Laura and Kirk are comparing how much they have been running. Laura has already
run 36 miles and Kirk has run 64. Laura begins running 21 miles per week and Kirk runs 17 miles
per week. How many additional weeks, w, will it take for their total distance run to be equal?

Answer:

(4)

Step-by-step explanation:

Let's make the smaller number equal to x. Since they are consecutive odd numbers, the larger number is x+2.

Twice the smaller number is 2x. Three times the larger number is 3(x+2). If twice the smaller is subtracted from three times the larger, then the expression should be: 3(x+2) - 2x

Then, since the result of this is four more than the smaller, this expression is x+4.

Finally, we put it all together, so we get: 3(x+2) - 2x = x + 4. Option 4 is our correct answer.

Hence, the option (4) is correct.

What is the equation?

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Here given that,

Two numbers are consecutive odd integers. If twice the smaller is subtracted from three times the larger, the result is four more than the smaller.

Let us assume the smaller number is [tex]x[/tex].

The larger number is  [tex](x+2)[/tex].

Two numbers are consecutive odd integers. If twice the smaller is subtracted from three times the larger than it is

[tex]3(x+2)-2x[/tex]

So, the result is four more than the smaller.

i.e., [tex]3(x+2)-2x=x+4[/tex]

Hence, the option (4) is correct.

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The complete table of values of the function is

x | f(x)

0 | 1

1 | 2

2 | 4

3 | 8

The ordered pairs are (x, y) = (0, 1), (1, 2), (2, 4) and (3, 8)

The equation of the function is given as

f(x) = 2ˣ

On the incomplete table of values, we have the following x values

x = 0, 1, 2, 3

Next, we substitute x = 0, 1, 2, 3 in the equation f(x) = 2ˣ

So, we have:

f(0) = 2⁰ = 1

f(1) = 2¹ = 2

f(2) = 2² = 4

f(2) = 2³ = 8

So, the complete table is

x | f(x)

0 | 1

1 | 2

2 | 4

3 | 8

When represented as ordered pairs, we have

(x, y) = (0, 1), (1, 2), (2, 4) and (3, 8)

See attachment for the graph

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Answer:

The probability is 81%

Step-by-step explanation:

Answer:

5 coffees will cost $9.25

Step-by-step explanation:

If you divide $5.55 by the 3 coffees, you get $1.85 which is the price per coffee. Multiply $1.85 by 5 to get $9.25 which is the cost for 5 coffees

Answer:

n > 8

Step-by-step explanation:

Let's call the unknown number n. Set up the inequality: (n-6)×4>n

Distribute on the left side, subtract the n from the right to the left, and continue solving.

By using the concept of proportionality, it can be concluded that

y = 5x is the proportional relation

Third option is correct

What is proportionality?

Suppose there are two quantities. Proportionality indicates that if there's a change in the value of one quantity, the value of other quantity also changes but maintaining a constant ratio

Proportionality are often direct or inverse

Direct proportion

Two quantities are said to be in direct proportion if on increasing the value of one quantity, the value of other quantity also increases and vice versa.

For example cost of an article and quantity of an article are in direct proportion

Inverse proportion

Two quantities are said to be in inverse proportion if on increasing the value of one quantity,  the value of other quantity decreases and vice versa.

For example Number of men and number of days taken by those men to complete a work are in inverse proportion

For the first option

7x - 2 = y

y = 7x - 2

Here a non zero constant (-2) is added after the term with variable x

So this relation is not proportional

For the second option

y = 2x + 4

Here a non zero constant (4) is added after the term with variable x

So this relation is not proportional

For the third option

y = 5x

Here, no non zero constant is added after the term with variable x

So this relation is proportional.

For the fourth option

y + 1 = 3x

y = 3x - 1

Here a non zero constant (-1) is added after the term with variable x

So this relation is not proportional

So the correct option is the third option

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Answer: (7/x) + 10

A quotient is a result you get after dividing two numbers, for example, 10 divided by 2 is 5. 5 is the quotient because it's the result of 10/2. Hence, the quotient of seven and a number is simply (7/x), x being any number. And that value is added to 10, leaving us with the expression (7/x) + 10.

The formula for the perimeter of the rectangle is:

P(x) = 14x - 16

We know that for a rectangle of length L and width W the perimeter is given by the formula:

P = 2*(W + L)

In this case we know that:

W = 2x - 1

L = 5x - 7

Replacing that in the perimeter formula we get:

P(x) = 2*(2x - 1 + 5x - 7)

Now we can simplify this so we get:

P(x) = 2*(2x + 5x - 1 - 7)

P(x) = 2*(7x - 8)

P(x) = 14x - 16

That is the perimeter of the rectangle in terms of x.

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The equation of the perpendicular bisector for the line is y = 1/3(x) - 2

Given: the endpoints of the line (4,6) and (8,-6)

The bisector of the line will divide the line into two i.e. the bisector will be at the point of the line.

