Need help!!! A rocket scientist is designing a rocket to visit the planets in the solar system. The velocity that is needed to escape a planet’s gravitational pull is called the escape velocity. The escape velocity depends on the planet’s radius and its mass, according to the equation V escape=square root(2gR where R is the radius and g is the gravitational constant for the particular planet. The rocket’s maximum velocity is exactly double Earth’s escape velocity. The earth’s gravitational pull is 9.8 m/s^2 The earth’s radius is 6.37 x10 ^6 For which planets will the rocket have enough velocity to escape the planet’s gravity?

The correct answer is C. It is the graph of f(x) translated 11 units to the left.

The correct answer is:

C. It is the graph of f(x) translated 11 units to the left.

When we have a function of the form g(x) = f(x - a), it represents a horizontal translation of the graph of f(x) by 'a' units to the right if 'a' is positive and to the left if 'a' is negative.

In this case, g(x) = f(x - 11), which means that the graph of f(x) is being translated 11 units to the right. However, the answer options do not include this specific transformation. The closest option is option C, which states that the graph of g(x) is translated 11 units to the left.

The graph of f(x) = x is a straight line passing through the origin with a slope of 1. If we apply the transformation g(x) = f(x - 11), it means that we are shifting the graph of f(x) 11 units to the right. This results in a new function g(x) that has the same shape and slope as f(x), but is shifted to the right by 11 units.

Therefore, the correct answer is C. It is the graph of f(x) translated 11 units to the left.

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Maxwell is faster than Hayley by 0.5 miles per hour

The first step is to calculate the average speed of Hayley

Average= distance/time

3/4÷1/6

= 3/4 × 6/1

= 9/2

= 4.5

The next step is to calculate the average speed of Maxwell

= 2/3 ÷ 2/15

= 2/3 × 15/2

= 5

The difference between the average speed of both individuals

= 5-4.5

= 0.5

Hence Maxwell is faster than Hayley by 0.5 miles per hour

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Answer:

x = 10

Step-by-step explanation:

(1/4(x +2) = 3

x+2 = 12

x = 10

Answer:

The number is 6.

Step-by-step explanation:

\(\frac{1}{4}=0.25\)

0.25 × (y × 2) = 3

0.25 × 2y = 3

0.5y = 3

0.5y ÷ 0.5 = 3 ÷ 0.5

y = 6

Check:

0.25 × (y × 2) = 3

0.25 × (6 × 2) = 3

0.25 × 12 = 3

3 = 3

Answer: \((x-3)^2+(y+4)^2=64\)

Step-by-step explanation:

The equation of a circle is \((x-h)^2+(y-k)^2=r^2\). h and k are the points of the center corresponding with x and y respectively. r is radius. All we have to do is plug the values in.

\((x-3)^2+(y-(-4))^2=8^2\)

With our values plugged in, we can now simplify.

\((x-3)^2+(y+4)^2=64\)

Therefore, our final equation is \((x-3)^2+(y+4)^2=64\).

Emplοyee's annual cοntributiοn: $3,097.71

Emplοyee's mοnthly deductiοn: $258.14

An algebraic expressiοn is a mathematical phrase that cοntains variables, cοnstants, and mathematical οperatiοns. It may alsο include expοnents and/οr rοοts. Algebraic expressiοns are used tο represent quantities and relatiοnships between quantities in mathematical situatiοns, οften in the cοntext οf prοblem-sοlving.

The emplοyee's percent is 100% decreased by the emplοyer's percent.

100%−73%=27%

Based on the information you provided, Rubina Shaw's annual premium for the HMO plan is $11,473. Her employer pays 73 percent of this premium, so Rubina's portion of the premium would be:

27% × $11,473 = 0.27 × $11,473 = $3,097.71

The emplοyee's annual cοntributiοn is the prοduct οf the emplοyee's percent and the tοtal premium.

The emplοyee's mοnthly deductiοn is the emplοyee's annual cοntributiοn divided by the number οf mοnths in a year.

