Mathematics College

Which expression is equivalent to 3i(4 + 7i)?

Answers

Answer 1
3i(4+7i)=3i*4+21i^2=12i-21  (i^2=-1)
Answer 2
the answer is 3i(4)+21i

I hope this helps

Related Questions

Which statements are true about the polynomial 28vw + 49v + 35w? Check all that apply.

Answers

Answer:

There are no common variables among all three terms.

The resulting expression when factoring out the GCF is 7(4vw + 7v + 5w).

Step-by-step explanation:

those r the two answers

Answer:

B & E

Step-by-step explanation:

Edg

What triangle has 0 reflectional symmetries?

Answers

Answer:

A. right scalene triangle

Final answer:

A triangle with 0 reflectional symmetries is a scalene triangle. Equilateral triangles, such as those on an icosahedron, have multiple symmetries. Symmetry in different contexts, like physics and chemistry, can result in a net effect of zero.

Explanation:

A triangle that has 0 reflectional symmetries is a scalene triangle, where all three sides and all three angles are of different lengths and magnitudes, respectively. An equilateral triangle, like the ones that form the faces of an icosahedron, has multiple lines of symmetry because of its equal sides and angles. On another note, in vector algebra, a null vector has all components equal to zero, which implies it has no direction or magnitude. Similarly, the molecular geometry of BF3 is described as trigonal planar and possesses symmetry, resulting in a net dipole moment of zero despite having polar B-F bonds.

In physics-related symmetry, charges or forces can cancel each other out leading to a net force of zero. For instance, if equal charges are placed at the corners of a square with a charge at the center, the net Coulomb force on the center charge will be zero due to the symmetry. Similarly, in collisions, certain angles or scenarios can result in a term becoming zero, like having a head-on collision where the incoming ball stops (v1 = 0), or the balls deflect at a 90-degree angle resulting in cos(θ1 - θ2) being zero.

What is the length of the segment with endpoints (-3,4) and (5,4)?

Answers

The answer is 8 units
Use phytagorean theorem to solve the problem.
l² = Δx² + Δy²

Δ means change. Δx means the change of x, and Δy means the change of y.
l² = (x₂ - x₁)² + (y₂ - y₁)²
l² = (5 - (-3))² + (4 - 4)²
l² = (5 + 3)² + 0
l² = 8²
l = 8

The length of the segment is 8

The sum of 2 numbers is 80. The ratio of the numbers is 3 to 5. Find the large number

Answers

larger : smaller = 5 : 3
larger : total = 5 : (3 +5) = 5 : 8

The total of 8 "ratio units" represents the sum 80, so each ratio unit represents 10. The larger number is 5 ratio units, so is 50.

an athlete is training to run a marathon. she plans to run 2 miles the first week. she increases the distance by 8% each week. which function models how far she will run in the nth week?

Answers

Pls tell me I'm having a quiz with my teacher


P.S.= She is really evil
She will run 2 miles first week.

Second week she will run 2 miles + extra 8%:
first_week + 8%*first_week

Third week she will run same distance as in second + extra 8% above what she ran in second week:
second_week + 8%*second_week

Fourth week she will run same distance as in third + extra 8% above what she ran in third week:
third_week + 8%*third week

By taking out common factors we get:
Week 1: 1*2 miles
Week 2: (1+0.08) * week1
Week 3: (1+0.08) * week2
Week 4: (1+0.08) * week3

We can see that each succesive week we multiply by 1.08.
Week 1: 1*2 miles
Week 2: (1+0.08) * week1
Week 3: (1+0.08) * (1+0.08)*  week1
Week 4: (1+0.08) * (1+0.08)* (1+0.08)* week1

If we use n for a number of week we can see that factor (1+0.08) appears n-1 times. We multiply this factor so we need to put n-1 in an exponent. 
Our function is given by:
[tex]d=2*1.08^{n-1} miles[/tex]
where n is number of a week

the graph shows y in direct variation with x. Find the value of Y when X=-15


A.) -30
B.) -24
C.)-18
D.) -12

Answers

y = 2x
y = 2*(-15) = -30 . . . . . selection A is appropriate

Answer:

A -30

Step-by-step explanation:

If you pay attention you will see I did this on USATestPrep and I know the answer

Mrs. reed baked four pans of lasagna for a family party. use the rectangles to represent the pans.

