The cost, C, in dollars, of playing g games at an arcade game
center is modeled by the linear function C = 0.5g + 2.
Determine the rate of change of the function and explain
what this value means in terms of the context.
Determine the initial value of the function and explain what
this value means in terms of the context.

Final answer:

An algebraic expression that represents 'x squared is less than 15' can be written directly as 'x² < 15', without additional mathematical operations.

Explanation:

The question asks for an algebraic expression that represents the inequality 'x squared is less than 15'. This is straightforward to write and does not require completing the square or solving a quadratic equation. The algebraic expression that correctly represents this inequality is simply x² < 15.

To explain further, the inequality suggests that the square of x (x²) must be less than the value 15. We do not need to perform any additional steps or manipulations like factoring or applying the quadratic formula, as the expression represents a basic inequality in its simplest form.

The sale price of the coats is 160% of the purchase price of the coats.

Step-by-step explanation:

The owner buys the coats at a purchase price= $60

He sells the coats for a selling price= $96

Now, the question is:

The selling price $96 is what percentage of the purchase price $60

step 1: 96= x% of 60

step 2: 96= (x/100)*60

step 3: 96= 6x/10

step 4: 960/6 = x

step 5: x = 160%

1/4=.25

3/12=.25

yes they are equal

Answer:

B salary

Step-by-step explanation:

Your employment status, salary, and bank account balances are never disclosed on your report and have no bearing on your rating.

Although your income has no bearing on your credit score, it's still crucial to understand the five key components of a FICO credit score, the most widely used credit score by lenders.

History of payments (35%): Your credit score is mostly influenced by whether you have a history of making on-time payments on your credit accounts.

Your salary does not directly affect your credit score, but it does affect your ability to pay off credit card debt.

Therefore, Your race, gender, marital status, level of education, religion, political party, or source of income are all factors that are never taken into account when calculating your credit ratings.

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If the caterpillar crawled 22cm farther than the ant, then we are adding 53 and 22 to get 75cm.

Answer:

75cm

Step-by-step explanation:

53 + 22 = 75

Answer: ( 11, -2 )

Step-by-step explanation:

The mid point of a line is calculated using the formula:

M = ([tex]\frac{x_{1}+x_{2}}{2}[/tex] , [tex]\frac{y_{1}+y_{2}}{2}[/tex] )

From the question , the mid point is already given , substituting , we have :

(5 , - 7.5 ) = ([tex]\frac{x-1}{2}[/tex] , [tex]\frac{y-13}{2}[/tex] )

Equating the x component to x and the y component to y , we have

5 = [tex]\frac{x-1}{2}[/tex]

x - 1 = 10

x = 11

Also

- 7.5 = [tex]\frac{y-13}{2}[/tex]

-15 = y - 13

-15 + 13 = y

Therefore : y = -2

Therefore : the location of point P is ( 11, -2 )

Consider the two numbers as

x and y

. From the given data, we write:

x−y=3

x+y=13

From the first equation, we determine a value for x.

x−y=3

Add y to both sides.

x=y+3

In the second equation, substitute x with (y+3).

x+y=13

(y+3)+y=13

Open the brackets and simplify.

y+3+y=13

2y+3=13

Subtract 3 from each side.

2y=10

Divide both sides by 2.

y=5

In the first equation, substitute y with 5.

x−y=3

x−5=3

Add 5 to each side.

x=8

Answer:

The vertex is the point (1,-8)

Step-by-step explanation:

we have

[tex]y=-4x^{2} +8x-12[/tex]

Convert to vertex form

step 1

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]y+12=-4x^{2} +8x[/tex]

step 2

Factor the leading coefficient

factor -4

[tex]y+12=-4(x^{2} -2x)[/tex]

step 2

Complete the square. Remember to balance the equation by adding the same constants to each side

[tex]y+12-4=-4(x^{2} -2x+1)[/tex]

[tex]y+8=-4(x^{2} -2x+1)[/tex]

step 3

Rewrite as perfect squares

[tex]y+8=-4(x-1)^{2}[/tex]

therefore

The vertex is the point (1,-8)

Final answer:

The sum of the two numbers is 60 and their quotient is 4. Using the substitution method, we find that the two numbers are 48 and 12.

