232 + x = 360

x = 360 - 232

x = 128

Answer:

B. A. D.

Step-by-step explanation:

Answer:

3,2

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

We know that ∠ 1 + ∠ 2 + ∠3 = 180 → (1)

and ∠ 3 + ∠ 4 = 180 → (2)

From (2) ∠ 3 = 180 - ∠ 4

Substitute ∠ 3 = 180 - ∠ 4 into (1)

∠ 1 + ∠ 2 + 180 - ∠ 4 = 180 ( add ∠ 4 to both sides )

∠ 1 + ∠ 2 + 180 = 180 + ∠ 4 ( subtract 180 from both sides )

∠ 1 + ∠ 2 = ∠ 4 → C

Answer:

8 quarts

Step-by-step explanation:

According to the scenario, computation of the given data are as follows,

Water = 2 quarts

Orange Juice = 1quarts

Mango Juice = 2 quarts

Strawberry juice = 1 quart

Pineapple Juice = 2 quarts

So, Total mixture = Sum of all ingredients in quarts

= 2 + 1 + 2 + 1 + 2 = 8 quarts

Hence, Maria makes 8 quarts of punch.

Answer: y= -3(x+4)

Step-by-step explanation:

Answer:

2.5

Step-by-step explanation:

Lets simpify one side first

8x - 2x + 7 +2

8-2 = 6

so 6x

7-2 = 5

6x+9

10x - 5 = 6x +5

(You add 5 due to it being negative on the other side)

+5             +5

10x= 6x +10

-6x    -6x

4x = 10

Divide each side by 4

x = 2.5 or 10/4 or 5/2

Answer: No

Step-by-step explanation: To find whether these are equivalent, we first need to simplify the equation on the right.

8x-2x+7-2

8x-2x+5  (work-    7-2 = 5)

6x+5       (work-    8x-2x=6x) These are like terms, so we can subtract them

now that we have simplified, let's write the equations once again.

10x-5=6x+5

they are surely not equivalent

Answer:

679.6

Step-by-step explanation:

Answer:

8⁴

Step-by-step explanation:

8*8*8*8 =8⁴

8 exponent 4

Answer:

[tex]8^{4}\\[/tex]

Step-by-step explanation:

An exponent describes how many times the base is repeatedly shown. For instance:

6³

6 is the base and 3 is the exponent. Because the exponent is 3, the base is repeated that many times. Here's what I mean:

6² = 6 (6) (6)

So in 8 (8) (8) (8), the base would be 8 and this is repeated 4 times. So the exponent would be 4.

So your answer would look like [tex]8^{4}[/tex].

Answer:

It will look like this

Step-by-step

No it is not correct.

answer:

16.24 or 12 square root of 18

Answer:

The full mass is 500 kg.

Step-by-step explanation:

Let's break this down.

4% of the mass is 20 kg.

4% = 4/100 or 0.04

"of" = multiply

mass = our unknown value, x

is = equal sign

20 kg = our end result

Let's make an equation out of this.

4% of the mass is 20 kg.

0.04 • x = 20

Divide both sides by 0.04.

x = 500

The full mass is 500 kg.

Hope this helps!

Answer:

500 kg

Step-by-step explanation:

4% = 20 kg

→ Find 1% by dividing both sides by 4

1% = 5 kg

→ Find 100% by multiplying both sides by 100

100% = 500 kg

Answer:

[tex]2\sqrt{5}[/tex]

Step-by-step explanation:

The picture (attached) shows two isosceles right triangles, so the altitude marked x splits the bottom side in half, 4 units and 4 units.

Each triangle is a right triangle with one leg of length 4, hypotenuse 6. Use the Pythagorean Theorem (leg)^2 + (leg)^2 = (hypotenuse)^2.

[tex]4^2+x^2=6^2\\16+x^2=36\\x^2=20\\x=\sqrt{20}\\x=2\sqrt{5}[/tex]

Answer:

Los emprendedores se enfrentan a muchos desafíos en el mundo empresarial ultracompetitivo de hoy. Afortunadamente, los emprendedores también tienen más recursos que nunca para abordar esos problemas.

Hoy en día, muchos emprendedores enfrentan los siguientes 10 desafíos. Quizás ya te hayas enfrentado a algunos de ellos. Siga leyendo para saber por qué existe cada desafío y para obtener soluciones y soluciones para que pueda operar su negocio de manera eficiente y exitosa.

Answer:

answer what?

Step-by-step explanation:

She need 1 2/3 more cups

Hope this helped :3

Answer:

33 square units

Step-by-step explanation:

Assuming that each line on this grid increases by a value of one, the area of the polygon can be determined by breaking it down into a large rectangle and two smaller triangles.

The area of a rectangle is simply [tex]A = bh[/tex], where b represents the base and h represents the height.

Counting the size of each side, we can determine that they are 6 units for the base and 4 units for the height.

Substituting in the values, we get:

[tex]A = (6)(4)\\A = 24[/tex]

The area of the rectangle is 24 square units

The area of a triangle is simply [tex]A = \frac{1}{2} bh[/tex].

The base of each triangle is 3, and the height of each triangle is also 3.

Substituting in the values, we get:

[tex]A = \frac{1}{2} (3)(3)\\A = \frac{1}{2} (9)\\A = 9 / 2\\A = 4.5[/tex]

The area of each triangle is 4.5 square units

To get the area of the polygon, we simply add up the area of the rectangle and both triangles

[tex]A = 24 + 4.5 + 4.5\\A = 24 + 9\\A = 33[/tex]

The total area of the polygon is 33 square units.

Answer:

got em

Step-by-step explanation:

Answer:

x=6.9

Step-by-step explanation:

[tex]x^{2} =6*8[/tex]

[tex]x=\sqrt{48}[/tex]

[tex]x=6.9[/tex]

[tex]hope[/tex] [tex]it[/tex] [tex]helps...[/tex]

[tex]have[/tex] [tex]a[/tex] [tex]great[/tex] [tex]day!!![/tex]

Answer:

C) 16.97

Step-by-step explanation:

If the sides are 12, the hypotenuse is 12*(2^1/2) to the 45 - 45 - 90.

When you put 2*(2^1/2) into the calculator, you get 16.97.

Answer:

16.97

Step-by-step explanation:

Equation used:  c=[tex]\sqrt{ax^{2} +bx^{2} }[/tex]

Equation filled out: c=[tex]\sqrt{12x^{2} +12x^{2} }[/tex]

Next step:  c=[tex]\sqrt{288}[/tex]

Total: 16.97056 though to the hundreath place 16.97

So if both legs are 12 inches each, that mean that 12^2 +12^2  which totals out too 288, then you find the full square of 288 which leads out to 16.97!

Answer:

the answer will be 244rhruiewowworbvrueie

Answer:

0 i think

Step-by-step explanation:

Answer:

The answer is -69,420 ! 69,420 - 69,420 = 0. next you multiply it and its 0 again then you add it 69,420 then subtract it equals 0 then subtract again it equals -69,420 then multiply it equals -69,420 then you have to add 69,420 it equals 0 again then you subtracted 69,420 and that means its -69,420!

Step-by-step explanation: