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schepotkina [342]
2 years ago
12

In a standard television set, the screen height is 0.75 times the screen width. If a television set measures 34 inches along the

diagonal, what is the screen width?
Mathematics
1 answer:
S_A_V [24]2 years ago
3 0
We can solve this by using the  P<span>ythagorean theorem which is below:

a^2 + b^2 = c^2

Or we can say
</span>w^2 + h^2 = d^2
<span>w = widht
h = height
d = diagonal measure


With that said, we know the height is .75 times the width so .75w. We also know d = 34, which is our diagonal measure.
w = don't know yet but need to find
h = .75w
d = 34
Now lets plugin the information we know into our equation

</span>w^2 + h^2 = d^2
w^2 + (.75w)^2 = 34^2
Now lets to the math
w^2 + (.75w)^2 = 34^2
w^2 + (.75w)^2 = 1156
w^2 + .5625w^2 = 1156
Combine like terms
w^2 + .5625w^2 = 1156
1.5625w^2 = 1156
Divide both sides of the equal sign by 1.5625
\frac{1.5625w^2}{1.5625} = \frac{1156}{1.5625}
w^2 = 739.84
Now take the square root on both sides of the equal sign
\sqrt{w^2} = \sqrt{739.84}
w = 27.2

So the width is 27.2
We can check this by putting 27.2 back into our original equation
w^2 + (.75w)^2 = 34^2
27.2^2 + (.75\times 27.2)^2 = 34^2



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The sphere area of a sphere is 200.96 square centimeters. What is the approximate volume of the sphere? Use 3.14 for pi. Round y
julsineya [31]

We are given

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so, we can use surface area formula

S=4\pi r^2

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200.96=4\pi r^2

we can solve for r

r=3.9989cm

now, we can find volume

V=\frac{4}{3} \pi r^3

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V=\frac{4}{3} \pi (3.9989)^3

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V=267.86cm^3.............Answer

7 0
3 years ago
Find the value of x such that 365 based seven + 43 based x = 217 based 10.
Pepsi [2]

We need to find the base x in the following equation:

365_7+43_x=217_{10}

First, lets convert 365 from base 7 to base 10. This is given by

365_7=3\times7^2+6\times7^1+5\times7^0

where the upperindex denotes the position of eah number. This gives

\begin{gathered} 365_7=3\times49+6\times7+5\times1 \\ 365_7=147+42+5 \\ 365_7=194_{10} \end{gathered}

that is, 365 based 7 is equal to 194 bases 10.

Now, lets do the same for 43 based x. Lets convert 43 based x to base 10:

43_x=4\times x^1+3\times x^0

where again, the superindex 0 and 1 denote the position 0 and 1 in the number 43. This gives

43_x=(4x+3)_{10}

Now, we have all number in base 10. Then, our first equation can be written in base 10 as

194_{10}+(4x+3)_{10}=217_{10}

For simplicity, we can omit the 10 and get

194+4x+3=217

so, we can solve this equation for x. By combining similar terms. we have

197+4x=217

and by moving 197 to the right hand side, we obtain

\begin{gathered} 4x=217-197 \\ 4x=20 \end{gathered}

Finally, we get

\begin{gathered} x=\frac{20}{4} \\ x=5 \end{gathered}

Therefore, the solution is x=5

8 0
1 year ago
A news service conducted a survey of 1026 adults ages 18 years or older in a certain​ country, August 31minus−September ​2, 2015
Musya8 [376]

Answer:

B. To determine the percent of adults in the country who believe the federal government wastes 51 cents or more of every dollar.

Step-by-step explanation:

Given that:

sample size = 1026

sample proportion = 0.36

Margin of error = 55% = 0.55

Confidence interval level = 99%

The purpose of this question is to determine the research objective:

The research objectives indicate the intention of the study, the objectives,\ or the main idea. This main idea arises from a need (the research problem) and refined into specific questions (i.e. the research questions). From, the given information, the research objective is to determine the percent of adults in the country who believe the federal government wastes 51 cents or more of every dollar.

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3 years ago
Two lines intersect at a point, forming ​ ∠1 , ∠2 , ∠3 , and​ ​ ∠4 ​ .
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The answer is:  [B]:  " 60° " .
________________________________________
Because at whatever location,  <span>∠2 and ∠4 are vertical angles;
</span>
and all vertical angles have equal measurements.

Given:   m∠1  is 120°, and ∠1 is supplementary to ∠2 ;

then m∠1 + m∠2 = 180° .

So, m∠2 = (180 - 120)° = 60° .

As aforementioned:

m∠4 = m∠2 = 60° ;  which is:  Answer choice:  [B]:  " 60° " .
___________________________________________________
3 0
3 years ago
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