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3 years ago

Solve the inequality. -4x + 15 < -21

Mathematics

1 answer:

Dmitriy789 [7]3 years ago

6 0

Answer:

x>9

Step-by-step explanation:

-4x + 15 < -21

Subtract 15 from each side

-4x + 15-15 < -21-15

-4x < -36

Divide each side by -4, remembering to flip the inequality

-4x/-4> -36/-4

x >9

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Point G is the centroid of the right △ABC with m∠C=90° and m∠B=30°. Find AG if CG=4 ft.

o-na [289]

Answer: $\text{Length of AG=}\frac{2\sqrt{63}}{3}$

Explanation:

Please follow the diagram in attachment.

As we know median from vertex C to hypotenuse is CM

$\therefore CM=\frac{1}{2}AB$

We are given length of CG=4

Median divide by centroid 2:1

CG:GM=2:1

Where, CG=4

$\therefore GM=2$ ft

Length of CM=4+2= 6 ft

$\therefore CM=\frac{1}{2}AB\Rightarrow AB=12$

In $\triangle ABC, \angle C=90^0$

Using trigonometry ratio identities

$AC=AB\sin 30^0\Rightarrow AC=6$ ft

$BC=AB\cos 30^0\Rightarrow BC=6\sqrt{3}$ ft

$CN=\frac{1}{2}BC\Rightarrow CN=3\sqrt{3}$ ft

In $\triangle CAN, \angle C=90^0$

Using pythagoreous theorem

$AN=\sqrt{6^2+(3\sqrt{3})^2\Rightarrow \sqrt{63}$

Length of AG=2/3 AN

$\text{Length of AG=}\frac{2\sqrt{63}}{3}$ ft

5 0

3 years ago

Products of equal value totaling $480 are sold to an audience of an unknown amount of people. the entrance fee is $10 per person

Sholpan [36]

Y = $\frac{10x+480}{x}$

This is because the total cost is 10x + 480 and then that needs to be divided by the amount of people.

8 0

3 years ago

Mr. Chen filled a wading pool with 20 gallons of water. How many pints of water did he put in a pool

eduard

Answer:

160 pints

Step-by-step explanation:

Every 1 gallon = 8 pints.

20x8=160

8 0

3 years ago

Read 2 more answers

Factor completely p^2-13p+42

ira [324]

Factoring the expression would look like this :
(p - 7) (p - 6)

5 0

3 years ago

Please help me ASAP!

Snezhnost [94]

Answer:

y = 6.5

Step-by-step explanation:

When triangles are similar, we can set up a proportion to compare the sides. I will have the "left" side on the bottom of the fractions, and the side I am solving for on the top.

$\frac{y}{6} =\frac{13}{12}$

[Cross multiply]

12y = 78

y = 6.5

Have a nice day!

I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.

- Heather

7 0

2 years ago