Answers

You should draw four rectangles to represent the four pans of lasagna.

the width of rectangle is 12cm less than the length . the perimeter is 156cm find the width and the length

Answers

P= perimeter= 156
L= length
W= width= L-12

P= 2(L + W)
plug in the information you know
156= 2(L + (L-12))
156= 2(2L-12)
multiply 2 by everything in parentheses
156= 4L-24
add 24 to both sides
180= 4L
divide both sides by 4
45 = L


W= L-12
W= 45-12
W= 33


Check:
P= 2(L + W)
156= 2(45+33)
156= 2(78)
156= 156

Hope this helps! :)

Kiera wanted to find the approximate number of historical books at the library she works at. She used the computer to randomly take a sample of 80 books and found that 6 of them were considered historical books. There are 21,360 books at this library. What is the best estimate of the amount of historical books at this library?

Answers

A sample of 80 books was taken randomly using a computer and 6 of them were considered to be historical books.

It means probability of sample would be 6 out of 80 i.e. P = 6 over 80 = 0.075 or 7.5%.

It says there are 21,360 books in the library, so Population would be 21,360 books. We can use outputs of the sample survey to represent complete collection of books in the library.

So best estimate of total historical books in the library would be 7.5% of total population.

Best estimate = 7.5% of 21,360

Best estimate = 0.075 x 21,360

Best estimate = 1602 books.

Hence, there are approximately 1602 historical books in the entire library.

The sum of a number divided by 8 and 7 is equal to 9 .

Answers

[tex]n-the\ number\\\\\dfrac{n}{8}+7=9\qquad\text{subtract 7 from both sides}\\\\\dfrac{n}{8}=2\qquad\text{multiply both sides by 8}\\\\\boxed{n=16}[/tex]

Tom Hornet purchases $7,000 of ten-year term life. He is 31 years old


What is his annual premium?

What is his quarterly premium?


The difference between the two payment options?

(Remember to compare annual premium to annual premium!) :

Answers

The annual premium is 5.07 x 7 = 35.49
The quarterly premium is 35.49 x .26 = 9.23
And the difference between the two payment options is 1.43
(Use the table in the question, it has all the information you need).

Answer:I can confirm 35.49, 9.23, 1.43

Step-by-step explanation:

In a circle with radius 4 cm the diameters AC and BD are perpendicular to each other. Prove that ABCD is a square. Find the area of ABCD.

Answers

This can be proven by using the Pythagorean theorem.    Draw a circle and label the radius 4 cm.  Then draw the diameters in to create a perpendicular intersection at the center.  If you then label the points that make the diameter, you will see that when connected they create right isosceles triangles.  a^2 + b^2 = c ^2, so 4 x 4 + 4 x 4 = c^2.  32 = c^2.  Because you are going to be multiplying it by itself to calculate the area, you have you answer of 32 square centimeters.  NO need to find the square root and them square it again!

Find the interest on the loan if you borrowed $2,000 at 8% for 1 year.

Answers

Future Value = Present Value*(1 + interest rate)^(# of years)

Future Value = $2,000(1+0.08)^1

Future Value = $2,000(1.08) = $2,160

To find the interest on the loan, we need to do our Future Value - Present Value.

Future Value - Present Value = $2,160 - $2,000 = $160

What is the solution to this inequality 2(x-4)+14<= x-1

Answers

2x - 8 + 14 <= x-1
2x +6 <= x-1
x <=-7

Convert the following measurements.
a. 2 cubic yards to cubic feet
b. 135 cubic feet to cubic yards
c. 6,912 cubic feet to cubic inches
d. 279,936 cubic inches to cubic feet

Solve the following addition problem. Remember to carry as necessary.

7 cu. yd. 9 cu. ft. 134 cu. in. + 1 cu. yd. 12 cu. ft. 200 cu. in.

Solve the following subtraction problem. Remember to borrow as necessary.

9 cu. yd. 113 cu. in. – 4 cu. ft. 129 cu. in.

