MATHEMATICS HIGH SCHOOL

Let f(x)=1/x and g(x)=x^2+5x find (f×g)(x)

Answers

Answer 1

Answer:

Answer:

(f×g)(x) = x +5.

Step-by-step explanation:

Given : f(x)= $(1)/(x)$ and g(x) = x²+5x.

To find : find (f×g)(x).

Solution: We have given f(x)= $(1)/(x)$ and g(x) = x²+5x.

For (f×g)(x) = f(x) * g(x) .

Plug the values

(f×g)(x) = $(1)/(x)$ * x²+5x.

(f×g)(x) = $(x^(2)+5x )/(x)$

On taking x common from the numerator

(f×g)(x) = $(x(x+5))/(x)$ .

(f×g)(x) = x +5.

Therefore, (f×g)(x) = x +5.

Answer 2

Answer: just multiply
remember the distributive proeprty a(b+c)=ab+ac
(f *g)(x)=f(x)g(x)=(1/x)(x^2+5x)=(x^2/x)+(5x/x)=x+5

(f*g)(x)=x+5

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Suppose a varies directly as b, and a=7 when b=2 find b when a =21

Answers

because α varies directley to β
$\alpha = k \beta$
(k = constant)

α=7 when β=2
7= 2k
k= $(7)/(2)$

so when α=21
21= $(7)/(2)$ b
b= 6

Final answer:

To solve for 'b' when 'a' = 21 in a direct variation relationship where 'a' = 7 when 'b' = 2, first determine the constant of proportionality. Then, insert 'a' into the formula and solve for 'b'. The solution of 'b' would be 6.

Explanation:

In this scenario, we are given that a varies directly as b, which means we can state this relationship as a = kb, where k is a constant of proportionality. Initially, we're given that a = 7 when b = 2. From this, we can find that k = a / b, so k = 7 / 2 = 3.5. Therefore, our direct variation equation is a = 3.5b.

When a = 21, we can substitute this into the direct variation equation and solve for b. Thus, 21 = 3.5b, and by dividing both sides by 3.5, we can find that b = 6.

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Im thinking of a number , multiply it by 4 and add 5 to the product, you get 41. Find the numbera) 9
b) 10
c) 11
d) 12

Answers

A

I hope this helps:D

Answer:

Answer is a) 9

Step-by-step explanation:

9 x 4 = 36

36 + 5 =41

Hope this help (｡･ω･｡)

Edit:

or you can use this method

41 - 5 = 36

36 divides by 4, then you will get 9

You would like to buy a gaming system. The cost of the system is $500 and thecost of internet access is $40 per month.

Answers

This question has no direct question, so here are some facts if you want them:

This equation can be expressed as a linear equation.

The equation can be expressed as: y =40x + 500

The y-intercept is 500, and the slope is 40.

If you type in a graphing website like desmos, then you can actually graph the line if you wanted (or needed) to.

I'm not really sure what the question is, but maybe if you needed help, here you go.

Final answer:

To calculate the total cost of the gaming system and internet subscription, add the one-time cost of the gaming system to the monthly cost of internet access multiplied by the number of months.

Explanation:

This problem pertains to calculating ongoing costs over a period of time, often referred to as monthly expenses. The one-time cost of the gaming system is $500. After purchasing the system, you would incur a recurring cost for internet access which is $40 per month.

If, for example, you wanted to calculate your total cost for one year (12 months), you would begin with the initial $500, then add $40 multiplied by the 12 months: $500 + ( $40 * 12 ) = $980. This method applies to any number of months you want to calculate.

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Write an equation in the form Ax+By=C, given that m=2/3 and y intercept is (0,-3) where a,b, And c are integers

Answers

Answer:

2x - 3y = 9

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept

We have

$m=(2)/(3),\ (0,\ -3)\ro b=-3$

Substitute:

$y=(2)/(3)x-3$

Convert to the standard form (Ax + By = C):

$y=(2)/(3)x-3$ multiply both sides by 3

$3y=3\!\!\!\!\diagup\cdot(2)/(3\!\!\!\!\diagup)x-(3)(3)$

$3y=2x-9$ subtract 2x from both sides

$-2x+3y=-9$ change the signs

$2x-3y=9$

Which property of equality justifies the following statement?"If 5x = 60, then x = 12.. "

Symmetric Property

Transitive Property of Equality

Division Property of Equality

Algebra Properties

Answers

5x=60
x=60/5

C division property
You divide five from both sides

Normally freezing point of water is 32°F. A city treats its streets before the snow storm. In treated streets, the freezing point of water changes to -38°F. What is the new freezing point of treated water?