help me! need to show work!

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

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).

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By using the continuous compound interest the balance is growing $4,673.56 after 6 years.

Interest that compounded continuously to the principal amount. This interest rate provides exponential growth to period of time.

Formula of continuous compound interest rate;

[tex]P(t) = P_0e^{rt}[/tex] , where P₀ is the principal amount, r is the interest rate and t is the time period.

Given that the principal amount is $20000 and and interest rate 3.5% in a year.

And here we use formula of continuous compound interest rate;

[tex]P(t) = P_0e^{rt}[/tex]

Here, we have the value P₀ = $20000 , r = 3.5 % / 100 = 0.035% in a year and t = 6 years

Substitute these above values in the formula;

p(t) = $20000 × [tex]e^{0.035}[/tex] ×[tex]e^{6}[/tex]

P{t} = $24673.56

P{t} = $24673.56 nearest one cent

The final balance is $24673.56.

Therefore, the total continuous compound interest is $4,673.56.

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Answer:

2

Step-by-step explanation:

Took the test ;)

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.

12 *4 = 48 total miles in 50 minutes

48 / 50/60 =  57.6 miles per hour

The solutions to the quadratic equation x² = 7x + 4 are found by using the quadratic formula, which results in two solutions: [tex](\frac{7 + \sqrt{65}}{2 },\frac{7 - \sqrt{65}}{2 })[/tex]

The solutions to the quadratic equation x² = 7x + 4 can be found by first rewriting the equation in standard form as x² - 7x - 4 = 0. To solve this quadratic equation, we can factor it, complete the square, or use the quadratic formula. In this case, let's factor the equation if possible. Unfortunately, this quadratic does not factor neatly. Therefore, we apply the quadratic formula which is [tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex] , where a = 1, b = -7, and c = -4.

After substitution, we get [tex]x = \frac{7 \pm \sqrt{49 + 16}}{2}[/tex]. This simplifies to x = [tex]\frac{7 \pm \sqrt{65}}{2}[/tex], resulting in two solutions: [tex]x = \frac{7 + \sqrt{65}}{2 }[/tex]and [tex]x = \frac{7 - \sqrt{65}}{2 }[/tex]. Therefore, the solution set is [tex](\frac{7 + \sqrt{65}}{2 },\frac{7 - \sqrt{65}}{2 })[/tex]

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.

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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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.

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.

Final answer:

The probability that a randomly selected blue marble came from the first box is 7/31, which is approximately 0.2258 when rounded to four decimal places.

Explanation:

The probability that the blue marble came from the first box can be found using Bayes' theorem and the concept of conditional probability. First, we need to determine the probability of drawing a blue marble from either box (P(Blue)). Then, we calculate the probability of drawing a blue marble from the first box (P(Blue|First box)). Finally, we apply Bayes' theorem to find the probability that the blue marble came from the first box (P(First box|Blue)).

Here are the relevant probabilities:

P(First box) = 1/2 (since there are only two boxes)

P(Second box) = 1/2

P(Blue|First box) = 3/5 (3 blue out of 5 total marbles)

P(Blue|Second box) = 2/7 (2 blue out of 7 total marbles)

Using these probabilities, we calculate P(Blue):

P(Blue) = P(Blue|First box) * P(First box) + P(Blue|Second box) * P(Second box) = (3/5) * (1/2) + (2/7) * (1/2) = 3/10 + 1/7 = 21/70 + 10/70 = 31/70

Now, we apply Bayes' theorem to get P(First box|Blue):

P(First box|Blue) = [P(Blue|First box) * P(First box)] / P(Blue) = [(3/5) * (1/2)] / (31/70) = (3/10) / (31/70) = (3/10) * (70/31) = 21/310 = 7/31 or approximately 0.2258 (rounded to four decimal places)

Therefore, the probability that the marble came from the first box is 7/31.