A square garden is surrounded by a concrete walkway of width x. The length of the walkway is 15 feet long
a) Write an expression for the area of the garden.
The formula for the area of a square is A = s^2, where s is
a side length of the square.
A(x) = (15 + 2x)
b) Consider the information given above and discuss the maximum and minimum size of the concrete walkway. Be sure to explain your estimates.

Answer:

60 square inches

Step-by-step explanation:

The width of the second frame is 2 times the width of the first frame, or 2 * 5 inches = 10 inches.

The area of the second frame is its length multiplied by its width, or 6 inches * 10 inches = 60 square inches.

Answer: 0.235

Step-by-step explanation:

To round up you need a number = 5 or > 5

So to round to 2 sig fig, the number will have to be 0.235

Answer: y = 10(x) + 56

Step-by-step explanation:

y=10(4) + 56

y = 40 + 56

y = 96

Answer:

1a. y = 10 x + 16

1b. 16

2a. y = 600x + 1500

2b. $8700

Step-by-step explanation:

1a. A linear model represents a relationship between two variables as a straight line. In this case, we want to represent the relationship between the number of hours a canoe is rented for and the total cost of the rental, including the deposit.

We can create a linear model by using the equation y = mx + b, where y is the total cost, x is the number of hours the canoe is rented for, m is the slope of the line (the rate at which the cost changes per hour), and b is the y-intercept (the total cost when x is 0).

Since the total cost includes a non-refundable deposit, we need to add this to the y-intercept. The deposit is not dependent on the number of hours the canoe is rented for, so it is not represented in the slope.

Based on the information given, the total cost is $56 when the canoe is rented for 4 hours, and the rental fee is $10 per hour. We can use these values to solve for the y-intercept and the slope:

y = mx + b

56 = (10) (4) + b

56 = 40 + b

b = 56 - 40

b = 16

So the linear model representing the relationship between the number of hours a canoe is rented for and the total cost of the rental, including the deposit, is: y = 10 x + 16

1b. We know that the total cost is $56 when the canoe is rented for 4 hours, and the rental fee is $10 per hour. We can use these values to solve for the y-intercept, which represents the non-refundable deposit:

y = (10) (4) + b

56 = 40 + b

b = 56 - 40

b = 16

So the non-refundable deposit is $16. This means that the total cost of the rental, including the deposit and the hourly fee, is $56.

2a. We can create a linear model by using the equation y = mx + b, where y is the total cost, x is the number of solar heaters produced, m is the slope of the line (the rate at which the cost changes per heater), and b is the y-intercept (the total cost when x is 0).

Based on the information given, it costs $7500 to produce 10 solar heaters, and it costs $13,500 to produce 20 solar heaters. We can use these values to solve for the y-intercept and the slope:

y = mx + b

7500 = m(10) + b

13500 = m(20) + b

Subtracting the second equation from the first equation gives:

-6000 = m(10) - m(20)

6000 = m(20) - m(10)

6000 = m(20 - 10)

6000 = m(10)

m = 6000/10

m = 600

Substituting this value for m in either of the original equations and solving for b gives:

7500 = (600)(10) + b

7500 = 6000 + b

b = 7500 - 6000

b = 1500

So the linear model representing the relationship between the number of solar heaters produced and the total cost of production is:

y = (600) x + 1500

According to this model, the total cost of producing 15 solar heaters would be $10,500.

2b. To find the total cost of producing 12 solar heaters, we can use the linear model that represents the relationship between the number of solar heaters produced and the total cost of production:

y = (600) x + 1500

Where y is the total cost, x is the number of solar heaters produced, m is the slope of the line (the rate at which the cost changes per heater), and b is the y-intercept (the total cost when x is 0).

To predict the total cost of producing 12 solar heaters, we can substitute 12 for x in the equation:

y = (600) (12) + 1500

y = 7200 + 1500

y = 8700

According to this model, the total cost of producing 12 solar heaters would be $8700.

