Question 12 options:
Nick determines the remainder of
, using the remainder theorem.
How does she proceed to the correct answer?
Fill in the blanks from the work bank below: (do not enter spaces)
x = 1 x = -1 x = 0 -23 -19 -15 -29
Nick evaluates the numerator of the rational expression when
. He concludes that the remainder of the division is
Answers
The input value for the expression is 1 and the remainder is -15.
What is the remainder theorem?The Remainder Theorem begins with an unnamed polynomial p(x), where "p(x)" simply means "some polynomial p with variable x". The Theorem then discusses dividing that polynomial by some linear factor x a, where an is simply a number.
Given polynomial is 5x⁴⁵ - 3x¹⁷ +2x⁴ - 19 and is divided by x + 1. Find the value of the polynomial at 1 and then calculate the remainder by synthetic solution.
F(x) = 5x⁴⁵ - 3x¹⁷ +2x⁴ - 19
F(1) = 5 - 3 + 2 - 19
F(1) = -19 + 4
F(1) = -15
The remainder will be calculated by synthetic calculation,
1 __5 ___-3___2_____-19
|
| ______5___ 2______4
5 2 4 -15
The remainder of the given expression is -15.
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Related Questions
4. LA and B form a linear pair. If
MZA = (6x – 19) and mZB = (11x-22),
find mZB.
I
A. 59
B. 65
C. 115
D. 121
Help!
Answers
Answer:
Supplementary angles - d ... 4. The complement of an angle of t° is an angle of_70-7_º mais. 5. If 4 1 and 22 are ... Linear Pair Postulate - If two angles form a linear pair, then they are supplementary. 1. 2 ... LA and Z B are complementary.
Step-by-step explanation:
The value of x is 13, then the measure of angle ∠B will be 121 degrees. Then the correct option is D.
What is an angle?Angle is the space between the line or the surface that meets. And the angle is measured in degree. For complete 1 rotation, the angle is 360 degrees.
Linear angle - If the total of two angles is 180 degrees, they are said to be linear angles.
The angle ∠A and ∠B form a linear pair.
If ∠A = (6x – 19) and ∠B = (11x – 22).
Then we have
∠A + ∠B = 180°
(6x – 19) + (11x – 22) = 180
17x – 41 = 180
17x = 221
x = 13
The value of x is 13, then the measure of angle ∠B will be
∠B = (11 × 13 – 22)
∠B = 143 – 22
∠B = 121
More about the angled link is given below.
https://brainly.com/question/15767203
The product of 1and 3/4 is ____________ 3/4.
Answers
Answer:
https://youtu.be/cqF6M25kqq4
Step-by-step explanation:
An Internet service provider sampled 540 customers and found that 55 of them experienced an interruption in their service during the previous month. Construct a 95% confidence interval for the proportion of all customers who have experienced a service interruption. (0.080, 0.123) (0.873, 0.924) (0.076, 0.127) (0.102, 0.898)
Answers
Answer: a 95% confidence interval for the proportion of all customers who have experienced a service interruption: (0.076, 0.127).
Step-by-step explanation:
Let p be the population proportion of all customers who have experienced a service interruption.
Confidence interval for p:[tex]\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex], where [tex]\hat{p}[/tex] = sample proportion, n= sample size, z* = critical z-value.
Given: n = 540
[tex]\hat{p}=\dfrac{55}{540}=0.102[/tex]
z* = 1.96
The required confidence interval:
[tex]0.102\pm (1.96)\sqrt{\dfrac{0.102(1-0.102)}{540}}\\\\=0.102\pm (1.96)(0.013024)\\\\=0.102\pm$$0.02552704\\\\=(0.102-$$0.02552704, 0.102+0.02552704)\\\\\approx(0.076, 0.127)[/tex]
Hence, a 95% confidence interval for the proportion of all customers who have experienced a service interruption: (0.076, 0.127).
For which product or quotient is this expression the simplest form? (image attached)! please help :((
Answers
Answer:
D
Step-by-step explanation:
For simplify the work we can start to factorise all the possibles expressions:
2x + 8.
8 is multiple of 2, so it can became
2(x+4)
x^2 - 16 this is a difference of two squares, so it can be rewritten as:
(x+4)(x-4)
x^2 + 8x + 16
we have to find two numbers whose sum is 8 and whose product is 16
the two number are 4 and 4
it becames:
(x+4)(x+4)
x+ 4 can‘t be simplified
if we look at the expression, we can find that x-4 appears at the numerator so
x^2 - 16 must be at numerator
but the second factor (x+4) doesn’t appear, so has been simplified. This situation can be possible only in the D option
in fact
(x+4)(x-4)/2(x+4) * (x+4)/(x+4)(x+4)
it became
(x+4)(x-4)/2 * 1/(x+4)(x+4)
(x-4)/2(x+4)
Answer:
Step-by-step explanation:
I got 100% on the test
Is this correct? Can someone help me pls
Answers
Answer:
ye
Step-by-step explanation:
what is 24 1/2 by 12 4/5?
