Algebra (Comparing Two Linear Functions)

Answer:

g-games

r-rides

1.5 g + 2.5r= 16.5

g=2r

Step-by-step explanation:

g: # of games played

r: # of rides ridden

total amount spent:  1.50g + 2.50r = 16.50

relationship of games to rides: g = 2r

Hope this helped! :D

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The number of games is 3.

The number of rides is 8.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number of rides = m + 5

Number of games = m

Now,

Each game costs $1.50 and each ride costs $5. Isaac spent $44.50 altogether at the carnival.

This means,

1.50m + 5(m + 5) = 44.50

1.50m + 5m + 25 = 44.50

6.50m = 44.50 - 25

m = 19.5/6.50

m = 3

Now,

The number of games = 3.

The number of rides.

= m + 5

= 3 + 5

= 8

Thus,

The number of games is 3.

The number of rides is 8.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ2

Answer:

50 inches, or 4 1/6 feet

Step-by-step explanation:

If one inch is equal to 6 1/4 feet, we can translate this number from feet to inches.

4 1/6 feet = 75 inches.

Now we can take 75 and find out 2/3 of it.

2/3 of 75 is 50.

The answer is 50 inches.

If you want to convert the answer from feet to inches, its simple.

12 × 4 = 48

50 - 48 = 2

2 inches is equal to 1/6 of a foot.

The answer in feet, is 4 1/6 foot.

Step-by-step explanation:

speed=distance÷time

A.V.S=440÷11=40m/s

hope it helps.. Please mark brainliest.

Answer:

40 m/s

Step-by-step explanation:

Find:

We are asked to find the unit rate, How many meters per 1 second?

Know:

440 meters in 11 seconds

Solve:

440 meters in 11 seconds

  ? meters in 1 second

   440/11  = 40 meters per second

Answer:

The average speed of the person is 40 m/s

Answer:

1,519

Step-by-step explanation:

96 ( 32 ÷ n ÷ 2 ) –s –t^r

since n = 4, r = 3, s = 9, and t = 2. we will just substitute for the values like this

96 ( 32 ÷ (4 ÷ 2) ) –9 ( –2³)

96 ( 32 ÷ 2 ) –9 –8

96 ( 16 ) –17

=1,536 –17

=1,519

i hope i helped

Answer:

Both answers C & E are correct

Step-by-step explanation:

[tex]\sf\frac{7}{10}-\frac{4}{40}[/tex]

First, make the denominator the same to solve the fraction.

For that, multiply both the numerator and denominator by 4 in the fraction 7/10.

[tex]\sf\frac{7*4}{10*4}-\frac{4}{40}\\\\\sf\frac{28}{40}-\frac{4}{40}\\\\\sf\frac{28-4}{40}\\\\\sf\frac{24}{40}[/tex]

To write the answer in its simplest form divide both the numerator and denominator by 8.

[tex]\sf\frac{3}{5}[/tex]

Therefore, the answer is [tex]\sf\frac{24}{40}[/tex] = [tex]\sf\frac{3}{5}[/tex]

Hope this answer helps you

Answer:

$1984.80

Step-by-step explanation:

165.40 times 12 equals 1984.80

Answer:

He pays $1984.80 on his loan in one year.

Step-by-step explanation:

If he pays 165.40 per month, and there are 12 months in one year, then we must multiply the values together.

165.4*12 = 1984.8

He pays $1984.80 on his loan in one year.

The percentage decrease of the depth of the lake from January to August is 20%.

The difference between the initial and final numbers is shown as a percentage reduction. It displays a percentage loss of value compared to the original regardless of the units. The decrease is equal to the initial amount less the final amount.

Given,

The depth of lake in January = 943 feet

The depth of lake in August = 754.4 feet

The difference is = (943-754.4) feet

                             = 186.6 feet

So, the percentage decrease of the depth of the lake from January to August will be =  (186.6 ÷ 943) × 100

                        = 20%

Therefore, the answer is 20%.

To know more about percentage decrease refer to:

https://brainly.com/question/13631568

#SPJ1

Answer:

Step-by-step explanation:

1.5/0.15=10

1.5 is 10 times greater than 0.15

The solution is 10

The number of times the number 1.5 is greater than the number 0.15 is 10

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented A

Now , the value of A is

Let the first number be P = 1.5

Let the second number be Q = 0.15

Now , the number of times the number P is greater than Q is given by the equation

A = P / Q

Substituting the values in the equation , we get

A = 1.5 / 0.15

On simplifying the equation , we get

A = 10

Therefore , the value of A is 10

Hence , the number of times 1.5 is greater than 0.15 is 10 times

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ2

Answer:

1 or 3

Step-by-step explanation:

Total 9 rows will have exactly 42 projects.

