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2 years ago

Simplify the following expression.

Mathematics

1 answer:

expeople1 [14]2 years ago

3 0

Answer: $3x^{2}-24x$

Step-by-step explanation:

1. To simplify the expression given in the problem, you must apply a property of exponents called Quotient of powers, which states that when you divide two powers that have the same base, you must subtract the exponents.

2. Keeping this property on mind you have, you can rewrite the expression as following and simplify:

$\frac{-12x^{4}}{-4x}+\frac{96x^{2}}{-4x}=3x^{2}-24x$

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At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of mi

tangare [24]

Answer:

The price for a small glass of milk is $0.95, and the price for a breakfast taco is $1.15.

Step-by-step explanation:

Let the price of a taco be x and the price for a small glass of milk be y.

$x + y = 2.1$

$2x + 3y = 5.15$

Multiply the first equation by 2:

$2x + 2y = 4.2$

Subtract the new third equation from the second equation:

$(2x + 3y) - (2x + 2y) = 5.15 - 4.2$

$y = 0.95$

Hence, the price for a small glass of milk is $0.95.

Substitute y into the first equation.

$x + 0.95 = 2.1$

$x = 1.15$

Therefore, the price for a breakfast taco is $1.15.

Hope this helped!

3 0

2 years ago

Read 2 more answers

A pack of five basic solid T-shirts costs $29.95 in a store. The sales tax where they are sold is 7.75%. What is the unit cost o

Anna71 [15]

Answer:

6.45

Step-by-step explanation:

29.95+7.75%=32.27

32.27/5

6.45

3 0

2 years ago

Read 2 more answers

What is 2 to the power of 2 multiply 5

solniwko [45]

Answer: 20

1) simplify 2^2 to 4

4*5

2) simplify

20

8 0

3 years ago

Simplify completely****

andreyandreev [35.5K]

Answer:

$\displaystyle \frac{x + 7}{3}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Terms/Coefficients
Factoring

Step-by-step explanation:

Step 1: Define

$\displaystyle \frac{x^2 + 12x + 35}{3x + 15}$

Step 2: Simplify

[Fraction] Factor numerator: $\displaystyle \frac{(x + 5)(x + 7)}{3x + 15}$
[Fraction] Factor denominator: $\displaystyle \frac{(x + 5)(x + 7)}{3(x + 5)}$
[Fraction] Divide: $\displaystyle \frac{x + 7}{3}$

4 0

3 years ago

I have 10 goats, n of which are male. I need to choose 2 of them to make a casserole.

snow_tiger [21]

Answer: There are 4 male goats.

Step-by-step explanation:

We know that n of the 10 goats are male.

The probability that in a random selection, the selected goat is a male, is equal to the quotient between the number of male goats (n) and the total number of goats (10)

The probability is;

p = n/10

Now the total number of goats is 9, and the number of male goats is n -1

then the probability of selecting a male goat again is:

q = (n-1)/9

The joint probability (the probability that the two selected goats are male) is equal to the product of the individual probabilities, this is

P = p*q = (n/10)*((n-1)/9)

And we know that this probability is equal to 2/15

Then we have:

(n/10)*((n-1)/9) = 2/15

(n*(n-1))/90 = 2/15

n*(n-1) = 90*2/15 = 12

n^2 - n = 12

n^2 - n - 12 = 0

This is a quadratic equation, we can find the solutions if we use Bhaskara's formula:

For an equation:

a*x^2 + b*x + c = 0

The two solutions are given by:

$x = \frac{-b +- \sqrt{b^2 - 4*a*c} }{2*a}$

For our case, the solutions will be:

$n = \frac{1 +- \sqrt{(-1)^2 - 4*1*(-12)} }{2*1 } = \frac{1+- 7}{2}$

The two solutions are:

n = (1 - 7)/2 = -3 (this solution does not make sense, we can not have a negative number of goats)

The other solution is:

n = (1 + 7)/2 = 4

This solution does make sense, this means that we have 4 male goats.

5 0

2 years ago