Write a polynomial function in standard form with real coefficients whose zeros include 1,4i, and -4i

In A'B'C'D, line segment A'B has a slope of 0 and a length of 5/4

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

A = (1, 4) and B = (6, 4)

The line AB is a horizontal line that passes through the point y = 4

This means that the slope of the segment A'B' is 0

The length is then calculated as

A'B' = difference in the x-coordinate * scale factor

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

A'B' = (6 - 1) * 1/4

Evaluate

A'B' = 5/4

Hence, the length A'B' is 5/4

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(-3/4) x (3/4)

---When we multiply fractions, we multiply horizontally/across

(-3 x 3) / (4 x 4)

-9 / 16

Answer: -9/16

Hope this helps!

Answer:Given: Three lines AD, CF, and BE intersect at point O such that and

To prove: O is the midpoint of all three lines, i.e., AO = BO = CO

Proof:

Since point O lies on line AD, we can write

(1) AO + OD = AD

Similarly, since O lies on line BE, we have

(2) BO + OE = BE

Also, since O lies on line CF, we have

(3) CO + OF = CF

From the given information, we have

(4) AD = BE

Substituting (4) in (1) and (2), we get

(5) AO + OD = BO + OE

Adding (3) to (5), we get

(6) AO + BO + CO + OD + OE + OF = AD + BE + CF

From the given information, we have

(7) CF = AD + BE

Substituting (7) in (6), we get

(8) AO + BO + CO + OD + OE + OF = 2AD + 2BE

Since we know that AD = BE, we can simplify (8) as

(9) AO + BO + CO + OD + OE + OF = 4AD

Dividing both sides of (9) by 4, we get

(10) AO + BO + CO = AD

But from (4), we also know that AD = BE, so we can write

(11) AO + BO + CO = BE

Dividing both sides of (11) by 2, we get

(12) AO = BO = CO

Hence, we have proved that O is the midpoint of all three lines, i.e., AO = BO = CO.

Step-by-step explanation:

Answer:n=-7

Step-by-step explanation: (-2y+5)+(-5y-3)=-7y+2 so our answer is -7.

Answer:

gain of 700 or 700

Step-by-step explanation:

A loss of 700 would be -700 and the opposite of that is 700.

Helping in the name of Jesus.

Answer:

$270:$30

Step-by-step explanation:

add up the ratios = 10

then do 300/10 = 30

so 1 ratio = 30

this means the ratio will be: $270:$30

Let me know if this helped

Answer:

$176420

Step-by-step explanation:

Monthly payment = $992

Yearly payment = 992 × 12 = $11064

Total payment = 11064 × 30 = $331920

Interest = 331920 - 155500 = $176420. The interest seems too much, are you sure there's no mistake in the question? Maybe the monthly payment is more than what you've written here?

The most common point total scored was 10 with a frequency of 9 or 25% of the total frequency.

To create the score frequency distribution, we have to list the unique values in the data set and count how many times each value appears.

1                                   1                       1/24 =  0.042 = 4.2%

3                                  2                      2/24 = 0.083  = 8.3%

4                                  1                       1/24 = 0.042  = 4.2%

5                                  1                       1/24 = 0.042  = 4.2%

6                                  1                       1/24 = 0.042 = 4.2%

7                                  2                      2/24 = 0.083 = 8.3%

8                                  1                       1/24 = 0.042   = 4.2%

9                                  2                      2/24 = 0.083  = 8.3%

10                                 6                      6/24 = 0.25   = 25%

11                                  1                       1/24 = 0.042 = 4.2%

12                                 2                      2/24 = 0.083 = 8.3%

13                                 2                      2/24 = 0.083 = 8.3%

14                                 2                      2/24 = 0.083  = 8.3 %

                                 ----------                                  

                                    24                                    

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The product of the two external segments and the sum of the lengths of each segment in the circle are equal if two secants are drawn to the circle from a single shared exterior point. The x has a value of 2 units.

If two secant segments are drawn to a circle from an exterior point, the product of the measurements of one secant segment and its external secant segment is equal to the product of the measurements of the second secant segment and its external secant segment.

So, we know that:

BE * AE = CE * DE

Now, insert the values as follows:

(x+1) * (x+12) = (x+4) * (x+5)

x² + x + 12x + 12 = x² + 4x + 5x + 20

13x + 12 = 9x + 20

4x = 8x

x= 2

Then: x = 2 units

Therefore, the product of the two external segments and the sum of the lengths of each segment in the circle are equal if two secants are drawn to the circle from a single shared exterior point. The x has a value of 2 units.

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The value of k that satisfies the given condition is approximately 0.4041.

In the expansion of (1+kx)⁵, the coefficient of x⁵ is given by the term:

C(5,k) * (kx)⁵ = k⁵ * C(5,k) * x⁵

where C(5,k) is the binomial coefficient or the number of ways to choose 5 items out of k.

So, we have the equation:

k⁵ * C(5,k) = -672

We can use a table of binomial coefficients to find C(5,k) for different values of k, but this can be time-consuming. Alternatively, we can use the fact that C(5,k) = C(5,5-k) and rewrite the equation as:

k⁵ * C(5,5-k) = -672

Expanding C(5,5-k), we get:

k⁵ * C(5,5-k) = k⁵ * C(5,k) = -672

Now, we can use trial and error to solve for k. Using this method, we can find that k = -4 or k ≈ 0.4041. However, since k must be positive (since it appears as a factor in the expansion), the only valid solution is k ≈ 0.4041.

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Step-by-step explanation:

let the first letter of their name represent

their age

s=2j

h=j-5

s+j+h=35

replace s AND h with the values above

2j+j+j-5=35

4j=35+5

4j=40

j=10

replace j in the equation s=2j

s=2×10

s=20

replace j in the equation h=j-5

h=10-5

h=5

Answer:

We can write 4x^2 + y^2 - 4xy - 16 as the product:

(2x - y + 4)(2x - y - 4)

Step-by-step explanation:

To write 4x^2 + y^2 - 4xy - 16 as a product, we can use the technique of completing the square. First, we can rearrange the terms to group the x terms and the y terms:

4x^2 - 4xy + y^2 - 16

Next, we can complete the square for the x terms and the y terms separately. For the x terms, we can add and subtract (2x)^2:

4x^2 - 4xy + (2x)^2 - (2x)^2 + y^2 - 16

Simplifying the first three terms gives:

(2x - y)^2 - (2x)^2 + y^2 - 16

For the y terms, we can add and subtract 16:

(2x - y)^2 - (2x)^2 + (y - 4)^2 - 16^2

Simplifying the second term gives:

-(4x^2) + 16x - (y^2) + 16y - 16^2

Therefore, we can write 4x^2 + y^2 - 4xy - 16 as the product:

(2x - y + 4)(2x - y - 4)

Answer:

f(2) = 3

Step-by-step explanation:

At f(2) we can notice that there is 2 y-values (one is an open circle and another is a closed circle)

But, an open circle means that the function is not defined at that point
But a closed circle means that it is defined

So we ignore the open circle and the closed circle is 3

So f(2) = 3

The value of null and alternative hypothesis are change beliefs and certainty test statics, p-value, and inference are the null hypothesis and conclude that there is insufficient evidence to suggest a significant relationship.

Climate Change Beliefs:

Null Hypothesis (H0): There is no significant relationship between climate change beliefs and certainty.

Alternative Hypothesis (Ha): There is a significant relationship between climate change beliefs and certainty.

Test Statistic: Pearson's correlation coefficient (r)

The Pearson correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, we will use it to determine the relationship between climate change beliefs and certainty.

P-Value: The p-value is the probability of obtaining a test statistic as extreme as the observed value, assuming that the null hypothesis is true.

Inference: If the p-value is less than the significance level (usually 0.05), we reject the null hypothesis and conclude that there is a significant relationship between climate change beliefs and certainty. If the p-value is greater than the significance level, we fail to reject the null hypothesis and conclude that there is insufficient evidence to suggest a significant relationship.

Class Time Use:

Null Hypothesis (H0): There is no significant relationship between class time use, income class, and sleeping.

Alternative Hypothesis (Ha): There is a significant relationship between class time use, income class, and sleeping.

Test Statistic: Multiple regression analysis

Multiple regression analysis is used to determine the relationship between a dependent variable and two or more independent variables. In this case, class time use, income class, and sleeping will be the independent variables, and we will use it to determine the relationship with the dependent variable.

P-Value: The p-value is the probability of obtaining a test statistic as extreme as the observed value, assuming that the null hypothesis is true.

Inference: If the p-value is less than the significance level (usually 0.05), we reject the null hypothesis and conclude that there is a significant relationship between class time use, income class, and sleeping.

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The first 5 terms in the sequence are 5, 4.75, 4.5, 4.25 and 4

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

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

a2 = -0.25 + a1

So, we have

a2 = -0.25 + 5 = 4.75

For other terms. we have

a3 = -0.25 + 4.75 = 4.50

a4 = -0.25 + 4.50 = 4.25

a5 = -0.25 + 4.25 = 4.0

Hence, the first 5 terms in the sequence are 5, 4.75, 4.5, 4.25 and 4

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We are given that the sample size $\sf\:n = 18$, sample mean $\sf\:\bar{X} = 103$, sample standard deviation $\sf\:S = 10$, and margin of error $\sf\:E = 6.05$ for a 98% confidence interval estimate for the population mean.

Using the formula for the margin of error, we can find the value of the t-score that corresponds to a 98% confidence level with 17 degrees of freedom (since we have 18 samples):

$\sf\:t_{0.01/2, 17} \implies 2.898$

Now, we can use the formula for a confidence interval estimate to find the lower and upper bounds of the interval:

$\sf\:\bar{X} - E \implies 103 - 6.05 < \mu < \bar{X} + E \implies 103 + 6.05$

Substituting in the values we have:

$\sf\:103 - 6.05 < \mu < 103 + 6.05$

Simplifying:

$\sf\leadsto\:96.95 < \mu < 109.05$

Therefore, a 98% confidence interval estimate for the population mean is $\sf\: (96.95, 109.05)$ rounded to two decimal places.

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After the first quarter, the interest earned would be:

$1,000.00 * 0.02 = $20.00

So the new balance would be:

$1,000.00 + $20.00 = $1,020.00

After the second quarter, the interest earned would be:

$1,020.00 * 0.02 = $20.40

So the new balance would be:

$1,020.00 + $20.40 = $1,040.40

After the third quarter, the interest earned would be:

$1,040.40 * 0.02 = $20.81

So the new balance would be:

$1,040.40 + $20.81 = $1,061.21

After the fourth quarter, the interest earned would be:

$1,061.21 * 0.02 = $21.22

So the final balance after 4 years would be:

$1,061.21 + $21.22 = $1,082.43

Therefore, the balance after 4 years would be $1,082.43.

Answer:

B) 48

Step-by-step explanation:

3, 13, 22, 30, 37, 43…

3 to 13 is +10

13 to 22 is +9

22 to 30 is +8

We are adding one less each time

3, 13  , 22,   30,   37,    43   …

 +10  +9   +8    +7    +6    +5

Add 5 to 43

43+5 = 48

Answer:

cos 2x

f(x)=4•sin(x)•cos(x)

Step-by-step explanation:

a) There are 2 x 2 = 4 sample points in the sample space

b) Tree Diagram

O D.\nH\nHe\nT\nH\nT\n

Sample space: D. HH, HT, TH, TT

c) P(no tails) = P(HH)

= 1/4

d) P(exactly one tail) = P(HT, TH)

= 2/4

= 1/2

e) P(2 tails) = P(TT)

= 1/4

f) P(at least one tail) = P(HT, TH, TT)

= 3/4

In mathematics, tree diagrams are often used in probability and statistics to show all the possible outcomes of an event. In computer science, they are used to represent the hierarchical structure of files and directories in a file system

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Step-by-step explanation:

To solve the inequality:

-3 > 5 - b

We can start by isolating the variable b on one side of the inequality. We can do this by subtracting 5 from both sides of the inequality:

-3 - 5 > -b

Simplifying the left-hand side of the inequality, we get:

-8 > -b

To isolate b, we can multiply both sides of the inequality by -1. When we do this, we need to reverse the inequality sign:

8 < b

So the solution to the inequality is:

b > 8

This means that b must be greater than 8 for the inequality to be true.

Answer:

Step-by-step explanation:

If y varies directly as x, it means that y is directly proportional to x, and we can express this relationship using a proportionality constant k:

y = kx

To find the value of k, we can use the given information that y = 2 when x = 3:

2 = k(3)

Solving for k, we get:

k = 2/3

Now that we know the value of k, we can use the formula to find y when x = 1:

y = (2/3)x

y = (2/3)(1)

y = 2/3

Therefore, when x = 1, y = 2/3.

The caloric content for ice cream C is 250 calories while the caloric content for ice cream B is 270 calories.

To determine the caloric content, we will assign algebraic notations to each of the dessert types.

1 Icecream + 2 Blueberry pie =   790 calories

3 icecream + 2 Blueberry pie = 1290 calories

Now the first equation will be subtracted from the second equation as follows:

2 icecream = 500 calories

So, 1 ice cream is 250 calories.

Also, since, 1 icecream serving equals 250 calories, 2 Blueberry pies = 790 - 250 = 540 calories, and 1 Blueberry pie equals 270 calories.

Complete question:

Johnny's cafe serves desserts. One serving of ice cream and two servings of blueberry pie provides 790 calories. Three servings of ice cream and two servings of blueberry pie provides 1290 calories. Find the caloric content of each item.

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The solution of the trigonometric problem is  y = -3

Starting with the equation

3/2 cos^-1(y/6) = pi

First, we can simplify by dividing both sides by 3/2 ....

cos^-1(y/6) = pi / (3/2)

cos^- 1(y/6) = 2pi / 3

Next, we can take the cosine of both sides to get...

cos (cos^-1(y/6 ) )

= cos( 2pi/3)

y/6 = -1/2

y = -3

Therefore, the exact solution to the equation 3/2 cos^-1(y/6) = pi is y = -3.

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An exponential function would be more appropriate than a linear function, as exponential growth

To determine which type of function best fits the data, we can analyze the difference in the y values (Value of Investment) as x increases.

Differences between consecutive y values:

16,357.04 - 14,944.54 = 1,412.50

17,974.72 - 16,357.04 = 1,617.68

19,891.18 - 17,974.72 = 1,916.46

The differences between consecutive y values are increasing as x increases. This suggests that an exponential function would be more appropriate than a linear function.

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The total cost of the several items that originally cost $128.25 with a coupon for 35% off and sales tax of 4% is C. $86.70.

The original cost is discounted by 35% using a discount factor of 0.65 and increased by a sales tax factor of 1.04.

After the multiplications, the product shows the total cost that Mary incurred for buying the items.

Original cost of several items Mary is buying = $128.25

Coupon discount = 35%

Discount factor = 0.65 (100 - 35)

Sales tax rate = 4%

Sales tax factor = 1.04 (100 + 4)

The total cost of the items = $86.70($128.25 x 0.65 x 1.04)

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Answer:

1. f. System of Equations

2. e. No solutions

3. i. One solution

4. h. Like Terms

5. b. Substitution

6. c. Solution

7. a. Elimination

8. d. Infinitely Many Solutions

9. g. Variable

10. j. Coefficients

Step-by-step explanation:

Ur welcome :)

Answer: 3t(9t + 5)

Step-by-step explanation:

Sure! Factoring involves breaking down an expression into simpler factors that, when multiplied together, give the original expression.

To factor 27t² + 15t, we can look for the greatest common factor (GCF) of the two terms. The GCF of 27t² and 15t is 3t, because both terms can be divided by 3t.

So we start by factoring out the 3t:

27t² + 15t = 3t(9t + 5)

Notice that we can check if the factorization is correct by using the distributive property to multiply the factor 3t by the expression inside the parentheses:

3t(9t + 5) = 3t(9t) + 3t(5) = 27t² + 15t

Therefore, 27t² + 15t can be fully factorized as 3t(9t + 5).

Answer:

15 19/20

Step-by-step explanation:

95 cents means 95/100 then reduce that and you get 19/20 and then on the end you still have the $15

Rounding to three decimal places, the confidence interval is (0.419, 0.574).

The sample proportion, p′ = 0.842, which is the point estimate of the population proportion, must be determined in order to calculate the confidence interval. Given that CL = 0.95 is the requested confidence level, = 1 - CL = 1 - 0.95 = 0.05 ( 2) ( 2) = 0.025.

Confidence interval=proportion±margin of error

CI = p ± ME

The proportion is:

p = x / n

p = 55/110

p = 0.5

Margin of error=critical value × standard error

ME = CV × SE

n > 30, so we can approximate CV with a normal distribution.

At P=88%, CV=1.55.

SE = √(pq / n)

SE = √(0.5 (1−0.5)/110)

SE = 0.048

So the margin of error is:

ME = 1.55 × 0.048

ME = 0.074

So the confidence interval is:

CI = 0.5 ± 0.074

CI = (0.426, 0.574)

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Question:

Use the given degree of confidence and Sample data to construct income confidence interval for the population proportion p. n=110, x=55; 88% confidence

A) 0.426 B)0.442 C)0.425 D)0.421