The Fundamental mathematical operation are Addition,Subtraction

Multiplication and Division.

Given,

The total number projects in the science fair is 405.

The  coordinator displays the projects in rows of 42.

To know the exact number of rows having 42 projects

we will divide total project by 42 i.e; 405/42.

The quotient will be the number of row exactly having 42 projects

and the last row will contain less than 42 projects which is remainder.

i.e;  Dividing 405 by  42

    quotient will be 9.

      remainder will be 27.

So,Total 9 rows will have exactly 42 projects.

To find more question related to mathematical operations click on the link below:

https://brainly.com/question/20628271

#SPJ1

Answer:

116.64

Step-by-step explanatio hope this helps

Answer:

Your answer is [tex]1\frac{1}{3}[/tex]

Step-by-step explanation:

(attached)

Answer:

[tex]1 \frac{1}{3}[/tex] or 4/3 or 1.3333...

Step-by-step explanation:

1/2--5/6

When you subtract a negative, it is the same as adding a positive. 1/2+5/6

Create like denominators:

3/6+5/6

Simplify:

8/6

1 1/3 or 1.3333...

Answer: Spain

After Rome, St.Paul wanted to go to Spain.

Step-by-step explanation:

Paul planned to visit Macedonia

Answer:

1/2, 1, 0, 1/2

Step-by-step explanation:

We can solve this by rounding each fraction to either 0, 1/2, or 1.

The first fraction, 7/12, is pretty close to 6/12, which is 1/2 of 12.

So we can round this to 1/2.

The second fraction, 5/6, is closer to 6/6 (1) than 3/6 (1/2).

So we can round this to 1.

The third fraction, 2/11 is closer to 0 than 5.5/11 (1/2).

We can round this to 0.

4/9 is closer to 4.5/9 (1/2) than 0.

We can round this to 1/2.

Therefore, when we round all of these fractions, we are left with 1/2, 1, 0, 1/2.

Answer: -1/2

Step-by-step explanation: To solve this problem, we can use the properties of logarithms to isolate the variable x on one side of the equation. The properties of logarithms tell us that the logarithm of a product is the sum of the logarithms of the factors, and that the logarithm of a power is the exponent times the logarithm of the base.

If log₂(4x + 6) = 4, we can rewrite the left side of the equation as follows: log₂(4x + 6) = log₂(2^4 * (2x + 3))

Then, using the property of logarithms that the logarithm of a product is the sum of the logarithms of the factors, we can simplify the equation as follows: log₂(4x + 6) = 4 + log₂(2x + 3)

Now, we can use the property of logarithms that the logarithm of a power is the exponent times the logarithm of the base to simplify the equation even further: log₂(4x + 6) = 4 + 1 * log₂(2x + 3)

Since the logarithm of a power is the exponent times the logarithm of the base, this means that the logarithm of a number is the logarithm of that number divided by the logarithm of the base. Therefore, we can divide both sides of the equation by log₂ to isolate the variable x on one side of the equation:

log₂(4x + 6) / log₂ = 4 + 1 * log₂(2x + 3) / log₂

(4x + 6) / 1 = 4 + (2x + 3) / 1

4x + 6 = 4 + 2x + 3

4x + 6 = 2x + 7

2x = -1

x = -1/2

Therefore, if log₂(4x + 6) = 4, then x = -1/2.

Answer:

P-2l/2=w

Step-by-step explanation:

P = 21 + 2w

Solve for w

Subtract 21 from both sides.

P - 21 = 2w

Divide both sides by 2.

P-21/2 = w

Carleen owns a Dog as her pet.

The logical thinking definition is analysing a situation or problem using reason and coming up with potential solutions.

Given that, Amy, Brenda and Carleen own a cat, a dog and a fish, but not necessarily in that order.

It is saying that Amy hats a cat, which ca be meant she has a pet cat

Therefore, Amy owns a pet cat.

Now, Brenda can not have a hairy pet because she has allergic conditions, so the only pet in the given list with no hair is the fish

Therefore, Brenda owns a pet fish.

Now, only Carleen is left, and a pet dog is left.

Therefore, Carleen owns a pet dog.

Hence, Carleen owns a Dog as her pet.

For more references on logical thinking, click;

https://brainly.com/question/3368793

#SPJ1

Answer: 0.65=13/20

Step-by-step explanation: First, rewrite the decimal number as a fraction and put 1 in the denominator's place. 0.65/1
Then, multiply to get rid of 2 decimal places. Then, multiply top and bottom by 10^2 which equals 100

0.65/1 × 100/100= 65/100

Find the Greatest Common Factor or GCF of 65 and 100, and reduce the fraction by dividing both the numerator and denominator by GCF = 5,

[tex]\frac{65/5}{100/5}[/tex]=13/20

Hope this helps!

Answer: x = 59

Step-by-step explanation:

i dont know what you are trying to figure out but x = 59 im guessing u need

Answer:

Step-by-step explanation:

First, add

90

and subtract

2

x

from each side of the equation to isolate the

x

term while keeping the equation balanced:

8

x

−

90

+

90

−

2

x

=

2

x

−

36

+

90

−

2

x

8

x

−

2

x

−

90

+

90

=

2

x

−

2

x

−

36

+

90

(

8

−

2

)

x

−

0

=

0

+

54

6

x

=

54

Now, divide each side of the equation by

6

to solve for

x

while keeping the equation balanced:

6

x

6

=

54

6

6

x

6

=

9

x

=

9

There will be 0.48 grams will be left in the sample after 59 years.

Function is a type of relation, or rule, that maps one input to specific single output.

Since we have given that initial sample of 171 g of a radioactive substance decays according to the function

[tex]A(t) = 171e ^ {- 0.04(t) }[/tex]where t is given in years

Here, Initial amount of radioactive substance = 171 grams

We need to find the amount of substance that will be left in the sample after 59 years.

So, t = 59 years

So, it becomes,

[tex]A(t) = 171e ^ {- 0.04(59) }\\\\A(t) = 0.48[/tex]

Hence, there will be 0.48 grams will be left in the sample after 59 years.

Learn more about function here:

https://brainly.com/question/2253924

#SPJ1

Answer:

9

Step-by-step explanation:

Slope is rise over run, and we can see on the char that every time the x-value increases by 1, the y-value increases by 9, so the slope is 9/1, or 9.

Answer:   -4,-2

Step-by-step explanation:

(i)Take y-5=-4x

Make y as subject of formula i.e. y=-4x+5

Now compare it with y=mx+c

Then Slope m=-4

(ii) 3y-9=-6x

Making y as subject of formula i.e. 3y=-6x+9

Divide through by 3

then it will become y=-2x+3

Now comparing it with y=mx+c

then Slope m=-2

After 15 minutes the pan will have a temperature of 36°F

Newton's Law of Cooling, if a body with temperature T₁ is placed in surroundings with temperature To, different from that of T₁, the body will either cool or warm to temperature T(t) after t minutes, where T(t) = T₀ + (T₁-T₀)e^(kt)

Given: T₁ = 120°F,  T₀ = 0°F. After 5 minutes, T(t) = 80°F

T(t) = T₀ + (T₁-T₀)e^(kt)

80 = 0 + (120-0)e^(5k)

80 = 120e^5k

e^5k = 80/120

e^5k = 2/3

5k = ln(2/3)

k = ln(2/3) / 5

k = -0.0811

The temperature of the pan after 15 minutes will be:

T(t) = T₀ + (T₁-T₀)e^(kt)

T(15) = 0 + (120-0)e^(-0.0811×15)

T(15) = 120e^(-0.0811×15)

T(15) = 36°F

Learn more about Newton's Law of Cooling on:

brainly.com/question/19534304

#SPJ1

Answer:

y = -x + 4

Step-by-step explanation:

m = y2-y1 / x2-x1

m = 4-6/ 0-(-2)

m = -2/2

m = -1

y = -x + b

4 = -(0) + b

b = 4

y = -x + 4

Could you please give me brainliest for this? Thanks!

B(x) as a product of linear factors is B(x) = (x+2)(x+7)(x-1)

The linear factors of a polynomial are the first-degree equations that are the building blocks of more complex and higher-order polynomials. Linear factors appear in the form of ax + b and cannot be factored further.

if ( x+2) is a factor of the polynomial, then x+2 can divide the polynomial without remainder.

see attached document for detailed division of the polynomial [tex]x^{3}+8x^{2} +5x-14[/tex].

In conclusion B(x) as a product of linear factors is B(x) = (x+2)(x+7)(x-1)\

Learn more about linear factors: https://brainly.com/question/26791528

#SPJ1

Step-by-step explanation:

i think its no, but im not sure.

The time it would take the two sisters to paint 80 mugs is 8 hours.

From the question, we are to determine how long it would take the sisters to paint 80 mugs

From the given information,

"The younger sister can paint 2 mugs every half hour"

That is,

The younger sister can paint 4 mugs every hour

Also

"The older sister can paint 6 mugs every hour?"

Let x represent the number of hours it would take them to paint 80 mugs.

Then, we can write that

4x + 6x = 80

10x = 80

x = 80/10

x = 8

Hence, the time it would take is 8 hours

Learn more on Calculating time here: https://brainly.com/question/12355798

#SPJ1