Select the correct answer.
Write (21 − 4i) − (16 + 7i) + 28i as a complex number in standard form.

A.
5 + 39i
B.
5 + 17i
C.
5 − 39i
D.
5 − 17i

Answer:

The answer is 11 300.06

[tex](4 \times 1000) + (3 \times 100) + (6 \times \frac{1}{100}) + (7 \times 1000) [/tex]

[tex] = 4000 + 300 + \frac{6}{100} + 7000[/tex]

[tex] = 11 \: 300 + 0.06[/tex]

[tex] = 11 \: 300.06[/tex]

Answer:

Un número entero es un número entero que puede ser positivo, negativo o cero. Ejemplos de enteros son: -5, 1, 5, 8, 97 y 3,043. Ejemplos de números que no son enteros son: -1.43, 1 3/4, 3.14,. 09 y 5.643,1.

Answer:

The answer is option D

Step-by-step explanation:

32m + 56mp

First factor out the HCF out

The HCF of 32and 56 is 8

So we have

8 ( 4m + 7mp)

next factor m out

We have the final answer as

Hope this helps you

Answer:

148 cm ^2

Step-by-step explanation:

Hey there!

Well is the area of the base is 30 then we can conclude that the side lengths are 5 and 6.

Then if the volume is 120 we can do,

120 ÷ 30 = 4

So the height is 4 cm.

Now we already have the area of the base we just need to find the area of the rest of the rectangles.

If the bottom base is 30 then the top base is also 30.

30 + 30 = 60cm^2

Now we can do the two rectangles on the side that have side lengths of 5 and 4.

5*4 = 20

20+20 = 40 cm^2

Now we can do the two final rectangles that have side lengths of 6 and 4.

6*4=24

24 + 24 = 48 cm^2

Now we can add all the areas up,

48 + 40 + 60

= 148 cm^2

Hope this helps :)

Answer:

45

Step-by-step explanation:

The final had an extra credit as 25, so without it it would be 135. Then, you would divide by three to find that the first test had 45 points.

Answer:

45

Step-by-step explanation:

The final had an extra credit as 25, so without it it would be 135. Then, you would divide by three to find that the first test had 45 points.

Answer:

1,110

Step-by-step explanation:

calculator

Answer:

5/2, 4/5 are terminating decimals

Step-by-step explanation:

5/2 = 2.5  this is a terminating decimal

4/5 = .8 this is a terminating decimal

2/7 = .285714(repeating)  This is a repeating decimal

4/3 = 1.3(repeating)  this is a repeating decimal

Answer:

Hey There!!

4/5 and 5/2 are your answers!

Step-by-step explanation

Answer:

The correct option is;

False

Step-by-step explanation:

The coefficient of x^k·y^(n-k) is nk,   False

The kth coefficient of the binomial expansion, (x + y)ⁿ is  [tex]\dbinom{n}{k} = \dfrac{n!}{k!\cdot (n-k)!} = C(n,k)[/tex]

Where;

k = r - 1

r = The term in the series

For an example the expansion of (x + y)⁵, we have;

(x + y)⁵ = x⁵ + 5·x⁴·y + 10·x³·y² + 10·x²·y³ + 5·x·y⁴ + y⁵

The third term, (k = 3) coefficient is 10 while n×k = 3×5 = 15

Therefore, the coefficient of x^k·y^(n-k) for the expansion  (x + y)ⁿ = [tex]C(n,k)[/tex] not nk

Answer:

True

Step-by-step explanation:

apec

Answer:

x² + 4x + y² + 10y + 20 = 0

Step-by-step explanation:

Step 1: Expand (x + 2)²

x² + 2x + 2x + 4 + (y + 5)² = 9

Step 2: Combine like terms

x² + 4x + 4 + (y + 5)² = 9

Step 3: Expand (y + 5)²

x² + 4x + 4 + y² + 5y + 5y + 25 = 9

Step 4: Combine like terms

x² + 4x + 4 + y² + 10y + 25 = 9

Step 5: Move 9 over

x² + 4x + 4 + y² + 10y + 25 - 9 = 0

Step 6: Combine like terms

x² + 4x + y² + 10y + 20 = 0

Answer:

x^2+y^2+4x+10y+20=0

Step-by-step explanation:

(x+2)^2+(y+5)^2=9

x^2+4x+4+y^2+10y+25-9=0

general form: x^2+y^2+4x+10y+20=0

Answer:

B. The student incorrectly calculated the scale factor to be –2

Step-by-step explanation:

Given that :

After a dilation with a center of (0, 0), a point was mapped as (4, –6) → (12, y).

The student determined y to be -2

If a figure dilated with a center of (0, 0) and scale factor k, then

(x , y) → (kx , ky)

(4, -6) → (12, y)

[tex]k = \dfrac{x'}{x}[/tex]

[tex]k = \dfrac{12}{4}[/tex]

k = 3

Thus; the scale factor is 3

Now; the y-coordinate can now be calculated as;

ky = (3 × -6)

ky = -18

Therefore; the value of y = -18 and the student incorrectly calculated the scale factor to be -2.