Explanation:

Let's call the two numbers x and y. We're given that the sum of the two numbers is 60, so we can write the equation:

x + y = 60

We're also given that their quotient is 4, so we can write the equation:

x / y = 4

To solve this system of equations, we can use the substitution method. Solving the second equation for x, we get:

x = 4y

Substituting this value of x into the first equation, we get:

4y + y = 60

Combining like terms, we have:

5y = 60

Dividing both sides by 5, we find:

y = 12

Substituting this value of y back into the equation x = 4y, we get:

x = 4(12)

Simplifying, we find:

x = 48

So the two numbers are 48 and 12.

Answer:

Therefore ,the distance, on a coordinate plane, between the points G(2.-3) and D(2, 4) is [tex]GD = 7\ units[/tex]

Step-by-step explanation:

Given:

point G( x₁ , y₁) ≡ ( 2 ,-3)  

point D( x₂ , y₂) ≡ (2 , 4)  

To Find:

Distance between GD=?

Solution:

Distance Formula between two point is given by

[tex]l(GD) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}[/tex]

Substituting the values we get

[tex]l(GD) = \sqrt{((2-2)^{2}+(4-(-3))^{2} )}[/tex]

[tex]l(GD) = \sqrt{((0)^{2}+(4+3))^{2} )}=\sqrt{49}=7\\l(GD)=7\ units[/tex]

Therefore ,the distance, on a coordinate plane, between the points G(2.-3) and D(2, 4) is [tex]GD = 7\ units[/tex]

There are 10 kangaroos and 24 dingoes in this animal rescue.

Step-by-step explanation:

Given,

Total head count = 34 heads

∴ Kangaroos + Dingoes = 34

Let us assume,

Number of kangaroos as "x" and number of dingoes as "y"

The equation can be framed as x + y = 34

The number of feet for kangaroo = 2 feet

The number of feet for dingoes = 4 feet

The total number of feet = 116 feet

So, the equation can be framed as 2x + 4y = 116

Step 1 : Muliply the 1st equation by 2.

The new equation is 2x + 2y = 68

step 2 : Subtract the above equation with the second equation.

    2x + 2y = 68

  -2x - 4y = -116

          -2y = -48

step 3 : Therefore, y =24. Substitute y=24 in the 1st equation.

x + 24 = 34

x = 34-24

x = 10

Kangaroos, x = 10 kangaroos

Dingoes, y = 24 dingoes

Final answer:

To find the number of kangaroos and dingoes, we can use a system of equations to solve for their values. Given the number of feet and heads, we can form equations to represent these quantities. Solving these equations simultaneously yields the solution of 10 kangaroos and 24 dingoes.

Explanation:

To solve this problem, we can use a system of equations. Let's denote the number of kangaroos as 'k' and the number of dingoes as 'd'. We are given two pieces of information:

1. The total number of feet is 116, where each kangaroo has 2 feet and each dingo has 4 feet. So, the equation would be: 2k + 4d = 116.

2. The total number of heads is 34. Since each animal has only one head, the equation would be: k + d = 34.

We can solve these equations simultaneously to find the values of k and d. Multiplying the second equation by 2, we get: 2k + 2d = 68. Subtracting this equation from the first equation, we have: (2k + 4d) - (2k + 2d) = 116 - 68. Simplifying, we get: 2d = 48. Dividing both sides by 2, we find that d = 24.

Substituting this value back into the second equation, we can find k: k + 24 = 34, k = 10.

Therefore, there are 10 kangaroos and 24 dingoes at the animal rescue.

Answer:

2.40

Step-by-step explanation:

tangent of an angle= opposite side/ adjacent side

tan(T)= RS/ RT

tan(T)= 12/5

tan(T)= 2.40 (nearest hundredth)

Answer:

34/5

Step-by-step explanation:

6*5=30 + 4 = 34

34/5

The mixed number 6 4/5 can be converted into an improper fraction by multiplying the whole part by the denominator and adding the numerator to the result, giving us 34/5.

To convert the mixed number 6 4/5 into an improper fraction, you follow these steps:

So, (6*5)+ 4 = 34. Therefore, the mixed number 6 4/5 can be written as the improper fraction 34/5.

