Subtract -7a^2 + 3a -9 from 5a^2 - 6a -4

Answer should be polynomial in standard form

Final answer:

The doormat measuring 1/2 yard by 2/3 yard will not fit on a step that is 1/4 square yard because the doormat's area, 1/3 square yard, is larger than the step's area.

Explanation:

The question "Will a doormat measuring 1/2 yard by 2/3 yard fit on a step that is 1/4 square yard?" involves understanding of measuring areas in yards and comparing the area of the doormat with that of the step. First, we calculate the area of the doormat by multiplying its length and width (1/2 yard * 2/3 yard = 1/3 square yard).

Next, we compare the area of the doormat, which is 1/3 square yard, to the area of the step, which is 1/4 square yard. Since 1/3 square yard is larger than 1/4 square yard, the doormat will not fit perfectly on the step as it is too big.

Answer:

c

Step-by-step explanation:

Answer:

The m∠B is 68°

Step-by-step explanation:

Given the right angled triangle ABC in which right angled is at A.

AB = 7 units and AC = 17 units

we have to find the measure of ∠B.

By trigonometric ratios,

[tex]cot \angle B=\frac{AB}{AC}[/tex]

[tex]cot \angle=\frac{7}{17}[/tex]

[tex]\angle B=cot^{-1}(\frac{7}{17})[/tex]

[tex]\angle B=67.619864948\sim 68^{\circ}[/tex]

Hence, the m∠B is 68°

Option 1 is correct

Answer:115.20

Step-by-step explanation:

Final answer:

To make a 20L mixture 50% antifreeze, 7.5L of the mixture should be drained and replaced with pure antifreeze. This calculation is based on the original 20% antifreeze concentration and the goal of reaching a 50% concentration without changing the total volume.

Explanation:

The question asks how much of a 20L mixture, which is 20% antifreeze, needs to be drained and replaced with pure antifreeze so the mixture will be 50% antifreeze. To solve this, first calculate the current amount of antifreeze in the mixture: 20L * 20% = 4L. Let's say x liters are drained and replaced with pure antifreeze. The volume of the solution does not change, the remaining 20L. After replacement, the quantity of antifreeze is (4 - 0.2x + x) liters (since we subtract the antifreeze drained, which is 20% of x, and add back x liters of pure antifreeze), and we require this to be 50% of the total, which is 10L (50% of 20L).

Setting up the equation: 4 - 0.2x + x = 10. Simplifying gives 0.8x = 6, so x = 7.5. Therefore, 7.5L of the mixture should be drained and replaced with pure antifreeze to achieve a 50% concentration.

To find out how long it takes for a light bulb to consume 9450 watt-hours, when it uses 1800 watt-hours per day, divide 9450 watt-hours by 1800 watt-hours per day, which equals 5.25 days.

The question involves calculating how long it takes for a light bulb to consume a certain amount of energy (9450 watt-hours) given its daily consumption rate (1800 watt-hours per day).

To find the duration, you simply divide the total energy by the daily consumption rate:

Total energy to be consumed = 9450 watt-hours

Daily energy consumption = 1800 watt-hours per day

Duration = Total energy ÷ Daily energy consumption

Duration = 9450 watt-hours ÷ 1800 watt-hours/day = 5.25 days

Therefore, it will take 5.25 days for the light bulb to consume 9450 watt-hours of energy.

For the large tire with a diameter of 60 inches, it would make 38 rotations after traveling 600 feet. The small tire with a radius of 9 inches would make 127 rotations in the same distance.

First, let's convert the feet into inches since the tire measurements are given in inches. There are 12 inches in a foot, so 600 feet is equal to 7200 inches. Now, we need to determine the circumference of each tire, which we can find using the formula for the circumference of a circle which is 2πr (twice the product of pi and the radius).

For the large tire, the diameter is 60 inches, so the radius (r) is half the diameter, which is 30 inches. Thus, the circumference of the large tire would be 2π*30, which is about 188.5 inches. The large tire would therefore make about 7200/188.5 = 38 rotations.

The small tire has a radius (r) of 9 inches, so its circumference is 2π*9, which is about 56.55 inches. The small tire would hence make about 7200/56.55 = 127 rotations.

Please note that the numbers are rounded off to the nearest whole number as requested.

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The large tire makes approximately 38 rotations, and the small tire makes approximately 128 rotations when each travels a distance of 600 feet.

To find the number of rotations a tire makes, you first need to know the circumference of the tire, which represents the distance the tire would cover in one full rotation. The circumference of a circle (or tire, in this case) is calculated as 2πr, where r is the radius of the circle.

For the large tire with a diameter of 60 inches (which makes the radius 30 inches because the radius is half the diameter): The circumference is 2π × 30 = 188.5 inches. Convert this to feet because the distance given is in feet. So, 188.5 inches is about 15.7 feet. Divide the total distance by the circumference to find the number of rotations: 600 feet / 15.7 feet = approximately 38 rotations.

For the small tire with a radius of 9 inches: The circumference is 2π × 9 = 56.5 inches, which is about 4.7 feet. Divide the total distance by the circumference to find the number of rotations: 600 feet / 4.7 feet = approximately 128 rotations.

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Answer:

[tex]log_3(9)=2[/tex]

Step-by-step explanation:

[tex]3^2 = 9[/tex]

Logarithmic form is the reverse of exponential form

To convert exponential form in to log form we use a rule

[tex]b^x=a[/tex]  can be written as [tex]log_b(a)=x[/tex]

WE apply the same rule in our exponential equation to convert it into log form

[tex]3^2 = 9[/tex]

The base of exponent is the base of log

[tex]log_3(9)=2[/tex]

Answer:

False

Step-by-step explanation:

In any binomial expansion of the form

[tex](x+a)^n = \Sigma_0^n nCr x^{n-r} a^{r}[/tex]

We find that each term has decreasing powers of x by 1 and increasing powers of a by 1, such that the sum of exponents is always n

Hence product of exponents of each term cannot be n.

The given statement is false.

Only the sum of the exponents of each term in a binomial expansion has degree n

Final answer:

The associative property in mathematics states that the way in which numbers are grouped or associated does not affect the result of the operation. Community property refers to the legal framework in which the ownership of property is divided equally between spouses in a marriage or a domestic partnership.

Explanation:

The associative property is a property in mathematics that states that the way in which numbers are grouped or associated does not affect the result of the operation. For example, for addition, the associative property states that (a + b) + c = a + (b + c). This property holds true for addition and multiplication, but not for subtraction and division.

Community property, on the other hand, is a concept in the field of law, specifically property law. Community property refers to the legal framework in which the ownership of property is divided equally between spouses in a marriage or a domestic partnership. It is most commonly associated with community property states in the United States.

To find the score Gavin needs on his next test to have an average of 90, we understand that the sum of his first three tests and the fourth test, divided by four, must equal 90. Translating this understanding to an equation gives: (261 + x4) / 4 = 90, which can be solved for x4.

The subject posed deals with the understanding of mean averages and algebra. The mean, or average, is calculated by adding up all the values and dividing by the total number of values. In Gavin's case, his mean score of 87 over three tests can be represented algebraically as (x1 + x2 + x3) / 3 = 87. The challenge is to find out what Gavin needs to score in his next test (let's call this x4) to have a new mean score of 90.

To set up the equation we need to understand that now the average is calculated over four tests, and it must equal 90. Thus, the equation to solve is ((x1 + x2 + x3) + x4) / 4 = 90. As we know that the sum of his first three test scores is 87 * 3 (because (x1 + x2 + x3) / 3 = 87), we substitute that sum (261) into the equation:

(261 + x4) / 4 = 90. Solving this equation for x4 will give the score Gavin needs on his next test to achieve an average of 90.

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The correct answer is D.

I just took the test.

6x² -5x -56 = 0 . . . . . subtract the constant

(3x +8)(2x -7) = 0 . . . .factor*

The zero product property says the product will be zero only when one (or both) of the factors is zero.

First Factor

... 3x +8 = 0

... x + 8/3 = 0 . . . . divide by the coefficient of x

... x = -8/3 . . . . . . subtract 8/3

Second Factor

... 2x -7 = 0 . . . . . . set the factor to zero

... x -7/2 = 0 . . . . . divide by the coefficient of x

... x = 7/2 . . . . . . . add 7/2

_____

*Comment on factoring

There are various ways to do this. In basic terms, we want to find numbers that are factors of the product 6·(-56) whose sum is -5. We found those numbers to be -21 and 16. Then we can rewrite the -5x term using these numbers and factor by grouping.

... 6x² -5x -56 = (6x² -21x) +(16x -56) = 3x(2x -7) +8(2x -7) = (3x +8)(2x -7)

Answer:

B. x = -8/3, or x= 7/2

Step-by-step explanation:

A is the correct answer trust me

Answer:

A) j is farther from 0 than k is

Step-by-step explanation:

The sample space or sets showing the possible orders of the other three runners is S = {FGI, FIG, GFI, GIF, IFG, IGF}.

Sets are the collection of well-defined elements. A set is represented by a capital letter symbol and the number of elements in the finite set is shown as curly bracket {..}.

Four runners, Fran, Gloria, Haley, and Imani, compete on a relay team.

Haley is the first runner in the relay. The other runners can run in any order.

The sample space or sets showing the possible orders of the other three runners will be

S = {FGI, FIG, GFI, GIF, IFG, IGF}

Thus, the correct option is C.

More about the sets link is given below.

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The correct factorization for [tex]\(4x^2 - 50\) is \(2(x\sqrt{2} - 5)(x\sqrt{2} + 5)\)[/tex], where [tex]\(\sqrt{2}\)[/tex] is included in each term.

The given quadratic expression [tex]\(4x^2 - 50\)[/tex] can be factored using the difference of squares method.

The difference of squares formula is[tex]\(a^2 - b^2 = (a + b)(a - b)\).[/tex]

In this case, a = 2x and [tex]\(b = \sqrt{50}\).[/tex]

1. Identify the expression as a difference of squares: [tex]\(4x^2 - 50 = (2x)^2 - (\sqrt{50})^2\).[/tex]

2. Apply the difference of squares formula:[tex]\(4x^2 - 50 = (2x + \sqrt{50})(2x - \sqrt{50})\).[/tex]

3. Further simplify by factoring out 2: [tex]\(4x^2 - 50 = 2(2x + \sqrt{50})(2x - \sqrt{50})\).[/tex]

The correct factorization for [tex]\(4x^2 - 50\) is \(2(x\sqrt{2} - 5)(x\sqrt{2} + 5)\)[/tex], where [tex]\(\sqrt{2}\)[/tex] is included in each term.

Answer:

Step-by-step explanation:

17.5