inverse of y=5x^2+10

Final answer:

To determine if a proportion is true, we must verify that the cross-products of the ratios are equal. Only two of the given proportions, 16/36 = 12/27 and 15/20 = 24/32, are true when applying this method.

Explanation:

To determine if a proportion is true, we check whether the cross-products are equal. In other words, for a proportion in the form a/b = c/d, if a * d equals b * c, the proportion is true.

Let's apply this to the provided proportions:

12/15 = 47/50 is not true because 12*50 does not equal 15*47.

16/36 = 12/27 is true because 16*27 equals 36*12.

15/20 = 24/32 is true because 15*32 equals 20*24.

4/16 = 2/14 is not true because 4*14 does not equal 16*2.

Proportions can be a useful tool in many areas of mathematics, such as solving for unknown variables and comparing relative frequencies. Remember, if you encounter large numbers or fractions, simplifying before checking the cross-product can often make the process easier.

Answer:

If this cycle continued indefinitely, how much money that eventually resulted from the initial deposit is

500,000 (C is the answer)

The answer to the question would be, All whole numbers from 0 to 10

If the graph shows the number of birdhouses Penn and his father can build if they have enough time to build no more than 10 birdhouses, the domain of the graph is given as [0, 10).

From the graph given, we are to find the domain of the graph. From the graph, we can see that;

We are to find the domain of the given graph. The domain of the graph is the input values for which the graph exists.

The domain of the graph is the values along the x-axis of the graph. Hence the domain of the graph is given as [0, 10).

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Answer:

Next numbers: 3430, 24010

Step-by-step explanation:

AS you can see you just need to discover the pattern by dividing the subsequent numbers by the direct number before that:

490/70=7

70/10=7

So both numbers indicate the patter on multiply by 7.

So to calculate the next number we first have to multiply 490*7= 3430

Now we just have to multiply the 3430 by 7 and that would be 24010.

So the next numbers would be 3430 and 24010,

The volume of the cube can't equal 15cm ³ because 15 has no cube roots, the volume of the cube equals 15 cm squared.

The volume of a cube is equal to the product of the length, width, and height of a cube.

The volume of a cube is given by the formula as

The volume of a cube =  length × breadth× height

The cube root of a number is the component that we multiply by itself three times to produce that number.

The cube root is denoted by the'∛ ' symbol.

Example: ∛216 = ∛(6 × 6 × 6) = 6.

Here the length of each edge of a cube is x centimeters.

If we write the cube of a number

1³ = 1

2³ = 8

3³ = 27

Now we have a volume of 15 that contains no cube root.

A cube root is also contained in the volume of the cube.

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Answer:

b) ∠4 and ∠3

c) ∠4 and ∠5

e) ∠3 and ∠6

Step-by-step explanation:

Supplementary angles: If the two angles are supplementary, then the angles add upto 180 degrees.

We need to find which pairs add upto 180 degrees.

From the given figure, ∠4 + ∠3 = 180°

ii) ∠5 + ∠6 = 180°

iii) ∠4 + ∠5 = 180°

iv) ∠3 + ∠6 = 180°

v) ∠7 + ∠8 = 180°

So, the following pairs are supplementary.

b) ∠4 and ∠3

c) ∠4 and ∠5

e) ∠3 and ∠6

Answer:8

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

600 is greater than 500 it would be 1.2 greater

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Final answer:

The average rate of change of a function on an interval is calculated by finding the difference in the function's values at the endpoints of the interval, and then dividing that difference by the length of the interval. In this case, the interval is [50, 70], so the average rate of change of the function is (f(70) - f(50)) / (70 - 50).

Explanation:

The average rate of change of a function on an interval is calculated by finding the difference in the function's values at the endpoints of the interval, and then dividing that difference by the length of the interval.

In this case, the interval is [50, 70], so the average rate of change of the function is (f(70) - f(50)) / (70 - 50).

For example, if the function is f(x) = 2x + 3, then the average rate of change on the interval [50, 70] would be (f(70) - f(50)) / (70 - 50) = (2(70) + 3) - (2(50) + 3) / 20 = (143 - 103) / 20 = 40 / 20 = 2.

Final answer:

After three days, starting with 9-2x widgets, producing 2x+1 widgets daily, and destroying 3-x widgets daily, the student is left with 3 + 7x widgets, in terms of x.

Explanation:

Let's find out how many widgets are left after three days, starting with 9-2x widgets, producing 2x+1 widgets daily, and destroying 3-x widgets daily.

To calculate the total number of widgets after one day, we add the produced widgets (2x+1) and subtract the destroyed widgets (3-x) from the initial amount (9-2x):

At end of day 1: (9-2x) + (2x+1) - (3-x) = 9 - 2x + 2x + 1 - 3 + x = 7 + x

Repeat this process for two more days:

At end of day 2: (7+x) + (2x+1) - (3-x) = 7 + x + 2x + 1 - 3 + x = 5 + 4x

At end of day 3: (5+4x) + (2x+1) - (3-x) = 5 + 4x + 2x + 1 - 3 + x = 3 + 7x

Therefore, after three days, you are left with 3 + 7x widgets, in terms of x.

