Answer: [tex]x^4-x^3-16x^2+16x[/tex]
Step-by-step explanation:
Factor theorem : If x=a is a zero of a polynomial p(x) then (x-a) is a factor of p(x).
Given: Zeroes of polynomial : -4,0, 1, and 4.
Then Factors = [tex](x-(-4)), (x-0), (x-1) and (x-4)[/tex] [By factor theorem ]
[tex]=(x+4), (x-0), (x-1) and (x-4)[/tex]
Multiplying these factors to get polynomial in standard form.
[tex](x+4)\times(x-0)\times(x-1)\times(x-4) \\\\= x(x+4)(x-4)(x-1)\\\\= x(x^2-4^2)(x-1)\\\\= x(x^2-16)(x-1)\\\\= x(x^2-16)(x-1)\\\\=x(x^2x+x^2\left(-1\right)+\left(-16\right)x+\left(-16\right)\left(-1\right))\\\\= x(x^3-x^2-16x+16)\\\\=x^4-x^3-16x^2+16x[/tex]
Hence, B is the correct option.
4,336 is 10 times as much as?
Answer:
433.6
Step-by-step explanation:
What is 3.173 rounded to the nearest tenth
THE answer is 3.173≅3.2(nearest tenth)
Sixty percent of the cost of the dining set is the same as one half the cost of the dining set decreased by $180. What is the cost of the dining set?
Answer:
The cost of the dining set = $200
Step-by-step explanation:
Let
Cost of the dining set=x
Sixty percent of the cost of the dining set
= 60% of x
=60/100 * x
= 0.6x
One half the cost of the dining set decreased by $180.
=1 1/2 of x - 180
= 1.5 * x - 180
= 1.5x - 180
Sixty percent of the cost of the dining set is the same as one half the cost of the dining set decreased by $180
0.6x = 1.5x - 180
Collect like terms
0.6x - 1.5x = -180
-0.9x = -180
Divide both sides by -0.9
x= -180 / -0.9
=200
x= $200
Check:
0.6x
= 0.6(200)
=120
1.5x - 180
=1.5(200) - 180
= 300 - 180
=120
Call: Im(formula = Repair.Costs ~ Miles.Driven, data = Dataset) Residuals: Min 1Q Median 3Q Max -247.81 -144.68 29.07 64.89 343.86 Coefficients: Estimate (Intercept) 72.807562 Miles.Driven 0.009792 Std. Error 89.456108 0.001601 t value 0.814 6.117 Pr>It) 0.432 5.2e-05 *** Signif. codes: 0) ****' 0.001 '**'0.01 '*' 0.05'.'0.1''1 Residual standard error: 180.3 on 12 degrees of freedom Multiple R-squared: 0.7572, Adjusted R-squared: 0.7369 F-statistic: 37.42 on 1 and 12 DF, p-value: 5.2e-05
Using these regression results, what is the estimated repair cost on a car that has 74,000 miles on it?
Answer:
797.42
Step-by-step explanation:
Given the Output of a linear regression data using R;
From the result table;
Intercept = 72.807562
Gradient or slope = 0.009792
General form of a linear equation:
y = mx + c
Where y = response variable ; x = explanatory variable ; c = intercept and m = gradient / slope
Hence, the regression equation becomes :
y = 0.009792x + 72.807562
Using these regression results, what is the estimated repair cost on a car that has 74,000 miles on it?
x = 74,000
y = 0.009792(74000) + 72.807562
y = 724.608 + 72.807562
y = 797.42
Answer:
The estimated repair cost on a car that has 74,000 miles on it is $797.42.
Step-by-step explanation:
The statement: Im(formula = Repair.Costs ~ Miles.Driven, data = Dataset) implies that the variable "Repair.Costs" is the dependent variable and the variable "Miles.Driven" is the independent variable.
From the provided data the regression equation formed is:
[tex]\text{Repair.Costs}=72.807562+0.009792\cdot \text{Miles.Driven}[/tex]
Compute the estimated repair cost on a car that has 74,000 miles on it as follows:
[tex]\text{Repair.Costs}=72.807562+0.009792\cdot \text{Miles.Driven}[/tex]
[tex]=72.807562+0.009792\cdot 74000\\\\=72.807562+724.608\\\\=797.415562\\\\\approx 797.42[/tex]
Thus, the estimated repair cost on a car that has 74,000 miles on it is $797.42.
. Which category(s) does 75% belong? I. Real II. Whole III.Rational IV. Integer V. Irrational VI. Natural *
A. III and IV only
B. I and III only
C. I, II, IV, V, and VI only
D. I, II, III, IV, and VI only
E. I, II, and III
Answer: B.) 1 and 111 only
Real, rational
Step-by-step explanation: Real is an encompassing terms when defining numbers as it includes all integers, whole, rational and irrational numbers. Therefore 75% belondmgs to a category of real numbers.
75% which is equivalent to 75/100 is a rational number as it can be written in the form p/q . where both p and q are integers and q is not 0. This also means 75% is not an irrational number.
75% = 0.75 is neither a whole number nor an integer as it contains decimal.