Answers
Answer:
313.6
Step-by-step explanation:
24 1/2 * 12 4/5 = 1568/5 = 313 3/5
= 313.6
Hope I helped (p.s. maybe brainliest?)
Answer:
24 1/2 ÷ 12 4/5 = 1 117/128
Step-by-step explanation:
:))
x=30 y=6
X x Y - 4 + 15 /2=?
Also Anyone on here got Queston cove?
Lol
Answers
Answer:
Hey mate.....
Step-by-step explanation:
This is ur answer.....
= 30 × 6 - 4 + 15 / 2= (30 × 6) - (4 + 15) / 2
= (180 - 19) / 2
= 161 / 2
= 80.5
Hope it helps!
mark me brainliest pls.....
Follow me! :)
The following MINITAB output presents the results of a hypothesis test for a population mean μ.
One-Sample Z : X
Test of mu = 73.5 vs not = 73.5
The assumed standard deviation = 2.3634
Variable N Mean StDev SE Mean 95% 01 Z P
X 145 73.2461 2.3634 0.1963 (72.8614, 73.6308) -1.29 0.196
A. Is this a one-tailed or two tailed test?
B. What is the null hypothesis?
C. What is the P-value?
D. Use the output to compute the P-value for the test of H0 : μ ≥ 73.6 versus H1 : μ < 73.6.
Answers
Answer:
A. This is a two tailed test.
B. H0: μ= 73.5
C. P-value= 0.196
D. The P-Value is 0.460172 for one tailed test .
Step-by-step explanation:
The given data is
Variable N Mean StDev SE Mean 95% 01 Z P
X 145 73.2461 2.3634 0.1963 (72.8614, 73.6308) -1.29 0.196
A. Is this a one-tailed or two tailed test?
This is a two tailed test because H0: μ= 73.5 against Ha: μ ≠ 73.5
B. What is the null hypothesis?
H0: μ= 73.5
C. What is the P-value?
P-value= 0.196
D. Use the output to compute the P-value for the test of H0 : μ ≥ 73.6 versus H1 : μ < 73.6.
For z= -1.29 the P-Value is 0.460172 for one tailed test .
The result is not significant at p < 0.05.
i need help asap please and thank you
Answers
Answer:
113
Step-by-step explanation:
First we need to find theother 2 angles of the triangle.
We are given that the top angle is 60°
We know that the angles of a triangle add up to 180°
To find the bottom left angle of the triangle...
We can see that it is alternate exterior angles so they will equal.
To find the third angle of the triangle...
180 - 60 (given angle) -53 (alternate exterior angle) = 67°
Now we know that the bottom right angle inside the triangle is 67°.
To find x...
subtract 67 from 180 because the like is a combination of x and the 67° angle we just found. (a straight line angle = 180°)
180 - 67 = 113
Use synthetic division to solve (2x3+4x2 – 35x+15) +(x-3). What is the quotient?
O 2x2–2x-29+
102
X+ 3
102
O 2x2 - 2x-29+
X-3
2x + 10x2 - 6x
2x2 + 10x-5
Answers
Given:
[tex](2x^3+4x^2-35x+15)\div (x-3)[/tex]
To find:
The quotient by using the synthetic division.
Solution:
We have,
[tex](2x^3+4x^2-35x+15)\div (x-3)[/tex]
Here,
Dividend = [tex](2x^3+4x^2-35x+15)[/tex]
Divisor = [tex]x-3[/tex]
The coefficient of dividend are [tex]2, 4, -35, 15[/tex]. Write the coefficients of the dividend on the top row and we need to use 3 as divisor for synthetic division. The synthetic division is show below:
[tex]3 | 2\quad \quad 4\quad \quad -35\quad \quad 15\\\quad{}\quad{} \quad \quad \ 6\quad \quad \ \ \ 30\quad -15\\\overline{\quad 2\quad \quad 10\quad \quad -5\quad \quad 0\ \ \ }[/tex]
The bottom row represents the coefficients of quotient but the last element of bottom row is the remainder.
Degree of dividend is 3 and degree of division is 1. So, the degree of quotient must be [tex]3-1=2[/tex].
The quotient is [tex]2x^2+10x-5[/tex] and the reminder is 0.
Therefore, the correct option is D.
