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3 years ago

Solve each inequality and graph it’s solution

Mathematics

1 answer:

asambeis [7]3 years ago

7 0

$13 < x+12\leq20\ \ \ \ |-12\\\\1 < x\leq8\to x\in\left(1,\ 8\right>\\---------------------\\33\geq5+7x\geq12\ \ \ \ |-5\\\\28\geq7x\geq17\ \ \ \ |:7\\\\4\geq x\geq\dfrac{17}{7}\\\\4\geq x\geq2\dfrac{3}{7}$

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Rewrite 3 1 over 5<br> as a mixed number?

Rufina [12.5K]

Answer:

3 1/5

Step-by-step explanation:

"1 over 5" means 1/5

3 "1 over 5" would then translate to: 3 1/5

6 0

4 years ago

Read 2 more answers

Find the missing side lengths. Leave your answers as radicals in simplest form.

tankabanditka [31]

Answer:

$x = \frac{7\sqrt{6}{3}$

$y = \frac{7\sqrt{6}}{3}$

Step-by-step explanation:

Reference angle = 60°

Opposite = $\frac{7\sqrt{2}}{2}$

Hypotenuse = x

Adjacent = y

✔️To find x, apply the trigonometric function SOH:

Sin 60° = Opp/Hyp

$sin 60° = \frac{\frac{7\sqrt{2}}{2}}{x}$

$\frac{\sqrt{3}}{2} = \frac{\frac{7\sqrt{2}}{2}}{x}$ (sin 60 = √3/2)

$\frac{\sqrt{3}}{2} = \frac{7\sqrt{2}}{2}*\frac{1}{x}$

$\frac{\sqrt{3}}{2} = \frac{7\sqrt{2}}{2x}$

Cross multiply

$\sqrt{3}*2x = 7\sqrt{2}*2$

$2\sqrt{3}*x = 14\sqrt{2}$

Divide both sides by 2

$\sqrt{3}*x = 7\sqrt{2}$

Divide both sides by √3

$x = \frac{7\sqrt{2}}{\sqrt{3}}$

Rationalize

$x = \frac{7\sqrt{2}*\sqrt{3}}{\sqrt{3}*\sqrt{3}}$

$x = \frac{7\sqrt{6}{3}$

✔️To find y, apply the trigonometric function TOA:

Tan 60° = Opp/Adjacent

$Tan 60° = \frac{\frac{7\sqrt{2}}{2}}{y}$

$\sqrt{3} = \frac{\frac{7\sqrt{2}}{2}}{y}$ (tan 60 = √3)

$\sqrt{3} = \frac{7\sqrt{2}}{2}*\frac{1}{y}$

$\sqrt{3} = \frac{7\sqrt{2}}{2y}$

Cross multiply

$\sqrt{3}*2y = 7\sqrt{2}$

$2\sqrt{3}*y = 7\sqrt{2}$

Divide both sides by √3

$y = \frac{7\sqrt{2}}{\sqrt{3}}$

Rationalize

$y = \frac{7\sqrt{2}*\sqrt{3}}{\sqrt{3}*\sqrt{3}}$

$y = \frac{7\sqrt{6}}{3}$

4 0

3 years ago

Which pair of expressions is equivalent? A. f + g + f + g and 2(f +g) B. 2f + 4g – f – g and 2(f + g) C. 0.5f + g + 1.5f – g and

Ivan

Answer:

disdifisdifd

Step-by-step explanation:

4 0

3 years ago

4 plates and 3 cups cost 20.70 dollars. 5 plates and 4 cups cost 26.40 dollars . each plates cost the same amount as the other p

Basile [38]

Here, we need to construct 2 linear equation.
Let x be the plate and y be the cup.
1) 4x + 3y = 20.70
2) 5x + 4y = 26.40

From equation 1, we solve for y.
3y = 20.70 - 4x
y = (20.70 - 4x) / 3

Substitute into equation 2.
5x + 4((20.70 - 4x) / 3) = 26.40
5x + 27.60 - 5.33x = 26.40
-0.33x = 26.40 - 27.60
-0.33x = -1.2
x = 3.64

We already get value of x. Now, calculate for value of y.
y = (20.70 - 4x) / 3
y = (20.70 - 4(3.64)) / 3
y = 2.05

The cost for 1 plate is 3.64 dollars and 1 cup is 2.05 dollars.

7 0

3 years ago

Given the speeds of each runner below, determine who runs the fastest? ron runs 15 feet per second. Brooke runs 85 feet in 9 sec

gavmur [86]

Ron runs the fastest

Brooke runs 9.4 feel per second

Adam runs 10.4 feet per second

And if you times 15 * 60 you get 900

And if you times 15 * 9 which is 135 which only proves Ron’s the fastest

4 0

3 years ago