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Ksju [112]
3 years ago
7

An architect designs a diagonal path across a rectangular patio. The path is 29 meters long. The width of the patio is x meters,

and the length of the path is 5 meters more than the width.
Which equation can be used to find the dimensions of the patio?

0.5(x)(x + 5) = 29
0.5(x)(x + 5) = 841
x2 + (x + 5)2 = 29
x2 + (x + 5)2 = 841
Mathematics
1 answer:
Murljashka [212]3 years ago
7 0

The sides and diagonal of a rectangle form a right triangle. The Pythagorean theorem can be used to relate the dimensions of that triangle. The legs are x and x+5; the hypotenuse is 29. We know 29²=841, so the Pythagorean theorem tells you

... x² + (x+5)² = 841 . . . . . matches the last choice

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the points (80,20) and (120,30) form a proportional relationship. What is the slope of the line that passes though these points?
Nutka1998 [239]

Answer:

1/4

Step-by-step explanation:

gradient formula= Δy/Δx

80-120/20-30=1/4

3 0
3 years ago
How do you solve for (w-2)²-63=0 where w is a real number
Murrr4er [49]
(w-2)^2 = 63

FOIL left hand side:
(w-2)^2 = w^2 - 4w + 4

So,
w^2 - 4w + 4 = 63
w^2 - 4w - 59 = 0

Then use quadratic equation to get values of w = 2 + 3*root(7) and w = 2 - 3*root(7).
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4 0
3 years ago
A cd/mp3 player for a car cost 170 dollars it is on sale for 12% off with a free installation
Vikki [24]

Answer:

$149.60

Step-by-step explanation:

12% = .12

.12 × 170= 20.40

$170- 20.4= $149.60

6 0
3 years ago
Blake and James are planning to go on a trip. Blake already has some money saved. She earns $96 more by working overtime. James
rosijanka [135]

Blake saved \bold{\$ 433.80}

Option - A

<u>SOLUTION: </u>

Given, Blake and James are planning to go on a trip.  

Blake already has some money saved.  

Let the amount saved by Blake be \$ n.

She earns \$96 more by working overtime.  

Then, total amount by Blake =\$(n+96)

James has \$ 53 more than 4 times the amount of money that Blake has saved.  

Then, total amount by James will be \$ 53+4 \times \$ n=\$(4 n+53)

If they have \$2,318 in all, we have to find how much money had Blake originally saved

Now, total amount = \$2318

\begin{array}{l}{\rightarrow \text { Amount by Blake }+\text { amount by James }=2318} \\\\ {\rightarrow \mathrm{n}+96+4 \mathrm{n}+53=2318 \rightarrow 5 \mathrm{n}+149=2318 \rightarrow 5 \mathrm{n}=2318-149 \rightarrow 5 \mathrm{n}=2169 \rightarrow \mathrm{n}=433.8}\end{array}

7 0
4 years ago
Suppose a large shipment of microwave ovens contained 12% defectives. If a sample of size 474 is selected, what is the probabili
melisa1 [442]

Answer:

P(\hat p>0.14)

And using the z score given by:

z = \frac{\hat p -\mu_p}{\sigma_p}

Where:

\mu_{\hat p} = 0.12

\sigma_{\hat p}= \sqrt{\frac{0.12*(1-0.12)}{474}}= 0.0149

If we find the z score for \hat p =0.14 we got:

z = \frac{0.14-0.12}{0.0149}= 1.340

So we want to find this probability:

P(z>1.340)

And using the complement rule and the normal standard distribution and excel we got:

P(Z>1.340) = 1-P(Z

Step-by-step explanation:

For this case we have the proportion of interest given p =0.12. And we have a sample size selected n = 474

The distribution of \hat p is given by:

\hat p \sim N (p , \sqrt{\frac{p(1-p)}{n}})

We want to find this probability:

P(\hat p>0.14)

And using the z score given by:

z = \frac{\hat p -\mu_p}{\sigma_p}

Where:

\mu_{\hat p} = 0.12

\sigma_{\hat p}= \sqrt{\frac{0.12*(1-0.12)}{474}}= 0.0149

If we find the z score for \hat p =0.14 we got:

z = \frac{0.14-0.12}{0.0149}= 1.340

So we want to find this probability:

P(z>1.340)

And using the complement rule and the normal standard distribution and excel we got:

P(Z>1.340) = 1-P(Z

4 0
4 years ago
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