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3 years ago

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Question 15

1 answer:

ycow [4]3 years ago

8 0

The perimeter of the smaller triangle is 8+12+16=36. The big triangle has perimeter 54. So our scale factor is 54/36=3/2. So we scale up the short side, 8, by 3/2, giving our answer:

Answer: 12

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Which of the following constants can be added to x2 + x to form a perfect square trinomial?

solmaris [256]

The constant should be added to form a perfect square trinomial will be 1/4. Then the correct option is D.

<h3>What is a quadratic equation?</h3>

It's a polynomial with a value of zero. There exist polynomials of variable power 2, 1, and 0 terms. A quadratic equation is an equation with one statement in which the degree of the parameter is a maximum of 2.

The expression is x² + x.

Then the constant should be added to form a perfect square trinomial.

Then the constant will be

The square of the half of the coefficient of the variable x is to be added to make a perfect square.

Then the constant will be 1/4.

Then the perfect square will be

$\rm \rightarrow x^2 + x + \dfrac{1}{4}\\\\\\\rightarrow x^2 + 2 \times \dfrac{1}{2} x + \left (\dfrac{1}{2} \right )^2\\\\\\\rightarrow \left (x + \dfrac{1}{2} \right)^2$

More about the quadratic equation link is given below.

brainly.com/question/2263981

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4 0

2 years ago

Jason’s gas tank can hold 12 gallons of gas. His gas tank was empty and he filled it up 2/3 full. He spent $20.16. How much did

natita [175]

Answer:

$2.52 per gallon.

Explanation:

$\frac{2}{3} \times 12 = 8$

$8c = 20.16$

$c = 2.52$

7 0

2 years ago

An oak tree is 60 feet tall and casts a 40-foot shadow. What is the approximate distance from the top of the oak tree to the top

Murljashka [212]

The approximate distance from the top of the tree to the top of the shadow is 20ft

7 0

3 years ago

Read 2 more answers

Which statements are always true regarding the diagram? Check all that apply. m∠3 + m∠4 = 180° m∠2 + m∠4 + m∠6 = 180° m∠2 + m∠4

Nostrana [21]

Answer:

The true statements are:

m∠ 3 + m∠ 4 = 180° ⇒ 1st

m∠ 2 + m∠ 4 + m∠ 6 = 180° ⇒ 2nd

m∠ 2 + m∠ 4 = m∠ 5 ⇒ 3rd

Step-by-step explanation:

* Look to the attached diagram to answer the question

# m∠ 3 + m∠ 4 = 180°

∵ ∠ 3 and ∠ 4 formed a straight angle

∵ The measure of the straight angle is 180°

∴ m∠ 3 + m∠ 4 = 180° ⇒ <em>true</em>

# m∠ 2 + m∠ 4 + m∠ 6 = 180°

∵ ∠ 2 , ∠ 4 , ∠ 6 are the interior angles of the triangle

∵ The sum of the measures of interior angles of any Δ is 180°

∴ m∠ 2 + m∠ 4 + m∠ 6 = 180° ⇒ <em>true</em>

# m∠ 2 + m∠ 4 = m∠ 5

∵ In any Δ, the measure of the exterior angle at one vertex of the

triangle equals the sum of the measures of the opposite interior

angles of this vertex

∵ ∠ 5 is the exterior angle of the vertex of ∠ 6

∵ ∠2 and ∠ 4 are the opposite interior angles to ∠ 6

∴ m∠ 2 + m∠ 4 = m∠ 5 ⇒ <em>true </em>

# m∠1 + m∠2 = 90°

∵ ∠ 1 and ∠ 2 formed a straight angle

∵ The measure of the straight angle is 180°

∴ m∠1 + m∠2 = 90° ⇒ <em>Not true</em>

# m∠4 + m∠6 = m∠2

∵ ∠ 4 , ∠ 6 , ∠ 2 are the interior angles of a triangle

∵ There is no given about their measures

∴ We can not says that the sum of the measures of ∠ 4 and ∠ 6 is

equal to the measure of ∠ 2

∴ m∠4 + m∠6 = m∠2 ⇒ <em>Not true</em>

<em></em>

# m∠2 + m∠6 = m∠5

∵ ∠ 5 is the exterior angle at the vertex of ∠ 6

∴ m∠ 2 + m∠ 6 = m∠ 5 ⇒ <em>Not true</em>

6 0

3 years ago

Read 2 more answers

19. Use the unit circle to find the value of tan 315º.<br> Show work pls.

Free_Kalibri [48]

Answer: -1

Step-by-step explanation:

First change tan(315) to:

$\frac{\sin(315)}{\cos(315)}$

Then evaluate the sine and cosine function. What is the y component of 315 degrees? What is the x component of 315 degrees?

$-\frac{\sqrt{2} }{2} /\frac{\sqrt{2} }{2} =-1$

7 0

3 years ago