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3 years ago

12

Solve 13 +4x = 3x - 15 for x

1 answer:

natka813 [3]3 years ago

4 0

Solving for x or x=-15

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A student answers 160 of 200 questions on an exam correctly. What percent of the questions did he answer correctly?

Alexandra [31]

Dive correct answers by total questions:

160/200 = 0.80

Multiply by 100 to get percent:

0.80 x 100 = 80%

5 0

3 years ago

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Root 3 cosec140° - sec140°=4<br>prove that<br><br>

Lorico [155]

Answer:

Step-by-step explanation:

We are to show that $\sqrt{3} cosec140^{0} - sec140^{0} = 4\\$

<u>Proof:</u>

From trigonometry identity;

$cosec \theta = \frac{1}{sin\theta} \\sec\theta = \frac{1}{cos\theta}$

$\sqrt{3} cosec140^{0} - sec140^{0} \\= \frac{\sqrt{3} }{sin140} - \frac{1}{cos140} \\= \frac{\sqrt{3}cos140-sin140 }{sin140cos140} \\$

From trigonometry, 2sinAcosA = Sin2A

$= \frac{\sqrt{3}cos140-sin140 }{sin140cos140} \\\\= \frac{\sqrt{3}cos140-sin140 }{sin280/2}\\= \frac{4(\sqrt{3}/2cos140-1/2sin140) }{2sin280}\\\\= \frac{4(\sqrt{3}/2cos140-1/2sin140) }{sin280}\\since sin420 = \sqrt{3}/2 \ and \ cos420 = 1/2 \\ then\\\frac{4(sin420cos140-cos420sin140) }{sin280}$

Also note that sin(B-C) = sinBcosC - cosBsinC

sin420cos140 - cos420sin140 = sin(420-140)

The resulting equation becomes;

$\frac{4(sin(420-140)) }{sin280}$

= $\frac{4sin280}{sin280}\\ = 4 \ Proved!$

3 0

3 years ago

A 14-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 9 fee

timama [110]

Answer:

10.7 feet

Step-by-step explanation:

The ladder, the ground and the wall form the shape of a right angled triangle as shown in the image below.

The hypotenuse of the triangle is 14 feet (length of ladder)

The base of the triangle is 9 feet long (the distance from the base of the ladder to the wall)

We need to find the height of the triangle. We can apply Pythagoras rule:

$hyp^2 = a^2 + b^2$

where hyp = hypotenuse

a = base of the triangle

b = height of the triangle

Therefore:

$14^2 = 9^2 + b^2\\\\196 = 81 + b^2\\\\b^2 = 196 - 81 = 115\\\\b = \sqrt{115} \\\\b = 10.7 feet$

The wall reaches 10.7 feet high.

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3 years ago

9 9/15 - 2 13/15 = <br> i have know idea what it is plz help

maria [59]

Step-by-step explanation:

plase see it my step work solution

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3 years ago

The ratio of children to teachers at preschool is 14:5. How many children are at the preschool if there are 30 teachers

elena55 [62]

If the ratio is 14 childen to every 5 teachers, and there are thirty teachers... there are 84 children. hope I could help!

6 0

2 years ago

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