Kelly and Greta are asked to write an equation for the scenario below. “One person was able to plant 4 trees in the same amount of time that 5 people working together were able to plant 20 trees.” The girls agree that x represents the number of people working and y represents the number of trees planted. Kelly wrote the equation , and Greta wrote the equation . Which person is correct, and why? Kelly is correct; each person plants more trees than the person before them. Kelly is correct; and . Greta is correct; each person plants 4 more trees than the person before them. Greta is correct; and .

At the point where the tangents meet the circle, the angles are 90.

So using angle sum of a quadrilateral:

360 - (90 + 90) = 180

so 180 = x + 40

x = 180 - 40

x = 140

The quadratic formula is

[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]

In this problem, a = 2, b = -4, c = 1

[tex] x = \dfrac{-(-4) \pm \sqrt{(-4)^2 - 4(2)(1)}}{2(2)} [/tex]

[tex] x = \dfrac{4 \pm \sqrt{16 - 8}}{4} [/tex]

[tex] x = \dfrac{4 \pm \sqrt{8}}{4} [/tex]

[tex] x = \dfrac{4 \pm 2\sqrt{2}}{4} [/tex]

[tex] x = 1 \pm \dfrac{\sqrt{2}}{2} [/tex]

12.

 -4/7*-3/5*7/3 = -4/5

-4/5 / -7/3 = 12/35

14.

-2/3*1/2*-6/7 = 2/7

You're Welcome!

Answer:

its 0.60

Step-by-step explanation:

I did the quiz

The probability a random voltage is less than 124.2 volts is 0.60. Thus, option (C) is correct.

To find the probability that a random voltage is less than 124.2 volts, we need to know the distribution of the voltages. Let's assume that the distribution follows a normal distribution.

The Z-score formula is

Z = (X - μ) / σ,

where X is the value we are interested in, μ is the mean of the distribution, and σ is the standard deviation.

We want to find the probability that a random voltage is less than 124.2 volts.

Since the voltage is uniformly distributed, we can find this probability by calculating the proportion of the range that is less than 124.2 volts.

The range of the voltage is 125 - 123 = 2 volts.

The proportion of the range that is less than 124.2 volts is

= 124.2 - 123

= 1.2 volts / 2 volts

= 0.60.

Therefore, the probability a random voltage is less than 124.2 volts is 0.60.

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The equation that shows how the width depends on the length for rectangles with an area of 24 inches squared is w = 24/l.

To find the equation that shows how the width (w) depends on the length (l) for rectangles with an area of 24 inches squared, we need to set up a proportion using the formula for the area of a rectangle. The area of a rectangle is equal to the length multiplied by the width, so we have the equation: l * w = 24.

Now let's solve for w in terms of l:

By substituting different values for l, we can find corresponding values for w and see how they are related.

In 27 different ways  Alberto, Ben, and Chike can form a wall to defend against a penalty kick.

A permutation is an arrangement of things where order matters, AB and BA are two different permutations.

The combination is a selection of things where order does not matter, AB and BA are the same combinations.

Given, three soccer players Alberto, Ben, Chike are forming a wall to defend against a penalty kick.

∴ The first place can be filled in 3 different ways.

Second and third place can also be filled with 3 different ways as repetition isn't allowed is not mentioned.

So, In 3×3×3 ways they line up side by side which is 27 different ways.

learn more about permutation here :

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There are six different ways Alberto, Ben, and Chike can line up to form a wall defending against a penalty kick. This is a high school level Mathematical problem known as permutation. This kind of logic applies whenever the order of arrangement matters.

The subject matter involves a combinatorial problem, specifically a permutation. In this situation, Alberto, Ben, and Chike can occupy any of the three positions in the lineup. As such, the number of permutations (P) can be calculated by multiplying the number of choices for each position. That is, there are three choices for the first position, two remaining for the second, and one for the third. Thus, the answer is P = 3*2*1 = 6 different ways.

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Answer:

The sum rule is f' + g'

The difference rule is f' − g'

The product rule is f g' + f' g

The quotient rule is (f' g − g' f )/g2

Final answer:

The basic rules for computing derivatives include the Constant, Power, Constant Multiple, Sum, Difference, Product, Quotient, and Chain rules. These rules are crucial for finding the rate of change of functions and can be applied in various combinations to handle more complex functions.

Explanation:

Basic Derivative Rules

When calculating derivatives, there are several basic rules that are often used. These are foundational tools in calculus that help us find the rate at which functions change. Here's a list of the basic derivative rules:

Constant Rule: The derivative of a constant is zero.

Power Rule: For any real number n, the derivative of xⁿ is [tex]nx^{(n-1)}[/tex]. This rule can be applied multiple times to terms that are added together, yielding the sum of their derivatives.

Constant Multiple Rule: The derivative of a constant multiplied by a function is the constant multiplied by the derivative of the function.

Sum Rule: The derivative of a sum of functions is the sum of the derivatives of each function.

Difference Rule: The derivative of a difference of functions is the difference of the derivatives of each function.

Product Rule: The derivative of the product of two functions is the first function times the derivative of the second plus the second function times the derivative of the first.

Quotient Rule: The derivative of a quotient of two functions is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator.

Chain Rule: The derivative of a composite function can be found by taking the derivative of the outer function evaluated at the inner function, and then multiplying it by the derivative of the inner function.

Each of these rules follows our intuition about how functions change and can be confirmed through examples and experiences. We can use these rules to methodically find derivatives of more complex functions.

Answer:

5%

Step-by-step explanation:

150,000/100=1500   7500/1500=5

The commission rate of the real estate agent for the home sale is calculated by dividing the commission amount by the total sale price and then converting this into percent. Following these steps, the commission rate was 5%.

