I need question 7 solved using SOA CAH TOA! Please!

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Answer:

  a) (x³ -x² +x +2) +2/(x+1)

  b) (x² +2x -5) +6/(x+3)

Step-by-step explanation:

Polynomial long division is virtually identical to numerical long division, except that the quotient term does not require any guessing. It is simply the ratio of the leading terms of the dividend and divisor. As with numerical long division, the product of the quotient term and the divisor is subtracted from the dividend to form the new dividend for the next step.

The process stops when the dividend is of lower degree than the divisor.

In part (a), you need to make sure the dividend expression has all of the powers of x present. This means terms 0x³ and 0x² must be added as placeholders in the given dividend. They will become important as the work progresses.

Answer:

Step-by-step explanation:

Slope intercept form is

\(y=mx+b\)

Start with your equation and move y terms to one side and all other terms to the other side:

\(1-x-2y=-6\)

\(1-x+6=2y\)

Combine numbers:

\(7-x=2y\)

Divide both sides by 2

\(\frac{7}{2} - \frac{x}{2} =y\)

Write y on the left hand side and put the rest of the equation in standard slope intercept form:

\(y=-\frac{1}{2}x+\frac{7}{2}\)

This is slope intercept form with m = -1/2 and b =7/2

Answer:

Step-by-step explanation:

The volume of a cone is

\(V=\frac{h\pi r^2}{3}\\ \\ V=\frac{12\pi (8^2)}{3}\\ \\ V=256\pi\ m^3\\ \\ V\approx 804.2\ m^3\)

Answer:

First Choice

Step-by-step explanation:

Domain: (-oo,oo); Range: (-oo,oo)

Answer:

-3x -12

Step-by-step explanation:

-6x +3x = -3x

-3-9 = -12

The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.

The correct answer choice is option B.

Malcolm's gift card = $50.

Cost Malcolm's car wash per visit = $7

Martha's gift card = $180

Cost Martha's car wash per visit = Difference between gift card balance of first and second visit

= $180 - $160

= $20

How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7

= $13

Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13

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Answer:m=2570

Step-by-step explanation:2.57kilos= 2570m

The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

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The algebraic expression for the area is:

A = (2H - 8)*H/2

Here we want to write the expression:

"the area of a triangle that has a base 8 inches less than 2 times wider than the height."

Remember that for a triangle of base B and height H, the area is:

A = B*H/2

So if the base is 8 inches less than 2 times the height, we can write:

B = 2*H - 8

Replacing that in the area equation we get:

A = (2H - 8)*H/2

That is the equation for the area.

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Answer:

x=144

Step-by-step explanation:

90-36=54

that's their difference so just add 54 to 90

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Answer:

a. \(\tt \frac{1}{9}\)

b. \(\frac{1}{16}\)

c. 4

Step-by-step explanation:

\(\tt a. \:3^{-2}\)

We can use the negative exponent rule, which states that \(\boxed{\tt a^{-n} = \frac{1}{a^n}}\) So, we have:

\(\tt 3^{-2} = \frac{1}{3^2} = \frac{1}{9}\)

\(\hrulefill\)

\(\tt b.\: -2^{-4}\)

We can use the rule that \(\boxed{\tt -a^{-n} = (-1)^n \cdot a^n}.\) So, we have:

\(\tt -2^{-4} = (-1)^4 \cdot 2^{-4} = 1 \cdot \frac{1}{2^4} = \frac{1}{16}\)

\(\hrulefill\)

\(\tt c. \:(\frac{1}{2})^{-2}\)

We can use the negative exponent rule, which states that \(\boxed{\tt a^{-n} = \frac{1}{a^n}}\). So, we have:

\(\tt (\frac{1}{2})^{-2} = \frac{1}{(\frac{1}{2})^2} = \frac{1}{\frac{1}{4}} = 4\)

Answer:

Step-by-step explanation:

(a) 3^-2 = 1/9

(b) (-2)^-4 = 1/(-2)^4 = 1/16

(c) (1/2)^-2 = 1/(1/2)^2=1 / 1/4 = 4

Answer:

C) concrete details about what the author saw and looked for his mother

Answer:

Step-by-step explanation:

The lateral surface area of a rectangular prism is 2(l + w)h sq units.

A rectangular prism is a three-dimensional shape, that has six faces (two at the top and bottom and four are lateral faces).

The lateral surface area of a rectangular prism is given by

Where l, w, and h are the length, width, and height, respectively. To find the lateral surface area, we need the values of l, w, and h.

Without these values, it is not possible to determine the lateral surface area of the rectangular prism.

Therefore, the lateral surface area of a rectangular prism is 2(l + w)h sq units.

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Notice that the 3% increase is calulated with the memberships sold the year before, and the memberships sold the year before had a 3% increase based on the memberships sold the year before that one, and so on.

We're looking at a compund growth, wich we can model using an exponential function.

Remember that this kind of growth can be modeled using the formula:

Where:

• a, is the initial amount

• r, is the percentage growth (as a decimal)

• n, is the number of times this growth is applied

Now, using this and the data given, let:

• m, be the number of memberships sold.

• t ,the time elapsed from 2001, in years

This way,

This way, for 2020 the gym would have

Around 964 memberships sold

Answer:

Step-by-step explanation:

For single-game tickets, the cost C depends simply on the number of games attended g, and is given by:

C = 14.50g

For season tickets, there is an upfront cost of $318, plus an additional cost of $1.25 per game attended. So the cost C is given by:

C = 318 + 1.25g

Note that the 318 represents the cost for the entire season, regardless of the number of games attended. The 1.25g term represents the additional cost per game for attending g games.

Let the angle between two unit vectors u and v be 3.14/3, then by using the formula for dot product:

cos(θ) = u.v/ ||u||.||v|| = ||u||.||v||

=> ||u + v|| = ||u|| + ||v|| = sqrt(2 - 2cos(3.14/3)) = 2 √(3)/2

The given system can be written in the matrix form as AX = B, where

A = [1 -3 0; 2 k -1 -1; 1 2 k -2]

B = [-3; -2; 1]

Determinant of A = (1-k)(k^2 - k - 4) = 0 => k = 0 or (k = 1 +- √(5))/2

When k = 0, the matrix A is singular => No solution

When k = (1 + √(5))/2, the matrix A is invertible => Unique solution

When k = (1 - √(5))/2, the matrix A is invertible => Unique solution

The given matrix can be written as

A = [2 1 -1; 3 2 -3; 3 1 -2]

By finding the characteristic equation we can find the eigen values.

det(A - λI) = 0 =>

[(2-λ) 1 -1; 3 2 -3; 3 1 (2-λ)] = 0 =>

λ^3 - 7λ^2 + 11λ - 6 = 0 =>

λ = 2 (double eigenvalue), λ = 1 ± √(2) (complex conjugate eigenvalues)

To find the eigenvector we solve (A - λI)x = 0 =>

For λ = 2: [0 1 -1; 3 0 -3; 3 1 0]x = 0 => x = t(1,1,1) => eigenvector is (1,1,1)

For λ = 1 + sqrt(2): [1 1 -1; 3 1 -3; 3 1 -2 - sqrt(2)]x = 0 => x = t(1, 1, 1) => eigenvector is (1, 1, 1)

For λ = 1 - sqrt(2): [1 1 -1; 3 1 -3; 3 1 -2 + sqrt(2)]x = 0 => x = t(1, 1, 1) => eigenvector is (1, 1, 1)

Let f(x) = (x-1)(x-2)(x-3)(x-4) and g(x) = (x-1/4)(x-1/3)(x-1/2)(x-1).

Then the limit 1 f(x)/g(x) = lim 1 (x-1)(x-2)(x-3)(x-4)/((x-1/4)(x-1/3)(x-1/2)(x-1)) = lim (x-1)(x-2)(x-3)(x-4) /((x-1/4)(x-1/3)(x-1/2)(x-1))

As x approaches 1, the limit is infinity and as x approaches any of the other roots, the limit is 0. Hence, the limit does not exist.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Property of an isosceles triangle,

Opposite angles of the equal sides in an isosceles triangle are equal in measure.

m∠D = m∠F

(2x + 8) = (3x + 4)

3x - 2x = 8 - 4

x = 4

m∠D = m∠F = (3×4 + 4)°

                    = 16°

m∠D = m∠F = 16°

Since, sum of interior angles of a triangle = 180°

m∠D + m∠E + m∠F = 180°

16° + m∠E + 16° = 180°

m∠E = 180° - 32°

m∠E = 148°

Answer:

\(\frac{5}{3}\)

Step-by-step explanation:

We have two fractions being multiplied.

\(\frac{3}{4} * 2\frac{2}{9}\)

Convert 2 2/9 into an improper fraction by multiplying the whole number by the denominator and add the numerator :

2 * 9

18 + 2

20

\(\frac{3}{4} * \frac{20}{9}\)

Remember that when multiplying fractions you have to multiply across :

\(\frac{3*20}{4*9}\)

\(\frac{60}{36}\)

Divide both sides by 6.

\(\frac{5}{3}\)

Fractions are integers or numbers that have a numerator and a denominator. The numerator is the number at the top and the denominator is the number at the bottom. They can be represented mathematically as:

\(\frac{x}{y}\) , where x = numerator and y = denominator

\(\frac{3}{4}\) × \(2\frac{2}{9}\) in fraction form is \(1\frac{2}{3}\)

From the question, we have a mixed fraction \(2\frac{2}{9}\) .

       \(2\frac{2}{9}\) = \(\frac{20}{9}\)

\(\frac{3}{4}\) × \(\frac{20}{9}\)

= \(\frac{5}{3}\)

We can convert the improper fraction above to a mixed fraction

= \(1\frac{2}{3}\)

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Answer:

B I am pretty sure

Step-by-step explanation:

One angle measure provided (27 degrees), to determine the lengths of the sides or the measures of the other Angles.

The triangle, we need more information about the triangle, such as the lengths of the sides or the measures of other angles. The given information, "27 degrees," only specifies one angle of the triangle, but it is not sufficient to solve the triangle completely.

To solve a triangle, we typically need at least three pieces of information, which can include side lengths, angle measures, or a combination of both. With only one angle measure provided (27 degrees), we are unable to determine the lengths of the sides or the measures of the other angles.

To fully solve the triangle, we would need additional information such as the lengths of the sides or measures of at least two more angles. Without this additional information, it is not possible to provide a complete solution or determine the lengths of the sides or the measures of the other angles in the triangle.

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Answer: 4(x−5)

Step-by-step explanation:

I think this is right. If it’s not Im sorry. But if it is hope this helps!

Answer:

i think its

x^2 + (y + 2)^2 = 21.

Step-by-step explanation:

Answer:

D, g(x) = 1/4 x^2

Step-by-step explanation:

You can try plugging in the x and y values into each equation. The answer to this would be D, where if you plug in 2 as the x value, you get 1/4 * 4 which equals 1. This also makes sense because 2x would have a narrower curve while 1/2x would have a wider curve.

The percent of increase in the temperature of the liquid 67.97% .

We have that these are a few ways to decipher the appropriate safety protocol for this lab experiment

From the question we are told that

Generally

Safety precautions are the unforgettable rules and regulations that governs a laboratory.

This might vary across experiments such as the one in this scenario.

Therefore,  the percent of increase in the temperature of the liquid 67.97% .

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If Point A is located at (1, 2) and Point B is located at (4, 6), the length of the line between points A and B is 5 units.

To determine the length of the line between points A and B, we can use the distance formula, which is a formula used to calculate the distance between two points in a coordinate plane. The distance formula is:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points and d is the distance between them.

Using the coordinates of points A and B, we can substitute their values into the distance formula to find the length of the line between them:

d = √((4 - 1)² + (6 - 2)²)

d = √(3² + 4²)

d = √(9 + 16)

d = √25

d = 5

Rounded to the nearest whole number, the length of the line is also 5 units.

In conclusion, we can use the distance formula to find the length of the line between two points in a coordinate plane. The distance formula uses the coordinates of the two points to calculate the distance between them. The resulting distance can be rounded to the nearest whole number, if needed.

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True, While "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

The statement "-1000 2/3 is not a real fraction" is true. A real fraction is a mathematical expression that represents a ratio of two real numbers. In a fraction, the numerator and denominator are both real numbers, and they can be positive, negative, or zero.

In the given statement, "-1000 2/3" is not a valid representation of a fraction. The presence of a space between "-1000" and "2/3" suggests that they are separate entities rather than being part of a single fraction.

To represent a mixed number (a whole number combined with a fraction), a space or a plus sign is typically used between the whole number and the fraction. For example, a valid representation of a mixed number would be "-1000 2/3" or "-1000 + 2/3". However, without the proper formatting, "-1000 2/3" is not considered a real fraction.

It's important to note that "-1000 2/3" can still be expressed as an improper fraction. To convert it into an improper fraction, we multiply the whole number (-1000) by the denominator of the fraction (3) and add the numerator (2). The result would be (-1000 * 3 + 2) / 3 = (-3000 + 2) / 3 = -2998/3.

In conclusion, while "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

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