A man starts walking north at 5 ft/s from a point P. Five minutes later a woman starts walking south at 7 ft/s from a point 500 ft due east of P. At what rate are the people moving apart 15 min after the woman starts walking? (Round your answer to two decimal places.) ft/s

Answer:

\(f(x)=4(x+6)^2-134\)

Step-by-step explanation:

We are required to write the function\(f(x) = 4x^2 + 48x + 10\) in vertex form.

First, bring the constant to the left-hand side.

\(f(x) -10= 4x^2 + 48x\)

Factorize the right hand side.

\(f(x) -10= 4(x^2 + 12x)\)

Take note of the factored term(4) and write it in the form below.

\(f(x) -10+4\Box= 4(x^2 + 12x+\Box)\)

\(\Box = (\frac{\text{Coefficient of x}}{2} )^2\\\\\text{Coefficient of x}=12\\\\\Box = (\frac{12}{2} )^2 =6^2=36\)

Substitute 36 for the boxes.

\(f(x) -10+4\boxed{36}= 4(x^2 + 12x+\boxed{36})\)

\(f(x) -10+144= 4(x^2 + 12x+6^2)\)

\(f(x) +134= 4(x+6)^2\\f(x)=4(x+6)^2-134\)

The function written in vertex form is \(f(x)=4(x+6)^2-134\)

Answer:

C

Step-by-step explanation:

I just finished the unit test on Edge. and got a 100% and I selected "c" as my answer.

Hey there!

0.3x=0.2−0.2x

Step 1: Simplify both sides of the equation.

0.3x=0.2−0.2x

0.3x=0.2+−0.2x

0.3x=−0.2x+0.2

Step 2: Add 0.2x to both sides.

0.3x+0.2x=−0.2x+0.2+0.2x

0.5x=0.2

Step 3: Divide both sides by 0.5.

0.5x/0.5=0.2/0.5

x=0.4

Therefore, x = 0.4

Answer:

43 is the answer to your question

The large jar has better value for money than the smaller one.

To see which jar is the best value for the money, we need to take the quotient between the cost of each jar and the size. The smaller that value gets, the best value we have.

For the first jar we have:

q = £4.10/540 = 0.0075

For the second jar we have:

q' = £2.81/360 = 0.0078

Then we can see that the large jar has the best value for money.

Learn more about quotients at:

https://brainly.com/question/629998

#SPJ1

6 ÷ [ 3 × (5 - 3) ÷ (4² + 3) ] ÷ 2

= 6 ÷ [ 3 × 2 ÷ 19 ] ÷ 2

= 6 ÷ 6/19 ÷  2

= 19/2

= 8.5

Ok done. Thank to me :>

Answer:

0.275 is the answer for this question.

Answer:

1 1/3

Step-by-step explanation:

Answer:

7/6

Step-by-step explanation:

1/3+4/8+6/18=7/6

The missing value 'x' in the two-way relative frequency table is 0.36.

To convert the two-way table to a two-way relative frequency table, we need to calculate the relative frequencies for each category. Relative frequency is calculated by dividing the frequency of a particular category by the total count in that row or column.

Let's denote the missing value as 'x'. To find the value of 'x', we need to ensure that the sum of the relative frequencies in each row and each column adds up to 1.

First, let's calculate the relative frequencies for each category:

Likes hockey: The total count in this row is 12 + 18 = 30.

Relative frequency of "Likes hockey" = 12/30 = 0.4

Relative frequency of "Doesn't like hockey" = 18/30 = 0.6

Likes baseball: The total count in this column is 12 + 14 = 26.

Relative frequency of "Likes baseball" = 12/26 ≈ 0.4615

Relative frequency of "Doesn't like baseball" = 14/26 ≈ 0.5385

To ensure that the relative frequencies add up to 1, we can set up the following equations:

0.4 + x = 1 (sum of relative frequencies in the "Likes hockey" row)

0.4615 + 0.5385 + x = 1 (sum of relative frequencies in the "Likes baseball" column)

Simplifying the equations, we have:

x = 0.6 (1 - 0.4) = 0.6 * 0.6 = 0.36

For more such questions on relative frequency

https://brainly.com/question/27562468

#SPJ8

The x-intercept of the function is (-1/3, 0) and (5, 0)

Given is a graph of a parabola having equation y = -3x²+14x+5, we need to find the x-intercept of the graph,

So to find the x-intercept put y = 0,

Therefore,

-3x²+14x+5 = 0

-3x²+15x-x+5 = 0

-3x(x-5)-1(x-5) = 0

(-3x-1)(x-5) = 0

Therefore,

x = -1/3 and x = 5

Hence the x-intercept of the function is (-1/3, 0) and (5, 0)

Learn more about x-intercept click;

https://brainly.com/question/14180189

#SPJ1

solve  -6x2-3x+12 dived by 3x-3 using pemdas

Step-by-step explanation:

The question is how to divide this this is how to solve it

The midpoint of three points with the position vector 1/3(a + b + c) is given by:

P = (b + c - B - C) / 2 + (1/3)(b + c)

The point with the position vector 1/3(a + b + c) is given by:

P = F - (2/3)D - (1/3)E + (1/3)(b + c)

To find the point with the position vector 1/3(a+b+c), we can use the fact that the position vector of a point that divides a line segment in a given ratio can be found by taking the weighted average of the position vectors of the endpoints.

