All categories

2 years ago

For which value(s) of x are the triangles congruent?

Mathematics

1 answer:

Varvara68 [4.7K]2 years ago

8 0

Step-by-step explanation:

The solutions are 2 and 5

Because it's asking what would make the triangles congruent, you would set up the equation like this because the angles (angle 3 and angle 4) need to be equal:

x^2 = 7x - 10

Next, you add 10 to both sides. This is so that you can move it to the other side, addition is the inverse of subtraction.

x^2 + 10 = 7x

Now subtract 7x from both sides. Subtraction is the inverse of addition. You do this to get it on the other side so you can factor it. You can move the 10 and 7x to the other side in any order or at the same time, I just did it like this.

x^2 - 7x + 10 = 0

Now, factor. I don't really know how to explain factoring, you just get a feel for it with a lot of practice.

(x - 2)(x - 5) = 0

You can use FOIL to check this if you want to. x(x) is x^2, -2(-5) is 10), -2x - -5x is -7x. Now, find what you need to do to make what's in each of the groups of parentheses equal to 0.

x - 2 = 0

x = 2

One of the solutions is 2, because you add 2 to x to get 0.

x - 5 = 0

x = 5

The other solution is 5, because you add 5 to x to get 0. Lastly, check your solutions by plugging them in to the original equation.

2^2 = 7(2) - 10

4 = 14 - 10

So 2 is definitely a solution.

5^2 = 7(5) - 10

25 = 35 - 10

5 is also a solution.

Hope that helps :]

You might be interested in

4x^3(5x) = what,<br> will mark brainliest

Rzqust [24]

Answer:

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

I need help I don’t know how to do this

Law Incorporation [45]

Answer:

its about checkers cou nt and answer

Step-by-step explanation:

5 0

3 years ago

a high school track teams long jump record is 21 feet and 2 1/4 inches. this year Tims best long jump is 20 feet and 9 1/2 inche

Alex787 [66]

Answer:

4.75 inches.

Step-by-step explanation:

We must introduce the symbols for inches and feet.

Here we will use, x' = x feet and x" = x inches

A high school track teams long jump record is 21 feet and $2\dfrac{1}{4}$ inches i.e. 21'2.25" this year.

Now, Tim's best long jump is 20 feet and $9\dfrac{1}{2}$ inches i.e. 20'9.5".

So, the difference between the record jump and Tim's best jump is

(21'2.25" - 20'9.5")

= (21'2.25" - 21') + (21' - 20'9.5")

= 2.25" + 2.5" {Since, 1' = 12" i.e. 21' = 20' 12"}

= 4.75"

Therefore, Tim has to jump 4.75 inches farther to break the record. (Answer)

3 0

2 years ago

Please help thanks math

12345 [234]

Answer should be 63 because you multiply to find area

8 0

3 years ago

A researcher tests five individuals who have seen paid political ads about a particular issue. These individuals take a multiple

devlian [24]

Answer:

$t=\frac{46-40}{\frac{5.148}{\sqrt{5}}}=2.606$

The degrees of freedom are given by:

$df=n-1=5-1=4$

The p value wuld be given by:

$p_v =2*P(t_{(4)}>2.606)=0.060$

For this case the p value is higher than the significance level so then we can conclude that the true mean is not significantly different from 40

The distribution with the critical values are in the figure attached

Step-by-step explanation:

Information given

48, 41, 40, 51, and 50

The sample mean and deviation can be calculated with these formulas:

$\bar X= \frac{\sum_{i=1}^n X_i}{n}$

$s =\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

$\bar X=46$ represent the mean height for the sample

$s=5.148$ represent the sample standard deviation

$n=5$ sample size

$\mu_o =40$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test

Hypothesis to test

We want to test if the true mean for this case is equal to 40, the system of hypothesis would be:

Null hypothesis: $\mu = 40$

Alternative hypothesis: $\mu \neq 40$

The statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

Replacing we got:

$t=\frac{46-40}{\frac{5.148}{\sqrt{5}}}=2.606$

The degrees of freedom are given by:

$df=n-1=5-1=4$

The p value wuld be given by:

$p_v =2*P(t_{(4)}>2.606)=0.060$

For this case the p value is higher than the significance level so then we can conclude that the true mean is not significantly different from 40

The distribution with the critical values are in the figure attached

6 0

3 years ago

For which value(s) of x are the triangles congruent?​

For which value(s) of x are the triangles congruent?