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3 years ago

The two triangles are similar what is the value of x? x=___

Mathematics

1 answer:

Dennis_Churaev [7]3 years ago

7 0

Answer:

Step-by-step explanation:

What we have to know is that when two triangles are similar their sides will always be proportional. So we will create a proportion that goes like this... $\frac{\Delta1side}{\Delta1base} =\frac{\Delta2side}{\Delta2base}$ but since it doesn't tell us the exact value of triangle 1. We will have to add 3 and 12 to get 15 which is the base of the first triangle. Now we're ready to write the proportion.

$\frac{4x}{15}=\frac{3x+1}{12}$

Now we cross multiply and solve the equation...

$48x=15(3x+1)\\48x=45x+15\\3x=15\\x=5$

So the value of x is 5.

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Find all of the points of the form (x, −x) which are 7 units from the origin.

Morgarella [4.7K]

Answer:

(-7, 0) and (7, 0)

Step-by-step explanation:

All the points that are 7 units from the origin are on the circle:

x² + y² = 7²

The maximum and minimum values of x obtained when y = 0:

x² = 7²
√x² = √7²
x = ± 7

min x = -7 and
max x = 7

The points are:

(-7, 0) and (7, 0)

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3 years ago

Read 2 more answers

Which equation is a radical equation.

OlgaM077 [116]

Hi there! :)

A radical equation is an equation in which a variable (ex. x, y, a, v) is under a radical sign. The only equation that has a variable under a radical (x) is the second option. There is an x next to the 2 under the radical.

I hope this helps, DM me if you have anymore questions. :)

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3 years ago

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Choose a justification for each step in the derivation of the sine difference identity.

Natali [406]

Answer:

Step 1:

✔ Cofunction identity

Step 5:

✔ Sine difference identity

Step 6:

✔ Cofunction Identity

Step 7:

✔ Cosine function is even, sine function is odd.

Step-by-step explanation:

8 0

3 years ago

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(A) A small business ships homemade candies to anywhere in the world. Suppose a random sample of 16 orders is selected and each

Leviafan [203]

Following are the solution parts for the given question:

For question A:

$\to (n) = 16$

$\to (\bar{X}) = 410$

$\to (\sigma) = 40$

In the given question, we calculate $90\%$ of the confidence interval for the mean weight of shipped homemade candies that can be calculated as follows:

$\to \bar{X} \pm t_{\frac{\alpha}{2}} \times \frac{S}{\sqrt{n}}$

$\to C.I= 0.90\\\\\to (\alpha) = 1 - 0.90 = 0.10\\\\ \to \frac{\alpha}{2} = \frac{0.10}{2} = 0.05\\\\ \to (df) = n-1 = 16-1 = 15\\\\$

Using the t table we calculate $t_{ \frac{\alpha}{2}} = 1.753$ When $90\%$ of the confidence interval:

$\to 410 \pm 1.753 \times \frac{40}{\sqrt{16}}\\\\ \to 410 \pm 17.53\\\\ \to392.47 < \mu < 427.53$

So $90\%$ confidence interval for the mean weight of shipped homemade candies is between $392.47\ \ and\ \ 427.53$ .

For question B:

$\to (n) = 500$

$\to (X) = 155$

$\to (p') = \frac{X}{n} = \frac{155}{500} = 0.31$

Here we need to calculate $90\%$ confidence interval for the true proportion of all college students who own a car which can be calculated as

$\to p' \pm Z_{\frac{\alpha}{2}} \times \sqrt{\frac{p'(1-p')}{n}}$

$\to C.I= 0.90$

$\to (\alpha) = 0.10$

$\to \frac{\alpha}{2} = 0.05$

Using the Z-table we found $Z_{\frac{\alpha}{2}} = 1.645$

therefore $90\%$ the confidence interval for the genuine proportion of college students who possess a car is

$\to 0.31 \pm 1.645\times \sqrt{\frac{0.31\times (1-0.31)}{500}}\\\\ \to 0.31 \pm 0.034\\\\ \to 0.276 < p < 0.344$

So $90\%$ the confidence interval for the genuine proportion of college students who possess a car is between $0.28 \ and\ 0.34.$

For question C:

In question A, We are $90\%$ certain that the weight of supplied homemade candies is between 392.47 grams and 427.53 grams.
In question B, We are $90\%$ positive that the true percentage of college students who possess a car is between 0.28 and 0.34.

Learn more about confidence intervals:

brainly.in/question/16329412

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2 years ago

How to convert 80 kilometers per hour is 60 miles per hour?

Tatiana [17]

1 km = 0.62 mi
1 mi = 1.6 km

80*0.62
-or-
60*1.6

Hope this helps

5 0

3 years ago