Answer:
Step-by-step explanation:
p(A) = a^3 + 3a^2 + 9a + 27
put brackets around the 1st and second terms and another set around the 3rd and 4th
P(a)= (a^3 + 3a^2) + (9a + 27)
Using the distributive property, pull out the common factor for each of the 2 terms that contain the brackets.
P(a) = a^2 ( a + 3) + 9(a + 3)
Let a + 3 = x
P(a) = a^2x + 9x
Put brackets around these 2 terms
P(a)= x(a^2 + 9)
Substitute a + 3 for x
P(a) = (a + 3) ( a^2 + 9)
What is a cubic polynomial function with zeros -20, -15, and -6?
What is a quartic polynomial function with zeros -20, -16, -11, and -9?
What are the zeros of x^3 + 16x^2 + 60x? What are their multiplicities?
Answer:(x + 1)(x - 1)(x + 5)(x - 3) is the fully factored form of the polynomial.
The zeros are (-1, 0), (1, 0), (-5, 0), and (3, 0).
x^4 + 2x^3 - 16x^2 - 2x + 15
We can use the rational roots theorem to find some of the possible roots, and after finding just one root, we can simplify this polynomial.
List factors of 15:
1, 3, 5, 15.
List factors of 1:
1.
Our possible rational factors are:
+/- 1, +/- 3, +/- 5, +/- 15.
To find factors, we can use the remainder theorem.
Replace all x values with 1.
1^4 + 2(1)^3 - 16(1)^2 - 2(1) + 15 = 0
Because the answer is zero, it means that 1 is a root.
We can divide this polynomial by x - 1 to find a simplified form.
After dividing, our quotient is: x^3 + 3x^2 - 13x - 15
We can continue finding factors by using the rational roots theorem. Once we have only three terms, we can try to factor using the AC method.
Our next possible root is -1.
(-1)^3 + 3(-1)^2 - 13(-1) - 15 = 0
We know that -1 is also a root, and so we can divide the polynomial by x + 1.
After diving we're left with x^2 + 2x - 15.
Now, we can try to factor using the AC method.
List factors of -15.
1 * -15
-1 * 15
3 * -5
-3 * 5 (these digits satisfy the criteria.)
Split the middle term.
x^2 - 3x + 5x - 15
Factor binomials.
x(x - 3) + 5(x - 3)
Rearrange binomials.
(x + 5)(x - 3)
Add in the two factors we already factored out.
(x - 1)(x + 1)(x + 5)(x - 3)
Step-by-step explanation:
How do I solve 8/x-0.16=0.64
Answer:
yo my bad
x=10 the other person solved it
Answer:
x=10
Step-by-step explanation:
8/x=0.8
8=0.8x
x=10
The differnce in price in colerd pencils and mechanical pencils is $0.20. If I purchased 18 colord pencils and 22 mechanical pencils for $27.60, what is the cost of the mechical pencil
Answer: Mechanical Pencils are $0.60
Colored Pencils are $0.80
Step-by-step explanation:
18c+22m=27.60
c-m=.20
+m +m
so c= .20+m
Susitituete 18(.20+m)+22m=27.60
3.6+18m +22m=27.60
40m=27.60
40m=24
m=.60
c=.20+(.60)
c=.80
Which of the following represents the domain and range for the logarithmic
function below?
Help please
Find the length of the chord made by 3x2 - y2 = 3 and y + x – 5 = 0.
Answer:
The correct answer is "9√2 units".
Step-by-step explanation:
The given equations are:
⇒ [tex]3x^2-y^2=3[/tex]...(equation 1)
⇒ [tex]y+x-5=0[/tex]...(equation 2)
According to the 2nd equation, we get
⇒ [tex]y+x-5=0[/tex]
⇒ [tex]y=5-x[/tex]
On substituting the value of "y" in the 1st equation, we get
⇒ [tex]3x^2-y^2=3[/tex]
[tex]3x^2-(5-x)^2=3[/tex]
[tex]3x^2-(25+x^2-10x)=3[/tex]
[tex]2x^2+10x-28=0[/tex]
On taking common, we get
[tex]x^2+5x-14=0[/tex]
On applying factorization, we get
[tex]x^2+7x-2x-14=0[/tex]
[tex]x(x+7)-2(x+7)=0[/tex]
[tex](x+7)(x-2)=0[/tex]
[tex]x+7=0[/tex]
[tex]x=-7[/tex]
or,
[tex]x-2=0[/tex]
[tex]x=2[/tex]
Now,
The points are:
(-7, 12) = (x₁, y₁)
(2, 3) = (x₂, y₂)
By using the distance formula, the length of chord will be:
= [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
On substituting the values in the above formula, we get
= [tex]\sqrt{(2-(-7))^2+(3-12)^2}[/tex]
= [tex]\sqrt{(9)^2+(-9)^2}[/tex]
= [tex]\sqrt{81+81}[/tex]
= [tex]9 \sqrt{2}[/tex] units
I need help with this please:
Answer:
B and C
Step-by-step explanation:
4/7 = 0.57
2/3 > 4/7
is this khan academy?
Answer:
C
Step-by-step explanation:
Because 2/5 equal .4 in decimal. .57 is equal to 4/7 and 2/3 is .666 repeating
PLEASE HELP !! ILL GIVE BRAINLIEST !!
Answer:
∠VWT and ∠UTW
∠STW and ∠XWT
Step-by-step explanation:
A scoop used to measure powdered drink mix is in the shape of a cone with a radius of 5 cm.
5 cm
What is the height of the scoop if its volume is 757 cm3
15 cm
9 cm
7 cm
3 cm
A city councilwoman is concerned that the new contractor she hired is taking too long to replace defective streetlights. She would like to perform a hypothesis test to determine if the replacement time for streetlights under the new contractor is in fact longer than the replacement time under the previous contractor, which was 3.2 days on average. She selects a random sample of 12 streetlight service calls and obtains the following times to replacement (in days). Use a significance level of 0.05
6.2 7.15.4 5.57.52.6 4.3 2.9 3.7 0.7 5.6 1.7
Required:
a. Define μ in the context of the problem and state the appropriate hypotheses.
b. State and check the conditions for a hypothesis test of the mean. Since the sample size is smaller than 30, you will need to calculate a normal probability plot to determine if the data come from a normal distribution.
Answer:
There is significant evidence to conclude that the replacement time for streetlights under the new contractor is longer than the replacement time under the previous contractor.
Step-by-step explanation:
Given the data :
6.2 7.1 5.4 5.5 7.5 2.6 4.3 2.9 3.7 0.7 5.6 1.7
The hypothesis:
H0: μ = 3.2
H1 : μ > 3.2
n = sample size = 12
The sample mean, xbar = ΣX / n
xbar = 53.2 / 12
xbar = 4.43
Using calculator;
Sample standard deviation, s = 2.147
The test statistic :
(xbar - μ) ÷ (s/sqrt(n))
(4.43 - 3.2) ÷ (2.147/sqrt(12)
1.23 / 0.6197855
Test statistic = 1.985
The Pvalue using the Pvalue from Tscore calculator :
Tscore = 1.985 ; df = 12 - 1 = 11
Pvalue = 0.036
Since Pvalue < α ; We reject the Null
Hence, we conclude that the replacement time for streetlights under the new contractor is longer than the replacement time under the previous contractor.
Plz help me well mark brainliest if you are correct!
Answer:
The line segment RU
Step-by-step explanation:
The radius of a circle is defined as the distance from the center to the edge. Since answer D represents that definition, it is a radius.
Answer: D
Step-by-step explanation:
The radius of a circle is the half the line in the middle so the only ones that form half a line across the middle is line segment RU
Hope this helped! :)
Can somebody help me please?
A woman bought 200 mangoes for $8.00. she discovered that 8 of the mangoes got spoiled,but then sold the rest at $0.60 a dozen. find her percentage profit on the sales.
click on pics.........................
What is the slope of the line represented by the equation y = x-3?
0 -3
5
O
3
Answer:
slope (m) = 4/5
Step-by-step explanation:
Equation of straight line: y = mx + b
∴ 4/5 is the slope
a chemist is researching different sustainable fuel sources
Answer:
Wind
Hydroelectric Power
Solar
Geothermal
PLEASE HELP IMMEDIATELY!!
Answer:
}
Step-by-step e.xplanati:kljkjk
Find the area of the semicircle. Round to the nearest hundredth if necessary.
9514 1404 393
Answer:
8π m² ≈ 25.13 m²
Step-by-step explanation:
The formula for the area of a circle is ...
A = πr²
The area of a semicircle is half that. Also, the radius (r) is half the diameter. So. the area of this semicircle is ...
A = (1/2)π(4 m)² = 8π m² ≈ 25.13 m²
__
Comment on pi
If you use the 3-digit value 3.14 for pi to compute this 4-digit result, you will get 25.12.
Cquation
Question 2 of 5
How many solutions does 6 -3x = 12 - 6x have?
A. Infinitely many solutions
B. Two solutions
C. One solution
D. No solutions
6. Write 12/5 as a percent 100% 120% O140% О111%
Answer:
140%
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what is the slope of the line that passes through the points (5,3) and (-4,1)
Answer:
x = 1
y . =2
slope =
[tex]\frac{y}{x} \\\\\frac{2}{1} \\\\Slope = 2[/tex]
Step-by-step explanation:
Find the area of EFGH
Answer:
42
Step-by-step explanation:
(8+13)*4/2 = 42
Answer:
42 in
Step-by-step explanation:
PLEASE HELP ASAP
Find the greatest common factor of these two expressions:
30x^8 w^4 v^3 and 12w^7 v^5
Answer:
[tex]Factor = 6w^4 v^3[/tex]
Step-by-step explanation:
Given
[tex]30x^8 w^4 v^3[/tex] and [tex]12w^7 v^5[/tex]
Required
Determine the common factor.
To do this, we simply factorize each. SO, we have:
[tex](1)\ 30x^8 w^4 v^3=: 2 * 3 * 5 * x^8 * w^4 * v^3[/tex]
[tex](2)\ 12w^7 v^5:=\ 2 * 2 * 3 * w^4*w^3 * v^3 * v^2[/tex]
Check for similar factors.
[tex]Factor = 2 *3 * w^4 * v^3[/tex]
[tex]Factor = 6w^4 v^3[/tex]
The above represents the similar factor
Which is a function?
O {(-3,5), (1,4), (3,7), (1,7),(4,9)}
O {(7,9), (13,-2), (8,4), (7,0), (4,12)}
O {(2,1),(-1,7), (6,-2), (10,3), (-6,0)}
O {(-2,4), (7,4), (-6,8), (-2,8), (1,1)
Write a number of grams between 10 and 20, and then write an equivalent amount in milligrams.
Answer:
15 grams and 15000 milligrams
Step-by-step explanation:
help please need asap
Answer:
A. Obtuse B. Right C. Acute D. Acute Hope this helps :)
What is the volume, in cubic feet of the tent.
Answer:
96ft³
Step-by-step explanation:
Okay, so the formula for finding the volume of a triangular prism is base x height, so we first have to find the base:
6 x 4 ÷ 2 = 12
So then we plug our numbers into the formula:
12 x 8 = 96
So, the volume of the tent is 96ft³
hope this helps:)
John took all his money from his savings account. He spent $108 on a radio and 5/9 of what was left on presents for his friends. Of the money remaining, John put 5/6 into a checking account and the last remaining $80 was left to charity. How much money did John originally have in his savings account?
Answer:
I believe its 313$
Step-by-step explanation:
John originally have $1,118 in his savings account.
Here,
We have to find the original savings account of John.
What is Number system?
A system of writing to express numbers is called Number system.
Now,
Let us assume amount of money John originally have in his savings account = $x
Money spent on a radio = $108
Remaining money = x - 108
Money spent on presents for his friends = Two third of remaining money = 5/9 (x - 108).
(Because 1 - 5/9 = 1/1 - 5/9 = 4/9)
Remaining money = 4/9 (x - 108).
Five sixth of his remaining money into a checking account = 5/6 * 4/9(x - 108)
( because 1 - 5/6 = 1/1 -5/6 = 1/6)
Remaining money = 1/6 *4/9 (x - 108).
Final remaining money = 1/6 *4/9 (x - 108)
And that is equal to the money donated to charity.
We can setup an equation now.
1/6 *4/9 (x - 108) = 80
4(x - 108) = 80 * 9 *6
x - 108 = 20 * 54
x = 1080 + 108
x = 1,188
Therefore, John originally have $1,118 in his savings account.
Learn more about the number system visit:
https://brainly.com/question/17611657
#SPJ2
Given an equilateral triangle with sides of length 9, find the length of the altitude.
Please help asap please help
Answer:
C. 40 + (-58) + 160Step-by-step explanation:
It would be easier with C., the other options are already easy to calculate
40 + (-58) + 160 = 40 + 160 + (-58) = 200 - 58 =142Solve: 7.2h = 57.6 A. h= 0.8 B. h = 8 C. h = 50.4 D. h = 80
Answer:
B. h=8
Step-by-step explanation:
The answer is B. h=8. I know because I solved to get h by itself. First, I set up the problem.
7.2h=57.6
Then, I divided each side by 7.2, so I could get h by itself.
h=8
You can check to make sure this is correct by plugging in the value we got for h into the equation.
7.2(8)=57.6
In conclusion, the answer is B. h=8
A political pollster wants to know what proportion of voters are planning to vote for the incumbent candidate in
an upcoming election. A poll of 150 randomly selected voters is taken from the more than 2,000 voters in the
population, and 78 of those selected plan to vote for the incumbent candidate.
Based on this sample, which of the following is a 90% confidence interval for the proportion of all voters who
plan to vote for the incumbent candidate?
Answer:
90% confidence interval -> {0.4529, 0.5871}
Step-by-step explanation:
Check conditions for a 1-proportion z-interval:
np>10 -> 150(0.52)>10 -> 78>10 √
n(1-p)>10 -> 150(1-0.52)>10 -> 72>10 √
Random sample √
n>30 √
For a 90% confidence interval, the critical value is z=1.645
The formula for a confidence interval is:
CI = p ± z√[p(1-p)/n]
Given:
p = 78/150 = 0.52
n = 150
z = 1.645
Therefore, the 90% confidence interval is:
CI = 0.52 ± 1.645√[0.52(1-0.52)/150] = {0.4529, 0.5871}
Context: We are 90% confident that the true proportion of all voters who
plan to vote for the incumbent candidate is contained within the interval