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2 years ago

Consider the equation 40x - 25y = 15

Mathematics

1 answer:

PilotLPTM [1.2K]2 years ago

6 0

Answer:

A) 8x - 5y = 3

Step-by-step explanation:

To create infinite solutions, the equation has to be the same line

First we can reduce the equation by dividing by 5

40x -25y =15

40/5 x -25/5 y =15/5

8x-5y =3

This is the same line , so if this is the second equation, it will give us infinite solutions

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Cammie can mow 1/2 acre in 25 minutes. If her rate is constant, Cammie says she can mow 1 1/4 acres in one hour. Is Cammie corre

Sergeu [11.5K]

Answer: No, Cammie is not correct. She can mow $1\frac{1}{5}\ acres$ in one hour (See explanation).

Step-by-step explanation:

Convert the mixed number to an impoper fraction:

1. Multiply the whole number part by the denominator of the fraction and add the product to the numerator.

2. The denominator does not change.

Then:

$1\frac{1}{4}=\frac{(1*4)+1}{4}=\frac{5}{4}$

Let be "x" the acres Cammie can mow in one hour.

You know that she can mow $\frac{1}{2}\ acre$ in 25 minutes, then you can set up the following proportion (Remember that 1 hour has 60 minutes):

$\frac{\frac{1}{2}}{25}=\frac{x}{60}$

Solving for "x", you get:

$\frac{\frac{1}{2}}{25}=\frac{x}{60}\\\\(60)(\frac{1}{50})=x\\\\x=\frac{6}{5}$

Convert from improper fraction to mixed number:

1. When you divide 6 by 5, the quotient is 1. This will be the whole number part.

2. The remainder is 1. This will be the numerator.

3. The denominator does not change.

Then:

$x=1\frac{1}{5}$

Therefore, she can mow $1\frac{1}{5}\ acres$ in one hour.

3 0

2 years ago

What is the remainder of f(x)=x^4-2x^3-27x^2-9x+18 when divided by binomial x+4

givi [52]

Answer:

The remainder will be 6.

Step-by-step explanation:

We have the function:

$f(x)=x^4-2x^3-27x^2-9x+18$

And we want to find the remainder after it is divided by the binomial:

$x+4$

We can use the Polynomial Remainder Theorem. According to the PRT, if we have a polynomial P(x) being divided by a binomial in the form (x - a), then the remainder will be given by P(a).

Here, our divisor is (x + 4). We can rewrite this as (x - (-4)).

Therefore, a = -4.

Then according to the PRT, the remainder will be:

$f(-4)=(-4)^4-2(-4)^3-27(-4)^2-9(-4)+18=6$

The remainder will be 6.

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2 years ago

The value of the 7 in 27,459 is how many times the value of the 7 in 40,735?

alukav5142 [94]

Answer:

Step-by-step explanation:

The 7 in 27,459 is in the thousands place.

The 7 in 40,735 is in the hundreds place.

Any digit in the thousands place has 10 times the value of the same digit in the hundreds place. (The multiplier is 1000, instead of 100.)

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In the base-10 number system, each digit location has 10 times the value of the location to its right. The value is determined by the place the digit occupies in the number. That is why it is called a place-value number system.

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3 years ago

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A water tank contains 100 fluid Ounces of water. Jacob fills up cups that hold 8 fl. oz. each. How many cups has he filled when

Kamila [148]

7 and a half cups.

Step-by-step explanation:

Dvide 60 by 8

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2 years ago

What is the domain and range?

ycow [4]

Answer:

Domain- the set of possible values of the independent variable or variables of a function.

Range- the set of values that a given function can take as its argument varies.

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3 years ago