Option d is correct, ,[tex]ac+ad+ae+bc+bd+be[/tex] is the equivalent expression of [tex](a+b)(c+d+e).[/tex]
The expression [tex](a+b)(c+d+e)[/tex] can be expanded using the distributive property.
We multiply each term in the first set of parentheses by each term in the second set of parentheses and combine like terms.
[tex](a+b)(c+d+e) = a(c+d+e) + b(c+d+e)[/tex]
Expanding further:
[tex](a+b)(c+d+e) = ac + ad + ae + bc + bd + be[/tex]
Hence,[tex]ac+ad+ae+bc+bd+be[/tex] is the equivalent expression of [tex](a+b)(c+d+e).[/tex]
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Form a third-degree polynomial function with real coefficients, with leading coefficient 1, such that - 2 + i and 7 are zeros.
In standard form, this third-order polynomial - call it p(x) - has real coefficients a, b, c, d so that it is written as
p(x) = a x ³ + b x ² + c x + d
We're told the leading coefficient is a = 1, so
p(x) = x ³ + b x ² + c x + d
Since the coefficients are all real, any complex roots with non-zero imaginary part occurs alongside its complex conjugate, so the fact that -2 + i is a root means that its conjugate, -2 - i is also a root.
Then by the factor theorem, we can write p(x) as the product of linear terms involving its roots:
p(x) = (x - (-2 + i )) (x - (-2 - i )) (x - 7)
Now just expand this to get
p(x) = x ³ - 3 x ² - 23 x - 35
a computer store sells six different computers four different monitors five different printers and three different multimedia packages how many different computer systems are available?
please help this is urgent
Answer:
Im pretty sure its 18.
Step-by-step explanation:
Using the Fundamental Counting Theorem, it is found that 360 different computer systems are available.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
In this problem, the store sells six different computers four different monitors five different printers and three different multimedia packages, hence the parameters are [tex]n_1 = 6, n_2 = 4, n_3 = 5, n_4 = 3[/tex], and the number of systems is:
[tex]N = 6 \times 4 \times 5 \times 3 = 360[/tex]
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This is your chance to demonstrate your basketball skills! You have been chosen to participate in a paper-ball throwing contest. Directions: 1. Use the scrap paper to make 10 paper balls per group. (Wad the paper balls up tightly so they are easier to aim.) 2. Place a trash can (or other large container) 5 feet away. 3. Predict how many paper balls you will be able to get into the basket. Type your prediction. 4. Type your results as a fraction. 5. Type your results as a decimal.
Answer:
I Predict I can make all 10/10 paper balls into the trash can.
Step-by-step explanation:
Sadly, I was wrong, I only got 8 paper balls into the trash can...Its not my fault though, my cat kept attacking my midair balls, anyway I got 8/10 which means I got 80 percent which means I got...move decimal one left...I got (in decimal) .8 (I'm ticked that I missed any cat or no cat, My fav sport is basketball and usually in really good with my shots)
HELP me please with 9,10,11,12
Answer:
9.) The Outlier is 18
-The outlier is the number that stands out and is different
Evaluate the expression shown below and write your answer as a fraction in simplest form.
Answer:
33/4=8.25 or 8 1/4
Step-by-step explanation:
Solve for x. Round to the nearest tenth!
Answer:
x=1.7
Step-by-step explanation:
sin20=x/5
x=5sin20
x=1.7
Kathy gets to school at 8.20 a.M every day.It takes her 12 minutes to get from her house.Kathy wants to get to school 15 minutes earlier what time should kathy leave her house?
Answer:
7:53
Step-by-step explanation:
subtract 15 minutes from the time she arrives.
you get 8: 05 a.m. the distance from home to school is 12 minutes to reach at 8:0 5 subtract 12 minutes to know what time she'll leave...
if you remove 12 minutes from 8 or 5 a.m. get 7:53 a.m.
