To fill an order, the factory dyed 21 yards of silk indigo and 75 yards teal. How many yards of silk did it dye for that order?

Answer:

\( = 2\frac{2}{15} \)

Step-by-step explanation:

\( 3\frac{1}{3} - 1\frac{1}{5} \)

Convert both fractions to improper fractions

\( = \frac{10}{3} - \frac{6}{5} \)

To subtract, find a common denominator of 3 and 5.

\( = \frac{50 - 18}{15} \)

\( = \frac{32}{15} \)

\( = 2\frac{2}{15} \)

A) The algebraic expression will be 12d + 7 = 91

B) He drives 7 miles per day to work.

For 11 days straight, Ms. Chung drove the same distance every day going to and coming from work.

The distance she drove on Saturday was; 0.9 miles.

The number of miles she drives per day:

84 miles/12

= 7 miles per day

Let the number of miles she travels be day = d

12d + 7 = 91 miles

12d + 7 = 91

12d = 91 - 7

12d = 84

d = 84/12

d = 7 miles per day

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Answer:

A soccer field is 100 Yards.

Step-by-step explanation:

120-100=100yds.

Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:

10x + 5y ≥ 500 (minimum 500 units of vitamins)

5x + 10y ≥ 600 (minimum 600 units of minerals)

15x + 15y ≥ 1200 (minimum 1200 calories)

We want to minimize the cost, which is given by:

0.5x + 0.4y

This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:

10x + 5y = 500

5x + 10y = 600

15x + 15y = 1200

Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.

Next, we can calculate the value of the cost function at each corner point of the feasible region:

Corner point A: (20, 40) -> Cost = 20

Corner point B: (40, 25) -> Cost = 25

Corner point C: (60, 0) -> Cost = 30

Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.

Answer: 18 feet

Step-by-step explanation:

The area of a rectangle is given by \(A=lw\), which means that the length of the unknown side is \(\frac{216}{12}=18\) feet.

Answer:

x = 23

Step-by-step explanation:

simplify both sides of the equation then isolate the variable.

Answer:

x = 23

Step-by-step explanation:

x/20 + 20 ( -2/5 )/20 = 3/4

combine fractions with common denominator

x - 8/20 = 3/4

Multiply all terms by the same value to eliminate fraction denominators

20 . x - 8/20 = 3/4 = 20. 3/4

Cancel multiplied terms that are in the denominator

x - 8 = 20 . 3/4

Multiply the numbers

x - 8 = 15

Add 8 to both sides of the equation

x - 8 + 8 = 15 + 8

simplify

add the numbers

x = 23

The value of x that makes the line containing (1,2) and (5,3) perpendicular to the line containing (x,4) and (3,0) is x = 2.

To determine the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0), we need to find the slope of both lines and apply the concept of perpendicular lines.

The slope of a line can be found using the formula:

slope = (change in y) / (change in x)

For the line containing (1,2) and (5,3), the slope is:

slope1 = (3 - 2) / (5 - 1) = 1 / 4

To find the slope of the line containing (x,4) and (3,0), we use the same formula:

slope2 = (0 - 4) / (3 - x) = -4 / (3 - x)

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.

So, we can set up the equation:

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

Simplifying this equation:

-4 = -4 / (3 - x)

To remove the fraction, we can multiply both sides by (3 - x):

-4(3 - x) = -4

Expanding and simplifying:

-12 + 4x = -4

Adding 12 to both sides:

4x = 8

Dividing both sides by 4:

x = 2

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Part 1

The equation is \(y=a(x+8)(x-72)\).

Using the point \((62, -490)\) to solve for \(a\),

\(-490=a(62+8)(62-72) \implies a=\frac{7}{10}\\\\\therefore \boxed{y=\frac{7}{10}(x+8)(x-72)}\)

Part 2

When \(x=-8\), \(y=0\).

When \(x=2\), \(y=-490\).

So, the average rate of change is \(\frac{-490-0}{2-(-8)}=\boxed{-49}\)

The correct answer is option A: "If x doesn't equal 3, then 2x + 5 doesn't equal 11."

More precisely, if f is a function that maps elements from a set A to elements in a set B, then the inverse function of f, denoted as f^(-1), is a function that maps elements in set B back to elements in set A.

The given statement is: "If x equals 3, then 2b + 5 equals 11."

Therefore, the correct answer is option A: "If x doesn't equal 3, then 2x + 5 doesn't equal 11."

The inverse function f^(-1) is defined such that f(f^(-1)(x)) = x for all x in B, and f^(-1)(f(x)) = x for all x in A. In other words, applying the inverse function to the output of the original function returns the input value.

The existence of an inverse function depends on the properties of the original function. For example, a function must be one-to-one (or injective) to have an inverse function, which means that each input maps to a unique output. If a function is not one-to-one, then its inverse function may not exist or may have limited domain and range.

