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3 years ago

ANSWER ASAPPP PLEASEEEEEE

Mathematics

1 answer:

Law Incorporation [45]3 years ago

5 0

The following sum is irrational. √16 is rational because it's perfect square, the result is 4. But √8 is not rational because it's not perfect square.

The answer is second option

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Triangle DEF is a right triangle. If FE=5 and DF=13, find DE.

Nadya [2.5K]

Answer:

Step-by-step explanation:

I am amusing you are looking for the hypotenuse since this is middle school.

If you have the legs and are looking for the hypotenuse you use the Pythagorean Theorem $a^{2} + b^{2} = c^{2}$

The legs are a and b, and the hypotenuse is c

The work would look like this

$13^{2} + 5^{2} = c^{2} \\169+25= c^{2} \\194= c^{2} \\\sqrt{194} = \sqrt{c^{2} } \\13.9283883... = c$

extra notes

I rounded to 13
If you didn;t know you cancles exponents with roots

so the $c^{2}$ is cancled by aka $\sqrt{c}$

Hope this helped :)

4 0

3 years ago

A bridge is sketched in the coordinate plane as a parabola represented by the equation h=40-0.01x2, where h refers to the height

ElenaW [278]

Answer:

The length of the bridge is 126.492 feet.

Step-by-step explanation:

Let $h(x) = 40-0.01\cdot x^{2}$ , where $x$ is the position from the middle of the bridge, measured in feet, and $h(x)$ is the height of the bridge at a location of x feet, measured in feet. In this case, the length of the bridge is represented by the distance between the x-intercepts of the parabola, which we now find by factorization:

$40-0.01\cdot x^{2} = 0$ (Eq. 1)

$x^{2} = \frac{40}{0.01}$

$x =\pm \sqrt{\frac{40}{0.01} }$

$x = \pm 63.246\,ft$

Given that the parabola is symmetrical with respect to y-axis, then the length is two times the magnitude of the value found above, that is:

$l = 2\cdot (63.246\,ft)$

$l = 126.492\,ft$

The length of the bridge is 126.492 feet.

3 0

3 years ago

Divide: 5 divided by 5/6

Alenkasestr [34]

I know the answer!!! The answer is 6

3 0

3 years ago

Teacher raises A school system employs teachers at

Cerrena [4.2K]

By adding a constant value to every salary amount, the measures of

central tendency are increased by the amount, while the measures of

dispersion, remains the same

The correct responses are;

(a) The shape of the data remains the same

(b) The mean and median are increased by $1,000

Reasons:

The given parameters are;

Present teachers salary = Between $38,000 and $70,000

Amount of raise given to every teacher = $1,000

Required:

Effect of the raise on the following characteristics of the data

(a) Effect on the shape of distribution

The outline shape of the distribution will the same but higher by $1,000

(b) The mean of the data is given as follows;

$\overline x = \dfrac{\sum (f_i \cdot x_i)}{\sum f_i}$

Therefore, following an increase of $1,000, we have;

$\overline x_{New} = \dfrac{\sum (f_i \cdot (x_i + 1000))}{\sum f_i} = \dfrac{\sum (f_i \cdot x_i + f_i \cdot 1000))}{\sum f_i} = \dfrac{\sum (f_i \cdot x_i)}{\sum f_i} + \dfrac{\sum (f_i \cdot 1000)}{\sum f_i}$

$\overline x_{New} = \dfrac{\sum (f_i \cdot x_i)}{\sum f_i} + \dfrac{\sum (f_i \cdot 1000)}{\sum f_i} = \dfrac{\sum (f_i \cdot x_i)}{\sum f_i} + 1000 = \overline x + 1000$

Therefore, the new mean, is equal to the initial mean increased by 1,000

Median;

Given that all salaries, $x_i$ , are increased by $1,000, the median salary, $x_{med}$ , is also increased by $1,000

Therefore;

The correct response is that the median is increased by $1,000

Where;

n = The number of teaches;

Given that, we have both a salary, $x_i$ , and the mean, $\overline x$ , increased by $1,000, we can write;

$\sigma_{new} =\sqrt{\dfrac{\sum \left ((x_i + 1000) -(\overline x + 1000)\right )^{2} }{n}} = \sqrt{\dfrac{\sum \left (x_i + 1000 -\overline x - 1000\right )^{2} }{n}}$

$\sigma_{new} = \sqrt{\dfrac{\sum \left (x_i + 1000 -\overline x - 1000\right )^{2} }{n}} = \sqrt{\dfrac{\sum \left (x_i + 1000 - 1000 - \overline x\right )^{2} }{n}}$

$\sigma_{new} = \sqrt{\dfrac{\sum \left (x_i + 1000 - 1000 - \overline x\right )^{2} }{n}} =\sqrt{\dfrac{\sum \left (x_i-\overline x \right )^{2} }{n}} = \sigma$