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4 years ago

-QUICK PLEASE-

Mathematics

1 answer:

Zepler [3.9K]4 years ago

6 0

Answer:

Option B. 0.75 gallons is the right answer.

Step-by-step explanation:

Let the load of dishwasher used in house A = x gallons

Let the load of dishwasher used in house B is = y gallons

and similarly we assume for house C = z gallons

Now from the given question

On Friday amount of water used in all three houses = 17.5 gallons

From the table we will make the equation

x + 2y + 2z = 17.5-----(1)

For Saturday

2x + 3y + 4z = 31.5 ----(2)

For Sunday

2x + 2y + 3z = 24.75 -----(3)

By subtracting equation 3 from 2

y + z = 31.5 - 24.75 = 6.75 ------(4)

Equation (1) multiplied by 2 - equation (2)

2×(x + 2y + 2z) - (2x + 3y + 4z) = 17.5×2 - 31.5

y = 35 - 31.5 = 3.5

By putting y = 3.5 in the equation (4)

z = 6.75 - 3.5 = 3.25

By putting y = 3.5 and z = 3.25 in the equation (1)

x + 7 + 6.5 = 17.5

x = 17.5 - 13.5 = 4

Now the difference between load of dishwasher that uses least water and the most.

x - z = 4 - 3.25 = 0.75 gallons

Option B is the right answer.

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Let u = <3, -1>, v = <-6, -6>. Find 9u + 2v.

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3 years ago

Evaluate the following expression. 5^-3

Ulleksa [173]

5^-3 is 1/125

The negative in the exponent makes it so there is a 1 over the problem if there was no negative. When you have a negative in the exponent, the answer will be the reciprocal (opposite) of the question with no negative.
For example,

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3 years ago

If isosceles triangle ABC has a 130° angle at vertex B, which statement must be true?

scZoUnD [109]

Answer:

Option B m<ZA+m<ZB = 155° is correct option.

Step-by-step explanation:

We know that sum of angles of triangle is equal to 180°

And Isosceles triangle, 2 angles are same

So, let Angle 1 = x

Angle 2 = x

Angle 3 = 130°

Finding values of angle x

x+x+130=180

2x=180-130

2x=50

x=25

So, Angle 1 = 25 °

Angle 2 = 25°

As, angle B is greater than 90°, the sum of angles added must be greater than 90°

So, Option A, C and D can't be correct, as their sum is less than 90°

Option B m<ZA+m<ZB = 155° is correct option.

Verify:

m<ZA = 25° (as found earlier)

m<ZB = 130° (given)

So, m<ZA+m<ZB = 155°

25°+130° = 155°

8 0

3 years ago

Let f(x) = x+2/x+6 <br> f^-1(-6) =

GREYUIT [131]

We can explicitly find the inverse. If $f^{-1}(x)$ is the inverse of $f(x)$ , then

$f\left(f^{-1}(x)\right) = \dfrac{f^{-1}(x)+2}{f^{-1}(x)+6} = x$

Solve for the inverse :

$\dfrac{f^{-1}(x) + 2}{f^{-1}(x) + 6} = x$

$\dfrac{f^{-1}(x) + 6 - 4}{f^{-1}(x) + 6} = x$

$1 - \dfrac4{f^{-1}(x) + 6} = x$

$1 - x = \dfrac4{f^{-1}(x) + 6}$

$f^{-1}(x) + 6 = \dfrac4{1-x}$

$\implies f^{-1}(x) = \dfrac4{1-x} - 6$

Then when x = -6, we have

$f^{-1}(-6) = \dfrac4{1-(-6)} - 6 = \dfrac47-6 = \boxed{-\dfrac{38}7}$

Alternatively, we can first solve for x such that $f(x) = -6$ . Then taking the inverse of both sides, $x = f^{-1}(-6)$ . (The difference in this method is that we don't compute the inverse for all x.)