Answer:

I would say the answer is C.

Answer:

For f(x)+2, it goes along the y axis, 2 units.

For f(x+2), it goes along the x axis, -2 untis.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Factorize 175 and 50

175 = 5 * 5 * 7

50  = 5 * 5 * 2

[tex]\frac{\sqrt[3]{175}}{\sqrt[3]{}50}=\sqrt[3]{\frac{175}{50}}\\\\\\ =\sqrt[3]{\frac{5*5*7}{5*5*2}}\\\\\\=\sqrt[3]{\frac{7}{2}}[/tex]

Answer:

A(ABCD) ≈ 17.285 cm²

Step-by-step explanation:

A = √s(s - a)(s - b)(s - c)

s = (a + b + c)/2

a ; b ; c = the sides of the triangle

s = (AB + BC + AC)/2 = (5cm + 4.5cm + 6.5cm)/2 = 16cm/2 = 8 cm

A(ABC) = √8(8 - 5)(8 - 4.5)(8 - 6.5)

= √8×3×3.5×1.5

= √126

≈ 11.225 cm²

     2. A(ACD) = √s(s - AC)(s - CD)(s - AD)

s = (AC + CD + AD)/2 = (6.5cm + 3.5cm + 4cm)/2 = 14cm/2 = 7 cm

A(ACD) = √7(7 - 6.5)(7 - 3.5)(7 - 4)

= √7×0.5×3.5×3

= √36.75

≈ 6.060 cm²

     3. A(ABCD) = 11.225cm² + 6.060cm² = 17.285 cm²

Answer:

4.1 feet

Step-by-step explanation:

Two shapes are said to be similar if they have the same shape and their sides are in the same proportion, i.e. the ratio of their sides are equal.

Given the two figures attached, the height of the first figure is 11 ft, while its width is 8 ft. For the second figure, its height is x feet and its length is 3 ft. Since the two figure are similar therefore the ratio of their sides are equal. Therefore:

[tex]\frac{x}{11} =\frac{3}{8}\\ \\x=\frac{3*11}{8}=4.125\\ \\x=4.1\ feet(to\ nearest\ tenth)[/tex]

Answer:

4/9

Step-by-step explanation:

So, the ratio of the books is 8:10:6. After 2 books were taken off of each shelf, it became 6:8:4. All of these numbers added up is 18. So that means 8/18 of the books are math books, which can be simplified to 4/9.

Answer:

4/9

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the value of a family's home, in Camrose AB, given by the following exponential function f(x) = 130000(1.06)^x, where x is the number of years after the family purchases the house for $130,000. In order to calculate the best estimate for the instantaneous rate of change in the value of the home when the family has owned it for 5 years, we will have to substitute x =5 in the given function and solve as shown;

f(x) = 130000(1.06)ˣ

f(5) = 130000(1.06)⁵

f(5) = 130000*(1.06)⁵

f(5) = 130000*1.338226

f(5) = 173,969.38

Hence, the instantaneous rate of change in the value of the home when the family has owned it for 5 years is approximately  $173,969

Answer:

1.03921568627

Step-by-step explanation:

Answer: while solving an equation involving fractions we eliminate the fraction by multiplying the LCD of all the denominators present in the equation . LCD means Least common Denominator so for this question when we try to eliminate the denominator we first try to find the LCM (2,4,6) because that will give us the LCD.

2=2

4=2·2

6=2·3

LCM = 2·2·3

LCM = 12

It means we need to multiply the 12 to each term of equation to eliminate the fractions before solving.

12

To eliminate the fractions, multiply the equation by the 12

A equation is an expression that shows the relationship between two or more variables and numbers.

Given the equation:

[tex]x-\frac{5}{4}+2x=\frac{5}{6}+x[/tex]

To eliminate the fractions, multiply by the L.C.M of the denominator of the fraction i.e. 12 to get:

12x - 15 + 24x = 10 + 12x

Find out more on Equation at: https://brainly.com/question/2972832

Answer:

B -5, and 5

Step-by-step explanation:

you can't have zero on the bottom

Answer: 1/5

Step-by-step explanation:

We need to calculate the area of rectangle and trapezium and the Circumference of the circle.

Area of rectangle :

Length(L) = 10 ; width (W) = 6

Area = L * W = (10 * 6)ft = 60ft^2

Area of trapezium :

Height (h) = 4ft ; length(a) = 2ft ; length(b) = 4ft

Area = 0.5 ( a + b) h

Area = 0.5(2 +4) * 4 = 0.5(6)*4 = 12ft^2

Area of circle :

πr^2 ; r = radius of circle ; r= 2ft

3.142 * 2^2 = 3.142 * 4 = 12.568 ft^2

Probability = required outcome / Total possible outcomes.

