If a =-5i and b = -4x the value of a+b in the fully simplified form will be 5i-4x.
What is a complex number?It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.
It is given that,a =-5i and b = -4x
We have to find the value of a+b in a fully simplified form.
We have to apply the arithmetic operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
=a+b
= -5i-4x
Thus, if a =-5i and b = -4x the value of a+b in the fully simplified form will be 5i-4x.
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Given a polynomial and one of its factors, find the remaining factors of the polynomial. x^4 + 2x^3 – 8x – 16; x + 2
Answer:
The other factors are: [tex](x-2)[/tex] and [tex](x^2+2x+4)[/tex]
Step-by-step explanation:
Given
Polynomial: [tex]x^4 + 2x^3 - 8x - 16[/tex]
Factor: [tex]x + 2[/tex]
Required
Find other factors
[tex]x^4 + 2x^3 - 8x - 16[/tex]
Group into two
[tex]x^4 + 2x^3 - 8x - 16 = (x^4 + 2x^3) - (8x + 16)[/tex]
Factorize:
[tex]x^4 + 2x^3 - 8x - 16 = x^3(x + 2) -8 (x + 2)[/tex]
Factor out common term
[tex]x^4 + 2x^3 - 8x - 16 = (x^3 -8)(x + 2)[/tex]
Rewrite [tex]x^3- 8[/tex] as [tex]x^3 + 2x^2 - 2x^2+ 4x - 4x - 8[/tex]
[tex]x^4 + 2x^3 - 8x - 16 = (x^3 + 2x^2 - 2x^2+ 4x - 4x - 8)(x + 2)[/tex]
Rearrange the terms
[tex]x^4 + 2x^3 - 8x - 16 = (x^3 + 2x^2 + 4x - 2x^2 - 4x - 8)(x + 2)[/tex]
Factorize
[tex]x^4 + 2x^3 - 8x - 16 = (x(x^2+2x+4)-2(x^2+2x+4))(x + 2)[/tex]
Factor out [tex](x^2+2x+4)[/tex]
[tex]x^4 + 2x^3 - 8x - 16 = (x-2)(x^2+2x+4)(x + 2)[/tex]
So, the other factors are: [tex](x-2)[/tex] and [tex](x^2+2x+4)[/tex]
Ellen has a coupon for 1.55 off a loaf of bread. The regular price of bread is 4.63. The loaf is cut into 14 slices. What is the price per slice if Ellen uses her coupon?
Answer:
0.22 or 22 cents
Step-by-step explanation:
4.63 (original bread price) - 1.55 (coupon) = 3.08
divided by 14 slices of bread is 22 cents
Answer:
$0.22 per slice
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Apply the coupon to the loaf of bread first. $1.55 off a loaf of bread means subtracting this amount from the original price of bread.
$4.63 - $1.55 = $3.08If the loaf is cut into 14 slices, we should divide the loaf of bread's new price by 14.
$3.08 / 14 = $0.22The price per slice if Ellen uses her coupon is $0.22 per slice.
Thank you L for helping me w/ this question :)
b. After the 10th graduation
ceremony, how many total
graduates are there? Explain how
you determined your answer.
Answer:
chccucuxudhwhhwhsvahajw 10th g - ceremony
Without using a calculator, choose the statement that best describes the square root of
174.
Answer:
The square root of 174 with one digit decimal accuracy is 13.1.
Step-by-step explanation:
willie has 4 treasure chests which have a combined weight of 240 pounds. If each chest weighs at least 20 pounds what is the heaviest possible weight of one of the chests?
A. 177
B. 180
C. 217
D. 234
Answer:
B. 180
Step-by-step explanation:
There is a condition that each chest needs to be at least 20 pounds and we can use that to our advantage. Because we want one of the boxes to be really heavy, we need the other three to be really light. Let's set the heavy box as variable y. Set each of the other three boxes equal to 20. Because the combined weight is 240, then the equation so far is 240 = (20*3)+y.