Solve the following multiplication problem.

11 cu. yd. 17 cu. in. × 135

What’s the capacity of a 3 cubic foot carton in cubic inches?

The Great Pyramid was built in Egypt more than 4,000 years ago. It was built by King Khufu, or Cheops, who intended to use it as a tomb. The pyramid contains about 2,300,000 blocks of stone, each weighing 2 1⁄2 tons. Can you calculate the approximate total weight of the Great Pyramid, in pounds?

Convert the following liquid measures.
a. 5 gallons to pints
b. 128 tablespoons to fluid ounces
c. 93 pints to quarts
d. 13 quarts to cups
e. 69 teaspoons to tablespoons
f. 112 cups to gallons
g. 18 fluid ounces to teaspoons
h. 3 gallons to fluid ounces

A local dairy farmer collects 490 gallons of milk a day from his cows. He keeps 1⁄35 of the milk for his own use, and sells the rest. Each quart of milk sells for 35 cents. In dollars, how much does he earn from selling his milk each day? (There are 100 cents in a dollar.)

A swimming pool has a capacity of 1,386 cubic feet. One gallon of water will fill 231 cubic inches of space. How many gallons of water will it take to fill the entire pool? (Hint: Convert the capacity of the pool to cubic inches first.)

The instructions on a bottle of laundry detergent tell you to add two capfuls of detergent to each gallon of water. One capful of detergent is equal to about one tablespoon. If your washing machine holds 11 gallons of water, how many tablespoons of detergent will you need to add? How many fluid ounces of detergent?

Convert the following dry measurements.
a. 11 bushels to quarts
b. 3 pecks to pints
c. 97 quarts to bushels
d. 1,120 quarts to pecks

Twelve apple pies can be made from one bushel of apples. How many apple pies can be made from one peck of apples?

Mr. Osaka sprinkles 1.694 pints of dry, powdered plant food on his garden three times a year. In quarts, what’s the total amount of plant food he uses in one year?

Answers

1) Convert the following measurements.
a. 2 cubic yards to cubic feet
1 cubic yard-------- > 27 cubic feet
2---------------------- X
x=2*27=54 cubic feet

b. 135 cubic feet to cubic yards
1 cubic yard-------- > 27 cubic feet
x----------------------- 135
x=135/27=5 cubic yard

c. 6,912 cubic feet to cubic inches
1 cubic feet--------------- > 1728 cubic inches
6912 cubic feet------------- x
x=11943936 cubic inches

d. 279,936 cubic inches to cubic feet
1 cubic feet--------------- > 1728 cubic inches
x------------------------------ 279,936 cubic inches
x=162 cubic feet

2) Solve the following addition problem. Remember to carry as necessary.

7 cu. yd. 9 cu. ft. 134 cu. in. + 1 cu. yd. 12 cu. ft. 200 cu. in.
7 cu. yd
9 cu. ft-------- > 9/27=0.33333 cu yd
134 cu. in-----> 134*2.1433e-5=0.00287
1 cu. yd
12 cu. ft------- 12/27=0.44444 cu yd
200 cu. in----200*2.1433e-5=0.00429 cu yd

(7+0.33333+0.00287)+(1+0.44444+0.00429)=8.78493 cu yd

3 Solve the following subtraction problem. Remember to borrow as necessary.

9 cu. yd. 113 cu. in. – 4 cu. ft. 129 cu. in.
9 cu yd
113 cu in---------113*2.1433e-5=0.00242 cu yd
4 cu. ft--------4/27=0.14814 cu yd
129 cu. in----------129*2.1433e-5=.00276
(9+0.00242)-(0.14814+.00276)=8.85152 cu yd

4 Solve the following multiplication problem.

11 cu. yd. 17 cu. in. × 135
11 cu yd
17 cu in----------17*2.1433e-5=0.00036 cu yd

