Solving systems by eliminations; finding the coeficients
please write all the problems down on paper, 10 points for each problem, and Brainliest

If one zero of the polynomial 3x^2 + 8x + k is  the reciprocal of the

other, then k = 3 by applying product of roots formula.

The quadratic polynomial is 3x^2 + 8x + k.

Let the roots of  3x^2 + 8x + k be m and n where m and n are reciprocal of each other. Therefore, n = 1/m

Thus, the product of roots is = m*n = m*(1/m) = 1 ____(1)

The general equation of a quadratic equation can be written as,

ax^2 + bx + c = 0

where a and b are coefficients of x^2 and x respectively and c is a constant term.

From product of roots formula we know that,

Product of roots =constant term/ coefficient of x^2 = c/a

Therefore, for polynomial is 3x^2 + 8x + k we get,

Product of roots = k/3 ____(2)

From equating equation (1) and (2) we get,

k/3 = 1

⇒ k = 3

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The given question is incomplete, the complete question is

"If one zero of the polynomial 3x^2+8x+k is the reciprocal of the other, then find the value of k."

To discover the probability that the ceramics piece is painted, we basically separate the number of painted pieces by the whole number of pieces: P(painted) = 183/837 ≈ 0.2185

b. To discover the likelihood that the painted ceramics piece is painted in a curvilinear enhancement, we utilize Bayes' hypothesis:

P(curvilinear | painted) = P(painted | curvilinear) * P(curvilinear) / P(painted)

We are given that there are 183 painted pieces, of which 14 are painted in a curvilinear enrichment. In this manner,

P(painted | curvilinear) = 14/183 ≈ 0.0765

We are moreover given that there are 837 pieces in add up, of which 183 are painted.

P(painted) = 183/837 ≈ 0.2185, we ought to discover the likelihood that a painted piece is painted in a curvilinear enrichment, which is given as 14 out of 183 painted pieces. P(curvilinear) = 14/183 ≈ 0.0765

P(curvilinear | painted) = (0.0765) * (0.0765) / (0.2185) ≈ 0.0266

thus, given that the pottery piece is painted, the likelihood that it is painted in a curvilinear enhancement is roughly 0.0266, or 2.66%.

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Answer:

Okay, let's solve this step-by-step:

   There is a spinner with 14 equal areas, numbered 1 through 14

   We want to find the probability that the result is a multiple of 3 or a multiple of 4

   There are 14 possible outcomes (numbers 1 through 14) when the spinner is spun.

   Of these 14 numbers:

   4 are multiples of 3: 3, 6, 9, 12

   4 are multiples of 4: 4, 8, 12, 16

   However, 12 is also a multiple of both 3 and 4, so we have counted it twice.

   We need to subtract 1 from each to account for this:

   Multiples of 3: 3

   Multiples of 4: 4

   So there are 3 possible multiples of 3 and 3 possible multiples of 4.

   In total, there are 3 + 3 = 6 possible multiples of 3 or 4.

   To calculate probability:

   Probability = (Number of favorable outcomes) / (Total possible outcomes)

   = 6 / 14

   = 3/7

   Converting to a percent: 3/7 = 42.9%

   Rounded to the nearest whole percent: 43%

Therefore, the probability that the result is a multiple of 3 or a multiple of 4 is 43%.

Step-by-step explanation:

The height of the cylindrical water tank is 4.6 feet. Therefore, the answer is A.

The cylindrical water tank holds 1,100 liquid gallons and has a radius of 3.2 feet.

Therefore, the height of the tank can be calculated as follows:

7.48 liquid gallons = 1 ft³

1100 liquid gallons = ?

cross multiply

volume of the tank = 1100 / 7.48 = 147.058823529 ft³

Therefore, let's find the volume of the cylindrical tank.

volume of the cylindrical tank = πr²h

where

Therefore,

r = 3.2 feet

h = ?

The volume of the cylindrical tank in feet cube is 147.058823529 ft³

Let's find the height, h

volume of the cylindrical tank = 3.14 × 3.2² × h

147.058823529 = 3.14 × 10.24 × h

32.1536h = 147.058823529

divide both sides by 32.1536

h = 147.058823529 / 32.1536

h = 4.57363405653

Therefore,

height of the water tank = 4.6 feet

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The quarterly dividend payment per share based on the question above will be: $0.02.

