Factor completely 56a2b3 − 35ab.
7ab(8ab2 − 5)
7a(8b2 − 5ab)
Prime
7a(8ab3 − 5b)

The 12 inches wire costs 60 cents, so the cost of 1 inch of wire is

Rate = 60/12 = 5 cents

So the cost of 1 inch of wire which is the rate is 5 cents.

Now we have to find the cost (in cents) of 27 inches wire.

We know the cost of 1 inch of wire is 5 cents so the cost of 27 inches of wire is

= Total inches of wire * Price of 1 inch of wire

= 27 * 5

= 135

The cost of 27 inches of wire is 135 cents

Final answer:

By establishing a relationship between the total number of aquatic plants and animals and knowing that animals are 80% of the plants, we can determine that there are 72 aquatic animals in the eco-garden.

Explanation:

To calculate the number of aquatic animals in the eco-garden, we need to first establish the relationship between the number of animals and plants. According to the information, the number of aquatic animals is 80% of the number of aquatic plants. If we denote the number of aquatic plants as 'P' and aquatic animals as 'A', then A = 0.80 × P.

Given that there are a total of 162 aquatic plants and animals, we can represent this as A + P = 162. Since A is 80% of P, we can substitute the first relationship into the second equation, which gives us 0.80 × P + P = 162. Simplifying this, we get 1.80 × P = 162.

To find the value of P, we divide both sides by 1.80 to get P = 162 / 1.80, which yields P = 90. This indicates there are 90 aquatic plants. To determine the number of aquatic animals, we use the relationship A = 0.80 × P, so A = 0.80 × 90, resulting in A = 72.

Therefore, there are 72 aquatic animals in the eco-garden.

A multiplication problem shows the process of calculating the product when one number is multiplied by another. This can be represented using an array model, an area model, or a multiplication sentence. Specific representation will depend on the model provided.

In mathematics, a multiplication problem represents the process of finding the product or result when one number is multiplied by another.

However, without a specific model being given in the question, providing a precise answer becomes challenging. In general terms, a multiplication model could be in the form of an array, an area model, or a multiplication sentence. To understand this better, let's illustrate with an example.

In all the cases, the multiplication problem is demonstrating how to find the product of two numbers or quantities.

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The ratio of tulips to daffodils in Robert's garden is 3:2. This is obtained by dividing the number of tulips by the number of daffodils (36/24), and simplifying the result.

This problem pertains to ratios. Given that Robert planted 24 daffodil bulbs and 36 tulip bulbs, the ratio of tulips to daffodils is obtained by dividing the number of tulips by the number of daffodils. Thus, the ratio is 36/24. This simplifies to 1.5 when expressed as a decimal. However, we need the ratio in its simplest form, so let's convert 1.5 into a whole number. By multiplying both numbers by 2, we get the ratio 3:2. Therefore, the ratio of tulips to daffodils in Robert's garden is 3:2

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Rhombus B, which has dimensions three times larger than Rhombus A, has an area that is nine times larger than the area of Rhombus A.

This question is based on geometry and compares the areas of two rhombuses. Firstly, remember that the area of a rhombus is obtained by the formula A = base x height. For Rhombus A, with a base of 7 inches and area 35 square inches, this implies that its height is 5 inches (since 7 x 5 = 35). Therefore, the height of Rhombus B which is three times larger than that of Rhombus A would be 15 inches, and its base would be 21 inches (three times that of Rhombus A).

Now applying these values into the formula for the area of a rhombus, for rhombus B we get A = 21 x 15, which equals 315 square inches - this is the area of Rhombus B. Comparing this with the area of Rhombus A (35 square inches), we find that Rhombus B is 9 times larger than Rhombus A (because 315 divided by 35 equals 9).

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By increasing the base and height of Rhombus A by three times, the resulting area of Rhombus B is nine times the area of Rhombus A. The area of Rhombus A is 35 square inches and the area of Rhombus B is 315 square inches.

The subject of this question is area of rhombuses. A key concept to remember is that the area of a rhombus is calculated by the formula: Area = base x height.

Rhombus A has base of 7 inches and an area of 35 square inches. This means the height h of Rhombus A is A/base = [tex]35/7 = 5[/tex] inches.

The base and height of Rhombus B are three times the base and height of rhombus A. So, Rhombus B has a base of [tex]7 * 3 = 21[/tex] inches and height of [tex]5 * 3 = 15[/tex] inches.

To find the area of Rhombus B, you apply the same formula, Substituting the values we get, B = base x height = [tex]21 * 15 = 315[/tex] square inches. Therefore, the area of Rhombus B is nine times the area of Rhombus A since 315/35 = 9.

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Answer:

(y - 8x) (y + 7x)

Step-by-step explanation:

This person's videos helped me out so much with questions like these.

Brian McLogan -

1) Factoring an expression with a greater than one and two square variables 8x^2 -6xy -9y^2

2) Learn How to Factor a Trinomial in Your Head When a is not Equal to One

I'm not paid to do this, I genuinely recommend you watch these two videos, because it helped me tremendously when I once did a question like this.

Have a blessed day!

Frank finished 5/8 of the report.

To find the fraction of the book report that Frank finished, you need to add together the fractions of the report he wrote before and after dinner. Frank wrote 1/2 of the report before dinner and 1/8 of the report after dinner. To add these fractions, you need to find a common denominator. The least common multiple of 2 and 8 is 8, so you can rewrite 1/2 as 4/8. Adding 4/8 and 1/8 gives you a total of 5/8.

Therefore, Frank finished 5/8 of the report.

The scientific notation of 19 hundred thousandths which is 0.000019 is 1.9 x 10^-5.

The number 19 hundred thousandths would mean 19 divided by 1,000,000 which equals 0.000019. When we convert this decimal to scientific notation, it becomes 1.9 x 10^-5. In scientific notation, we want to express a number as a value between 1 and 10 multiplied by a power of 10. So, to convert 0.000019 to scientific notation, we need to move the decimal point five places to the right, which gives us 1.9. The '10^-5' shows that the decimal point has moved five places to the right from the original number.

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why you just give the question give the question && the answer !!!

Answer:

why you just give the question give the question && the answer !!!

The absolute maximum and minimum values of the function f(x) = ln(x^2 + 5x + 12) on the interval [-3, 1] are f(1) = ln(18) (maximum) and f(-2) = ln(4) (minimum).

To find the absolute maximum and absolute minimum values of the function f(x) = ln(x2 + 5x + 12) on the interval [-3, 1], we first need to find the critical points of the function within this range. The critical points are those at which the derivative equals zero or does not exist.

The absolute maximum value within the interval is ln(18) and the absolute minimum value is ln(4).

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The absolute maximum value of f(X)  on the interval [-3, 1] is approximately ( 2.890), which occurs at ( x = 1), and the absolute minimum value is approximately (1.749 ), which occurs at ( x = -5/2).

To find the absolute maximum and minimum values of[tex]\( f(x) = \ln(x^2 + 5x + 12) \)[/tex] on the interval [tex]\([-3, 1]\)[/tex], we first need to find the critical points and check the values of the function at those points and at the endpoints of the interval.

1. Find the critical points: Critical points occur where the derivative of the function is zero or undefined.

First, let's find the derivative of (f(x):

[tex]\[ f'(x) = \frac{1}{x^2 + 5x + 12} \cdot (2x + 5) \][/tex]

Setting ( f'(x)) equal to zero:

2x + 5 = 0

x = -5/2

Since this value x = -5/2 lies within the interval [-3, 1], it's a critical point.

2. Check the endpoints and critical point:

[tex]- \( f(-3) = \ln((-3)^2 + 5(-3) + 12) = \ln(9 - 15 + 12) = \ln(6) \)[/tex]

[tex]- \( f(1) = \ln(1^2 + 5(1) + 12) = \ln(1 + 5 + 12) = \ln(18) \)[/tex]

[tex]- \( f\left(-\frac{5}{2}\right) = \ln\left(\left(-\frac{5}{2}\right)^2 + 5\left(-\frac{5}{2}\right) + 12\right) = \ln\left(\frac{25}{4} - \frac{25}{2} + 12\right) = \ln\left(\frac{25 - 50 + 48}{4}\right) = \ln\left(\frac{23}{4}\right) \)[/tex]

3. Compare the values:

  - ln(6) = 1.792

  - ln(18) = 2.890

  - [tex]ln\left(\frac{23}{4}\right)[/tex] = 1.749

So, the absolute maximum value of f(X)  on the interval [-3, 1] is approximately ( 2.890), which occurs at ( x = 1), and the absolute minimum value is approximately (1.749), which occurs at ( x = -5/2).

Answer: x = 2 and x cannot be any value for which v(x) = 0

Step-by-step explanation:

Tony's gross pay for 46 hours of work, including 6 hours of overtime, is $563.50. The Social Security tax on this amount is $34.94, and the Medicare tax is $8.17.

Calculating Tony's Gross Pay

Tony's regular pay for 40 hours at an hourly rate of $11.50 is calculated by multiplying the hourly rate by the number of regular hours he worked. Therefore, his regular pay is 40 hours × $11.50/hour = $460. To calculate the overtime pay, we must first determine the overtime rate. The overtime rate is 1.5 times the normal hourly rate, thus the overtime hourly rate is 1.5 × $11.50/hour = $17.25/hour. Tony worked 6 hours overtime, so his overtime pay is 6 hours × $17.25/hour = $103.50. Tony's gross pay is the sum of his regular pay and overtime pay, which is $460 + $103.50 = $563.50.

Calculating Deductions for Social Security and Medicare

The Social Security tax and Medicare tax are calculated as percentages of the gross pay. The Social Security tax at 6.2% of $563.50 is $563.50 × 0.062 = $34.937, which rounds to $34.94. The Medicare tax at 1.45% of $563.50 is $563.50 × 0.0145 = $8.17075, which rounds to $8.17.

Answer:

Perimeter = 182 cm, area = 2,028 cm^2

Step-by-step explanation: