Lily owed Megan $129.42. So far, she has paid Megan $32.56.
The remaining amount Lily has yet to pay Megan is $

Hello,

[tex]Let's\ say \\\\z=\sqrt{3+4*i} =a+b*i\\\\z^2=3+4*i=(a+b*i)^2=a^2-b^2+2i*a*b\\\\\\if \ a\neq 0\\\left\{\begin{array}{ccc}a^2+b^2&=&3\\2ab=4\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}b=\dfrac{2}{a}\\a^2-(\dfrac{2}{a})^2=2\\\end{array}\right.\\\\\\a^4-4=3*a^2\\a^4-3a^2-4=0\\\\\Delta=(-3)^2-4*1*(-4)=25=5^2\\\\a^2=4\ or \ a^2=-1 (impossible)\\\\So:\\(a=2\ and\ b=1)\ or\ (a=-2\ and\ b=-1)\\[/tex]

Roots are thus 2+i and -2-i

There is an other using a geometrical formula (formule de Moivre)

Answer:

40/30

Step-by-step explanation:

Since tan∅= o/a, 40 is opposite, and 30 is adjacent to angle A, 40/30 is the ratio for tanA.

Answer:40/30

Step-by-step explanation:

....

Answer:

9x-18=y

Step-by-step explanation:

by switching the places of x and y and solving for y

Answer:

f = - [tex]\frac{15}{4}[/tex]

Step-by-step explanation:

Given

f + [tex]\frac{1}{4}[/tex] = - [tex]\frac{7}{2}[/tex]

Multiply through by 4 ( the LCM of 2 and 4 ) to clear the fractions

4f + 1 = - 14 ( subtract 1 from both sides )

4f = - 15 ( divide both sides by 4 )

f = - [tex]\frac{15}{4}[/tex]

Answer:

3% = 0.03 = [tex]\frac{3}{100}[/tex]

Answer: 3/100

Step-by-step explanation:

3%=0.03=3/100

Have a great day!!

Answer:

Orange juice

Step-by-step explanation:

The bottle of apple juice costs 3 dollars for 2 liters, and the bottle of orange juice costs 3.99 dollars for 3 liters. To see which bottle has the better deal, we need to make the liters the same so we can compare them.

We can divide the 2 liters for 3 dollars ratio by 2 to get that 1 liter of apple juice costs 1.5 dollars, and we can divide the orange juice ratio by 3 to get that 1 liter of orange juice costs 1.33 dollars. We see that for 1 liter, orange juice is cheaper, so it is the better deal.

Answer:

[tex]S_5=\dfrac{170}{9}[/tex]

Step-by-step explanation:

Given that,

The sum of first n term of a sequence is[tex]S_n=20-\dfrac{10}{2n-1}[/tex]

We need to find the sum of the first 5 terms.

Put n = 5,

[tex]S_5=20-\dfrac{10}{2(5)-1}\\\\=20-\dfrac{10}{10-1}\\\\=20-\dfrac{10}{9}\\\\=\dfrac{170}{9}[/tex]

So, the sum of first 5 terms is equal to [tex]\dfrac{170}{9}[/tex].

Answer:

i think its 10.5

Step-by-step explanation:

Answer:

David was 32 two years ago

Step-by-step explanation:

D = 2H + 4

H = 15

D = 30+4

D = 34

David was 32 two years ago

Answer:

Step-by-step explanation:

If cost price (CP) is greater than selling price (SP) , then the item is sold for loss.

Loss = CP - SP

Loss% = [tex]\frac{loss}{CP}*100[/tex]

If SP is greater than Cp, then the item is sold for a profit.

Profit =SP -CP

Gain % = [tex]\frac{gain}{CP}*100[/tex]

a)  CP = $50    ; SP = $30   ; CP > SP,  loss

Loss = 50 - 30 = $ 20

Loss % = [tex]\frac{20}{50}*100=20*2[/tex]

            = 40% loss

b) CP = £ 5000 ; SP = £6250  ; SP > CP ,  Profit

Profit = 6250 - 5000 = £ 1250

Profit % = [tex]\frac{1250}{5000}*100=25[/tex]

          25% Profit

Step-by-step explanation:

we don't see a picture, and you don't not give us any detailed information (all specific numbers like the scale factor are missing in your text). so, it is impossible to calculate anything.

but you can do it yourself very easily.

let's call the same factor "f".

that means you have to multiply the side lengths of every side of ABC by that factor f to get the cushions side lengths is the sides in DEF.

that's it.

that's all that has to be done.

so, assuming that A -> D, B -> E, C -> F

then

AB × f = DE

BC × f = EF

CA × f = FD

as I said - that's it. just use the actual numbers and multiply.

All the lengths of DE, EF, and DF are, 4 , 8 and 12 respectively.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

Triangle ABC and DEF are similar.

And, the scale factor from ABC to DEF is 2.

Now, We get;

This means that each side of the triangle ABC were multiplied by the scale factor 2 in order to get the triangle DEF.

Based on the above, you can set up the following equations;

⇒ DE = 2AB

⇒ EF = 2BC

⇒ DF = 2CA

Finally, substituting the corresponding lengths of the triangle ABC into the equations, and then evaluating, you get the following result:

⇒ DE = 2 x 2 = 4

⇒ EF = 2 x 4 = 8

⇒ DF = 2 x 6 = 12

Thus, All the lengths of DE, EF, and DF are, 4 , 8 and 12 respectively.

