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2 years ago

Use the coordinate plane to help you identify the length of each leg then use the Pythagorean Theorem to find the length of CD

Mathematics

1 answer:

Nitella [24]2 years ago

7 0

Answer:

CE= 9cm, DE= 5cm, CD= 10.2956cm

Step-by-step explanation:

Let E be the point of the other triangle.

Using Pythagoras' Theorem,

CD= square root symbol (CE^2 + DE^2)

= square root symbol (9^2+5^2)

= 10.2956cm (6 sf)

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What is 3 2/7 x 2 4/5 (Answer with a mixed number in simplest form) Thankyou!!

SCORPION-xisa [38]

Answer:

9 1/5

Step-by-step explanation:

3 2/7 * 2 4/5

Change to improper fractions

( 7*3+2)/7 * ( 5*2+4)/5

23/7 * 14/5

Rewriting

14/7 * 23/5

2 * 23/5

46/5

Changing back to a mixed number

5 goes into 45 9 times with 1 left over

9 1/5

7 0

3 years ago

Read 2 more answers

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3 years ago

If the fallowing pair represents a direct variation, find the missing value. (2,-4) and (-6, y)

erik [133]

-8y it should be right

5 0

3 years ago

Read 2 more answers

B: Alex is 12 years older than George.

UkoKoshka [18]

Answer:

The ratio of George age to Carl's age is 1:12.

Step-by-step explanation:

Let the age of George be 'g'.

Let the age of Alex be 'a'.

Also Let the age of Carl be 'c'.

Given:

The sum of their ages is 68.

So equation can be framed as;

$g+a+c=68 \ \ \ \ equation 1$

Also Given:

Alex is 12 years older than George.

So equation can be framed as;

$a =g+12 \ \ \ \ equation \ 2$

Now Given:

Carl is three times older than Alex.

$c=3a$

But $a =g+12$

So we get;

$c = 3(g+12) \\\\c= 3g+36 \ \ \ \ equation \ 3$

Now Substituting equation 2 and equation 3 in equation 1 we get;

$g+a+c=68\\\\g+g+12+3g+36=68\\\\5g+48=68$

Subtracting both side by 48 using subtraction property of equality we get;

$5g+48-48=68-48\\\\5g=20$

Now Dividing both side by 5 using Division property of equality we get;

$\frac{5g}{5}=\frac{20}{5}\\\\g =4$

Hence George age $g = 4 \ years$

Now Alex age $a=g+12 = 4+12 =16\ years$

Also Carl's age $c=3g+36=3\times 4+36 =12+36 =48\ years$

Now we need to find the ratio of George age to Carl's age.

$\frac{g}{c}=\frac{4}{48} = \frac{1}{12}$

Hence the ratio of George age to Carl's age is 1:12.

3 0

3 years ago

A political candidate has asked you to conduct a poll to determine what percentage of people support him. If the candidate only

Nadusha1986 [10]

Answer:

The sample size required is, n = 502.

Step-by-step explanation:

The (1 - α)% confidence interval for population proportion is:

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

The margin of error is:

$MOE=z_{\alpha/2}\sqrt{\frac{\hat p\ \cdot (1-\hat p)}{n}}$

Assume that 50% of the people would support this political candidate.

The margin of error is, MOE = 0.05.

The critical value of z for 97.5% confidence level is:

z = 2.24

Compute the sample size as follows:

$MOE=z_{\alpha/2}\sqrt{\frac{\hat p\ \cdot (1-\hat p)}{n}}$

$n=[\frac{z_{\alpha/2}\times \sqrt{\hat p(1-\hat p)}}{MOE}]^{2}$

$=[\frac{2.24\times \sqrt{0.50(1-0.50)}}{0.05}]^{2}\\\\=501.76\\\\\approx 502$

Thus, the sample size required is, n = 502.

4 0

3 years ago