Answer: divisor: x+4, dividend: 2x^3+11x^2+18x+9, quotient: 2x^2+5x+3
Step-by-step explanation:
An airplane is flying with a constant altitude at a speed of 450 mph in a direction 10° north of west directly towards its final destination. The airplane then encounters wind blowing at a steady 34 mph in a direction 85° north of east. If the pilot does not correct his course after encountering the wind, at what speed and in what direction (counterclockwise from east) will the plane be traveling? Speed: _____mph Direction:______ ° If the airplane had encountered no wind at all, it would have reached its final destination in two hours along its original course. Assuming the pilot never corrected his course and that the wind continues to blow at the given speed and direction, how far from its final destination is the airplane after two hours of flying under the given conditions?____ miles
Answers
Answer:
21
Step-by-step explanation:
Katrina is rolling a six-sided number cube.
1) Determine the probability Katrina will roll a number equal to or less than 2.
2) Determine the probability Katrina will roll a number greater than 2.
Answers
Answer:
Step-by-step explanation:
1. 1 or 2 so 2 options
2 out of 6 is 33%
2. 3 or 4 or 5 or 6 so 4 options
4 out of 6 is 66%
Pls answer just the answer
Answers
Answer:
588000
Step-by-step explanation:
if i am wrong pls tell me cause i think there's a different answer gl g
Answer:
$103,421.88
Step-by-step explanation:
Given:
P = 70000
r = 0.05
n = 1
t = 8
Work:
[tex]A=P(1+\frac{r}{n} )^{nt}\\\\A=70000(1+\frac{0.05}{1} )^{1*8}\\\\A=70000(1.05)^8\\\\A=103421.88[/tex]
PLEASE HELP FAST!!! ILL MARK AS BRAINLIEST!!!!what is the area and perimeter of a box that is x-3 and x+9?
Answers
Answer: x^2 +6x-27
Step-by-step explanation:multiply x and x. Multiply 9 and -3. multiply x and 9, then multiply x and -3. Add 9x+-3x= 6x
x^2 +6x -27
WILL MAKE BRAINLIEST!!!
write the equation given the slope and y-intercept
1.) m= 1, b=2
2.) m= 1/4, b=0
3.) m= -3, b= 0.5
4.) m= 0.2, b=0.8
Answers
2) y=1/4x
3) y=-3x+0.5
4) y=0.2x+0.8
Which angle number represents an angle vertical to ZUXR?
T
X1
R
3/2
S
Y
4
5
U
W
Answers
Answer:
angle number 1
Step-by-step explanation:
An angle that is vertical to <UXR is an angle that is directly opposite to <UXR, which share the same vertex, X, as <UXR.
From the diagram given, the angle number that shares the same vertex as <UXR and is directly opposite to <UXR is angle number 1 (<SXT).
<1 = <UXR
Which city has a higher median?
Answers
The correct answer is Arcadia
Let me explain why...
The median is the number that's in-between the other 2 numbers so for Millersburg the median around 200ish but the median for Arcadia is is exactly 240.This means that Arcadia is your answer
Hope you have an amazing day <3
-Yo MaMa
-12 + 45
25 + -77
Theres more in pic
Answers
Answer
|-12|+|45|=|12|+|45|= 12+45=57
Step-by-step explanation:
When you take the absolute value of a negative number it is the same thing as taking as a positive number. The absolute value is just that number. Once you teach the absolute value of each number perform the operation given In the problem.
Pls help !!!! Due today
Answers
Answer:
Im not so sure but i think its the 3rd option 168cm^2
Step-by-step explanation:
a spreadsheet is _____.
Answers
Answer:
Step-by-step explanation:
a calculator spread out :P or maybe many calculators.. oh... it's a matrix of calculators... yes..
Answer:
software used to input, track, and calculate numbers
Step-by-step explanation:
Edge 2021
john takes a small business loan
for $18,000. the term for
repayment is 60 months and
the annual interest rate is 5.25%.
using the monthly payment
formula, what is the estimated
monthly payment?
Answers
9514 1404 393
Answer:
$341.75
Step-by-step explanation:
You have not provided the formula, so we'll use one we like:
A = P(r/12)/(1 -(1 +r/12)^(-n)) . . . . principal P, annual rate r, n months
A = $18,000(0.0525/12)/(1 -(1 +0.0525/12)^-60) ≈ $341.75
The monthly payment is about $341.75.
Which of the following is the quotient of the rational expressions shown
below? Make sure your answer is in reduced form.
7x²/2x + 6/
3х - 5/X +3
Answers
Option (E) 7x^2/(6x-10) is the reduced form of the rational expression is the correct answer.
What is a rational expression?A rational expression is the ratio of two polynomials. It looks like fractions that have variables in their denominators. A rational expression is considered simplified if there are no common factors in its numerator and denominator.
