Can someone please help me with these questions!

By conservation of momentum, we will see that the mass of Gru is 32 kilograms.

Here we need to use the conservation of momentum.

Initially, Gru is stop, and Agnes with a mass of 30kg has a velocity of 1.2 m/s, so the total initial momentum is:

P = 30kg*1.2m/s = 36 kg*m/s.

At the end, the total mass is M, the mass of Gru, plus the mass of Agnes:

(M + 30kg).

And the final speed is 0.5 m/s, then the final momentum is:

P' = (M + 30kg)*0.5m/s

And the final momentum must be equal to the initial momentum:

36 kg*m/s =  (M + 30kg)*0.5m/s

Now we can solve that for M:

( 36 kg*m/s)/(0.5 m/s) = M + 30kg

72kg = M + 30kg

72kg - 30kg = 32 kg = M

The mass of Gru is 32 kilograms.

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Answer:

83.08

Step-by-step explanation:

this means that they want only two numbers after the decimal point

if the number is up to five round it up and call it one the add it to the number before it

hope it helps

83.08 is the correct notation of 83.07718 to two decimal places.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

To write a number correctly to two decimal places, you need to look at the third decimal place digit.

If this digit is 5 or greater than 5, you will need to round up the second decimal place digit by adding 1 to it.

If this digit is less than 5, you simply leave the second decimal place digit as it is.

In the case of 83.07718, the third decimal place digit is 7, which is greater than 5. Therefore, we need to round up the second decimal place digit (7) by adding 1 to it, resulting in 83.08. This is the number written correctly in two decimal places.

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[tex]~~(x^2 -3x)^2 -14(x^2 -3x) +40\\\\=u^2-14u+40~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;[\text{Let}~ u = x^2 -3x]\\\\=u^2 - 10u-4u +40\\\\=u(u-10)-4(u-10)\\\\=(u-4)(u-10)\\\\=(x^2 -3x -4)(x^2 -3x -10)~~~~~~~~~~~~~;[\text{Substitute back}~ u = x^2 -3x]\\\\=(x^2 -4x+x-4)(x^2 -5x+2x-10)\\\\=\textbf{[}x(x-4) +(x-4) \textbf{]} \textbf{[}x(x-5) +2(x-5) \textbf{]} \\\\=(x+1)(x-4)(x+2)(x-5)[/tex]

Answer:

The second picture is the correct answer the graph must be decreasing..

Step-by-step explanation:

The second picture is the correct answer the graph must be decreasing..

The midpoint theorem simply states that the line segment that joins the two sides of the triangle is parallel to the third side.

Your information is incomplete. Therefore, an overview of the theorem will be given. It should be noted that the midpoint theorem states that the line drawn through the mid point of one side of the triangle is parallel to another side.

To find the midpoint, one can measure the distance between the two end points and divide the results by 2.

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Answer:

5 hours

Step-by-step explanation:

Mark recieves 3mg per hour. This can be rewritten as y=3x. Cassie recieves 2x+5. To solve, use substitiution. 3x=2x+5. To solve, subtract "2x" from "3x." You then get x=5.

Answer:  [tex]8\sqrt{2}[/tex]

================================================

Work Shown:

x = length of each leg

Use the pythagorean theorem to get...

[tex]a^2+b^2 = c^2\\\\x^2+x^2 = 16^2\\\\2x^2 = 256\\\\x^2 = 256/2\\\\x^2 = 128\\\\x = \sqrt{128}\\\\x = \sqrt{64*2}\\\\x = \sqrt{64}*\sqrt{2}\\\\x = 8\sqrt{2}\\\\[/tex]

Or as an alternative path, you can divide the hypotenuse by [tex]\sqrt{2}[/tex] and then rationalize the denominator.

Both of these methods apply to 45-45-90 triangles only.

Answer:

[tex]8\sqrt{2}[/tex]

Step-by-step explanation:

We can sum the angles in a triangle to 180°:

m<D + m<E + m<F = 180°

m<D + 90° + 45° = 180°

m<D = 45°

Therefore, the triangle is an isosceles right triangle, since the base angles, <F and <D are the same measure. Because the triangle is isosceles, the legs are congruent, meaning that

DE = EF

We can use the Pythagorean Theorem([tex]a^{2} + b^{2} = c^{2}[/tex]) and plug in 16 as c, and DE and EF as a and b:

[tex]DE^{2} + EF^{2} = 16^{2}[/tex]

Since DE is the same as EF, we can substitute it in:

[tex]DE^{2} + DE^{2} = 256\\2DE^{2} = 256\\DE^{2} = 128\\DE = \sqrt{128}[/tex]

The square root of 128 is the same as [tex]8\sqrt{2}[/tex] since 128 can be factored into 64 x 2. So [tex]8\sqrt{2}[/tex] is the answer.

