Which polynomial function has a leading coefficient of 2, root –4 with multiplicity 3, and root 10 with multiplicity 1?
f(x) = 2(x – 4)(x – 4)(x – 4)(x + 10)
f(x) = 2(x + 4)(x + 4)(x + 4)(x – 10)
f(x) = 3(x – 4)(x – 4)(x + 10)
f(x) = 3(x + 4)(x + 4)(x – 10)
Answers
Answer:
B
Step-by-step explanation:
The leading coefficient is 2 so that rules out C and D. The function also has a root of -4 but the function has to be the opposite giving you +4 and -10.
So, the answer would be 2(x+4)(x+4)(x+4)(x-10)
I got this right on the unit test!!!!
Answer:
b
Step-by-step explanation:
Related Questions
Sami travels 15 blocks on his skateboard in 5 minutes. At this speed,
how many blocks can he travel in 18 minutes?
Answers
Answer:
54 blocks in 18 min
Step-by-step explanation:
3 blocks per min
3x18=54 ur welcome hope this helps
A smaller number is 3 less than half a larger number. The larger number is 10 times 1 less than the smaller number. Let x represent the smaller number, and let y represent the larger number. Which equations can be used to model the situation? Check all that apply. x = one-half y minus 3 2 x minus y = negative 6 2 x minus y = negative 3 x = one-half (y minus 3) y = 10 (x minus 1) Mark this and return
Answers
The required equations can be used to model the situation is x = 1/2y - 3 and y = 10(x-1)
What is equation ?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."
Equations can be classified as either conditional equations or identities. Any value of the variables results in an identity being true. Only certain values of the variables in a conditional equation result in truth. When two expressions are joined together by the equals sign ("="), the result is an equation.
If the smaller number is 3 less than half a larger number, this is expressed as:
x = 1/2y - 3 ⇒(1)
If the larger number is 10 times 1 less than the smaller number, this is expressed as;
y = 10(x-1) ⇒ (2)
Substitute equation 2 into 1 as shown;
x = 1/2y - 3
x = 1/2(10x-10)- 3
x = 5x - 5 - 3
-4x = -8
x = 2
The required equations can be used to model the situation is x = 1/2y - 3 and y = 10(x-1)
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Answer:
a d
Step-by-step explanation:
Sue has $1.80 in dimes and nickels. If she has 9 more dimes than nickels, How many of dimes and nickels does she have?
Answers
Answer:
15 dimes6 nickelsStep-by-step explanation:
Let d represent the number of dimes. Then d-9 is the number of nickels. The total value (in cents) is ...
10d +5(d-9) = 180
15d -45 = 180 . . . . . simplify
d -3 = 12 . . . . . . . . . .divide by 15
d = 15
15 -9 = 6 = number of nickels
Sue has 15 dimes and 6 nickels.
Answer:
15 dimes, 6 nickels
Step-by-step explanation:
D = # of dimes, and N = # of nickels
10D + 5N = 180
D = N + 9
Substitute:
10 (N + 9) + 5N = 180
10N + 90 + 5N = 180
15N = 90
N = 6
D = 15
x/3=y/8=z/5 và 2x+3y-z=50
Answers
x＝6
(x, y, z)＝(6, 16, 10)
Hope my answer helped u :)
All the following are Perfect Squares except for which one?
198
121
81
64
Answers
Answer:
Step-by-step explanation:
198 is not a perfect square
All the given numbers are perfect squares except 198
The given numbers:
1981218164To find:
non perfect square number among the given numbersA perfect square is obtained by multiplying two equal integers
The perfect squares obtained by multiplying two equal integers are shown below.
