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3 years ago

In ΔOPQ, m∠O = (3x+12)^{\circ}(3x+12)

Mathematics

1 answer:

zaharov [31]3 years ago

6 0

Answer:

The measure of angle P is 80 degrees

Step-by-step explanation:

we know that

The sum of the interior angles in a triangle must be equal to 180 degrees

In this problem we have that

$m\angle O+m\angle P+m\angle Q=180^o$

substitute the given values

$(3x+12)^o+(4x+4)^o+(x+12)^o=180^o$

solve for x

$(8x+28)=180$

$8x=180-28$

$8x=152$

$x=19$

<em>Find the measure of angle P</em>

$m\angle P=(4x+4)^o$

substitute the value of x

$m\angle P=(4(19)+4)=80^o$

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Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three op

lutik1710 [3]

The statement that is true about the quadratic function is (b) the graph of the function is a parabola.

<h3>How to determine the true statements?</h3>

The quadratic function is given as

f(x) = x2 – 5x + 12

Rewrite as

f(x) = x² – 5x + 12

All quadratic functions are parabola

This means that option (b) is true

Set x = -10 to calculate f(-10)

So, we have

f(-10) = (-10)² – 5(-10) + 12

Evaluate

f(-10) = 162

This means that option (a) is false

Set x = 20 to calculate f(20)

So, we have

f(20) = (20)² – 5(20) + 12

Evaluate

f(20) = 312

This means that option (d) is false

Set x = 0 to calculate f(0)

So, we have

f(0) = (0)² – 5(2) + 12

Evaluate

f(0) = 12

This means that option (e) is false

The leading coefficient in f(x) = x² – 5x + 12 is positive

Graphs with positive leading coefficient opens up

This means that option (c) is false

Hence, the true statement about the quadratic function is (b)

Read more about quadratic functions at

brainly.com/question/1214333

#SPJ1

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1 year ago

Which of the following best describes the expression 6(y + 3)?

Crank

Answer:

The product of a constant factor of six and a factor with the sum of two terms.

Step-by-step explanation:

The constant factor is 6, and the sum of two terms is y + 3.

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3 years ago

Priya brought these items at the grocery store

Soloha48 [4]

That’s so cool I love going grocery shopping

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2 years ago

Show that 5x^2 + 2x - 3 < 0 can be written in the form | x + 1/5 | < 4/5

Sliva [168]

Step-by-step explanation:

First let solve the inequality

$5 {x}^{2} + 2x - 3 < 0$

Factor by grouping

$5 {x}^{2} + 5x - 3x - 3 < 0$

$5x(x + 1) - 3(x + 1)$

So the factor are

$(5x - 3)(x + 1)$

So the factor are

$x = \frac{3}{5}$

and

$x = - 1$

Solutions to a quadratic can be represented by a absolute value equation because remeber quadratics

creates 2 roots and/or double roots.

The inequality

$|x - b| < c$

works as

b is the midpoint between 2 roots. And c is the

$|x + b| = c$

We know that the midpoint between both roots is-1/5.

$|x - ( - \frac{1}{5} )| < c$

$|x + \frac{1}{5} | < c$

Let use roots 3/5

$| \frac{3}{5} + \frac{1}{5} | = \frac{4}{5}$

-1 works as well.

$| - 1 + \frac{1}{5} | = | - \frac{4}{5} | = \frac{4}{5}$

So the absolute value equation is

$|x + \frac{1}{5} | < \frac{4}{5}$

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3 years ago

The square footage of a house is 1200 square feet. What type of data is this?

DIA [1.3K]

The answer for the question shown above is: <span>The square footage of a house that is 1200 square feet is the "</span>Area".

The explanation is shown above:

1- By definition, the area is the measure of a two-dimensional surface.Its units can be written in m^2, ft^2, in^2...However, in the International System of Units is m^2.

2. This is very useful when you want to know the surface of a house. If it is a rectangular house, you can calculate the area as below:

A=LxW

Where L is the length and W is the width

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