Write the whole number as an equivalent fraction with the indicated denominator.

Answer:

Step-by-step explanation:

We know that the 1st equation + 2nd equation + 3rd equation = 45.  Now we just need to identify from the infor given what these equations are, then set them to equal 45.

It has already been determined that the 1st equation is x.

The second equation is "3 more than twice the first".  Twice the first is 2x, and 3 more is +3; therefore, the second equation is: 2x + 3.

The third equation is "2 more than the first".  2 more than is +2, so the third equation is x + 2.

Now we have all 3:

1st:  x

2nd:  2x + 3

3rd:  x + 2

Add them all up and set them equal to 45:

x + 2x + 3 + x + 2 = 45.

You don't have choices listed, so it's either that one above, or simplified down to:

4x + 5 = 45

After that, any simplification done will be solving the equation.

It will take approximately 6.24 minutes for both faucets to fill the bathtub when used simultaneously.

To solve this problem, we need to find the combined rate at which both faucets can fill the bathtub. The hot water faucet can fill the tub in 13 minutes, and the cold water faucet can fill it in 12 minutes. We can express their rates as fractions of the tub they can fill per minute as 1/13 and 1/12, respectively.

When we add these rates together, we get the combined rate:

Rate of hot water faucet + Rate of cold water faucet = combined rate

1/13 + 1/12 = (12 + 13) / (13  imes 12) = 25 / 156

The combined rate is 25/156 tubs per minute. To find out how long it will take for both faucets to fill the tub together, we take the reciprocal of the combined rate:

Time to fill the tub = 1 / (combined rate) = 156 / 25 = 6.24 minutes

Therefore, it will take approximately 6.24 minutes for both faucets to fill the bathtub when used simultaneously.

Answer:

The rate of change is 25. It means the cost increased by $25 per day.

Step-by-step explanation:

The given table is

Time (days)       Cost ($)

       3                   75

       4                  100

       5                  125

       6                  150

It means the graph of this constant function passing through the points (3,75) and (4,100).

If a line passing through two points, then the slope of the line is

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{100-75}{4-3}[/tex]

[tex]m=\frac{25}{1}[/tex]

[tex]m=25[/tex]

Therefore the rate of change is 25. It means the cost increased by $25 per day.

The given equation resulting in one solution, which is z = 1/9.

To find the number of solutions to the equation -2 + 10 + 7z = 16z + 7, we first simplify and solve for z. Start by combining like terms on the left side:

-2 + 10 = 8, so the equation becomes 8 + 7z = 16z + 7.

Next, we get all the terms with z on one side and the constants on the other:

Subtract 7z from both sides:

8 = 16z - 7z + 7

Combine z terms:

8 = 9z + 7

Subtract 7 from both sides:

1 = 9z

Divide both sides by 9:

z = 1/9

The density of a material is equal to its mass divided by its volume.

The equation that represents the relationship between density (D), mass (M), and volume (V) is: D = M/V.

This equation shows that the density of a material is equal to its mass divided by its volume.

For example, if you have an object with a mass of 10 grams and a volume of 2 cubic centimeters, you can calculate its density by dividing the mass by the volume: D = 10g / 2cm³ = 5g/cm³.

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The density (D) of a material is directly proportional to the mass (M) and inversely proportional to its volume (V). The mathematical equation for this relationship is D = k * (M / V).

The density (D) of a material is directly proportional to the mass (M) and inversely proportional to its volume (V). To translate this into a mathematical equation, we can write:

D = k * (M / V)

Where D represents the density, M represents the mass, V represents the volume, and k represents the proportionality constant.

This equation demonstrates that as the mass of the object increases, the density also increases, while as the volume increases, the density decreases.

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In the situation, x + (-x) is combined making zero and other y + (-y) is making zero.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.

Summation = addition of two or more numbers or variable

Subtraction = Minus of any two or more numbers with each other called subtraction.

Division = divide any two numbers or variable called division.

Multiplication = to multiply any two or more numbers or variables called multiplication.

If we combine any two opposite quantities then their summation must be zero.

For example,

if you combine 5 and -5 then it will be 0.

If you combine 10 and -10 then it will be 0.