The coordinate of the midpoint can be calculated using the formula below:

Xm = (X1 +X2)/2  and Ym = (Y1 +Y2)/2

Where X1 = 4, Y1 =6 and X2= 8, Y2= -6

Xm = (4+8)/ 2 = 12/2 = 6  and Ym = (6+(-6))/2 = 0/2 = 0

Thus, midpoint(6, 0)

slope  = y2-y1 / x2-x1

Thus, the slope of the line segment (m₁)  = -6-6 / 8-4 = -12/4 = -3

When the two lines are perpendicular, the product of their slope is -1 i.e.

m₁ × m₂ = -1

where m₁ and m₂ represent the slope of the lines

Let the slope of the bisector be  m₂

-3 × m₂ = -1

m₂ = 1/3

Equation of perpendicular bisector with coordinate (6,0):

y - 0 = 1/3(x-6)

y = 1/3(x-6)

y = 1/3(x) - 2

Therefore, the equation for the perpendicular bisector of the line segment is y = 1/3(x) - 2

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The length of the other two sides of the rectangular garden is 6 meters and the perimeter of the garden is 18 meters.

According to the question,

We have the following information:

Two sides of a rectangular garden are 3 meters long. The area of the garden is 18 square meters.

We know that the following formula is used to find the area of rectangle:

Length*width = 18

Length*3 = 18

Length = 18/3

Length of the rectangular garden = 6 meters

Now, perimeter of the rectangular garden:

2(length+width)

2(6+3)

2*9

18 meters

Hence, the length of the other two sides of the rectangular garden is 6 meters and the perimeter of the garden is 18 meters.

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Answer:

y = 1.2·x

x = 1;  y = 1.2·1 = 1.2

x = 2;  y = 1.2·2 = 2.4

x = 3;  y = 1.2·3 = 3.6

Answer:

Option D: 8.19 inches

Step-by-step explanation:

i hope this helps..have a great day! :)

Answer:

Step-by-step explanation:

from the figure we understand that it is an isosceles triangle, therefore 2 sides and two congruent angles, BD and CD are congruent, therefore 3x = x + 16.

let's solve

3x = x + 16

2x = 16

x = 8

-----------------------------

check

3 × 8 = 8 + 16

24 = 24

thee answer is good

Regarding the given matrix, it is found that:

1. a. The matrix has three rows.

1. b. The matrix has five columns.

1. c. The matrix has two dimensions.

2. The entry is 2.

3. The entry is 7.

4. The entry is -2.

5. The entry is 0.

6. The entries are: m21 and m33.

The matrix is composed by three lines of elements, and each line has five elements, hence:

The number of dimensions of the matrix are:

2, which are the rows and the columns.

The entries are symbolized as follows:

mrc.

In which:

Hence the entry m11, for example, is the element at the first row and at the first column, which is of 2.

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Answer:

A fruit seller buys 712 fruits of which 3/4 are apples. The apples that he bought 1/3 were found to be rotten if he sold all the good apples at Rs.5 1/4 each.

Step-by-step explanation:

Answer:

28, -27, 108, -42

Step-by-step explanation:

when x=2, 11x+6 = 22+6=28,

2x+28x+48= 30x+48=60+48=108

when x=-3, 11x+6 = -33+6=-27,

2x+28x+48= 30x+48=-90+48=-42

Answer:

I got 28, -27, 108, and -42. See explanation for the answer for which problems

Step-by-step explanation:

11x + 6 = ?

2x + 28x + 48 = ?

x = 2 and x = -3

Let's start with the first equation

Using x = 2

11(2) + 6 = ?

22 + 6 = 28

Using x = -3

11(-3) + 6 =?

-33 + 6 = -27

Second equation

Using x = 2

2(2) + 28(2) + 48 = ?

4 + 56 + 48 = 108

Using x = -3

2(-3) + 28(-3) + 48 = ?

-6 - 84 + 48 = -42

Answer: x=25/4 or 6.25, y=79/16 or 4.9375

Step-by-step explanation:

Normally, we would have to set up a system of linear equations, but in this case we can solve for x and plug in from there. x=5/2 or 2.5 when solving for the variable. Now we go to the second equation, plug for x, and solve for y. 5/2 times 5/2 is 25/4, multiplied by 3 is 75/4. Subtract 75/4 from -1, and divide both sides by -4.

The terms which are equivalent to the slope in a proportional relationship include:

Proportional relationships are those in which the ratios of two variables are equal. Another way to think about them is that one variable in a proportional relationship is always a constant value multiplied by the other. This is known as the "constant of proportionality."

The proportionality constant is the ratio that connects two given values in a proportional relationship. The constant of proportionality is also known as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.

The slope of a line indicates its steepness. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). The slope formula is the rise over run formula, where the fraction consists of a rise, whether the line is going up or down, divided by the run.

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Complete question

Select all the terms which are equivalent to the slope in a proportional relationship.

Constant of proportionality

Origin

Inverse

Rise over run

Unit rate

Answer:

yes if b is odd then b+6 is odd

Step-by-step explanation:

example

consider a odd number 1,3,5,7,and 9

1+6=7

3+6=9

5+6=11

7+6=13

9+6=15

all answers are odd number

The quantity of sugar required to make 78 cookies is 8.1 cups.