The student initially has 9-2x widgets, and each day there's a net change of 3x-2 widgets. After three days, the student is left with 7x+3 widgets.

The student starts with 9-2x widgets. Each day, they produce 2x+1 widgets and destroy 3-x widgets. To find out how many widgets the student is left with after three days, we need to account for the daily production and the daily destruction of widgets and sum them up over the three days.

Let's calculate the daily net change in widgets. The number of widgets produced each day is 2x+1, and the number destroyed is 3-x, so the net change in widgets each day is:

(2x+1) - (3-x) = 2x + 1 - 3 + x = 3x - 2

Now, let's multiply this daily net change by three days:

3 days × (3x - 2) = 9x - 6

Finally, let's add this to the initial number of widgets to find the total:

(9-2x) + (9x - 6) = 9 - 2x + 9x - 6 = 7x + 3

Therefore, after three days, the student is left with 7x + 3 widgets in terms of x.

The average time it takes to fill one bag of leaves is 0.17 hours or 10 minutes.

The average time it takes to fill one bag of leaves is 0.17 hours or 10 minutes.

To find the average time it takes to fill one bag of leaves, we need to divide the total time spent raking leaves by the number of bags filled. In this case, the total time spent raking leaves is 12 hours and the number of bags filled is 48.

Therefore, the average time it takes to fill one bag of leaves is:

Average time = Total time / Number of bags filled

Average time = 12 hours / 48 bags = 0.25 hours/bag = 15 minutes/bag.

When markups are based on the selling price, the selling price is seen as 100% since markup is a percentage of the selling price. The cost and markup together make up 100% of the selling price.

When markups are based on the selling price, the selling price can be seen as 100%.

This is because the markup is calculated as a percentage of the selling price rather than the cost of the item.

Assuming that the entire selling price is 100%, the markup portion and the cost portion together make up this 100%.

The cost and markup are represented as percentages of the selling price, so if you know the cost and markup percentages, you can calculate the selling price.

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Answer:

[tex]\frac{-5}{8} [/tex]

Step-by-step explanation:

Given :  Height of an ice sculpture changes by negative 5 over 32 meters every hour.

To Find: what will be the change in height after 4 hours?

Solution:

Height changes in 1 hour by [tex]\frac{-5}{32}[/tex]

So, the change in height after 4 hours = [tex]\frac{-5}{32} \times 4[/tex]

                                                               = [tex]\frac{-5}{8} [/tex]

Hence,the change in height after 4 hours will be [tex]\frac{-5}{8} [/tex]

the answer is A

 see attached picture:

To determine the number which, when divided into 1/16 groups, gives 15/16, we should multiply 15/16 by 16. Therefore, 15/16 is 1 sixteenth of a group of 15.

The question is essentially asking for a number which, when divided into 1/16 groups, would give 15/16.To find 1 sixteenth of a number, divide the number by 16. In this case, we want to find 1 sixteenth of what number is equal to 15/16. So, 15/16 is equal to 1/16 of what number. To find this number, we can simply invert the operation. Instead of dividing by 1/16, we should multiply 15/16 by 16. This gives us:

15/16 * 16 = 15.

Therefore, 15/16 is 1 sixteenth of 15.

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Answer:

he missed 5 targets. -75 ÷ -15

The derivative of [tex]\( f(x) = \frac{7x}{3 + x^2} \)[/tex]  is [tex]\( f'(x) = \frac{-7x^2 + 21}{(3 + x^2)^2} \)[/tex].

To find the derivative of the function [tex]\( f(x) = \frac{7x}{3 + x^2} \)[/tex] , we can use the quotient rule. The quotient rule states that if you have a function [tex]\( g(x) = \frac{u(x)}{v(x)} \)[/tex] , then the derivative [tex]\( g'(x) \)[/tex] is given by:

[tex]\[ g'(x) = \frac{u'(x)v(x) - u(x)v'(x)}{[v(x)]^2} \][/tex]

In this case, let u(x) = 7x  and v(x) = 3 +[tex]x^2[/tex] . Now, find the derivatives u'(x)  and  v'(x):

u'(x) = 7

v'(x) = 2x

Now, apply the quotient rule:

[tex]\[ f'(x) = \frac{(7)(3 + x^2) - (7x)(2x)}{(3 + x^2)^2} \][/tex]

Simplify the expression:

[tex]\[ f'(x) = \frac{21 + 7x^2 - 14x^2}{(3 + x^2)^2} \][/tex]

Combine like terms:

[tex]\[ f'(x) = \frac{-7x^2 + 21}{(3 + x^2)^2} \][/tex]

So, the derivative of [tex]\( f(x) = \frac{7x}{3 + x^2} \)[/tex]  is [tex]\( f'(x) = \frac{-7x^2 + 21}{(3 + x^2)^2} \)[/tex].

Complete Question: What is the derivation of (7x)/(3+[tex]x^2[/tex]).