64 = 8 x 8 (it is a perfect square)81 = 9 x 9 (it is a perfect square)121 = 11 x 11 (it is a perfect square)The non-perfect square is shown below
198 = 14.07 x 14.07 (14.07 is not an integer, hence 198 is not a perfect square)Thus, all the given numbers are perfect squares except 198
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I need this practice problem answered I will provide the answer options in another pic
Answers
The inverse of a matrix can be calculated as:
\(\begin{gathered} \text{When} \\ A=\begin{bmatrix}{a} & {b} & {} \\ {c} & {d} & {} \\ {} & {} & \end{bmatrix} \\ \text{Then A\textasciicircum-1 is:} \\ A^{-1}=\frac{1}{ad-bc}\begin{bmatrix}{d} & -{b} & {} \\ {-c} & {a} & {} \\ {} & {} & \end{bmatrix} \end{gathered}\)Then, let's start by calculating the inverse of the given matrix:
\(\begin{gathered} \begin{bmatrix}{4} & {1} & {} \\ {-2} & {3} & {} \\ {} & {} & \end{bmatrix}^{-1}=\frac{1}{4\cdot3-1\cdot(-2)}\begin{bmatrix}{3} & -{1} & {} \\ {-(-2)} & {4} & {} \\ {} & {} & \end{bmatrix} \\ \begin{bmatrix}{4} & {1} & {} \\ {-2} & {3} & {} \\ {} & {} & \end{bmatrix}^{-1}=\frac{1}{14}\begin{bmatrix}{3} & -{1} & {} \\ {2} & {4} & {} \\ {} & {} & \end{bmatrix} \end{gathered}\)The problem says he multiplies the left side of the coefficient matrix by the inverse matrix, thus:
\(\begin{gathered} \begin{bmatrix}{4} & {1} & {} \\ {-2} & {3} & {} \\ {} & {} & \end{bmatrix}^{-1}\begin{bmatrix}{4} & {1} & {} \\ {-2} & {3} & {} \\ {} & {} & \end{bmatrix}\cdot\begin{bmatrix}{x} & {} & {} \\ {y} & {} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{4} & {1} & {} \\ {-2} & {3} & {} \\ {} & {} & \end{bmatrix}^{-1}\begin{bmatrix}{2} & {} & {} \\ {-22} & {} & {} \\ {} & {} & {}\end{bmatrix} \\ \end{gathered}\)*These matrices will be the options to put on the first and second boxes.
Then:
\(\begin{gathered} \begin{bmatrix}{x} & {} & {} \\ {y} & {} & {} \\ {} & {} & {}\end{bmatrix}=\frac{1}{14}\begin{bmatrix}{3} & -{1} & {} \\ {2} & {4} & {} \\ {} & {} & \end{bmatrix}\cdot\begin{bmatrix}{2} & {} & {} \\ {-22} & {} & {} \\ {} & {} & {}\end{bmatrix}\text{ This is for the third box} \\ \begin{bmatrix}{x} & {} & {} \\ {y} & {} & {} \\ {} & {} & {}\end{bmatrix}=\frac{1}{14}\begin{bmatrix}{3\times2+(-1)\times(-22)} & & {} \\ {2\times2+4\times(-22)} & & {} \\ {} & {} & \end{bmatrix}=\frac{1}{14}\begin{bmatrix}{28} & & {} \\ {-84} & & {} \\ {} & {} & \end{bmatrix}\text{ This is the 4th box} \\ \begin{bmatrix}{x} & {} & {} \\ {y} & {} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{28/14} & & {} \\ {-84/14} & & {} \\ {} & {} & \end{bmatrix}=\begin{bmatrix}{2} & & {} \\ {-6} & & {} \\ {} & {} & \end{bmatrix}\text{ And finally this is the last box} \end{gathered}\)
Which has a greater average rate of change over the interval where -1≤x≤3; the function
g(x)=x²+6x or the function f(x) = 2*. Provide justification for your answer.
Answers
Answer: Step-by-step explanation:
To find the average rate of change of a function over an interval, we can use the following formula:
average rate of change = (y2 - y1)/(x2 - x1)
Where x1 and x2 are the values of x at the beginning and end of the interval, and y1 and y2 are the corresponding values of the function at those points.