So,

The first situation ⇒

Combining x and -x

x + (-x) = 0

The second situation ⇒

Combining y and -y

y + (-y) = 0

Hence, In the situation, x + (-x) is combined making zero and other y + (-y) makes zero.

To learn more about the arithmetic operators,

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12 *4 = 48 total miles in 50 minutes

48 / 50/60 =  57.6 miles per hour

The simplified expression is (x - 5) / (2x).

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

The expression given is 3 (x - 5) / (6x)

We can simplify this expression by following the order of operations, which is a set of rules that tells us which operations to perform first in a mathematical expression.

The order of operations.

Perform any calculations inside parentheses first.

Exponents (ie: powers and square roots, etc.)

Multiplication and Division (from left to right)

Addition and Subtraction (from left to right)

Using the order of operations, we can simplify the expression as follows:

We start by simplifying the expression inside the parentheses.

x - 5 represents five less than x.

Next, we multiply the result of step 1 by 3.

= 3 (x - 5)

= 3x - 15

Finally, we divide the result of step 2 by the product of 6 and x.

= (3x - 15) / (6x)

= (3(x - 5)) / (6x)

= (x - 5) / (2x)

Therefore,

The simplified expression is (x - 5) / (2x).

Learn more about expressions here:

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To vertically subtract 30.06 from 100.6, start by borrowing 1 from the tens place and adding it to the ones place. Then, borrow 10 from the hundreds place and add it to the tens place. Finally, combine the result to get 70.54.

To vertically subtract 30.06 from 100.6, you'll need to line up the decimal points vertically. Start by subtracting the hundredths place (0.06) from the hundredths place (0.00). Since 6 is bigger than 0, you'll need to regroup. Borrow 1 from the tens place by making it 9, and add it to the ones place, making it 10. Then, you can subtract 6 from 10, which gives you 4. Next, subtract the whole number part (30) from the whole number part (100). Since 0 is smaller than 3, regroup again by borrowing 10 from the hundreds place and adding it to the tens place, making it 20. Then, subtract 3 from 10, which gives you 7. Finally, combine the result by placing the decimal point in the correct position, which gives you the answer: 70.54.

Final answer:

Algebraically, the relation y = x^3 - 4x is not symmetric to the x-axis or y-axis but is symmetric with respect to the origin when both x and y are replaced with their negatives.

Explanation:

To determine if the relation y = x3 − 4x is symmetric with respect to the x-axis, y-axis, or the origin, we perform a series of tests substituting -x for x (to test y-axis symmetry), -y for y (to test x-axis symmetry), and both -x for x and -y for y (to test origin symmetry).

Y-axis symmetry test:

Replace x with -x:

y = (-x)3 - 4(-x)

y = -x3 + 4x ≠ x3 − 4x (not symmetric to y-axis)

X-axis symmetry test:

Replace y with -y:

-y = x3 - 4x ⇒ y = -x3 + 4x ≠ x3 − 4x (not symmetric to x-axis)

Origin symmetry test:

Replace both x with -x and y with -y:

-y = (-x)3 - 4(-x)

-y = -x3 + 4x

y = x3 − 4x (symmetric to origin)

Answer:

There are 22 cats and 8 dogs.

Step-by-step explanation:

Let the cats be represented by = c

Let the dogs be represented by = d

Given, that the pet store has 30 pets.

First equation forms :

[tex]c+d=30[/tex]            ........(1)

Also given, the cats cost $50 each and dogs cost $100 each and the total for all is $1900. Now second equation forms:

[tex]50c+100d=1900[/tex]     .........(2)

From equation (1) we get [tex]c=30-d[/tex]

Putting this value of c in equation 2:

[tex]50(30-d)+100d=1900[/tex]

[tex]1500-50d+100d=1900[/tex]

=> [tex]50d=400[/tex]

=> [tex]d=8[/tex]

Now,[tex]c+d=30[/tex]

So, [tex]c=30-8[/tex]

[tex]c=22[/tex]

Hence, there are 22 cats and 8 dogs.

The holes of the graph are located at (5, 3) and (-1, 11)

How to determine the hole of the graph

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

The graph

The holes of the graph are at (5, 3) and (-1, 11)

This is so because the function is not defined at this value

Also, we can see that

The function has it vertical asymptotes are x = 2 and x = -2

Answer:

2

Step-by-step explanation:

Took the test ;)