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2 years ago

26. (02.08)

Mathematics

1 answer:

Mama L [17]2 years ago

7 0

Answer:

X^2 -5x -36

Step-by-step explanation:

formula of an area of a rectangle: ab

a-length

b-width

(x+4)*(x-9) = x^2 -5x -36

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Two cones are similar. The volume of the larger cone is 27 cm³ and the volume of the smaller cone is 8 cm³. The height of the sm

aev [14]

ANSWER

The height of the larger cone is 3cm

EXPLANATION

Since the two cones are similar we can use the scale factor to determine the height of the larger cone.

It was given that, the volume of the larger cone is 27 cm³ and the volume of the smaller cone is 8 cm³.

The scale factor for the volume is

${k}^{3} = \frac{27}{8}$

The scale factor for the length is

$k = \sqrt[3]{ \frac{27}{8} }$

$k = \frac{3}{2}$

To find the height of the larger cone, we multiply by

$h = \frac{3}{2} \times 2 = 3$

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2 years ago

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A sample of 100 footballs showed an average air pressure of 13 psi. The standard deviation of the population is known to be .25

Vladimir79 [104]

Answer:

0.025 is the standard error of mean.

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 100

Sample mean = 13 psi

Population standard deviation = 0.25 psi

We have to find the standard error of the mean.

Formula:

Standard error =

$\dfrac{\sigma}{\sqrt{n}} = \dfrac{0.25}{\sqrt{100}} = \dfrac{0.25}{10} = 0.025$

0.025 is the standard error of mean.

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3 years ago

write the equation of the line that passes through the given points expressed in slope-intercept form. m=2/3, (-4,5)

solniwko [45]

Answer:

$y = \frac{2}{3}x + \frac{23}{3}$

Step-by-step explanation:

To write the equation of a line with a point and a slope, use the point-slope form of a linear equation. Substitute m = 2/3 and the point (-4,5) into the equation.

$y - y_1 = m(x-x_1)\\y - 5 = \frac{2}{3}(x --4)\\y - 5 = \frac{2}{3}(x+4)$

Convert to slope intercept form by using the distributive property.

$y - 5 = \frac{2}{3}(x+4)\\y - 5 = \frac{2}{3}x +\frac{8}{3}\\y = \frac{2}{3}x + \frac{8}{3} + 5\\y = \frac{2}{3}x + \frac{23}{3}$

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2 years ago

I need help on algebra

boyakko [2]

Just remember the syllables PEMDAS which stand for Parentheses, Exponents, Multiplication, Division, Addition and Subtraction. If you can’t remember it, just write it on the side of your paper. But make sure to use it in that order.

5 0

3 years ago

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Find the equation of the line that is parallel to the given line and passes through the given point

Sati [7]

Answer:

$\huge\boxed{y=-\dfrac{1}{4}x-1\to x+4y=-4}$

Step-by-step explanation:

$\text{Let}\ k:y=m_1x+b_1;\ l:y=m_2x+b_2\\\\l\ ||\ k\iff m_1=m_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\==========================\\\\\text{We have}\ x+4y=-6.\\\text{Convert to the slope-intercept form:}\\\\x+4y=-6\qquad\text{subtract}\ x\ \text{from both sides}\\\\4y=-x-6\qquad\text{divide both sides by 4}\\\\y=\dfrac{-x}{4}-\dfrac{6}{4}\\\\y=-\dfrac{1}{4}x-\dfrac{3}{2}\to m_1=-\dfrac{1}{4}$

$\text{Lines are to be parallel. Therefore}\ m_2=-\dfrac{1}{4}.\\\\\text{We initially have the form equation}\ y=-\dfrac{1}{4}x+b.\\\\\text{The line passes through the point}\ (9,\ -3).\\\\\text{Substitute the coordinates of the point to the equation of a line:}\\\\x=9,\ y=-3\\\\-3=-\dfrac{1}{4}(9)+b\\\\-3=-\dfrac{9}{4}+b\qquad\text{add}\ \dfrac{9}{4}\ \text{to both sides}\\\\-\dfrac{12}{4}+\dfrac{9}{4}=b\to b=-\dfrac{3}{4}$

$x=8,\ y=-3\\\\-3=-\dfrac{1}{4}(8)+b\\\\-3=-2+b\qquad\text{add 2 to both sides}\\\\-1=b\to b=-1$

$\text{Therefore the equation is:}\ y=-\dfrac{1}{4}x-1.\\\\\text{Convert to the standard form}\ Ax+By=C:\\\\y=-\dfrac{1}{4}x-1\qquad\text{multiply both sides by 4}\\\\4y=-x-4\qquad\text{add}\ x\ \text{to both sides}\\\\x+4y=-4$

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3 years ago