Simplify (4 − 8i)(2 − 7i).

8 + 56i2

−48 − 44i

64 − 44i

8 − 44i + 56i2

Answer:

Step-by-step explanation:

Some foundation pieces:

Floor is 30 ft^2

tiles are 3w

Equation:

30=(3w)*10

3=3w

1=w

Now that you know that w has to 1 you can write the formula 30=(3w)×10

Answer:

No

Step-by-step explanation:

If its a square garden then that means all 4 sides are 12 meters so 12 times 4 equals 48. This meaning you need 48 meters of wire to wire the entire fence garden.

Answer:

no

Step-by-step explanation:

if the garden is to be fence on all 4 sides then the total length of wire needed is 48 meters as 12*4=48 so since 19<48 it will not be enough  

Answer:

Step-by-step explanation:

If the ratio is soda to juice, set up the proportion like this:

[tex]\frac{s}{j}[/tex]

and everything related to soda goes on top and everything related to fruit juice goes on the bottom.  You just want the ratio, so it is best stated as follows:

[tex]\frac{soda}{juice}[/tex]

just to be clear on what s and j mean!

You could use this proportion to solve problems with one unknown.

Answer:

108

Step-by-step explanation:

36÷4= 9

9 is the unit rate

5×9=45

Natasha has 45 sweets

3×9= 27

Richard has 27 sweets

36+ 45+ 27= 108

All together they have 108 sweets

In total, there are 108 sweets. This answer is derived by finding the value of one part of the ratio and then multiplying this by the sum of all parts of the ratio.

The question is about the distribution of sweets among Sarah, Natasha and Richard in the ratio 4:5:3. You have been given that Sarah, represented by the first term of the ratio, gets 36 sweets. To find how many sweets there are altogether, we first need to determine the value of one part of the ratio.

In this case, if 4 parts are equivalent to 36 sweets, then one part is equivalent to 36 divided by 4 which equals 9 sweets.

Now, to find the total sweets, we need to sum all parts of the ratio which is 4 parts for Sarah, 5 parts for Natasha and 3 parts for Richard. Total parts = 4 + 5 + 3 = 12. This total is then multiplied by the value of one part of the ratio. Here, total sweets = 12 parts * 9 sweets = 108 sweets.

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Answer:

Step-by-step explanation:

According to southeastern.edu,

The first statement is true for the sample "those surveyed" the population but not necessarily the entire population. Statistic.

The second statement implies that the soccer team is the population. All members of the population are surveyed. Parameter.

The third statement states that a sample of 100 of all swimming teams are surveyed. Statistic.

The fourth statement implies that the population is all members of the golf team, and that all members of the population are surveyed. Parameter.

Answer:

70 points

Step-by-step explanation:

Let n represent Noah's score, m as Maya's score, and c as Claire's score.

n=20

m=30

c=?

Let's try make an equation for this problem. The mean score for the three of them is 40, so the following equation is possible:

n+m+c/3=40

Now replace the variable with their values and continue to simplify.

20+30+c/3=40

Multiply both sides by 3.

20+30+c=120

Add 20 and 30 together.

50+c=120

Subtract 50 from 120 to find c.

c=70

Claire's score is 70 points.

Final answer:

To find Claire's score, calculate the total points based on the mean score and then subtract the scores of Noah and Maya. This calculation reveals that Claire's score was 70 points.

Explanation:

The question asks for the score of Claire based on the mean score of Noah, Maya, and Claire combined. Noah scored 20 points, Maya scored 30 points, and the mean score for all three players was 40 points.

To find Claire's score, we first calculate the total points scored by all three. The mean score is the total points divided by the number of scores, which in this case is 3. Therefore, we multiply the mean score (40 points) by 3 to get the total points.

Mean score × number of players = Total points

40 × 3 = 120 points

Next, we subtract Noah's and Maya's scores from the total to find Claire's score.

Total points - Noah's score - Maya's score = Claire's score

120 points - 20 points - 30 points = 70 points

Therefore, Claire's score was 70 points.

