Caroline was comparing the price of salmon at two stores. At SuperGrocery B, 3
pounds of salmon costs $24.63. The table below represents the total cost, in dollars
and cents, y, that it costs for a pounds of salmon at SuperGrocery A.
SuperGrocery A
Pounds (z) Total Cost (y)
2
$23.70
2.5
$29.63
3.5
$41.48
4.5
$53.33
How much more expensive is it, per pound, to buy salmon at
SuperGrocery A than at SuperGrocery B?

Given statement solution is :- a) The area of one semi-circle at one end is  58.09 square feet.

b) The area of the garden is 274.42 square feet.

c) The area in square metres is approximately 58.09 square feet.

The area of the garden is approximately 274.42 square feet, and the area in square meters is approximately 25.49 square meters.

a) To find the area of one semi-circle at one end, we need to calculate the area of a complete circle and then divide it by 2. The formula for the area of a circle is A = πr², where A represents the area and r is the radius.

Since the diameter of the semi-circle is equal to the width of the rectangular portion, which is 8.6 feet, the radius will be half of that, which is 8.6 / 2 = 4.3 feet.

Now we can calculate the area of the semi-circle:

A = (π * 4.3²) / 2

A ≈ 58.09 square feet

b) To find the area of the garden, we need to sum the area of the rectangular portion with the areas of the two semi-circles.

Area of the rectangular portion = length * width

Area of the rectangular portion = 18.4 feet * 8.6 feet

Area of the rectangular portion ≈ 158.24 square feet

Area of the two semi-circles = 2 * (area of one semi-circle)

Area of the two semi-circles ≈ 2 * 58.09 square feet

Area of the two semi-circles ≈ 116.18 square feet

Total area of the garden = area of the rectangular portion + area of the two semi-circles

Total area of the garden ≈ 158.24 square feet + 116.18 square feet

Total area of the garden ≈ 274.42 square feet

c) To convert the area from square feet to square meters, we need to know the conversion factor. Since 1 foot is approximately 0.3048 meters, we can use this conversion factor to convert the area.

Area in square meters = Total area of the garden * (0.3048)²

Area in square meters ≈ 274.42 square feet * 0.3048²

Area in square meters ≈ 25.49 square meters

Therefore, the area of one semi-circle at one end is approximately 58.09 square feet. The area of the garden is approximately 274.42 square feet, and the area in square meters is approximately 25.49 square meters.

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The solution of x in the inequality is x > 2

The inequality is given as:

5x + one third(3x + 6) > 14

Rewrite properly as:

5x + 1/3(3x + 6) > 14

Open the brackets

5x + x + 2 > 14

Subtract 2 from both sides of the inequality

5x + x + 2 - 2> 14 - 2

Evaluate the difference

5x + x > 12

Evaluate the like terms

6x > 12

Divide both sides of the inequality by 2

x > 2

Hence, the solution of x in the inequality is x > 2

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Answer:

x > 2, like the other guy said

Step-by-step explanation:

I hope this helps

Answer:

Step-by-step explanation:

Answer:

13.27 cm

Step-by-step explanation:

I am using (xy) to mean the length of the side xy

7^2 + (xy)^2 = 15^2

49 + (xy)^2 = 225

(xy)^2 = 225-49

(xy)^2 = 176

Side (xy) = sqrt(176) = 13.2664991614 = 13.27 cm

Answer:

-1

Step-by-step explanation:

plug in y, subtract 12 from seven, divide -5 by 5

The values of x and y are -1 and 4 respectively.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Linear equations may include one or more variables.

Given are a system of linear equations.

5x + 3y = 7

y = 4

We already have the value of y as 4.

Substituting that value of y = 4 in the first equation 5x + 3y = 7, we get,

5x + (3 × 4) = 7

5x + 12 = 7

Subtracting both sides by 12, we get,

5x + 12 - 12 = 7 - 12

5x = -5

Dividing both sides by 5, we get,

5x / 5 = -5 / 5

x = -1

Hence the value of x is -1 and the value of y is 4.

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Answer:

4

Step-by-step explanation:

Nothing higher than 12 can be a possiblity for 24.

24     1,  2,  3,  4,  6,  8,  12, 24.

32     1, 2,  4,  8,  16

36     1,  2,  3,  4,  6,  9,  12, 18

The one number that shows up the most and at the highest value, is 4. So the GCF is 4

Answer:

Step-by-step explanation:

Hope it helps you

The total cost of all the items he wants to buy with the applied discount and before tax is $9.9.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, Bashir has a loyalty card good for a 10% discount at his local hardware store.

So, Each good he buys at (100 - 10)% = 90% of the value before tax.

He wants to buy some items that cost $11  before the discount and tax.

Therefore the amount he has to pay is,

= (90/100)×11.