The close price for the week will be: $5.45.

For one to find the closing price for the week, we have to divide the total cost of the shares by using the number of shares that was bought so it will be:

Close price = Total cost / Number of shares

                    = $2,790.40 / 512

                    = $5.45

To know the quarterly dividend payment per share, we have to calculate the annual dividend payment per share before we can get it so it will be:

Annual dividend per share = Total annual dividend / Number of shares

                                              = $40.96 / 512

                                                = $0.08

From the question, the dividend was paid quarterly, we then divide the annual dividend per share by 4 so as to get the quarterly dividend per share:

Quarterly dividend per share = Annual dividend per share / 4

                                                  = $0.08 / 4

                                                   = $0.02

Hence the quarterly dividend payment per share will be: $0.02.

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See text below

Ignoring commission, 512 shares of Targa Resources (TRGP) were purchased for $2,790.40 at the clos for the week. Find the close price for the week. Then, find the quarterly dividend payment per share if the annual dividend amount paid was $40.96. (7pts)

EARNINGS

52-WEEK

TICK

VOL.

WEEK'S

LATEST

THIS NEXT DIV

High Low

Name

Sym.

100s

Yld.

P/E Last Chg.

Year

Year

Year

Amt

8.50

3.20

Targa Resources

TRGP

412574 1.8

PO

dd

+0.41

0.25

0.18

0.12

Answer: It will cost $2.88 to frame Jayla's math certificate with the fancy frame.

Step-by-step explanation: To calculate the cost of framing Jayla's math certificate, we need to determine the perimeter of the certificate, which is the sum of the lengths of all four sides.

Perimeter = 2 × (height + width)

Perimeter = 2 × (19 + 29)

Perimeter = 2 × 48

Perimeter = 96 centimeters

So the perimeter of the certificate is 96 centimeters.

To find the cost of framing, we need to multiply the perimeter by the cost per centimeter of the fancy frame:

Cost = perimeter × cost per centimeter

Cost = 96 × $0.03

Cost = $2.88

Therefore, it will cost $2.88 to frame Jayla's math certificate with the fancy frame.

Answer: 0.5

Step-by-step explanation:

1/2% is equal to 50 out of 100, or 50/100.

So you turn that into a decimal (fifty one hundredths).

0.50

You can get rid of the 0 at the end.

0.5

Hope this helps!!! :)

(a) The probability that both missiles will hit the target is 1/10.

(b) The probability that at least one missile will hit the target is 11/20.

To find the probability that both missiles will hit, we multiply the individual probabilities of each missile hitting

P(both missiles hit) = P(first missile hits) × P(second missile hits)

P(both missiles hit) = (1/4) × (2/5)

P(both missiles hit) = 2/20

P(both missiles hit) = 1/10

So the probability that both missiles will hit the target is 1/10.

(b) To find the probability that at least one missile will hit, we need to find the probability that both missiles miss and then subtract that from 1 (since the probability of either missile hitting is the complement of both missiles missing)

P(at least one missile hits) = 1 - P(both missiles miss)

P(at least one missile hits) = 1 - P(first missile misses) × P(second missile misses)

P(at least one missile hits) = 1 - (3/4) × (3/5)

P(at least one missile hits) = 1 - 9/20

P(at least one missile hits) = 11/20

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The line of reflection must be the line halfway between the x-coordinates of the corresponding vertices of each polygon. This line is x=4.

So, the line of reflection is x=4.

A line of reflection is a line used in mathematics that functions like a mirror, reflecting all points on one side of the line onto the other side so that each point is equally distant from the line as its reflected point on the other side. It is also known as the mirror line or the axis of reflection.

To determine the line of reflection that maps polygon ABCDE to polygon A' B' C' D' E', we need to look for a line that is equidistant from each corresponding pair of points.

Reflection across the x-axis or y-axis will not work because the corresponding vertices of the two polygons have different y-coordinates or x-coordinates, respectively.

Reflection across x=5 or y=6 will also not work because the line is not equidistant from each corresponding pair of points.

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The expression for the area of the triangle is given as follows:

A = 1.5x^4 + x³ - 0.5x².

The area of a rectangle of base b and height h is given by half the multiplication of dimensions, as follows:

A = 0.5bh.