Answer:

4(a + b)^2

p = 6/5 or 1.2

Step-by-step explanation:

Question One

z = a^2 + b^2

y = ab

4z = 4*a^2 + 4*b^2

8y = 8*ab

=================

4z + 8y = 4a^2 + 8ab + 4b^2

4z + 8y = 4(a^2 + 2ab + b^2)

4z + 8y = 4(a + b)^2

Question Two

2(p + 1) + 8(p - 1) = 5p

2p + 2 + 8p - 8 = 5p

2p + 8p + 2 - 8 = 5p

10*p - 6 = 5p

10*p = 5p + 6

10p - 5p = 6

5p = 6

p = 6/5 or 1.2

The sides of the box are 12in by 12in by 30in.

The interior diagonal =[12^2+12^2+30^2]0.5

=[144+144+900]^0.5

=1188^0.5

The final answer is 34.47in.

My deepest apology if this is not what you meant.

= 34.47in.

Answer:

34.47

Step-by-step explanation:

Row A:   x = 3

y = 2x - 3

y = 2(3) - 3 = 3      This is correct

Row B: x = 5

y = 2x - 3

y = 2(5) - 3 = 7        This is correct

Row C: x = 7

y = 2x - 3

y = 2(7) - 3 = 11      this is correct

Row D: x = 10

y = 2x - 3

y = 2(10) - 3 = 17  THIS IS INCORRECT, SO ROW D

Answer:

Road D

Step-by-step explanation:

5 out of 20 people said that they like the new packaging of Toasty Toasts.

Step-by-step explanation:

According to the graph, the probability of 2 successes is 0.36, which rounds to 0.4.

The number of success is X = 2, the P(success) = 0.4 according to the given histogram.

It's a field of mathematics that studies the probability of a random event occurring. From 0 to 1, the value is expressed.

Number of successes is represented by X (given)

X = 2

The number of successes are plotted on the X - axis of the histogram

So according to the graph , P(success at X = 2) = 0.36

Rounding off the probability to 0.4

Hence, the P(success at X = 2) = 0.4 according to the histogram.

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Answer:

[tex]\boxed{\text{L = 90 in}^{2};\text{ S = 115 in}^{2}}[/tex]

Step-by-step explanation:

Data:

s = 5 in

l = 9 in

1. Lateral surface area

The general formula for the lateral surface area L of a regular pyramid is

L =½pl

where p represents the perimeter of the base and l the slant height.

The base is a square, so

p = 4 × 5 = 20 in

L = ½pl = ½ × 20 × 9 = [tex]\boxed{\text{90 in}^{2}}[/tex]

2. Total surface area

Total surface area = lateral surface area + area of base

S = L + B

B = b² = 5² = 25 in²

S = 90 + 25 = [tex]\boxed{\text{115 in}^{2}}[/tex]

the answer of this question is 8 bro..........................................................

Answer: [tex]y-\frac{1}{2}=-(x+\frac{1}{2})[/tex]

Step-by-step explanation:

The point-slope form of the equation of the line is:

[tex]y-y_1=m(x-x_1)[/tex]

Where "m" is the slope of the line and [tex](x_1,y_1)[/tex] is a point of the line.

You know the value of the slope and you also know a point of the line, then you need to substitute values into [tex]y-y_1=m(x-x_1)[/tex].

Therefore, you get that the equation of this line in  point-slope form is:

[tex]y-\frac{1}{2}=-1(x-(-\frac{1}{2})\\\\y-\frac{1}{2}=-(x+\frac{1}{2})[/tex]

Answer:

y = -x

Step-by-step explanation:

Given in the question,

co-ordinate(-1/2 , 1/2)

gradient of the line = -1

Standard equation form of a straight line

here y1 = 1/2

        x1 = -1/2

        m = -1

Plug values in the equation

y - 1/2 = -1(x + 1/2)

y -1/2 = -x - 1/2

y = -x

1/42

First, find the probability of Willie winning the grand prize. He has 1 ticket out of the 7 total tickets, so the probability is 1/7.

Now, find the probability of Emily winning the second prize. After the grand prize winner has been announced, there are only 6 tickets left. Emily has 1, so the probability is 1/6.

Finally, multiply the two probabilities together to find the probability that they will both happen together. To multiply fractions, multiply the numerators together and multiply the denominators together. This leaves us with (1 * 1) / (7 * 6), which is easy to simplify to 1/42, which is the final probability.

Answer:

1/42

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

Since AP and BP are tangents from the same point, they are equal. So 2x+12=4x-8. So solving for x, we get 2x=20. So x=10. Plugging that in, we get 20+12=32. So the answer is 32.

Answer:

50x.2 is the correct expression. :)

Step-by-step explanation:

50x.2 =10

So you would get a $10 discount off of a $50 video game.

Hope this helps! If you don't mind, please mark as brainliest! Thx :)

Answer:

0.80($50)

Step-by-step explanation:

1.00 times the $50 cost is the initial price of the video.

(1.00 - 0.20) times $50 is the discounted price.

0.80($50) is the desired expression.

Next time, please be sure to share the answer choices.  Thanks.

Answer:

$59.4

Step-by-step explanation:

The original price of the shoes was £60 before the 10% discount was applied, resulting in a final price of £54.

1. First, let's denote the original price of the shoes as [tex]\( x \)[/tex] pounds.

2. Since Nathalie bought the shoes during the sale, she received a 10% discount.

3. Therefore, she paid 90% of the original price after the discount. This can be represented as [tex]\( 0.90x \)[/tex].

4. According to the given information, Nathalie paid £54 for the shoes. So, we can set up the equation:

[tex]\[ 0.90x = 54 \][/tex]

5. To find the original price [tex](\( x \))[/tex], we need to isolate it by dividing both sides of the equation by 0.90:

[tex]\[ x = \frac{54}{0.90} \][/tex]

6. Solving the equation gives us:

[tex]\[ x = 60 \][/tex]

7. Hence, the original price of the shoes was £60 before the 10% discount was applied.

The complete question is here:

In a sale, normal prices are reduced by 10% Nathalie bought a pair of shoes in the sale for £54. What was the original price of the shoes?

Answer:

it's A&B

Step-by-step explanation:

Answer:

[tex]\large \boxed{\mathrm{\bold{A.} } \ \frac{2}{x^4-y^4} \cdot \frac{1}{x^4 +y^4}} \\\\\\ \large \boxed{\mathrm{\bold{B.} } \ \frac{2}{(x^4)^2 -(y^4)^2 } }[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{2}{x^8-y^8 }[/tex]

Factor the denominator.

[tex]\displaystyle \frac{2}{(x^4)^2 -(y^4)^2 }[/tex]

[tex]\displaystyle \frac{2}{(x^4-y^4)^2 }[/tex]

[tex]\displaystyle \frac{2}{(x^4-y^4)(x^4 +y^4) }[/tex]

Split the fraction into two fractions.

[tex]\displaystyle \frac{2}{x^4-y^4} \cdot \frac{1}{x^4 +y^4}[/tex]

[tex] {2}x^{2} + 8 {y}^{2} = 16 \\ \\ 1. \: {2x}^{2} = - 8 {y}^{2} + 16 \\ 2. \: {x}^{2} = - 4y^{2} + 8 \\ 3. \: x = \sqrt{ - 4y^{2} + 8} \\ x = - \sqrt{ - 4y^{2} + 8 } \\ \\ answer \\ x = \sqrt{ - 4y^{2} + 8 } \\ x = - \sqrt{ - 4y^{2} + 8} [/tex]

Answer:

Step-by-step explanation:

2x² + 8y² = 16

divide both sides of equation by the constant

2x²/16 + 8y²/16 = 16/16

x²/8 + y²/2 = 1

x² has a larger denominator than y², so the ellipse is horizontal.

General equation for a horizontal ellipse:

  (x-h)²/a² + (y-k)²/b² = 1

with

  a² ≥ b²

  center (h,k)

  vertices (h±a, k)

  co-vertices (h, k±b)

  foci (h±c, k), c² = a²-b²

Plug in your equation, x²/8 + y²/2 = 1.

