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3 years ago

Find the x and y intercepts of the following function. g(x)=x^2-5x-84

Mathematics

1 answer:

Ahat [919]3 years ago

8 0

Answer:

see explanation

Step-by-step explanation:

To find the y- intercept let x = 0 in the function

g(0) = 0 - 0 - 84 = - 84 ← y- intercept

To find the x- intercepts let y = 0, that is

x² - 5x - 84 = 0

To factor the quadratic

Consider the factors of the constant term (- 84) which sum to give the coefficient of the x- term

The factors are - 12 and + 7, since

- 12 × 7 = - 84 and - 12 + 7 = - 5, thus

(x - 12)(x + 7) = 0

Equate each factor to zero and solve for x

x - 12 = 0 ⇒ x = 12

x + 7 = 0 ⇒ x = - 7

x- intercepts are x = - 7 and x = 12

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Sphinxa [80]

$y + 4 = -36

Subtract 4 both sides.

y = -40

Check solution. 

-40 + 4 = -36

This is correct.

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3 years ago

A stack of six bricks is two feet high. How many bricks are in a stack of 20 feet high? How high is a stack of 20 bricks?

Flura [38]

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3 years ago

Read 2 more answers

m_a_m_a [10]

Answer:

$2.5

Step-by-step explanation:

Number of pounds of banana needed = 5 pounds

Cost per pound of banana = 0.50

To solve using place value blocks :

Ignoring the decimal in the cost per pound:

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3 years ago

5,5,3 Is this a triangle? Explain.

Vlad1618 [11]

Problem 1

Answer: <u>Yes</u> a triangle can be formed with side lengths 5,5,3

--------------------

Explanation:

Take any two sides and add them up. If we get a sum larger than the third side, then a triangle is possible. This is the triangle inequality theorem.

5+5 = 10 is larger than 3

5+3 = 8 is larger than 5

This shows a triangle is possible. The triangle is isosceles because two sides are the same length.

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Problem 2

Answer: <u>Yes</u> a triangle can be formed with side lengths 8,8,8

--------------------

Explanation:

This triangle is equilateral because all sides are the same length.

Take any two sides, add them up, and you'll find the sum is larger than the third side.

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Problem 3

Answer: <u>No</u> a triangle cannot be formed with sides 7,8,15

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Explanation:

Yes it is true that

8+15 = 23 is larger than 7

7+15 = 22 is larger than 8

but

7+8 = 15 is not larger than 15

So this means a triangle is not possible.

Imagine you had 3 strips of paper that were 7 inches, 8 inches and 15 inches long. The 7 and 8 inch strips add to 15 inches, but those two smaller strips only form a straight line. We cannot pull them so a triangle forms. If we did, then the third side would be smaller than 15 inches. This is one way to get hands on to see why the triangle inequality theorem works.

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Problem 4

Answer: <u>Yes</u> a triangle is possible with side lengths 5,6,10

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Explanation:

Same idea as before. We can take any two sides, add them, and get a sum larger than the third side. A triangle is possible.

5+6 = 11 is larger than 10
6+10 = 16 is larger than 5
5+10 = 15 is larger than 6

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3 years ago

A system of equations has no solution. if y = 8x 7 is one of the equations, which could be the other equation? 2y = 16x 14 y = 8

SCORPION-xisa [38]

A system of equations has no solution. if y = 8x+ 7 is one of the equations, The other equation will be y = 8x - 7.

<h3 /><h3>What is the system of two equations?</h3>

A set of two linear equations with two variables is called a system of linear equations. They create a system of linear equations when evaluated collectively.

The first equation is given as:

y = 8x + 7

The equations in the system would have different constant values if the system of equations had no solution.

y=8x+b

Where:

b is a variable that is not equal to 7.

The equation whose standard form is y=ax+b has no solution. Only equation 2 satisfies the generalized form.

Hence.if y = 8x+ 7 is one of the equations, The other equation will be y = 8x - 7.

To learn more about the system of two equations refer to the link;

brainly.com/question/21620502

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