In this case, we are asked to compare the average rate of change of the functions g(x) and f(x) over the interval where -1≤x≤3.
For the function g(x) = x²+6x, we can plug in the given values for x1, x2, y1, and y2 to find the average rate of change:
average rate of change = (g(3) - g(-1))/(3 - (-1))
= (9 + 18 - (1 - 6))/(4)
= 27/4
= 6.75
For the function f(x) = 2, we can plug in the given values for x1, x2, y1, and y2 to find the average rate of change:
average rate of change = (f(3) - f(-1))/(3 - (-1))
= (2 - 2)/(4)
= 0
Since the average rate of change of the function g(x) is greater than the average rate of change of the function f(x), the function g(x) has a greater average rate of change over the interval where -1≤x≤3.
I hope this helps clarify the comparison of the average rate of change for these two functions. Do you have any other questions?
The mapping diagram represents a relation where x represents the independent variable and y represents the dependent variable. A mapping diagram with one circle labeled x values containing values negative 3, negative 1, 1, 3, and 5 and another circle labeled y values containing values 0, 2, and 5 and arrows from negative 3 to 0, negative 1 to 2, 1 to 0, 3 to 2, and 5 to 5. Is the relation a function? Explain. No, because for each input there is not exactly one output No, because for each output there is not exactly one input Yes, because for each input there is exactly one output Yes, because for each output there is exactly one input
Answers
Yes, because for each input there is exactly one output. Therefore, the relation represented by the mapping diagram is a function.
To determine if the relation represented by the given mapping diagram is a function, we need to check if each input (x value) has exactly one output (y value) associated with it.
From the given mapping diagram, we can see that:
The input value -3 is associated with the output value 0.
The input value -1 is associated with the output value 2.
The input value 1 is associated with the output value 0.
The input value 3 is associated with the output value 2.
The input value 5 is associated with the output value 5.
As we can see, each input value has exactly one output value associated with it. Therefore, the relation represented by the mapping diagram is a function.
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El mayor es Novecientos mil cuatrocientos ochenta y nueve , y cuarenta mil dos
Answers
El número "Novecientos mil cuatrocientos ochenta y nueve" se representa como 900,489 en notación numérica.
Por otro lado, el número "cuarenta mil dos" se representa como 40,002.
Si estamos buscando determinar cuál de estos dos números es mayor, podemos comparar las cifras en cada posición.
Comenzando desde la izquierda, el primer dígito de 900,489 es 9, mientras que el primer dígito de 40,002 es 4.
Dado que 9 es mayor que 4, podemos concluir que 900,489 es mayor que 40,002.
En general, al comparar números, se debe observar cada posición en orden de mayor a menor importancia.
Esto significa que el primer dígito a la izquierda es el más significativo y tiene más peso en el valor total del número.
Si los dígitos en la posición más significativa son iguales, se debe pasar a la siguiente posición hasta que se encuentre una diferencia.
En este caso, dado que el primer dígito de 900,489 es mayor que el primer dígito de 40,002, no es necesario comparar los dígitos en posiciones posteriores.
Por lo tanto, podemos concluir que el número "Novecientos mil cuatrocientos ochenta y nueve" (900,489) es mayor que "cuarenta mil dos" (40,002).
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Three reams of recycled paper and five reams of cardstock weigh one hundredpounds. If seven reams of recycled paper weighs as much as five cardstock, howmuch does one ream of each type of paper?
Answers
Answer:
recycled: 10 pounds
cardstock: 14 pounds
Explanation:
Let's call x the weight of one ream of recycled paper and y the weight of one ream of cardstock.
