The third degree polynomial function with zeros of −3, −1, and 4, and a y-intercept of −13 is y = -13/12 (x³ - 13x + 12)
Polynomial function:
polynomial function refers a functions of single independent variables, in which variables can occur more than once, raised to an integer power.
Given,
Third-degree, with zeros of −3, −1, and 4, and a y-intercept of −13.
Here we need to construct a polynomial function with the stated properties and reduce all fractions to lowest terms.
The standard form for the third degree polynomial function is written as,
y = K (x + zero1) (x + zero2) (x + zero3)
Here we know the values of zeros as -3, -1 and -4.
Apply it on the general form,
y = K (x -3) (x - 1) (x + 4) ----------------------(1)
And the value of y intercept is -13 then the value of x is 0.
So, it can be written as,
-13 = K(0 - 3) (0 - 1) (0 + 4)
-13 = K (-3)(-1)(4)
-13 = K (12)
K = -13/12
Now, we have to apply these value on the equation (1), then we get,
y = -13/12 (x -3) (x - 1) (x + 4)
When we expand these, then we get the polynomial function as,
y = -13/12 (x³ - 13x + 12)
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w - 1/2 = 8 1/4 solve for w
Answer:
W = 35/4 aka 8 3/4 or 8.75
Step-by-step explanation:
Answer: w = 35/4
Step-by-step explanation: w−
2
1
=8
4
1
Multiply both sides of the equation by 4, the least common multiple of 2,4.
4w−2=8×4+1
Multiply 8 and 4 to get 32.
4w−2=32+1
Add 32 and 1 to get 33.
4w−2=33
Add 2 to both sides.
4w=33+2
Add 33 and 2 to get 35.
4w=35
Divide both sides by 4.
w= 35/4
Make
x
the subject of the formula
3
a
x
=
m
+
n
Answer:
Below
Step-by-step explanation:
3ax = (m+n) divide both sides by 3 a
x = (m+n) / 3a that's it
I know a) is 100
Confused about b) I got 81 but its wrong
Need an explanation along with answer
Answer:
45
Step-by-step explanation:
At this point, b) is basically asking for how many two digits numbers have a greater digit on the right from 0-9, because we already know the other two digits in the four-digit pin.
01-09 has 9 poissibilites.
12-19 has 8 possibilites.
23-29 has 7 possibilites.
34-35 has 6 possibilites.
45-49 has 5 possibilites.
56-59 has 4 possibilities.
67-69 has 3 possibilities.
78-79 has 2 possibilities.
89 has 1 possibility.
90-99 has 0 possibilities.
9+8+7+6+5+4+3+2+1+0=45 possibilities.
Answer:
A) 100 codes, B) 45 codesStep-by-step explanation:
Part AEach of the digits 3 and 4 can get numbers 0 through 9, in total 10 options per each digit:
10*10 = 100 combinationsPart BThe two- digit combinations with the last digit being larger has the following cases:
Digit 4 is 9, then digit 3 can get 0 through 8 ⇒ 9 options,Digit 4 is 8, then digit 3 can get 0 through 7 ⇒ 8 options,...Digit 4 is 1, then digit 3 can get 0 ⇒ 1 optionTotal number of possibilities:
9 + 8 + 7 + ... + 1 = (9 + 1)*9/2 = 10*9/2 = 45Please help with my question
Answer:
what is ur questions we cant see them