(11+0.00036)*135=1485.0486 cu yd

5 What’s the capacity of a 3 cubic foot carton in cubic inches?
3 cu feet---------> 3*1728=5184 cu in

6 The Great Pyramid was built in Egypt more than 4,000 years ago. It was built by King Khufu, or Cheops, who intended to use it as a tomb. The pyramid contains about 2,300,000 blocks of stone, each weighing 2 1⁄2 tons. Can you calculate the approximate total weight of the Great Pyramid, in pounds?
2 1/2=(4+1)/2=5/2=2.5
weight=2,300,000*2.5=5750000 ton-------> *2204.62=12676565000 lb

7 Convert the following liquid measures. 
a. 5 gallons to pints ------*8=40 pints
b. 128 tablespoons to fluid ounces -----*0.5=64 fluid onces
c. 93 pints to quarts --------*0.5=46.5 quarts
d. 13 quarts to cups ---*4=52 cups
e. 69 teaspoons to tablespoons---------*0.3333=23 tablespoons
f. 112 cups to gallons--------*0.0625= 7 gallons
g. 18 fluid ounces to teaspoons---------*6=108 teaspoons
h. 3 gallons to fluid ounces-----*128= 384 ounces

8 A local dairy farmer collects 490 gallons of milk a day from his cows. He keeps 1⁄35 of the milk for his own use, and sells the rest. Each quart of milk sells for 35 cents. In dollars, how much does he earn from selling his milk each day? (There are 100 cents in a dollar.)

(34/35)*490=476 gallons to sell------------> *4=1904 quarts
1904*0.35=666.40 dollars

9 A swimming pool has a capacity of 1,386 cubic feet. One gallon of water will fill 231 cubic inches of space. How many gallons of water will it take to fill the entire pool? (Hint: Convert the capacity of the pool to cubic inches first.)
1,386 cubic feet----------> *1728=2395008 cu in
1 gallons will fill --------------- > 231 cu in of space
x--------------------------------- 2395008 cu in
x= 10368 gallons 

10 The instructions on a bottle of laundry detergent tell you to add two capfuls of detergent to each gallon of water. One capful of detergent is equal to about one tablespoon. If your washing machine holds 11 gallons of water, how many tablespoons of detergent will you need to add? How many fluid ounces of detergent?

2 capfuls of detergent-----------> 1 gallon of water----------> 2 tablespoon
                                                    11--------------------------- > X

x=11*2=22 tablespoon
22 tablespoon-----------------> *0.5=11 fluid onces

11 Convert the following dry measurements.
a. 11 bushels to quarts -------*37,2367=409.60 quarts
b. 3 pecks to pints---------*18.6184=55.85 pints
c. 97 quarts to bushels ------ *0.02685=2.6044 bushels
d. 1,120 quarts to pecks--------* 0.107421=120.31 pecks

12 Twelve apple pies can be made from one bushel of apples. How many apple pies can be made from one peck of apples?
1 peck---------> *0.25=0.25 bushel

12 apple pies-------------- > 1 bushel
x---------------------------------0.25 bushel
x=0.25*12=3 apple pies

13 Mr. Osaka sprinkles 1.694 pints of dry, powdered plant food on his garden three times a year. In quarts, what’s the total amount of plant food he uses in one year?

1.694 pints*3=5082 pints in one year--------------> *0.5=2541 quarts


A number devised by six is 306. What is the number?

Answers

306 × 6 = the number

306 × 6 = 1836

In the regular nonagon shown, what is the measure of angle x?

Answers

The answer is 45 hope this helps

I cant see any nonagons sorry.

Melinda rents paddle boats down at the pier. She uses 5.5 feet of nylon rope to tie off each boat. She started with 80 feet of rope. After securing all the boats, she was left with more than 3 feet of rope. How many boats did Melinda tie off?

Answers

First write an expression for the problem:
b= boats
80-5.5b > 3
-5.5b > -77
(divide both sides of the in equality by -5.5)
NOTE: when you divide in equalities by negatives you MUST FLIP THE SIGN!

b < 14

boats= less than 14 boats in order to have greater than 3ft of rope left.

Answer: 
Melinda must have tied off less than 14 boats.

Let me know if you still have any questions!

Answer: Less than 14

Step-by-step explanation: My teacher helped me on this problem and i got less then 14 and i submitted it and it was right i really this helped

I = $1,200 * 8/100 * 240/360 =

Answers

The correct answer is:

$64.

