MATHEMATICS HIGH SCHOOL

Which of the following is the inverse of y=3x

Answers

Answer 1

Answer:

Answer:

$y=(1)/(3)x$

Step-by-step explanation:

Given: $y=3x$

We need to find the inverse of given function.

If $y=f(x)$ is a function then inverse [/tex] x=f^{-1}(x)[/tex]

Inverse function is symmetry about the line y=x

Step 1: switch x and y

$x=3y$

Step 2: solve for y

divide both sides by 3

$y=(1)/(3)x$

Inverse function: $f^(-1)(x)=(1)/(3)x$

Hence, The inverse function is $y=(1)/(3)x$

Answer 2

Answer: y/3=x or y divided by 3 is equals x. They are the same thing just but the equation in word form.

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0.6239 as a fraction
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After John worked at a job for 10 years, his salary doubled. If he started at $x, his salary after 10 years is $_____.

7. The XYZ Office Supplies Company sells calculators in bulk at wholesale prices, as well as individually at retail prices. Next year's sales depend on market conditions, but executives use probability to find estimates of sales for the coming year. The following tables are estimates for next year's sales. WHOLESALE SALES Number Sold Probability 2,000 0.1 5,000 0.3 10,000 0.4 20,000 0.2 Number Sold Probability RETAIL SALES 600 0.4 1,000 0.5 1,500 0.1 What profit does XYZ Office Supplies Company expect to make for the next year if the profit from each calculator sold is $20 at wholesale and $30 at retail?

Answers

Answer

given,

WHOLESALE SALES

Number Sold 2,000 5,000 10,000 20,000

Probability 0.1 0.3 0.4 0.2

RETAIL SALES

Number Sold 600 1,000 1,500

Probability 0.4 0.5 0.1

Wholesale Sold

= 2000 (0.10) + 5000 (0.3) + 10000 (0.4) + 20000 (0.2)

= 9700

Cost = 9700 x $20

= $ 194,000

Retail Sale

= 600 (0.4) + 1000 (0.5) + 1500 (0.1)

= 890

Cost = 890 x $30

= $ 26,700

Profit this year

= $ 194,000 + $ 26,700

= $ 220,700

A pair of equations is shown below:y = 3x − 5
y = 6x − 8

Part A: Explain how you will solve the pair of equations by substitution or elimination. Show all the steps and write the solution. (5 points)

Part B: If the two equations are graphed, at what point will the lines representing the two equations intersect? Explain your answer.

Answers

y = 3x - 5
y = 6x - 8

y = y
3x - 5 = 6x - 8
3x - 6x = -8 + 5
-3x = -3
x = -3/-3
x = 1

y = 3x - 5 ⇒ 3(1) - 5 = 3 - 5 ⇒ y = -2
y = 6x - 8 ⇒ 6(1) - 8 = 6 - 8 ⇒ y = -2

x = 1 ; y = -2 or (1,-2) is the point of intersection.

Answer:

y = 3x - 5

y = 6x - 8 We simply subtract the second equation from the first. This eliminates y:

0 = 3x - 6x - 5 - (-8)

0 = -3x - 5 + 8

3x = 3

x = 1

Now substitute for x in first equation:

y = 3(1) - 5

y = -2.

B. x = 1 and y = -2 are the values that satisfy both equations. So the liones will intersect at this point (1, -2).

y = 3x - 5

y = 6x - 8 We simply subtract the second equation from the first. This eliminates y:

0 = 3x - 6x - 5 - (-8)

0 = -3x - 5 + 8

3x = 3

x = 1

Now substitute for x in first equation:

y = 3(1) - 5

y = -2.

B. x = 1 and y = -2 are the values that satisfy both equations. So the liones will intersect at this point (1, -2).

Step-by-step explanation:

no need for one be sure to parapharse

an open rectangular box with square ends is fitted with an overlapping lid that covers the top and front face determine the maximum volume of the box if 1square meter of metal is used in its construction

Answers

Volume is a three-dimensional scalar quantity. The maximum volume of the box is 0.8m³.

What is volume?

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

Surface area of the box = 2x² + 3xy

Surface area of lid = 2xy

Total area = 2x² + 5xy = 6

y = (6-2x²)/5x

Volume of the box, V = x²y

V = x²[(6-2x²)/5x] = (6x/5)-(2x³/5)

Now, for the volume to be the maximum,

dV/dx = 0

(6/5)-(6x²/5) = 0

x² = 1

x = ±1

y = 4/5

Thus, the maximum volume of the box = x²y = (1)²×(4/5) = 0.8 m³

Hence, the maximum volume of the box is 0.8m³.

