1) The definitely true for the statement is b) P(-5) = 3.
2) The three roots are 5, 3 + 4i, and 3 - 4i. Option D is correct.
What is the remainder theorem for polynomials?If there is a polynomial p(x), and a constant number 'a', then
[tex]\dfrac{p(x)}{(x-a)} = g(x) + p(a)[/tex]
where g(x) is a factor of p(x)
Given;
1) When the polynomial P(x) is divided by x+5, the remainder is 3.
If a polynomial P(x) is divided by (x-a), then the remainder is P(a).
If the polynomial P(x) is divided by (x+5), then the remainder will be P(-5).
So, P(-5) = 3
Therefore, the definitely true for the statement is b) P(-5) = 3.
2) P is a 3 degree polynomial with real coefficients and three zeros. Two of the zeros are 5 and 3+4i.
The complex roots always exist in conjugate pairs so,
3 + 4i and 3 - 4i
Thus, the three roots are 5, 3 + 4i, and 3 - 4i. Option D is correct.
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Help with this math problem
Answer:
The minimum cost of the X-ray machines is 12,197dollars.
Step-by-step explanation:
First, we check whether it’s a Quadratic Equation or not
The general form of the Quadratic equation [tex]f(x) =[/tex] [tex]ax^{2} + bx + c[/tex]
Let’s compare it with the given equation, we get
a = 1
b = -520
c = 79,79
Hence, it’s a quadratic equation.
Now, we will use the VERTEX FORMULA as we are asked to find the ‘minimum’ unit cost.
X = [tex]\frac{-b}\[2a[/tex] = [tex]\frac{-(-520)}\[2(1)[/tex] = [tex]260[/tex]
So , number of X-ray machines are = 260 (value of x)
To find the minimum unit cost, plug the value of x into the given equation, and we get
[tex]f(260) = (260)^{2} -520(260) + 79,797[/tex]
[tex]=12,197[/tex]
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What is the period of this graph?
Answer:
Look at the pic for answer.
Step-by-step explanation:
I need help with how to find x and y
The value of x and y from the given figure are 3 and 36
Similarity theorem of trianglesFrom the given similar triangles, the following expression is true
4/6 = x/54
Cross multiply
6x = 4 *54
x = 4 * 9
x = 36
Similarly
y/6 = 27/54
y/6 = 1/2
x =3
Hence the value of x and y from the given figure are 3 and 36
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Write the equation for the function graphed below.
Answer:
f(x) = (x + 1)^2 + 2
Step-by-step explanation:
A parabola function has different forms:
standard form: f(x) = ax + bx + c^2
vertex form: f(x) = a (x − h)^2 + k
Our equation that includes a horizontal translation is h
- negative h shifts right
- positive h shifts left
this graph shows a shift to the left by 1 so h = 1
Our equation that includes a vertical translation is k
- negative k shifts down
- positive k shifts up
this graph shows a shift to the up by 2 so k = 2
- a represents a compression / stretch which seems not to be in this graph
combine, f(x) = (x + 1)^2 + 2
When eighteen is reduced by two-thirds of a number, the result is 14. Find the number.
The number is
Step-by-step explanation:
ATTACHED IS THE SOLUTION!!!Fill in the blanks find P A And si
The answer will be Rs. 4330.
Step-by-step explanation:
Because if you subtract 340 from 4670, you will get the answer which is 4330.
If $4500 is invested at 10% annual interest, which is compounded continuously, what is the account balance after 3 years, assuming no additional deposits or withdrawals are made?
Answer:
$6074.36
Step-by-step explanation:
The formula for continuous compounding is
F = Pe^(rt)
F = $4500 × e^(0.1 × 3)
F = $6074.36
Answer: $6074.36
An 8-pack of clay pots costs $15.76. What is the unit price?
Which of the following represents a geometric sequence with a common ratio r = 6?
1, 6, 36, 216, 1,296
3, 18, 24, 144, 864
7, 13, 19, 25, 31
648, 108, 18, 3, 0.5
Answer:
The first sequence is correct being (6)^k
Step-by-step explanation:
To find a ratio divide a term by its previous member such as 36/6 to give you r=6.
Support her statements using scale factors of 5 and 6.
Reflection: Marissa wants to describe the relationship between the scale factor and perimeter of an image and its pre-image and between the scale factor and area of an image and its pre-image. What should she say about the relationship between the scale factor and perimeter of an image and its pre-image? What should she say about the relationship between the scale factor and area of an image and its pre-image? Support her statements using scale factors of 5 and 6.
Answer:
The relationship between the scale factor and perimeter of an image and its pre-image is a, b = perimeter = 2a + 2b. the relationship between the scale factor and area of an image and its pre-image is k∧2 (ab).
Step-by-step explanation:
Relationship between the scale factor and perimeter of an image and its pre-image.
Scale factor = k
Pre-image lengths: a, b = perimeter = 2a + 2b
Image lengths: ka, kb = perimeter = 2ka + 2 kb = k (2a + 2b) = 2 * preimage perimeter.
She has to say that the perimeter of the image is the perimeter of the preimage times the same scale factor.
What should she say about the relationship between the scale factor and area of an image and its pre-image?
area of the pre-image = ab
are of the image = (ka)(kb) = k^2 (ab)
The area of the image is the area of the preimage times the square of the scale factor.
Support her statements using scale factors of 5 and 6.
Scale factor 5
length of the pre-image = 3 x 4 = perimeter = 2 (3 + 4) = 2(7) = 14
length of the image = 3*5 x 4*5 = 15 x 20 = perimeter = 2 (15 + 20) = 2 (35) = 70
14 * 5 = 70 which shows the prediction
area of the pre-image = 3 * 4 = 12
area of the image = 15 * 20 = 300
12 * (5^2) = 12*25 = 300 which is the value predicted.
Now you can do the same using scale factor 6.
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What is the simplified form of StartRoot StartFraction 72 x Superscript 16 Baseline Over 50 x Superscript 36 Baseline EndFraction EndRoot? Assume x ≠ 0.
StartFraction 6 Over 5 x Superscript 10 Baseline EndFraction
StartFraction 6 Over 5 x squared EndFraction
Six-fifths x Superscript 10
Six-fifths x squared
The simplification form of the provided expression is 6/5x¹⁰ option first is correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have an expression:
[tex]\rm = \sqrt{\dfrac{72x^{16}}{50x^{36}}}[/tex]
[tex]\rm = \sqrt{\dfrac{72}{50}} \sqrt{\dfrac{x^{36}}{x^{16}}}[/tex]
[tex]\rm = \sqrt{\dfrac{36\times2}{25\times2}} \sqrt{\dfrac{x^{36}}{x^{16}}}[/tex]
[tex]\rm ={\dfrac{6x^{8}}{5x^{18}}}[/tex]
[tex]\rm ={\dfrac{6}{5x^{10}}}[/tex]
Thus, the simplification form of the provided expression is 6/5x¹⁰ option first is correct.
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Answer:
6x3
Step-by-step explanation:
Edge 2023
Rewrite the expression as a fraction.
Answer:
4/15
Step-by-step explanation:
in fractions, the number that goes on top is the dividend (the first number in the division problem) which is 4 in this case and the number that goes on the bottom of the fraction is the divisor, which is 15 in this case. therefore, the answer is 4/15.
Please help me answer this question genius
(i) The Maclaurin's series is:
1 ₊ x ₊ x²/2! . 1 ₋ 3x⁴/4! ₊ ...........
(ii) Integral of limit o to 1∫ e^sinx is 0
Maclaurin's expansion is as follows:
y(x) = y₀ ₊ x y₁(0) ₊ x²/2! y₂(0) ₊ x³/3! y₃(0) ₊ ........
y = e^sinx
y(0) = e^sin0
y(0) = 1
Differentiate y with respect to x
y₁(x) = e^sinx . cos x
y₁(0) = 1 [i.e y₁ = cosx.y]
y₁(0) = 1
Differentiate y₁ with respect to x
y₂(x) = cosc . y₁ ₋ sinx . y
∴ y₂(0) = 1 ₋ 0 = 1
Differentiate y₂ with respect to x
y₃ = cosx . y₂ ₋ (2 sinx ₊ cosx)y₁
y₃(0) = 1 ₋(0 ₊ 1)1
y₃(0) = 0
Differentiate y₃ with respect to x
y₄ = cosx . y₃ sinx . y₃ ₋ (2sinx ₊ cosx)y₂ ₋ (2cos x ₋ sinx) y₁
y₄(0) = 0 ₋ (3 . 0 ₊ 1)1 ₋ (2 ₋ o) 1
y₄(0) = -3
∴ From maclaurin's equation we get:
e^sinx = 1 ₊ x . 1 ₊ x²/2! . 1 ₊ x³/3! (0) ₊ x⁴/4! (₋3) ₊ ....
=1 ₊ x ₊ x²/2! . 1 ₋ 3x⁴/4! ₊ ...........
Hence we get the the series expansion as 1 ₊ x ₊ x²/2! . 1 ₋ 3x⁴/4! ₊ ...........
