Answers
Answer:
p = 9
Explanation:
There is no remainder when a polynomial is completely divided by divisor.
Here:
divisor: (x - 6)polynomial: f(x) = x³ - 13x² + 6px - 72Set to zero:
(x - 6) = 0x = 6Insert into equation.
f(6) = 0
(6)³ - 13(6)² + 6p(6) - 72 = 0
216 - 468 + 36p - 72 = 0
-324 + 36p = 0
36p = 324
p = 324/36
p = 9
Related Questions
System A
x−4y=1
5x+6y=−5
System B
x=1+4y
5x+6y=−5
1) How can we get System B from System A?
CORRECT (SELECTED)
Replace one equation with itself where the same quantity is added to both sides
2) Based on the previous answer, are the systems equivalent? In other words, do they have the same solution?
CORRECT (SELECTED)
Yes
Answers
1. System B from System A by replacing one equation with itself where the same quantity is added to both sides
2. Yes, both system A and system B are equivalent and therefore has the same solution
How to prove the statementsSystem A
x − 4y= 1
5x + 6y= −5
System B
x = 1+4y
5x + 6y= −5
1. System B can be gotten from system A by
from the first equation of A
x − 4y= 1
Make 'x' subject of formula
x = 1 + 4y
This makes it equal to tat of system B
Thus, replacing one equation with itself where the same quantity is added to both sides
2. System A
x = 1 + 4y
5x + 6y= −5
System B
x = 1 + 4y
5x + 6y= −5
From the above equations, we can see that both system A and system B are equivalent and therefore has the same solution.
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Evaluate a=5 and y= -7 for y-2a
Answers
Answer: -17
Step-by-step explanation:
y - 2a
= -7 - 2(5)
= -7 - 10
= -17
Find the slope of the straight line that passes through (–2, –4) and (3, –5).
A. m= -1/5
B. m = –1
C. m = 1/5
D. m = 1
Answers
Step by step
To find slope, (y2-y1) over (x2-x1)
(-5)-(-4) over 3-(-2)
-1 over 5
m = -1/5
[tex]\large\boxed{\textsf{A.}\ m=-\frac{1}{5}}[/tex]
We can use the slope formula, where our points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]:
[tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]
This is also known as "rise over run" because it represents the change in vertical ([tex]y[/tex]) position divided by the change in horizontal ([tex]x[/tex]) position.
Substitute the values from the points given:
[tex]\dfrac{(-5)-(-4)}{3-(-2)}[/tex]
Subtract:
[tex]\boxed{\dfrac{-1}{5}}[/tex]
32y+54x+56=y what is y
Answers
is this the kind of thing youre looking for?
explanation:
A support cable for a 56-foot tower forms a 67° angle with the ground.
What is the length of the cable to the nearest foot?
56 ft.
61 ft.
60 ft.
75 ft.
Answers
to find the length of the cable, you need to use trigonometry. So you have 56ft as the opp of 67degree and cable as hypotenuse of 67degree.
thus Sin(67)=OPP/HYP
=56/HYP
HYP=56/Sin(67)
=60.83618113
=61 ( nearest foot )
Therefore Ans: 61ft
Find the area of a rectangle with
side lengths of in. and in.
2|3
in.
415
in.
Simplify your answer completely.
in.2
Answers
Answer:
Area = length * width
= 4/5 * 2/3
= 8/15
Answer:
[tex]area = \frac{8}{15} {in}^{2} [/tex]
Step-by-step explanation:
The solution is in the attached file
y is directly proportional to x and inversely proportional to the square of w. Give the equation:
Answers
Answer: y=kx/w^2
Step-by-step explanation:
y is directly proportional to x
y∝x
y=kx
y inversely proportional to the square of w.
y ∝ (1/(w)^2)
y=k/w^2
y=kx/w^2
what is the average rate of change if this function interval x = -3 to x = 0
Answers
The average rate of change of the function, over the given interval is 2.
This question is incomplete, the complete question is:
What is the average rate of change of f(x) = 2x+10, if this function interval are x = -3 to x = 0.
What is the average rate of change over the interval?The average rate of change of f(x) over the interval [a,b] is expressed as;
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Given that;
f(x) = 2x + 10Interval: [ -3, 0 ], a = -3 and b = 0We substitute our values into the expression above.
[tex]\frac{f(b)-f(a)}{b-a}\\\\\frac{f(0)-f(-3)}{0-(-3)}\\\\\frac{[2(0)+10]-[2(-3)+10]}{0-(-3)}\\\\\frac{[10]-[-6+10]}{3}\\\\\frac{[10]-[4]}{3}=\frac{6}{3}=2[/tex]
Therefore, the average rate of change of the function, over the given interval is 2.
