which quadratic equation has the roots 3 + i and 3 - i

Answer:

h. The data value 0.76 is a possible outlier.

b. The display is not symmetric and appears to be positively skewed.

d. The stem-and-leaf display shows that 0.45 is a good representative value for the data.

Step-by-step explanation:

STEM | LEAF

3 ___ | 4

3 ___ | 5, 6, 6, 7, 8

4 ___ | 0, 0, 0, 1, 1, 2, 2, 2, 2, 2, 3, 4

4 ___ | 5, 6, 6, 7, 8, 8, 9

5 ___ | 1, 4, 4

5 ___ | 5, 8

6 ___ | 1

6 ___ | 6, 6, 7, 8

7 ___

7 ___ | 6

The data point which seems a bit further out from the rest of the values : 0.76

0.45 is the median value and gives a reasonable representative value of the data.

Majority of the data accumulates on the left and this makes distribution positively skewed.

The area of triangle DEF is four times larger than the area of triangle ABC.

We have,

Right triangle ABC was dilated with a scale factor of 2.

When a triangle is dilated with a scale factor of 2, the resulting triangle is enlarged by a factor of 2 in each dimension.

Since area is a two-dimensional measure, it will be enlarged by a factor of the square of the scale factor.

In this case, the scale factor is 2, so the area of triangle DEF will be

=  2²

= 4 times larger than the area of triangle ABC.

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Solution :

If \(S_n\) is the total spending generated after n transactions, then \(a_n\) is the spending generated during the n-th transaction. Since the government spends D dollars, then \(a_1\) = D.

Then the second person will receive D dollars and spend \(D_c\) dollars. Therefore, \(a_2=D_c\). The next person will receive \(D_c\) dollars, which means they are spending \(a_3 = (D_c)c = Dc^2\) dollars. Therefore,

\(a_1 = D\)

\(a_2=D_c\)

\(a_3 = Dc^2\)

\(a_4 = (Dc^2)c= Dc^3\)

....

\(a_n=Dc^{n-1}\)

∴ \(S_n=a_1+a_2+a_3+....+a_n\)

  \(S_n = D+Dc+Dc^2+Dc^3+...+Dc^{n-1}\)

  \(S_n= D(1+c+c^2+...+c^{n-1})\)

  \(S-n=D . \frac{1-c^n}{1-c}\)

Answer:

7/9 becuase Jerry already have 2/3 of a cake and Mandy gave him a 5/6 so it's 7/9

Answer: 1 1/2

Step-by-step explanation:

2/3+5/6= 4/6+5/6

= 9/6

= 3/2 = 1 1/2

The average rate of change of the function over the interval is 1

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

f(x) = x

The interval is given as

From x = 4 to x = 9

The function is a linear function

This means that it has a constant average rate of change

So, we have

f(4) = 4

f(9) = 9

Next, we have

Rate = (9 - 4)/(9 - 4)

Evaluate

Rate = 1

Hence, the rate is 12

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Therefore, the interest portion of the seventh payment is:7,000 x (1 + r + r2 + r3 + r4 + r5 + r6) / r7 - 7,000.

We have the following payments and their corresponding times of payment:At the end of year 1: $1,000At the end of year 2: $2,000At the end of year 3: $3,000At the end of year 4: $4,000At the end of year 5: $5,000At the end of year 6: $6,000At the end of year 7: $7,000

At the end of year 8: $8,000At the end of year 9: $9,000At the end of year 10: $10,000The present value of these payments is:PMT x [(1 - (1 + r)-n) / r]where PMT is the payment, r is the interest rate per year, and n is the number of years till payment.

For the first payment (end of year 1), the present value is:1,000 x [(1 - (1 + r)-1) / r]which equals

1,000 x (1 - 1 / (1 + r)) / r = 1,000 x ((1 + r - 1) / r) = 1,000

For the second payment (end of year 2), the present value is:2,000 x [(1 - (1 + r)-2) / r]which equals 2,000 x (1 - 1 / (1 + r)2) / r = 2,000 x ((1 + r - 1 / (1 + r)2) / r) = 2,000 x (1 + r) / r2

For the seventh payment (end of year 7), the present value is:

7,000 x [(1 - (1 + r)-7) / r]

which equals

7,000 x (1 - 1 / (1 + r)7) / r = 7,000 x ((1 + r - 1 / (1 + r)7) / r) = 7,000 x (1 + r + r2 + r3 + r4 + r5 + r6) / r7

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Answer:

Hope this helps ;) don't forget to rate this answer !

Step-by-step explanation:

To find the dimensions of the rectangular box that require the least amount of material for its construction, we can follow these steps:

Determine the volume of the box. The volume of a rectangular box is given by the formula V = lwh, where l is the length, w is the width, and h is the height of the box.

Determine the surface area of the box. The surface area of a rectangular box is given by the formula SA = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height of the box.

Minimize the surface area while keeping the volume constant. To minimize the surface area, we can try different combinations of l, w, and h and choose the combination that results in the smallest surface area while still maintaining the required volume. This can be done by setting up and solving a system of equations.

Calculate the minimum material required for the construction of the box. Once we have found the dimensions that minimize the surface area, we can use the surface area formula to calculate the minimum amount of material required for the construction of the box.

Construct the box using the minimum amount of material. Once we have calculated the minimum amount of material required, we can use this information to construct the box using the least amount of material possible.

The system of equations is.

\(\begin{cases}\text{x}+\text{y}=60 \\15\text{x}+10\text{y}=800 \end{cases}\)

And the solutions are y = 50 and x = 10.

Let's define the two variables:

With the given information we can write two equations, then the system will be:

\(\begin{cases}\text{x}+\text{y}=60 \\15\text{x}+10\text{y}=800 \end{cases}\)

Now let's solve it.

We can isolate x on the first  to get:

\(\text{x} = 60 - \text{y}\)

Replace that in the other equation to get:

\(15\times(60 - \text{y}) + 10\text{y} = 800\)

\(-2\bold{y} = 900 - 800\)

\(-2\bold{y} = 100\)

\(\text{y} = \dfrac{100}{-2} = \bold{50}\)

Then \(\bold{x=10}\).

Therefore, the solutions are y = 50 and x = 10.

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Answer:

12

Step-by-step explanation:

To find perimeter, add the lengths of each side. 5 + 4 + 3 = 12

Answer:

12

Step-by-step explanation:

5+4+3

Answer:

30in²

Step-by-step explanation:

A=1/2(4)(5+10)

A=2x15

A=30in²

Answer:

\(a. \: 6x + 12 - 10 = 6x + 2 \\ 6x + 2 = 6x + 2 \\ infinite \: solutions \\ \\ b. \: 6x + 12 - 12 = 6x + 2 \\ 6x = 6x + 2 \\ no \: solutions \\ \\ c. \: 6x + 12 - 10 = 2x + 10 \\ 6x + 2 = 2x + 10 \\ 4x = 8 \\ x = 2 \\ one \: solution \\ \\ d. \: 4x - 2 = 4x - 8 + 6 \\ 4x - 2 = 4x - 2 \\ infinite \: solutions \\ e. \: 6x - 12 = - 12 + 6x \\ infinite \: solutions\)

Answer:

A) Infinitely Many Solutions

B) No Solution

C) One Solution (x = 2)

D) Infinitely Many Solutions

E) Infinitely Many Solutions

Step-by-step explanation:

A) 6(x+2)-10=6x+2

Simplify:

6 (x + 2) - 10 = 6x + 2

6x + 12 - 10 = 6x + 2

12 - 10 = 2

2 =2

Infinitely Many Solutions

B) 6(x+2)-12=6x+2

Simplify:

6 (x + 2) - 12 = 6x + 2

6x + 12 - 12 = 6x + 2

12 - 12 = 2

0 = 2

No Solution

C) 6(x+2)-10=2x+10

6 (x + 2) - 10 = 2x + 10

6x + 12 - 10 = 2x + 10

6x +2 = 2x + 10

4x = 8

x = 2

One Solution

D) 4x-2=4(x-2)+6

4x - 2 = 4 (x - 2) + 6

4x - 2 = 4x - 8 + 6

-2 = -8 + 6

-2 = -2

Infinitely Many Solutions

E) 2(3x-6)=6(-2+x)

2 (3x - 6) = 6 (-2 + x)

6x - 12 = -12 + 6x

6x = 6x

0 = 0

Infinitely Many Solutions

The calculated value of k on the line is 9

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

XZ is the perpendicular bisector of segment WY

This means that

WX = XY

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

3k - 4 = 2k + 5

So, we have

3k - 2k = 4 + 5

Evaluate

k = 9

Hence, the value of k is 9

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Answer:

Step-by-step explanation: First since the cookies are 36.44 dollars and the total spent is 102.44, use 102.44-36.44= 66 dollars

66/11=6 cupcake boxes

6 cupcake boxes + 1 cookie box = 7 boxes in total

The little lines through the 4 sides mean all the sides are the same length.

The area is side x side = 8 x 8 = 64 square cm.

Perimeter is the sum of the 4 sides = 8 + 8 + 8 +8 = 32 cm.

Answer:

Perimeter

P =a+a+a+a =4a

P = 4*8

P=32cm

Area

A = a*a = \(a^{2}\)

A = \(8^{2}\)

A = 64\(cm^{2}\)

To calculate the interest for 1/2 a month over a period of 8 years, we first need to calculate the total number of months in 8 years:

Total number of months = 8 years x 12 months/year = 96 months

Next, we can calculate the interest for half a month:

Interest = Principal x Rate x Time

Where:

- Principal = $90,900.00

- Rate = 8.25% (annual interest rate)

- Time = 0.5/12 years (half a month, expressed in years)

Rate needs to be converted to a monthly rate, so we divide it by 12:

Rate = 8.25% / 12 = 0.6875% (monthly interest rate)

Time needs to be expressed in years, so we divide it by 12:

Time = 0.5/12 years

Now we can calculate the interest:

Interest = $90,900.00 x 0.006875 x 0.0416667

Interest = $25.08 (rounded to the nearest cent)

Therefore, the interest for 1/2 a month on a principal of $90,900.00 with an annual interest rate of 8.25% over a period of 8 years is $25.08.

Answer:

The interest for 1/2 month is $312.47, and the total interest for 8 years is $30, 032.64

Step-by-step explanation:

Make a plan:

Draw the conclusion:

Hope this helps!

The correct transformation that describes why rectangles ABCD and A′B′C′D′ are similar is Rectangle ABCD was dilated by a scale factor of 5 to form rectangle A′B′C′D′.

Dilation is a transformation that changes the size of an object while maintaining its shape. In this case, the coordinates of rectangle ABCD were multiplied by a scale factor of 5 to obtain the coordinates of rectangle A′B′C′D′.

This means that each side length of rectangle ABCD was multiplied by 5 to get the corresponding side length of rectangle A′B′C′D′.

The reflection across the y-axis and the rotation of 90° counterclockwise would result in different shapes and orientations, not maintaining the similarity between the two rectangles.

The dilation by a scale factor of 15 or 1/5 would also change the proportions and not result in a similar rectangle.

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To find the amount of wet food Luck mixed with the dry food, we can use the fact that he put 5/4 cups into each of the 4 bowls. Therefore, he used a total of 5/4 x 4 = 5 cups of wet food.

Thus, Luck mixed 3 cups of dry food and 5 cups of wet food to prepare the dog's meal.

Answer:

$16.43.

Step-by-step explanation:

At the grocery store, you spent $485.72. With 2% cashback, you would get 485.72 * 0.02 = 9.7144 dollars worth of cashback.

At other places, you spend $671.28. With 1% cashback, you would get 671.28 * 0.01 = 6.7128 dollars worth of cashback.

9.7144 + 6.7128 = 16.4272, which is about $16.43 of cashback.

Hope this helps!

The amount of cashback that you earned will be $16.42.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

Suppose you earn 2% cash back at grocery stores and 1% on all other purchases. If you spent $485.72 at the grocery store and $671.28 on all other purchases.

The total cashback is calculated as,

⇒ 0.02 x $485.72 + 0.01 x $671.28

⇒ $9.71 + $6.71

⇒ $16.42

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Answer:

m∠R = 60°

explanation:

Let the angle be x,

x + x + 60° = 180°

2x = 180° - 60°

2x = 120°

x = 60°

Answer:

Step-by-step explanation:

Sum of interior angles in a triangle = 180degree

PQ=QR so triangle PQR is an isosceles triangle

The two base angles of an isosceles triangle are equal

So <R = <P

m<R + m<P + 60degree = 180degree

m<R = (180-60)/2 = 60degree

The results of operations between vectors are, respectively:

Case A: u + w = <- 3, - 1>

Case B: - 6 · v = <6, 6>

Case C: 3 · v - 6 · w = <- 21, - 15>

Case D: 4 · w + 3 · v - 5 · u = <39, 4>

Case E: |w - v| = √(4² + 3²) = 5

In this problem we must determine the operations between vectors, this can be done by following definitions:

Vector addition

v + u = (x, y) + (x', y') = (x + x', y + y')

Scalar multiplication

α · v = α · (x, y) = (α · x, α · y)

Norm of a vector

|u| = √(x² + y²)

Now we proceed to determine the result of each operation:

Case A:

u + w = <- 6, - 3> + <3, 2>

u + w = <- 3, - 1>

Case B:

- 6 · v = - 6 · <- 1, - 1>

- 6 · v = <6, 6>

Case C:

3 · v - 6 · w = 3 · <- 1, - 1> - 6 · <3, 2>

3 · v - 6 · w = <- 3, - 3> + <- 18, - 12>

3 · v - 6 · w = <- 21, - 15>

Case D:

4 · w + 3 · v - 5 · u = 4 · <3, - 2> + 3 · <- 1, - 1> - 5 · <- 6, - 3>

4 · w + 3 · v - 5 · u = <12, - 8> + <- 3, - 3> + <30, 15>

4 · w + 3 · v - 5 · u = <39, 4>

Case E:

|w - v| = |<3, 2> - <- 1, - 1>|

|w - v| = |<4, 3>|

|w - v| = √(4² + 3²) = 5

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The radius of the cylinder is 2.25 feet.