Now, we can solve for y. 240-60 = 180, so the heaviest box has to be 180 lb.
What is a formula that can be used to find the area of one triangular section of the door how do you know the formula will work?
Answer:
[tex]Area = \frac{1}{2} L B[/tex]
Step-by-step explanation:
Given
See attachment for complete question
Required
Determine the formula of one of the triangular sections
From the attachment, we have that:
[tex]L = Length[/tex]
[tex]B = Height[/tex]
The area of the triangle is:
[tex]Area = \frac{1}{2} * L * B[/tex]
[tex]Area = \frac{1}{2} L B[/tex]
How to know the formula works?
From the attachment, we can see that the rectangle is divided into two equal triangular sections.
The area of the rectangle is:
[tex]Area = L* B[/tex]
[tex]Area = LB[/tex]
Because the rectangle is divided into two equal triangular sections.
This implies that, the area of one of the triangular sections is half the area of the rectangle.
So:
[tex]Area(Triangle) = \frac{1}{2}Area(Rectangle)[/tex]
Substitute LB for the area of the rectangle
[tex]Area(Triangle) = \frac{1}{2}LB[/tex]
By comparison:
[tex]Area(Triangle) = \frac{1}{2}LB[/tex] and [tex]Area = \frac{1}{2} L B[/tex] are the same
I need this questions done for my class, we went over this but I forgot. Can you guys say the answer and explain so I don’t forget again? Thank you so much!
1) 2/5 x 3 =?
Since we cannot possibly cancel the denominators, let us multiply 2 and 3.
Answer will become, 6/5.
2) 2/3x3 =?
We can cut 3 and 3.
Answer will become, 2.
3) 2/5 x 3=?
This is a repeated question and the answer remains the same as the 1st question's answer, 6/5.
4) 3/2 x 3=?
We cannot cancel the denominators, let us multiply 2 and 3.
Answer is, 9/2.
50 students were randomly sampled and asked if they preferred Coke or Pepsi. 12 preferred Pepsi. If there are 620 students in the school how many students would you expect in the entire school to prefer Coke?
Answer:
around 470 students would prefer coke
Step-by-step explanation:
50 - 12 = 38
38 / 50 = 76%
620 (0.76) = 471.2
decrease £220 by 15%
If we decrease £220 by 15% then it would be £187
What is percentage?"It is a number or ratio that can be expressed as a fraction of 100."
To find the percent of a number:x percent of number p is,
x% of p = p × (x/100)
For given example,
We need to decrease £220 by 15%
First we find the 15 percent of £220
15 percent of £220 is,
⇒15% of £220 = 220 × (15/100)
⇒15% of £220 = 220 × 0.15
⇒15% of £220 = £33
Now, we decrease £220 by 15%,
£220 - £33 = £187
Therefore, if we decrease £220 by 15% then it would be £187
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Mrs. Norman has 40 pairs of shoes. 6/8 of her shoes are sneakers. How many of her shoes are sneakers?
Answer:
30 of her shoes are sneakers
Step-by-step explanation:
40 divided by 8 = 5
5 x 6 = 30
hope this helps!
Answer:
30 of her shoes are sneakers
Step-by-step explanation:
you have to divide 40 by 8 which is 5 and 5 x 6 is 30 hope you have a great day
Nov 19 F
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Question Progress
Exam Paper Progress
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Grade For This Paper
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6006
YA
ad
Shape
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a) Use the * tool to plot the point
with coordinates (4, 1)
1
point
B
3
2.
1
b) Write down the coordinates of the
midpoint of AB.
4 -3 -2-10
- 1
1 2 3 4
(1
А
-3
-4
Total marks: 2
Answer:
l.mao you could just send a picture, it's a bit hard to actually answer any of the questions if it's jam-packed like that
Sonya added two rational expressions, and then simplified her answer. The simplified answer was x + 1. What are the missing values in her original expression?
