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arlik [135]
3 years ago
10

Triangle ABC is congruent to triangle DEF. If DE = 41, EF = 23, DF = 36, and AC = 5x - 9, what is x? Round to the nearest tenth.

(1 point)
09.0
9.4
10.0
6.4
Mathematics
1 answer:
Aloiza [94]3 years ago
5 0

Similar shapes may or may not be congruent.

The value of x is (a) 9.0

The corresponding sides are:

  • AB and DE
  • BC and EF
  • AC and DF

The side lengths are:

\mathbf{DE = 41}

\mathbf{EF = 23}

\mathbf{DF = 36}

\mathbf{AC = 5x - 9}

Because the shapes are congruent, and AC corresponds to DF.

This means that:

\mathbf{AC = DF}

So, we have:

\mathbf{5x - 9 = 36}

Collect like terms

\mathbf{5x = 9 + 36}

\mathbf{5x = 45}

Divide both sides by 5

\mathbf{x = 9.0}

<em>Hence, the correct option is (a) 9.0</em>

Read more about congruent triangles at:

brainly.com/question/12413243

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Answer:

The distance in the x-coordinates from A(–2, 2) to the center of dilation F(1, 1) is 3 unit(s)

Step-by-step explanation:

Give points:

A(-2,2)

Center of dilation F(1,1)

The distance in the x-coordinates fro A to F can be given by =\ |x_2-x_1\ |=\ |1-(-2)\ |=\ |1+2\ | = 3\ units.

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3 years ago
Which of the following is a solution of 4x + 2y ≤ 6?
cestrela7 [59]

Answer:

D. (1,0)

Step-by-step explanation:

Just plug in each coordinate for x and y into 4x+2y and see which one is less than or equal to 6.

Lets go through all of the possible answers:

<u>A</u>. (0,4)

4(0) + 2(4) ≤ 6

0 + 8 ≤ 6

8 ≤ 6

This is false.  8 is not less than or equal to 6.

<u>B</u>. (5,0)

4(5) + 2(0) ≤ 6

20 + 0 ≤ 6

20 ≤  6

This is false.  20 is not less than or equal to 6.

<u>C</u>. (5,7)

4(5) + 2(7) ≤ 6

20 + 14 ≤ 6

34 ≤ 6

This is false because 35 is not less than or equal to 6

<u>D</u>. (1,0)

4(1) + 2(0) ≤ 6

4 + 0 ≤ 6

4  ≤ 6

This is true, because 4 is less than 6.  

6 0
3 years ago
In a study conducted in the United Kingdom about sleeping positions, 1000 adults in the UK were asked their starting position wh
earnstyle [38]

Answer:

0.41 - 1.96\sqrt{\frac{0.41(1-0.41)}{1000}}=0.380

0.41 + 1.96\sqrt{\frac{0.41(1-0.41)}{1000}}=0.440

The 95% confidence interval would be given by (0.380;0.440)

0.41 - 2.58\sqrt{\frac{0.41(1-0.41)}{1000}}=0.370

0.41 + 2.58\sqrt{\frac{0.41(1-0.41)}{1000}}=0.450

The 99% confidence interval would be given by (0.370;0.450)

Step-by-step explanation:

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. And the critical value would be given by:

z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96

The confidence interval for the mean is given by the following formula:  

\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}

If we replace the values obtained we got:

0.41 - 1.96\sqrt{\frac{0.41(1-0.41)}{1000}}=0.380

0.41 + 1.96\sqrt{\frac{0.41(1-0.41)}{1000}}=0.440

The 95% confidence interval would be given by (0.380;0.440)

And for the 99% confident interval the critical value would be 2.58 and if we replace we got:

0.41 - 2.58\sqrt{\frac{0.41(1-0.41)}{1000}}=0.370

0.41 + 2.58\sqrt{\frac{0.41(1-0.41)}{1000}}=0.450

The 99% confidence interval would be given by (0.370;0.450)

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Answer:

Step-by-step explanation:

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80 = 20*4

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