Leila's vegetable garden has an area of 400 ft. It is the shape of a rectangle with a length of 40 ft and a width of She has decided to expand the garden to make room for several new varieties of lettuce. The new garden will be a larger rectangle. She plans on making the new length 2 times the current length and the new' width 4 times the current width.
(a) Fill in the blanks to describe the size of Leila's new garden.
___ ft x ___ ft = ___ ft²
(b) How will the expansion change the area of the garden?
The area of the new garden will be _____ times the area of the current garden.
(c) Leila's friend Keiko also wants to expand her rectangular garden. Keiko wants her new garden to be a rectangle that has 20 times the area of her current garden. She goes to Leila for advice. Fill in the blank so that Leila's advice to Keiko is correct.
Make the new length 5 times the current length, and make the new width _____times the current width.

The solution for the function R(x) = x - 7 / x + 2 ≤ 0 is −2<x≤7 or x (-2, 7].

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.

Given:

The function R(x) = x - 7 / x + 2

The given condition x - 7 / x + 2  ≤ 0

Solve the inequality as shown below

Here, the critical points are x = 7 and x = -2

Check the denominator for the critical point, x = -2 will not be suitable for the function as it becomes undefined,

Thus

−2<x≤7 or x (-2, 7]

Therefore, the solution for the function R(x) = x - 7 / x + 2 ≤ 0 is −2<x≤7 or x (-2, 7].

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The average rate of change of the function on the interval from x = 3 to x = 5 is 40.

In mathematics, the average rate of change is a measure of how much a dependent variable (such as y) changes in proportion to a change in the independent variable (such as x). It is calculated by dividing the change in the dependent variable by the change in the independent variable during a certain time period. If the value of y rises by 5 units when the value of x rises by 2 units, the average rate of change is 5/2 Equals 2.5 per unit change in x. Calculus students frequently use this idea to compute the slope of a line on a graph or to calculate the rate at which a function changes. It is a crucial idea in several domains.

How to solve?

f(x) = 10(2)x,the interval is from x = 3 to x = 5

At x = 3,  10(2)3 = 80

at x = 5, 10(2)5 = 160

total change over the interval from x = 3 to x = 5 is 160 - 80 = 80.

the length of the interval is 5 - 3 = 2,

average rate of change is 80 / 2 = 40.

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Answer:

p = - 123/10 = -123/10 = -12.3

Step-by-step explanation:

-3(0.5 + 3p) = -6(p - 5.9)

Use the distributive property to multiply -3 by 0.5 + 3p

-1.5 - 9p = -6 (p - 5.9)

Use the distributive property to multiply -6 by p - 5.9

-1.5 - 9p = -6p + 35.4

Add 6p to both sides

-1.5 - 3p = 35.4

Add 1.5 to both sides

-3p = 35.4 + 1.5

Add 35.4 and 1.5 to get 36.9

-3p = 36.9

Divide both sides by -3

p = 36.9/-3

Expand 36.9/-3 by multiplying both numerator and the denominator by 10.

p = 369/-30

Reduce the fraction 369/-30 to lowest terms by extracting and canceling out 3.

p = -123/10

The statement that is true about the algebraic expression 450 −15t is B. A student has 450 marbles. They give t marbles to each of their 15 friends. The expression represents the total marbles the student is left with.

In mathematics, an algebraic expression is an expression composed of variables and constants as well as algebraic operations (addition, subtraction, etc.). Terms combine to form expressions.

In this case, when a student has 450 marbles. They give t marbles to each of their 15 friends.

The expression represents the total marbles the student is left with will be:

= 450 - (15 × t)

= 450 - 15t

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The two integers are equal to 1 and 7 respectively.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Let x represent the smaller number. Then the given relationships say ...

1/x + 2/(x+6) = 9/7

Multiplying by 7x(x+6), we have ...

7(x+6) +14x = 9x(x+6)

9x² +54x = 21x +42 . . . . .eliminate parentheses, swap sides

9x² +33x = 42 . . . . . . . . ...subtract 21x

3x² +11 -14 = 0 . . . . . . . . . .subtract 42 and divide by 3

(3x +14)(x -1) = 0 . . . . . . . . factor

Values of x that make this true are x = 1 and x = -14/3. Then for the positive integer x=1, the other integer is x+6=7.

Therefore, the two integers are equal to 1 and 7 respectively.

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The distances from the point (x,y) are given as follows:

Suppose that we have two points with coordinates given by [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].

The shortest distance between them is given by the equation presented as follows:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The coordinates of the focus of the parabola are given as follows:

(-3,2).

Hence the distance of the point (x,y) to the focus of the parabola is given as follows:

√(x+3)²+(y-2)².

