If point Q is reflected across x = 1, what are the coordinates of its reflection image?

[tex](1-3i)(1-i)(1+i)(1+3i)=\\(1^2-(3i)^2)(1^2-i^2)=\\(1+9)(1+1)=\\10\cdot2=20[/tex]

Answer:

[tex]\huge\boxed{(1-3i)(1-i)(1+i)(1+3i)=20}[/tex]

Step-by-step explanation:

[tex](1-3i)(1-i)(1+i)(1+3i)\\\\\text{use the commutative property}\\\\=(1-3i)(1+3i)(1-i)(1+i)\\\\\text{use the associative property}\\\\=\bigg[(1-3i)(1+3i)\bigg]\bigg[(1-i)(1+i)\bigg]\\\\\text{use}\ (a-b)(a+b)=a^2-b^2\\\\=\bigg[1^2-(3i)^2\bigg]\bigg[1^2-i^2\bigg]\\\\=\bigg(1-9i^2\bigg)\bigg(1-i^2\bigg)\\\\\text{use}\ i=\sqrt{-1}\to i^2=-1\\\\=\bigg(1-9(-1)\bigg)\bigg(1-(-1)\bigg)\\\\=\bigg(1+9\bigg)\bigg(1+1\bigg)\\\\=(10)(2)\\\\=20[/tex]

Answer:

33 minutes

Step-by-step explanation:

To find the mean, you first must add up the values given.

45 + 25 + 35 + 20 + 40 = 165

Now, divide the sum by the number of values you have.

165/5 = 33

The mean number of minutes she spent practicing is 33.

Answer:

4

Step-by-step explanation:

y=mx+b

b=y-intercept.

In this case...

mx=-5<-- this is the slope of the line.

b=4<-- y intercept.

Hope this helps, any further questions, please feel free to ask.

Answer:

This graph is nonlinear

The initial displacement of the weight is 40cm

The weight first returns to equilibrium when t=1/2

Step-by-step explanation:

thats the answer i only had time to give not to explain

Answer:

the answer is in the photo ^^

Step-by-step explanation:

the correct thing is there for confirmation ;)

Answer:

C

Step-by-step explanation:

4,800 times 7% is 336, and 1200 times 14% is 168, and 168 is half as much as 336, so the correct answer is c

Answer:

C

Step-by-step explanation:

Multiply .7 to 6000 and solve

Answer:

1: V:56.52  SA:94.2  Ratio: 3:5

2: V:113.04  SA:62.8  Ratio: 9:5

3: V:113.04  SA:138.16  Ratio: 9:11

4: V:113.04  SA:131.88  Ratio: 6:7

Step-by-step explanation:

Hey there!

By using the following formula for volume of a cylinder I got,  

[tex](3.14) r^2h[/tex]

1: 56.52

2: 113.04

3: 113.04

4: 113.04

Now to find SA we'll use the following formula,

1: 94.2

2: 62.8

3: 138.16

4: 131.88

Now for the ratio,

56.52:94.2 - 3:5

113.04:62.8 -  9:5

113.04:138.16 - 9:11

113.04:131.88 - 6:7

Hope this helps :)

Answer:

5

Step-by-step explanation:

Given

[tex]\frac{30b}{6b}[/tex]

Cancel the b on the numerator/ denominator.

Also the 30 and 6 can both be cancelled by 6 , thus

[tex]\frac{30b}{6b}[/tex] = [tex]\frac{30}{6}[/tex] = 5

Answer:

[tex]\boxed{5}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{30b}{6b}[/tex]

[tex]\sf Simplify[/tex]

[tex]\displaystyle \frac{30}{6} \times \frac{b}{b}[/tex]

[tex]5 \times 1[/tex]

[tex]=5[/tex]

Answer:

MN = 14 ft

Step-by-step explanation:

NP tangent => ∡PNM = 90°

Pythagoras

MN = √MP² - NP²

= √50² - 48²

= √(50 - 48)(50 + 48)

= √2×98

= √196

= √14²

= 14 ft

Answer:

17.32 minutes

Step-by-step explanation:

The standard deviation for a uniform distribution is:

[tex]\sigma =\frac{b-a}{\sqrt12}[/tex]

If a = 20 minutes and b = 80 minutes, the standard deviation is:

[tex]\sigma =\frac{80-20}{\sqrt12} \\\sigma=17.32\ minutes[/tex]

The standard deviation of the distribution of consumer usage time of computers in the public library is 17.32 minutes.