If 3 reams of recycled paper and 5 reams of cardstock weigh 100 pounds, we can write the following equation
3x + 5y = 100
Additionally, if 7 reams of recycled paper weigh as much as 5 cardstock, we get
7x = 5y
So, taking into account the last equation, we can replace 5y by 7x in the first equation
3x + 5y = 100
3x + 7x = 100
Then, we can solve for x
10x = 100
10x/10 = 100/10
x = 10
Finally, we can replace x = 10 on 7x = 5y and solve for y as follows
7x = 5y
7(10) = 5y
70 = 5y
70/5 = 5y/5
14 = y
Therefore, the weight of one ream of each type of paper is
recycled: 10 pounds
cardstock: 14 pounds
Two angles of a triangle have the same measure and the third one is 30 degrees greater than the measure of each of the other two. Find the measure of the LARGEST angle in the triangle.
Answers
Answer:
75 degrees
Step-by-step explanation:
Isosceles triangle with 3rd angle being 30 degrees:
2x + 30 = 180
2x = 150
X = 75
Show all steps!
K-2= 6
Answers
Add the 2 to 6 on the other side of the =sign
Which leaves K alone and K equals 8
Answer:
8
Step-by-step explanation:
k - 2 = 6
+2 +2
k = 8
Whenever solving for these your first goal is to get rid of any constants isolating the variable by itself. To get rid of -2 we add 2 to both sides, whatever we do to the left we do to the right and vice versa. When we add 2 to 6 we get 8 and that is how we got our answer.
normally distributed with an average of 12.601 seconds and standard deviation of 1.5707 seconds. Would it be unusual to see a time between 10.2 and 13.86 seconds? Question 8 options: 1) It is impossible for a value in this interval to occur with this distribution of data. 2) A value in this interval is not unusual. 3) We do not have enough information to determine if a value in this interval is unusual. 4) A value in this interval is borderline unusual. 5) A value in this interval is unusual.
Answers
The correct option regarding the normal distribution is given as follows:
2) A value in this interval is not unusual.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:
\(Z = \frac{X - \mu}{\sigma}\)
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The parameters for this problem are given as follows:
\(\mu = 12.601, \sigma = 1.5707\)
The probability is the p-value of Z when X = 13.86 subtracted by the p-value of Z when X = 10.2, hence:
\(Z = \frac{X - \mu}{\sigma}\)
Z = (13.86 - 12.601)/1.5707
Z = 0.8
Z = 0.8 has a p-value of 0.7881.
\(Z = \frac{X - \mu}{\sigma}\)
Z = (10.2 - 12.601)/1.5707
Z = -1.53
Z = -1.53 has a p-value of 0.0630.
Hence:
0.7881 - 0.0630 = 0.7251 > 0.5 -> not unusual.
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started her dance class at 6:45 PM. She spent 85 minutes in dance class. At what time did Michelle finish her dance class?
Answers
Answer:
8:05 or 8:10
Step-by-step explanation:
6:35 plus 60 minutes 6:95 then change it to 7:60 to 8:05 pm or 8:10 pm
the answer is 8:05 to 8:10
Answer:
8:10
Step-by-step explanation:
Solve the triangle. Round decimal answers to the nearest tenth.
Answers
The measure of the angle s 50. 2 degrees
How to determine the valueTo determine the angle, we need to know the different trigonometric identities.
These trigonometric identities are;
sinecosinetangentcotangentcosecantsecantFrom the information given, we have that;
The ratios of the identities are;
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
sin θ = opposite/hypotenuse
Then, we have that;
cos A = 16/25
divide the values
cos A = 0. 64
Find the inverse
A = 50. 2 degrees
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what is the slope of the line determined by any two solutions to the equation ( 2 / x ) + ( 3 / y ) ?
Answers
The slope of the given line ( 2 / x ) + ( 3 / y ) = 0 which is calculated by solving the equation is equal to ( - 3 / 2).
Slope Definition:A line's slope is defined as the ratio of the change in y coordinate to the change in x coordinate.
The net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx.
Hence, the expression for the change in y-coordinate with respect to the change in x-coordinate is,
m = y/x = y/x = change in y/change in x
where "m" represents a line's slope.
Furthermore, the slope of the line can be shown as
tan θ = Δy/Δx
So, tan θ to be the slope of a line.
As given in the question,
Given equation of the line is equal to ( 2 / x ) + ( 3 / y ) = 0
Simplify the given equation to get the slope intercept form :
( 2 / x ) + ( 3 / y ) = 0
⇒ ( 2 / x ) = - ( 3 / y )
⇒ 2y = -3x
⇒ y = ( - 3 / 2 ) x + 0 __(1)
Standard slope intercept form of the line is given by :
y = mx + c __(2)
Where m is the slope of the line
Compare (1) and (2) to get the slope of the line we get,
Slope of the line 'm' = ( - 3 / 2 )
Therefore, the slope of the given line by simplify the equation
( 2 / x ) + ( 3 / y ) = 0 in slope intercept form is equal to ( - 3/2).
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A rectangle measured 3/4 units long and 1/3 unit wide. find the area.
Answers
Area of a rectangle = length * width
____________________
Then
The Area = (3/4)*(1/3) =(3*1)/(4*3)=3/12=1/4
Work out 30% of $150
Answers
Answer:
$\(45\)
Step-by-step explanation:
\(30\)% \(\mathrm{of}\) $\(150\)
\(=\frac{30}{100}\times 150\\\)
\(=\) $\(45\)
The length of a side of a cube can be determined
by Ending the cube root of its volume. If a cube has
a volume of 64 cm', what is the length of a sde?
A 4.0 cm
B. 8.0 cm
C. 160 cm
D 32.0 cm
Answers
Answer:
Side of cube = 4 cm
Step-by-step explanation:
Given:
Volume of cube = 64 cm³
Find:
Side of cube
Computation:
Volume of cube = side³
64 = side³
Side of cube = 4 cm
Evaluate the definite integral of sin^5(x)dx from 0 to pi/2.
Answers
Step-by-step explanation:
The definite integral of sin^5(x)dx from 0 to pi/2 can be evaluated using the method of substitution.
Let u = sin(x), then du = cos(x)dx
The integral becomes:
∫sin^5(x)dx = ∫u^5du from 0 to sin(π/2)
= (u^6)/6 evaluated at sin(π/2) and 0
= (sin^6(π/2))/6 - 0
= (1^6)/6
= 1/6
So, the definite integral of sin^5(x)dx from 0 to pi/2 is equal to 1/6.
List all the subsets of the given set.
{e, n, t}
Answers
The subsets of the set {e, n, t} are given as follows:
{{}, {e}, {n}, {t}, {e,n}, {e,t}, {n,t}, {e,n,t}}.
How to obtain the number of subsets in a set?Considering a set with n elements, the number of subsets in the set is the nth power of 2, that is:
\(2^n\)
The set for this problem is given as follows:
{e, n, t}
The cardinality is given as follows:
n = 3.
Hence the number of subsets is given as follows:
2³ = 8.
The subsets are given as follows:
{{}, {e}, {n}, {t}, {e,n}, {e,t}, {n,t}, {e,n,t}}.
In which {} is the empty set.
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Ravi says,” if 10 years are added to my age, then my age becomes 25.”if Ravi’s present age is x years,
then find the linear equation satisfying the given condition.
Answers
Answer:
The linear equation satisfying the given condition is,
\(x=t+15\)
where x is Ravi's age and t is the number of years
(after 10 years (t=10) his age becomes 25)
Step-by-step explanation:
Let x be Ravi's age
Now, his current age is unknown, but if you add 10 to it, then it becomes 25, so
x + 10 =25
so, his current age is x = 25 =10
x = 15
Now, we find the linear equation satisfying the given condition,
Let t be the number of years that have passed since the present time
so, if 0 years have passed, his age will be 15 years
after 1 year, his age will be 16 years
after 10 years, his age will be 25 years and so on
so
\(x = t + 15\)
this satisfies the given condition, since if we add ten years i.e t = 10,
then we get 25
The equation is:
⇨ x + 10 = 25Work/explanation:
Here's the linear equation for Ravi's age.
Ravi's age is x.
If you add 10 to x you get x + 10.
That gives 25.
So the linear equation is x + 10 = 25.
Find a • b. a = <5, 2>, b = <4, 5> (2 points) a <20, 10> b <9, 7> c -10 d 30
Answers
The dot product of vectors a and b is option D. 30.
How did we get the value?To find the dot product of two vectors, you need to multiply their corresponding components and then sum the results.
Let's calculate the dot product of vectors a = <5, 2> and b = <4, 5>:
a • b = (5 x 4) + (2 x 5)
= 20 + 10
= 30
Therefore, the dot product of vectors a and b is 30.
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How many fluid ounces are in 2 pints
Answers
Answer: 32 ounces
Step-by-step explanation:
1 pint = 16 ounces, 16 x 2 = 32 ounces.
Solve the inequality for x. –2x + 3 < –13
Answers
Answer:
x > 8
Step-by-step explanation:
When you divide or multiply both sides of an inequality by a negative number, the equality is switched.
-2x + 3 < -13
(-2x + 3) - 3 < -13 - 3
-2x < -16
-2x/-2 < -16/-2
x > 8
Answer:
x > 8
Step-by-step explanation:
In order to solve the inequality for x, we must get x by itself on one side of the equation.
-2x + 3 < -13
3 is being added to -2x. The inverse of addition is subtraction. Subtract 3 from both sides of the equation.
-2x + (3-3) < (-13-3)
-2x < -13 -3
-2x < -16
x is being multiplied by -2. The inverse of multiplication is division. Divide both sides of the equation by -2.
-2x/-2 < -16/-2
When dividing or multiplying by a negative number, remember to flip the inequality sign.
-2x/-2 > -16/-2
x > -16/-2
x > 8
The solution to the inequality is x>8
Pls help me someone this is annoying me
Answers
Answer:
They are both 42 cm
Step-by-step explanation:
1. Lin runs 2 miles in 2/5 for an hour, Tyler runs 8 2/4 miles in 4/3 of an hour. How long
does it take each of them to run 10 miles at that rate?
Answers
please help! ASAP!
Find the perimeter of the figure below.
Answers
Answer:
30 ft
Step-by-step explanation:
The Pythagorean theorem can be used to find the length of the unknown side. It tells you the sum of the squares of the legs is equal to the square of the hypotenuse.
12² +a² = 13²
a² = 169 -144 = 25
a = √25 = 5
The sum of the side lengths is ...
(12 +5 +13) ft = 30 ft
The perimeter is 30 feet.
If z is directly proportional to the product of x and y and if z is 21 when x is 6 and y is 7, then x, y, and z are related by the equation z =
Answers
Answer:
z = \(\frac{1}{2}\) xy
Step-by-step explanation:
given z is directly proportional to xy then the equation relating them is
z = kxy ← k is the constant of proportion
to find k use the condition z = 21 when x = 6 and y = 7
21 = k × 6 × 7 = 42k ( divide both sides by 42 )
\(\frac{21}{42}\) = k , that is
k = \(\frac{1}{2}\)
equation relating them is
z = \(\frac{1}{2}\) xy
The sum of the 112th term of the geometric series is 256 and the common ratio is 3/4. Find the first term of the first geometric series.
Answers
Answer:
First term = 64
Step-by-step explanation:
We are given the formula for the nth term of a geometric series to be;
S_n = (a1(1 - rⁿ))/(1 - r)
Where:
S_n is the sum of n terms
A1 is first term
r is common ratio
We are given;
S_112 = 256
r = ¾
Thus;
256 = a1(1 - ¾^(112))/(1 - ¾)
256 = a1(4)
a1 = 256/4
a1 = 64