Answer:

ok

Step-by-step explanation:

3x+1=4x-8= -6

x=-6

this is the x

I hope you have understand

That is a change in the hypotenuse's length of -2.6 inches per second.

What in math is a rate?

A rate is a unique ratio where the two words are expressed in several units. For instance, the price is 69 for 12 ounces if a 12-ounce can of maize costs 69. This is not a proportion of two comparable units, like shirts. This ratio compares two dissimilar units: ounces and cents

h = sqr(b^2 + a^2), b=30, a=40, b'=-5, a'=-7

h' = [(1/2)/sqr(b^2+a^2)](2bb' + 2aa') = sqr(30^2+40^2)(30(5)+40(-7)

= (150-280)/sqr2500 = (-130)/50 =-- -13/5 = -2.6 inches per second

2.6 inches are lost from the hypotenuse every second.

Check the response by observing what transpires in one second.

30 to 35 on the short leg

greater leg descends from 40 to 37

From 50 to 47.4 is the hypotenuse

In one second, 50-47.4 equals a 2.6 reduction. That is a change in the hypotenuse's length of -2.6 inches per second.

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Answer:

Below

Step-by-step explanation:

y+3=5(x+4)      Expand R side, then subtract 3 from both sides of equation

y = 5x+ 17     Done .

Answer:

y = 5x+17

Step-by-step explanation:

To get this equation to slope intercept form, get the y variable by itself on one side of the equal sign.

y+3=5(x+4)

[Distribute the 5 to x and 4]

y+3 = 5x+20

[Subtract 3 from both sides]

y = 5x+17

[Done!]

The expression "quantity negative three and one fourth times d plus three fifths end quantity minus quantity two and seven eighths times d plus seven tenths end quantity" or (-3 1/4d + 3/5) - (2 7/8d + 7/10) is equivalent to "negative forty nine over 8 times d minus one tenth" or -49/8d - 1/10.

An algebraic expression is a number, variable, or the combination of both and operational symbols.

To determine the equivalent of the expression "quantity negative three and one fourth times d plus three fifths end quantity minus quantity two and seven eighths times d plus seven tenths end quantity" or simply (-3 1/4d + 3/5) - (2 7/8d + 7/10), combine all like terms and perform the necessary operations.

(-3 1/4d + 3/5) - (2 7/8d + 7/10)

⇒ -3 1/4d + 3/5 - 2 7/8d - 7/10

⇒ (-3 1/4 - 2 7/8)d + 3/5 - 7/10

⇒ (-13/4 - 23/8)d + 6/10 - 7/10

⇒ (-26/8 - 23/8)d - 1/10

⇒ -49/8 d - 1/10

Hence, the equivalent expression is "negative forty nine over 8 times d minus one tenth" or -49/8d - 1/10.

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Total amount he will pay is equal to 62.880 after giving discount of 35% and adding the sales tax of 7.5%.

Discount is the total price which is deducted from the original terms so as we have to pay less.

Discount is always given on the marked price of the article.

Marked price is the cost at which article is marked.

Chandler buy shoes of $89.99.

Total discount on shoes = 35%

Price after getting Discount = 58.4935

Sales Tax = 7.5 %

Price after sales tax = 58.4935 + 7.5% of 58.4935

= 62.880

So total amount he will pay is equal to 62.880.

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23 pounds of type A coffee were used and 92 pounds of type B coffee were used, using the concept of formula equation we get -

A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign.

Let assume that, x represent the number of pounds of type A coffee that were used in the blend.

and y represent the number of pounds of type B coffee that were used in the blend.

Type A coffee costs Lena $4.10 per pound, and type B coffee costs $5.35 per pound.

The total cost of the mixture is $586.50.