For the given situation,
The rational expression is
7x²/(2x + 6) ÷ (3х - 5)/(x +3)
⇒ [tex]\frac{\frac{7x^{2} }{2x+6} }{\frac{3x-5}{x+3} }[/tex]
In conversion of division to multiplication, we need to change the division sign to multiplication sign and reciprocal the rational expression for simplification.
⇒ [tex](\frac{7x^{2} }{2x+6} )(\frac{x+3}{3x-5} )[/tex]
⇒ [tex](\frac{7x^{2} }{2(x+3)} )(\frac{x+3}{3x-5} )[/tex]
⇒ [tex](\frac{7x^{2} }{2(1)} )(\frac{1}{3x-5} )[/tex]
⇒ [tex]\frac{7x^{2} }{6x-10}[/tex]
Hence we can conclude that option (E) 7x^2/(6x-10) is the reduced form of the rational expression is the correct answer.
Learn more about rational expression here
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what is an equation of the line that passes through the points (4,-6) and has a slope of -3
1) y = -3x + 6
2)y = -3x - 6
3)y = -3x + 10
4) y = -3x + 14
Answers
Answer:
1) y = -3x + 6
Step-by-step explanation:
1) First, write the equation of the line in point-slope form with the given information. Use the point-slope formula [tex]y-y_1 = m (x-x_1)[/tex] and substitute values for [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex].
Since [tex]m[/tex] represents the slope, substitute -3 in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of the point the line intersects, substitute the x and y values of (4,-6) into the formula as well. This gives the following equation:
[tex]y+6 = -3(x-4)[/tex]
2) Now, isolate the y in the equation to put it in slope-intercept form and find the answer.
[tex]y + 6 = -3(x-4)\\y + 6 = -3x+12\\y = -3x+6[/tex]
So, the first option is correct.
what is the total surface area?
Answers
Answer:
231.5in squared
Step-by-step explanation:
Both faces area formula
Rectangle: l x w
triangle: b x h / 2
Luna packed two chocolate bars for her trip. One s'mores uses 1/2 of a bar. If she has one s'mores a day, about how many days will the chocolates last?
Answers
Answer:
4 days.
Step-by-step explanation:
Each bar has 2 halves.
That means that in total, Luna has 4 halves, or, 4/2 parts.
If she uses half of a bar each day, then she will last 4 days.
What is the approximate volume of a half sphere with a diameter of 8 cm?
Answers
Answer:
134.04
Step-by-step explanation:
Please help me :) I will give BRAINLIEST !! Please help it’s so confusing for me!
Answers
Answer:
Step-by-step explanation:
An apartment complex developer is considering building apartments in College Town, but first wants to do a market study. A sample was selected of monthly rent values ($) for 80 studio apartments in College Town with sample mean of 498.76. (Based on past experience, the developer assumes a known value of s = $65 for the population standard deviation.)
a. Develop a 98% confidence interval for the mean monthly rent for all studio apartments in this city.
b. Suppose the apartment developer wants a 98% confidence interval estimate of the population mean with a margin of error of E = $15. What sample size is needed?
Answers
Answer:
a. The 98% confidence interval for the mean monthly rent for all studio apartments in this city is between $481.85 and $515.67
b. A sample size of 102 is needed.
Step-by-step explanation:
Question a:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.01 = 0.99[/tex], so Z = 2.327.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.327\frac{65}{\sqrt{80}} = 16.91[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 498.76 - 16.91 = $481.85
The upper end of the interval is the sample mean added to M. So it is 498.76 + 16.91 = $515.67
The 98% confidence interval for the mean monthly rent for all studio apartments in this city is between $481.85 and $515.67
Question b:
This is n for which M = 15. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]15 = 2.327\frac{65}{\sqrt{n}}[/tex]
[tex]15\sqrt{n} = 2.327*65[/tex]
[tex]\sqrt{n} = \frac{2.327*65}{15}[/tex]
[tex](\sqrt{n})^2 = (\frac{2.327*65}{15})^2[/tex]
[tex]n = 101.68[/tex]
Rounding up:
A sample size of 102 is needed.
What is the axis of symmetry for this function?
y=x2 - 2x - 3
.
Answers
Answer:
x=1
Step-by-step explanation:
You can find the axis of symmetry from the equation of a function by using the formula x= -b / 2a ( ax^2 + bx + c).
In this particular function, you can see that b is 1 and c is -3.
x= -b / 2a
x= - (-2) / 2(1)
x= 2 / 1
x= 1
What is the answer please I need help if you send a link I will report because your just trying to scam someone
Answers
Answer:
The median is 6.
Step-by-step explanation: