The slope of a vertical line is<br> The slope of a horizontal line is

If f(x)=3-2xand g(x)= 1/x+5, what is the value of f/g (8)?

Eva8 [605]

Answer:

$-\frac{104}{41}$

Step-by-step explanation:

$\frac{f(x)}{g(x)}=\frac{3-2x}{\frac{1}{x} +5}$

To make this easier to deal with, we can plug in 8 first:

$\frac{f(8)}{g(8)}=\frac{3-2(8)}{\frac{1}{(8)}+5 }$
Then we can simplify the terms to get $\frac{3-16}{\frac{1}{8} +5}=\frac{-13}{\frac{1}{8} +5}$
The denominator of this fraction needs to have its own common denominator. To do so, we can multiply the 5 by $\frac{8}{8}$ to give us: $\frac{1}{8}+\frac{40}{8}$
We can then simplify this to $\frac{41}{8}$
Now putting this back into our original fraction we have: $\frac{-13}{\frac{41}{8} }$
This is also equivalent to $\frac{(\frac{-13}{1} )}{(\frac{41}{8} )}$ which means we need to take the whole denominator of the fraction and flip it and multiply it by the numerator to get: $\frac{-13}{1}*\frac{8}{41}$
This then simplifies to $\frac{-104}{41}$

3 0

2 years ago

Solve the problem...

Gre4nikov [31]

Answer:

x = 59
y = 16.64
z = 19.42

Step-by-step explanation:

The sum of angles in a triangle is 180°, so angle x is the complement of the one marked 31°.

x = 90 -31

x = 59

__

The tangent relation tells you ...

tan(31°) = 10/y

y = 10/tan(31°) = 10/0.6009

y ≈ 16.64

__

The sine relation tells you ...

sin(31°) = 10/z

z = 10/sin(31°) = 10/0.5150

z ≈ 19.42

5 0

3 years ago

What is the ratio of the volumes of two similar rectangles, if the ratio of their perimeters is 2:9?

erma4kov [3.2K]

Answer:

Step-the base is equal to length * width.

the formula for the volume of a rectangular prism becomes length * width * height.

the ratio of the volume of a three sided figure is the ratio of their corresponding sides cubed.

so if the ratio of their volumes is 125/64, then the ratio of their corresponding sides id 5/4 because 5^3 = 125 and 4^3 = 64.

since the base area is equal to length * widfth, then the ratio of the areas becomes 5^2 / 4^2 which is equal to 25/16.

the ratio of the base area becomes 25/16.

to confirm, use an example:

original prism has dimensions as shown below:

length = 20

width = 40

height = 60

volume = 20 * 40 * 60 = 48000

base area = 20 * 40 = 800

prims that has sides in a ratio of 5/4 to original prism is shown below:

length = 20 * 5/4 = 25

width = 40 * 5/4 = 50

height = 60 * 5/4 = 75

volume = 25 * 50 * 75 = 93750

base area = 25 * 50 = 1250

ratio of the volumes = 93750 / 48000 = 1.953125

ratio of the base areas = 1250 / 800 = 1.5625

125/64 = 1.953125

25/16 = 1.5625

the formulas work.

the ratio of the volume is 125/64

the ratio of the base area is 25/16by-step explanation:

volume = 20 * 40 * 60 = 48000

base area = 20 * 40 = 800

prims that has sides in a ratio of 5/4 to original prism is shown below:

length = 20 * 5/4 = 25

width = 40 * 5/4 = 50

height = 60 * 5/4 = 75

volume = 25 * 50 * 75 = 93750

base area = 25 * 50 = 1250

8 0

1 year ago

Please Help I will mark Brainliest or whatever Match each function formula with the corresponding transformation of the parent f

gladu [14]

Answer:

1 -> D

2 -> C

3. -> F

4. -> E

5. -> A

6. -> B

Step-by-step explanation:

Match each function formula with the corresponding transformation of the parent function y = (x - 1)∧2

1. y = ( x - 1) 2 - 3 A. Reflected over the y-axis

2. y = - ( x - 1) 2 B. Translated up by 1 unit

3. y = ( x + 3) 2 C. Reflected over the x-axis

4. y = ( x - 2) 2 D. Translated down by 3 units

5. y = ( x + 1) 2 E. Translated right by 1 unit

6. y = ( x - 1) 2 + 1 F. Translated left by 4 units

Using the standard transformation rules

f(x) -> a*g(bx-h) + k, we can obtain the following results

Answers:

1 -> D

2 -> C

3. -> F

4. -> E

5. -> A

6. -> B

4 0

2 years ago

Someone please answer this, I would really be appreciative.

Iteru [2.4K]

Answer:

y-30 = 3(x-1)

Step-by-step explanation:

Point-slope form of an equation is

y-y1 = m(x-x1) where (x1,y1 ) is a point and m is the slope

We know on day 1 they exercised 30 minutes (1,30) where x is the number of days and y is the minutes. The rate increased 3 minutes each day so m = 3

y-30 = 3(x-1)

3 0

2 years ago

The slope of a vertical line is The slope of a horizontal line is