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Answer:

Step-by-step explanation:

8)Volume of cylinder = πr²h= π*3*3*10 =90π cubic inches

Volume of cone = 1/3πr²h = π*3*3*5/3= 15π cubic inches

Volume of rocket = 90π + 15π = 105π cubic inches

9) Matt made an error. radius = diameter/2 = 15/2= 7.5 cm.Instead using 7.5 in volume formula, he used diameter.

Answer:

6, -4

Step-by-step explanation:

abs(-1+x)=5

-1+x=5 and -1+x=-5

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

-1+x=5

x=5-(-1)=5+1=6

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

-1+x=-5

x=-5-(-1)=-5+1=-4

Answer:

s = 20   F = 100    T = 60

Step-by-step explanation:

F = 5s                F + s + T = 180

T = 5s - 40

I picked numbers until I found the one that worked. For me, 20 worked for the second angle.

The measure of first angle, second angle, and the third angle is 100, 20 and 60.

Given that,

Based on the above information, the calculation is as follows:

F = 5s                

F + s + T = 180

T = 5s - 40

Now

5s + s + 5s - 40 = 180

11s = 220

s = 20

F = 100

T = 100 - 40

= 60

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Answer: 4x + 76 = 688, $153 per ticket

Step-by-step explanation:

there are 4 tickets but you don't know the price of the tickets. Let x represent the price. Insurance costs $19. They got insurance ($19) on all 4 tickets (19 x 4) to get a insurance total of $76.

To get the price of one ticket we need to solve the equation.

4x + 76 = 688

subtract 76 from both sides.

4x = 612

divide by 4.

x = 153

each ticket costs $153

Final answer:

The price of one airline ticket, without insurance, is $153. This was found by setting up an equation for the total cost (4 tickets plus insurance for each at $19 per ticket) and solving for the price of one ticket.

Explanation:

To solve the problem, we first set up an equation to represent the total cost for the family's purchase of 4 airline tickets with travel insurance. We let x represent the price of one ticket, and since the travel insurance costs $19 per ticket, the cost of insurance for one ticket can be represented as 19 + x. There are 4 tickets, so the total cost of insurance for four tickets is $19 multiplied by 4 (which equals $76). Therefore, the equation for the total cost is:

Total Cost = 4x (price of tickets) + $76 (cost of insurance for all tickets)

According to the question, the total cost for the family is $688. So we can set up the equation:

4x + 76 = $688

To find the value of x, we subtract 76 from both sides of the equation:

4x = $688 - $76

4x = $612

Now divide both sides by 4 to solve for x:

x = $612 / 4

x = $153

Therefore, the price of one ticket is $153.

=================================================

Explanation:

In general if

u = < a, b > and v = < c, d >

then,

u+v = < a+c, b+d >

Basically we add the x coordinates separately and the y coordinates are added separately.

----------

So,

u = < -3, 4 >

v = < 8, 2 >

u + v = < -3+8, 4+2 >

u + v = < 5, 6 >

The value of numerators are 3 and 5

Solution:

Let the numerators of two fractions be x and y

Two fractions have denominators 4 and 6. Their sum is 19/12

Therefore,

[tex]\frac{x}{4} + \frac{y}{6} = \frac{19}{12}[/tex]

Cross multiply L.H.S to get simplified

[tex]\frac{6x+4y}{24} = \frac{19}{12}\\\\6x + 4y = 38 ------- eqn 1[/tex]

If the numerators are switched their sum is 7/4

Therefore,

[tex]\frac{y}{4} + \frac{x}{6} = \frac{7}{4}[/tex]

On simplification, we get

[tex]\frac{6y + 4x}{24} = \frac{7}{4}\\\\4x + 6y = 42 -------- eqn 2[/tex]

Solve eqn 1 and eqn 2

Multiply eqn 1 by 4

24x + 16y = 152 --------- eqn 3

Multiply eqn 2 by 6

24x + 36y = 252 ---------- eqn 4

Subtract eqn 3 from eqn 4

24x + 36y = 252

24x + 16y = 152

( - ) -------------------

20y = 100

Substitute y = 5 in eqn 1

6x + 4(5) = 38

6x = 38 - 20

6x = 18

Thus the value of numerators are 3 and 5

Jeremy made 110 this week from mowings yards

This week, Jeremy made a total of $110 from mowing yards. This total was obtained by adding the amounts he earned from each yard: $25, $35, and $50.