If you are looking for an easier way to do this, once you are able to recognize DEF is an isosceles triangle, you can say [tex]DE \times \sqrt{2} = 16[/tex] as this applies to all isosceles right triangles. This simplifies to:

[tex]DE = \frac{16}{\sqrt{2}} \\DE = \frac{16}{\sqrt{2} } \times \frac{\sqrt{2}}{\sqrt{2} } \\DE = \frac{16\sqrt{2} }{2} \\DE = 8\sqrt{2}[/tex]

The area of the shaded region will be 46.17 ft.²The number of unit squares that cover the surface of a closed-form is the figure's area.

The space filled by a flat form or the surface of an item is known as the area.

The number of unit squares that cover the surface of a closed-form is the figure's area. Square centimeters and other similar units are used to measure area.

Given data;

Semicircle radius , r = 9 ft.

The height of the triangle, h=r=9 ft

The triangle is located where it is inscribed in the semicircle. The diameter of the semicircle is given as b, the base length of the triangle.

The diameter of the semicircle = 2 × The radius of the semicircle

D=2r

D= 2 × 9 ft

D= 18 ft.

Triangle base length,b = D= 18 ft.

The area of the triangle is found as;

[tex]\rm A= \frac{1}{2}bh \\\\ A = \frac{1}{2} \times 18 ft. \times 9 ft. \\\\ A = 81 \ ft^2[/tex]

[tex]A_{semi}={\rm \frac{A_{circle}}{2}} \\\\ A_{semi}= \frac{\pi \ r^2}{2}\\\\\ A_{semi}= \frac{3.14 \times 9^2}{2} \\\\ A_{semi} = 127.17 ft^2[/tex]

The area of the shaded region is;

a= 127.17 ft.² - 81 ft.²

a = 46.17 ft.²

Hence,the area of the shaded region will be 46.17 ft.²

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Answer:

here ....x = 2 and y = 3

[tex] = xy - y + x \times x[/tex]

[tex] = 2 \times 3 - 3 + 2 + 2 \times 2[/tex]

[tex] = 6 - 3 + 2 + 4[/tex]

[tex] = 12 - 3[/tex]

[tex] = 9[/tex]

Answer:

y = 15/-4 + 2.5x

Step-by-step explanation:

10x - 4y = 15

-4y = 15 - 10x

y = 15/-4 + 2.5x

Answer:

Step-by-step explanation:

Solution

The first step is to simplify the top of the fraction. Subtract 5.6 - 2.7

The numerator (top) and denominator(bottom) are decimal fractions. They are 2.9 for the top and 2.9 for the bottom.

The whole expression reduces down to 1, which is an integer.

Note

You have choices. If you want exact answers you will have to list those choices.

Answer: 1

The total cost of 35 T-shirts, 45 pairs of shorts, and 25 windbreakers is $973.75.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Cost of 1 T-shirt = $7.50

Cost of 35 T-shirts = 7.50 x 35

                                = 262.5

Cost of 1 Shorts = $9.00

Cost of 45 T-shirt = 9.00 x 45

                             = 405

Cost of 1 windbreakers = $12.25

Cost of 25 windbreakers = 12.25 x 306.25

So, The total cost of 35 T-shirts, 45 pairs of shorts, and 25 windbreakers

= 262.5+405+306.25

=  $973.75

Hence Her total cost is $973.75.

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Answer:

The prime factorization of 14 is 2 x 7.

Step-by-step explanation:

The prime factorization of 14 is 2 x 7.

Answer:

14 is a composite number

Step-by-step explanation:

Answer: C

Step-by-step explanation:

[tex]16x+8 \geq 12x+20\\ \\ 4x+8 \geq 20\\ \\ 4x \geq 12\\ \\ \boxed{x \geq 3}[/tex]

Answer:

81 days

Step-by-step explanation:

Formula to solve this type of equation [tex]t=\frac{k}{p}[/tex]

t is time

k is a constant

p is people

We must substitute the values into the equation

[tex]54=\frac{k}{9}[/tex]

[tex]k=486[/tex]

Now we must substitute it to find the time

[tex]t=\frac{486}{6}[/tex]

you get 81

It would take [tex]6[/tex] builders  [tex]36[/tex] days to complete the same house.

Builders are those person whose job is to build or repair houses and other buildings.

We have,

[tex]9[/tex] builders take [tex]54[/tex] days to complete a house.

So,

[tex]1[/tex]  builder will take  [tex](\frac{54}{9})[/tex]  days to complete a house,

In the same way,

[tex]6[/tex]  builder will take  [tex](\frac{54}{9}*6)[/tex]  days to complete a house,

i.e.

[tex]6[/tex]  builder   [tex]=(\frac{54}{9}*6)= 36[/tex] days.

Hence, we can say that it would take [tex]6[/tex] builders  [tex]36[/tex] days to complete the same house.

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Answer:

6.5 x 10^7

Step-by-step explanation:

give brainliest, please!

hope this helps :)

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. The correct option is B.

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

When the indicated operation 4R₁ → R₁ is applied then the matrix will be,

[tex]\left[\begin{array}{ccc}1&2&0\\-2&-1&3\end{array}\right] \rightarrow \left[\begin{array}{ccc}4&8&0\\-2&-1&3\end{array}\right][/tex]

Hence, the correct option is B.