(x-0)²/(2√2)² + (y-0)²/(√2)² = 1

h = k = 0

a = 2√2

b = √2

c² = a²-b² = 6

c = √6

center (0,0)

vertices (0±2√2,0) = (-2√2, 0) and (2√2, 0)

co-vertices (0, 0±√2) = (0, -√2) and (0, √2)

foci (0±√6, 0) = (-√6, 0) and (√6, 0)

Answer:

[tex]\frac{2c}{3x^2c}+ \frac{36x^3c}{3x^2c} +\frac{24x^2}{3x^2c} [\tex]

Step-by-step explanation:

We need to find sum of 2 / 3x^2 +12x and 8 / c

So, solving:

[tex](\frac{2}{3x^2} + 12 x ) +\frac{8}{c}[/tex]

Taking LCM of 3x^2 and 1 i.e. 3x^2

[tex]=(\frac{2 + 12 x(3x^2)}{3x^2} ) +\frac{8}{c}\\=(\frac{2 + 36x^3}{3x^2} ) +\frac{8}{c}\\=\frac{2 + 36x^3}{3x^2} +\frac{8}{c}\\LCM \,\, 36x^2 c\\=\frac{(2 + 36x^3)c + 8(3x^2)}{3x^2c}\\=\frac{2c + 36x^3c + 24x^2}{3x^2c}\\= \frac{2c}{3x^2c}+ \frac{36x^3c}{3x^2c} +\frac{24x^2}{3x^2c}[/tex]

Answer:

  B.  14.34

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relationship between the side opposite the angle of interest and the hypotenuse:

  Sin = Opposite/Hypotenuse

For the given triangle, this means ...

  sin(35°) = b/25

  b = 25·sin(35°)

  b ≈ 14.34

Answer:

possible values of 4th term is 80 & - 80

Step-by-step explanation:

The general term of a geometric series is given by

[tex]a(n)=ar^{n-1}[/tex]

Where a(n) is the nth term, r is the common ratio (a term divided by the term before it) and n is the number of term

[tex]ar^{5-1}=40\\ar^4=40[/tex]

[tex]ar^{7-1}=10\\ar^6=10[/tex]

We can solve for a in the first equation as:

[tex]ar^4=40\\a=\frac{40}{r^4}[/tex]

Now we can plug this into a of the 2nd equation:

[tex]ar^6=10\\(\frac{40}{r^4})r^6=10\\40r^2=10\\r^2=\frac{10}{40}\\r^2=\frac{1}{4}\\r=+-\sqrt{\frac{1}{4}} \\r=\frac{1}{2},-\frac{1}{2}[/tex]

Let's solve for a:

[tex]a=\frac{40}{r^4}\\a=\frac{40}{(\frac{1}{2})^4}\\a=640[/tex]

Now, using the general formula of a term, we know that 4th term is:

4th term = ar^3

Plugging in a = 640 and r = 1/2 and -1/2 respectively, we get 2 possible values of 4th term as:

[tex]ar^3\\1.(640)(\frac{1}{2})^3=80\\2.(640)(-\frac{1}{2})^3=-80[/tex]

possible values of 4th term is 80 & - 80

In matrix from, the system is

[tex]\dfrac{\mathrm d}{\mathrm dt}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}3&-1&-1\\1&1&-1\\1&-1&1\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}[/tex]

The coefficient matrix has eigenvalues [tex]\lambda[/tex] such that

[tex]\begin{vmatrix}3-\lambda&-1&-1\\1&1-\lambda&-1\\1&-1&1-\lambda\end{vmatrix}=-(\lambda-2)^2(\lambda-1)=0\implies\lambda=2_{(2)},\lambda=1[/tex]

(where the subscript denotes multiplicity of the eigenvalue).

[tex]\lambda=2[/tex]:

[tex]\begin{bmatrix}1&-1&-1\\1&-1&-1\\1&-1&-1\end{bmatrix}\vec\eta_1=\vec0[/tex]

[tex]\implies\eta_{1,1}-\eta_{1,2}-\eta_{1,3}=0\implies\eta_{1,1}=\eta_{1,2}+\eta_{1,3}[/tex]

By picking [tex]\eta_{1,1}=1[/tex], we can then set [tex]\eta_{1,2}=1[/tex] and [tex]\eta_{1,3}=0[/tex], and vice versa, to find two corresponding eigenvectors,

[tex]\vec\eta_1=\begin{bmatrix}1\\1\\0\end{bmatrix},\vec\eta_2=\begin{bmatrix}1\\0\\1\end{bmatrix}[/tex]

[tex]\lambda=1[/tex]:

[tex]\begin{bmatrix}2&-1&-1\\1&0&-1\\1&-1&0\end{bmatrix}\vec\eta_3=\vec0[/tex]

[tex]\implies2\eta_{3,1}-\eta_{3,2}-\eta_{3,3}=0\implies2\eta_{3,1}=\eta_{3,2}+\eta_{3,3}[/tex]

We obtain [tex]\vec\eta_3[/tex] independent of [tex]\vec\eta_1,\vec\eta_2[/tex] by picking [tex]\eta_{3,2}=\eta_{3,3}=1[/tex], so that the third corresponding eigenvector is

[tex]\vec\eta_3=\begin{bmatrix}1\\1\\1\end{bmatrix}[/tex]

Then the general solution to this system is

[tex]\begin{bmatrix}x\\y\\z\end{bmatrix}=C_1e^{2t}\vec\eta_1+C_2te^{2t}\vec\eta_2+C_3e^t\vec\eta_3[/tex]

[tex]\begin{cases}x=C_1e^{2t}+C_2te^{2t}+C_3e^t\\y=C_1e^{2t}+C_3e^t\\z=C_2te^{2t}+C_3e^t\end{cases}[/tex]

To find the general solution of the given system of differential equations, we can solve each equation separately and obtain the general solution for x(t), y(t), and z(t).

The given system of differential equations is:

dx/dt = 3x - y - z

dy/dt = x + y - z

dz/dt = x - y + z

To find the general solution, we can treat each equation separately.

For dx/dt = 3x - y - z, we can rewrite it as:

dx / (3x - y - z) = dt

Integrating both sides gives us:

ln|3x - y - z| = t + C1, where C1 is the constant of integration.

Exponentiating both sides gives us:

|3x - y - z| = e^(t+C1)

Since |3x - y - z| is always positive, we can remove the absolute value signs:

3x - y - z = e^(t+C1)

Now, we can solve the remaining two equations in a similar manner to find y(t) and z(t).

By solving the three equations, we can obtain the general solution for x(t), y(t), and z(t).

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Answer:

The third choice is correct

Step-by-step explanation:

The given expression is

[tex]2^n-1[/tex]

when n=7, we substitute into the formula to obtain;

[tex]2^7-1[/tex]

Note that;

[tex]2^7=2\times 2\times 2\times 2\times 2\times 2\times 2=128[/tex]

[tex]2^7-1=128-1=127[/tex]

The third choice is correct

Answer:

[tex]\$412.64[/tex]

Step-by-step explanation:

we know that

The formula to calculate continuously compounded interest is equal to

[tex]A=P(e)^{rt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

[tex]t=9\ years\\ P=\$315\\ r=0.03[/tex]  

substitute in the formula above  

[tex]A=\$315(e)^{0.03*9}=\$412.64[/tex]

Answer: $412.64

Step-by-step explanation: you’re welcome :)

Answer:

The correct answer is option C.  490 units ²

Step-by-step explanation:

Area of cuboid = 2(lb + bh + lh)

From the figure we can see that a rectangular prism.

To find the surface area of prism

Here l = 14 units

b = 7 units and h = 7 units

Surface area = 2((14 * 7) + (7 * 7) + (14 * 7))

= 490 units ²

Answer:

490 units squared

Step-by-step explanation:

Answer:

She started with 26 boxes.

Step-by-step explanation:

She started with x boxes. Then she bought 8 more boxes. Now she had x + 8 boxes. Then half the boxes were destroyed, so she has the other half of the boxes. Half of the boxes is (x + 8)/2. She has now 17 boxes, so (x + 8)/2 = 17.

(x + 8)/2 = 17

Multiply both sides by 2.

x + 8 = 34

Subtract 8 from both sides.

x = 26

She started with 26 boxes.

Answer:

0

Step-by-step explanation:

Each expression is a way to write the sum ...

3 + 5 + 7 + 9

That sum in each case is 24, so the difference is 24-24 = 0.

Answer:

it is not 0 !!!

Step-by-step explanation:

got it wrong bc of top answer

Answer:

  see attached

Step-by-step explanation:

nCk models k objects taken from a group of n.

  nCk = n!/(k!·(n-k)!)

Fill in n=8 and k=3 to get ...

  8C3 = 8!/(3!·5!)