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2 years ago

What is the answer to x=3x-20 and y=-6+30

Mathematics

1 answer:

NISA [10]2 years ago

5 0

Answer:y=24 and x=10

Step-by-step explanation:

To find the value of x and y in x=3x-20 and y=-6+30

We gets

y=24

To get x

x=3x-20

Collect like terms

x-3x=-20

Divide through by -2

-2x=-20

x=10

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6x - 9 < 39 (solve the inequalities)

x ≥ 1

x < 8 (find the intersection)

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3 years ago

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The advertised size of a pizza is the length of its diameter. (An 8-inch pizza has a diameter of 8 in)Q1: What is the area of a

Alexxandr [17]

<span>In this question, we assume the pizza is a circle with radius r and diameter d. The radius is also known as (d/2). The area of a circle is A=pie*r^2. Q1: The area of a 16 inch pizza is A = pie * (16/2)^2 = pie * 8^2 = pie *64 = 201.06 in^2. Q2: To determine the cost per slice, just divide the total cost by the number of slices. In this case you would divide 12.50 by 8 (total slices) to get 12.50/8=$1.56/slice. Q3: The cost per square inch of the pizza would be total cost divided by the total area in square inches. This would give you 12.50/201.06 = $0.06 per square inch.</span>

8 0

3 years ago

Factor the cubic polynomial 6x3 – 11x2 – 12x 5. use the rational root theorem and synthetic division

pochemuha

The factorization of given cubic polynomial 6x³ - 11x² - 12x + 5 is:

6x³ - 11x² - 12x + 5 = (x + 1)(x - $\frac{5}{2}$ )(x - $\frac{1}{3}$ )

For given question,

We have been given the cubic polynomial 6x³ - 11x² - 12x + 5

We need to factorize given cubic polynomial.

By the rational roots theorem, any rational zero of f(x) is expressible in the form ± $\frac{p}{q}$ for integers p, q with p a divisor of the constant term 5 and q a divisor of the coefficient 6 of the leading term.

Factors of p = 5: 1, 5

Factors of q = 6: 1, 2, 3, 6

That means that the only possible rational zeros are:

±{ $\frac{1}{1} ,\frac{1}{2} ,\frac{1}{3} ,\frac{1}{6} ,\frac{5}{1} ,\frac{5}{2} ,\frac{5}{3} ,\frac{5}{6}$ }

= ±{ $1 ,\frac{1}{2} ,\frac{1}{3} ,\frac{1}{6} ,5 ,\frac{5}{2} ,\frac{5}{3} ,\frac{5}{6}$ }

We need to find the exact zeros of given cubic polynomial.

For x = 1,

6(1)³ - 11(1)² - 12(1) + 5 = -12

This means, x = 1 is not a zero of given cubic polynomial.

For x = -1,

6(-1)³ - 11(-1)² - 12(-1) + 5 = 0

This means, x = -1 is a zero of given cubic polynomial and (x + 1) is a factor.

To factorize given cubic polynomial we use synthetic division.

The synthetic division (6x³ - 11x² - 12x + 5) ÷ (x + 1) is as shown in following image.

⇒ 6x³ - 11x² - 12x + 5 = (x + 1)(6x² - 17x + 5)

The factors of above quadratic polynomial 6x² - 17x + 5 are:

⇒ 6x² - 17x + 5 = (x - $\frac{5}{2}$ )(x - $\frac{1}{3}$ )

So, the factors of given cubic polynomial are:

⇒ 6x³ - 11x² - 12x + 5 = (x + 1)(x - $\frac{5}{2}$ )(x - $\frac{1}{3}$ )

Therefore, the factorization of given cubic polynomial 6x³ - 11x² - 12x + 5 is: 6x³ - 11x² - 12x + 5 = (x + 1)(x - $\frac{5}{2}$ )(x - $\frac{1}{3}$ )

Learn more about the polynomial here:

brainly.com/question/16594008

#SPJ4

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1 year ago

The measure of one angle is 130 which statement is true regarding the 130 angle and angle 3

Dafna11 [192]

According to Figure that is shown below, the correct answer for this problem is:

<span>B. They are alternate interior angles, so angle 3 also measures 130°.

</span>The same happens with 7 and 11. This is an obtuse angle, that is, this kind of angles measures more than 90° but less than 180°.