= $9.9

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Answer:

-5+√2 and -5-√2

Step-by-step explanation:

With the quadratic formula:

\(\displaystyle x^2 + 10x + 25 = 2\\\\x^2+10x+23=0\\\\x=\frac{-10\pm\sqrt{10^2-4(1)(23)}}{2(1)}=\frac{-10\pm\sqrt{100-92}}{2}=\frac{-10\pm\sqrt{8}}{2}=\frac{-10\pm2\sqrt{2}}{2}=-5\pm\sqrt{2}\)

We can also complete the square (which is faster):

\(x^2+10x+25=2\\(x+5)^2=2\\x+5=\pm\sqrt{2}\\x=-5\pm\sqrt{2}\)

Answer:

X - axis

Step-by-step explanation:

\( H(9, - 1) \rightarrow H'(9, 1)\)

Since in the above reflection x coordinate remains the same and y-coordinate changes from 1 to - 1, hence point H is reflecting across X - axis.

The radius of the gear should be approximately 2.8644 inches.It is important to note that when making calculations involving units, we need to make sure that all units are consistent and convert them when necessary. In this case, we converted the answer from feet to inches to match the given unit.

To find the radius of the gear that will pull a chain at 60 ft/min when rotating at 40 rev/min, we can use the formula:

chain speed = 2 x pi x radius x rotational speed

where pi is a mathematical constant approximately equal to 3.14.

We know that the chain speed is 60 ft/min and the rotational speed is 40 rev/min, so we can substitute those values into the formula:

60 = 2 x 3.14 x radius x 40

Simplifying the equation, we get:

radius = 60 / (2 x 3.14 x 40)

radius = 0.2387 ft

To convert feet to inches, we can multiply the answer by 12:

radius = 0.2387 x 12 = 2.8644 inches.

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a) The loan that Neil made for the purchase of a new refrigerator is P33,030.

b) The total amount to be repaid over a period of two years is P35,672.16.

The loan amount is the difference between the purchase price of a new refrigerator and the deposit (down payment).

The total amount to be repaid over the loan period includes the loan amount and the interest.

These amounts can be computed using an online finance calculator, including the monthly payments.

The cost of a new refrigerator = P36,700

Deposit (down payment) = 10%

The amount of the loan = P33,030 (P36,700 - P3,670)

N (# of periods) = 24 months (2 years x 12)

I/Y (Interest per year) = 7.5%

PV (Present Value) = P33,030

FV (Future Value) = P0

Results:

PMT = P1,486.34

Sum of all periodic payments = P35,672.16 ($1,486.34 x 24)

Total Interest = P2,642.16

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Answer:

90 inches tall

Step-by-step explanation:

5/6 of 12 is 10 so the blocks are 10 inches tall each 10x9 is 90

Hello!

4^16

note that 16 = 4²

thus (16)^8 = (4²)^8 = 4^(2 × 8) = 4^16.

Answer:

multicultural

Step-by-step explanation:

Answer:

A. Multicultural

Step-by-step explanation:

It shows later in the sentence that they ate Thai noodles and Egyptian falafel those come from different cultures so it must be multicultural

Answer:

d = 25/14

Step-by-step explanation:

5(2d+2) = 3 (8d-5)    

10d + 10 = 24d - 15   | +15

10d + 25 = 24d        | - 10d

25 = 14 d                  | :14

d = 25/14

Answer:

Part A)

784 feet in the air (after five seconds).

Part B)

After 12 seconds.

Step-by-step explanation:

The height h (in feet) of a rocket t seconds after being fired is modeled by the function:

\(h(t)=-16t^2+160t+384\)

Part A)

We want to find the rocket's maximum height.

Since our function is a quadratic, the maximum height will occur at its vertex. The vertex of a quadratic is given by:

\(\displaystyle \Big(-\frac{b}{2a}\, f\Big(-\frac{b}{2a}\Big)\Big)\)

In this case, a = -16, b = 160, and c = 384.

So, the vertex occurs at:

\(\displaystyle t=-\frac{160}{2(-16)}=\frac{160}{32}=5\text{ seconds}\)

The maximum height is reached after five seconds.

Then the maximum height is:

\(h(t)_\text{max}=h(5)=-16(5)^2+160(5)+384=784\text{ feet}\)

Part B)

When the rocket reaches the ground, its height h above the ground will be 0. Hence:

\(h(t)_\text{ground}=0=-16t^2+160t+384\)

Solve for t. We can first divide both sides by -16:

\(t^2-10t-24=0\)

Factor:

\((t-12)(t+2)=0\)

Zero Product Property:

\(t-12=0\text{ or } t+2=0\)

Solve for each case:

\(t=12\text{ or } t=-2\)

Time cannot be negative. Hence, our only solution is:

\(t=12\text{ seconds}\)

The rocket reaches the ground 12 seconds after it is fired.

The two solutions of the equation:

(6x - 12)/3 + 4 = 18/x

Are x = 3 and x = -3

Here we have the following equation:

(6x - 12)/3 + 4 = 18/x

Notice that in the right side we have x on a denominator, then x can not be zero, so x ≠ 0.