Learn more about Volume:

brainly.com/question/13338592

#SPJ2

so would it be 8 meters because it has 8 sides

The stopping distance (s) of a car varies directly as the square of its speed (v). If a car traveling 20 mph requires 60 ft to stop, find the stopping distance for a car traveling 40 mph. Round to the nearest tenth.

Answers

Answer:

The stopping distance for a car traveling 40 mph is 240 feet.

Step-by-step explanation:

We are given the following in the question:

The stopping distance (s) of a car varies directly as the square of its speed (v)

$s\propto v^2$

Removing the sign of proportionality and adding constant of proportionality, we get

$s = kv^2$

where k is constant of proportionality.

Now, when s = 60 feet, v = 20 mph

Putting values, we get,

$60 = k(20)^2\n\nk = (60)/(400) = 0.15$

Putting value of k in the equation, we get,

$s = 0.15v^2$

We have to find the stopping distance for a car traveling 40 mph.

$s = 0.15(40)^2 = 240\text{ feet}$

Thus, the stopping distance for a car traveling 40 mph is 240 feet.

(x-5) divided by (x^2+3x-40)

Answers

Answer:

1/ x +8

*The 1 over x + 8

Answer:

$(1)/(x+8)$

Step-by-step explanation:

Here is your original equation:

$(x-5)/(x^(2) +3x-40)$

What we need to focus on is simplification, specifically simplifying the denominator. First, let's isolate the denominator (we'll get back to $x-5$ later):

$x^(2) +3x-40$

Next, we take a look at -40. Our goal is to find what factors of 40 create a sum of 3 so we can separate the equation for polynomial division.

Let's begin building our expressions. We know that $x^(2)$ has an exponent of 2. When variables are multiplied, the exponents are added, meaning that $x*x=x^(2)$ . (Or $x^(1) + x^(1) =x^(2)$ , the 1s just don't show)

We can also see that -40 is a negative number. A negative multiplied by a positive makes a negative product, so we can also include one positive and one negative in each expression.

$x^(2) +3x-40 = (x+)(x-)$

Next, let's look at the factors of 40:

1 and 40 2 and 20 4 and 10 5 and 8

Which of these factors can make a sum of 3? Remember that one number has to be positive and the other has to be negative!

$8-5=3$

In this instance, our positive number is 8 and our negative number is 5. They create the sum of 3 that we're splitting in $3x$ . Therefore, $8(-5)=-40$ .

$x^(2) +3x-40 = (x+8)(x-5)$

Now let's go back to our original equation and substitute our old expression with the new one:

$(x-5)/((x+8)(x-5))$

Do you notice that the numerator and part of the denominator are equal? This means that they can cancel each other out! Think of it as a $(1)/(1)$ .

$(x-5)/((x+8)(x-5))$ = $(1)/(x+8)$

Therefore, your simplified answer is $(1)/(x+8)$ !

Here's the whole process:

$(x-5)/(x^(2) +3x-40) \n\n(x+?)(x-?)\n\n40:\n1, 40\n2, 20\n4, 10\n5, 8\n\n8-5=3 \n(8x-5x=3x)\n\n(x+8)(x-5)\n\n(x-5)/((x+8)(x-5))=(1)/(x+8) \n\n(1)/(x+8)$

To check your answer, confirm your expressions using the box method attached.

I hope this helps! If you have any more questions or concerns about the answer or the process, let me know!

What is the work to this ? 6=-3(x+2)

Answers

♥ To solve this you are going to find x. ♥

♥ X in this case is representing a unknown variable, meaning we are not sure of the number x, and to finish the solution to your problem we have to find x.

♥ So to find x the first step is to simplify both sides of the equation.

♥ Starting with distribution:

$6=(-3)(x)+(-3)(2) \n 6=-3x+-6 \n 6=-3x-6$

♥ Now we want to flip the equation.

$-3x-6=6$

♥ Our next and almost final step, is to add the number -3 to both sides of our problem. This is going to help us tremendously.

$-3x-6+6=6+6 \n -3x=12$

♥ Now our last step before we get our answer is to divide both sides of the problem. In this case we are going to do this:

$(-3x)/(-3) = (12)/(-3)$

♥ And then because of that we get our final answer of: -4.

♥ x=-4 ♥

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