$3,097.71 ÷ 12

= $258.14

Emplοyee's annual cοntributiοn: $3,097.71

Emplοyee's mοnthly deductiοn: $258.14

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Complete question:

Find the employee's total annual contribution and the employee's monthly deduction. Rubina Shaw, family plan. HMO annual premium is $11,473. Employer pays 73 percent.

Answer:

$23161.10

Step-by-step explanation:

Assuming this is compounded annually, we use our simple interest rate formula: A = P(1 + r)^t

Step 1: Convert months to years

60 months/12 month/year = 5 years

Step 2: Plug in known variables

A = 18400(1 + 0.0471)^5

Step 3: Solve

When you plug step 2 into your calc you should get 23161.1 as your answer. I am assuming that this isn't compounded quarterly or monthly, but just yearly.

Answer:

2.013  to 3 DP's.

Step-by-step explanation:

f(4.04)  will be very close to the tangent line.

Equation of tangent line

is y - 4 = m(x - 10)

m = (4-2) / (10-4) = 1/3

y - 4 = 1/3(x - 10)

y = 1/3x - 10/3 + 4

y = 1/3x + 2/3

So the require estimate of f(4.04)

= 1/3(4.04) + 2/3

= 2.013333

≈ 1.160

Hi there !

115.9% =1159/1000 = 1.159 ≈ 1.160

Good luck !

The number of square inches of cardboard that are needed to make one

the container is 18.

We have,

The volume of the triangular prism.

= Area of the triangle x height

Now,

Height = 6 in

And,

To find the area of a triangle, we can use Heron's formula.

A = √(s(s-a)(s-b)(s-c))

where s is the semi-perimeter of the triangle, calculated as:

s = (a + b + c) / 2

In this case, the side lengths of the triangle are 3.2 in, 3.2 in, and 2 in.

Let's calculate the area using Heron's formula:

s = (3.2 + 3.2 + 2) / 2 = 4.2

A = √(4.2(4.2 - 3.2)(4.2 - 3.2)(4.2 - 2))

A = √(4.2 x 1 x 1 x 2.2)

A = √(9.24)

A ≈ 3.04 square inches

Now,

The volume of the triangular prism.

= Area of the triangle x height

= 3.04 x 6

= 18.24 in²

Now,

Area of one cardboard.

= 1² in²

= 1 in²

Now,

The number of square inches of cardboard that are needed to make one

container.

= The volume of the triangular prism / Area of one cardboard

= 18.24 in² / 1 in²

= 18.24

= 18

Therefore,

The number of square inches of cardboard that are needed to make one

the container is 18.

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Answer:

$49.8225

Step-by-step explanation:

9.5%=0.095

45.50*0.095=4.3225

45.50+4.3225=49.8225

Answer: The length of the prism is 8 yards

Step-by-step explanation:

First, take the volume of the prism, divide it by the width (2 1/2). Once you get that divide that answer by height (5 3/4) getting you the length of the prism (8 yards)

Answer:

Whats the problem?

Step-by-step explanation:

Answer:

no fail

Step-by-step explanation:

The amount that she owes after she factors in interest will be $33,455.64.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

Rita necessities to apply for a line of credit for another vehicle. Her advance is $25,000. The financing cost on the advance is 6% and is accumulated yearly. She intends to take care of the advance in 5 years.

Then the amount is given as,

A = $25,000 x (1 + 0.06)⁵

A = $25,000 x (1.06)⁵

A = $25,000 x 1.3382

A = $33,455.64

The amount that she owes after she factors in interest will be $33,455.64.

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The error in the subtraction of the given fraction is that the LCM was not used before subtraction of numerators and as such if correctly answered the final fraction is; -15/4

We are given the subtraction of fraction expression as;

3/4 - 9/2

Now, the first step in this subtraction is to find the L.C.M of both denominators.

Factors of 2 ; 1, 2

Factors of 4; 1, 2, 4

Thus, the L.C.M of both denominators is; 2 * 2 = 4

Now, the next step is to divide the LCM by the denominator and multiply by the numerator while retaining the LCM as common denominator to get;

[(3 * 4/4) - (9 * 4/2)]/4

= (3 - 18)/4

= -15/4

The method used in the question to subtract the fraction did not take into account finding the LCM.

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Answer: 1.8%

Step-by-step explanation:

The annual interest rate is 1.8% if Moira borrowed $4,500 from her grandfather to pay for her first year of college.

It is defined as the interest based on the principal amount, it does not include the compounded amount. The interest calculates on the initial amount or borrowed amount.

It is given that:

Moira borrowed $4,500 from her grandfather to pay for her first year of college.

Three years later, she repaid the $4,500 along with an interest of $243.

Using the formula:

I = Prt

P = $4500

I = $243

t = 3

243 = 4500(r)(3)

243 = 13500r

r = 0.018

r = 1.8%

Thus, the annual interest rate is 1.8% if Moira borrowed $4,500 from her grandfather to pay for her first year of college.

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The first hiker is 2 miles east and 1 mile north of the starting point, so the position can be represented by the coordinate pair (2, 1).

What is the Pythagorean theorem in plain English?

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. The Perpendicular, Base, and Hypotenuse are the names of the three sides of this triangle.

The second hiker is 2 miles west and 3 miles south of the starting point, so the position can be represented by the coordinate pair (-2, -3).

The Pythagorean theorem can be used to calculate the separation between the two points:

d = √((2 - (-2))²  + (1 - (-3))² ) = √((2 + 2)² + (1 + 3)²) = √(4² + 4²) = √(16 + 16) = √32

So, the two hikers are approximately 5.66 miles apart.

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Answer:

1/2, 5/8, 3/4, 7/16, 3/8, 5/16

Answer:

7/16, 5/16, 5/8, 3/8, 3/4, 1/2

Step-by-step explanation:

you see the biggest numbers mean the more times its been split so the smaller each peice would be so therefor the biggest number would be the smallest tool and vice versa

The density in trees per acre upon completion will be 500 trees per acre.

In this scenario, let's say the landscaping provider donates 2750 seedlings.

Density of trees per acre = Total number of trees / Total area of land

Hence, applying the formula leads us to:

Density of trees per acre = 2750 trees / 5.5 acres

The answer comes out to be roughly around 500 trees/acre. So when completed, approximately 500 trees are estimated to be present in each acre of the landscape.

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Answer:

3, 2√2, √7

Step-by-step explanation:

compute the square roots of the next three prime numbers:

√7

√11

√13

Therefore, the next three terms of the sequence are:

{1, √2, √3, 2, √5, √7, √11, √13}

chatgpt

chat

Answer:

D. x+10

Step-by-step explanation:

-2x² - 16x +40 = -2(x²+8x -20) = -2(x+10)(x-2)

Answer:

A

Step-by-step explanation:

Solution to the system by using elementary row operations of equations is \(x1 = 3\) and \(x2 = 1\).

This can be understand by:

Step 1: Subtract 3 times the first equation from the second equation:

\(4x1 + 5x2 = 30\\-3(3x1 + 6x2) = 18\\ -x1 + -x2 = -12\)

Step 2: Add the equations to eliminate x2:

\(3x1 + 6x2 = 18\\-x1 + -x2 = -12\\2x1 = 6\)

Step 3: Divide both sides by 2 to solve for x1:

\(2x1 = 6\\x1=6/2\\x1 = 3\)

Step 4: Substitute x1 = 3 into either equation to solve for x2:

\(3(3) + 6x2 = 18\\6x2 = 6\\x2 = 1\)

Therefore, the solution to the system of equations is x1 = 3 and x2 = 1.

To reduce a matrix into row-echelon form, a series of procedures known as elementary row operations is used. These operations include multiplying one row by a nonzero value and adding it to another row, adding two rows together, switching two rows, and adding two rows together. They can be used to determine a matrix's inverse and to resolve linear equations.

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Part 1: The polynomial that represents the area of the hot tub = x² ft²; pool = (12x²-60x+75)ft² ; patio =.