P(point chosen inside rectangle is inside trapezium) = Area of trapezium / Area of rectangle

= 12/60

= 1/5

Answer:

[tex]d + q = 20[/tex]

[tex]0.25d + 0.10q = 3.05[/tex]

Step-by-step explanation:

Given

Coins = 20

Value = $3.05

Required

Determine the equation that represent this

From the question, we have that

d = the number of dimes

q = the number of quarters

This implies that;

[tex]d + q = 20[/tex]

Also;

[tex]1 d=\$0.25\ \ and\ \\1 q= \$0.10[/tex]---------- Standard unit of conversion;

This implies that

[tex]0.25d + 0.10q = 3.05[/tex]

Hence, the equations are:

[tex]d + q = 20[/tex]

[tex]0.25d + 0.10q = 3.05[/tex]

Answer:

This is simple! (Kind of)

Step-by-step explanation:

First, notice how HJ is tangent. HG is a radius intersecting HJ at H.

This means, (According to some theorem that I forgot the name of) that GHJ is a right angle.

Thus, we can use the 180* in a triangle theorem.

[tex]180=90+54+6x+6[/tex]

So, let's solve!

[tex]30=6x\\5=x[/tex]

So, there you go! Nice and simple!

Hope this helps!

Stay Safe!

Step-by-step explanation:

hope it helps yoy..........

Answer:

7/16=x/4

4 times 7/16= 4 times x/4

7/4=x

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex] \frac{7}{16} = \frac{x}{4} [/tex]

Apply cross product property

[tex]16 x = 7 \times 4[/tex]

Multiply the numbers

[tex]16x = 28[/tex]

Divide both sides of the equation by 16

[tex] \frac{16x}{16} = \frac{28}{16} [/tex]

Calculate

[tex]x = 1.75[/tex]

Hope this helps...

Best regards!!

Answer:

Step-by-step explanation:

Use F.O.I.L

F - First

O- Outside

I- Inside

L- Last

First multiply the ds from both to get [tex]d^{2}[/tex], next multiply the first d and the -4 and get -4d, then the 8 and the second d = 8d, and finally the 8 and -4 to get -32

you get [tex]d^{2}[/tex]-4d + 8d - 32

Answer:

An exterior angle of a triangle is equal to the sum of the opposite interior angles.

Answer:

Two remote interior angles.

Answer:

Shape - Cube

Area= 864

Step-by-step explanation:

The shape folds to become a cube and all the edges are the same size.

Area of a cube is Length * Width * Height = Area

12*12*12= 864

Answer:

Shape - Cube

Area= 864

Step-by-step explanation:

The shape folds to become a cube and all the edges are the same size.

Area of a cube is Length * Width * Height = Area

12*12*12= 864

Answer:

15w - 10x + 30.

Step-by-step explanation:

-5(2x - 3w - 6)

= (-5 * 2x) + (-5 * -3w) + (-5 * -6)

= -10x + 15w + 30

= 15w - 10x + 30.

Hope this helps!

Answer:

Step-by-step explanation:

[tex] - 5(2x - 3w - 6)[/tex]

Multiply each term in the parentheses by -5

[tex] - 5 \times 2x - 5 \times ( - 3w) - 5 \times ( - 6)[/tex]

Calculate the product

[tex] - 10x - 5 \times ( - 3x) - 5 \times ( - 6)[/tex]

Multiplying two negatives equals a positive [tex]( - ) \times ( - ) = ( + )[/tex]

[tex] - 10x + 5 \times 3w - 5 \times ( - 6)[/tex]

Calculate the product

[tex] - 10x + 15w - 5 \times ( - 6)[/tex]

Multiply the numbers

[tex] - 10x + 15w + 30[/tex]

Hope this helps..

Best regards!!

Answer:

I guess that you want to know the transformations:

We start with:

f(x) = y = 4*x + 3

a)the transformed function is:

f(x) = y = -4*x - 3

So the sign changed.

This means that we go from (x, y) to (x, - y)

This is a reflection over the x-axis which changes the sin of the y component.

b) Now we go to f(x) = 4*x + 3

So the coefficient in the leading term changed.

This is a horizontal contraction:

A horizontal contraction of factor K for the function g(x) is: g(K*x)

In our case, we have:

f(K*x) = 4*(k*x) + 3 = x + 3

4*k*x = x

4*k = 1

k = 1/4

Then the transformation is an horizontal contraction of scale factor 1/4.

Answer:

Option A 25 ft is the correct answer.

Step-by-step explanation:

Given that:

One square corral at a stable has an area 625 [tex]ft^2[/tex].

And one side corral is along a barn.

To find:

How much of a barn's wall is used for the edge of corral?

Solution:

First of all, kindly refer to the attached figure to have a better understanding of the given dimensions and situation.

Given that Corral is square shape with Area, A = 625 [tex]ft^2[/tex]

Formula for area of a square is given as:

[tex]A = Edge^2[/tex]

Putting the value of A as given to find the Edge:

[tex]625 = Edge^2\\\Rightarrow Edge^2 =25 \times 25\\\Rightarrow Edge = 25\ ft[/tex]

It is given that one side of Corral is along a barn.

So, barn's wall used for the edge of corral = 25 ft

Option A 25 ft is the correct answer.

Answer: A 25ft I did it on edge and got it correct and please do as brainlest and have a good day.