The subject of this question falls under Mathematics, specifically the topic of percentages. To find the commission rate of the real estate agent, you need to divide the commission ($7500) by the total sale price ($150,000) and then multiply by 100 to convert it to percent.

Following these steps:

So the real estate agent's commission rate was 5%

.

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Something

What is ADJ and HYP?

After taking 30 1/2 steps, each covering 5/8 yard, a band member moves a total of 19 1/16 yards across the football field.

The student asks how many yards a band member moves across the football field if he or she takes 30 1/2 steps where each step covers 5/8 yard. To find the total distance covered, we multiply the number of steps by the distance per step. Here's the calculation:

The band member moves 19 1/16 yards across the football field after taking 30 1/2 steps at a 8-to-5 step interval.

if the original price was $19 then the price now would be $12.35. we would solve this by   turning 35% into a decimal.. we get .35

what we do next is multiply 19 by .35 and we get 6.65

next, we subtract 6.65 from 19

and our final answer is: $12.35

To simplify this expression would be 5x + 13

To Expand this expression would be 3x + 3 + 2x + 10

3(x + 1) + 2(x + 5)     use distributive property

= (3)(x) + (3)(1) + (2)(x) + (2)(5) = 3x + 3 + 2x + 10    combine like terms

= (3x + 2x) + (3 + 10) = 5x + 13

Answer:

-3.5 feet/second

Step-by-step explanation:

A scuba driver descends 63 feet in 18 seconds.

The integer represents descends 63 feet = -63 feet

Rate of change per second = Distance divided by the number of second to reach the distance

= [tex]\frac{-63}{18}[/tex]

= -3.5 feet/second

Answer:

50 ≤ x ≤ 100

Step-by-step explanation:

The variable x represents the number of books Hugh needs to sell to earn at least $400. The 400 needs to be replaced with 100 because that is the highest number of books Hugh has to sell.

Answer:

2 refills

Step-by-step explanation:

Hope this helps!

Question: The population has decreased by 300 residents over the past 5 years. The same number of residents left each year. What was the change in the town's population each year?

Answer: 300( total residents left) ÷ 5( # of years)= 60

The answer you want would be 60.

The change in the town's population each year is 60.

Given that,

Based on the above information, the calculation is as follows:

[tex]= 300\div 5[/tex]

= 60

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All points in the shaded area are answers to the inequality.  Thus you need to find the point which is in the shaded area of the graph.

Only the point (3, -1) is within range.  Thus answer D is correct.

Answer:

Option D, (3, -1)

Step-by-step explanation:

In the inequality shown in the graph all the points which lie above the line (in the shaded part) will be the solution.

Option A) (0, -5)

Since this point lies below the line so it is not the solution.

Option B) (0, 0)

It's below the line again therefore not the solution.

Option C) (5, -5)

It lies below the line. Therefore it is not the solution.

Option D. (3, -1)

This point lies on the line therefore satisfies the condition.

Therefore Option D. (3, -1) is the only solution.

It should be 750.60. If you are rounding to the nearest TENTH. Hope this is right!

I believe the answer is 750         Hope this Helps :D

16x-15=8x

16x=8x+15

16x-8x=15

8x=15

X=15/8

16x -15=8x

-16x.    -16x

-15=-8x

———

-8

1.875=x

Here is your answer:

1. The rectangle has a "right angle." Remember that right angles are angles that look like a  L.

2. The polygon has a "obtuse angle." Remember that obtuse angles are higher then right angles.

3. The parallelogram has a "acute angle." Remember that acute angles are lower then right angles.

Hope this helps!

x=14, i hope this helped

It's da last answer good luck but if it is wrong dnt sue me lol

Final answer:

The proper nouns in the provided sentences have been identified and underlined, including names of people, places, and institutions such as 'United States', 'George Washington', 'John Adams', 'Abigail', and '1600 Pennsylvania Ave.'.

Explanation:

To underline the proper noun in each sentence, we must identify the specific names of people, places, or institutions. Proper nouns are capitalized and denote a particular entity. Here's how they appear underlined in the given sentences:

Since BD bisects angle ABC,

∠ ABD = ∠ DBC

So, ∠ DBC = 2x + 22     (1)

Also, ∠ DBC = ∠ ABC - ∠ ABD.

= 8x - (2x + 22)

= 8x - 2x - 22

= 6x - 22     (2)

From (1) and (2),

2x + 22 = 6x - 22

2x - 6x = -22 - 22

- 4x = - 44

x = 11

∠ DBC =  2x + 22 = 2(11) + 22 = 44

Hence, ∠ DBC = 44°.

3/4 of 8 miles is 6, so he ran 6 miles of the race.

Simplify (x+7)(x+4)

Apply FOIL method to multiply the expression

First Outer Inner and Last

First : x * x = x^2

Outer : x * 4 = 4x

Inner : 7 * x = 7x

Last : 7 * 4= 28

Now we write all the terms down and  combine like  terms

[tex]x^2 + 4x + 7x + 28[/tex]

[tex]x^2 + 11x + 28[/tex]

We simplified it completely

[tex]x^2 + 11x + 28[/tex]

If it travels 55 miles per ONE HOUR - and our goal is to determine the distance in FOUR HOURS - we must multiply these two numbers together.

4 x 55 = 220 Miles

Answer: 47/48

Step-by-step explanation:

9

16

+

5

12

=

(9 × 12) + (5 × 16)

16 × 12

=

188

192

=

188 ÷ 4

192 ÷ 4

=

47

48