Answer:
a = 2
b = - 6
c = 0
Step-by-step explanation:
Since, -3,0 and 2 are the zeroes of the polynomial
[tex] Plug \:x = 0\: in \:p(X) \\
\implies p(0)= 0\\
\therefore 0= 0^3 +(a-1)(0)^2 +b(0)+c\\
\therefore 0= 0 +(a-1)\times 0 +b(0)+c\\
\therefore 0= 0 +0+0+c\\
\red{\bold{\therefore 0=c}}.....(1)\\\\
p(X)=x³+(a-1)x²+bx+c. \\
Plug \:x = -3\: in \:p(X) \\
[tex] \implies p(-3)= 0\\
\therefore 0= (-3)^3 +(a-1)(-3)^2 +b(-3)+c\\
\therefore 0= -27 +(a-1)\times 9 +b(-3)+c\\
\therefore 0= - 27 +9a-9 - 3b+c\\
\therefore 0= - 36+9a-3b+c\\
\therefore 36 =9a-3b+c... (2)\\
Plug \:c= 0\: in \:equation \: (2)\\
36= 9a - 3b + 0\\
36= 9a - 3b\\
36= 3(3a - b) \\
\purple {\bold{12 = 3a - b}} .... (3)\\\\
Plug \:x = 2\: in \:p(X) \\
\implies p(2)= 0\\
\therefore 0= 2^3 +(a-1)(2)^2 +b(2)+c\\
\therefore 0= 8 +(a-1)\times 4 +b(2)+c\\
\therefore 0= 8 +4a-4+2b+c\\
\therefore 0= 4 +4a+2b+c\\
\therefore - 4=4a+2b+c.....(4)\\
Plug \:c= 0\: in \:equation \: (4)\\
- 4 = 4a +2b+0\\
-4= 2(2a+b)\\
\orange{\bold{-2=2a + b}} .......(5)\\\\[/tex]
Adding equation (3) and (5), we find:
12 = 3a - b
-2 = 2a + b
_________
10 = 5a
10/5 = a
a = 2
Plug a = 2 in equation (5)
-2= 2(2) + b
-2 = 4 + b
-2 - 4 = b
-6 = b
b = - 6
Find the value of x. Use the photo I uploaded to help plz.
A. X=2
B. X=3
C. X=33
D. X=52
PLEASE ANSWER FAST
Answer like
number 1. answer is _________________
number 2. answer is _________________
number 3. answer is _________________
number 4. answer is _________________
number 5. answer is _________________
Answer:
number 1. answer is 561%
number 2. answer is 1
number 3. answer is 7/80
number 4. answer is 31.25%
number 5. answer is 60%
Step-by-step explanation:
hope this helps!
Answer:
1. 561%
2. 1
3. 7/80
4. 31.25%
5. 6%
Step-by-step explanation:
To start off, lets learn how to convert decimals to percent's.
Converting is actually not too hard. All you need to do is multiply the decimal by 100.
So 5.61 * 100
That would be 561 and then you add a percent sign to the end.
To convert a percent to a decimal is just the opposite of what we just did. Simply divide the percent by 100.
So 100% /100
A number divided by itself is 1
So 100% = 1
To make this problem easier, you can convert the fraction to a decimal.
8 3/4 = 8.75%
Now divide it by 100
8.75/ 100
0.0875
Now just convert it back to a fraction.
0.0875 = 7/80
Convert to a decimal.
5/16 = 0.3125
Multiply by 100
31.25
add percent sign
31.25%
Last one.
Convert to decimal
3/5 = 0.6
Multiply by 100
6%
If you need help on conversions or anything else don't be afraid to reach out! I hope this helps!
What are the coordinates of point A?
Answer:
the left side should be -5 the other side should be 7
Answer:
(7, -5)
Step-by-step explanation:
what is the volume of a regular octahedron inside a cube with the length of its sides measuring 4 centimeters
Answer:
We conclude that the volume of a regular octahedron will be:
[tex]\:\:V\:\approx \:30.17[/tex] cmStep-by-step explanation:
Given
The length of one of the side or edge of a regular octahedron = a = 4 cm
To determine
The volume of a regular octahedron = V
Using the formula to determine the volume of a regular octahedron
[tex]V\:=\:\frac{\sqrt{2}}{3}a^3[/tex]
substituting a = 4 in the volume equation
[tex]V=\frac{\sqrt{2}\cdot \:4^3}{3}[/tex]
[tex]V=\frac{64\sqrt{2}}{3}[/tex] ∵ 4³ = 64
[tex]\:\:V\:\approx \:30.17[/tex] cm
Therefore, we conclude that the volume of a regular octahedron will be:
[tex]\:\:V\:\approx \:30.17[/tex] cmfind the x in the given triangle and at last do the proof...please help
Answer:
x = 42.67
Step-by-step explanation:
HELP I'LL GIVE BRAINLIEST TO THE CORRECT ANSWER!!! THIS IS TIME PLZ HELP!!!
(look at the screenshot)
Ruby is visiting San Francisco. From her hotel she walks 2 blocks east and 4 blocks north to a coffee shop. Then she walks 6 blocks west and 5 blocks north to a museum. Where is the museum in relation to her hotel? SHOW YOUR WORK!!!
The museum is __ blocks(s) __ (east or west) and __ block(s) (north or south) of her hotel.
Answer:
2 blocks west and 5 steps north
Step-by-step explanation:
Suppose we collect a simple random sample of 200 registered voters from a large city. We find that 25% of the voters in the sample are Independents. Find a 95% confidence interval for the percentage of registered voters in the city that are Independents. Round your answer to at least two decimal places.
Answer:
0.05<x<0.06
Step-by-step explanation:
The formula for calculating the confidence interval is expressed as;
CI = p' ±z * √p(1-p)/n
z is the z score at 95% CI
p is the proportion of the independent sample
n is the sample size
p' = X/n
p' = 0.25/200
p' = 0.00125
Given
z = 1.96
p = 25% = 0.25
n= 200
Substitute into the formula;
CI = p' ±1.96 *√0.25(1-0.25)/200
CI = p' ±1.96 * √0.25(0.75)/200
CI = p' ±1.96 * 0.0306
CI = p' ±0.0605
CI = 0.00125 ±0.0605
CI = (0.048, 0.06175)
CI = (0.05, 0.06)
0.05<x<0.06
21) Karen gets paid $5 for every hour plus $15 a day when she works in her neighbor's yard. If she made $40 yesterday, how many hours did she work?
show the work.
Answer:
40/5 = 8
So Karen worked 8 hours yesterday.
Step-by-step explanation:
Algebra 1 plz help me
Answer:
Step-by-step explanation:
solution is (4,3)
OR
x=4
y=3
this point lies in both the tables.
we have to find a pair which lies on both.
Name the plane represented by the front of the box.
BJC, DBF, GBF, or CAB
Answer:cab
Step-by-step explanation:
Answer: c. GBF
Step-by-step explanation:
please answer the following
Answer:
it 10
Step-by-step explanation:
Find factors of following polynomial
A) 7 + 4 + 56 + 32 B) + 9 + 8 + 72
C) (42− 12 + 9 2− 92 )
plz answer properly
I will mark the person brainliest who answers properly
Step-by-step explanation:
the cotrect one is C
❤❤❤❤
The price of an Item yesterday was $160. Today, the price rose to $248. Find the percent increase.
Answer:
jguifutrdduturdrfuy
Step-by-step explanation:
what is 3/4 divided by 1/2
Doug is analyzing the daily profits from the past month for three of his restaurant franchises. He has calculated the mean and standard deviation of the data, in dollars, as shown below.
Location A Location B Location C
Mean = 6,127.85
SD = 413.51 Mean = 6,296.07
SD = 440.67 Mean = 6,191.28
SD = 330.83
For which store does 68% of the data lie between $5,714.34 and $6,541.36 (1 SD from the mean)?
2.
For which location does 95% of the data lie between $5,529.62 and $6,852.94 (2 SD from the mean)?
3.
Which location had the highest average daily profit during the past month?
Answer:
it is b a c on plato
Step-by-step explanation:
Rick has a piece of lumber that is 12 feet long. He cuts it into pieces that are each 3/4 of a foot long. How many pieces of 3/4 foot lumber will he be able to make?
Answer:
He will be able to make 16 pieces of lumber
Step-by-step explanation:
is this answer, right?
Answer:
1) Incorrect should be 35%, 2)incorrect should be 23%
Step-by-step explanation:
37 + 24 = 61 61 + 54 = 115 115 + 36 = 151 college students
1) 54 = x 2) 36 = x
151 = 100 151 = 100
151x/151 = 5400/151 151x/151 = 3600/151
x = 35.7... x = 23.8...
do not round do not round
up since you can't up since you can't
get more people get more people
Ashlee purchases gifts for three friends. She chooses a book for $12.80 and then finds two identical necklaces. Her budget is is $48.00 before tax. What is the maximum she can spend on each necklace?
Answer: $17.60
Step-by-step explanation:
48.00-12.80=35.2.
35.2/2
17.60
Then divide by 2 to get the maximum you could spend on each.
I need help with the problem that is in the attached image.
Answer: c
Step-by-step explanation: i did the test
Evaluate the following expression when n = 6.
|n - 6| - |5 - n|
Answer:
-1
Step-by-step explanation:
1. Substitute n with 6 because n=6
2. Then you simply solve both sides so (6-6)-(5-6) because n=6
3.so then you get the absolute value of 0 subtracted by the absolute values of -1
4. So because all absolute values change it to positive you get 0-1 instead of 0- - 1
5. So the final answer is -1
Sorry if this was confusing, I’m really bad at explaining. :)
Answer:
|n-6|-|5-n|
=|6-6|-|5-6|
=|0|-|-1|
=0-1
=-1
The answer to this question
Answer:
divide 9 and 21
Step-by-step explanation:
if you divide 9 and 21 u will get ur answer
Ann received a $70 gift card for a coffee store. She used it in buying some coffee that cost $8.21 per pound. After buying the coffee, she had $45.37 left on her card. How many pounds of coffee did she buy?
Answer:
She bought 3 pound of coffee.
Step-by-step explanation:
70 - 45.37 = 24.63
24.63 ÷ 3 = 8.21
Answer:
3 pounds
Step-by-step explanation:
which COULD be the new coordinates of point D?
Answer:
It is B
Step-by-step explanation:
4, -4 is longer than 2 units
-2, -2 is longer than 2 units
-1, -4 is longer than 2 units
The cost of one apple and one banana at the school canteen is $1 and the cost of 3 apples and 2 bananas is $2.40. Find the cost of a single banana, using simultaneous equation, elimination method. Show full working out.
Answer:
I don't know
I don't know
Henry rode his motorcycle from his house to a friend's house. After riding 10 miles, he realizes he has traveled 2/3 of the way. How far is Bob's house from his friend's house?
A. 20 miles
B. 15 miles
C. 12 miles
D. 25 miles
Step-by-step explanation:
2/3 of diatance = 10 miles
3/3 of distance = 10 * (3/2) = 15 miles.
The distance between the houses is 15 miles. (B)
Let the total distance covered= x
Distance covered= 10 miles
According to the question,
2/3 of x= 10
=> 2/3 × x= 10
=> 2x/3= 10
=> 2x= 10× 3
=> 2x= 30
=> x= 30/2
=> x= 15
Bob's house is 15 miles away from Henry's house.
What is the polar form of (x + 3)2 + y2 = 9?
r = −6 cos(θ)
r = −3 cos(θ)
r = 3 cos(θ)
r = 6 cos(θ)
Answer:
r = -6 cos(θ)
Step-by-step explanation:
got it right on edge
The equation (x + 3)² + y² = 9 into polar form is r = -6 cos(θ). The correct answer would be option (A).
What is the polar form?The polar form of a complex number is given by r(cos(θ) + i sin(θ)), where r is the distance from the origin and θ is the angle formed by the point and the positive x-axis.
To convert the equation (x + 3)² + y² = 9 into polar form, we can complete the square on the x and y terms:
(x + 3)² + y² = (x² + 6x + 9) + y² = 9
Then we can express x and y in terms of r and θ:
x = r cos(θ) , y = r sin(θ)
Substituting these values into the equation and simplifying:
r² cos²(θ) + 6r cos(θ) + r² sin²(θ) = 9
r²(cos²(θ) + sin²(θ)) + 6r cos(θ) = 0
r² + 6r cos(θ) = 0
r(r + 6cos(θ)) = 0
Since r ≠ 0
So, the polar form of the equation is:
r = -6cos(θ)
Thus, the correct answer would be an option (A).
To learn more about the Polar Coordinates click here:
https://brainly.com/question/614180
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If all people were pea pickers, then how long would it take for the entire population of Earth to pick 1 mol of peas at the rate of one pea per second, working 15 hours per day, 365 days per year
It will take [tex] 1.392 \times {10}^{10} \: years[/tex] for the entire population of the Earth to pick a mole of pea at the specified rate.
1 mole of a substance is given by :
[tex]6.022 \times {10}^{23} [/tex]Rate per person = 1 pea per secondWorking 15 hours per day ; 365 days per year
1 person will pick = (1 × 365 × 15) = 5475 peas per year Taking the world population as 7,900,000,000 people Number of peas picked per year = (7,900,000,000 × 5475) = 43252500000000The time taken to pick 1 mole of pea will be :
1 mole of pea ÷ Number of peas picked per year [tex] \frac{6.022 \times {10}^{23} }{4.325 \times {10}^{13} } = 1.392 \times {10}^{10} \: years[/tex]The time taken to pick 1 mole of pea will be
[tex]1.392 \times {10}^{10} \: years[/tex]
Learn more : https://brainly.com/question/18904995
use the diagram below to find the lengths of the following answer question 18-25. Be sure to include all necessary work. Leave your answer in the simplest radical form when necessary.
Answer:
18. AE = 6
19. BG = 6
20. CF = 5
21. GF = 2
22. CE = 3
23. AC = 3·√5
24. A_F = 10
25. DA = 3·(√5 - 1)
Step-by-step explanation:
Whereby the point C is the center of the circle, we have;
CB = CG = CE = 3 = The radius of the circle with center at C
CE = 3
CF = √(4² + 3²) = 5 by Pythagoras' theorem
CF = 5
GF = CF - CG = 5 - 3 = 2
GF = 2
BG = CB + CG = 3 + 3 = 6
BG = 6
Whereby, BC is a tangent to the circle with center, C, we have;
A_F = √(8² + 6²) = 10 by Pythagoras' theorem
A_F = 10
AE = A_F - EF = 10 - 4 = 6
AE = 6
AC = √(6² + 3²) = 3·√5 by Pythagoras' theorem
AC = 3·√5
DA = AC - CD = 3·√5 - 3 = 3·(√5 - 1)
DA = 3·(√5 - 1).
Reagan found chips for sale at two stores. At Store A, the chips were 6 bags for $4. At store B, the chips were $6 for 4 bags. Reagan said the unit rate was 1:1.5. Which store did she find the unit rate for
PLEASE SOLVE
WILL GIVE BRANLIEST
Answer:
Store B
Step-by-step explanation:
Please mark brainliest.
Which is a correct expansion of the following expression?
18(x – 3) – 26
A. 18x – 80
B. 18x + 80
C. 18x + 28
D. – 62x
Answer:
A. 18x – 80
Step-by-step explanation:
18(x - 3) - 26
18x - 54 - 26
18x – 80