Sheldon is a long distance runner. He can run a mile at a consistent pace of 6 4/5 minutes. How many miles can he run in 30 minutes, if he keeps that pace? miles. please put as fraction
Answer:
n
Step-by-step expmlanation:
Answer:
10-15 miles I believe
convert 10 hours into minutes
Answer:
600 minutes
Step-by-step explanation:
60 minutes in an hour
60 × 10 is 600
Find the value of x
140
5x
80"
O A. 12
OB. 16
O C. 18
O D. 28
Answer:
o d. 28
Step-by-step explanation:
how many students must be enrolled for the teacher to make 1,000 profit per month
Answer:
20
Step-by-step explanation:
AABC is dilated by a factor of to produce AA'B'C! 3 What is A'B' , the length of AB after the dilation? What is the measure of 24? A. AB = 68, MZA= 28" B. AB'= 15, mZA= 62 C. ABP = 17, m.ZA'= 14° D. A'B'= 17, mAA'= 28.
ILL MARK BRANLIEST
Answer:
a it is a because u can see it
If f (2) = 2x2 + 3x – 9 and g(x) = 3x2 + 8 find (f + g)(x)
Answer:
3x² + 13
Step-by-step explanation:
f(2) = 2(2)² + 3(2) - 9 = 8+6-9 = 5
g(x) = 3x² + 8
added together: 3x² + 8 + 5 = 3x² + 13
if one zero of the following polynomial 8x^2-13x-4k is the reciprocal of the other, then find k
Answer:
Step-by-step explanation:
hello :
if x1 and x2 this zero for ax²+bx+c you have : x1 = 1 /x2 means :x1 × x2 =1
but : x1 × x2 = c /a
in this exercice : a =8 and b = -13 and c = - 4k
so : c/a =-4k/8
so : -4k/8 = 1
-4k = 8 k = 8/-4 k = -2
this polynomial is : 8x²-13x +8
A box is shaped like an octagonal prism. Here is what the base of the prism looks like. If the height of the box is 7 inches, the volume of the box will be [1] cubic inches.
Answer:
The volume of the box is 33.796 cubic inches
Step-by-step explanation:
Given
[tex]Height = 7in[/tex]
See attachment for the base of the prism
Required
The volume of the box
From the attachment, we have:
[tex]a = 1in[/tex] -- side length of the octagon
The area is then calculated as:
[tex]Area = 2 * (1 + \sqrt 2)a^2[/tex]
So, we have:
[tex]Area = 2 * (1 + \sqrt 2)* 1^2[/tex]
[tex]Area = 2 * (1 + \sqrt 2)* 1[/tex]
[tex]Area = 2 * (1 + \sqrt 2)[/tex]
Evaluate the square root
[tex]Area = 2 * (1 + 1.414)[/tex]
[tex]Area = 2 * (2.414)[/tex]
[tex]Area = 4.828[/tex]
The volume is then calculated as:
[tex]Volume = Height * Base\ Area[/tex]
[tex]Volume = 7 * 4.828[/tex]
[tex]Volume = 33.796[/tex]
Answer:
287 is the right answer
Step-by-step explanation:
Hopes this helps.
2x – y = 7
y = 2x + 3
Answer:
2x – y = 7 answer for this one is x-1/2y+7/2 (the '/' is a fraction)
y = 2x + 3 is x=1/2y+-3/2
Step-by-step explanation:
IS A RIGHT ??! PLZ HELP ASAP !!
Answer:
I think so
Step-by-step explanation:
Please mark brainliest and I will give you a good report
If p and q vary directly and p is 30 when q is 6, determine q when p is equal to 9.
Answer:
here is the link the.hh/g49
Step-by-step explanation:
Answer:
q = 45
Step-by-step explanation:
Since q is 30 when p is 6, we divide to find the rate.
30/6=5.
If the rate is 5 we multiply the new p, 9 by five as well.