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Rate of consumption refers to the rate at which a particular resource or material is being used up. It is usually expressed as the amount consumed per unit of time, such as kilograms per hour, gallons per day, etc. The rate of consumption can be used to measure the efficiency of a process, as well as to predict future needs for the resource or material. It is also important to consider the environmental impacts of consumption, as the rate of consumption can have a significant effect on the environment if it is too high.

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By using the elimination method, the solutions to this system of three linear equations include the following:

x = 1.

y = 1.

z = 0.

In order to determine the solutions to a system of three linear equations, we would have to evaluate and eliminate each of the variables one after the other, especially by selecting a pair of linear equations at each step and then applying the elimination method.

Given the following system of linear equations:

-2x + 2y + 3z = 0                .........equation 1.

-2x - y + z = -3          .........equation 2.

2x + 3y + 3z = 5            .........equation 3.

From equation 1 and equation 3, we would eliminate x as follows:

-2x + 2y + 3z = 0

2x + 3y + 3z = 5__

5y + 6z = 5                  .........equation 4.

Next, we would pick a different pair of linear equations to eliminate x:

-2x + 2y + 3z = 0

-2x - y + z = -3___

3y + 2z = 3               ........equation 5.

From equation 4 and equation 5, we would eliminate z to get the value of y:

(3y + 2z = 3) × 3 ⇒ 9y + 6z = 9

9y + 6z = 9

5y + 6z = 5

4y = 4

y = 4/4

y = 1.

For the value of z, we have:

3y + 2z = 3

3(1) + 2z = 3

2z = 3 - 3

z = 0

For the value of x, we have:

-2x + 2y + 3z = 0

-2x + 2(1) + 3(0) = 0

-2x + 2 = 0

-2x = -2

x = 2/2

x = 1.

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The unit rate of cups of lemonade per lemon is in the ratio of 6:1.

The unit rate is the ratio of two or more quantities or values that are compared to one another.

Unit rates are also known as the constants of proportionality, constant rate, rate of change, or slope.

The number of lemons required to make 18 cups of lemonade = 3 lemons

Rate of lemonade per lemon = 18/3 = 6/1

Ratio = 6:1 or 1:6

Conversely, the rate of lemon per cup of lemonade = 1/6

Thus, we can conclude that for Zendaya to make 6 cups of lemonade, she requires 1 lemon, or alternatively, the ratio of lemon to a cup of lemonade is 1:6.

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Answer:

13.1

Step-by-step explanation:

Answer:

Around 13 ounces

Step-by-step explanation:

Answer:

The rate at which the horizontal velocity of the ball changes every second is, 19%.

Step-by-step explanation:

The exponential decay function is given by:

\(y=a(1-r)^{t}\)

Here,

y = final value

a = initial value

r = decay rate

t = time

The relationship between the elapsed time, t, in seconds, since Mustafa threw the ball, and its horizontal velocity, V (t) is:

\(V(t)=4\cdot (0.81)^{t}\)

The expression for the horizontal velocity of the ball represents the exponential decay function.

On comparing the two equations we get:

\(1-r=0.81\\r=1-0.81\\r=0.19\)

Thus, the rate at which the horizontal velocity of the ball changes every second is, 19%.

This is Linear graph.

Linear graph is represented in the form of a straight line. ... If the graph of any relation gives a single straight line then it is known as a linear graph. The word "linear" stands for a straight line. The linear graph is a straight line graph that is drawn on a plane connecting the points plotted on x and y coordinates.

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Answer:

box 1 =30 box 2= 60

Step-by-step explanation:

box 1 = 5 times 3 times 2 = 30

box2 = 5 times 3 times 4 = 60

Answer:

30 + 60=90 or 90 Cubic feet

Step-by-step explanation:

Box 1:

V= (3)(5)(2)

V= 30

Box 2:

V= (3)(5)(4)

V= 60

The system of graphs is a very unique concept which helps to understand various concepts in a visual way.

How does this occur?

The two lines intersect at (-3, -4), which is the system of equations' solution.

This is how the equation can be solved-

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Chris' gross pay for the week after selling computer equipment worth $17,000 is $2,600.

The gross pay is the addition of the base pay and the sales commission.

The sales commission is graduated and computed as follows:

Chris' base pay = $300

Sales Commissions:

First $5,000 = 10%

Above $5,000 = 15%

Last week's sales = $17,000

10% Commission = $500 ($5,000 x 10%)

15% Commission = $1,800 ($17,000 - $5,000 x 15%)

Total Commission = $2,300

Gross pay = Base Pay + Commission

= $2,600 ($300 + $2,300)

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M = 270,000 * (0.5833% * (1 + 0.5833%)^240) / ((1 + 0.5833%)^240 - 1).  Calculating this equation will give us the monthly mortgage payment for Abigail and Curtis Siebert.

Abigail and Curtis Siebert have a $270,000 mortgage at an interest rate of 7% for a term of 20 years.

