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Inessa [10]
1 year ago
11

The ABC Toy Company is creating two similar pieces for a board game, as shown below. Find the value of x that makes the two piec

es similar.
Triangle ABC is shown with sides AB marked as 6, BC marked as 7, and AC marked as y. Triangle DEF is shown with sides DE marked
Mathematics
1 answer:
pantera1 [17]1 year ago
7 0

Using proportions, the value of x that makes the triangle similar is of x = 14.

<h3>What is a proportion?</h3>

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, we want the triangles to be similar, hence the lengths of it's sides follow the proportion given next:

\frac{6}{12} = \frac{7}{x}

Applying cross multiplication:

6x = 12 x 7

x = 2 x 7

x = 14.

The value of x that makes the triangle similar is of x = 14.

More can be learned about proportions at brainly.com/question/24372153

#SPJ1

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Factor the expression.<br> 9y^2– 36
Nata [24]

Answer:

Answer: 9 (y - 2) (y + 2)

Step-by-step explanation:

Factor the following:

9 y^2 - 36

Factor 9 out of 9 y^2 - 36:

9 (y^2 - 4)

y^2 - 4 = y^2 - 2^2:

9 (y^2 - 2^2)

Factor the difference of two squares. y^2 - 2^2 = (y - 2) (y + 2):

Answer: 9 (y - 2) (y + 2)

5 0
3 years ago
What is the formula to find a simple interest rate
Sphinxa [80]
Simple interest formula: A = P(1 + rt) where P is the Principal amount of money to be invested at an Interest Rate R% per period for t Number of Time Periods. Where r is in decimal form; r=R/100; r and t are in the same units of time.
4 0
3 years ago
Individuals filing federal income tax returns prior to March 31 had an average refund of $1102. Consider the population of "last
lions [1.4K]

Answer:

a) The null hypothesis states that the last-minute filers average refund is equal to the early filers refund. The alternative hypothesis states that the last-minute filers average refund is less than the early filers refund.

H_0: \mu=1102\\\\H_a:\mu < 1102

b) P-value = 0.0055

c) The null hypothesis is rejected.

There is enough statistical evidence to support the claim that that the refunds of the individuals that wait until the last five days to file their returns is on average lower than the early filers refund.

d) Critical value tc=-1.96.

As t=-2.55, the null hypothesis is rejected.

Step-by-step explanation:

We have to perform a hypothesis test on the mean.

The claim is that the refunds of the individuals that wait until the last five days to file their returns is on average lower than the early filers refund ($1102).

a) The null hypothesis states that the last-minute filers average refund is equal to the early filers refund. The alternative hypothesis states that the last-minute filers average refund is less than the early filers refund.

H_0: \mu=1102\\\\H_a:\mu < 1102

b) The sample has a size n=600, with a sample refund of $1050 and a standard deviation of $500.

We can calculate the z-statistic as:

t=\dfrac{\bar x-\mu}{s/\sqrt{n}}=\dfrac{1050-1102}{500/\sqrt{600}}=\dfrac{-52}{20.41}=-2.55

The degrees of freedom are df=599

df=n-1=600-1=599

The P-value for this test statistic is:

P-value=P(t

c) Using a significance level α=0.05, the P-value is lower than the significance level, so the effect is significant. The null hypothesis is rejected.

There is enough statistical evidence to support the claim that that the refunds of the individuals that wait until the last five days to file their returns is on average lower than the early filers refund.

d) If the significance level is α=0.025, the critical value for the test statistic is  t=-1.96. If the test statistic is below t=-1.96, then the null hypothesis should be rejected.

This is the case, as the test statistic is t=-2.55 and falls in the rejection region.

4 0
3 years ago
It takes three identical water pumps 7 hours to fill a pool,<br> Find the constant of variation.
guapka [62]

Answer:

21

Step-by-step explanation:

You have to multiply 3 and 7 to get 21.

4 0
3 years ago
ABC has the points A(1,7) B(-2,2) and C(4,2) as it’s vertices
tekilochka [14]

<u>Part 1</u>

Using the distance formula,

AB=\sqrt{(-2-1)^{2}+(2-7)^{2}}=\sqrt{34}\\\\BC=\sqrt{(-2-4)^{2}+(2-2)^{2}}=6\\\\AC=\sqrt{(1-4)^{2}+(7-2)^{2}}=\sqrt{34}

So, the measure of the longest side is 6 units.

<u>Part 2</u>

Triangle ABD will have vertices A(1,7), B(-2, 2), and D(1,2).

We already know that AB=\sqrt{34}

Using the distance formula,

AD=\sqrt{(1-1)^{2}+(7-2)^{2}}=5\\\\BD=\sqrt{(-2-1)^{2}+(2-2)^{2}}=3

So, ABD is a scalene triangle.

<u>Part 3</u>

From part 2, we know that the length of side AD is 5 units.

6 0
2 years ago
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