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ7

Answer:

i don't understand the question

Answer:

Correct answer B 130

Step-by-step explanation:

<FAE=90

<AFE=40

We have a triangle, so <FEA= 180-90+40=50

<FEA+FEB= 18-, so 180-50=130

AB parralel to CD then <ECD=130

Answer:

Step-by-step explanation:

The total distance = 1/6 + 3/8 miles Change the denominators to 24

D = 1/6 + 3/8 = 4*1/6*4 + 3*3 / 8 * 3

D = 4/24 + 9/24

D = 13/24 of mile.

Answer:

The measure of angle θ is 7π/4. The measure of its reference angle is 45°, and tan θ is -1.

Answered by GAUTHMATH

Answer:

Domain → (-∞, ∞)

Range → (-2, ∞)

Step-by-step explanation:

1). Domain of a function is defined by the input values (set of x-values) and Range of the function is defined by the output values (set of y-values).

From the graph attached,

Function is defined for all real values of x.

Therefore, domain of the function will be (-∞, ∞).

On y-axis values of the function vary from -2 (excluding 2) to positive infinity.

Therefore, range of the function will be (-2, ∞).

2). Average rate of change of a function in the interval (a, b) is defined by,

Average rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]

By using this expression we can find the average rate of change in the given interval.

Please give the correct interval for which the average rate of change is to be calculated.

Answer:

t ≈ 3.65 s

Step-by-step explanation:

Let the distance the object travels after leaving the balloon be x.

Using Newton's equation of motion, we have;

s = ut + ½gt²

We are given;

s = 30 m

u = -10 m/s (negative because it is an upward motion)

Thus;

30 = -10t + ½(10)t²

30 = -10t + 5t²

5t² - 10t - 30 = 0

Using quadratic formula, we have;

t ≈ 3.65 s

Answer:

[tex]x = 68[/tex]

Step-by-step explanation:

Sine are Cosine are Complementary Angles.

We can use this formula

[tex] \sin(x) = \cos(y) [/tex]

when x+y=90.

Add the expressions in the parentents to 90 and solve for x.

[tex]x - 20 + 42 = 90[/tex]

[tex]x + 22 = 90[/tex]

[tex]x = 68[/tex]

The answer is

[tex]x = 68[/tex]

Answer:25

Step-by-step explanation: Subtract 7 from 2, you get -5. then multiply both sides of the equation by -5 ( to make -1/5n to n) and you get n=25

Answer:

The answer is "[tex]\text{Total number of boxes} =\frac{a}{n \ boxes}[/tex]"

Step-by-step explanation:

Total pounds carried by the vehicle are "a" pounds.

This will be spread into many boxes, each containing "n" pounds.

It implies that:

[tex]\text{Total pounds = box number} \times \text{amount of pounds from every box} \\\\a = \text{box number} \times n\\\\\text{Box number} = \frac{a}{n \ boxes}[/tex]

1. How to find f(4)?

2. Substitution and Evaluate

[tex] \large{f(4) = - {(4)}^{2} - 6(4) + 12} [/tex]

Follow BODMAS/PEMDAS rules as well! Exponent first.

[tex] \large{ f(4) = - 16 - 24 + 12} \\ \large{f(4) = - 40 + 12} \\ \large{f(4) = -2 8}[/tex]

3. Final Answer

Answer:

volume of the sphere=4/3πr³

=4/3×3×2³

=32 feet³

Answer:

32 ft³

Step-by-step explanation:

Hi there!

[tex]V=\frac{4}{3} \pi r^3[/tex] where r is the radius

Plug in the given radius, 2 ft

[tex]V=\frac{4}{3} \pi (2)^3[/tex]

Plug in the given value of π, 3

[tex]V=\frac{4}{3} (3) (2)^3\\V=\frac{4}{3} (3) (8)\\V=(4)(8)\\V=32[/tex]

Therefore, the volume of the sphere is 32 ft³.

I hope this helps!

Answer:

[tex] {y}^{2} = - 2x + 5[/tex]

Step-by-step explanation:

vertex = [tex]( \frac{5}{2} \: ,0)[/tex]

Answer:

40°

100 + 80 = 180

60 + 80 = 140

140+ 40 = 180

Step-by-step explanation:

Answer:

m<C+m<D=100 degrees   m<D=40 degrees

Step-by-step explanation:

Answer:

13.95 units

Step-by-step explanation:

[tex] \sin \: 35 \degree = \frac{8}{x} \\ \\ \therefore \: x \: = \frac{8}{\sin \: 35 \degree} \\ \\ \therefore \: x \: = 13.9475744 \\ \\ \therefore \: x \: = 13.95 \: units[/tex]

Answer:

graph c

Step-by-step explanation:

it is the longest one

Answer:

$2.96

Step-by-step explanation:

Here, we want to get the expected value

To get the expected value, we have to multiply each payout by its corresponding probability and add up for all

So what this mean is that the expected value is the summation of the products of each pay out and their probability

We have the expected value calculated as;

0(0.12) + 1(0.2) + 2(0.38) + 5(0.2) + 10(0.1)

= 0 + 0.2 + 0.76 + 1 + 1 = $2.96

[tex]\displaystyle\bf 2^{2x+1}-9\cdot 2^x+4=0 \quad ; \qquad \boxed{ 2^x=t \; ; \; 2^{2x}=t^2} \\\\2t^2-9t+4=0 \\\\D=81-32 =49 \\\\ t_1=\frac{9+7}{4} =4 \\\\ t_2=\frac{9-7}{4} =\frac{1}{2} \\\\1) \ 2^x=4 \Longrightarrow x_1=2 \qquad 2) \ 2^x=2^{-1}\Longrightarrow x_2=-1 \\\\Answer: \boxed{x_1=2 \quad ; \quad x_2=-1}[/tex]

Answer:

x = sqrt(3)

Step-by-step explanation:

Use Thales theorem