I apologize about the quality the shaded region is the trapezoid part not the square in the middle

(a) Setting A(w)=458, we get:

Subtracting 800 from the above equation we get:

Dividing the above equation by -18 we get:

Therefore Omar has been saving for 19 weeks.

(b) Recall that to evaluate a function at a given value, we substitute the variable by the given value.

Evaluating A(w) at w=5 we get:

Simplifying the above result we get:

Answer:

(a) 19.

(b) $710.

Answer:

The answer selected is correct

Step-by-step explanation:

When talking about balance, having -X (being X in the negative) , means owing X.

Dylan owes $19.25

Elise owes $42.75

Francesca owes $23

Jamaal owes $35.50

So naturally, Dylan owes the least.

The solution that we have that would have to do with the measurement of the unknown side would be 12.

How to solve for the unknown

The Pythagoras theorem says that the length of the suym of the square of a triangle is the same as the sum of the square of the other two sides.

From the definition that we have above.

We have the shortest side as 5.

The longest side as 13

Then we would have

13² - 5² = 25 - 169

= 144

Next we would have to take the square root of 144

= √144

= 12

Hence we would say that the length of the unknown is given as 12

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C. 6

To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.so

Step 1

given

a)let

b) now, replace and calculate

therefore, the answer is

C. 6

I hope this helps you

s = 28π/3

The radius, r = 8

The angle, θ = 7π/6 radian

The length of the arc, s = rθ

s = 8 x 7π/6

s = 28π/3

For the point 1)

- The domain will be: (note that this is not an interval, it is a set of two points)

-The range is the set R of all real numbers (since the line extends to infinite)

-The first graph is NOT a function

For the point 2)

-The domain will be the interval

-The range is the interval:

-The second graph is a function.

She walked 3 1/4 miles per day.

Given,

Jane walked 9 3/4 miles in the course of 3 days.

If we calculate this mixed number into a fraction,

We get:

9 3/4 miles = {(9×4)+3} / 4 miles

=39/4 miles.

So, Jane walks 39/4 miles in 3 days.

Therefore, in one day she walked:

(39/4 ÷ 3) miles

= 13/4 miles per day

Let's now convert this fraction into a mixed number:

when 13 is divided by 4 we get the remainder as 1 and the quotient as 3.

So, a mixed number is given by:

quotient remainder/divisor

Hence 13/4 = 3 1/4.

So, Jane walked 3 1/4 miles per day.

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Given:

The dimension of square shape floor is 200 feet by 200 feet.

The area of the square is calculated as,

Now, given that the 1/2 bottle will cover approximately 2000 quare feet.

It gives,

So, the number of bottles required are,

Answer: option B)

Given data:

The weight of man and daughter = 90

The weight of man and cat is = 70

The weight of cat and daughter = 40 .

The man weights 60 kg.

then daughter weight = 90-60 = 30.

Thus the daughter weight is 30kg.

therefore the cat weight iwith daughter, 40-30 = 10 .

also with father, 70-60 = 10 .

Thus, the father weight is 60 kg.

The daughter weight is 30 kg and

The cat weight is 10 kg.

We are to determine the amount that you have pay back after borrowing a principal amount ( P ) for ( t ) number of years which is compounded annualy at rate ( R ).

You borrowed a principal amount of:

The time duration for which we have borrowed the money for is:

The annual interest rate coumpounded each year is:

Step 1: Determine the simple interest that accumulated at the end of ( t ) years.

The folllowing formula is used to determine the simple interest that the borrower has to pay once the period of borrowing/lending is over i.e ( t ) years.

The simple interest is the proportional rate of interest ( R ) and the initial borrowed/loaned amount called principal amount ( P ).

Use the above simple interest formula ( I ) by plugging in the respective values as follows:

Therefore, the total amount of interest that the borrower must pay as an extra ( over the borrowed amount ) is $27.

Step 2: Determine the total amount that is to be returned/paid to the lender

The total amoun that is to be paid by the borrower ( you ) to the lender is the principal amount borrowed ( P ) and the amount of interest accumulated for the contractual time period i.e ( I ).

Therefore, the amount that you need to pay altogether is:

Solution

We have the following:

5!= 5*4*3*2= 20*3*2= 60*2= 120

Explanation:

endpoints (5,7) and (1,3)

The equation of circle formula:

To find the centre(a, b), we need to find the midpoint of the two given points:

The radius is the distance between the centre of the circle and any of the two points.

We will apply the distance formula:

Using the equation of circle:

Explanation

When the discriminant is negative, this implies that

Answer: In this case, the equation has no real solutions;

Answer:

Expected value = 2.21

Explanation:

The formula to obtain the expected value is given by:

We will proceed to calculate the given scenario as given below:

Therefore, the expected value of this scenario is 2.21

SOLUTION:

We want to know the scale factor of the transformation from;

We do this by taking ratios of corresponding sides, they should be the same in either case;

Thus , the scale factor is;

Thus, the scale factor is 2.

The area of a circle is given by:

Since the radius is half the diameter we have that r=6. Then the area is:

Therefore, the answer is the first one.

We have an expression with 2 unknowns, and we have values for one unknown. We have to calculate then the other unknown value:

Expression:

Then, when x=-1

When x=0

When x=4

SOLUTION:

The conversion formula from tons to pounds is;

Thus, converting this to pounds, the Blue whale would weigh;

Thus, the whale weighs 300,000 pounds

Answer:

The answer is C: 150/y

Step-by-step explanation:

Given:

Required:

To identify the horizontal and vertical asymptotes, and to point the graph.