Now, let's start by simplifying the left side:

(6x - 12)/3+  4 = 18/x

2x - 4 + 4 = 18/x

2x = 18/x

Now we can multiply both sides by x so we get:

2x^2 = 18

Now divide both sides by 2:

x^2 = 18/2

x^2 = 9

Finally, apply the square root in both sides:

√x^2 = ±√9

x = ±3

The two solutions are x = 3 and x = -3

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Answer:

0.4 hours

Step-by-step explanation:

or 24 minutes :D

Answer:

481

Step-by-step explanation:

Answer:

Step-by-step explanation:  85 students and 80 adults        

Step-by-step explanation:

\(sinθ = \frac{3}{5} \: \: cosθ = \frac{4}{5} \\ now \\ tanθ = \frac{sinθ}{cos θ } \\ = \frac{3}{5 } \div \frac{4}{5} \\ = \frac{3}{5} \times \frac{5}{4} \\ = \frac{3}{4} \)

Hope it will help :)❤

The binomial factors of x³- 4x²+x+6​ are (x+2), (x+3), and (x-1).

Using the splitting and grouping the terms:

x³ + 4x² + x - 6

= x³ + 2x² + 2x² + x - 6  [Splitting 4x² = 2x² + 2x²]

= (x³ + 2x²) + (2x² + x - 6)

= x² (x + 2) + (2x² + 4x - 3x - 6)

= x² (x + 2) + [ 2x (x + 2) - 3 (x + 2)]

= x² (x + 2) + (x + 2) (2x - 3)

= (x + 2) ( x² + 2x - 3)

= (x + 2) ( x² + 3x - x - 3)

= (x + 2) [x (x + 3) - 1 (x + 3)]

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

Hence, the binomial factors are (x + 2), (x + 3) and (x - 1)

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The function of the graph is g(x) = [x]+2

A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

definition of terms

y = output variable

x = input variable

m = slope

c = y intercept

The c from the graph is +2

m for points (1, 3) and (-3, -1)

= (-1 - 3) / (-3 - 1)

= -4/-4

= 1

substituting to the equation  y = mx + c

y = x + 2

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The equations that can be used to solve for y, the length of the room, are: y(y + 5) = 750, y² – 5y = 750, and y(y – 5) + 750 = 0.

It states that when multiplying a number by a group of numbers added together, you can multiply the number by each individual number in the group and add the products together to get the same answer.

In order to find the length of the room, we need to solve for y in each of the equations given.

First, let's solve for y in the equation y(y + 5) = 750. We can use the distributive property to expand the equation to y² + 5y = 750.

Then, we can subtract 750 from both sides of the equation to get y² + 5y - 750 = 0.

To solve the equation, we need to factor it. We can use the difference of squares formula to factor the equation, yielding (y + 25)(y - 30) = 0. Therefore, one solution for y is y = -25, and the other solution is y = 30.

Second, let's solve for y in the equation y² – 5y = 750.

To solve this equation, we can add 5y to both sides to get y² = 5y + 750. Then, we can divide both sides by y to get y = 5y + 750.

We can then subtract 5y from both sides to get y - 5y = 750. Finally, we can divide both sides by 5 to get y = 150.

Third, let's solve for y in the equation y(y – 5) + 750 = 0.

To solve this equation, we can use the distributive property to expand the equation to y² – 5y + 750 = 0.

Then, we can subtract 750 from both sides to get y² – 5y = -750.

To solve the equation, we need to factor it. We can use the difference of squares formula to factor the equation, yielding (y + 25)(y - 30) = 0. Therefore, one solution for y is y = -25, and the other solution is y = 30.

In conclusion, the equations that can be used to solve for y, the length of the room, are y(y + 5) = 750, y2 – 5y = 750, and y(y – 5) + 750 = 0. The solutions for y are y = -25 and y = 30.

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Answer:

See below

Step-by-step explanation:

A: The linear equations are x + y = 125 and x = y + 45.

B: Everyday Angela spends 40 minutes in playing golf.

C: No, it is not possible for Angela to spend 80 minutes playing soccer every day.

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

Part A:

Let x be the number of minutes Angela plays soccer every day

Let y be the number of minutes Angela plays golf every day

According to the problem statement the linear equations are -

x + y = 125 (total time playing both sports is 125 minutes)

x = y + 45 (Angela plays 45 more minutes of soccer than golf)

Part B:

Substitute x = y + 45 into the first equation -

(y + 45) + y = 125

Use the addition operation -

2y + 45 = 125

2y = 80

y = 40

Angela spends 40 minutes playing golf every day.

Part C:

If Angela spends 80 minutes playing soccer every day, then

x = 80

y + 45 = 80 (using the equation x = y + 45)

y = 35

But this would mean that she plays golf for 35 minutes and soccer for 80 minutes, which adds up to a total of 115 minutes.

This is not possible since the problem states that Angela plays both sports for a total of 125 minutes every day.

Therefore, it is not possible for Angela to have spent 80 minutes playing soccer every day.

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