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3 years ago

Solve the following linear inequality: -3 ≤ 2x + 5 /3 < 6

1 answer:

5 0

$-3\leq\dfrac{2x+5}{3} < 6\ \ \ \ \ |\cdot3\\\\-9\leq2x+5 < 18\ \ \ \ |-5\\\\-14\leq2x < 13\ \ \ \ \ |:2\\\\-7\leq x < \dfrac{13}{2}\to x\in\left[-7,\ \dfrac{13}{2}\right)$

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Please help!!!!!!!!!!!!!

aivan3 [116]

Answers:

Step-by-step explanation:

We must simplify each option to see if they are equivalent to $-\frac{3}{8}$ .

Lets try A.

$-\frac{6}{16}$ can be simplified to $-\frac{3}{8}$ by dividing both the numerator and denominator by 3.

$-\frac{6}{16}$ ÷ $\frac{3}{3} = -\frac{3}{8}$

A is correct!

Lets try B

$\frac{12}{32}$ simplifies to $\frac{3}{8}$ . However, because this answer is not negative, it is not equivalent.

Lets try C

There is a negative in the numerator, making this fraction negative. So yes, $\frac{-3}{8} = -\frac{3}{8}$ .

Bonus Info: If there was a negative in both the numerator and denominator, the two negatives would cancel eachother out, making the fraction positive

C is correct!

Lastly, Lets try D

There is a negative in the denominator, so this fraction is negative. $\frac{9}{-24}$ can be simplified by dividing by 3 to $-\frac{3}{8}$ .

$\frac{9}{-24}$ ÷3 = $-\frac{3}{8}$

D is correct!

Hope this helped you!~

6 0

4 years ago

Find the cosine of angle B.

Alexandra [31]

$\boxed { \text {Cosine Rule : } a^2 = b^2 + c^2 - 2bc \cos(A) }$

9² = 12² + 15² - 2 (12) (15) cos (B)

81 = 144 + 225 - 360 cos(B)

81 = 369 - 360 cos (B)

360 cos (B) = 369 - 81

360 cos (B) = 288

cos (B) = 0.8

Answer: Cosine B = 0.8

$\boxed { \text {Cosine Rule : } a^2 = b^2 + c^2 - 2bc \cos(A) }$

12² = 15² + 9² - 2 (15)(9) cos (A)

144 = 225 + 81 - 270 Cos A

144 = 306 - 270 Cos A

270 Cos A = 162

Cos A = 3/5 or 0.6

Answer: Cosine Angle A = 3/5

4 0

3 years ago

Simplify the expression please

Reika [66]

$\bf -2(3+2i)+2(4-5i)\implies 
\\\\\\
-6+8-10i-4i\implies \boxed{2-14i}$

3 0

4 years ago

A point on the rim of a wheel has a linear speed of 33 cm/s. If the radius of the wheel is 50 cm, what is the angular speed of t

Zigmanuir [339]

Answer:

The angular speed of the wheel in radians per second is 0.66.

Step-by-step explanation:

Recall the following statement:

A linear speed (v) is given by,

$v=\omega \times r$ ...... (1)

Here, $\omega$ represents the angular speed of the wheel and r represents the radius of the wheel.

From the given information:

Linear speed (v) = 33 cm/s

Radius of the wheel (r) = 50 cm

Now to find the angular speed in radian per second.

$33 =50 \times \omega$

Divide both sides by 50.

$0.66 rad/sec= \omega$

Hence, the angular speed of the wheel in radians per second is 0.66.

4 0

3 years ago

Jenny is making a tie-dyed shirts for her class with her school colors

tia_tia [17]

Answer:

2 ounces of yellow, six of blue.

Step-by-step explanation:

If you teacher wants you to simplify put: yellow: 1, blue: 3

If not, put: yellow: 2, blue: 6

4 0

3 years ago