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If he is not eligible for Roth IRAs, then he cannot contribute to Roth IRAs. However, he can contribute $3,330 monthly under his company's Matching Program.

The Individual Retirement Account to which employees in the United States can contribute after-tax earnings is called the Roth IRA.

Under its governing principles, certain individuals whose annual income exceeds stipulated amounts are INELIGIBLE to contribute.

Recall that the question indicates that his company offers a matching program with a ratio 1:1 up to 3% of his annual salary.

Since his annual salary is $111, 000,

3% x 111,000 = 3,330.

This means that annually, the total matching contribution due to Adrian would be:

3,330 x 2 = 6, 660.

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Answer: (2,-2)

Step-by-step explanation:

Rotating 90 degrees counterclockwise (about the origin) maps (x,y) onto (-y,x), so the answer is N'(2,-2)

The formula for calculating the mark up percentage is as follows:

sticker price - invoice price/invoice price • 100 = percent mark up

Percentage mark up can be described as follows:

percentage mark up = selling price per unit - cost price per unit / cost price per unit × 100

Therefore,

Mark up is the difference between a product's selling price and cost as a percentage of the cost.

Therefore, the formula for calculating the mark up percentage is as follows:

sticker price - invoice price/invoice price • 100 = percent mark up

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The limit of the given expression lim x → 0 [4eˣ/2 − 4 − 2x − 12x² +  x³] is determined as -2.

The limit of the given expression is calculated as follows;

lim x → 0 [4eˣ/2 − 4 − 2x − 12x² +  x³]

= (4e⁰)/2 - 4 - 2(0) - 12(0) + (0)

= (4)/2 - 4

= 2 - 4

= - 2

Thus, the limit of the given expression lim x → 0 [4eˣ/2 − 4 − 2x − 12x² +  x³] is determined as -2.

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Answer:

B, I solved then used interval notion to convert it.

Answer:

the answer is b

Answer:

the answer is b

Answer:

Graphs can be used to represent functions

The value of a is less than 0.

The function is given as:

The parent function of f(x) is:

So, by comparison:

The function becomes:

Next, we identify the vertex (in this case, the vertex is the minimum point on the graph)

So, we have:

Substitute these values in

So, the function becomes

From the graph, we have the following point;

So, the function becomes

Subtract 2 from both sides

Square both sides

Divide both sides by -9

So, we have:

-1 is less than 0.

Hence, the value of a is less than 0.

Step-by-step explanation:

Answer:

The value of a in this function is 0

Step-by-step explanation:

The given function is

[tex]f(x) = a(x + k)^\frac{1}{n} + c.[/tex]

Here , f(x) is y = [tex]x^{\frac{1}{2} }[/tex] So , n = 2.

By substituting the value we get the function :

[tex]f(x) = a(x + k)^\frac{1}{2} + c.[/tex]

The vertex of the graphs are : (k, c) = (-5 ,2)

The function becomes:

[tex]f(x) = a(x + 5)^\frac{1}{2} + 2[/tex]

The following point on the graph shows : (x, y) = (-4 , 5)

The function becomes:

[tex]5 = a(-4+ 5)^\frac{1}{2} + 2\\5 = a(-9)^\frac{1}{2} + 2\\\\\3 = a(-9)^{\frac{1}{2} }(Subtract 2 from both side )\\\\9 = a (-9) ( Square both sides) \\\\-1 =a ( Divide both side by -9)\\[/tex]

a = -1

Here , -1 is less than zero

Hence , the value of a is less than o.

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Answer:

(3)+1. 12-2=9+1 so 9 is the answer

For the given function h(x), we have:

a) at x = -2 and x = 2.

b) y = 0 and y = 3.

First, we want to get the values of x at which we have maximums. To do that, we need to see the value in the horizontal axis at where we have maximums.

By looking at the horizontal axis, we can see that the maximums are at:

x = -2 and at x = 2.

Now we want to get the maximum values, to do that, we need to look at the values in the vertical axis.

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Answer: The correct answer is A, [tex](-2)^{2}[/tex].

Step-by-step explanation:

A negative multiplied with another negative is a positive. Squaring is multiplying an integer by itself. Thus, it would look like -2×-2, which is equal to 4. I hope this helps!! :)

The amount that the home will be worth after 7 years is  $457763.67

The geometric sequence is sometimes called the exponential sequence. The formula for calculating the nth term of an arithmetic sequence is expressed as:

Tn = ar^n-1

where

a is the first term = 120,000

r is the common ratio = 150000/120000 = 1.25

Required

7th term

Substitute

T7 = 120,000(1.25)^7-1
T7 = 120,000(1.25)^6

T7 = 120,000(3.8147)

T7 = $457763.67

Hence the amount that the home will be worth after 7 years is  $457763.67

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Answer:

(c) $457,763.67

Step-by-step explanation:

hope this helps:)