which equation is the inverse of y=100-x2

The speed of the train is 40 km/h, and the speed of the plane is 180 km/h.

To solve the word problem regarding the speeds of a train and a plane, we first let the speed of the train be x km/h. According to the problem, the plane's speed is 20 km/h less than 5 times the speed of the train, which can be expressed as 5x - 20 km/h. Since they both travel the same amount of time, we can set up an equation based on their speeds and distances traveled:

Time taken by the train = Distance / Speed of the train = 160 / x

Time taken by the plane = Distance / Speed of the plane = 720 / (5x - 20)

Since the time is the same for both:

160 / x = 720 / (5x - 20)

Cross-multiply to solve for x:

160(5x - 20) = 720x

800x - 3200 = 720x

80x = 3200

x = 40

Find factors of x^2 and 72, that, when combined, will give you 17x

x ^2 + 17x + 72

x 9

x 8

(x + 9)(x + 8) is your factor.

hope this helps

Angle F will have the same measure as angle D, which is 53°, because they are vertical angles and thus congruent.

The question asks about the measure of angle F given that it is a vertical angle to angle D, which measures 53°. In geometry, vertical angles (also known as opposite angles) are pairs of non-adjacent angles formed when two lines intersect. Vertical angles are congruent, which means they have the same measure. Therefore, since angle D is 53°, angle F, being its vertical angle, will also have a measure of 53°.

Angle D and angle F are vertical angles, which means they are congruent. If angle D measures 53°, then angle F will also measure 53°. This is because vertical angles are equal in measure.

To find the volume of the cylinder-shaped juice can, calculate using the formula V = π r² h with the radius being half of the can's width and the given height. The volume is found to be approximately 1804 cm³ when rounded to the nearest whole number.

Calculating the Volume of a Cylinder:

To calculate the volume of a cylinder, you should use the formula V = π r² h. First, we need to determine the radius of the juice can. Since it is given that the can is 12 centimeters wide, that means the diameter is 12 centimeters, and therefore, the radius (r) is half of that, which is 6 centimeters. We also have the height (h) of the can, which is 16 centimeters. Plugging these values into the formula gives us:

V = 3.14 × 6² × 16

Now, we calculate:

V = 3.14 × 36 × 16

V = 3.14 × 576

V = 1803.84 centimeters cubed (cm³)

When we round this to the nearest whole number, the volume of the juice can is approximately 1804 cm³.

The factors of x^2 + 3x – 4 are (x + 4) and (x - 1), found by determining the factors of -4 that add up to 3.

The factors of x2 + 3x – 4 can be found using the method of factoring quadratics. To factor this quadratic expression, we look for two numbers that multiply to give the constant term (-4) and add to give the coefficient of the middle term (3). Those numbers are 4 and -1, as 4 × -1 = -4 and 4 + (-1) = 3. Therefore, the expression can be factored into (x + 4)(x - 1).

Visualizing with algebra tiles or drawing on the concepts of geometric representation of polynomials, we can understand that this factoring corresponds to breaking down the area of a rectangle (represented by x2 + 3x – 4) into two smaller rectangles whose dimensions give the factors (x + 4) and (x - 1).

Answer:

it is 80 and 75

Step-by-step explanation:

I go to RSM and when I answered this answer it said that it was correct

The solution of the inequality 5x + 13 ≥ − 37 will be greater than or equal to negative 10.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequality is given below.

5x + 13 ≥ − 37

Simplify the inequality for 'x', then we have

5x + 13 ≥ − 37

5x ≥ − 50

x ≥ − 10

The solution of the inequality 5x + 13 ≥ − 37 will be greater than or equal to negative 10.

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As per the inverse of a function, the value of [tex]f^{-1}(3)[/tex] is 13.

"An inverse function is defined as a function, which can reverse into another function."

The given function is

[tex]f(x) = \frac{2x+1}{x-4}[/tex]

⇒ [tex]y = f(x) = \frac{2x+1}{x-4}[/tex]

⇒ [tex]xy - 4y = 2x + 1[/tex]

⇒ [tex]xy - 2x = 4y + 1[/tex]

⇒ [tex]x(y - 2)= 4y + 1[/tex]

⇒ [tex]x = \frac{4y+1}{y-2}[/tex]

⇒ [tex]f^{-1}(x) = \frac{4y+1}{y-2}[/tex]

Now, [tex]f^{-1}(3) = \frac{4(3)+1}{3-2} = (12+1) = 13[/tex]

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Answer:

198.44 feet

Step-by-step explanation:

Hence, the number of party favors you can buy is $[tex]45[/tex].

