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3 years ago

Use angle ADB and angle EDF to write and solve an equation to find the value of x

Mathematics

2 answers:

-Dominant- [34]3 years ago

7 0

Answer:

x = 11

Step-by-step explanation:

Since they are vertical angles, they are congruent to each other and therefore we can set them equal to each other to solve.

4x + 11 = 5x

x = 11

tangare [24]3 years ago

7 0

Answer:

4x+11=5x

x = 11

Step-by-step explanation:

Set angle ADB an angle EDF equal to each other because they are vertical angles.

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Carmine buys 2 plates for $4 each. He also buys 12 bowls. Each bowl costs twice as much as each plate. The store is having a sal

Tasya [4]

Answer

2p+12b=12

Step-by step explanation

I used p for plates and b for bowls\

2p+12b=4+(4*2)

2p+12b=12

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3 years ago

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What is the volume of a rectangular prism with a 4 inch base and a height of 4?

timofeeve [1]

V=lwh
V= (4)(4)(4)
V= 64 in cubed
$v = lwh$

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3 years ago

There are 5 questions on a multiple choice exam, each with five possible answers. If a student guesses on all five questions, wh

Mrac [35]

Answer:

$20.5\%$

Step-by-step explanation:

Let's write out a case for two specific questions being correct and the rest being incorrect:

$\frac{1}{5}\cdot \frac{1}{5}\cdot \frac{4}{5}\cdot \frac{4}{5}\cdot \frac{4}{5}$ ,

The $\frac{1}{5}$ represents the chances of getting the question correct, as there are 5 answers and 1 correct answer choice.

The $\frac{4}{5}$ represents the chances of getting the question incorrect, as there are 5 answers and 4 incorrect answer choices.

The equation above does show the student getting two answers correct and three answers incorrect, but it only shows one possible case of doing so.

We can choose any two of the five questions to be the ones the student gets correct. Therefore, we need to multiply this equation by the number ways we can choose 2 from 5 (order doesn't matter): $\binom{5}{2}=10$ .

Therefore, the probability the student gets two questions correct is:

$\frac{1}{5}\cdot \frac{1}{5}\cdot \frac{4}{5}\cdot \frac{4}{5}\cdot \frac{4}{5}\cdot \binom{5}{2}=\frac{1}{5}\cdot \frac{1}{5}\cdot \frac{4}{5}\cdot \frac{4}{5}\cdot \frac{4}{5}\cdot 10=0.2048\approx \boxed{20.5\%}$

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3 years ago

(5x^4y^3)^2 Simplify

Allisa [31]

This simplifies to 25x^8 16y^6.

You square everything in this probelm to get rid of the parentheses.

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3 years ago

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Find the exact value of cot(15degrees) using half angle formulas?

liubo4ka [24]

Double angle (or half angle, depending how you look at it) identities:

$\cos^2\dfrac x2=\dfrac{1+\cos x}2$

$\sin^2\dfrac x2=\dfrac{1-\cos x}2$

$\implies\cot^2\dfrac x2=\dfrac{\cos^2\frac x2}{\sin^2\frac x2}=\dfrac{1+\cos x}{1-\cos x}$

So we have

$\cot^215^\circ=\dfrac{1+\cos30^\circ}{1-\cos30^\circ}=\dfrac{1+\frac{\sqrt3}2}{1-\frac{\sqrt3}2}$

$\implies\cot^215^\circ=7+4\sqrt3$

$\implies\cot15^\circ=\sqrt{7+4\sqrt3}=2+\sqrt3$

Note that when taking the square root, we should take into account that that could yield two possible solutions, but we know $\cos15^\circ>0$ and $\sin15^\circ>0$ , so it's also the case that $\cot15^\circ>0$ .

Also, the reason we have equality in the last step can be explained like so:

$7+4\sqrt3=4+4\sqrt3+3=4+4\sqrt3+(\sqrt3)^2=(2+\sqrt3)^2$

(not unlike the process used to complete the square)

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3 years ago

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