Answer:
[tex]a = 2[/tex] and [tex]b = 4[/tex]
Step-by-step explanation:
Given
The expression is:
[tex]\frac{x^2 + ax - 4}{x + 2} + \frac{x + b}{x + 2} = x + 1[/tex] --- missing from the question
Required
Find a and b
Take LCM
[tex]\frac{x^2 + ax - 4+x + b}{x + 2} = x + 1[/tex]
Cross Multiply
[tex]x^2 + ax - 4+x + b = (x+2)*(x + 1)[/tex]
Open brackets
[tex]x^2 + ax - 4+x + b = x^2+2x + x + 2[/tex]
[tex]x^2 + ax - 4+x + b = x^2+3x + 2[/tex]
Collect Like Terms
[tex]x^2 + ax +x + b- 4 = x^2+3x + 2[/tex]
[tex]x^2 + (a +1)x + b- 4 = x^2+3x + 2[/tex]
By comparing the coefficients:
[tex]a + 1 = 3[/tex]
[tex]a = 3 - 1[/tex]
[tex]a = 2[/tex]
[tex]b - 4 = 2[/tex]
[tex]b = 4[/tex]
Hence,
[tex]a = 2[/tex] and [tex]b = 4[/tex]
Answer:
a = 2
b = 6
Edg 2021
A boat travels due north for 20km and then turns and travels due east for 7km. How far away is the boat from where it started?
Answer:
21
Step-by-step explanation:
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
(20)^2 + (7)^2 = [tex]c^{2}[/tex]
400 + 49 = [tex]c^{2}[/tex]
c= [tex]\sqrt{449}[/tex] = 21.1 ~ 21
(hope its right)
URGENT pls help will mark brainliest, 40 points
Answer:
14answer 3
15answer1
16answer1
PLZ HELP I NEED IT VERY MUCH THANK YOU BRAINLIEST AND % STARS THANK YOIU
Can someone help solve it
Answer:
C
Step-by-step explanation:
The answer is C (the third one)
Describe all numbers x that are at a distance of 4 from the number 9. Express this using absolute value notation.
Answer:
|x - 9| = 4
Step-by-step explanation:
All numbers x that are at a distance of 4 fro the number 9
Given two numbers a and B, the absolute distance between them is written as :
|a - b| = c
Hence all numbers x at distance of x from 9
|x - 9| = 4
{x : |x - 9| = 4}
a car cost $20000 when it was purchased. the value of the car decreases by 8% each year. find the rate of decay each month and select the correct answer below.
-0.6667%
-0.81%
-0.0067%
-0.6924%
Jack and Jane are married and both work. However, due to their responsibilities at home, they have decided that they do not want to work over 65 hours per week combined. Jane is paid $14 per hour at her job, and Jack is paid $10 per hour at his. Neither of them are paid extra for overtime, but they are allowed to determine the number of hours per week that they wish to work. If they need to make a minimum of $850 per week before taxes, what is the maximum amount of hours that Jack can work per week according to these limits?
By setting up a system of equations we can easily solve this problem. Let's denote Jane's working hours with x and Jack's working hours with y. Since they don't want to work more than 65 hours, the first equation is x+y=65. The second equation is 14x+7y=770. By solving this system of equation , we find that y=20 hours, which is Jack's maximum working hours.
HELP FAST DUE SOON Find the area of the parallelogram
Answer:
12 u^2
Step-by-step explanation:
The person below I think got the answer right.
The formula is area= base x height or a=bxh
Answer:
12u^2
Step-by-step explanation:
In one of the boxes, it tells you the formula for finding the area of a parallelogram. Area=base x height or A = b x h. The base is 6 units and the height is 2 units.
A = b x h
12 = 6 x 2
what is the slop of (5,2) and (-6,3)
Answer:
m = - [tex]\frac{1}{11}[/tex]
Step-by-step explanation:
Carl is boarding a plane. He has 2 checked bags of equal weight and a backpack that weighs 4 kg. The total weight of Carl's baggage is 35kg
Write an equation to determine the weight, w, of each of Carl's checked bags.
