Using the Factor Theorem, it is found that the correct option regarding the complex zeros of f(x) is given by:
D The function has one real zero and two nonreal zeros.
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
In this problem, the function is given by:
f(x) = x³ - 3x² + 16x + 48.
Using a calculator, the roots are given by:
[tex]x_1 = -1.89767, x_2 = 2.44884 + 4.39288i, x_3 = 2.44884 - 4.39288i[/tex]
The first root is real, while the second and third are complex(nonreal), hence option D is correct.
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If p2-8 = 17, which of the following
is a possible value of P
Answer:
+ 5, - 5
Step-by-step explanation:
p^2 - 8 = 17
p^2 = 17 + 8
p^2 = 25
= 5 x 5
p^2 = 5^2
p = ± 5
The price of a skateboard is reduced by 25%. The original price was $120. Find the new price.
A.
$95
B.
$80
C.
$90
New price = 90 dollars
25% of 120 = 30
Price is reduced 25% from 120 so,
120 - 30 = 90
Amount of discount = 30
HElppppp pleaseee......
Answer: \sqrt[4]{xy^{2} }
Step-by-step explanation: Siplified
I need help with 5,6,7 please
Answer:
see explanation
Step-by-step explanation:
the arc length of a circle is calculated as
arc = circumference of circle × fraction of circle
(5)
circumference (C) is calculated as
C = 2πr ( r is the radius )
here diameter = 12 , then r = 12 ÷ 2 = 6
C = 2π × 6 = 12π ≈ 37.7 m ( to the nearest tenth )
(6)
JK = 2πr × [tex]\frac{75}{360}[/tex]
= 2π × 7 × [tex]\frac{5}{24}[/tex]
= 14π × [tex]\frac{5}{24}[/tex]
= [tex]\frac{14\pi (5)}{24}[/tex] ≈ 9.2 in ( to the nearest tenth )
(7)
7.5 = 2πr × [tex]\frac{120}{360}[/tex]
7.5 = 2πr × [tex]\frac{1}{3}[/tex] ( multiply both sides by 3 to clear the fraction )
22.5 = 2πr ( divide both sides by 2π )
r = [tex]\frac{22.5}{2\pi }[/tex] ≈ 3.6 ft
Lydia received her salary on Friday. She spent one-half of her salary on rent and then spent $168 on her electric and water bill. Next she spent one-half of what was left on her phone bill. After spending $57.00 on gas for her car, Lydia had $92.00 left. How much did Lydia spend on rent?
A. $298
B. $466
C. $764
D. $932
Answer:
B) $466Step-by-step explanation:
Let the amount of rent is R
Calculate the value of R in reverse order of spending
R = (92 + 57)*2 + 168 = 466Correct choice is B
Answer:
B. $466
Step-by-step explanation:
[tex]\textsf{let}\: x= \textsf{Lydia's salary}[/tex]
[tex]\implies \textsf{rent}=\dfrac{1}{2}x[/tex]
Modelling the given information to find the total salary:
[tex]\implies \left(x-\dfrac{1}{2}x-168\right)-\dfrac{x-\frac{1}{2}x-168}{2}-57=92[/tex]
[tex]\implies \dfrac{1}{2}x-168-\dfrac{\frac{1}{2}x-168}{2}-57=92[/tex]
[tex]\implies \dfrac{1}{2}x-\dfrac{\frac{1}{2}x-168}{2}=317[/tex]
[tex]\implies x-(\frac{1}{2}x-168)=634[/tex]
[tex]\implies x-\frac{1}{2}x+168=634[/tex]
[tex]\implies \dfrac{1}{2}x=466[/tex]
[tex]\implies x=932[/tex]
Therefore, Lydia's total salary was $932
[tex]\implies \textsf{rent}=\dfrac{1}{2}(932)=\$466[/tex]
A department in a factory has three 3/4-horsepower motors, five 1/4-horsepower motors, six 3 1/3-horsepower motors, and eight 1/2-horsepower motors. What is the total connected motor load in horsepower rating?