The dimensions for this problem are given as follows:

Hence the area of the triangle is given as follows:

A = 0.5(3x² - x)(x² + x)

A = 0.5(3x^4 + 3x³ - x³ - x²)

A = 0.5(3x^4 + 2x³ - x²)

A = 1.5x^4 + x³ - 0.5x².

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Answer:

Step-by-step explanation:

18

Answer:

[tex]y = {1.5}^{x} [/tex]

[tex] ln(y) = ln( {1.5}^{x} ) [/tex]

[tex] ln(y) = x ln(1.5) [/tex]

[tex]x = \frac{ ln(y) }{ ln(3) - ln(2) } [/tex]

[tex]y = \frac{ ln(x) }{ ln(3) - ln(2) } [/tex]

The evaluated solution for the  given  question comprises of sample point of a that are  {HHT, HTH, THH, HHHT, HHTH, HTHH, THHH} , the event probability is 0.875 and the probability of implementing a, b is 3/4  below under the condition of a fair coin is tossed three times, and the events a and b are defined.

a)  Points sample  for event a: {HHT, HTH, THH, HHHT, HHTH, HTHH, THHH}
Points  sample  for event b: {HTT, THT, TTH, HHH}
Points  sample  for event a b: {HTT, THT, TTH, HHH, HHT, HTH, THH}
  Points  sample for event ac: {TTT}
  Points  sample for event a c: {TTT, HHHH}

b)  Event a probability= 7/8 = 0.875
  Event b probability= 1/2 = 0.5
  Event ab probability = 3/8 = 0.375
  Event ac probability   = 1/8 = 0.125
  Event a c probability  = 1/16 + 1/8 = 0.1875

c) Probability of a b implementing additive rule
    P(a b) = P(a) + P(b) - P(a ∩ b)
     P(a ∩ b) = P(a) + P(b) - P(a b)
     P(a ∩ b) = (7/8) + (1/2) - (3/8)
     P(a ∩ b) = 9/8 - 3/8
     P(a ∩ b) = 6/8
     P(a ∩ b) = 3/4

d)  Hence, events a and b are not mutually exclusive due to the lack of chances of having common sample points {HHH}.


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The length of the square garden is s = ( 3x - 4 ) feet

Given data ,

Let the length of the square garden be s

Now , The area of a square is given by the formula A = s², where s is the length of one side of the square.

We are given that the area of the garden is:

A = 9x² - 24x + 16

To find the length of the garden, we need to take the square root of the area:

s = √(A)

Substituting the given expression for A, we get:

s = √(9x² - 24x + 16)

We can simplify this expression by factoring the quadratic under the square root sign:

s = √[(3x - 4)(3x - 4)]

Using the property that the square root of a product is equal to the product of the square roots, we can simplify further:

s = (3x - 4)

Hence , the length of the garden is 3x - 4 feet

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Yes, the sample size of 4,706 is large enough to justify the use of the z formula.

To determine whether the sample size is large enough to justify the use of the z formula, we need to check whether the sample size is sufficiently large to meet the central limit theorem (CLT) conditions. The CLT states that the distribution of the sample mean of a sufficiently large sample size from any population, regardless of the distribution of the population, will be approximately normal.

One of the conditions for the CLT is that the sample size is large enough. There is no hard and fast rule for determining what is considered a "large" sample size, but a commonly used rule of thumb is that the sample size should be at least 30.

In this case, the sample size is 4,706, which is much larger than 30. Therefore, we can conclude that the sample size is large enough to justify the use of the z formula.

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The ratio of the area of the triangle to the area of the trapezoid is 3:8.

Area of the rectangle will be:

= 14 cm x 12 cm

= 168 cm²

Height of the triangle

= 14 cm - 8 cm

= 6 cm

Area of the triangle will be:

= 1/2 x 12 cm x 6 cm

= 36 cm²

Area of the trapezoid will be:

= 1/2 x (base1 + base2) x height

= 1/2 x (12 cm + 12 cm) x 8 cm

= 96 cm²

Ratio will be:

Area of the triangle / Area of the trapezoid

= 36 cm² / 96 cm²

= 3/8

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Eric will need at least 6 cans of finish to cover the entire outside of the box with three coats.