9*5=45
45 is q ok
help now pls thank u
Answer:
120 inches of strands
Step-by-step explanation:
finding the diagonal
=[tex]\sqrt{(100+576)}[/tex]
= 26 inches
perimeter of the window = 2(10+24)
= 68 inches
total strands needed to be purchased = [(2×26)+68] inches
= 120 inches of strands
For the experiment of drawing a single card
from a standard 52-card deck. Find (a)
the probability and (b) the odds in favor
of each of the following:
1. An Ace
2. A red Jack
3. An Ace or a Club
4. Not a heart, or a 7
Answer:
what do you mean? can you please explain this better so i can help you? :)
Step-by-step explanation:
Matthew invested $4,700 in an account paying an interest rate of 3 3/8% compounded
monthly. Peyton invested $4,700 in an account paying an interest rate of 3 1/4%
compounded continuously. After 14 years, how much more money would Matthew
have in his account than Peyton, to the nearest dollar?
Answer:
$126
Step-by-step explanation:
We solve using Compound Interest formula
For Matthew
Matthew invested $4,700 in an account paying an interest rate of 3 3/8% compounded monthly.
P = $4700
R = 3 3/8 % = 3.375 %
t = 14 years
n = Compounded Monthly = 12
Hence,
First, convert R as a percent to r as a decimal
r = R/100
r = 3.375/100
r = 0.03375 rate per year,
Then solve the equation for A
A = P(1 + r/n)^nt
A = 4,700.00(1 + 0.03375/12)^(12)(14)
A = 4,700.00(1 + 0.0028125)^(168)
A = $7,533.80
For Peyton, we are using a different compound interest formula because it is compounded continuously
Peyton invested $4,700 in an account paying an interest rate of 3 1/4%
compounded continuously.
P = $4700
R = 3 1/4 % = 3.25%
t = 14 years
n = Compounded continuously
First, convert R as a percent to r as a decimal
r = R/100
r = 3.25/100
r = 0.0325 rate per year,
Then solve the equation for A
A = Pe^rt
A = 4,700.00e^(0.0325)(14)
A = $7,408.01
After 14 years, the amount of money Matthew would have in his account than Peyton, to the nearest dollar is calculated as:
$7,533.80 - $7,408.01
= $125.79
Approximately = $126 to the nearest dollar
Answer:
126
Step-by-step explanation:
126 to the nearest dollar
Solve for the value of x! Please help don’t use this just for points
Answer:
x=3
Step-by-step explanation:
If all of the angles and sides are congruent, then you would just subtract 7 by 4 and get 3 for x.
5. A standard-size volleyball court has an area of 1,800 square feet. The base of the court is 60 feet. What is the height of the court?
Answer:
30 feet
Step-by-step explanation:
The area is found by multiplying the base and the height. So to find the answer, you divide 1,800 by 60 to get 30.
Quadrants on the coordinate plane Select the quadrant or axis where each ordered pair is located on a coordinate plane. Quadrant Quadrant II Quadrant III Quadrant IV I-axis y-axis (-9.-8) (1.0) (7.5.2 Stuck? Watch a video or use a hint. Report a problem
Answer:
lll
Step-by-step explanation:
4. Car types 318 words in 3 minutes. At this rate, how many words does Carl type in 5 minutes?
The image of (2, - 1) after a translation of (x, y) + (x -1, y+3) is
What's the solution ?
5^3x=25^(x+2)
there is no solution
A circle has a diameter of 42 inches. What is the circumference of the circle? Use 227 for π.
Answer:
132 in = C
Step-by-step explanation:
Please, write 22/7 to approximate π.
The circumference formula is C = 2πr or dπ, and here C = (42 in)π
Then an approximation to the circumference of this circle is
42(22/7) = 6(22 in) = 132 in = C
Please help! - Geometry - 15 points - One question -
Answer: m<DCB= 50 degrees
Step-by-step explanation:
120= (15x+5)+(22x+4)
120= 37x+9
111= 37x
x=3
15(3)+5
45+5=
50
Which of the following inequalitties is correct
-a > -b
-a > a
a > c
(Look at picture)
Answer:
You were right the correct option is
- a > - b