To calculate the monthly mortgage payment, we can use the formula for an amortizing mortgage:

M = P * (r * (1 + r)^n) / ((1 + r)^n - 1),

where M is the monthly mortgage payment, P is the principal amount (loan amount), r is the monthly interest rate, and n is the total number of monthly payments.

First, we need to convert the annual interest rate to a monthly interest rate. Since there are 12 months in a year, the monthly interest rate is 7% divided by 12, which is approximately 0.5833%.

The total number of monthly payments is the term of the mortgage multiplied by 12. In this case, it's 20 years * 12 months, which equals 240 months.

Now, we can substitute the values into the formula:

M = 270,000 * (0.5833% * (1 + 0.5833%)^240) / ((1 + 0.5833%)^240 - 1).

Calculating this equation will give us the monthly mortgage payment for Abigail and Curtis Siebert.

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Answer:

Point W, it is going left 0.5 units which is -0.5 and then he is going down 1.25 units which is -1.25 UNits. So your answer is Point W,  I hope that this helped you!

Step-by-step explanation:

Answer:

Point W

Step-by-step explanation:

To eliminate the y-terms in this system of equations, we can multiply the second equation by 2 and add it to the first equation.

We have,

To eliminate the y-terms in this system of equations, we can multiply the second equation by 2 and add it to the first equation.

This will result in the y-terms canceling out, and we will be left with only x-terms on one side of the equation, which we can then solve for x.

So, multiplying the second equation by 2, we get:

2(3x + 4y) = 2(5)

6x + 8y = 10

Now, adding this to the first equation, we get:

4x - 8y + 6x + 8y = 20 + 10

10x = 30

Dividing both sides by 10, we get:

x = 3

Now, we can substitute this value of x back into either of the original equations to solve for y.

4x - 8y = 2

So,

4(3) - 8y = 20

12 - 8y = 20

-8y = 8

y = -1

Therefore,

The solution to the system of equations is (x, y) = (3, -1).

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Answer: C

Step-by-step explanation:

For box and whiskers plot the box is where the majority of the data is.  the whiskers(the lines on both sides will tell you where the range of numbers lie)

The middle line in the box is the median number.

The question is worded oddly where they want least likely to be more than 30 which means which one will have less than 30. (Double negative question)

You want the majority of the data to be less than 30, which is subway.  C

Answer: It depends on the position.

Step-by-step explanation: Knights are better in closed positions and bishops are better in open positions. So they are better than the other in different scenarios.

Answer:

7: 63

8: 73

arithmetic sequence

y = 10x - 7

or f(n) = 10x -7

or

\(a_{n}\) = 3 + (n-1)10

Step-by-step explanation:

the output increases by 10 every time that the input increases by 1.  That gives us our common difference or slope.  The y intercept is -7. That is the value is you worked backwards until you get to n = 0.  The initial value  is 3.  That is when n is 1.

When n is 3, f(n) is 23

When n is 2, f(n) is 13

When n is 1, f(n) is 3

When n is 0, f(n) is -7

I am not sure if this is clear.  I am assuming that you have a lot of knowledge of linear equations and how to write arithmetic sequence.  If my explanation is confusing it is me and not you.

Answer:

a. 63,73

b. Arithmetic sequence

c.t(n)=10n-7

Explanation:

a. Here is the completed table:

n | t(n)

4 | 33

5 | 43

6 | 53

7 | 63

8 | 73

b.

The type of sequence is arithmetic.

An arithmetic sequence is a sequence of numbers where the difference between any two consecutive terms is constant.

In this case, the difference between any two consecutive terms is 10.

c.

The equation for the arithmetic sequence is:

t(n)=a+(n-1)d

where:

For Question:

Now

equation becomes:

t(4) = a+(4-1)10

33=a+30

a=33-30

a=3

Now, the Equation becomes

t(n) = 3+(n-1)10

t(n) = 3+10n-10

t(n)=10n-7

The number of fidgets and pop bought was 15 each

From the information given, we have that;

1 fidget costs $3

1 Pop cost $4

Let the number of Fidgets be x

Let the number of Pop be y

Then, we have that a total of 20 fidgets and Pop cots $75

We have that;

20x + y = 75

Now, substitute the value of x as 3, we get;

20(3) + y= 75

expand the bracket

y = 75 - 60

y = 15

The number of fidgets is expressed as;

20x/4 = 20(3) /4 = 15

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Answer: (x+3)(x-4)

Step-by-step explanation:

The value of n can be determined by finding the number of visible arcs in the pattern, which is 30 in this case.

To determine the value of n, we need to find the relationship between the total length of visible areas and the number of circles (n).

In the given pattern, each circle contributes to the visible area twice: once as its circumference and once as the overlapping part with the adjacent circles. Since the circumference of each circle is 1 unit, the visible area contributed by each circle is 2 units.

Therefore, the total length of visible areas can be expressed as 2n. Given that the total length is 60 units, we can set up the equation:

2n = 60

Solving this equation, we find:

n = 60/2 = 30

Thus, the value of n is 30.

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