Explanation:

We will mulitiply the first two numbers first.

We will first write 1200 as a fraction by putting it over 1:
1200/1 * 8/100.
We now multiply straight across: (1200*8)/(1*100) = 9600/100 = 96.

Now we will multiply this by the last fraction. Again we will make the whole number, 96, a fraction by placing it over 1:
(96/1)*(240/360).

Again we multiply straight across: (96*240)/(1*360)=23040/360.

When we divide this out, we get 64.

Answer:

$ 64

Step-by-step explanation:

I=$ 1200×8/100×240/360

Which could also be written as:

I=

[tex]1200\times \dfrac{8}{100}\times \dfrac{240}{360}\\ \\= 12\times 8\times \dfrac{24}{36}\\ \\=12\times 8\times \dfrac{2}{3}\\ \\=4\times 8\times 2[/tex]

=$ 64

The length of the longer leg of a right triangle is 19ft more than five times the length of the shorter leg. the length of the hypotenuse is 20ft more than five times the length of the shorter leg. find the side lengths of the triangle.

Answers

Let x represent the length of the shorter leg.

Longer leg: 5x +19
Hypotenuse: 5x +20

Pythagorean theorem:
.. x^2 +(5x +19)^2 = (5x +20)^2
.. x^2 +25x^2 +190x +19^2 = 25x^2 +200x +20^2 . . . . . . eliminate parentheses
.. x^2 -10x -39 = 0
.. (x -13)(x +3) = 0
.. x = 13 . . . . . . . . . . leg lengths must be positive

The side length of the triangle are 13, 84, 85 feet.
Final answer:

This problem can be solved by creating and solving a quadratic equation based on the Pythagorean theorem. We denote the length of the shorter leg as 'x', and substitute '5x+19' and '5x+20' as lengths of the longer leg and hypotenuse in the theorem.

Explanation:

The entire problem revolves around the application of the Pythagorean theorem, which in a right-angled triangle gives the relationship a² + b² = c², were a and b are the lengths of the shorter sides (legs) and c is the length of the longest side (hypotenuse).

Let's denote the length of the shorter leg as 'x'. From the problem, we know that the longer leg is 5x+19 and the hypotenuse is 5x+20. Using the Pythagorean theorem, we have:

((5x+19)² + x²) = (5x+20)².

You can solve this equation to find out the value of 'x', following which you can substitute this value back into 5x+19 and 5x+20 to find lengths of the longer leg and hypotenuse.

Learn more about Pythagorean theorem here:

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SOMEONE HELP ME PLEASE?????????????????????????????????????????????????

Which sentence contains a punctuation error?

One-quarter cup of chocolate chips does not seem like enough.

She is a well known basketball player.

This well-known recipe is the one I always use for oatmeal cookies.

He bakes loaves of the best-tasting bread we have ever eaten.

Thanks for helping.

Answers

He bakes loaves of the best-tasting bread we have ever eaten 

has a error 


The 4th sentence has a mistake

how many eggs are there in 4 1/4 dozen eggs?

Answers

51 eggs because there are 12 eggs in a dozen so it would be 4×12 which would be 48 and then 1/4 of 12 is 3 so 48+3=51

herman draws a scale model of one-half of the side house based on hermans scale model,what is the actual area of the entire side of the house?

Answers

The actual area of the entire side of the house is four times the area of Herman's scale model, as Herman's model represents only one-half of the side. So, if the area of Herman's model is A, then the actual area is 4A.

To find the actual area of the entire side of the house based on Herman's scale model, we need to follow these steps:

Understand the Scale: If Herman's scale model represents one-half of the side of the house, it means the scale is 1:2. This implies that every unit on the scale model represents two units in reality.

Find the Area of Herman's Model: Let's assume the area of Herman's scale model is A. Since it represents one-half of the side of the house, the actual area of one side of the house (let's call it X) would be 2A.

Calculate the Total Area of the Side of the House: Since there are two sides to a house, we need to double the area of one side: 2 * 2A = 4A.

Finalize the Answer: Therefore, the actual area of the entire side of the house is 4 times the area of Herman's scale model.

In summary, to find the actual area, we first double the area of Herman's scale model (as it represents only one-half of the side), then multiply it by 2 again to account for both sides of the house. This gives us a total of 4 times the area of Herman's model.

Here's the complete question:

"Herman draws a scale model of one-half of the side of a house. Based on Herman's scale model, what is the actual area of the entire side of the house?"

A wedding cake has a diameter of 12 inches. The cake decorator needs to know how many strawberries he will need to put around the outside, so he needs the circumference. What is the circumference? Leave the answer in terms of π.

Answers

Diameter = 12 in

Radius = 6 in

Circumference = 2[tex] \pi r[/tex] = 2 x [tex] \pi [/tex] x 6 = 12[tex] \pi [/tex] inches

In a circle with a radius of 3 ft, an arc is intercepted by a central angle of 2π3 radians. What is the length of the arc?
2π ft
​ 3π ​ ft
​ 6π ​ ft
​ 9π ​ ft

Answers

the correct question is 
In a circle with a radius of 3 ft, an arc is intercepted by a central angle of 2π/3 radians. What is the length of the arc? 

we know that
in a circle
2π radians -----------------> lenght of (2*π*r)
2π/3 radians--------------> X
X=[(2π/3)*(2π*r)]/[2π]=(2π/3)*r

 the lenght  of the arc=(2π/3)*3=2π ft

the answer is 2π ft




Answer:

The correct answer is 2π ft.

Step-by-step explanation:

Verified by correct test results.

An engineer is planning a new water pipe installation. The circular pipe has a diameter of d=20cm.
What is the area A of the circular cross section of this pipe?
Give your answer in terms of pi.
HELP

Answers

we know that
the area A of the circular cross section of the pipe is
A=pi*r²
D=20 cm------------- > r=D/2=20/2=10 cm
then
A=pi*10²=100*pi cm²

the answer is A=100*pi cm²

A square pyramid has a base area of 64ft2. The pyramids total surface area is 224ft2. What is the area of each triangular face?

Answers

check the picture below.

now the base has an area of 64 ft², as shown on the picture a 8x8 base, the total surface area, meaning the triangular faces area plus the base, we know is 224 ft².

well, what's the area of the triangular faces anyway?  well, if we just subtract hte base from the total surface area, what we're left with, is the lateral area, namely the area of the triangular faces only, 224 - 64.

now, there are four equal triangular faces, divide that by 4, and that's the area of one of them, (224 - 64) / 4.

Mary had some cookies.she gave 2/9 of them to matthew and ate 1/3 of them. she had 8 cookies left. how many did she have at first?

Answers

2/9 + 3/9 = 5/9. If 4/9 is eight cookies than 5/9 is 10. So, she had a total of 18 cookies to begin with
Final answer:

Mary originally had 18 cookies. This is determined by creating and solving a ratio based on the fractions of cookies Mary had left after giving some away and eating some.

Explanation:

The subject of this question is mathematics and it involves fractions. We can think of Mary's original number of cookies as 1 whole or 100%. We're told she gave away 2/9 of them and ate 1/3 of them, which means she hasn't touched 1 - 2/9 - 1/3 of the cookies.

First, we calculate the common denominator, which is 9. So, we must convert 1/3 to 3/9. Now, we have 1 whole - 2/9 - 3/9. This addition simplifies to: 9/9 - 2/9 - 3/9 = 4/9.

The 4/9 is equal to the 8 cookies she has left over. To find the original amount of cookies, we set up the following ratio: 4/9 = 8/x. Solve this ratio for x (which represents Mary's original number of cookies) by cross multiplying: 4x = 72. Divide both sides by 4 to get: x = 18 cookies.

Learn more about Fractions here:

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How do you write 4.5 with the same number of decimal places as 6.25

Answers

4.50 should be the right answer.
if you mean you want to have it go into the hundredths place (the second digit behind the period) you could just add a zero. the zero's dont change the number but help you incase your doing something like 9.75 - 8.5 just add a zero and you would get 9.75 - 8.50 = 1.25 
i hope this helps you :)

Estimate it’s the length in meters for poster. Explain

Answers

I don’t know what this question is asking.... can u make it clearer
Other Questions
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