The equation that defines the directrix is given as follows:

y = 4.

The y-coordinate of the point is of:

y.

Hence the distance is of:

|y - 4|.

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The solution of the system of equation is as follows;

System of equation can be solved using different method such as elimination method, substitution method and graphical method.

Let's solve the system of equation using substitution method as follows:

y = x² + 4

y = 2x + 4

Therefore,

2x + 4 = x² + 4

x² - 2x   = 0

x² = 2x

x = 2

Let's find y

y = 2x + 4

y = 2(2) + 4

y = 4 + 4

y = 8

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The set of rational numbers arranged from least to greatest is -3.5, -1/4, 1/3, 2, which is option (b).

Any number that can be represented as the ratio of two integers and where the denominator is not zero is referred to as rational.

The given sets of rational numbers are:

(a) -3.5, -1/4, 2, 1/3

(b) -3.5, -1/4, 1/3, 2

(c) 2, 1/3, -1/4, -3.5

(d) -1/4, 1/3, 2, -3.5

Note that 1/4 = 0.25 and 1/3= 0.33

Therefore, the set of rational numbers arranged from least to greatest is -3.5, -1/4, 1/3, 2, which is option(b).

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Answer:

11

Step-by-step explanation:

If it is correct, could you please give me brainliest? I would really appreciate it! Thank you!

Answer:

Step-by-step explanation:

This term refers to any set of circumstances that involves at least one person using some sort of communication to modify the perspective of at least one other person.

Answer: c

Step-by-step explanation:

j took the quiz on apex

Answer:

C

Step-by-step explanation:

Answer:

I think the Answer choice = C

Step-by-step explanation:

Answer: A

Step-by-step explanation:

The three angles in a triangle add to [tex]180^{\circ}[/tex]. Therefore, each angle measures [tex]\frac{180^{\circ}}{3}=60^{\circ}[/tex].

Answer:

1

Step-by-step explanation:

x²-10x+9 = 0

(x-9)(x-1) = 0

x-9 = 0  =>  x=9

x-1 = 0  =>  x=1

Answer:

Below

Step-by-step explanation:

The numerator factors , so you have this:

(m+4)(m-2) / (m+4)         the (m+4) 's cancel and you are left with (m-2)

The graph of the function y = - 2x + 6 is plotted and attached.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

We have the following equation of line -

y = - 2x + 6

Given is the following equation of line as -

y = - 2x + 6

The slope of the line would be [- 2] and the [y] intercept would be [6].

Refer to the graph attached.

Therefore, the graph of the function y = - 2x + 6 is plotted and attached.

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Answer: f^-1(x)=(3x-2)/4

Step-by-step explanation:

1. Change the x and y

y=(4x+2)/3 → x=(4y+2)/3

2. Swap sides (optional)

x=(4y+2)/3 → (4y+2)/3=x

3. Multiply the equation by 3 on both sides

(4y+2)/3=x → (3)*(4y+2)/3=x*(3)

4. Subtract 2 from both sides

(3)*(4y+2)/3=x*(3) → 4y=3x-2

5. Divide 4 from both sides

4y=3x-2 → y=(3x-2)/4

6 Substitute f^-1(x) for y

y=(3x-2)/4 → f^-1(3x-2)/4

Answer:

5 months and the cost is $430

Step-by-step explanation:

Let's start by figuring out the equations for both dance studios.

Q : 30 registration fee plus 80 per month.

R : 105 registration fee plus 65 per month.

We can use the variable m for months.

Registration is a flat fee, so that will be it's own term. Plus the costs per month. We will multiply the costs per month times months, m.

Q :  30 + 80m

R : 105 + 65m

Now, if we want to find out how many lessons until the costs are equal, we need to make the two equations equal to each other.

80m + 30 = 65m + 105

Now, we work backwards to find out what m is.

Subtract 30 on both sides.

80m = 65m + 75

Subtract 65m on both sides

15m = 75

Divide by 15 on both sides to isolate m.

m = 5

After 5 months, the total cost of the dance lessons will be equal at the two studios. To find out the cost, we must multiply the months back in. We can substitute 5 in for any of the equations as they are equal. I will use 80m + 30.

80(5) + 30 = ?

400 + 30 = ?

430 = ?

The cost for both studios will be equal at 5 months, with a cost of $430.

Answer:

hope it helps!

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

8y ≤ 10x  Divide both sides by 8

y ≤ 5/4x  Simplified

See the attached picture.  This is crossing the y axis at 0.  If you start at (0,0) and go up 5 and to the right 4.  You will see the second point graphed.  This demonstrates the slope of the line.  ≤ tells us that we are including everything below the line.

You should check out Desmos.  It is a free graphing program.  It is cool.

Answer:

P= 8

Step-by-step explanation:

-1 (-2p = -3p + 8)

2p = 3p - 8

-p = -8

p = 8

to check this...

-2(8) = -3(8) + 8

-16 = -24 + 8

-16 = -16

290 lbs is the same as 131.542 kg.

So, they should be administeted (131.542)(11.9) mg, which is about 15.65 mg.

Answer: what is the answer?

Step-by-step explanation:

a salad costs $0.25 per ounce!:)

Answer:

  no solution

Step-by-step explanation:

You want the solution to the absolute value equation |6y -7| = -1.

The expression on the left side of the equal sign is the output of the absolute value function. That output can never be negative: all negative input values are transformed to positive output values by the absolute value function.

The expression on the right side is negative. There is no value of the variable that will make the absolute value function give a negative output. There can be no solution.

Answer:

how much oz does it take to make mac and cheese and pizza? will edit when get answer

Step-by-step explanation:

Answer:

$36

Step-by-step explanation:

First, let us make an expression to solve this using the given information.

For that let the total cost be x.

Amount of the bill                     tip                     total cost

          100                 ⇒               20          ⇒           120

           30                  ⇒               20          ⇒            x

Accordingly,

100 ⇒ 120

30   ⇒  x

Use cross multiplication and solve for x.

100x = 120 × 30

100x = 3600

Divide both sides by 100.

x = $ 36

Answer:

10.59

Step-by-step explanation:

Answer:

Part (c):

Part (d):

Part (e):

Step-by-step explanation:

Given equations:

[tex]\textsf{1.\;\;Mr.\;Pace}: \quad y = \dfrac{3}{4}x + 4[/tex]

[tex]\textsf{2.\;\;Mr.\;Glintz}: \quad y = \dfrac{2}{3}x + 7[/tex]

[tex]\textsf{3.\;\;Ms.\;Liskey}: \quad y = 3x[/tex]

[tex]\textsf{4.\;\;Mr.\;Brininger}: \quad y = \dfrac{1}{2} + 10[/tex]

Plot the lines on the given coordinate plane.

(See attachment).

Draw a line at y = 25 to represent the distance at the finish line.

Find the points of intersection of the linear equation of each contestant and the finish line equation y =25.  The point with the smallest x-value is the contestant who is first place.

Mr Pace

[tex]\begin{aligned}\implies 25&= \dfrac{3}{4}x + 4\\\dfrac{3}{4}x&=21\\x&=28\; \sf seconds\end{aligned}[/tex]

Mr Glintz

[tex]\begin{aligned}\implies 25&= \dfrac{2}{3}x + 7\\\dfrac{2}{3}x&=18\\x&=27\; \sf seconds\end{aligned}[/tex]

Mr Liskey

[tex]\begin{aligned}\implies 25&= 3x\\x&=8.33\; \sf seconds\;(2\;d.p.)\end{aligned}[/tex]

Mr Brininger

[tex]\begin{aligned}\implies 25&= \dfrac{1}{2}x + 10\\\dfrac{1}{2}x&=15\\x&=30\; \sf seconds\end{aligned}[/tex]

Therefore, the order in which the contestants reached the finish line is:

From inspection of the attached graph, Ms Liskey (red line) passes all three contestants.  To find the time at which she passes the other contestants, substitute her equation into the contestant's equation and solve for x.

Mr Pace

[tex]\begin{aligned}\implies 3x&= \dfrac{3}{4}x + 4\\\dfrac{9}{4}x&=4\\x&=1.78\; \sf seconds\;(2\;d.p.)\end{aligned}[/tex]

Mr Glintz

[tex]\begin{aligned}\implies 3x&= \dfrac{2}{3}x + 7\\\dfrac{7}{3}x&=7\\x&=3\; \sf seconds\end{aligned}[/tex]

Mr Brininger

[tex]\begin{aligned}\implies 3x&= \dfrac{1}{2}x + 10\\\dfrac{5}{2}x&=10\\x&=4\; \sf seconds\end{aligned}[/tex]

Therefore:

If you want to win the race, either:

The volume of the jewelry box will be;

⇒ 343 inch³

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Edna bought a cube-shaped jewelry box that has 7-inch sides.

And, The volume of a cube with side s is s³.

Now,

Since, Edna bought a cube-shaped jewelry box that has 7-inch sides.

Hence, The volume of the jewelry box = 7³

                                                            = 7 × 7 × 7

                                                            = 343 inch³

Thus, The volume of the jewelry box will be;

⇒ 343 inch³

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