Answer:

From sin²θ + cos²θ = 1, we have;

sin⁴θ + cos⁴θ = 1 - 2·sin²θ·cos²θ

Step-by-step explanation:

The given equation is (sin⁴θ + cos⁴θ) = 1 - 2 sin²θ·cos²θ

We have;

(sin⁴θ + cos⁴θ) = 1 - 2 sin²θ·cos²θ gives;

(sin⁴θ + cos⁴θ) + 2 sin²θ·cos²θ= 1

Which is equivalent to sin⁴θ + 2 sin²θ·cos²θ +cos⁴θ  = 1

From which we can get;

(sin²θ + cos²θ)·(sin²θ + cos²θ)  = 1

Given that sin²θ + cos²θ = 1

Therefore;

1 × 1 = 1

To get to the initial equation in the question, we have;

sin²θ + cos²θ = 1

(sin²θ + cos²θ) × (sin²θ + cos²θ) = 1

(sin⁴θ + sin²θ·cos²θ + sin²θ·cos²θ + cos⁴θ = 1

∴ sin⁴θ + cos⁴θ = 1 - sin²θ·cos²θ + sin²θ·cos²θ  = 1 - 2·sin²θ·cos²θ

Therefore;

sin⁴θ + cos⁴θ = 1 - 2·sin²θ·cos²θ.

Answer:

16

Step-by-step explanation:

perimeter of B = 21

divide by 3 to get each side: 21/3 = 7 = Y

perimeter of hexagon is 50. subtract 2Y: 50 - 14 = 36

divide 36 by 4 to find X = 9

add X + Y

Answer:

Pyramid

Step-by-step explanation:

[tex]\text{Volume of a Square Pyramid }=\frac{1}{3} \times l^2 \times Height\\\\ \text{Volume of a Cone }=\frac{1}{3} \pi r^2 \times Height[/tex]

Given that the two solids have the same volume

[tex]\frac{1}{3} \times l^2 \times Height=\frac{1}{3} \pi r^2 \times Height[/tex]

If the length of a side of the square base of pyramid A is the same as the base radius of cone B. i.e l=r

[tex]\frac{1}{3} \times l^2 \times $Height of Pyramid=$\frac{1}{3} \pi l^2 \times $Height of cone$\\\\$Cancel out $ \frac{1}{3} \times l^2$ on both sides\\\\Height of Pyramid= \pi \times $ Height of cone$[/tex]

If the height of the cone is 1

[tex]H$eight of Pyramid= \pi \times 1 \approx 3.14$ units[/tex]

Therefore, the pyramid has a greater height.

Step-by-step explanation:

The dimensions are (8-2x) and (10-2x) We will say the depth of the box is x. The equation we use for the volume of the box is V=x(8-2x)(10-2x)

Answer:

part b of the answer is x=1.5 inches

Step-by-step explanation:

Answer:

[tex] L_o= 1500 cm[/tex]

And we know that the level is decreasing 20% each day so then we can use the following model for the problem

[tex] L_f = L_o (1-0.2)^t[/tex]

Where t represent the number of days and L the level for this case we want to fnd the level after two days so then t =2 and replacing we got:

[tex] L_f = 1500cm(0.8)^2 = 960cm[/tex]

Step-by-step explanation:

For this case we know that the initial volume of water is:

[tex] L_o= 1500 cm[/tex]

And we know that the level is decreasing 20% each day so then we can use the following model for the problem

[tex] L_f = L_o (1-0.2)^t[/tex]

Where t represent the number of days and L the level for this case we want to fnd the level after two days so then t =2 and replacing we got:

[tex] L_f = 1500cm(0.8)^2 = 960cm[/tex]

Answer:

Step-by-step explanation:

The order of a succession is a way that the terms (the first, the second, the third, etc.) can be distinguished according to a certain formation law or order criterion.