Now,

4.10x + 5.35y = 586.50 ............ (i)

This month's blend used four times as many pounds of type B coffee as type A.

so, y = 4x

Substituting y = 4x into equation (i), we get -

4.10x + 5.35 × 4x = 586.50

or, 4.10x + 21.4x = 586.50

or, 25.5x = 586.50

or, x =  586.50/25.5

or, x = 23

Next, y = 4x = 4 × 23

y = 92

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Answer:

Yup I think so to

Step-by-step explanation:

Answer:

Yes, it is an elimination problem.

x = -1.69230769

Step-by-step explanation:

You can eliminate 20y by adding both equations together.

Then, you will get 13x = -22.

Divide by 13 on both sides to get x= -1.69230769

The parallelogram's area is 130 yards square.

Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.

Create a square on paper by using a pencil. Tw dimensions make it up. A shape's area on paper is the space it takes up.

Imagine that your square is made up of smaller unit squares.

The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.

To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.

According to our question-

base*height

base=13

height=10

13*10

= 130 yds

Hence, The parallelogram's area is 130 yards square.

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Answer: EASY

Step-by-step explanation:

Answer:2.

2/5 times 5 is 10/5 or 2

Step-by-step explanation:

Using the distributive property we get 5y.

What is distributive property?

The operation on numbers that are available in brackets can be distributed for each number outside the bracket, according to the distributive property. It is one of the mathematical characteristics that is utilised the most. Commutative and associative qualities are the other two important features.

This property states that multiplying the total of two or more addends by a number will provide the same outcome as multiplying each addend by the number separately and then adding the results together.

Using the distributive property

18y - 13y = (18 - 13)y

(18-13) y

Subtract the numbers: 18-13=5

=5 y

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standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-4)}}} \implies \cfrac{-8}{2 +4} \implies \cfrac{ -8 }{ 6 } \implies - \cfrac{ 4 }{ 3 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{- \cfrac{ 4 }{ 3 }}(x-\stackrel{x_1}{(-4)}) \implies y -5 = - \cfrac{ 4 }{ 3 } ( x +4) \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y-5)=3\left( - \cfrac{ 4 }{ 3 } ( x +4) \right)}\implies 3y-15=-4(x+4) \\\\\\ 3y-15=-4x-16\implies 3y=-4x-1\implies {\Large \begin{array}{llll} 4x+3y=-1 \end{array}}[/tex]

The required scale factor  for the given line segment is 2.

In math, a line segment  is limited by two unmistakable focuses on a line. Or on the other hand we can say a line portion is essential for the line that interfaces two focuses. A line has no endpoints and broadens endlessly in both the bearing yet a line fragment has two fixed or positive endpoints.

Scale factor is the number used to duplicate one item by to get another item that appears to be identical however is an alternate size. It makes a precise duplicate just bigger or more modest than the first. Scale Variable increases the image or item similarly as though you broadened or shrank it on a copier.

We have,

QS : QS' = 4 : 8 = QU : QU' = 5 : 10 = 1 : 2

Then the scale factor is of the dilation is 2 (magnification)

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Answer:

Step-by-step explanation:

The given is the number of years she drives for and how much she drives in a year.

We can use this to figure out how many miles she drives in 3, 4, and 6 years.

To do that, just multiply the number of years by the number of miles she drives in a year

[tex]\frac{9000}{1} =\frac{miles}{x years}[/tex]

[tex]9000 * x years = 1 * miles[/tex]

[tex]3 * 9000 = 27,000\\4 * 9000 = 36,000\\6 * 9000 = 54,000[/tex]

Put points at (3,27000) , (4,36000) , (6,54000)

Draw a straight line through them (not like mine)

The balance when the account went into overdraft was -48.61

An overdraft occurs when something is withdrawn in excess of what is in a current account. For financial systems, this can be funds in a bank account.

Let x be the balance when the account went into overdraft

To get back to a positive balance he deposited money at a steady rate of $31.97 per week.