To find the minimum number of cans of finish needed for the job, we first need to calculate the total surface area of the box that will be covered with the finish.

The box has a length of 42 inches, a depth of 24 inches, and a height of 20 inches. To find the total surface area, we can use the formula for the surface area of a rectangular prism:

Surface area = 2(length x width + width x height + height x length)

Surface area = 2(42 x 24 + 24 x 20 + 20 x 42)

Surface area = 2(1008 + 480 + 840)

Surface area = 6656 square inches

Since the finish will be applied in three coats, we need to multiply the total surface area by three to get the total area of finish needed:

Total area of finish = 3 x 6656 square inches

Total area of finish = 19968 square inches

Now we can convert the total area of finish from square inches to square feet by dividing by 144:

Total area of finish = 19968 square inches / 144 = 138.67 square feet

Since each can of finish covers about 27.5 square feet, we can calculate the minimum number of cans needed by dividing the total area of finish by the coverage of each can:

Minimum number of cans = 138.67 square feet / 27.5 square feet per can

Minimum number of cans = 5.04 cans

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The probability of rolling a 5 when playing a game with a die is an example of empirical probability.

Empirical probability is determined through observation and experimentation, by counting the number of times an event occurs and dividing it by the total number of trials. In this case, the children have likely rolled the die multiple times and recorded the number of times a 5 was rolled.

They then calculated the probability of rolling a 5 by dividing the number of times a 5 was rolled by the total number of rolls. Empirical probability is commonly used in fields such as science and statistics, where data is gathered through experimentation and observation.

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Answer:

[tex] {21}^{2} + {x}^{2} = {35}^{2} [/tex]

[tex] {x}^{2} =784[/tex]

[tex]x = 28[/tex]

[tex] {y}^{2} + {32}^{2} = {35}^{2} [/tex]

[tex] {y}^{2} = 201[/tex]

[tex]y = \sqrt{201} = 14.18[/tex]

The ladder will reach about 14.2 feet up the side of the house.

Using a system of equations, the number of bracelets made and the number of necklaces made are:

A system of equations is two or more equations that can be solved simultaneously or at the same time.

Simultaneous equations can be solved concurrently.

Quantity of gold in each bracelet = 6 grams

Quantity of gold in each necklace = 24 grams

The total number of bracelets and necklaces made = 16

The total quantity of gold used in making the 16 pieces = 258 grams

Let the number of bracelets made = x

Let the number of necklaces made = y

x + y = 16 ...Equation 1

6x + 24y = 258 ...Equation 2

Multiply Equation 1 by 6:

6x + 6y = 96 ...Equation 3

Subtract Equation 3 from Equation 2:

6x + 24y = 258

-

6x + 6y = 96

18y = 162

y = 9

x = 7 (16 - 9)

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Answer:

$14,766.00

Step-by-step explanation:

Interest = principle x rate x time

I = 13800 (.14)(.5)

I = 966

Total:

Principle plus interest

13800 + 966 = 14,766

Helping in the name of Jesus.

Answer:

Let's first calculate the number of students who passed the test and completed the assignment. We know that 15 students passed the test and 6 students who failed the test and did not complete the assignment. Therefore, there are 25 - 15 - 6 = 4 students who failed the test but completed the assignment.

Now we can calculate the probability that a student who completed the homework passed the test by dividing the number of students who passed the test and completed the assignment by the total number of students who completed the assignment.

The number of students who passed the test and completed the assignment is 15 - 6 = 9. The total number of students who completed the assignment is 16 - 6 = 10. Therefore, the probability that a student who completed the homework passed the test is 9/10 or 0.9.

Step-by-step explanation:

The inverse of the graphs are added as an attachment

To plot the inverse of a graph, you can follow these steps:

See attachment for the graphs

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The probability that the brand W pencils will have a higher mean number of turns needed to sharpen than brand H is approximately 0.0005.

Let X be the number of turns needed to sharpen a brand W pencil and Y be the number of turns needed to sharpen a brand H pencil. Then, we are interested in finding P(X > Y), the probability that the mean number of turns needed to sharpen a brand W pencil is higher than the mean number of turns needed to sharpen a brand H pencil.

