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Misha Larkins [42]

3 years ago

10

If j and k are inversely proportional and j = 42 when k = 56, what is the value of j when k = 32? Express your answer as a decim

al rounded to the nearest tenth.

1 answer:

stellarik [79]3 years ago

4 0

Answer:

73.5

Step-by-step explanation:

In the attached file

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Plz help me identify the equations

Katarina [22]

if A= 4x^2

then x = sq root (A/4) = (sq root A)/2... 3rd option

7 0

3 years ago

Kayla drives her new car to work every day. It uses 1 3/5 gallons of gas for each round trip. How many round trips to work can K

omeli [17]

Answer:

10

Step-by-step explanation:

4 0

2 years ago

What is the measure of ZB?

brilliants [131]

Answer:

∠ B = 116°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180° , that is

∠ B + 28° + 36° = 180°

∠ B + 64° = 180° ( subtract 64° from both sides )

∠ B = 116°

5 0

2 years ago

Read 2 more answers

"A state legislator wishes to survey residents of her district to see what proportion of the registered voters are aware of her

aliya0001 [1]

Answer:

The correct answer to the following question will be "384".

Step-by-step explanation:

We are having,

$P(-0.05$

On solving, we get

⇒ $P(\frac{-0.05}{\sqrt{\frac{pq}{n}}}$

⇒ $\frac{0.05}{\sqrt{\frac{p(1-p)}{n}}} =1.96$

On applying cross-multiplication, we get

⇒ $0.05^2=1.96^2\times \frac{P(1-p)}{n}$

⇒ $0.05^2n=1.96^2-1.96^2p^2$

⇒ $1.96^2p^2-1.96^2p+0.05^2n=0$ ...(equation 1)

When "p" seems to be the population proportion, (equation 1) approach, which is special

∴ $b^2-4ac=0$

On putting the values in the above expression, we get

⇒ $(1.96)^4-4\times 0.05^2\times 1.96^2n=0$

⇒ $1.98^2-4\times 0.05^2n=0$

⇒ $n=\frac{1.96^2}{4\times 0.05^2}$

⇒ $n=384.16=384$

7 0

3 years ago

Can you help me to solve this

stealth61 [152]

Answer:

$\text{Triangle 1:}\\\\x=30\sqrt{2},\\\\\text{Triangle 2:}\\x\approx 36.18,\\?\approx12.37$

Step-by-step explanation:

*Notes (clarified by the person who asked this question):

-The triangle on the right has a right angle (angle that appears to be a right angle is a right angle)

-The bottom side of the right triangle is marked with a question mark (?)

<u>Triangle 1 (triangle on left):</u>

Special triangles:

In all 45-45-90 triangles, the ratio of the sides is $x:x:x\sqrt{2}$ , where $x\sqrt{2}$ is the hypotenuse of the triangle. Since one of the legs is marked as $30$ , the hypotenuse must be $\boxed{30\sqrt{2}}$

It's also possible to use a variety of trigonometry to solve this problem. Basic trig for right triangles is applicable and may be the simplest:

$\cos 45^{\circ}=\frac{30}{x},\\x=\frac{30}{\cos 45^{\circ}}=\frac{30}{\frac{\sqrt{2}}{2}}=30\cdot \frac{2}{\sqrt{2}}=\frac{60}{\sqrt{2}}=\frac{60\cdot\sqrt{2}}{\sqrt{2}\cdot \sqrt{2}}=\frac{60\sqrt{2}}{2}=\boxed{30\sqrt{2}}\\$

<u>Triangle 2 (triangle on right):</u>

We can use basic trig for right triangles to set up the following equations:

$\cos 20^{\circ}=\frac{34}{x},\\x=\frac{34}{\cos 20^{\circ}}\approx \boxed{36.18}$ ,

$\tan 20^{\circ}=\frac{?}{34},\\?=34\tan 20^{\circ}\approx \boxed{12.37}$

We can verify these answers using the Pythagorean theorem. The Pythagorean theorem states that in all right triangles, the following must be true:

$a^2+b^2=c^2$ , where $c$ is the hypotenuse of the triangle and $a$ and $b$ are two legs of the triangle.

Verify $34^2+(34\tan20^{\circ})^2=\left(\frac{34}{\cos20^{\circ}}\right)^2\:\checkmark$

3 0

3 years ago