Amount deposited per week = $31.97

Amount deposited 3 weeks = $95.91

Now amount in account after 3 weeks =x+95.91

We are given that After 3 weeks, he had $95.91 in the account.

So, x+95.91=47.3

x= 47.3-95.91

x= -48.61

Hence The balance when the account went into overdraft was -48.61

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Answer:

42

Step-by-step explanation:

Answer:five thousand six hundred eight

To solve the given equation, t² - t = 12, by factoring, we will use (t + 3)(t - 4) = 0. The correct option is the first option

From the question, we are to determine how to solve the given equation by factoring

From the given information,

The given equation is

t² - t = 12

First, we will solve the equation by factoring

t² - t = 12

Transfer the constant to the other side

t² - t - 12 = 0

Factorize the expression

t² -4t + 3t - 12 = 0

t(t - 4) +3(t - 4) = 0

(t + 3)(t - 4) = 0

Then,

t + 3 = 0 OR t - 4 = 0

t = -3 OR t = 4

Hence, to solve the equation we will use (t + 3)(t - 4) = 0

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The function g(x) is a piecewise function For x 4, 1 g(x) = |x + 1| and for

x 1, 3 g(x) = 2.

Suppose we have a function f(x).

f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).

f(x ± c) = Horizontal left/right shift by c units (x - + c, y).

(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).

f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).

f(-x) = Reflection over the y-axis, (-x, y).

-f(x) = Reflection over x-axis, (x, -y).

From the graph, we can conclude that g(x) is a piecewise function.

When x is - 4, 1 g(x) = |x + 1|.

And when x is 1, 3 g(x) = 2, A constant function.

Now, g(-2) = | - 2 + 1| = 1.

g(1) = | 1 + 1| = 2.

g(4) = 2.

The value of x when g(x) = 3 is - 4.

The value of x when g(x) = 1 is (0, - 2) as both satisfy g(x).

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The factored expression of 1/5c + 4/5 is 1/5(c + 4)

From the question, we have the following parameters that can be used in our computation:

1/5c + 4/5

From the above expression, we have the following highlights

In the above terms, we can see that the denominator of the terms is 5

When this denominator is removed, we have

Expression = c + 4

This means that

GCF =1/5

So, the factored expression is 1/5(c + 4)

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In this case, the terminal point of theta/2 can be determined using the following steps:

Since cos(theta/2) < 0 and the cosine function has a range of [-1, 1], it follows that theta/2 must be in the second or third quadrant (90 degrees to 180 degrees or 180 degrees to 270 degrees).

To find the terminal point of theta/2, we can use the formula for converting from polar to Cartesian coordinates: x = rcos(theta) and y = rsin(theta), where (x,y) is the Cartesian coordinates of the terminal point, r is the radius, and theta is the angle in radians.

In this case, the radius is 1 (since the terminal point is on the unit circle) and the angle is theta/2. Substituting these values into the formulas above, we get:

x = 1 * cos(theta/2)

y = 1 * sin(theta/2)

To find the values of cos(theta/2) and sin(theta/2), we can use the identity cos(theta/2) = sqrt((1 + cos(theta))/2) and sin(theta/2) = sqrt((1 - cos(theta))/2).

Substituting the given value of cos(theta) (-1/9) and the identities above into the formulas for x and y, we get:

x = sqrt((1 + (-1/9))/2) = -sqrt(2)/3

y = sqrt((1 - (-1/9))/2) = sqrt(8)/3

Thus, the coordinates of the terminal point of theta/2 are (-sqrt(2)/3, sqrt(8)/3).

The terminal point (a₁, a₂) for theta/2 is (-2/3, √(5) / 3).

To find the terminal point (a₁, a₂) of theta/2, use the half-angle identity for cosine:

cos(theta/2) = ± √((1 + cos(theta)) / 2)

Given that cos(theta) = -1/9 and cos(theta/2) < 0, the negative sign should be used in the half-angle identity.