Example:

a¹/a²/a³/a⁴ And successively

In the order of a sequence you can assign any letter.

Answer:

iii

Step-by-step explanation:

because of the amount taken from the cashews.and nuts and 1 of 3 were taken away

Answer:

(5 1/3)/7

Step-by-step explanation:

Divide 4 by 3, then times it by four and put it over the 7

Answer:

  D.  f(x) = |x|

Step-by-step explanation:

The absolute value parent function has nothing added or subtracted or multiplied. It is simply ...

  f(x) = |x|

Answer:

C.

Step-by-step explanation:

To find the area of a rectangle, times the length and the breadth together. So, it would be 16×5=80. option C is 80.

Answer:

80 sq.units

Step-by-step explanation:

A of rectangle = L×B

L= 16 units

B=5 units

A of rectangle = L×B

                        =16×5 units

                        =80 sq.units

Answer:

[tex]4x^2 - 8x + 20[/tex]

Step-by-step explanation:

The correct equation is:

[tex]8x^3 + 4x^2 + 100[/tex]

We want to divide that by (2x + 5)

To do the long division, divide each term by 2x and then subtract the product of the result and (2x + 5) from the remaining part of the equation.

When you get to 0, you have reached the end of the division.

Whatever term you get from each step of division is part of the quotient.

Go over the steps above carefully while following them below:

Step 1:

Divide [tex]8x^3[/tex] by 2x. You get [tex]4x^2[/tex].

Step 2

Multiply [tex]4x^2[/tex] by (2x + 5)  and subtract from [tex]8x^3 + 4x^2 + 100[/tex]:

[tex]8x^3 + 4x^2 + 100[/tex] - ([tex]8x^3 + 20x^2[/tex]) = [tex]-16x^2 + 100[/tex]

Step 3

Divide [tex]-16x^2[/tex] by 2x. You get [tex]-8x[/tex].

Step 4

Multiply -8x by (2x + 5) and subtract from [tex]-16x^2 + 100[/tex]:

[tex]-16x^2 + 100[/tex] - ([tex]-16x^2 - 40x[/tex]) = 40x + 100

Step 5

Divide 40x by 2x. You get 20.

Step 6

Multiply 20 by (2x + 5) and subtract from 40x + 100:

40x + 100 - (40x + 100) = 0

From the three steps of the division, we got [tex]4x^2[/tex], -8x and 20.

Therefore, the quotient is [tex]4x^2 - 8x + 20[/tex]

Answer:

c. jasper has apparently decreased the volume of items in his ending inventory as compared to the number of items in his beginning inventory

Step-by-step explanation:

First In First Out  FIFO is a type of inventory system in accounting, it literally implies that  the oldest purchase goes out first when you made a sale. The oldest purchase are charged based on cost of good sold. If price are rising, :

FIFO will yield a lower cost of good sold

FIFO will yield a higher net income

FIFO will yield higher tax liability

FIFO will yield a higher inventory

From the information given:

the business records show that the cost of the stores inventory items has been steadily increasing. the cost of the end of the year inventory is 200,000 and the cost of the beginning of the year inventory was 250,000.

What the statement implies is that:

jasper has apparently decreased the volume of items in his ending inventory as compared to the number of items in his beginning inventory

Answer:

The formula for speed is s=(distance traveled)/(time elapsed)

Answer:

[tex]\huge \boxed{S =\frac{d }{t} }[/tex]

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

The formula to find speed is as follows:

[tex]\Longrightarrow \ \ \displaystyle \sf speed =\frac{distance \ travelled }{time \ taken}[/tex]

[tex]\Longrightarrow \ \ \displaystyle S =\frac{d }{t}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Answer:

[tex]\boxed{\mathrm{view \: attachments}}[/tex]

Step-by-step explanation:

Vertex is the highest or lowest point of a parabola.