Answer:
Kayla , why do you find the question tricky? :/
Step-by-step explanation:
HP total = 3*3/4 + 5*1/4 + 6*3_1/3 + 8* 1/2
HP total = 9/4 + 5/4 + 18_6/3 + 8/2
HP total = 9/4 + 5/4 + 60/3 + 16/4
HP total = 27/12 + 15/12 + 240/12 +48/12
HP total = 330/12
HP total = 165/6
HP total = 55/2
HP total = 27_1/2
Answer:
27.5 HP
Step-by-step explanation:
Sum
3(3/4) + 5(1/4) + 6(3 1/3) + 8(1/2)9/4 + 5/4 + 20 + 424 + 3.527.5 HPHELP NEED ANSWER VERY SOON Which of the following box plots has the HIGHEST overall speed The box plots compare the speeds of cars traveling on a highway
Answer
North of the box plot speed over 72 is the answer because it is a very high speed of the chart and it shows that the its going over the average speed
If there are 9 tacos, 18 hot dogs, and 6 hamburgers, which foods have a ratio of 2:3?
Answer:
Hamburgers and Tacos.
Step-by-step explanation:
If you divide 6 by 3 you get 2, and if you divide 9 by 3 you get 3.
2:3
Pls help me and show work! Thank you <3
Answer: 18
Step-by-step explanation:
By the consecutive interior angles theorem, [tex]5x+7x+24=180 \longrightarrow x=13[/tex].
So, this means that using the corresponding angles theorem, [tex]7x+24=6y+7[/tex], and since [tex]x=13[/tex], this means that [tex]7x+24=115[/tex].
So, [tex]6y+7=115 \longrightarrow \boxed{y=18}[/tex]
A person invests 5500 dollars in a bank. The bank pays 4.25% interest compounded annually. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 11200 dollars?
The person must leave the money in the bank for about 10.1 years at interest 4.25% to reach $11200 when compounded annually.
What is compound interest?Compound interest is when interest is added to the principal of an investment, allowing the interest to compound over time. In other words, the beginning principal as well as the total interest from prior periods are both used to compute interest. In contrast to simple interest, which only affects the initial capital, this causes the investment to expand exponentially over time. Often utilised in banking and investment, compound interest is sometimes defined in terms of a yearly interest rate and the frequency with which it is compounded.
Given that, bank pays 4.25% interest compounded annually on the invested amount.
The compound interest is given as:
[tex]A = P(1 + r/n)^{(n*t)}[/tex]
Substituting the values of P = $5500, r = 4.25% = 0.0425, A = $11200, and n = 1.
[tex]11200 = $5500(1 + 0.0425/1)^{(1*t)}\\t = log(11200/5500)/log(1.0425) = 10.1 years[/tex]
Hence, the person must leave the money in the bank for about 10.1 years to reach $11200.
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Which term describes BCD
Check the picture below.
Triangle E has a perimeter of 125 inches. Two of
its side lengths are 26 inches and 55 inches.
What is its missing side length?
Answer:
44 inches
Step-by-step explanation:
perimeter of triangle = length of side 1 + length of side 2 + length of side 3
length of side 1 = 26
length of side 2 = 55
125 = 26 + 55 + length of side 3 = 81 + length of side 3
subtract 81 from both sides to get the length of side 3
length of side 3 = 44 inches
F(x)=2x-5 if x is 0
Please help hurry
Answer: -5
Step-by-step explanation:
2(0)-5
0-5 = -5
Which of the following is NOT an example of a non-fiction text?
A. Romance novel
B. Magazines
C. Biographies and autobiographies
D. Newspapers
after spending 80% of her daily allowance, Ola found out she had 25k left. How much was her total allowance?
Answer:
31.25 k
Step-by-step explanation:
80 % * x = 25 k
.80 x = 25 k
x = 25 k / .80 = 31.25 k
Answer:
125k
Step-by-step explanation:
You want to know Ola's daily allowance if 25k remained after 80% was spent.
SetupThe fraction remaining was 100% -80% = 20%. If that fraction of Ola's allowance (a) is 25k, we have ...
0.20a = 25k
SolutionDividing by 0.20, the value of 'a' is shown to be ...
a = 25k/0.20 = 125k
Ola's total daily allowance was 125k.
Solve the system using elimination.
