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Orlov [11]
3 years ago
8

What is the value of x?

Mathematics
1 answer:
Andrew [12]3 years ago
7 0
<h3>Answer:</h3>

x = 25

<h3>Solution:</h3>

\frac{40}{40+24} = \frac{x}{x +15} \\ \frac{40}{64} = \frac{x}{x +15} \\ \frac{5}{8} = \frac{x}{x +15} \\ 5(x +15) = 8x \\ 5x +75 = 8x \\ 75 = 3x \\ 25 = x

<h3>Explanation:</h3>

Angle BDR is congruent to angle QDC because they share common angles. Angles BRD and QCD are congruent because lines BR and QC are <em>parallel</em> and line DR intersecting them creates <em>two corresponding angles</em>, BRD and QCD. Because of the reasons I mentioned, Triangles DBR and DQC are similar by Angle Angle Similarity Postulate and because these two triangles are similar they must share the same scaling factor of corresponding sides (example: \frac{DQ}{DB}\\). So \frac{DQ}{DB} = \frac{DC}{DR}\\.

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Last year, a popular song was downloaded 8.71 X 10^7 times. Write the number of
denis23 [38]

Answer:

Actually it would be 87,100,000 in standard form.

Step-by-step explanation:

3 0
3 years ago
during a softball game kay hit a fly ball the function f(x) = -16t^2 + 64t + 4 describes the height of the softball in feet. mak
STatiana [176]
<h2>Hello!</h2>

The graph is attached.

To graph a parabola we need to know the following:

- If the parabola is open upwards or downwards

- They axis intercepts (if they exist)

- The vertex position (point)

We are given the function:

f(t)=-16t^{2}+64t+4

Where,

a=-16\\b=64\\c=4

For this case, the coefficient of the quadratic term (a) is negative, it means that the parabola opens downwards.

Finding the axis interception points:

Making the function equal to 0, we can find the x-axis (t) intercepts, but since the equation is a function of the time, we will only consider the positive values, so:

f(t)=-16t^{2}+64t+4\\0=-16t^{2}+64t+4\\-16t^{2}+64t+4=0

Using the quadratic equation:

\frac{-b+-\sqrt{b^{2}-4ac } }{2a}=\frac{-64+-\sqrt{64^{2}-4*-16*4} }{2*-16}\\\\\frac{-64+-\sqrt{64^{2}-4*-16*4} }{2*-16}=\frac{-64+-\sqrt{4096+256} }{-32}\\\\\frac{-64+-\sqrt{4096+256} }{-32}=\frac{-64+-(65.96) }{-32}\\\\t1=\frac{-64+(65.96) }{-32}=-0.06\\\\t2=\frac{-64-(65.96) }{-32}=4.0615

So, at t=4.0615 the height of the softball will be 0.

Since we will work only with positive values of "x", since we are working with a function of time:

Let's start from "t" equals to 0 to "t" equals to 4.0615.

So, evaluating we have:

f(0)=-16(0)^{2}+64(0)+4=4\\\\f(1)=-16(1)^{2}+64(1)+4=52\\\\f(2)=-16(2)^{2}+64(2)+4=68\\\\f(3)=-16(3)^{2}+64(3)+4=52\\\\f(4.061)=-16(4.0615)^{2}+64(4.0615)+4=0.0034=0

Finally, we can conclude that:

- The softball reach its maximum height at t equals to 2. (68 feet)

- The softball hits the ground at t equals to 4.0615 (0 feet)

- At t equals to 0, the height of the softball is equal to 4 feet.

See the attached image for the graphic.

Have a nice day!

3 0
3 years ago
Examine the diagram.
Tanya [424]

Answer:

What is the sum of the remote interior angles? - 95 degrees

What is the measure of angle A?

m angle A= 85

What is the measure of Angle B?

m angle B = 95

4 0
3 years ago
Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type.
Vinvika [58]

Answer:

The point estimate for population mean is 8.129 Mpa.

Step-by-step explanation:

We are given the following in the question:

Data on flexural strength(MPa) for concrete beams of a certain type:

11.8, 7.7, 6.5, 6.8, 9.7, 6.8, 7.3, 7.9, 9.7, 8.7, 8.1, 8.5, 6.3, 7.0, 7.3, 7.4, 5.3, 9.0, 8.1, 11.3, 6.3, 7.2, 7.7, 7.8, 11.6, 10.7, 7.0

a) Point estimate of the mean value of strength for the conceptual population of all beams manufactured

We use the sample mean, \bar{x} as the point estimate for population mean.

Formula:

Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}

\bar{x} = \dfrac{\sum x_i}{n} = \dfrac{219.5}{27} = 8.129

Thus, the point estimate for population mean is 8.129 Mpa.

4 0
3 years ago
Lisa's test grades are 79, 89, and 90. there will be one more test this year. if lisa wants her test average to be at least 88,
erik [133]
For this case, what we are going to do first is to assume that all the exams are worth the same percentage of the final grade.
 We have then that Lisa's average grade point equation is:
 88 =  \frac{79 + 89 + 90 + x}{4}
 Where,
 x: minimum note that lisa must obtain in the last exam.
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 Answer:
 
the lowest grade she can get on her last test is:
 
x = 94
5 0
4 years ago
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