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alexdok [17]
3 years ago
7

A graph creates a triangle with the x-axis, the line 3x-2y=0, and the line x+2y=10. Find the area of the triangle formed in squa

re units.
Mathematics
1 answer:
MariettaO [177]3 years ago
6 0

Answer:

18.75

Step-by-step explanation:

To identify the vertices of this triangle, you need to find the x intercepts of both lines, as where their solutions match. Let's start with setting them equal to each other. If you subtract 10 from both sides of the second equation, then both equations are left equaling zero.  You can also multiply both sides of the equation by -1 for easier solving later Now:

3x-2y=-2y-x+10

4x=10

x=2.5

y=3.75

This shows that the height of this triangle is 3.75. Now, to find the x intercepts of both equations, we simply have to plug in the y value as 0. For the first one, 3x-0=0, so x=0 as well and the coordinates are (0,0). For the second one, x+0=10, so x=10 and the coordinates are (10,0). This shows that the base is 10-0=10 units long. The formula for the area of a triangle is \frac{bh}{2}=\frac{10\cdot3.75}{2}=18.75. Hope this helps!

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Answer:

97.27 yd²

Step-by-step explanation:

First let's find the area of the right triangle on the left side. To do that, multiply 6x5, then divide the product by 2, since a right triangle is half a rectangle.

6x5=30

30/2=15

Area of triangle=15 yd²

Find area of the middle rectangle. So multiply the length by the width.

9x6=54

Area of rectangle=54 yd²

Find area of the half circle. Formula for area of circle is A=\pi r^{2}. Pi is about 3.14, and radius (r) is 3. Radius is half of the diameter of circle, and the 6 on the left says the diameter of circle.

\pix3^{2}≈28.27

Area of circle is about 28.27 yd²

Add up the three areas.

15+54+28.27=97.27

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3 years ago
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3 years ago
The diagram below shows the dimensions of a triangular park built in a new housing development. Two side lengths and one angle m
evablogger [386]
ANSWER

x = 50.5 \degree

EXPLANATION

We use the sine rule for solving triangles.

This is given by the formula,


\frac{ \sin(A) }{a}  =  \frac{ \sin(B) }{b}  = \frac{ \sin(C) }{c}


From the triangle,

\frac{ \sin(x) }{60}  =  \frac{ \sin(40) }{50}

We multiply both sides of the equation by 60 to get,

sin(x)  =  \frac{ 60\sin(40 \degree) }{50}


sin(x)  = 0.7713



We solve for x to obtain,

x = arcsin(0.7713)


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To the nearest tenth, we round to one decimal place to get,

x = 50.5 \degree

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A report on consumer financial literacy summarized data from a representative sample of 1,664 adult Americans. Based on data fro
daser333 [38]

Answer:

a. The 95% confidence interval for the proportion of all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance is (0.54, 0.588). This means that we are 95% sure that the true proportion of all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance is between these two bounds.

b. Because this confidence interval is entirely above 0.5, the interval is consistent with the statement that a majority of adult Americans would give themselves a grade of A or B.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

Sample of 1,664 adult Americans, 939 people in the sample would have given themselves a grade of A or B in personal finance.

This means that n = 1664, \pi = \frac{939}{1664} = 0.5643

95% confidence level

So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5643 - 1.96\sqrt{\frac{0.5643*0.4357}{1644}} = 0.54

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5643 + 1.96\sqrt{\frac{0.5643*0.4357}{1644}} = 0.588

The 95% confidence interval for the proportion of all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance is (0.54, 0.588). This means that we are 95% sure that the true proportion of all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance is between these two bounds.

(b) Is the confidence interval from part (a) consistent with the statement that a majority of adult Americans would give themselves a grade of A or B?

Yes, because the confidence interval is entirely above 0.5.

Because this confidence interval is entirely above 0.5, the interval is consistent with the statement that a majority of adult Americans would give themselves a grade of A or B.

8 0
2 years ago
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