And the weight of each of Carl's check bags
Answer:
(35 - 4)/2 = w and 15.5kg
Step-by-step explanation:
To get the weight of both bags you would have to first subtract the backpack's weight from the total weight. 35 - 4 = 31. Now divide by 2 to get the weight of one bag. 31/2 = 15.5. Each bag weighs 15.5 kg
Convert 4 years into hours.
Hint: 1 non-leap year =8760 hours and 1 leap year=8784 hours. One out of every 4 years is a leap year.
Answer: 4 years =35.064 hour
Step-by-step explanation:
8760 multiplied by 3 is 26,280
add the year hours
26,280+ 8784 = 35,064 hours
Answer:
35064
Step-by-step explanation:
Please help!!!!
Which point is on the graph of f(x) = 6*?
O A. (1,6)
O B. (6,1)
O C. (0,6)
O D. (0,0)
Answer: A: (1, 6)
Step-by-step explanation:
Please help i will give brainliest
Answer:
-4.2, -3.5, -2.1, -1.5, -1, -0.5, 0.5, 3.5, 4.8
Step-by-step explanation:
Answer:
-4.2
-3.5,
-2.1,
-1
-1.5
-0.5
1
3.5,
4.8
Step-by-step explanation: Please feel free to point out if I'm wrong or if I missed any (i did spaces so you could see easier, also from top to bottom is least to greatest)
Sneezie's Tissues currently packages
tissues in a box shaped like a
rectangular pyramid with length 9
centimeters, width 5 centimeters, and
height 4 centimeters. The design team
would like to change the box to a
rectangular prism with the same base
and height. How many times greater
will the volume be when the box is
changed?
Answer:
3 timesStep-by-step explanation:
Volume of the pyramid:
V = lwh/3Volume of the prism:
V = lwhSince all dimensions remain as is, the volume of the prism is:
lwh / (lwh/3) = 3 times greaterThe Sides Of A Quadrilateral Are Shown Below . Express The Perimeter In Terms Of X .
Answer:
C
Step-by-step explanation:
Because the quadruple x is equal to 9
2. In the middle school band, there is 1 oboe for every 7 clarinets. Write three equivalent ratios to compare the oboes to the clarinets
1/7, 2/14, 3/21
I took the test
The three equivalent ratios to compare the oboes to the clarinets are,
⇒ 2 : 14
⇒ 3 : 21
⇒ 4 : 28
What is mean by Ratio?A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.
We have to given that;
In the middle school band, there is 1 oboe for every 7 clarinets.
Here, The ratio of the oboes to the clarinets is,
⇒ 1 : 7
Hence, Three three equivalent ratios to compare the oboes to the clarinets are,
⇒ 1 : 7
⇒ 1 / 7
⇒ 1×2 / 7×2
⇒ 2 / 14
And, 1 : 7
⇒ 1×3 / 7×3
⇒ 3 / 21
And, 1 : 7
⇒ 1×4 / 7×4
⇒ 4 / 28
The three equivalent ratios to compare the oboes to the clarinets are,
⇒ 2 : 14
⇒ 3 : 21
⇒ 4 : 28
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The equation -3x2 + 12x = 10 is rewritten in the form of -3(x - p)2 + g = 0. What is the value of q?
A.-22
B.2
C.22
D.134
Answer:
A
Step-by-step explanation:
-3(x-p)2+g=0
-3x2+12x=10
-3(x2-4x)=10
-3(x2-4x+4)=10+12
x2-4x+4 = (x-2)2
-3(x-2)2=22
-3(x-2)2-22=0
q = -22
please help!!!!!!!!!!
Answer:
5x+3
Step-by-step explanation:
Answer:
5x + 3 = y
Step-by-step explanation:
y represents the answer
3 more means +3
Product is the answer when two or more values are multiplied together.
So, three more than the product of 5 and x would be 5x + 3 = y