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slava [35]
3 years ago
6

What is the length of side PQ?

Mathematics
2 answers:
alekssr [168]3 years ago
7 0
From the graph, B is to Q, A is to P, C is to R (judging by the little marks on the angles)
so AB: PQ=BC:QR
6:PQ=8:24
PQ=18
SIZIF [17.4K]3 years ago
3 0
PQ = 18
Since the triangles are similar the sides are proportional
The scale factor to dilate the smaller triangle to the bigger one is 3
6*3= 18
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A quadratic equation is shown below:
sweet [91]

Answer:

Part A:

( 1.8333, -0.08333)

Part B:

x = 2 or x = 5/3

Step-by-step explanation:

The quadratic equation

3x^{2}-11x+10=0 has been given.

Part A:

We are required to determine the vertex. The vertex is simply the turning point of the quadratic function. We shall differentiate the given quadratic function and set the result to 0 in order to obtain the co-ordinates of its vertex.

\frac{d}{dx}(3x^{2}-11x+10)=6x-11

Setting the derivative to 0;

6x - 11 = 0

6x = 11

x = 11/6

The corresponding y value is determined by substituting x = 11/6 into the original equation;

y = 3(11/6)^2 - 11(11/6) + 10

y = -0.08333

The vertex is thus located at the point;

( 1.8333, -0.08333)

Find the attached

Part B:

We can use the quadratic formula to solve for x as follows;

The quadratic formula is given as,

x=\frac{-b+/-\sqrt{b^{2}-4ac } }{2a}

From the quadratic equation given;

a = 3, b = -11, c = 10

We substitute these values into the above formula and simplify to determine the value of x;

x=\frac{11+/-\sqrt{11^{2}-4(3)(10) } }{2(3)}=\frac{11+/-\sqrt{1} }{6}\\\\x=\frac{11+/-1}{6}\\\\x=\frac{11+1}{6}=2\\\\x=\frac{11-1}{6}=\frac{5}{3}

6 0
4 years ago
You are planning a survey of starting salaries for recent computer science majors. In the latest survey by the National Associat
Ad libitum [116K]

Answer:

A sample size of at least 228 must be needed.

Step-by-step explanation:

We are given that in the latest survey by the National Association of Colleges and Employers, the average starting salary was reported to be $61,238. Assume that the standard deviation is $3850.

And we have to find that what sample size do we need to have a margin of error equal to $500 with 95% confidence.

As we know that the Margin of error formula is given by;

 <u>Margin of error</u> = Z_\frac{\alpha}{2} \times \frac{\sigma}{\sqrt{n} }

where, \alpha = significance level = 1 - 0.95 = 0.05 and  (\frac{\alpha}{2}) = 0.025.

            \sigma = standard deviation = $3,850

            n = sample size

<em>Also, at 0.025 significance level the z table gives critical value of 1.96.</em>

So, margin of error is ;

                        500=1.96 \times \frac{3,850}{\sqrt{n} }

                         \sqrt{n} = \frac{1.96 \times 3,850}{500}

                          \sqrt{n} = 15.092

 Squaring both sides we get,

                            n = 15.092^{2} = 227.8 ≈ 228

So, we must need at least a sample size of 228 to have a margin of error equal to $500 with 95% confidence.

4 0
3 years ago
38.9 divided by 2.91. What is it.
lisabon 2012 [21]
13.36 I don’t know if you need the rounded up form but if so 13.37
6 0
3 years ago
Read 2 more answers
PLEASE HELP! THIS IS AN EASY QUESTION!!!
Elenna [48]

Answer:

<em><u>about 23 units</u></em>

Step-by-step explanation:

8 0
3 years ago
In ΔQRS, the measure of ∠S=90°, the measure of ∠R=31°, and QR = 46 feet. Find the length of SQ to the nearest tenth of a foot.
ss7ja [257]

Answer:

SQ=23.7\ ft

Step-by-step explanation:

we know that

In the right triangle QRS

sin(R)=\frac{SQ}{QR} ----> by SOH (opposite side divided by the hypotenuse)

substitute the given values

sin(31^o)=\frac{SQ}{46}

solve for SQ

SQ=\frac{SQ}{46}sin(31^o)=23.7\ ft

4 0
4 years ago
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