3.4 MIXED FACTORING

1. Utilize all of the strategies for factoring in order to factor the following polynomials.
Reminder: Combine like-terms prior to factoring.

a. x² - 4x-2x+8

Answer: 6s + 10n less than or equal to 90

By using the parallelogram method, the addition of the vectors [tex]\vec a + \vec b[/tex] is (3, 1).

In Mathematics, a vector typically comprises two (2) points. First, is the starting point which is commonly referred to as the "tail" and the second (ending) point that is commonly referred to the "head."

Furthermore, the head to tail method of adding two (2) vectors requires drawing the first vector ([tex]\vec a[/tex]) on a graph and then placing the tail of the second vector ([tex]\vec b[/tex]) at the head of the first vector. Finally, the resultant vector would be drawn from the tail of the first vector ([tex]\vec a[/tex]) to the head of the second vector ([tex]\vec b[/tex]).

By adding the given vectors algebraically, we have the following:

[tex]\vec a + \vec b[/tex] = (2, -3) + (1, 4)

[tex]\vec a + \vec b[/tex] = [(2 + 1), (-3 + 4)

[tex]\vec a + \vec b[/tex] = (3, 1).

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Answer:

the answer is C

Step-by-step explanation:

the answer is C it converges

The exact values are;

sin⁡θ = -5/√29

cos⁡θ = 2/√29

sec⁡θ =√29/2

csc⁡θ = -√29/5

cot⁡θ = -2/5

We are given that

tan⁡θ=-5/2 and sin⁡θ>0

First quadrant: I, 0°<θ<90°

We can find the first quadrant between 0° and 90° , the values from 0 to the positive numbers for the x-axis and the y-axis, the functions sine, cosine and tangent will always have positive values.

sin⁡θ = -5/√29

cos⁡θ = 2/√29

sec⁡θ =√29/2

csc⁡θ = -√29/5

cot⁡θ = -2/5

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Answer:

In a 30°-60°-90° triangle, the length of the longer leg is √3 times the length of the shorter leg, and the length of the hypotenuse is twice the length of the shorter leg.

[tex]n = \frac{2}{ \sqrt{3} } = \frac{2 \sqrt{3} }{3} [/tex]

[tex]m = \frac{4 \sqrt{3} }{3} [/tex]

The remainder that is found when dividing 2x^2+7x-4 by x-3 is 35

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

Dividing 2x^2+7x-4 by x-3

This means that

Dividend = 2x^2 + 7x - 4

Divisor = x - 3

Set the divisor to 0

So, we have

x - 3 = 0

Evaluate

x = 3

Substitute 3 for x in the dividend equation, so, we have the following representation

Remainder = 2(3)^2 + 7(3) - 4

Evaluate

Remainder = 35

Hence, teh remainder is 35

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Answer:

The answer is **D. 30x+15y**.

```

5(6x + 3y) = 5*6x + 5*3y = 30x + 15y

```

Step-by-step explanation:

1. Distribute the 5:

```

5(6x + 3y) = (5 * 6x) + (5 * 3y)

```

2. Simplify:

```

5(6x + 3y) = 30x + 15y

```

Therefore, 5(6x + 3y) is equivalent to 30x + 15y.

The decimals as a power of 10 are given as follows:

A number in scientific notation is given by the notation presented as follows:

[tex]a \times 10^b[/tex]

With the base being [tex]a \in [1, 10)[/tex], meaning that it can assume values from 1 to 10, with an open interval at 10 meaning that for 10 the number is written as 10 = 1 x 10¹, meaning that the base is 1, justifying the open interval at 10.

Hence the numbers are represented as follows:

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The two roots of the quadratic equation x² - 5x + 3 = 0 are (5 + √13) / 2 and (5 - √13) / 2.

To find the roots of the quadratic equation x² - 5x + 3 = 0, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation.

Substituting the values of a, b, and c from the given equation, we have:

x = (-(-5) ± √((-5)² - 4(1)(3))) / 2(1)

x = (5 ± √(25 - 12)) / 2

x = (5 ± √13) / 2

Therefore, the roots of the equation are (5 + √13) / 2 and (5 - √13) / 2.

To verify that these are indeed the roots of the equation, we can substitute each of these values for x in the original equation and check if the equation is satisfied. For example, if we substitute (5 + √13) / 2 for x, we get:

(5 + √13)² - 5(5 + √13) + 3 = 0

Simplifying this equation, we get:

13 - 5√13 + 8 + 13 - 5√13 + 3 = 0

This equation is true, which means that (5 + √13) / 2 is a root of the equation x² - 5x + 3 = 0. Similarly, we can verify that (5 - √13) / 2 is also a root of the equation.

These roots can be found using the quadratic formula, which is a useful tool for solving quadratic equations.

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The solution to the equation x + 2(7 - x) = 12 is x = 2.

Given the equation in the question:

x + 2(7 - x ) = 12

To solve the  equation, you need to use algebraic techniques to isolate the variable x on one side of the equation.

x + 2(7 - x) = 12

Apply distributive property

x + 2×7 + 2×-x = 12

x + 14 - 2x = 12

Combine like terms by subtracting 14 from both sides:

x - 2x = 12 - 14

-x = -2

Solve for x by dividing both sides by -1:

-x/-1 = -2/-1

x = 2

Therefore, the value of x is 2.

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Answer:

exponential graph

Step-by-step explanation:

it is a exponential graph the is negative ,if you substitute x values and find the points to plot you'll see how it is plotted

Answer:

See graph

Step-by-step explanation:

The graph of any function can be identified by making an x-y table.

Choose some values for x (often -2, -1, 0, 1, 2)

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

f(-1) =  - 2^(-1) = - 1/2

f(-0) =  - 2^(-0) = - 1

f(1) =  - 2^(1) = - 2

f(2) =  - 2^(2) = - 4

Answer:

x = 3.5

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Divisions

Additions

Subtractions

~

First, simplify. Combine like terms. Like terms are terms that share the same amount of the same variables:

[tex]2x + 15 - 8 = 14\\2x + (15 - 8) = 14\\2x + (7) = 14[/tex]

Next, isolate the variable, x. First, subtract 7 from both sides of the equation:

[tex]2x + 7 = 14\\2x + 7 (-7) = 14 (-7)\\2x = 14 - 7\\2x = 7[/tex]

Finally, divide 2 from both sides of the equation:

[tex]2x = 7\\\frac{(2x)}{2} = \frac{(7)}{2}\\ x = \frac{7}{2}\\ x = 3.5[/tex]

x = 3.5 is your answer.

~

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Answer:

[tex]\bold{\Large \boxed{x=\frac{7}{2}}}[/tex]

Step-by-step explanation:

To solve the equation [tex] 2x+15-8=14 [/tex] for x, we need to isolate x on one side of the equation.

We can do this by first combining the constants on the right-hand side of the equation:

[tex]2x+15-8=14[/tex]

[tex]2x+7=14[/tex]

Next, we can isolate x by subtracting 7 from both sides of the equation:

[tex]2x=7[/tex]

Finally, we can solve for x by dividing both sides of the equation by 2:

[tex]x=\frac{7}{2}[/tex]

Therefore, the solution to the equation [tex]2x+15-8=14[/tex] is [tex]\bold{x=\frac{7}{2}}[/tex].

Answer:

Based on the hypothesis test conducted with a significance level of 5%, we fail to reject the null hypothesis that the proportion of smokers in the city is 20%. This means that we do not have sufficient evidence to conclude that the proportion of smokers is less than 20%. The p-value of 0.828 suggests that there is a high probability that the observed proportion of smokers in the sample is due to chance and not a true difference in the proportion of smokers in the population. Therefore, we cannot conclude that the city has a lower proportion of smokers than 20%.

In this hypothesis test set up by the researcher, the p-value is 0.828, which is greater than the significance level (0.05). Therefore, we do not reject the null hypothesis, meaning there is not enough statistical evidence to validate the researcher's claim that the proportion of smokers is less than 20%

A hypothesis test in statistics uses test statistics based on sample data to accept or reject a null hypothesis. In this scenario, the null hypothesis (H0) states that the proportion of smokers (p) is 20%. The alternative hypothesis (Ha) claims that the proportion of smokers is less than 20%. The p-value is a measure of the probability that the observed data could occur under the null hypothesis. In our case, a p-value of 0.828 means that there is an 82.8% chance of observing the data if the true proportion of smokers is 20%, or higher.

Usually a threshold known as the significance level (in this case 5% or 0.05) is used to determine whether the null hypothesis should be rejected or not. If the p-value is less than or equal to the significance level, it suggests that the observed data is inconsistent with the null hypothesis, and the null is usually rejected. However, since our p-value is greater (0.828 > 0.05), we would not reject the null hypothesis, suggesting that there is not enough evidence to support the researcher's claim that the proportion of smokers is less than 20%.

Therefore, the conclusion is that the researcher's claim cannot be validated using the provided data.

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There was no error in the procedure as we can see below.

In algebra, a formula expresses a relationship between two or more variables. Changing the subject of a formula means isolating a specific variable on one side of the equation. This is done by applying inverse operations in a specific order to eliminate all other variables and isolate the desired one.

We have the formula as;

[tex]A = \pi R^2 - \pi r^2\\A = \pi(R^2 - r^2)\\A/ \pi = R^2 - r^2\\R^2 = A/ \pi + r^2\\R = \sqrt{} A/ \pi + √r^2\\R = \sqrt{} A/ \pi + r[/tex]

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a. The missing probability is 0.112

b. The expected number of classes passed is 3.38.

c. Is it unusual for an average student to pass at most 2 classes in a given semester is 0.211

a. Since the whole of all probabilities must rise to 1, we are able to discover the lost likelihood by subtracting the whole of the given probabilities from 1:

1 - 0.001 - 0.098 - 0.175 - 0.419 - 0.195 = 0.112

Subsequently, P(X=2) = 0.112.

b. The anticipated number of classes passed can be found by increasing each possible value of X by its particular likelihood, and after that summing the items:

E(X) = 0(0.001) + 1(0.098) + 2(0.112) + 3(0.175) + 4(0.419) + 5(0.195)

= 3.38

Hence, the anticipated number of classes passed is 3.38.

c. To decide in case it is bizarre for an average student to pass at most 2 classes in a given semester, we have to calculate the likelihood of passing at most 2 classes:

P(X ≤ 2) = P(X=0) + P(X=1) + P(X=2)

= 0.001 + 0.098 + 0.112

= 0.211

Since this likelihood is more noteworthy than 0.05 (i.e., the commonly utilized threshold for determining whether an occasion is unordinary), it isn't abnormal for a normal understudy to pass at most 2 classes in a given semester. 

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Using the property of proportionality for the equation (6-x) : (7-x) :: (18-x) : (22-x), then, x = ⁶/₇.

Solving this problem by using the property of proportionality, which states that the ratio of the first two terms in a proportion is equal to the ratio of the last two terms. In this case:

(6-x) : (7-x) :: (18-x) : (22-x)

Solving for x, cross-multiply the ratios:

(6-x) x (22-x) = (7-x) x (18-x)

Expanding both sides:

132 - 28x + x² = 126 - 25x + x²

Simplifying, we get:

7x = 6

Therefore, x = ⁶/₇.

Thus, the solution to the proportion is:

(6-x) : (7-x) :: (18-x) : (22-x)

or

⁶/₇ : ¹/₇ :: ¹²/₇ : ¹⁶/₇

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Answer:

m∠R=x=37°; m∠QOR=53°

Step-by-step explanation:

Any line that is tangent to a circle (such as QR) is perpendicular to the circle's radius (QO). Therefore, ΔOQR is a right triangle, with the right angle at Q.

1. You can use  90 + (x+16) + x = 180   or    (x+16) + x = 90 to solve for x.

2. If needed, you can then use the solution from step 1 to find the measure of ∠QOR.

Answer:

D.The way you group numbers in a series of

multiplication problems doesn't change the final

product.

The correct statements are as follows:-

There is a cluster from 3 to 4.

There is a gap between 1 and 3.

There is a peak at 4.

The data is skewed left.

We have,

Scatter plots are graphs that show how two variables in a data collection relate to one another. On a two-dimensional plane or in a Cartesian system, it represents data points.

The right statements for the dot plots are as follows:-

There is a cluster from 3 to 4.

There is a gap between 1 and 3.

There is a peak at 4.

The data is skewed left.

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[tex]f(2) = g(2) = 4[/tex], which means that the graphs of the two functions intersect at x = 2.

To show that the graphs of the functions   [tex]f(x) = 2^x[/tex] and [tex]g(x) = \sqrt(4x + 1) + 1[/tex]  intersect at the abscissa point x = 2, we need to show that both functions have the same value at  [tex]x = 2.[/tex]

First, we evaluate f(2):

[tex]f(2) = 2^2 = 4[/tex]

Next, we evaluate g(2):

[tex]g(2) = \sqrt(4(2) + 1) + 1 = \sqrt9 + 1 = 4[/tex]

Therefore,  [tex]f(2) = g(2) = 4[/tex] , which means that the graphs of the two functions intersect at [tex]x = 2[/tex] .

To visualize this, we can plot the two functions on the same set of axes:

As we can see from the graph, the two curves intersect at the point (2, 4).

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The complete question is: How can you show that the graphs of the functions f(x) = [tex]2^x[/tex] and g(x) = √(4x + 1) + 1 intersect?

The probability that a respondent has both portable earbuds and a smart speaker is 0.16

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

This means that

P(earbuds) = 54.5%

P(smart speaker) = 30%

Using the above as a guide, we have the following:

P = P(earbuds) * P(smart speaker)

Substitute the known values in the above equation, so, we have the following representation

P = 54.5% * 30%

Evaluate

P = 0.16

Hence, the probability is 0.16

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Answer:

To calculate the speed of the airplane, we need to subtract the speed of the headwind from the speed of the tailwind.

To calculate the speed of the airplane, we need to subtract the speed of the headwind from the speed of the tailwind. Speed of airplane = (Speed of tailwind) - (Speed of headwind)

To calculate the speed of the airplane, we need to subtract the speed of the headwind from the speed of the tailwind. Speed of airplane = (Speed of tailwind) - (Speed of headwind)Speed of airplane = (150 mph) - (100 mph)

To calculate the speed of the airplane, we need to subtract the speed of the headwind from the speed of the tailwind. Speed of airplane = (Speed of tailwind) - (Speed of headwind)Speed of airplane = (150 mph) - (100 mph)Speed of airplane = 50 mph

To calculate the speed of the airplane, we need to subtract the speed of the headwind from the speed of the tailwind. Speed of airplane = (Speed of tailwind) - (Speed of headwind)Speed of airplane = (150 mph) - (100 mph)Speed of airplane = 50 mphTherefore, the speed of the airplane would be 50 mph.

If Yogi Charges 4.30$ per square foot for the carpet plus $75 installation fee, the total cost of installing carpet in the hotel lobby with Yogi is $2,225.

To determine the total cost of installing carpet in the hotel lobby with Yogi, we need to know the area of the lobby in square feet. Once we have the area, we can use Yogi's pricing scheme to calculate the total cost.

Assuming that we have measured the area of the lobby to be 500 square feet, we can calculate the total cost as follows:

Cost of carpet = area × price per square foot

= 500 × $4.30

= $2,150

Cost of installation = $75

Total cost = cost of carpet + cost of installation

= $2,150 + $75

= $2,225

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The truth statements about the function f(x) = 14(0.87)^x is Growth; y = 0

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

f(x) = 14(0.87)^x

An exponential function is represented as

y = ab^x

Where

a = initial value

b = growth/decay factor

In this case, the exponential function is a decay function

This means that

The value of b is less than 1 i.e.

b = 0.87 and 0.87 < 1

Hence, the function is a decay function

Recall that

f(x) = 14(0.87)^x

So, we have

y = 0 as the the equation of the asymptote

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According to the given question, Alice should use this equation f(t) = [tex]24,000(0.945)^t[/tex] to represent the value of the car after t years.

Depreciation is the expected decrease in the value of fixed assets over the course of a fiscal year. For physical assets like real estate, machinery, vehicles, and other items, large lump sum acquisitions are made.

The equation[tex]f(t) = 24,000(0.945)^t[/tex] represents the value of the car after t years, where 0.945 represents the remaining value of the car after one year of depreciation at a rate of 5.5%.

To calculate the value of the car after two years, for example, we would substitute t = 2 into the equation:

f(2) = [tex]24,000(0.945)^2[/tex]

f(2) = 24,000(0.893025)

f(2) ≈ 21,433.80

Therefore, the value of the car after two years would be approximately $21,433.80.

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Answer:

Step-by-step explanation: