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Nastasia [14]
3 years ago
12

Find all possible values of x in the similar triangles pqr stu

Mathematics
1 answer:
antoniya [11.8K]3 years ago
5 0
If triangles PQR and STU are similar then PQ corresponds to ST and PR corresponds to SU. Therefore, PQ/ST=PR/SU
Considering that, PQ= 7-x, ST= 13-x, PR= x²+5 and SU= x² +20
therefore, (7-x)/(13-x)= (x²+5)/(x²+20) 
               cross multiplying,
         7x² +140-x³+20x =13x²+65-x³-5x
combining the like terms,
          6x² +15x -75=0
          solving for x,
    x = 5/2 or -5 
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If ∠WOZ and ∠WOX are supplementary angles and ∠WOX and ∠XOY are complementary angles, then what is the value of x and m∠XOY?
omeli [17]

Answer:

D.x = 6; m∠XOY = 18°

Step-by-step explanation:

Supplementary angles add to 180 and complementary angles add to 90

∠WOZ + ∠WOX = 180

108 + ∠WOX = 180

∠WOX + ∠XOY = 90

∠WOX + 3x = 90

∠WOX  = 90 -3x

Replace WOX in the first equation

108 + ∠WOX = 180

108 + 90 -3x = 180

Combine like terms

198 -3x = 180

Subtract 198 from each side

-3x = 180-198

-3x = -18

Divide by -3

-3x/-3 = -18/-3

x = 6

∠XOY  = 3x = 3*6 = 18

5 0
3 years ago
Can someone help me please will give brainliest
wolverine [178]

Answer:

  see below

Step-by-step explanation:

Each point moves to half its previous distance from P. It is probably easier to count grid squares on the graph than it is to do the math on the coordinates.

If you're doing the math on the coordinates, it is convenient to use P = (0, 0), then multiply each of the coordinates of A, B, and C by 1/2. For example:

  A' = (1/2)A = (1/2)(8, 4) = (4, 2)

8 0
3 years ago
Write:<br> 3^-4 in standard form
pav-90 [236]

Answer:

\frac{1}{81}

Step-by-step explanation:

<u>Key skills: Exponents + Fractions</u>

Use the negative exponent property. If your number is x^-y then it would be the same as 1/x^y

3^-4 is the same as \frac{1}{3^{4}}

3^4 is 81, so your answer would be 1/81.

Hope you have a nice day and understood this!

4 0
3 years ago
Directions: for questions 1 through 4, find the diagonal length of each solid figure.
Alex787 [66]
\text{The length of the diagonal is }11.2\text{ mm}

Here, we want to find the diagonal of the given solid

To do this, we need the appropriate triangle

Firstly, we need the diagonal of the base

To get this, we use Pythagoras' theorem for the base

The other measures are 6 mm and 8 mm

According ro Pythagoras' ; the square of the hypotenuse equals the sum of the squares of the two other sides

Let us have the diagonal as l

Mathematically;

\begin{gathered} l^2=6^2+8^2 \\ l^2\text{ = 36 + 64} \\ l^2\text{ =100} \\ l\text{ = }\sqrt[]{100} \\ l\text{ = 10 mm} \end{gathered}

Now, to get the diagonal, we use the triangle with height 5 mm and the base being the hypotenuse we calculated above

Thus, we calculate this using the Pytthagoras' theorem as follows;

\begin{gathered} d^2=5^2+10^2 \\ d^2\text{ = 25 + 100} \\ d^2\text{ = 125} \\ d\text{ = }\sqrt[]{125} \\ d\text{ = }11.2\text{ mm} \end{gathered}

7 0
1 year ago
a math teacher claims that she has developed a review course that increases the score of students on the math portion of a colle
madam [21]

Answer:

A.

H_0: \mu\leq514\\\\H_1: \mu>514

B. Z=2.255. P=0.01207.

C. Although it is not big difference, it is an improvement that has evidence. The scores are expected to be higher in average than without the review course.

D. P(z>0.94)=0.1736

Step-by-step explanation:

<em>A. state the null and alternative hypotheses.</em>

The null hypothesis states that the review course has no effect, so the scores are still the same. The alternative hypothesis states that the review course increase the score.

H_0: \mu\leq514\\\\H_1: \mu>514

B. test the hypothesis at the a=.10 level of confidence. is a mean math score of 520 significantly higher than 514? find the test statistic, find P-value. is the sample statistic significantly higher?

The test statistic Z can be calculated as

Z=\frac{M-\mu}{s/\sqrt{N}} =\frac{520-514}{119/\sqrt{2000}}=\frac{6}{2.661}=2.255

The P-value of z=2.255 is P=0.01207.

The P-value is smaller than the significance level, so the effect is significant. The null hypothesis is rejected.

Then we can conclude that the score of 520 is significantly higher than 514, in this case, specially because the big sample size.

C.​ do you think that a mean math score of 520 vs 514 will affect the decision of a school admissions adminstrator? in other words does the increase in the score have any practical significance?

Although it is not big difference, it is an improvement that has evidence. The scores are expected to be higher in average than without the review course.

D. test the hypothesis at the a=.10 level of confidence with n=350 students. assume that the sample mean is still 520 and the sample standard deviation is still 119. is a sample mean of 520 significantly more than 514? find test statistic, find p value, is the sample mean statisically significantly higher? what do you conclude about the impact of large samples on the p-value?

In this case, the z-value is

Z=\frac{520-514}{s/\sqrt{n}} =\frac{6}{119/\sqrt{350}} =\frac{6}{6.36} =0.94\\\\P(z>0.94)=0.1736>\alpha

In this case, the P-value is greater than the significance level, so there is no evidence that the review course is increasing the scores.

The sample size gives robustness to the results of the sample. A large sample is more representative of the population than a smaller sample. A little difference, as 520 from 514, but in a big sample leads to a more strong evidence of a change in the mean score.

Large samples give more extreme values of z, so P-values that are smaller and therefore tend to be smaller than the significance level.

8 0
3 years ago
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