The coordinates of the vertices of trapezoid ABCD are A(2, 6), B(5, 6), C(7, 1), and D(−1, 1). The coordinates of the vertices of trapezoid A′B′C′D′ are A′(−6, −2), B′(−6, −5), C′(−1, −7), and D′(−1, 1). Which statement correctly describes the relationship between trapezoid ABCD and trapezoid A′B′C′D′? Responses Trapezoid ABCD is congruent to trapezoid A′B′C′D′ because you can map trapezoid ABCD to trapezoid A′B′C′D′ by reflecting it across the x-axis and then across the y-axis, which is a sequence of rigid motions. trapezoid A B C D, is congruent to , trapezoid A prime B prime C prime D prime, because you can map , trapezoid A B C D, to , trapezoid A prime B prime C prime D prime, by reflecting it across the , x, -axis and then across the , y, -axis, which is a sequence of rigid motions. Trapezoid ABCD is congruent to trapezoid A′B′C′D′ because you can map trapezoid ABCD to trapezoid A′B′C′D′ by rotating it 180° about the origin and then translating it 4 units left, which is a sequence of rigid motions. trapezoid A B C D, is congruent to , trapezoid A prime B prime C prime D prime, because you can map , trapezoid A B C D, to , trapezoid A prime B prime C prime D prime, by rotating it 180° about the origin and then translating it 4 units left, which is a sequence of rigid motions. Trapezoid ABCD is congruent to trapezoid A′B′C′D′ because you can map trapezoid ABCD to trapezoid A′B′C′D′ by reflecting it across the x-axis and then rotating it 90° clockwise, which is a sequence of rigid motions. trapezoid A B C D is congruent to trapezoid A prime B prime C prime D prime because you can map trapezoid A B C D to trapezoid A prime B prime C prime D prime by reflecting it across the x -axis and then rotating it 90° clockwise, which is a sequence of rigid motions., Trapezoid ABCD is not congruent to trapezoid A′B′C′D′ because there is no sequence of rigid motions that maps trapezoid ABCD to trapezoid A′B′C′D′.
The statement which correctly describes the relationship between trapezoid ABCD and trapezoid A'B'C'D' is "Trapezoid ABCD ≅ trapezoid A'B'C'D'.
The correct answer option is option C
What is the relationship between trapezoid ABCD and trapezoid A'B'C'D' ?The coordinates of the vertices of trapezoid ABCD are A (2,6), B (5,6), C (7,1), and D (-1,1).
The coordinates of the vertices of trapezoid A'B'C'D' are A' (-6, -2),B' (-6, -5), C' (-1, -7), and D' (-1, 1).
Given trapezoid ABCD:
Parent coordinates of ABCD = A (2,6), B (5,6), C (7,1), and D (-1,1)
Translated coordinates of A'B'C'D' = A' (-6, -2),B' (-6, -5), C' (-1, -7), and D' (-1, 1).
Based on the reflection rule:
Reflection across x axis (x , y) -> ( x , -y) and rotating it 90°clockwise (x , y) -> ( -y, x).
Therefore, if trapezoid ABCD is reflected across the x-axis and then rotating it 90°clockwise
ABCD ≅ trapezoid A'B'C'D'
Complete question:
The coordinates of the vertices of trapezoid ABCD are A (2,6), B (5,6), C (7,1), and D (-1,1). The coordinates of the vertices of trapezoid A'B'C'D' are A' (-6, -2),B' (-6, -5), C' (-1, -7), and D' (-1, 1). Which statement correctly describes the relationship between trapezoid ABCD and trapezoid A'B'C'D' ?
A. Trapezoid ABCD ≅ trapezoid A'B'C'D'
You can reflect trapezoid ABCD across the x-axis and then across the y-axis.
B. Trapezoid ABCD ≅ trapezoid A'B'C'D'
You can rotate trapezoid ABCD 180°about the origin and then translating it 4 units left.
C. Trapezoid ABCD ≅ trapezoid A'B'C'D'
You can reflect trapezoid ABCD across the x-axis and then rotating it 90°clockwise.
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What is an angle that is supplementary to ∠ECF?
Please help!!!
Answer:
HCE or ECH
Explanation:
Supplementary is angle that add up to 180° (A line)
Answer: HCE
Step-by-step explanation:
A supplementary angle is an angle that when added to another angle, equals 180 degrees, or a straight line.
Angles HCE and ECF add up to 180 degrees.
one lap of a running track is 350m Kyle jogs 5 complete laps at an average speed of 5 m/s how long does it take him in seconds
Answer:
350 seconds to jog 5 laps.
Step-by-step explanation:
One lap of a running track is 350m Kyle jogs 5 complete laps at an average speed of 5 m/s. How long does it take him in seconds?
First, to run one lap:
350m / 5 meters per second = 70 seconds
Now, solve for five laps:
70 seconds * 5 laps = 350 seconds to jog 5 laps.
Which of the following is equivalent to 36^-1/2
Answer:
1/6
Step-by-step explanation:
[tex]36^{-1/2}=\frac{1}{36^{1/2}}=\frac{1}{\sqrt{36}}=\frac{1}{6}[/tex]
Jacy went on a bike ride of 60 miles. He realized that if he had gone 10 mph faster, he would have arrived 8 hours sooner. How fast did he actually ride?
Answer:
Let r be the rate at which he travels and t be the time.
Then, rt = 60
If he travels 8 mph faster, he arrives 10 hours sooner, so
(r+8)(t - 10) = 60
Multiplying, rt - 10r + 8t - 80 = 60
Substituting rt = 60, we get
60 - 10r + 8t - 80 = 60
Then, 8t = 10r + 80
t = 5/4r + 10
Substitute this into rt = 60
r(5/4r + 10) = 60
5/4r^2 + 10r - 60 = 0
Multipling by 4/5
r^2 + 8r - 48 = 0
(r + 12)(r - 4) = 0
r = -12, 4
A negative solution does not make sense
Thus, r = 4 4 mph is the solution.
Checking, rt = 60, so 4t = 60, and t = 15
Showing that this meets the other condition,
(r+8)(t - 10) = (4+8)(15-10) = 12 * 5 = 60
It checks.
The lifetime (in hours) of an electronic component is a random variable with density function given by
\(f(y)=\left\{\begin{array}{ll}
\frac{1}{100} e^{-y / 100}, & y>0, \
0, & \text { elsewhere. }
\end{array}\right.
\)
Three of these components operate independently in a piece of equipment. The equipment fails if at least two of the components fail. Find the probability that the equipment will operate for at least 200 hours without failure.
The probability that the equipment will operate for at least 200 hours without failure is [tex](1-e^{-2} )^2[2e^-2+1][/tex].
Given:
mean = 1/100
Let X = the number of components that fail before 200 hours . The X has a binomial distribution n = 3 and p = 1 – e^-2.
probability p = 3/2[tex]p^{2} (1-p)[/tex] + 3/3 [tex]p^{3}[/tex].
= 3([tex]1-e^-2)^2[/tex][tex]e^-2[/tex] + ([tex]1-e^-2)^3[/tex]
= [tex](1-e^-^2)^2[3e^-^2 - e^-^2+1][/tex]
= [tex](1-e^{-2} )^2[2e^-2+1][/tex]
Therefore the probability that the equipment will operate for at least 200 hours without failure is [tex](1-e^{-2} )^2[2e^-2+1][/tex].
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I need help with this
The function (f-g)(x) = x²+3x+5
How to find (f-g)(x)?
A function is an expression, rule, or law that defines a relationship between an independent variable and a dependent variable
Given: f(x) = √16x⁴ = 4x² and g(x) = 3x²-3x-5
To evaluate (f-g)(x) such g(x) from f(x). Thus:
(f-g)(x) = 4x²-(3x²-3x-5)
= 4x²-3x²+3x+5
= x²+3x+5
Therefore, (f-g)(x) is x²+3x+5. The 4th option is the answer
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Rewrite −15(5x + 6y) using distribution.
−75x − 90y
−75x + 90y
−75x + 6y
−5x − 21y
What is the Distribution Property?
The distribution property in math is a process that allows an equation to be simplified to help easily solve problems. Expressions that qualify to use the distributive property are usually written in the format: a(b +c)
a is then distributed to both b and c, rewriting the equation as ab +ac, where a has been multiplied to both values.
In this problem, you can distribute -15 to both 5x and 6y.
This will leave you with and equation that resembles this:
(-15×5x) + (-15×6y)
Multiply -15 to the coefficient attached to the variable to get your answer.
Your answer is -75x + -90y or -75x-90y
find the product. [5 5 [-4 9
-2 3] 8 7]
The product of the given matrix is [tex]\left[\begin{array}{ccc}20&80\\32&3\end{array}\right][/tex]
What is a matrix?
A rectangular matrix is a set of numbers arranged into a predetermined number of rows and columns. The rows of a matrix are formed when the elements are placed in a horizontal matrix. The columns of a matrix are formed by the elements when they are stacked in the matrix vertically.
Here, we have given a matrix that is
A = [tex]\left[\begin{array}{ccc}5&5\\-2&3\end{array}\right][/tex] B = [tex]\left[\begin{array}{ccc}-4&9\\8&7\end{array}\right][/tex]
We have to find the product of this matrix
[tex]\left[\begin{array}{ccc}5&5\\-2&3\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}-4&9\\8&7\end{array}\right][/tex]
First, we multiply the first row of matrix A with the first column of matrix B then continue in this manner, we get
[tex]\left[\begin{array}{ccc}20&80\\32&3\end{array}\right][/tex]
Hence, the product of the given matrix is [tex]\left[\begin{array}{ccc}20&80\\32&3\end{array}\right][/tex]
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find an equation for the curve that passes through the point (1,0) and whose slope at (x,y) is xe^y.
An equation for the curve that passes through the point (1,0) and whose slope at (x,y) is xe^y is y = -1/x -1.
Define slope.The value of the steepness or the direction of a line in a coordinate plane is referred to as the slope of a line, also known as the gradient. Given the equation of a line or the coordinates of points situated on the straight line, slope can be determined using a variety of approaches. The slope is nothing more than the tangent to the angle formed with the x-axis measured. As a result, it is simply an angle's measurement.
Given,
The curve that passes through the point (1,0) and whose slope at (x,y) is xe^y.
Since x-2 is equal to the slope of the function f(x), we can express that as
dy/dx = x^-2
dx multiplication and integration of both sides:
y = -1/x + C
Connecting the provided point:
0 = -1/1 + C
C = -1
Consequently, the curve's equation is
y = -1/x -1
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10) Tell whether the slope of AB is parallel, perpendicular, or neither to the
slope of CD. A(-3, 2) and B(2, 4) C(4, 0) and D(6,-5)
AB slope is 2/5, CD slope is -5/2; Neither
AB slope is 2/5, CD slope is -5/2; Parallel
AB slope is 2/5, CD slope is -5/2: Perpendicular
AB slope is -5/2, CD slope is 2/5; Parallel
Answer:
its A
Step-by-step explanation:
What is the a equal to in the math problem below??
-6(a+8)
Answer: -6a-48
Step-by-step explanation:
-6(a+8)
distribute and you get
-6a-48
Find the value of Z such that 0.11 of the area lies to the right of Z.
Round your answer to 2 decimal places.
The value of z is 1.23.
Given:
the value of Z such that 0.11 of the area lies to the right of Z.
0.11 = 11%
z score is calculated :
z = x - μ / σ
where μ=0 and σ=1
so z value is equal to 1.23.
More details in the image uploaded.
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What is four-twelfths times seven? Your answer should be in whole or mixed number form.
Answer: twenty eight-twelfths (or seven-thirds in the simplest form)
Step-by-step explanation:
\Petty Marine Co. has a long-term plan to expand to a second location that's actually near some water, so they want to start a monthly annuity to save $170,000 in capital over 9 years. The best rate they can find is 8.5%. Find the monthly payment. Round to the nearest cent.
The monthly payment To pay off $170,000 in 9 years at 8.5%
Monthly PaymentThe monthly payment is the amount paid per month to pay off the loan in the time period of the loan. When a loan is taken out it isn't only the principal amount, or the original amount loaned out, that needs to be repaid, but also the interest that accumulates.
The formula of monthly payment is given as
M = PJ / 1- (1 + J)^-n
m = monthly payment p = principal J = interest rate per monthn = number of months to pay the loan.M = $2257.49
The monthly payment on this loan is $2257.49
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a small group selected by the pollsters to represent the most important characteristics of an entire population are known as a
Answer:
SampleStep-by-step explanation:
The small group selected by pollsters to represent the entire population is called a “Sample”.Please help please please please
Answer:
m<M = 76°
m<N = 76°
LN = 18 in
Step-by-step explanation:
The sum of interior angles in a triangle is equal to 180.
triangle LMN is an isosceles triangle and the measure of M is equal to N and LM = LN.
Now the measure of missing angle:
m<M + m<N + 28 = 180 subtract 28 from both sides
m<M + m<N = 152 since the measure of M is equal to N divide 152 by 2
152 ÷ 2 = 76 each angle is 76°
Christa sells bracelets during the summer months, and she made this pictograph to represent her sales. A pictograph is entitled Bracelets Sold. It shows the summer months and pictures of bracelets. A key shows one bracelet equals 4 bracelets. June, 3 bracelets. July, 5 bracelets. August, 2 bracelets. How many bracelets did Christa sell in June?
Answer: 32 bracelets
First multiply each bracelet by 4 to get the correct amount:
3x4=12
4x5=20
Then, add the two.
12+20=32
Step-by-step explanation:
What is the shortest distance from the point (9, 1) to the line y = 2x + 3? Round to the
nearest tenth.
The shortest distance from the point (9, 1) to the line y = 2x + 3 is 10 units
The coordinates of the point = (9,1)
The equation of the line is
y = 2x + 3
Here the slope of the line is 2
The shortest distance between the point and the second line will be the perpendicular distance between the point and line
The perpendicular line slope will be -(1/m)
= -(1/2)
This perpendicular line will pass through the point (9, 1)
The point slope form is
y - 1 = -(1/2)(x - 9)
y - 1 = -(1/2x) + 9/2
y = -(1/2)x + 9/2 + 1
y = -(1/2)x + 11/2
Solve the equation
y = 2x + 3
y = -(1/2)x + 11/2
0 = (2 + 1/2)x -5/2
5/2 x = -5/2
x = -5/2 / 5/2
x = -1
Then
y = 2(-1) + 3
y = -2 + 3
y = 1
The distance between the point (9,1) and (-1, 1)
= [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
= [tex]\sqrt{(-1-9)^2+(1-1)^2}[/tex]
= [tex]\sqrt{100}[/tex]
= 10 units
Hence, the shortest distance from the point (9, 1) to the line y = 2x + 3 is 10 units
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5. suppose a normal distribution has a mean of 4 and a standard deviation of 1.5. what is the z-score of x
If a normal distribution has a mean of 4 and a standard deviation of 1.5. what is the z-score of x= 5.5 is 1
The mean of the normal distribution = 4
Standard deviation of the normal distribution = 1.5
The value of x = 5.5
The z-score of the normal distribution = The mean of the normal distribution / Standard deviation of the normal distribution
Substitute the values in the equation
The z-score of the normal distribution = (5.5 - 4) / 1.5
Substract the terms
= 1.5 / 1.5
= 1
Hence, if a normal distribution has a mean of 4 and a standard deviation of 1.5. what is the z-score of x= 5.5 is 1
The complete question is:
suppose a normal distribution has a mean of 4 and a standard deviation of 1.5. what is the z-score of x = 5.5
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Can Anyone Help Me? I'm Stuck On This Question
Please Don't Give Bogus Answer Or I Will Report
The distance travelled by the car in 34 minutes is 22.667 miles.
We are given a car. The car is travelling at a steady speed. It travels 1.5 miles in 2.25 minutes. We need to find the distance travelled by the car in 34 minutes. First of all, we need to find the speed of the car. The speed of the car is the ratio of the distance travelled and the corresponding time taken.
v = s/t
v = 1.5/2.25
v = 0.667
Hence, the speed of the car is 0.667 miles per minute. The speed of the car remains constant throughout its journey. Let the distance travelled by the car be denoted by "d" . The distance travelled in 34 minutes is calculated below.
d = v*t
d = 0.667*34
d = 22.667
Hence, the distance travelled by the car in 34 minutes is 22.667 miles.
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For an inverse variation, write an equation that gives the value of k in terms of x and y.
The equation that gives the value of k in terms of x and y is k = y*x .
In the question ,
it is given that ,
the variation is an inverse variation .
So , equation representing the inverse proportionality is
y ∝ 1/x ,
to remove the proportionality sign (∝) , we introduce
the constant k which is called as Constant of Proportionality .
So , the equation becomes
y = k * 1/x
y = k/x
Simplifying further , we get
k = y*x
Therefore , The equation that gives the value of k in terms of x and y is k = y*x .
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……………………………………………………..
Answer:
Absolute value is to remove any negative sign in front of a number, and to think of all numbers as positive (or zero).
Hope this helped, good luck on your homework!
Answer: how far a number is from zero
Step-by-step explanation: Cannot be a negative. The absolute value of -12 is 12.
The population of the school increased by 16%, and now the population is 667. What was the population before the increase?
well, the population before the increase was "x", which oddly enough is the 100%, now if it increased by 16% that means 100% + 16% = 116%, and we happen to know that's 667
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 667& 116 \end{array} \implies \cfrac{x}{667}~~=~~\cfrac{100}{116} \\\\\\ \cfrac{x}{667}=\cfrac{25}{29}\implies 29x=(25)(667)\implies x=\cfrac{(25)(667)}{29}\implies x=575[/tex]
Mrs. Nicholas baked two batches of cookies. The first batch consisted of 120 gingerbread cookies and the second batch consisted of 150 shortbread cookies. Mrs. Nicholas saved the same fraction of cookies from each batch. If Mrs. Nicholas saved 20 more shortbread cookies than gingerbread cookies, what fraction of the cookies did she save?
Mrs. Nicholas baked two batches of cookies. The first batch consisted of 120 gingerbread cookies and the second batch consisted of 150 shortbread cookies. Mrs. Nicholas saved the same fraction of cookies from each batch. If Mrs. Nicholas saved 20 more shortbread cookies than gingerbread cookies then,
Here, given data as the first batch was 120 gingerbread cookies and the second batch consist of 150 shortbread cookies.
And, the same fractions of cookies from each batch were saved.
Let x parts of each of cookies were saved.
Then, the number of the saved gingerbread cookies = 120 x
While, the number of the saved shortbread cookies = 150 x
And, Again according to the question, the number of the saved shortbread cookies is 20 more than the number of the saved shortbread cookies.
That is equal to 150 x - 120 x = 20
⇒ 30 x = 20
⇒ x = 2/3
Hence the answer is, Mrs. Nicholas saved 2/3 part of each cookies.
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a carnival has a game where players can win stuffed animals. the rules allow for players to win no more than 10 small animals, no more than 6 large animals, and no more than 12 total animals. let x
The form of a system of inequalities that would allow you to solve for the number of each type of animal that can be won is 10x + 6y = 12.
Given:
A carnival has a game where players can win stuffed animals. the rules allow for players to win no more than 10 small animals, no more than 6 large animals, and no more than 12 total animals.
x be the number of small animals and y be the number of large animals
The number of small animals = 10x
Number of large animals = 6y
The equation:
= 10x + 6y = 12.
Therefore the form of a system of inequalities that would allow you to solve for the number of each type of animal that can be won is 10x + 6y = 12.
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