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3 years ago

If x is any real number, then x2 ≥ 1.

Mathematics

2 answers:

erastova [34]3 years ago

6 0

Answer:

x≤−1 or x≥1

Step-by-step explanation:

babymother [125]3 years ago

3 0

The answer is D x=1.5

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Find the measures of the angles of the triangle whose vertices are A = (-3,0) , B = (1,3) , and C = (1,-3).A.) The measure of ∠A

alekssr [168]

Answer:

$\theta_{CAB}=128.316$

$\theta_{ABC}=25.842$

$\theta_{BCA}=25.842$

Step-by-step explanation:

A = (-3,0) , B = (1,3) , and C = (1,-3)

We're going to use the distance formula to find the length of the sides:

$r= \sqrt{(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2}$

$AB= \sqrt{(-3-1)^2+(0-3)^2}=5$

$BC= \sqrt{(1-1)^2+(3-(-3))^2}=9$

$CA= \sqrt{(1-(-3))^2+(-3-0)^2}=5$

we can use the cosine law to find the angle:

it is to be noted that:

the angle CAB is opposite to the BC.

the angle ABC is opposite to the AC.

the angle BCA is opposite to the AB.

to find the CAB, we'll use:

$BC^2 = AB^2+CA^2-(AB)(CA)\cos{\theta_{CAB}}$

$\dfrac{BC^2-(AB^2+CA^2)}{-2(AB)(CA)} =\cos{\theta_{CAB}}$

$\cos{\theta_{CAB}}=\dfrac{9^2-(5^2+5^2)}{-2(5)(5)}$

$\theta_{CAB}=\arccos{-\dfrac{0.62}}$

$\theta_{CAB}=128.316$

Although we can use the same cosine law to find the other angles. but we can use sine law now too since we have one angle!

To find the angle ABC

$\dfrac{\sin{\theta_{ABC}}}{AC}=\dfrac{\sin{CAB}}{BC}$

$\sin{\theta_{ABC}}=AC\left(\dfrac{\sin{CAB}}{BC}\right)$

$\sin{\theta_{ABC}}=5\left(\dfrac{\sin{128.316}}{9}\right)$

$\theta_{ABC}=\arcsin{0.4359}\right)$

$\theta_{ABC}=25.842$

finally, we've seen that the triangle has two equal sides, AB = CA, this is an isosceles triangle. hence the angles ABC and BCA would also be the same.

$\theta_{BCA}=25.842$

this can also be checked using the fact the sum of all angles inside a triangle is 180

$\theta_{ABC}+\theta_{BCA}+\theta_{CAB}=180$

$25.842+128.316+25.842$

$180$

6 0

3 years ago

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A realtor is decorating some homes for sale, putting a certain number of decorative pillows on each twin bed and a certain numbe

VikaD [51]

The number of decorative pillows did the realtor arrange on each twin bed and queen bed is 6 and 9 respectively.

<h3>Simultaneous equation</h3>

let

Number of decorative pillows for twin bed = x
Number of decorative pillows for queen bed = y

x + y = 15

2x + y = 21

From equation (1)

x = 15 - y

Substitute x = 15 - y into (2)

2x + y = 21

2(15 - y) + y = 21

30 - 2y + y = 21

- 2y + y = 21 - 30

-y = -9

y = 9

Substitute y = 9 into

x + y = 15

x + 9 = 15

x = 15 - 9

x = 6

Learn more about simultaneous equation:

brainly.com/question/16863577

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2 years ago

A recent study reported that 40% of community college students in the U.S. Receive federal loans to pay for college tuition and

sweet [91]

Answer:

How are you asking questions but no pictures.

Step-by-step explanation:

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3 years ago

Rectangle BBB is shown below. Nadia drew a scaled version of Rectangle BBB using a scale factor of \dfrac15

Basile [38]

Answer:

Step-by-step explanation:

5 / 1/5 and 10 / 1/5

6 0

4 years ago

Look help please please

mr Goodwill [35]

Answer: the data set has a range of 100

Step-by-step explanation: it has a set of 100

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3 years ago

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