Simplify the expression to a + bi form:
(-10 + 8i) - (-4 - 4i)

Answer:

Step-by-step explanation:

Given the question

A rope is 24 feet long. It is cut into two pieces such that one piece is half the length of the other. Find the lengths of the two pieces of rope.

Options

The stated solution is correct (lengths of 16 feet and 8 feet).

Based on the way the variable is defined, the equation should be x + 2x = 24.

The equation is written correctly, but there is an error in solving the equation.

The way the variable is defined, and because x=16, the longer piece of rope would be 32 feet, which is not possible.

2

Let the length of one piece be x (shorter piece) and the other be y.

If the rope is cut into two pieces and 24ft long, then;

x+y = 24.......... 1

If one piece is half the length of the other, then x = y/2..... 2

substitute equation 2 into 1

y/2 + y = 24

take the LCM

y+2y/2 = 24

3y/2 = 24

cross multiply

3y = 48

Divide both sides by 3;

3y/3 = 48/3

y = 16 feet

Since x = y/2

x = 16/2

x = 8 feet

Based on the calculation above, I can conclude that;

- The student stated solution is correct (lengths of 16 feet and 8 feet)

- The way the variable is defined, and because x=16, the longer piece of rope would be 32 feet, which is not possible.

- Based on the way the variable is defined, the equation should be x + 2x = 24.

Answer:

x > 3

Step-by-step explanation:

Answer:

pascal

Step-by-step explanation:

the unit of pressure is pascal or you can divde pounds and square inches in there units

Answer:

2

Step-by-step explanation:

3−2(x+1)=2x−7

3+(−2)(x)+(−2)(1)=2x+−7(Distribute)

3+−2x+−2=2x+−7

(−2x)+(3+−2)=2x−7(Combine Like Terms)

−2x+1=2x−7

−2x+1=2x−7

Step 2: Subtract 2x from both sides.

−2x+1−2x=2x−7−2x

−4x+1=−7

Step 3: Subtract 1 from both sides.

−4x+1−1=−7−1

−4x=−8

Step 4: Divide both sides by -4.

−4x−4=−8−4

x=2

Answer:

22.5

Step-by-step explanation:

:)

Answer:

The equation in a point-slope form that  represents their distance from

home, y miles, after x hours, is y - 110 = 55(x - 2)

Step-by-step explanation:

The point-slope form of the linear equation is

[tex]y-y_{1}=m(x-x_{1})[/tex] , where

m is the slope of the line (average)

[tex](x_{1},y_{1})[/tex] is a point on the line

→ The family is driving home  from vacation at an average speed

    of 55 miles per hour

∴ m = 55

→ After 2 hours they  are 110 miles from home

∵ x is the number of hours

∵ y is the distance in miles after x hours

∴ [tex]x_{1}[/tex] = 2

∴ [tex]y_{1}[/tex] = 110

→ Substitute these values in the form of the equation above

∴ y - 110 = 55(x - 2)

The equation in a point-slope form that  represents their distance from

home, y miles, after x hours is y - 110 = 55(x - 2)

Answer:

6 months

Step-by-step explanation:

120 +10x = 204 - 4x

10x + 4x = 204 - 120

14x = 84

x = 6

Answer:

15(iv) 68 units²

Step-by-step explanation:

Please see the attached picture for full solution. (Pictures 1 &2)

*I also did Q15 part (iii) by accident so I have also attached its working above if you need it. (Picture 3 and onwards)

Answer:

sor

Step-by-step explanation:

Answer:

10/10 - 7/10 = 3/10

Step-by-step explanation:

Muffins made = 12

Burnt muffins = 2

Good muffins = 12 - 2 = 10

Franco served 7/10 of the remaining muffins

Muffins served = 7/10 × 10

= 7

Muffins unserved = 10 - 7 = 3

Fraction of the non burned muffins remaining = non burned muffins - served muffins

= 10/10 - 7/10

= 3/10

The answer is B

Answer:

23.4m

Step-by-step explanation:

1 hour = 60 min

2.5 hours = 180 min

180 ÷ 10 =18

18 × 1.3 = 23.4

Answer:

The y intercept is (0,-3) The slope is 7/1 i think  

let's solve your equation step-by - step

-3-3/4(c-4)=5/4

Step 1: simplify both sides of the equation.