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Which expression is equivalent to sin?
O sin-
sin
O sin 5
O sin 5
11
sin-
Answers
Answer: Option 4
Step-by-step explanation:
[tex]\sin \frac{7\pi}{6}=\sin \left(-\frac{\pi}{6} \right)=\sin \frac{11\pi}{6}[/tex]
Using equivalent angles, the equivalent expression to [tex]\sin{\left(\frac{7\pi}{6}\right)}[/tex] is:
[tex]\sin{\left(\frac{11\pi}{6}\right)}[/tex]
What are equivalent angles?Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.
In this problem, we have that [tex]\frac{7\pi}{6}[/tex] is on the third quadrant, as [tex]\pi < \frac{7\pi}{6} < \frac{3\pi}{2}[/tex]. Hence the equivalent angle on the first quadrant is:
[tex]\frac{7\pi}{6} - \pi = \frac{7\pi}{6} - \frac{6\pi}{6} = \frac{\pi}{6}[/tex]
The sine is negative on the third and fourth quadrants, hence the equivalent angle on the fourth quadrant is:
[tex]2\pi - \frac{\pi}{6} = \frac{11\pi}{6}[/tex]
Thus, the equivalent expression is:
[tex]\sin{\left(\frac{11\pi}{6}\right)}[/tex]
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Can someone please tell me the answer to this question?
Answers
Answer:
D) 12pm
Step-by-step explanation:
8 pm = 20:00
20:00 + 16:00*4 = 20:00 + 64:00 = 84:00
subtract the 24 hours in 84:00
84:00 - 3 X 24:00 = 12:00
12:00 = 12pm
What is the slope of a line parallel to the line whose equation is3x−4y=8?
−43
−34
34
43
Answers
The slope of the parallel line is 3/4
How to determine the slope?The equation is given as:
3x - 4y = 8
Rewrite as:
4y = 3x - 8
Divide through by 4
y = 3x/4 - 2
A linear equation is represented as:
y = mx + b
Where m represents the slope
By comparison:
m = 3/4
Parallel lines have equal slope
Hence, the slope of the parallel line is 3/4
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In one lottery game, contestants pick five numbers from 1 through 23 and have to match all five for the big prize (in any order). You'll get twice your money back if you match three out of five numbers. If you buy four tickets, what's the probability of matching three out of five numbers?
(Enter your answer as a fraction in lowest terms.)
Answers
The probability of matching three out of five numbers is 153/33649
How to determine the probability?The numbers are given as:
1 to 23
There are five matching numbers
The probability of getting a match is:
p = 5-k/n where k = 0, 1, 2
While the complement probability is
q = (n - 2)/n
Using the above formulas, the probability of getting from 5 is:
P = 5/23 * 4/22 * 3/21 * 18/20 * 17/19
Evaluate the product
P = 153/33649
Hence, the probability of matching three out of five numbers is 153/33649
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3 A bag contains red and blue marbles, such that the probability of drawing a blue marble is 8 An experiment consists of drawing a marble, replacing it, and drawing another marble. The two draws are independent. What is the probability that both of the marbles drawn are blue? a. b. $ 24% * 39% C. d 0 14% 3 A bag contains red and blue marbles , such that the probability of drawing a blue marble is 8 An experiment consists of drawing a marble , replacing it , and drawing another marble . The two draws are independent . What is the probability that both of the marbles drawn are blue ? a . b . $ 24 % * 39 % C. d 0 14 %
Answers
Answer:
My answer: B
Step-by-step explanation:
The probability mass function of random variable X which represents the number of blue marbles drawn in 2 draws with replacement.
X | P(X)
0 | 0.390625
1 | 0.46875
2 | 0.140625
The probability of drawing exactly one blue marble = 0.46875
Complete Question
A bag contains red and blue marbles, such that the probability of drawing a blue marble is 3/8. an experiment consists of drawing a marble, replacing it, and drawing another marble. The two draws are independent. A random variable assigns the number of blue marbles to each outcome.
To write the Probabilty mass function, we have to establish that in two draws with replacement, the possible number of blue marbles that can be drawn is 0, 1 and 2.