Calculate cos(theta/2):

cos(theta/2) = - √((1 + cos(theta)) / 2)

cos(theta/2) = - √((1 - 1/9) / 2)

cos(theta/2) = - √((8/9) / 2)

cos(theta/2) = - √(8/18)

cos(theta/2) = - √(4/9)

cos(theta/2) = - 2/3

Cos(theta/2) = -2/3. To find the terminal point (a₁, a₂), determine the values of a₁ and a₂.

Since cos(theta/2) is negative, a₁ is negative. To find the value of a₂, use the Pythagorean identity:

cos²(theta/2) + sin²(theta/2) = 1

Since cos(theta/2) = -2/3, calculate sin(theta/2):

sin²(theta/2) = 1 - cos²(theta/2)

sin²(theta/2) = 1 - (-2/3)²

sin²(theta/2) = 1 - 4/9

sin²(theta/2) = 5/9

sin(theta/2) = ± √(5/9)

sin(theta/2) = ± √(5) / 3

Since theta is in the second quadrant (cos(theta) = -1/9), sin(theta) is positive in the second quadrant. Therefore, sin(theta/2) = √(5) / 3.

Now, sin(theta/2) = √(5) / 3.

So, the terminal point (a₁, a₂) for theta/2 is (-2/3, √(5) / 3).

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Answer:

72891

Step-by-step explanation:

150,000 is the base number

In the first year it will be the same, so it'll only count 13 years

the equation is: 150,000(0.946)^x

how:

150,000(100%-5.4%)^x

150,000(94.6%)^x

150,000(0.946)^x

*it's 100%-5.4% because that's that's remaining each year if it's decreasing by 5.4%. you would convert the percentage into decimals because it's decreasing by a percentage, not a whole number

150000(0.946)^13

*13 is the number of years, so it's x

72891.356467

Answer: for 35x+21 the answer is 7(5+3)

for the second one, the answer is 4x+2x+2

the 3rd one the answer is 5(6-3x)

for the fouth one the answer is 40x+50

for the fifth one the answer is 4x+4x+3

Step-by-step explanation:

Answer:8a<8b

Step-by-step explanation:

8a<8b

In linear equation,  { 2x + 3y = 7.20 ,   { 4x + 2y = 8.80 the price per pound for oranges.

 What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                  Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Product B performed worse in the study because 32% failed to get relief with this product, whereas only 28% failed to get relief with Product A.

Working through this, the percentage who failed to find relief from product A is (25 - 18) / 25 = 28%. Doing the same type of calculation for product B, we can determine the percentage who failed to find relief as (50 - 34) / 50 = 32%. The description statement asks for which offered less relief, which we can find using the less than operator:

28% < 32%

Product A offered relief to all but 28% of the people, while product B offered relief to all but 32% of the people. Given that fewer people failed to find relief on product 28%, we can argue that more people did find relief on product A.

Given that the tests are both on multiples of 25 people, we can also see the percentages by multiplying the numerators and denominators to bring both to a scale of 100:

7/25 * 4/4 = 28% of product A users failed to find relief.

16/50 * 2/2 = 32% of product B users failed to find relief.

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A) During the interval (0, 2) of the domain the water balloon's height is increasing.

B) During the interval (2, 4) of the domain the water balloon's height is staying the same.

C) During the interval (8, 10) of the domain, the water balloon's height is decreasing the fastest.

D) The height of the balloon will be zero since the height of the balloon has remained the same from the 10th interval.

What is an interval?

In mathematics, an interval is quantified in terms of numbers. Every number between two specific integers is considered to be an interval. Between those two values, this range encompasses all real numbers. Real numbers can be of any type you can imagine.

All the numbers between a pair of provided numbers are considered an interval. It is crucial to indicate if the start and end numbers are included. The Number Line, Inequalities, and Interval Notation are the three primary methods for displaying intervals.

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