Answer:
3x +2y = 11 .... 1
x +5y = 8....2
x + 5y = 8
multiply by -3 on both sides
-3x - 15y = -24
-3x - 15y = - 24
3x +2y = 11
-13y = -13
y = 1
substitute the value of y in 1 or 2
3x +2y = 11
3x = 11 - 2y
3x = 11 - 2(1)
3x = 9
x = 3
(x;y) ( 3 ; 1)
eq(2)×3
3x+15y=24-(3)eq(1)-eq(3)
-13y=-13y=-13/-13y=1Putting in eq(2)
x+5=8x=8-5x=3Pair
(3,1)How do complementary angles relate to right angles?
two ships leave a harbor at
the same time. One ship travels
on a bearing S15°W at 10 miles per
hour. The other Ship travels on a
bearing N75°E at 10miles per hour.
bearing
How far apart will the ships be
after 3 hours?
Answer:
30√3 ≈ 51.96 miles
Step-by-step explanation:
The distance between the two ships can be found using the Law of Cosines, or using your knowledge of the side relationships in special triangles.
__
Each ship is traveling at 10 mph, so after 3 hours will have traveled 30 miles.
The triangle OS1S2 formed by the harbor and the two ship locations is an isosceles triangle with base angles of 30°. Each half of OS1S2 is a 30-60-90 triangle whose longer leg is √3 times half the hypotenuse. The sum of those two "longer legs" is the distance between the ships.
The distance between ships is 2×15√3 = 30√3 ≈ 51.96 miles.
_____
Additional comment
If you prefer to use the Law of Cosines, you are looking for the length of the side opposite the 120° angle in a triangle with sides of 30 miles.
c² = 30² +30² -2·30·30·cos(120°) = 30²(2-2·(-0.5)) = 3·30²
c = 30√3 . . . . . take the square root (miles)
When observing a performance or movement pattern, you should break down the complex skills into which of the following:
A. Stylistic parts
B. none of these
LC. Component parts
D. Tactical parts
When observing a performance or movement pattern, you should break down the complex skills into component parts.
What are complex skills?Complex skills are skills that are composed of many parts. This makes it difficult to engage in these sort of skills without a rigorous training.
Thus, when observing a performance or movement pattern, you should break down the complex skills into component parts.
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Question 10
If y varies inversely as x and y = -6 when x = 4, find the value of y when x = 5.
What is the missing fifth term in the
pattern below?
1,8, 27, 64, ___
Answer:
the pattern is going in the form of 1³ , 2³ , 3³ , 4³
therefore next term should be 5³ which is equal to 125. So the missing term is 125
I hope you got that.
By : Modern Einstein
A rectangle has a perimeter of 36 feet and a base of 14 feet. What is the height?
Answer:
The answer is 4.
Step-by-step explanation:
If this shape has a perimeter of 36, and the base has a length of 14, you subtract 36 - 28 because there are two sides that have a length of 14. You get 8 by subtracting 36 - 28, and divide the answer by 2.
Find the area of the pyramid net
Step 1
Find the area of the Square in the middle
Formula for finding square:
[tex]A = L*W[/tex]
Let's apply the formula and find our answer:
[tex]A = 2*2\\=4[/tex]
The area of the square is 4 units
Step 2
Find the area of all 4 triangles around the square
As you know, the formula for finding 1 triangle is as follows:
[tex]A = \frac{1}{2} *B*H[/tex]
But, to find the area of 2 triangles, we can use this formula:
[tex]A=B*H[/tex]
And to find 4 of them (with same dimensions;as required here), we can use this one:
[tex]A=2*B*H[/tex]
Let's apply the formula then! What are we waiting for!!!!
[tex]A=2*2*2\\=2*4\\=8[/tex]
The area of ALL of the triangles around the square is 8 units
Step 3
Add all areas to find FINAL ANSWER!
Easy!
4+8=12
The area of the Pyramid Net is 12 unitsAnswer:
12 is the answer because 2 x 2 = 4 but since it is a triangular face we half it and end up with 2, 2 x 4 is 8, the square it 2 x 2 = 4 so we add 4 and 8 which equals 12
Use cubic regression to find a
function that fits the following
points.
(1,-1), (2,-13), (3,-45),(-1,11)
y = [?]x3+[ ]x2+0 ]x+[ ]
The cubic regression function of the points (1,-1), (2,-13), (3,-45), (-1,11) is y = -2x³ + 2x² - 4x + 3
How to determine the function?The points are given as:
(x,y) = (1,-1), (2,-13), (3,-45), (-1,11)
A cubic regression function is represented as:
y = ax³ + bx² + cx + d
Next, we determine the cubic function using a graphing calculator.
From the graphing calculator, we have the following coefficients:
a = -2b = 2c = -4d = 3Recall that:
y = ax³ + bx² + cx + d
So, we have:
y = -2x³ + 2x² - 4x + 3
Hence, the cubic regression function of the points is y = -2x³ + 2x² - 4x + 3
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A company manufactures and sells shirts. The daily profit the company makes depends on how many shirts they sell. The profit, in dollars, when the company sells xx shirts can be found using the function f(x)=6x-70.f(x)=6x−70. Find and interpret the given function values and determine an appropriate domain for the function.
f(−2)=
, meaning if the company sells
shirts, they would make a profit of
dollars. This interpretation
in the context of the problem.
f(12)=f(12)=
, meaning if the company sells
shirts, they would make a profit of
dollars. This interpretation
in the context of the problem.
f(17.5)=f(17.5)=
, meaning if the company sells
shirts, they would make a profit of
dollars. This interpretation
in the context of the problem.
Based on the observations above, it is clear that an appropriate domain for the function is
.
The amount of the profit at x = -2 can not be determined because the number of the shirt can not be negative. Then the amount of the profit at x = 12 is $ 2 and at x = 17.5 is $ 35.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
A company manufactures and sells shirts.
The daily profit the company makes depends on how many shirts they sell.
The profit, in dollars, when the company sells x shirts can be found using the function f(x) = 6x − 70.
Find and interpret the given function values and determine an appropriate domain for the function.
Then at x = −2, then the profit will be
For this condition, the amount of the profit can not be determined because the number of the shirt can not be negative.
Then at x = 12, then the profit will be
f(12) = 6 × 12 − 70
f(12) = 72 − 70
f(12) = $ 2
Then at x = 17.5, then the profit will be
f(17.5) = 6 × 17.5 − 70
f(17.5) = 105− 70
f(17.5) = $ 35
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What is the probability that he will hit fewer than 8 of the bottles?
Using the binomial distribution, it is found that the probability that he will hit fewer than 8 of the bottles is of 0.012, given by option A.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem, we have that:
The probability of a bottle being hit is of p = 0.95.There are n = 10 bottles.The probability that he hits fewer than 8 of the bottles is given by:
[tex]P(X < 8) = 1 - P(X \geq 8)[/tex]
In which:
[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)[/tex]
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 8) = C_{10,8}.(0.95)^{8}.(0.05)^{2} = 0.0746[/tex]
[tex]P(X = 9) = C_{10,9}.(0.95)^{9}.(0.05)^{1} = 0.3151[/tex]
[tex]P(X = 10) = C_{10,10}.(0.95)^{10}.(0.05)^{0} = 0.5987[/tex]
Hence:
[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.0746 + 0.3151 + 0.5987 = 0.988[/tex]
[tex]P(X < 8) = 1 - P(X \geq 8) = 0.012[/tex]
The probability that he will hit fewer than 8 of the bottles is of 0.012, given by option A.
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what is the slope of a line that is perpendicular to the line shown? A-1/3 B-1 C-2/3 D-3/2
Answer:
-1
Step-by-step explanation:
perpendicular = always has a slope of neg 1
Answer:
-1
Step-by-step explanation:
It is -1. I can't explain, I just did it in my head, so sorry!
write a event that has a probability of 0
-5 3/4 - 3 1/2 i need helppp please quickly please
Answer:
-9.25
Step-by-step explanation:
Answer: Heyaa! ~
Your Exact Answer is... - 37/4 but your Decimal form is -9.25
Step-by-step explanation:
Convert the mixed numbers to improper fractions, then find the LCD and combine.
Hopefully this helps you!
-Matthew ~
Place the following temperatures in order from coldest to hottest: -8°C, 10°C, -5°F, 40°F
a.
-5°F, -8°C, 40°F, 10°C
b.
-5°F, -8°C, 10°C, 40°F
c.
-8°C, -5°F, 10°C, 40°F
d.
-8°C, -5°F, 40°F, 10°C
Answer: A
Step-by-step explanation: I hate when theres problems like this, considering theres celcius and fahrenheit but the correct answer is A