(ii) limit 0 to 1∫e^sinx
integration formula ∫e^x dx = e^x + c
limit 0 to 1 ∫e^sinx = [e^sinx + c ]limit 0 to 1
= e^sin0 ₋ e^sin1
= 1 ₋ 1
= 0
Hence we get the answer as 0
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What are the possible zeros for f(x) equals X to the third power minus 2X to the second power minus 4X +15
The roots of the polynomial are done by using a calculator will be -2.3671, 2.1835 + 1.2527i, and 2.1835 – 1.2527i.
What are the roots of the polynomial?The polynomial is given below.
[tex]\rm f(x) = a_0x^n + a_1 x^{n - 1}+ ....+ a_{n-2}x^2 + a_{n-1}x + a_nx^0[/tex]
The roots of the polynomial are equal to n or less than n.
And if one imaginary root is a + bi, then the other imaginary root will be a – bi.
The roots of the polynomial are done by using a calculator.
x = -2.3671, 2.1835 + 1.2527i, 2.1835 – 1.2527i
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A number divided by 7
Select one:
a. 7+x
b. 7/x
c. x/7
d. 7x
Answer:
c. x/7
Step-by-step explanation:
seven is dividing something, and X is the placeholder in this equation.
So, since x is being divided by seven, that rules out B., because that's backwards.
A. and D. don't involve division, so they're both incorrect as well.
Thus we are left with C. x/7
I walked 280m of the road from the park to the station. This is equivalent to 9/10 of the total distance. How many meters is the total distance from the park to the station?
Answer:
311 1/9 or 311.11 mStep-by-step explanation:
Let the total distance be x.
We have:
9/10 of x is 280 m.Set this as equation and solve for x:
(9/10)x = 280x = 280 ÷ 9/10x = 280 × 10/9x = 2800/9 = 311 1/9 or 311.11 mTotal distance from the park to the station is approximately 311 m.
Let that be d
9/10 of d=2809/10d=280d=280(10/9)d=311.1mNEED HELP ASAP !!!!
Which graphs represents the compound inequality x≤ 5 orx≥ 5?
Answer:
b
Step-by-step explanation:
At the city museum child admission is $6.10 and adult admission is $9.20. On Wednesday, 144 tickets were sold for a total sales of 1083.00. How many adult tickets were sold that day
Cancel tickets for his church is carnival for a total of 2820 children’s tickets cost three dollars each an adult tickets cost five dollars each the number of children so is 30 more than three times the number of adult tickets sold how many children tickets and how many adult tickets did he sell
Taking into account the definition of a system of linear equations, the number of adult tickets sold is 615 and the number of children's tickets sold is 195.
System of linear equationsA system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.
Amount of children tickets and adult tickets soldIn this case, a system of linear equations must be proposed taking into account that
"x" is the amount of children tickets sold."y" is the amount of adult tickets sold.Galen sold tickets of his church’s carnival for a total of $2,820. Children’s tickets cost $3 each and adult tickets cost $5 each. The number of children’s tickets sold was 30 more than 3 times the number of adult tickets sold.
So, the system of equations to be solved is
[tex]\left \{ {{3x+5y=2820} \atop {x=3y+30}} \right.[/tex]
There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, substituting the second equation in the first you get:
3×(3y+30)+5y=2820
Solving:
3×3y+3×30+5y=2820
9y+90+5y=2820
9y+5y=2820 - 90
14y= 2730
y= 2730÷ 14
y= 195
Remembering that x=3y +30, then:
x= 3×195 + 30
Solving
x=585 +30
x=615
Finally, the number of adult tickets sold is 615 and the number of children's tickets sold is 195.
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A sphere has a radius of 24 centimeters. What is its volume
Answer:
57905.8
Step-by-step explanation:
Use the formula:Plug in:
V = 4/3 * 24³π
= 4/3 * 13824π
= 18432π
= 57905.83579cm³
Rounded to nearest tenth:
57905.8
Answer: 18,432
Step-by-step explanation: ANSWER ON EDMENTUM/PLUTO
Tyrone paid $234.33 for a new watch, after-tax, and the tax rate is 7%. What was the original price of the watch?
the price of the watch plus tax = 100% + 7% = 107%
Divide the total cost by 107%:
234.33 / 1.07 = 219.00
The original price was $219.00
Comparing Fractions Choose the correct symbol to compare the fractions please see attached image
Answer:
>
Step-by-step explanation:
Given: [tex]\frac{1}{2} ? \frac{1}{3}[/tex]
Want: Which fraction is larger?
To identify the size of a fraction, converting it into a fraction is easier
[tex]\frac{1}{2}[/tex] = 0.5
[tex]\frac{1}{3}[/tex] = 0.33
where 0.5 is greater than 0.33
Choices:
< is less than symbol
> is greater than symbol
= is equal to
[tex]\frac{1}{2} > \frac{1}{3}[/tex]
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Visual Representation:
Mr. Tan, a manufacturer who produces
more medium-sized shirts than either
large-sized or small-sized T-shirts,
bases his decision on?
O A. Instinct
O B. Mean
O C. Median
O D. Mode
Mr. Tan bases his decision on the mode, which indicates that he produces more medium-sized shirts than either large-sized or small-sized T-shirts. The correct answer is option D: Mode.
To determine whether Mr. Tan bases his decision on instinct, mean, median, or mode, we need to consider the given information that Mr. Tan produces more medium-sized shirts than either large-sized or small-sized T-shirts.
Instinct refers to a natural or intuitive decision-making process that is not based on specific calculations or statistical measures. While Mr. Tan's decision-making process could involve some level of instinct, it is unlikely to be the primary basis for his decision.
The mean is the average value calculated by summing up all the values and dividing by the total number of values. However, the mean does not provide any information about the distribution of the sizes or the fact that Mr. Tan produces more medium-sized shirts.
The median is the middle value when the data is arranged in ascending or descending order. However, we do not have any information about specific values or the distribution of sizes, so we cannot determine the median.
The mode refers to the value or values that appear most frequently in a set of data. Since Mr. Tan produces more medium-sized shirts than either large-sized or small-sized T-shirts, it implies that medium-sized shirts are the mode in his production. This suggests that Mr. Tan's decision is based on the mode, as he produces more shirts of this size than any other size.
Therefore, based on the given information, it can be inferred that Mr. Tan bases his decision on the mode, which indicates that he produces more medium-sized shirts than either large-sized or small-sized T-shirts. The correct answer is option D: Mode.
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A photographer needs a frame for a 16 x 20 inch picture, such that the total area is 340 in^2. Calculate the width of the frame. Which of the following quadratic equations would be used when solving this?
2x^2 + 36x = 20
2x^2 + 72 = 20
4x^2 + 36x = 20
4x^2 + 72x = 20
Which of the numbers below are whole numbers?
A. 0
B. 0.388
C. 2454
D. 602.49
E. 996
F. 719557
Answer:
a whole number is a number with no decmils other than .0000 and is not a fraction where the top and bottom are equal
whole: a,c,e&f
not:b&d
Ming drove to the lake and back. On the trip there she drove 30 km/h and on the return trip she went 24 km/h. How long did the trip there take if the return trip took five hours?
The trip to the lake took 4 hours.
How long did the trip to the lake take?The first step is to determine the distance of the trip.
Distance = average speed x time
24 km/h x 5 = 120 km
Time = distance / average speed
120 / 30 = 4 hours
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The Super 20 Hotel currently contracts out its cleaning service to Great Maids cleaners who charge $50 a room. They also charge an additional $185 no matter how many rooms they clean. Which equation could be used to determine the cost C of the Great Maids cleaning n rooms?
Answer:
a computer is an electronic device,which input data/instruction,store and processes it and produces output in the desired from
Suppose you just purchased a digital music player and put 6 tracks on it. After listening to it you decide you only like 2 songs. With the random feature on the player, each of the 6 songs is played once in random order. Find the probability that among the first 2 songs played
A. You like both of them
B. You like neither of them
C. You like exactly 1
The probability that among the first 2 songs played ;a) 6% , not unusual b) 40% and c) 48.4%
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
We have the following information from the statement:
n = 6, r = 2
a)
P (like both of them) = P (like first song) x P (like second song)
P = 2/6 x 1/5
P = 0.06 = 6%
The probability that among the first 2 songs played and You like both of them is 6%.
b)
P (like neither) = P (not like first song) x P (not like second song)
P = 4/6 x 3/5
P = 0.4 = 40%
c) P (like exactly one of them) = P (first song liked) x P (second song not liked) + P (first song not liked) x P (second song liked)
P = ( 2/6 x 1/5) + (4/6 x 3/5)
P = 0.484 = 48.4%
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A recipe that makes 18 chocolate chip cookies calls for 2.5 cups of flour. How many cookies can you make if you have 3.75 cups of flour (and enough of the other ingredients)?
Answer:
27
Step-by-step explanation:
3.75/2.5x18=27
How do i find the domain of F and write in interval notation??? I completely confused
Answer:
898
Step-by-step explanation:
898999