To solve this problem, we will add together the amounts of money that Jeremy earned for each yard he mowed. This is because when we want to find out a total amount across several different items or events, we use addition.

First, Jeremy earned $25 for mowing the first yard. Then, he earned $35 for mowing the second yard. Finally, he mowed the largest yard and charged $50 for it.

Now we add these numbers together: $25 + $35 + $50 = $110.

So, Jeremy made a total of $110 mowing yards this week.

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If we're talking about simple interest (and not compound interest), then

i = P*r*t

i = 5000*0.03*1

i = 150

----------

notes:

The interest earned in one year on $5,000 at an interest rate of 3% is $150. To find the interest earned on $5000 at 3% for one year, multiply the principal amount by the interest rate and time.

To calculate the interest earned with simple interest:

Interest = Principal x Rate x Time

Interest = $5000 x 0.03 x 1 year = $150

The perimeter of the garden is 57.14 m and

the total area of the garden is 178.28 sq. m.

Solution:

Given length of the rectangle = 16 m

Width of the rectangle = 8 m

Radius of the semi-circle = half of the width of the rectangle

Radius = 4 cm

Perimeter of the garden is two lengths of the rectangle and 2 curve sides of the semi-circle.

Perimeter = [tex]2l+2(\frac{2\pi r}{2} )[/tex]

               = [tex]2l+2\pi r[/tex]

               = [tex]2(16)+2\times\frac{22}{7}\times4[/tex]

               = 32 + 25.14

               = 57.14 m

Total area of the garden is the area of the rectangle and area of the two semi-circles.

Area of the garden = [tex](l\times w)+ 2(\frac{\pi r^2}{2})[/tex]

                              = [tex](l\times w)+ \pi r^2[/tex]

                              = [tex]16\times8+\frac{22}{7} \times 4\times 4[/tex]

                              = 128 + 50.28

                              = 178.28 square meter

Hence, the perimeter of the garden is 57.14 m and

the total area of the garden is 178.28 sq. m.

Answer: c. 22X

Step-by-step explanation:

Answer:

22x

Step-by-step explanation:

7 + 1 5

or

7+15

22

Answer:

It is angle k and angle l

Step-by-step explanation:

When opposite sides are given, especially for a right triangle, the longer the length the bigger the angle. The hypotenuse, which is across the right angle is always longest. The shortest side will always have the smallest angle. Check the image if it helps.

Answer:

3,600 from $26 tickets  and  1,400 from $40 tickets.  

Step-by-step explanation:

Let x = number of $26 tickets and y= number of $40 tickets

x + y = 5000  ⇒ x = 5000 - y

26x + 40y = 149,600

26(5000 - y) + 40y = 149600

130,000 - 26y + 40y = 149600

14y = 19600

y = 19600/14 = 1,400

x = 5000 - 1400 = 3,600

So, 3,600 from $26 tickets  and  1,400 from $40 tickets.

To determine the number of tickets sold at each price, set up a system of equations using the given information and solve for the variables.

To determine how many tickets should be sold at each price, we can set up a system of equations using the given information.

Let's assume the number of $26 tickets sold is x and the number of $40 tickets sold is y.

The total number of tickets sold is x + y, so we have the equation x + y = 5000.

The revenue generated from $26 tickets is 26x, and the revenue generated from $40 tickets is 40y. The total revenue

is given as $149,600, so we have the equation 26x + 40y = 149600.

Solving this system of equations will give us the values of x and y.

The area of forest after 5 years is 2846.93 square kilometer

Solution:

Given that, A certain forest covers an area of 4500 square kilometer

Suppose that each year this area decreases by 8.75%

To find: Area after 5 years

The decrease function is given as:

[tex]y = A(1-r)^t[/tex]

Where,

y is the value after t years

A = initial amount

r = decreasing rate in decimal

t is the number of years

Here in this sum,

A = 4500

t = 5 years

[tex]r = 8.75 \% = \frac{8.75}{100} = 0.0875[/tex]

Substituting the values in formula,

[tex]\begin{aligned}&y=4500(1-0.0875)^{5}\\\\&y=4500(0.9125)^{5}\\\\&y=4500 \times 0.632651\\\\&y=2846.93\end{aligned}[/tex]

Thus the area of forest after 5 years is 2846.93 square kilometer