The difference between the means of X and Y is 4.6 - 5.2 = -0.6. The standard error of the difference between the means can be calculated as:

SE = sqrt[(0.67^2/30) + (0.33^2/30)] = 0.178

The test statistic is:

Z = (-0.6 - 0) / 0.178 = -3.37

Using a standard normal distribution table, the probability of getting a Z-score less than -3.37 is approximately 0.0005.

Therefore, the probability that the brand W pencils will have a higher mean number of turns needed to sharpen than brand H is approximately 0.0005.

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Dominik used 7/8 cup of sugar for a bread recipe. he used 3/4 cup of sugar for a muffin recipe.

To find out how much sugar Dominik used in total for both recipes, we need to add the amounts of sugar he used in each recipe.

7/8 cup + 3/4 cup

To add these two fractions, we need to find a common denominator. In this case, the smallest common denominator is 8, which is the same as the denominator of the first fraction.

7/8 cup + 3/4 cup = (7/8) cup + (6/8) cup

Now we can add the two numerators

(7/8) cup + (6/8) cup = 13/8 cup
Hence, Dominik used 13/8 cups of sugar for both recipes combined.

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Mrs. Brown should consider the box and whisker plot as well as the stem and leaf plot to represent the data and determine the 5-number summary.

Mrs. Brown should consider using a box plot (also called a box and whisker plot) and/or a modified box plot.

A box plot is a useful graphical representation because it shows the overall shape of the data and displays the 5-number summary, which includes the minimum value, first quartile (Q1), median (second quartile, Q2), third quartile (Q3), and the maximum value. A modified box plot also provides this information and additionally identifies any potential outliers in the data.

Therefore, Mrs. Brown should consider the box and whisker plot as well as the stem and leaf plot to represent the data and determine the 5-number summary.

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Correct question is "Mrs. Brown records the rainfall in Seattle, Washington during each month of 2021. (8.75, 4.68, 2.61, 1.03, 1.12, 1.91, 0.00, 0.11, 3.02, 5.76, 10.62, 4.38} Mrs. Brown wants to use a graphical representation that will allow her students to see the overall shape of the data and provide enough information to determine the 5-number summary then find which representations should Mrs. Brown consider? "

The tank used 3,528 square inches of glass to make, assuming that there is no overlap or waste in the glass cutting process.

The tank has four vertical rectangular sides, a bottom, and no top. Since there is no top, we do not need to include the area of any glass for the top of the tank.

The area of each rectangular side is given by multiplying the height by the width. The area of the bottom is given by multiplying the length by the width. Therefore, the total area of glass used to make the tank is:

Area = 2(height x width) + 2(height x length) + (length x width)

Substituting the given values, we get:

Area = 2(23 x 18) + 2(23 x 12) + (18 x 12)

Area = 1,656 + 1,656 + 216

Area = 3,528

Therefore, the tank used 3,528 square inches of glass to make, assuming that there is no overlap or waste in the glass-cutting process.

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Using the binomial probability formula, we get a probability of approximately 1 or 100%.

This problem involves a binomial probability distribution, where we are interested in the number of successes (colleges with distance learning courses) in a fixed number of trials (picking 13 institutions), where each trial has a constant probability of success (the probability that a college offers distance learning courses).

We can use the binomial probability formula

P(X = k) = C(n, k) * p^k * (1-p)^(n-k)

where X is the number of successes, k is the number of successes we are interested in, n is the total number of trials, p is the probability of success, and C(n, k) is the binomial coefficient.

Substituting the given values, we get

P(X = k) = C(13, k) * 0.96^k * 0.04^(13-k)

To find the probability that at least one college offers distance learning courses, we can find the probability that none of the 13 colleges offer distance learning courses and subtract it from 1

P(X ≥ 1) = 1 - P(X = 0)

P(X = 0) = C(13, 0) * 0.96^0 * 0.04^13 = 0.000000005096

P(X ≥ 1) = 1 - 0.000000005096 ≈ 1

Therefore, the probability that at least one college out of 13 offers distance learning courses is approximately 1 or 100%.

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Answer:

Step-by-step explanation:

100000³ = 100000 × 100000 × 100000

100000 × 100000 × 100000 =

10000000000 × 100000 =

1e+15 or 1.000.000.000.000.000

Answer:

20 tables

Step-by-step explanation:

12a is the small tables and 8b is the 8 large tables so they are adding it together and getting 20 tables.