-3-3/4(c-4)=5/4

-3+-3/4 c+3=5/4 (distribute)

(-3/4 c)+(-3+3)=5/4 (combine like terms)

-3/4c=5/4

-3/4 c =5/4

Step 2: Multiply both sides by 4/(-3)

(4/-3)*(-3/4 c)=(4/-3)*(5/4)

Answer:c=-5/3

Answer:

[tex]-\frac{5}{3}[/tex]

Step-by-step explanation:

Hi there !

[tex]-3-\frac{3}{4}(c-4)=\frac{5}{4}\\ \\-3-\frac{3c}{4}+3=\frac{5}{4}\\ \\-\frac{3c}{4}=\frac{5}{4}\\ \\-3c=5\\\\3c=-5\\\\c=-\frac{5}{3}[/tex]

Good luck !

Step-by-step explanation:

#4: 156-120= 36

36÷4=9

Answer: B; 9 people per year

Step-by-step explanation:

#5: 84-60=24

24÷4=6

Answer: C; 6 degrees Fahrenheir per hour

Answer: x=−4

If I Helped, Please Mark Me As Brainliest, Have A Great Day :D

Answer:

5555665555555555555

Answer:

[tex](\frac{9}{2},-\frac{1}{2} )[/tex]

Step-by-step explanation:

Use the midpoint formula to find the midpoint of the line segment.

degree

The largest exponent in the polynomial is called the degree, and the coefficient of the variable raised to that exponent is called the leading coefficient. The constant in a polynomial has no variable written next to it.

Answer:

the answer is  5/8, 65%, 2/3, 0.7

Step-by-step explanation:

Answer:

11/25

Step-by-step explanation:

Answer:

2 mL³

Step-by-step explanation:

Use the density formula, D = m/v, where m is the mass and v is volume.

Plug in the mass and density, then solve for the volume:

D = m/v

6.2 = 12.4/v

6.2v = 12.4

v = 2

So, the volume is 2 mL³

Answer:

4910.8672217

Step-by-step explanation:

I dont have a step by step, i am so sorry

Answer:

4910.8672217

Step-by-step explanation:

Answer:

M1= 62 M2= 45 M3= 24

Step-by-step explanation:

For angle 1:

180-118 = 62

Angle 2:

180- (73+62)

Angle 3:

part 1

180-73= 107

part 2

180-(107+49)= 24

Answer:

Step-by-step explanation:

You have to solve for 1 before you do anything.

<1 + 118 = 180                The two left angles are supplementary

<1 +118-118=180-118

<1 = 62

Now you can go after angle 2

<1 + 73 + <2  =  180         All triangles have 180 degrees

62 + 73 + <2 = 180         Combine the left

135 + <2 = 180                Subtract 135 from both sides.

135-135+<2 = 180-135     Combine

<2 = 45

Angle 3 is a little trickier because the angle you need to find <3 is not labeled.

73 + x = 180

x = 180 - 73

x = 107

NOw you can find <3

107 + 49 + <3 = 180

156 + <3 = 180

<3 = 180 - 156

<3 = 24

I have left out the reasons for <3. Maybe you can supply them.

Answer:

(x-5)(x-6)

Step-by-step explanation:

when we look at something like this we have a, b, and c

a=1 (in front of x)

b=-11

c=30

our goal is trying to find factors of c that will give us b so in this case factors of 30 that will give us -11

so when you list all the factors of 30 you find that 6 and 5 both equal 30 when multiplied and add up to 11

but... we need -11 so if we change the signs both to negative that will give us a -11 when added and also a positive 30 when multiplied (-6)(-5)

so we then write it as (x-6)(x-5)

and if you FOIL that out you will end up getting the original equation :)

hope this helps!

Answer:

C. 1/4

Step-by-step explanation:

up 1, right 4