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algol [13]
3 years ago
10

Solve and graph the absolute value inequality: |4x + 1| ≤ 5. a. number line with closed dots on −1.5 and 1 with shading going in

the opposite directions.
b. number line with open dots on −1.5 and 1 with shading in between. c. number line with closed dots on −1 and 1 with shading in between. d. number line with closed dots on −1.5 and 1 with shading in between.
Mathematics
1 answer:
Afina-wow [57]3 years ago
7 0
4x + 1 <= 5               ;  x = 1

4x +1 >=  -5              ;  x = - 1.5

Now we know that x is between -1.5 and 1, so you should shade between -1.5 and 1. The circle will be closed since the equality is =< and =>

The answer is option D

Hope this helps





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A rectangle is 4 ft long and 2 ft wide. find its area in square inches.​
denis-greek [22]

\text{Area of rectangle} = \text{length} \times \text{width}\\\\~~~~~~~~~~~~~~~~~~~~~~~=4 ~\text{ft}~\times ~2 ~\text{ft}\\\\~~~~~~~~~~~~~~~~~~~~~~~=8~ \text{ft}^2\\\\~~~~~~~~~~~~~~~~~~~~~~~=1152~\text{in}^2

8 0
2 years ago
4.) What is the exact value of sinθ when θ lies in Quadrant II and cosθ=−513
dimaraw [331]

Answer:

Part 4) sin(\theta)=\frac{12}{13}

Part 10) The angle of elevation is 40.36\°

Part 11) The angle of depression is 78.61\°

Part 12) arcsin(0.5)=30\°  or arcsin(0.5)=150\°

Part 13) -45\°  or 225\°

Step-by-step explanation:

Part 4) we have that

cos(\theta)=-\frac{5}{13}

The angle theta lies in Quadrant II

so

The sine of angle theta is positive

Remember that

sin^{2}(\theta)+ cos^{2}(\theta)=1

substitute the given value

sin^{2}(\theta)+(-\frac{5}{13})^{2}=1

sin^{2}(\theta)+(\frac{25}{169})=1

sin^{2}(\theta)=1-(\frac{25}{169})  

sin^{2}(\theta)=(\frac{144}{169})

sin(\theta)=\frac{12}{13}

Part 10)

Let

\theta ----> angle of elevation

we know that

tan(\theta)=\frac{85}{100} ----> opposite side angle theta divided by adjacent side angle theta

\theta=arctan(\frac{85}{100})=40.36\°

Part 11)

Let

\theta ----> angle of depression

we know that

sin(\theta)=\frac{5,389-2,405}{3,044} ----> opposite side angle theta divided by hypotenuse

sin(\theta)=\frac{2,984}{3,044}

\theta=arcsin(\frac{2,984}{3,044})=78.61\°

Part 12) What is the exact value of arcsin(0.5)?

Remember that

sin(30\°)=0.5

therefore

arcsin(0.5) -----> has two solutions

arcsin(0.5)=30\° ----> I Quadrant

or

arcsin(0.5)=180\°-30\°=150\° ----> II Quadrant

Part 13) What is the exact value of arcsin(-\frac{\sqrt{2}}{2})

The sine is negative

so

The angle lies in Quadrant III or Quadrant IV

Remember that

sin(45\°)=\frac{\sqrt{2}}{2}

therefore

arcsin(-\frac{\sqrt{2}}{2}) ----> has two solutions

arcsin(-\frac{\sqrt{2}}{2})=-45\° ----> IV Quadrant

or

arcsin(-\frac{\sqrt{2}}{2})=180\°+45\°=225\° ----> III Quadrant

5 0
3 years ago
What is a ratio comparing two quantities with different kinds of units
Andrews [41]
<em>A ratio camparing two quantities with different kinds of units is a ratio that tells the rate of change of one variable with a change in other variable.</em>
3 0
3 years ago
find the area of a circke with a radius of 9 mm. round to the nearest tenth. use 3.15 or 22/7 for Pi.​
GREYUIT [131]

Answer:

254.3 mm^2

Step-by-step explanation:

Area of a circle: A = π*r^2

π (pi) = 3.14

r (radius) = 9 mm

Substitute 3.14 for pi and 9 for radius:

A = π*r^2

A = 3.14*9^2

A = 3.14*81

A = 254.34 mm^2

Round to the nearest tenth:

254.34 ==> 254.3

Therefore, our final answer is 254.3 mm^2

Hope this helps!

6 0
2 years ago
5/8 + 3/4 divided by -2/3 - 5/6
exis [7]
-1.5 should be your answer.
if wrong I apologize.
5 0
3 years ago
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