Axis of symmetry is the line that cuts the parabola in half.

y-intercept is the point where the parabola touches the y-axis.

The maximum or minimum values are the highest or lowest values the parabola can reach.

x-intercepts are the points where the parabola touches the x-axis.

Answer:

5.5

Step-by-step explanation:

We use right triangle XVW.

For <W, VX is the opposite leg.

WX is the hypotenuse.

The trig ratio that relates the opposite leg to the hypotenuse is the sine.

[tex] \sin W = \dfrac{opp}{hyp} [/tex]

[tex] \sin W = \dfrac{VX}{WX} [/tex]

[tex] \sin 43^\circ = \dfrac{VX}{8~mi} [/tex]

[tex] VX = 8~mi \times \sin 43^\circ [/tex]

[tex] VX = 5.5~mi [/tex]

Answer: The coordinates of D are (1,-12) .

Step-by-step explanation:

Given : Translation rule : (x, y) → (x + 6, y – 10)  is applied to figure ABCD.

From the figure below, we have figure ABCD in which

The coordinates of D = (-5,-2)

According to the given translation rule :

D(-5,-2) → D'(-5 + 6, -2 – 10)    (coordinates of image point D')

i.e. D(-5,-2) → D'(1, -12)    [-5+6 = 1, -2-10 = -12]

Hence, the coordinates of D are (1,-12) .

Answer:

B. (1, –12)

Step-by-step explanation:

edge2021

Answer:

[tex]\large \boxed{\sf \ \ x=\pm8 \ \ or \ \ x=\pm2 \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

First of all, we can assume that x and y are different from 0, as we cannot divide by 0.

And from the first equation we can write y as a function of x as below.

[tex]y=\dfrac{16}{x}[/tex]

And then, we replace it in the second equation to get.

[tex]\dfrac{x}{\frac{16}{x}}+\dfrac{\frac{16}{x}}{x}=\dfrac{17}{4}\\\\<=> \dfrac{x^2}{16}+\dfrac{16}{x^2}=\dfrac{17}{4}\\\\\text{*** We multiply by }16x^2 \text{ both sides ***}\\\\x^4+16*16=\dfrac{17*16}{4}x^2\\\\x^4-68x^2+3600=0\\\\\text{*** The product of the zeroes is 3600 = 64*4 and the sum is 64+4=68 ***}\\\\\text{*** So we can factorise *** }\\\\x^4-64x^2-4x^2+3600=x^2(x^2-64)-4(x^2-64)=(x^2-64)(x^2-4)=0\\\\x^2=64=8^2 \ \ or \ \ x^2=4\\\\x=\pm8 \ \ or \ \ x=\pm2\\[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

a) 18

b) 20

c) 12

d) 12

Step-by-step explanation:

a) The triangle is half of the square, so you can find the area of the square(36) and divide by 2: so 18

b) There are 4 same sized blank triangles with area of 4 ( (2*4)/2 ) so 4 * 4 is 16. 16 is the blank area so the area of the shaded is 36 - 16: 20

c) There are 2 blank triangles which areas are 6, and 18, so you subtract those numbers from 36: 36 - (6+18) = 12

d) Another 2 same blank triangles with areas of 12 ( (6 *4)/2 )so you subtract them from 36 too: 36 - (12*2) = 36 - 24 = 12

Answer:

A

Step-by-step explanation:

Using ZPP we get x = 0, 2x + 4 = 0, x + 5 = 0. Solving these, we get x = 0, x = -2, x = -5.

Answer:

m = -9/4

Step-by-step explanation:

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Simply plug in the coordinates into the slope formula:

m = (16 - 7)/(2 - 6)

m = 9/-4

m = -9/4

Answer:

.72

Step-by-step explanation:

9 rounds up because 1-4 stay the same and 5-9 round up

Answer: 0.719 to the nearest hundredth is 0.72