What is inequality?

An inequality is a relation that makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.

Here given that,

Party favors are on sale for $[tex]2.40[/tex] each. You have $[tex]380[/tex] to spend on the decorations and gifts, and you have already spent $[tex]270[/tex] on decorating.

So,

[tex]380-270=[/tex] $[tex]110[/tex]

To find the number of party favors you can buy, we divide $[tex]110[/tex] by the favors that are on sale for $[tex]2.40[/tex] is

[tex]\frac{110}{2.40}[/tex] = $[tex]45[/tex]

Hence, the number of party favors we can buy is $[tex]45[/tex].

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Answer: There is a probability that a club member picked randomly is female, given that the person prefers swimming on weekends is 40%.

Step-by-step explanation:

Let E₁ be the event that members prefer swimming on weekends.

Let E₂ be the event that members prefer swimming on weekdays.

Let A be the event that the members are female.

Probability that members prefer swimming on weekends P(E₁) = 25%

Probability that members prefer swimming on weekdays P(E₂)= 75%

Probability that members prefer swimming on weekends and are female PA∩E₁)= 10%

Probability that members prefer swimming on weekdays and are female P(A∩E₂) = 55%

Using Conditional theorem, we will find the probability that a member is female given that the the person prefers swimming on weekends.

[tex]P(A\mid E_1)=\dfrac{P(A\cap E_1)}{P(E_1)}\\\\P(A\mid E_1)=\dfrac{10}{25}\\\\P(A\mid E_1)=0.4\\\\P(A\mid E_1)=0.4\times 100\%=40\%[/tex]

Hence, there is a probability that a club member picked randomly is female, given that the person prefers swimming on weekends is 40%.

Answer:

Given is :

∠M≅∠X

∠N≅∠Y

YO≅NZ

We have to prove that ΔMNO≅ΔXYZ

Using segment addition postulate we get YZ=YO+OZ and ON=NZ+OZ and YO=NZ is already given. Using substitution of YO for NZ; we get ON=YO+OZ

Now substituting YZ for YO+OZ we get ON=YZ and also YZ=YO+OZ.

Now applying AAS we get ΔMNO is congruent to ΔXYZ because of angle-angle-side theorem as we have already proved that two sides are congruent and a non-included angle in each triangle is congruent.

We have been given that

[tex]I = $54, P = $900, t = 18 \text{ months

}[/tex]

We know the formula,

[tex]I=Prt[/tex]

On substituting the given values, we get

[tex]54=900\cdot r\cdot \frac{18}{12}\\\\r=\frac{54\cdot 12}{900\cdot 18}\\\\r=\frac{1}{25}\\\\r=0.04\\\\r=4\%[/tex]

The annual rate interest is 4%

Answer:

f(x)=39.59

(1.09)

After 12 years: 111

After 35 years: 808

The exponential function models the data would be f(x) = 39.59 (1.09). After 12 years, the home’s value will be about $111 thousand and After 35 years, it will be about $808 thousand.

A function is defined as a relation between the set of inputs having exactly one output each.

Elias purchases a home for $38,900.

Let x be the number of years since the purchase. The function f(x) =()x models the data.

f(x) = 39.59 (1.09)

by using the model to predict the home’s value.

After 12 years, the home’s value will be about $

111 thousand.

After 35 years, the home’s value will be about $

808 thousand.

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Final answer:

The probability of flipping a coin six times and getting exactly three heads and three tails is calculated using the binomial formula and is found to be 31.25%.

Explanation:

The probability of flipping a coin six times and getting exactly three heads and three tails can be calculated using the binomial probability formula, which is P(x; n, p) = (n choose x) * p^x * (1-p)^(n-x), where 'n' is the number of trials, 'x' is the number of successes, and 'p' is the probability of success on any given trial.

In this instance, since we are flipping a fair coin, the probability 'p' of getting heads (success) on any single flip is 0.5. We want to find the likelihood of getting 'x' = 3 heads out of 'n' = 6 flips. Therefore, the equation becomes:

P(3; 6, 0.5) = (6 choose 3) * 0.5^3 * 0.5^(6-3)

The combination (6 choose 3) calculates the number of ways to choose 3 successes (heads) from 6 trials, which is 20. Plugging these values into the equation gives:

P(3; 6, 0.5) = 20 * (0.5^3) * (0.5^3) = 20 * (0.125) * (0.125) = 20 * 0.015625

This results in a probability of 0.3125, or 31.25%.

Therefore, the chance of flipping a coin six times and getting three heads and three tails is 31.25%.

Answer:

93,600.16

Step-by-step explanation: