Given −7 is one of the roots of the quadratic equation
(x + k)2 = 16, where k is a constant, find the values of k.

Answer:

B)

Step-by-step explanation:

Answer: the answer is B hope this helps

Step-by-step explanation:

The real zeros of the polynomial function P(x) = x⁵ − 50x³ + 49x are -1, 0, and 1.

To find the zeros of this function, we can factor it by first factoring out an x to get P(x) = x(x⁴ − 50x² + 49). Then, we can factor the quadratic expression inside the parentheses using the difference of squares formula, which gives us P(x) = x(x² − 1)(x² − 49). Simplifying further, we have P(x) = x(x − 1)(x + 1)(x - 7)(x + 7).

Therefore, the zeros of P(x) are the values of x that make each factor equal to zero. This gives us x = -7, -1, 0, 1, and 7. Since all of these values are real, we conclude that the number of real zeros of P(x) is 5.

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The number of miles ran by Mick is 29 miles and the number of miles ran by Keith is 47 miles.

Given that, last month, Keith ran 18 more miles than Mick.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the number of miles ran by Mick be x.

Then, the number of miles ran by Keith will be x+18.

Here, total distance ran by both of them is 76 miles

So, equation is x+x+18=76

⇒ 2x+18=76

⇒ 2x=76-18

⇒ 2x=58

⇒ x=29 miles

So, x+18=47 miles

Therefore, the number of miles ran by Mick is 29 miles and the number of miles ran by Keith is 47 miles.

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Answer:

24.5 so 24 and a half .....

The approximate value of x in the equation 5 to the power of 2x=20 is 0.93

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

5 to the power of 2x=20

As an expression, we have

5^(2x) = 20

Take the natural logarithm of both sides

so, we have the following representation

2x = ln(20)/ln(5)

Evaluate the quotients

This gives

2x = 1.86

So, we have

x = 0.93

Hence, the value of x is 0.93

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The area of the given figure which has the shape of a trapezium would be = 58.5cm²

To calculate the area of the trapezium given above, the formula for area of a trapezium should be used and this is given below;

Area of a trapezium= 1/2(a+b)h

Where;

a= 12cm

b= 7.5cm

height= 6cm

Area of trapezium = 1/2(12+7.5) × 6

= 19.5×3 = 58.5cm²

Therefore, the area of the given shape above is calculated as 58.5cm²

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The solutions to the equation cos 2x = -cos x are x = π/3 + 2πn and x = π + 2πn, where n is any integer

To find the solution to the equation cos 2x = -cos x, we need to use the double angle formula for cosine. The double angle formula for cosine is:

cos 2x = 1 - 2sin^2x

We can substitute this into the original equation to get:

1 - 2sin^2x = -cos x

Next, we can rearrange the equation to isolate the sine term:

2sin^2x = 1 + cos x

Now, we can use the Pythagorean identity, which states that sin^2x + cos^2x = 1, to substitute for sin^2x:

2(1 - cos^2x) = 1 + cos x

Simplifying and rearranging gives us:

2cos^2x + cos x - 1 = 0

This is a quadratic equation in terms of cos x, so we can use the quadratic formula to find the solutions:

cos x = (-1 ± √(1^2 - 4(2)(-1))) / (2(2))

cos x = (-1 ± √9) / 4

cos x = (-1 ± 3) / 4

This gives us two possible solutions for cos x:

cos x = (-1 + 3) / 4 = 1/2

cos x = (-1 - 3) / 4 = -1

Therefore, the solutions to the equation cos 2x = -cos x are x = π/3 + 2πn and x = π + 2πn, where n is any integer.

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The maximum value for directional derivative of the function at the point (1, 2, 3) is  29.69. It occurs in the direction of the gradient vector (3, -12, 27).

The directional derivative of a function in the direction of a unit vector u is given by the gradient of the function (denoted ∇f) dotted with the unit vector u.

\(D_uf =\) ∇f × u

Which can also be represent as

\(D_uf(P) = < f_x(P), f_y(P), f_z(P) > * u\)

the gradient of f at P ⇒ \(f_x(P), f_y(P), f_z(P)\)

a unit vector ⇒ u

\(f(x, y, z) = x^3 \ - y^3 + z^3\)

\(f_x, f_y, f_z = 3x^2, -3y^2, 3z^2\)

we are given that P = (1, 2, 3). ∴, the directional derivative of f at P in the direction of u is

\(D_uf(P) = 3(1)^2, -3(2)^2, 3(3)^2\) ⇒ \(3, -12, 27\)

The magnitude of this gradient vector is

||∇f|| = \(\sqrt{(3)^2 + (-12)^2 + (27)^2}\)

\(= \sqrt{9 + 144 + 729}\)

\(= \sqrt{882}\)

= 29.69

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Answer:

5

Step-by-step explanation:

Answer:

7 is the answer

Step-by-step explanation:

Answer:

EBC and ABE, as well as ABD and ABE

Step-by-step explanation:

Supplementary angles form an 180 degree angle. In other words, they form a straight line.

EBA and DBC are each greater than 90 degrees and are vertical angles, not supplementary angles.

EBC and ABE form a straight line. So they are supplementary angles.

ABD  and ABE form a straight line. So  they are also supplementary angles.

CBE and ABD are each less than 90 degrees and are vertical angles, not supplementary angles.

So, EBC and ABE, as well as ABD and ABE are the correct choices.

Answer:

Step-by-step explanation:

Based on the given information, we can infer the following preferences of Ances regarding her basketball team's scores:

Ances likes when her team scores 341 points.

Ances does not like when her team scores 342 points.

Ances likes when her team scores 26 points.

Ances does not like when her team scores 34 points.

Ances likes when her team scores 53 points.

Ances does not like when her team scores 42 points.

These preferences suggest that Ances has specific preferences for certain scores and dislikes other scores. It could be based on personal associations, superstitions, or simply personal preference.

It's important to note that these preferences are subjective and may not have any rational or logical basis. They are specific to Ances' personal preferences and may not reflect the overall performance or significance of the scores in a basketball game.

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The financial disadvantage that Premium Paper Corporation would recognize per year if they eliminate the Recipe Cards Division is $30,500.

To determine the financial advantage or disadvantage of eliminating the Recipe Cards Division, we need to compare the contribution margin of the division with the portion of fixed costs that can be avoided.

The annual contribution margin of the Recipe Cards Division is $25,000. However, out of the $75,000 in fixed costs, $19,500 cannot be avoided. This means that if the division is eliminated, only $75,000 - $19,500 = $55,500 of fixed costs can be avoided.

If the division is eliminated, the financial advantage or disadvantage can be calculated as follows:

Financial advantage/disadvantage = Contribution margin - Avoidable fixed costs

Financial advantage/disadvantage = $25,000 - $55,500 = -$30,500

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Percentage of data within 2 population standard deviations of the mean is 68%.

To calculate the percentage of data within two population standard deviations of the mean, we need to first find the mean and standard deviation of the data set.

The mean can be found by summing all the values and dividing by the total number of values:

Mean = (20*2 + 22*8 + 28*9 + 34*13 + 38*16 + 39*11 + 41*7 + 48*0)/(2+8+9+13+16+11+7) = 32.68

To calculate standard deviation, we need to calculate the variance first. Variance is the average of the squared differences from the mean.

Variance = [(20-32.68)^2*2 + (22-32.68)^2*8 + (28-32.68)^2*9 + (34-32.68)^2*13 + (38-32.68)^2*16 + (39-32.68)^2*11 + (41-32.68)^2*7]/(2+8+9+13+16+11+7-1) = 139.98

Standard Deviation = sqrt(139.98) = 11.83

Now we can calculate the range within two population standard deviations of the mean. Two population standard deviations of the mean can be found by multiplying the standard deviation by 2.

Range = 2*11.83 = 23.66

The minimum value within two population standard deviations of the mean can be found by subtracting the range from the mean and the maximum value can be found by adding the range to the mean:

Minimum Value = 32.68 - 23.66 = 9.02 Maximum Value = 32.68 + 23.66 = 56.34

Now we can count the number of data points within this range, which are 45 out of 66 data points. To find the percentage, we divide 45 by 66 and multiply by 100:

Percentage of data within 2 population standard deviations of the mean = (45/66)*100 = 68% (rounded to the nearest percent).

Therefore, approximately 68% of the data falls within two population standard deviations of the mean.

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Answer:

33 miles

Step-by-step explanation:

The illustration forms a right angled triangle. The opposite side of the triangle is where we are looking for . The adjacent side is the radius 4000 miles.

5280 ft = 1 mile

735 ft = ? miles

cross multiply

735/5280

miles = 0.13920454545  miles

The hypotenuse side is the height of the building + 4000 miles = 0.140 + 4000 = 4000.14  miles

using Pythagoras theorem

c² = a² + b²

c = 4000.14

a = 4000

4000.14² = 4000² + b²

b² = 4000.14² - 4000²

b² = 16001120.0196  - 16000000

b² = 1120.0196

b = √1120.0196

b = 33.4666938911

b = 33 miles

Explanation:

Let's represent apples and oranges with the variables:

• x: amount of apples

• y: amount of oranges

The sum of the amount of oranges and apples must be no more than 10:

If each apple cost $2, then x apples cost 2x. Also, if each orange cost $4, then y oranges cost 4y. The sum of these costs must be less than 22:

Answers:

a. The system is:

b. The graph:

In blue it's the graph of the first inequality and in green is the graph of the second inequality.

A total of 81 apples and 72 spears are there in total.

Ratio is a quantitative relation between two amounts showing the number of times one value contains or is contained within the other. A statement expressing the equality of two ratios A:B and C:D is called a proportion. We can express proportion as -

A : B ∷ C : D

AND

A x D = B x C

Product of extremes equal to product of means.

Given is in a Petri café they discovered that as many apples as pears are rotten, ⅔ of all apples are rotten and that ¾ of all pears are rotten.

Assume that there are [x] apples and [y] pears in total.

Then, rotten apples = 2x/3

rotten paears = 3y/4

Since, they are equal, we get -

2x/3 = 3y/4

2x (4) = 3y (3)

8x = 9y

The whole number coordinates satisfying the equation are - (81, 72). Refer to the graph attached.

Therefore, a total of 81 apples and 72 spears are there in total.

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Answer:

It is 49. You will know it is right down here:

Step-by-step explanation:

1323 when factorised = 3 *3*3*7*7

Therefore it is to be divided by 7*7 = 49

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Answer:

Step-by-step explanation:10 minutes 5 seconds per mile

6 minutes 15.93 seconds per kilometer

5.95 miles/hour

9.58 kilometers/hour

159.6 meters/minute

2.66 meters/second

Answer:

y = 3x + 3

Step-by-step explanation:

First find the slope, m, using 2 points on the line: (0, 3) and (-1, 0)

m = (0-3) / (-1-0) = -3/-1 = 3

Find the y-intercept, b, by looking at where the line intersects the y-axis:

b = 3

y = mx + b

y = 3x + 3

Answer:

XXXXXXXXXXXXXXXXXXXX Ion know

The regular price of one baseball bat is $80.40.

A discount is a drop in a product's or service's price. It is often provided by the vendor as an inducement to lure customers into making a purchase. Often, the discount is indicated as a percentage or a dollar amount off the list price.

The standard price and the discount rate must be known in order to determine a discount. Often, the discount rate is expressed as a percentage. We multiply the usual price by the discount rate to determine the discount amount.

Given that, coach buys 5 identical baseball bats for a total of $327.45.

Thus,

5P = 327.45

P = 65.49

So one bat cost him 65.90.

Now, the regular cost of the bat will be:

Price = 65.90 + 14.50

Price = 80.40

Hence, the regular price of one baseball bat is $80.40.

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Answer:

Step-by-step explanation:

Remark

What you want to do is get r on one side of the equal sign and everything else on the other.

Givens

V = pi r^2 h

Solution

Divide by pi

V/pi = pi r^2 h/pi

V/p = r^2 * h

Divide by h

V / h pi = r^2 h / h              Cancel h on the right side. Turn equation around

r^2 =  V / h pi

Take the square root of both sides

√r^2 = √(V / h pi )

r = √ (V / h pi)

Answer r =√ (V / h pi)

Answer:

C 82 degrees

Step-by-step explanation:

Since triangle, ABC is congruent to EFG which means that the measurement for A is the same measurement for C.

Answer:

1st option

Step-by-step explanation:

Just did it

The monthly payment amount is $217.42 and the finance charge is $413.02.

The payment amount and finance charge can be found by using the formula below

Payment amount formula: PMT = (P x R x (1 + R)^N) / ((1 + R)^N - 1)

Finance charge formula: Finance charge = Total payment - Loan amount

Where P = Loan amount

R = Interest rate per period

N = Number of periods

Given that a loan is made for $4800 with an APR of 12% and payments made monthly for 24 months

Therefore,P = $4800R = 12% / 12 = 1% per month

N = 24

Using the Payment amount formula above: PMT = (P x R x (1 + R)^N) / ((1 + R)^N - 1)

PMT = ($4800 x 0.01 x (1 + 0.01)^24) / ((1 + 0.01)^24 - 1)

PMT = $217.42

Hence, the monthly payment amount is $217.42 (rounded to two decimal places).

Using the finance charge formula above: Finance charge = Total payment - Loan amount

Total payment = Payment amount x Number of periods

Total payment = $217.42 x 24 = $5213.02

Finance charge = $5213.02 - $4800

Finance charge = $413.02

Hence, the finance charge is $413.02 (rounded to two decimal places).

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Answer:

Incomplete question

...

Answer:

3/5

Step-by-step explanation:

4/5-1/5= 3/5

Answer:

A ray is a a part of a line but a line segment is a line that connects two points

Step-by-step explanation:

A ray has one point at one end and an arrow that goes on forever, Though segments have 2 end points and do not go on forever.

"The angles formed by the lines that meet at each base are 90 degree angles and the distance between each base is the same."

was this your explanation? if so I think that it defines exactly the image shown on the quiz.

The six main criteria to define normality and abnormality include statistical infrequency, personal distress, others' distress, unexpected behavior, highly consistent/inconsistent behavior, and maladaptiveness/disability.

1. Abnormality as statistical infrequency: This criterion defines abnormality based on behaviors or characteristics that deviate significantly from the statistical norm.

2. Abnormality as personal distress: This criterion focuses on the individual's subjective experience of distress or discomfort. It considers behaviors or experiences that cause significant emotional or psychological distress to the person as abnormal.

For instance, someone experiencing intense anxiety or depression may be considered abnormal based on personal distress.

3. Abnormality as others' distress: This criterion takes into account the impact of behavior on others. It considers behaviors that cause distress, harm, or disruption to others as abnormal.

For example, someone engaging in violent or aggressive behavior that harms others may be considered abnormal based on the distress caused to others.

4. Abnormality as unexpected behavior: This criterion defines abnormality based on behaviors that are considered atypical or unexpected in a given context or situation.

For instance, if someone starts laughing uncontrollably during a sad event, their behavior may be considered abnormal due to its unexpected nature.

5. Abnormality as highly consistent/inconsistent behavior: This criterion involves comparing an individual's behavior to both their own typical behavior and the behavior of others. Consistent or inconsistent patterns of behavior may be considered abnormal.

For example, if a person consistently engages in risky and impulsive behavior, it may be seen as abnormal compared to their own usually cautious behavior or the behavior of others in similar situations.

6. It considers behaviors that are maladaptive, causing difficulties in personal, social, or occupational areas. For instance, someone experiencing severe social anxiety that prevents them from forming relationships or attending school or work may be considered abnormal due to the disability it causes.

The medical model and classification systems used in physical illnesses have both value and limitations when applied to psychological disorders. They provide a structured framework for understanding and diagnosing psychological disorders, allowing for standardized assessment and treatment. However, they can oversimplify the complexity of psychological experiences and may lead to overpathologization or stigmatization.

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