Probability of drawing a blue marble = P(B) = (3/8)
Probability of not drawing a blue marble = P(B') = 1 - (3/8) = (5/8)
- Probability of drawing 0 blue marbles in 2 draws with replacement = P(B') × P(B') = (5/8) × (5/8) = (25/64) = 0.390625
- Probability of drawing one blue marble in 2 draws with replacement
= [P(B) × P(B')] + [P(B') × P(B)]
= (2) × (3/8) × (5/8) = (30/64) = (15/32) = 0.46875
- Probability of drawing two blue marble in 2 draws with replacement = P(B) × P(B)
= (3/8) × (3/8) = (9/64) = 0.140625
The probability mass function of random variable X which represents the number of blue marbles draan in 2 draws with replacement.
X | P(X)
0 | 0.390625
1 | 0.46875
2 | 0.140625
b) Probability of drawing one blue marble in 2 draws with replacement
= [P(B) × P(B')] + [P(B') × P(B)]
= (2) × (3/8) × (5/8) = (30/64) = (15/32) = 0.46875
So, B is the answer.
The function ()=2f(x)=x2is transformed to
()=0.4(+1)2f(x)=0.4(x+1)2
Which statement describes the effect(s) of the transformation on the graph of the original function?
The parabola is narrower and shifted 1 unit to the right.
The parabola is narrower and shifted 1 unit to the left.
The parabola is wider and shifted 1 unit to the right.
The parabola is wider and shifted 1 unit to the left.
Answers
Answer:
StepWhat is the measure of z? Z X y 4 9 z = [ ? ]VI-by-step explanation:
9. Find the value of the
underlined digit in the
following number.
739,485
Answers
Answer:
There's no underlined digit
Answer:
See below
Step-by-step explanation:
3 is in the 10 000 place = 30 000
( just put zeroes in place of all of the following numbers)
4. 1/37 of 111 + 1/3 of ? = 0
(1) 3
2) 9
3) 1
4) can not be determined
Answers
Answer:
4
Step-by-step explanation:
1/37 of 111+1/3 of 3= 4
1/37 of 111 +1/3 of 9=6
1/37 of 111 +1/3 of 1=3.3
2x+15
4x + 5
x = [?]
X
O
Answers
Which point is a solution to the system?
A. (0, -1)
B.(2, 3) C.(4,0)
D. (6,-6)
Answers
Answer:
(0;-1)
Step-by-step explanation:
for more details see the attachment.
Write 13.13.13.13.13 in exponential form?
Answers
13.13.13.13.13 in exponential form is 13^5
How to rewrite the expression?The expression is given as:
13.13.13.13.13
The factors of the above expression are 13.
And each factor is grouped by product
There are five 13s in the expression.
So, we have:
13.13.13.13.13 = 13^5
Hence, 13.13.13.13.13 in exponential form is 13^5
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At a recent chess tournament, all 15 of the participants had to fill out a form that gave their names, address and age. The ages of the participants were recorded as follows: 36, 48, 54, 92, 57, 63, 66, 76, 66, 80, 82, 65, 39, 77, and 45. Use the data to construct a frequency table and histogram with 3 classes.(15 points) Classes Class Boundaries
Answers
The frequency table and histogram are shown in the attached picture.
What is a histogram?It is defined as the depiction of numerical data in a graph using a bar with no space. The histogram depicts the approximate distribution of the data.
We have:
The ages of the participants were recorded as follows:
36, 48, 54, 92, 57, 63, 66, 76, 66, 80, 82, 65, 39, 77, 45
The classes can be made:
30-42, 43-55, 56-68, 69-81, and 82-94
The histogram is shown in the picture.
Thus, the frequency table and histogram are shown in the attached picture.
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Select one of the factors of 3x² + 4x - 4.
O (x + 4)
O (3x + 2)
O (3x - 2)
O(x - 2)
Answers
Answer:
(3x-2)
Step-by-step explanation:
3x² + 4x - 4
look for two factors whose product is (3)(-4)=-12 and sum is +4
The factors will be +6 and -2
substitute these factors inplace of 4x to get:
3x² - 2x + 6x - 4
then factorize:
x(3x-2)+2(3x-2)
finally we get factors: (3x-2)(x+2)
If ∠ 1 = 26 o , find the measure of ∠ 4 .
Answers
The angle ∠4 of the given transversal shown in the diagram is gotten as; 26°.
How to find alternate angles?The alternate angle theorem states that when two parallel lines are cut by a transversal, then the resulting alternate interior angles or alternate exterior angles are congruent.
Now, we are told that ∠1 = 26° as seen in the attached diagram. However, it is clear that ∠2 is an alternate angle to ∠1. Thus, we can say that ∠2 = 26°.
Now, Corresponding angles are the pairs of angles that are found in the same relative position on different intersections.
From the diagram we see that ∠4 is a corresponding angle to ∠2. Thus;
∠4 = 26°.
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Factor the trinomial below.
x2 - 14x + 45
Answers
Answer:
(x-9) (x-5)
x = 9 x = 5
Step-by-step explanation:
find out which 2 numbers when multiplied give 45 and
when added give -14
they are -9 and -5
(x-9) (x-5)
x = 9 x = 5
Answer:
[tex]x_{1}=9, x_2=5[/tex]
Step-by-step explanation:
Recall a quadratic formula for quadratic equation [tex]ax^2+bx+c=0[/tex]: [tex]x_{1/2}=\frac{-b\pm \sqrt{b^2 -4ac}}{2a}[/tex]
Notice the constant in the given equation [tex]x^2-14x+45[/tex]:
[tex]a=1, b=-14, c=45[/tex]
Substitute the values into the formula:
[tex]x_{1/2}=\frac{-(-14)\pm \sqrt{(-14)^2 -4\cdot 1\cdot 45}}{2\cdot 1}[/tex]
Calculate the values:
[tex]x_{1/2}=\frac{14\pm \sqrt{196 -180}}{2}=\frac{14\pm\sqrt{16}}{2}=\frac{14\pm 4}{2}[/tex]
It follows that there are two solutions:
[tex]x_1=\frac{14+4}{2}=\frac{18}{2}=9[/tex] and [tex]x_2=\frac{14-4}{2}=\frac{10}{2}=5[/tex].
Find the measure of ∠2.
72°
60°
36°
54°
Answers
Answer:
(c) 36°
Step-by-step explanation:
We assume the pentagon is regular, so each central angle is congruent to the others. Each central angle is bisected by an apothem.
Angle 1Angle 1 is one of 5 congruent central angles, so its measure is ...
∠1 = 360°/5 = 72°
Angle 2Angle 2 is the result of one of the isosceles triangles having its central angle being bisected by an altitude. Its measure is half that of angle 1:
∠2 = 72°/2 = 36°
The measure of angle 2 is 36°.
Angle 3Angle 3 is the other acute angle in the right triangle in which angle 2 is one of the acute angles. Its measure is ...
∠3 = 90° -∠2 = 90° -36° = 54°
What is the area of a sector when r = 2 and 0 = 1.75 radians? [?] sq units Round your answer to the nearest tenth. Enter
Answers
Answer:
Step-by-step explanation:
The area of a sector in terms of radians as opposed to degrees is
[tex]A=\frac{\theta}{2\pi }*\pi r^2[/tex]
Filling in the formula accordingly gives us
[tex]A=\frac{1.75rad}{2\pi rad}*\pi (2)^2[/tex]
The radians cancel out, the pi's cancel out, the 2 in the denominator cancels out (divides into 2-squared once), leaving us with
A = 1.75(2) so
A = 3.5 units squared
1. Simplify (7y²)
(3y³)
Answers
Answer:
21 y power 5
Step-by-step explanation:
To access his bank’s ATM, Tom must choose a four-digit PIN. Any digit from 0 through 9 can be used in the PIN, but digits may not be repeated. How many possible PIN numbers are there?
Answers
Answer:
Try using the permutations formulae - nPr
n = 10
r = 4
you should get the answer. I don't have calculator on me and I'm lazy searching an online calculator. cheers
Which rules define the function graphed below? (-2,2) (0,6) (4,6)
Answers
Answer:
y = 2x + 3; y = -1/3 x + 3
Step-by-step explanation:
Both lines have y-intercept 3.
The slopes are 2 and -1/3.
The equations are: y = 2x + 3; y = -1/3 x + 3
QUESTION IS DOWN BELOW WORTH 30 POINTS
Answers
Answer:
395.84
Step-by-step explanation:
V=πr2h=π·3^2·14
Lenny bought x shares of stock for Sy per share last month. He paid
his broker a flat fee of $20. He sold the stock this month for Sp per
share, and paid his broker a 2% commission. Express Lenny's net
proceeds algebraically.
Answers
Lenny's net proceeds algebraically are found as;[tex]\rm |xy + 20 - \frac{98}{100} |[/tex]
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
Let the bought share will be $ x, and $y is the price per share
Paid fees to the broker = $ 20
The total amount spent = $(xy+20)
The price at which each share sells = $ A
Broker commission = 2 %
The total amount obtained after selling the shares;
⇒ ax - 2% of ax
⇒ 98 % of ax
Hence, Lenny's net proceeds algebraically are found as;[tex]\rm |xy + 20 - \frac{98}{100} |[/tex]
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Answer:
Step-by-step explanation:
what were Laura net proceeds