what's the slope, y intercept, and rate of change of y=2x+5?

 3.1       Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

The number of 1/8 cups in 3/4 cup is given by the equation A = 6 cups

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 number of cups be represented as A

Now , the equation will be

The amount of the bigger cup = 3/4

The size of the measuring cup = 1/8

So , the number of cups A = amount of the bigger cup / size of the measuring cup

Substituting the values in the equation , we get

The number of cups A = ( 3/4 ) / ( 1/8 )

On simplifying the equation , we get

The number of cups A = ( 3/4 ) x 8

The number of cups A = 3 x 2

The number of cups A = 6 cups

Therefore , the value of A is 6 cups

Hence , the number of cups is 6 cups

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Answer:

415 milliliters

Step-by-step explanation:

Given,

The quantity of orange juice she consumes = 355 milliliters,

And, the quantity of syrup she consumes = 6 centiliters,

Since, 1 centiliters = 10 milliliters

⇒ The quantity of syrup she consumes = (10×6) milliliters = 60 milliliters

Thus, the total liquid she consumed = The quantity of orange juice she consumes + the quantity of syrup she consumes

= 355 + 60

= 415  milliliters

The value of the 2¹/₂ divided by 1/3 is equal to 15/2, or 7¹/₂

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

So, we can rewrite the expression as:

2¹/₃ ÷ 1/3 = (5/2) ÷ (1/3)

Now, we multiply the first fraction by the reciprocal of the second fraction:

(5/2) ÷ (1/3) = (5/2) × (3/1)

Multiplying the numerators and denominators, we get:

(5 × 3) ÷ (2 × 1) = 15/2

Therefore, 2¹/₂ divided by 1/3 is equal to 15/2, or 7¹/₂.

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Final answer:

The student's question involves finding two numbers with a known sum of 30 and a difference of 12. By setting up a system of linear equations and solving them, the two numbers are determined to be 21 and 9.

Explanation:

The student is asked to solve a system of linear equations where two numbers have a known sum and difference. Let's define the numbers as x and y. According to the problem, x + y equals 30, and x - y equals 12. We can solve these equations simultaneously to find the values of x and y.

Adding the two equations: (x + y) + (x - y) = 30 + 12, which simplifies to 2x = 42, so x = 21. Substituting x back into one of the original equations, 21 + y = 30, gives y = 9. Therefore, the two numbers are 21 and 9.

This exercise demonstrates one of the fundamental rules of mathematics used to find unknown quantities. Regardless of the context, such arithmetic rules are universally valid, and misunderstanding these rules, like miscounting goats or students as in the provided examples, leads to errors.

Answer:

The correct option is 3.

Step-by-step explanation:

Let the number of gallons of gas she bought at the first station be x and the number of gallons of gas she bought at the second station be y.

It is given that the first gas station she used charged $3.50 per gallon and the second gas station charged $4.00 per gallon.

Total cost is defied as

[tex]T=3.50x+4.00y[/tex]

Alina spent no more than $45 on gas for a road trip.

[tex]T\leq 45[/tex]

[tex]3.50x+4.00y\leq 45[/tex]                  .... (1)

If she bought all number of gallons from the second station, then

[tex]4y\leq 45[/tex]

Divide both sides be 4.

[tex]y\leq 11.25[/tex]

Number of gallon can not negative.

[tex]0\leq y\leq 11.25[/tex]                     .... (2)

Inequality (1) relates the number of gallons of gas and inequality (2) represent all the possible values of x.

Therefore, the correct option is 3.

Answer:

3.5x + 4y ≤ 45, 0 ≤ y ≤ 11.25  (c)

A total of 6 students from the combined classes of 21 and 19 students will need to share computers in a lab with 34 computers available.

The question involves determining how many students will need to share a computer when both classes with 21 and 19 students, respectively, are in a computer lab with 34 computers at the same time. To solve this, you can add the number of students in both classes to get the total number of students, and then subtract the number of available computers to find out how many students will need to share.

Adding the two classes together, 21 + 19, we get a total of 40 students. Since there are 34 computers, we subtract this from the total number of students: 40 - 34 equals 6. Therefore, 6 students will need to share a computer.

Answer:

The correct option is (a) i.e.

h(-4) = -2

Step-by-step explanation:

The mathematical expression is given as :

[tex]h(x)=-2x-10[/tex]......(1)

Where

h(x) is dependent on x

We need to find the value of h(x) at x = -4 . Putting the value of x in equation (1) we get :

[tex]h(-4)=-2(-4)-10[/tex]

[tex]h(-4)=8-10[/tex]

h(-4) = -2

The value of h(-4) is -2. So, the correct option is (a). Hence, this is the required solution.

Answer:

a.350

b.240

c.210

d.270

Step-by-step explanation:

We have to find the product of given number using place value.

a.[tex]5\times 70[/tex]

Place of 7 in 70 =tens

[tex]5\times 7\; tens =35 \;tens[/tex]

[tex]5\times 70=35\times 10=350[/tex]

c.[tex]7\times 30[/tex]

Place of 3 in 30 =Tens

[tex]7\times 3 \;tens=21 \;tens[/tex]

[tex]7\times 30=21\times 10=210[/tex]

b.[tex]60\times 4[/tex]

Place of 6 in 60=Tens

[tex]6 \;tens\times 4=24 \;tens[/tex]

[tex]60\times 4=24\times 10=240[/tex]

d.[tex]90\times 3[/tex]

[tex]9\;tens\times 3=27\;tens[/tex]

[tex]90\times 3=27\times 10=270[/tex]

Answer:

150+10x

Where, x = number of lilies

Step-by-step explanation:

To find the total cost of a pair of pants priced at $29.95 with a 5% sales tax, calculate $29.95 multiplied by 0.05 for the tax amount, add that to the original price, and the total cost including tax is $31.45.

To calculate the total cost of a pair of pants with a sales tax, you first need to determine the amount of tax to be added to the price. Here's how you can do it:

Convert the sales tax rate from a percent to a decimal by dividing by 100. For a 5% sales tax, you get 0.05.

Multiply the price of the item by the decimal sales tax rate to find the amount of sales tax. So, $29.95 imes 0.05 = $1.4975.

Round the sales tax to the nearest cent, giving us $1.50.

Add the sales tax to the original price of the item. Therefore, $29.95 + $1.50 = $31.45, which is the total cost with tax.