Given that D, E, and F are the midpoints of line segments BC, AC, and AB, respectively, we know that:

D = (B + C) / 2

E = (A + C) / 2

F = (A + B) / 2

To find the point with the position vector 1/3(a+b+c), we can substitute a = 3F - 2D - E into the equation:

1/3(a + b + c) = 1/3((3F - 2D - E) + b + c)

Expanding the equation further:

1/3(a + b + c) = 1/3(3F - 2D - E + b + c)

= (F - (2/3)D - (1/3)E) + (1/3)(b + c)

Therefore, the point with the position vector 1/3(a + b + c) is given by:

P = F - (2/3)D - (1/3)E + (1/3)(b + c)

Substituting the midpoints:

P = (A + B) / 2 - (2/3)((B + C) / 2) - (1/3)((A + C) / 2) + (1/3)(b + c)

= (A + B - 2B - 2C - A - C + b + c) / 2 + (1/3)(b + c)

= (b + c - B - C) / 2 + (1/3)(b + c)

Therefore, the midpoint of three points with the position vector 1/3(a + b + c) is given by:

P = (b + c - B - C) / 2 + (1/3)(b + c)

The point with the position vector 1/3(a + b + c) is given by:

P = F - (2/3)D - (1/3)E + (1/3)(b + c)

For such more questions on midpoint of three points.

https://brainly.com/question/18226052

#SPJ11

Answer: Shade 6 pieces

Step-by-step explanation:

Because 2/5 of 15 is 6

Answer:

w = 18

Step-by-step explanation:

Step 0: Set up the equation

=> -3w - 4 + 5w = 32

Step 1: Move the same variable together

=> -3w + 5w = 32 + 4

Step 2: Add up and simplify

=> 2w = 36

Step 3: Divide both by 2

=> w = 18

Answer:

W=18

Step-by-step explanation:

-3w-4+5w=32

-3w+5w-4=32

2w-4=32

2w=32+4

2w=36

W=18

Step-by-step explanation:

Use the first fundamental theorem of calculus.

∫₆¹⁰ f'(x) dx = f(10) − f(6) = 8 − 8 = 0

Answer:

\(t=\frac{24-25}{\frac{2.2}{\sqrt{14}}}=-1.70\)    

The degrees of freedom are given by:

\(df=n-1=14-1=13\)  

The p value for this case would be given by:

\(p_v =P(t_{(13)}<-1.70)=0.0565\)  

Step-by-step explanation:

Information given

\(\bar X=24\) represent the mean height for the sample  

\(s=2.2\) represent the sample standard deviation

\(n=14\) sample size  

\(\mu_o =25\) represent the value that we want to test

t would represent the statistic

\(p_v\) represent the p value for the test

Hypothesis to verify

We want to cehck if the true mean is lees than 25 mph, the system of hypothesis would be:  

Null hypothesis:\(\mu \geq 25\)  

Alternative hypothesis:\(\mu < 25\)  

The statistic would be given by:

\(t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}\)  (1)  

Replacing the info given we got:

\(t=\frac{24-25}{\frac{2.2}{\sqrt{14}}}=-1.70\)    

The degrees of freedom are given by:

\(df=n-1=14-1=13\)  

The p value for this case would be given by:

\(p_v =P(t_{(13)}<-1.70)=0.0565\)  

Answer:

No solutions

Step-by-step explanation:

14(z + 3) = 14z + 21

Expand brackets.

14z + 42 = 14z + 21

Subtract 14z on both sides.

42 = 21

There are no solutions.

Answer:

No solution

Step-by-step explanation:

First, We have to simplify the right side.

Distribute 14, 14z+42.

Now the equation stands as 14z+42=14z+21

Subtract 14z from both sides,

this makes it 42=21.

We know when the solution is #=#, our answer is no solution.

Answer:

\((x^2y^5)5 = 5x^2y^5\)

Step-by-step explanation:

Remove the parentheses to factor.

\(= x^2y^5 \times 5\)

Flip the expression, creating a leading term and simplifying the equation.

\(= 5x^2y^5\)

Step-by-step explanation:

the answer is in the above image

The complete factorization of the polynomial function f(x) = x³ - 4x² - 3x + 18 is (x + 2)(x - 22).

What is a polynomial ?

A polynomial is a mathematical expression involving a sum of powers in one or more variables (indeterminates) multiplied by coefficients.

where n is a non-negative integer (the degree of the polynomial), x is the variable, and (the coefficients of the polynomial). The highest power of x in the expression is n, and this term is called the leading term. The coefficient of the leading term, a_n, is called the leading coefficient.

To find the other linear factors of the polynomial function f(x) = x³ - 4x² - 3x + 18, we can use long division by dividing the polynomial function by (x + 2).

Here's how the long division would look like:

x³ - 4x² - 3x + 18

       ÷ x + 2

__________________________

x² - 6x - 20

             ÷ x + 2

__________________________

x - 22

       ÷ x + 2

__________________________

-20

here -20 is the remainder.

The complete factorization of the polynomial function f(x) = x³ - 4x² - 3x + 18 is (x + 2)(x - 22).

So, the other linear factors are x - 22.

Therefore, The complete factorization of the polynomial function f(x) = x³ - 4x² - 3x + 18 is (x + 2)(x - 22).

To learn more about Polynomial from given link.

https://brainly.com/question/29780212

#SPJ1

Answer:

35 and 1/4

Step-by-step explanation:

6x47/8

6/1x47/8

282/8

35 1/4 or 35.25

Answer:$31,500

Step-by-step explanation:

To calculate the total amount Mario will pay, including the loan amount and interest, for the loan from First Bank of Trust, we need to calculate the interest and add it to the loan amount.

The formula to calculate simple interest is:

Interest = (Loan Amount) x (Interest Rate) x (Loan Length)

Let's plug in the values given:

Loan Amount = $25,000

Interest Rate = 6.5% (or 0.065 as a decimal)

Loan Length = 4 years

Interest = $25,000 x 0.065 x 4 = $6,500

Now, let's calculate the total amount Mario will pay:

Total Amount = Loan Amount + Interest = $25,000 + $6,500 = $31,500

Therefore, the total amount Mario will pay, including the loan amount and interest, for the First Bank of Trust loan is $31,500.

Using the translation vector of 3 units up and 1 unit right resulted to image coordinate of

(3, 7)

(3, 5)

(2, 5)

The image is attached

The translation vector is of the rule 3 units up and 1 unit to the right

The coordinate of the preimage are

(2, 4)

(2, 2)

(1, 2)

The translation is done as below

(2 + 1, 4 + 3) = (3, 7)

(2 + 1, 2 + 3) = (3, 5)

(1 + 1, 2 + 3) = (2, 5)

Learn more about translation at

https://brainly.com/question/1574635

#SPJ1

Answer:

the formula for this is y=mx+b

b stands for the y, m is the slope of the line,  and x stands for the x axis!

Step-by-step explanation:

i am pretty sure your answer is -1.4

hope this helps I to help you out attached a screenshot

Answer:

$2.99

Step-by-step explanation:

find 5% of $1.87 by multiplying 1.87 by 0.05. to get 0.0935. then multiply 0.0935 by 12 to get 1.122. round that to 1.12 and add it to the original 1.87 to get 2.99.

The value of the function F(3) will be 1/125. It is obtained by putting the value 3 in the place of x.

A connection between independent variables and the dependent variable is defined by the function. Functions help to represent graphs and equations.

A function is represented by the two variables one is dependent and another one is an independent function. The relation between them is shown as y if dependent and x is the independent variable.

F(x)=(1/5)ˣ

F(3)=(1/5)³

F(3)=1/125

Hence, the value of the function F(3) will be 1/125.

To learn more about the function refer to the link

https://brainly.com/question/12431044.

The degree of the polynomial is 14

The polynomial is given as:

y^2+7x^14-10x^2

Here, we assume that the variable of the polynomial is x

The highest power of x in the polynomial y^2+7x^14-10x^2 is 14

Hence, the degree of the polynomial is 14

Read more about polynomial at

https://brainly.com/question/4142886

#SPJ1

The Length and Width = 11 feet with minimum perimeter = 22 feet

What exactly is a math area?

The amount of space occupied by a flat (2-D) surface or an object's shape is known as its area. Draw a square on a piece of paper using a pencil. A 2-D figure, that is. The term "Area" refers to the area that a shape occupies on paper. Now picture that your square is composed of smaller unit squares.

Given that:

A=s^2 = 121, where s is a square side.

s=sqr121 = 11

length=width = 11

perimeter =4s=4(11)=22

A=LW

121=LW

L=121/W

utilizing calculus,

Perimeter = P = 2L+2W  = 2(121/W) + 2W = 242/W + 2W

Set the derivative equal to zero before determining W.

P'(W) = 2 -242/W^2 = 0

2W^2 =242

W^2 = 121

W =sqr121 = 11 = width of the rectangle that minimizes perimeter

L= 121/sqr121 = sqr121 = 11 = length of the rectangle that minimizes perimeter

L=W means a square with 4 sides each = 11

Learn more about area

https://brainly.com/question/25292087

#SPJ1

Answer:

1 2/7 ........................................

Answer:

1 2/7.

Step-by-step explanation:

Divide 9 by 7 :- this gives 1 with a remainder of 2.

So it is 1 2/7.