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3 years ago

What is the length of the side of a right triangle that has a side length of 12ft and a hypotenuse that measures 15ft

Mathematics

2 answers:

icang [17]3 years ago

6 0

Once again, In order to find the length of the hypotenuse, we need to use Pythagorean's Theorm.

This theorm states that a^2+b^2=c^2

a and b are sides, and c is the hypotenuse

$12^2 + b^2 = 15^2\\144+b^2 = 225\\b^2 = 81\\\sqrt{b^2} = \sqrt{81}\\b = 9$

The other side is 9

muminat3 years ago

4 0

Answer: 9 ft

Step-by-step explanation:

1. To solve this exercise you must apply the Pythagorean Theorem, which is:

$a=\sqrt{b^{2}+c^{2}}$

Where $a$ is the hypotenuse, and $b$ and $c$ are the other sides of the triangle.

2. Then, when you solve for one of the sides and substitute the values given in the problem into the formula shown above, you obtain that the length of the side of the rigth triangle is:

$b=\sqrt{(15ft)^{2}-(12ft)^{2}}$

$b=9ft$

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If kite ABCD is reflected across the x axis what are the results coordinates of point a

GenaCL600 [577]

Answer:

(-x,y)

Step-by-step explanation:

The x coordinate changes while the y stays the same when reflected across the x axis.

4 0

3 years ago

Location is known to affect the number, of a particular item, sold by an automobile dealer. Two different locations, A and B, ar

yKpoI14uk [10]

Answer:

We conclude that the true mean number of sales at location A is fewer than the true mean number of sales at location B.

Step-by-step explanation:

We are given that Location A was observed for 18 days and location B was observed for 13 days.

On average, location A sold 39 of these items with a sample standard deviation of 8 and location B sold 49 of these items with a sample standard deviation of 4.

Let $\mu_1$ = true mean number of sales at location A.

$\mu_2$ = true mean number of sales at location B

So, Null Hypothesis, $H_0$ : $\mu_1-\mu_2\geq0$ or $\mu_1 \geq \mu_2$ {means that the true mean number of sales at location A is greater than or equal to the true mean number of sales at location B}

Alternate Hypothesis, $H_A$ : $\mu_1-\mu_2$ or $\mu_1< \mu_2$ {means that the true mean number of sales at location A is fewer than the true mean number of sales at location B}

The test statistics that would be used here Two-sample t test statistics as we don't know about the population standard deviations;

T.S. = $\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }$ ~ $t_n__1_-_n__2-2$

where, $\bar X_1$ = sample average of items sold at location A = 39

$\bar X_2$ = sample average of items sold at location B = 49

$s_1$ = sample standard deviation of items sold at location A = 8

$s_2$ = sample standard deviation of items sold at location B = 4

$n_1$ = sample of days location A was observed = 18

$n_2$ = sample of days location B was observed = 13

Also, $s_p=\sqrt{\frac{(n_1-1)s_1^{2}+(n_2-1)s_2^{2} }{n_1+n_2-2} }$ = $\sqrt{\frac{(18-1)\times 8^{2}+(13-1)\times 4^{2} }{18+13-2} }$ = 6.64

So, test statistics = $\frac{(39-49)-(0)}{6.64 \times \sqrt{\frac{1}{18}+\frac{1}{13} } }$ ~ $t_2_9$

= -4.14

The value of t test statistics is -4.14.

Now, at 0.01 significance level the t table gives critical value of -2.462 at 29 degree of freedom for left-tailed test.

Since our test statistics is less than the critical values of t as -2.462 > -4.14, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the true mean number of sales at location A is fewer than the true mean number of sales at location B.

3 0

3 years ago

Explain relationship between the factors of a quadratic expression, the roots of the related quadratic equation, and the x-inter

Zinaida [17]

Step-by-step explanation:

So, let's use x2 - 3x - 28 as an example.

It's factors are (x - 7)(x + 4).

The roots are the x-values that make our expression equal 0. In order for x2 - 3x - 28 to equal 0, either of our factors need to equal 0, since 0 times anything is 0.

x2 - 3x - 28 = 0

(x - 7)(x + 4) = 0

x - 7 = 0

x = 7

(7 - 7)(7 + 4) = 0(11) = 0

x + 4 = 0

x = -4

(-4 - 7)(-4 + 4) = -11(0) = 0

That gives us two points on our graph, (7,0) and (-4,0). Where are those? On the x-axis! Thus, there are our x-intercepts.

By the way, for the future, along the x-axis, y = 0, so if you are asked for the x-intercepts (or roots), set y = 0 and solve for x.

Along the y-axis, x = 0, so if you are asked for the y-intercepts, set x = 0 and solve for y.

y = 02 - 3(0) - 28

y = -28

So, the y-intercept(s) of our same equation is y = -28, or (0,-28).

Boom.

3 0

3 years ago

rusak2 [61]

Answer:

recursive: a[1] = 7440; a[n+1] = a[n] -120
explicit: a[n] = 7440 -120(n -1)

Step-by-step explanation:

The sequence of amounts in Jackson's account will be ...

7440, 7320, 7200, ...

with a first value (a1) of 7440 and a common difference (d) of -120.

The recursive formula for an arithmetic sequence is ...

a[1] = a1

a[n+1] = a[n] +d

For our sequence, the recursive formula is ...

a[1] = 7440

a[n+1] = a[n] -120

The explicit formula for an arithmetic sequence is ...

an = a1 +d(n -1)

For our sequence, the explicit formula is ...

a[n] = 7440 -120(n -1)

5 0

3 years ago

What is the point-slope form of the line with slope -1/8 that passes through the point (-2, 1)?

Elina [12.6K]

Y-1=-1/8(x+2) You just plug your points into the formula

3 0

3 years ago

Read 2 more answers