To find the radius of the cylinder, we can use the formula for the volume of a cylinder:

V = πr²h

Given that the volume V is 400 cubic feet and the height h is 25 feet, we can substitute these values into the formula and solve for the radius r.

400 = 3.14 r² x 25

Dividing both sides of the equation by (3.14 * 25) to isolate r^2, we have:

r² = 400 / (3.14 x 25)

r² ≈ 5.08

Taking the square root of both sides to solve for r, we get:

r ≈ √5.08

r ≈ 2.25

Therefore, the radius of the cylinder is 2.25 feet.

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Answer:

800ml

Step-by-step explanation:

solution A= 2% alcohol

solution B=7% alcohol

1200ml=1.2L

1200ml=1200cm^3

X= solution B

solution A + solution B=(1200+x)cm^3

% alcohol= amount of alcohol/total solution(AorB)×100

☆in 1200ml of solution A there's

0.02x1200

2x12

=24ml of alcohol (in 1200ml of solution A)

0.07x X

=0.07Xml of alcohol (in some ml of solution B)

(24+0.07X)ml of alcohol in = solution A and solution B

solution A + solution B= 1200+X

0.04 (1200+X)=24+0.07X

48+0.04X=24+0.07X

48-24=0.07X-0.04X

24=0.03X

X=800ml

Answer:

The correct answer is $0

Step-by-step explanation:

The taxable income (line 6) on the 1040EZ form is:  

Taxable Income = -$3,650.

If the result is negative, it means the taxpayer's income is below the standard deduction threshold, and her taxable income would be $0.

Here,

To calculate the taxable income (line 6) on the 1040EZ form, we need to subtract the standard deduction from the adjusted gross income (AGI).

For the tax year 2021 (the last available information before my knowledge cutoff in September 2021), the standard deduction for a taxpayer filing as Single is $12,550.

Given that the taxpayer's adjusted gross income (AGI) is $8,900, we calculate the taxable income as follows:

Taxable Income = AGI - Standard Deduction

Taxable Income = $8,900 - $12,550

Taxable Income = -$3,650

If the result is negative, it means the taxpayer's income is below the standard deduction threshold, and her taxable income would be $0.

The taxpayer would not owe any federal income tax in this case.

However, she may still want to file her tax return to claim any potential tax credits or receive a refund if she had taxes withheld from her paycheck during the year.

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Step-by-step explanation:

17389+23589=2469

56793+4569=15992

becoms54566+2368x

Answer:

its B (-1,170 , -23,400) and (170, 3,400)

Step-by-step explanation:

the next one is 170 purses

The mean decreases from the original value.  The median stays the same.

(a) To find the new mean, we need to add up all the numbers in the list (except for the 523 that changed to 424) and divide by the number of schools (which is still 9). So the new mean is:

(164 + 225 + 227 + 250 + 261 + 268 + 277 + 379 + 424) / 9 = 272.89

The mean decreases from the original value.

(b) To find the new median, we need to arrange the numbers in order again:

164, 225, 227, 250, 261, 268, 277, 379, 424

The median is the middle value, which is still 261. So the median stays the same.

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Basically let's represent the number of girls with x.

There are 6 more boys than girls, so x+6

Let's sum it all up

x+x+6=40

Collect like terms;

2x+6=40

2x=40-6

2x= 34

Divide both sides by 2

x=17

17+6=23

Therefore there are 17 girls in the class and 23 boys.

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Answer:

159

Step-by-step explanation:

10 with a exponent of 2 is 100

3+5 with a exponent of 2 is 64

100+64=164

164 - 5 = 159

Answer:

6x = 9

Step-by-step explanation:

4x-5y  = 12

2x+5y  = -3

Add the equations together

4x-5y  = 12

2x+5y  = -3

-------------------

6x + 0y = 9

6x = 9

Answer:

B. 6x = 9

Step-by-step explanation:

4x - 5y = 12

+ 2x + 5y = -3

____________

6x + 0 = 9

Hence, option B. 6x = 9 is the correct answer.