Explanation:

Now the graph of the given function is

To find the horizontal asymptotes apply the limit

Answer

It will take 2 hours to fill the daily quota if all the machines are running.

Explanation

To find how long it takes to fill the daily quota if all the machines are running, we use the relation below:

Rate of machine 1 + Rate of machine 2 + Rate of machine 3 = Total rate of the machines

From the given data, the cost per pound of apple, CP=$1.89≈$2.

We have to estimate the cost of n=3.2≈3 pounds(lb) of apple.

The cost of n=3 lb of apple can be calculated as,

Therefore, the cost of 3. pounds of apples is about $6.048.

Let

y ------> the amount earned

x ----> the number of hours worked

In this problem we have a direct variation

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y=kx

where

k is the constant of proportionality

k=y/x

In this problem the value of k is hourly rate

so

we have

For y=$90 -------> x=5 hours

substitute

k=90/5

k=$18 per hour

substitute in the linear equation

y=18x

so

Part 1) What is the meaning of the 18 that appears in the table?

18 is the hourly rate ( amount earned by a one hour of work)

Part 2) Explain how Lin used this table to solve the problem.

using the table

For x=8 hours

the value of y=$144

Verify with the equation

y=18x

y=18(8)=144 -----> is ok

Part 3) At this rate, how much would Lin be paid for 3 hours of work? For 2.1 hours of work.

For x=3 hours

substitute in the equation

y=18x

substitute the value of x

y=18(3)=$54

For x=2.1 hours

y=18(2.1)=$37.8

We have to find the vertical and horizontal lines that passes through the point (3,6).

A vertical line will be defined as x = constant. If it passes trough a point (x,1,y1), the line will be defined as a x=x1, so the point (x1,y1) belongs to the line.

The same goes for horizontal lines, but in this case the line is defined as y = constant.

For a point (x1,y1), the horizontal line that pass through the point will be y = y1.

Then, for point (x,y)=(3,6), the vertical and horizontal lines as:

x=3 and y=6.

Answer:

Vertical line: x = 3

Horizontal line: y = 6.

A quadratic function in standard form with the given characteristics is (1/4) x² - 3x + 5.

Given that, the graph is passing through (2, 0), (10, 0) and (6, -4).

The standard form of a quadratic equation is given as:

ax² + bx + c = 0 where a, b, c are real numbers and a ≠ 0.

Now, the equation passes through (2, 0)

y = ax² + bx + c

0 = 4a + 2b + c  ----------------(1)

The equation passes through (6, -4)

y = ax² + bx + c

-4= 36a + 6b + c ----------------(2)

The equation passes through (10, 0)

y = ax² + bx + c

0 = 100a + 10b + c ----------------(3)

Using the Gauss elimination method to solve the system of equations we get,

a = 1/4, b = -3, and c = 5

The quadratic equation will be:

y = ax² + bx + c

y = (1/4) x² - 3x + 5

Therefore, a quadratic function in standard form with the given characteristics is (1/4) x² - 3x + 5.

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ANSWER :

49f and 7(f + 6f)

EXPLANATION :

From the problem, we have :

When multiplied, it will be 49f

When breaking it down, 7f is equal to f + 6f. Then it will be 7(f + 6f)

The next options f + 14 and f + 49 has two terms, so it will not be equivalent to the given expression with one term.

So the only expressions that are equivalent to the given expression are 1 and 2

We have a rectangular garden.

The length L is 8 feet more than 3 times its width.

3 times the width is 3w, so we will add 8 to it and equal it to the length L:

The perimeter will be 2 times the length plus 2 times the width. We can write it and transform it to an expression in terms only of w:

The perimeter has a value of P=16+8w.

We can draw the diagram as:

Part B: If the perimeter of Jims garden is 88 feet, what would be the width of the garden?

We will use the equation we derived in Part A, and we have to replace P=88, in order to find w.

The width is 9.75 feet.

The expression which represents the written form of the basic form expression; 2√3 as a single form is; √12.

It follows from the task content that the basic form expression be written as it's equivalent single form expression.

Since the given radical expression is; 2√3; it follows that the expression can be written as a single form expression as follows;

First, the square of 2, 2² is equal to 4;

Hence, by the converse;

2 = √4.

The given expression can therefore be written as; √4 • √3.

The expression above can therefore be written in its single form as; √(4 × 3) = √12.

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SOLUTION

The transformation of the function

To give the graph in the question is as follows.

The graph is move to the left from the origin by 1 unit on the x-axis, which is to add 1 to x, we have

Also,

The graph is the move upward along the y-axis by 7 unit, which is addition of 7 to the function

Then, the equations becomes

Therefore

The function that produce the graph in the image is

y = (√x+1) + 7

D= {-2,0,1, 2,3,4}

1) Considering that the Domain is the set of entries of a function, on the x-axis, and examining that graph we can state

- The lowest value for that is given by x=-2

- The highest value for that is x= 4

- The points (-2,-4) (0,0), (1,1), (2,2), (3,1) and (4,6)

2) So, we can write the set, the Domain, after examining the options as:

D= {-2,0,1, 2,3,4}

Notice that we're considering the x-coordinates

3) So the answer is D= {-2,0,1, 2,3,4}