Given that, you need 1.25 cups of sugar to make 1 dozen cookies.

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

Here,

The quantity of sugar to make 1 cookie

= 1.25/12

= 0.10417

The quantity of sugar to make 78 cookies

= 78×0.10417

= 8.1 cups

Therefore, the quantity of sugar required to make 78 cookies is 8.1 cups.

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The statements that are true about the ordered pair (−4, 0) and the system of equations include the following:

In order to determine which statements are true with respect to a solution of the given system of linear equations, we would have to test the given ordered pairs by substituting their values into the linear equations as follows;

For ordered pair (-4, 0), we have:

2x + y = -8x

2(-4) + 0 = -8(4)

-8 = -32 (False)

For ordered pair (-4, 0), we have:

x - y = -4

-4 - 0 = -4

-4 = -4 (True).

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The function is differentiate w.r.t. x get the answer is [tex]40x^7 + 16x^3[/tex]

Given,

In the question:

The function is:
f(x) =  [tex]x^4(5x^4+4)[/tex]

Differentiate the function with respect to x.

Now, According to the question:

f(x) = [tex]x^4(5x^4+4)[/tex]

Expand the expression:

f(x) = [tex]5x^8+4x^4[/tex]

Calculate the derivative

f'(x) =  [tex]\frac{d}{dx}(5x^8+4x^4)[/tex]

f'(x) = [tex]\frac{d}{dx}(5x^8)+\frac{d}{dx} (4x^4)[/tex]

Isolate Coefficients

f'(x) = 5 x [tex]\frac{d}{dx}(x^8)+4 \frac{d}{dx} (x^4)[/tex]

Apply the power rule

f'(x) = 5x [tex]8x^7+4[/tex] x[tex]4x^3[/tex]

f'(x) = [tex]40x^7 + 16x^3[/tex]

Hence, The function is differentiate w.r.t. x get the answer is [tex]40x^7 + 16x^3[/tex]

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Using the percentage, Rapunzel participated in 9581/100 matches.

In the given question we have to find the fraction of the wrestling matches did Rapunzel participate in.

Rapunzel's team participated in a total of 143 wrestling matches.

Rapunzel participated in 67 percent of the wrestling matches.

Total matches = 143

Participated in = 67%

Total number of matches in which Rapunzel participated is

= 143*67%

= 143* 67/100

= 9581/100

Rapunzel participated in 9581/100 matches.

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By the concept of polynomial, first second and third option are correct.\

What is polynomial?

At first it is important to know about algebraic expression

Algebraic expression consist of variables and numbers connected with addition, subtraction, multiplication and division.

An algebraic expression of the form [tex]a_0+a_1x+a_2x^2 + ....+a_nx^n[/tex] is called a polynomial of degree n

For the First Option

5 - 2a is in the form of [tex]b_0 + a_1a[/tex]

So the first option is a polynomial

For the second option

[tex]4 - 8^2 -16\\4 -64 -16\\-76[/tex]

which is a constant

And all constants are polynomial

So the second option is a polynomial

For the third option

[tex]5x^3 +4x^13x +1\\5x^3 + 12x^2 +1[/tex]

which is of the form [tex]a_0+a_1x + a_2x^2 + a_3x^3, a_1 = 0[/tex]

So the third option is a polynomial

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Answer:

$93.75

Step-by-step explanation:

$125 × 0.75 = $93.75

Answer:

$93.75

Step-by-step explanation:

125x0.25

31.25

125-31.25

$93.75

Hopes this helps

Answer:

The correct answer is D

Step-by-step explanation:

the negative power shows that on the exponent shows that the value is small and is being simplified.

When ever there is a negative power we increase zeros with respect to the exponent value.

Answer:

a) -2/3

b) x^2-1/2

Step-by-step explanation:

With a manufacturing cost of $80 per phone, the selling price of $292.5 would result in the largest annual profit.

Profit is the amount of gain realized from a transaction. The profit formula is useful for figuring out the profit from selling a specific product, typically in a business, or for figuring out the gain in any financial transaction. If the selling price is more than the cost price, a profit can be determined.

Given,

q = -6p+3030

p = 505 - q/6

R(q) = 505q - q²/6

C(q) = 80q

Now, the profit function,

P(q) = R(q) - C(q)

      = (505q - (q²/6)) - 80q

P(q) = 425q - q²/6

P(q) = 425 - q/3

q = 1275 units

Now, put it in the demand function,

p = 505 - q/6

  = 505 - 212.5

  = 292.5

Therefore, the selling price is $292.5.

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Answer:

-4

Step-by-step explanation:

When answering questions like these first, combine like terms you get 3x+5 =3x+8, Subtract 5 from both of the sides you get 3x=3x+3 remove 3x from both sides and you got 0=3 this is a contradicting statement meaning no solution ∅

B) Distribute first, 3x + 2 -x  = x + 3 + 3x +4

2, Combine the like terms 2x - 1 = 7 + 4x

3, Isolate variable and constants 2x = 8 + 4x

3(1) Cont- Isolation -2x = 8

Thus divide both side by -2 giving us -4