Part 2: Cost of hot tub= $320; pool=$2541; patio = $104

To determine the area of the hot tub, pool and patio is carried out using the formula for the area of rectangle. That is; Area of rectangle = length× width

length = X ft

width = X ft

area = x² ft²

length = (6x-15) ft

width = (2x-5) ft

area = 6x -15× 2x-5

= 12x²-30x-30x+75

= (12x²-60x+75)ft²

length= (10x-12) ft

width = 2 +(2x-5)

= (2x-3) ft²

The cost of hot tub, pool and patio when X= 8 would be as follows:

area = x²

X = 8

area = 64ft²

But 1 ft² = 5$

64 ft² = ?

cost of hot hub = 64×5 = $320

area = (12x²-60x+75)ft²

where X = 8

area = 12(8)²-60(8)+75

= 768-480+75

= 363ft²

But 1 ft² = $7

363ft² = ?

cost of the pool = 363×7 =$2541

Area = (2x-3) ft²

X = 8

area = 2(8)-3

= 13ft

But 1 ft² = $8

. 13ft² = ?

Cost of patio = 13×8 = $104

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Answer:

214 cubic feet (rounded to the nearest cubic foot)

Step-by-step explanation:

Step 1  Determine the volume of 1 box

Volume of a box or rectangular prism = dimensions multiplied by each other

Here, the given dimensions are 11 in by 8 in by 12 in

So the volume of one box would be 11 x 8 x 12 = 1056 cubic inches

Step 2 Determine volume of all 350 boxes

Volume of 1 box = 1056

So volume of all 350 boxes = 1056 x 350 = 369600 cubic in

Step 3 Convert cubic in to cubic ft

To convert to cubic feet we divide the amount of cubic inches by 1728 (this is because there are 1728 cubic inches in 1 cubic foot)

369600 / 1728 = 214 cubic feet (to the nearest cubic foot)

214 cubic feet of warehouse space is required for 350 boxes with the dimensions of 11in by 8in by 12in

Step-by-step explanation:

which part of the question do you need

Answer:

\(y =\frac{x}{4}\)

Step-by-step explanation:

We are given several functions, and we want to figure out which one is linear.

A linear function has both of its variables (x and y) with a power of 1. Variables with other powers do not mean that the function is linear.

Let's go through the list.

Starting with \(y=\frac{3}{x} -7\), we can see that x is in the denominator. If this is the case, it means that the power of x is -1.

Even though y has a power of 1, this is NOT linear, because x has a power of -1.

Now, with y=√x-2, this is also not linear. This is because √x = \(x^\frac{1}{2}\), even though y has a power of 1.

For x² - 1 = y, we can clearly see that x has a power of 2, while y has a power of 1. This means that the function is not linear.

This leaves us with \(y = \frac{x}{4}\). x is in a fraction, however it is not in the denominator. This means that the power of x in this function is 1. We can also see that the power of y in this function is 1.

This means that \(y=\frac{x}{4}\) is linear.

The probability that that arrow will land on the part labelled C after the first spin would be = 1/5.

To calculate the probability of the chosen event, the formula for probability should be used which is given as follows:

Probability = possible outcome/ sample space

Where possible outcome = 2

sample space = A,B,B,B,C,C,D,D,D,E = 10

Therefore the probability that the arrow will land on the part labelled C after the first spin = 2/10 = 1/5.

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Okay, here we have this:

Considering the provided information, we are going to find the area of the regular octagon, replacing in the following formula of the octagon area:

According with this, we can see that the correct answer is the first answer choice.

Answer:

just one: 7 you isolate the numbers by doing -3n + 4n = 7, and u get n = 7

Answer:

2

Step-by-step explanation:

my soulstinos were Solution 1)

3

n

+

7

=

−

1

3

n

+

7

−

7

=

−

1

−

7

3

n

+

0

=

−

8

3

n

=

−

8

3

n

3

=

−

8

3

3

n

3

=

−

8

3

n

=

−

8

3

Solution 2)

3

n

+

7

=

1

3

n

+

7

−

7

=

1

−

7

3

n

+

0

=

−

6

3

n

=

−

6

3

n

3

=

−

6

3

3

n

3

=

−

2

n

=

−

2

The solution is:

n

=

−

8

3

and

n

=

−

2