75% is not a natural number as natural numbers are counting numbers starting from 1.
Different amounts of force are applied to the same boat over several trials, and the acceleration is measured. In a graph of acceleration versus net force, what does the slope of the graph represent?
the speed of the boat <-- MY ANSWER
the inverse of the mass of the boat
the mass of the boat
the inverse of the speed of the boat
Thank you :)
Answer: The inverse mass of the boat (B)
Step-by-step explanation:
The relationship between force, mass and acceleration is: [tex]F = ma[/tex]. So, the slope of the graph represents the inverse of the mass of the boat.
From the question, we understand that the graph is acceleration vs net force.
This means that, the points on the graph will be:
[tex](F_1,a_1)[/tex] and [tex](F_2,a_2)[/tex]
The slope (m) of a linear graph is:
[tex]m =\frac{y_2 - y_1}{x_2 - x_1}[/tex]
In this case, it will be:
[tex]m =\frac{a_2 - a_1}{F_2 - F_1}[/tex] ---- slope
Recall that:
[tex]F = ma[/tex]
Make mass (m) the subject
[tex]m = \frac Fa[/tex]
See attachment for further explanation
Hence, the slope of the graph represents (b) the inverse of the mass of the boat
Read more about force, mass and acceleration at:
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Which of the following is required by k-means clustering ? a. defined distance metric b. number of clusters c. initial guess of centroids d. all of the above
Answer:
d. all of the above
Step-by-step explanation:
K-means clustering is a term used to describe a technique of vector quantization, that attempts to partition "n" observations into "k" clusters whereby each observation refers to the cluster with the closest mean which represents a model of the cluster.
This implies that the K-means algorithm recognizes the "k" number of centroids, and then assigns every data point to the closest cluster while the centroids remain as small as possible.
Hence, the following is required of K-means clustering:
1. defined distance metric
2. number of clusters
3. initial guess of centroids
Therefore, in this case, the correct answer is option D: All of the above.
find the unknown angles. please help
Answer:
60°, 60°, 60°
Step-by-step explanation:
Since, two side of the given triangle are congruent l. Therefore, measures of both the interior angle will be equal.
By remote interior angle theorem:
120° = x + x
120° = 2x
120°/2 = x
60° = x
Third angle = 180° - 120° = 60°
Hence measure of all the three angles of the triangle are 60°, 60° and 60°
zalman started solving 53 times 26 by breaking the problem into parts. Here is what he has done so far 50 times 20=1000 50 times 6=300 3 times 20= 60 what does he still need to multiply
Answer:
3 * 6 = 18
Step-by-step explanation:
53 * 26 =
= (50 + 3) * (20 + 6)
= 50 * 20 + 50 * 6 + 3 * 20 + 3 * 6
= 1000 + 300 + 60 + 18
Answer: 3 * 6 = 18
I have a rectangular garden. I usually grow
carrots in 2/5 of my garden but I want to
take 1/4 of the carrots section to grow
strawberries. After I make this change, how
much of my whole garden will be
strawberries?
Answer:
[tex]\frac{1}{10}[/tex]
Step-by-step explanation:
If you originally have [tex]\frac{2}{5}[/tex] of your garden reserved for carrots, are taking [tex]\frac{1}{4}[/tex] of the carrot space ( [tex]\frac{2}{5}[/tex] ) for strawberries, then the total amount of your garden left for strawberries will be [tex]\frac{2}{5}\cdot\frac{1}{4}[/tex]
[tex]\frac{2}{5}\cdot\frac{1}{4} = \frac{2}{20}[/tex]
[tex]\frac{2}{20}[/tex] simplifies down to [tex]\frac{1}{10}[/tex].
Hope this helped!
is 7.401 larger or smaller then 7.04
Answer:
Larger
Step-by-step explanation:
Since, 7.401 > 7.04
Therefore, 7.401 is larger than 7.04.
Answer:
Larger.
7.401 = 7.40 (rounding)
7.40 > 7.04
Bye!
Write an expression to match this situation and combine like terms: Ling has 4m pounds of flour. She buys another 2 packages of flour, each weighing m pounds. How much flour does ling have in terms of m?
Answer:
4m + 2m = 6m
Step-by-step explanation:
What is the value of (45−13)×52+56 expressed in simplest form?
What is the explicit rule for the geometric sequence? 4.05,1.35,0.45,0.15,...
Step-by-step explanation:
Since the above sequence is a geometric sequence
For an nth term in a geometric sequence
That's
[tex]A(n) = a( {r})^{n - 1} [/tex]
where
r is the common ratio
a is the first term
n is the number of terms
From the question
a = 4.05
r = 1.35 / 4.05 = 0.33
Substitute the values into the above formula
We have
[tex]A(n) = 4.05( {0.33})^{n - 1} [/tex]
Hope this helps you
g 3.23 Marbles in an urn. Imagine you have an urn containing 5 red, 3 blue, and 2 orange marbles in it. (a) What is the probability that the first marble you draw is blue
Answer:
[tex]P(Blue) = 0.3[/tex]
Step-by-step explanation:
Given
Red = 5
Blue = 3
Orange = 2
Required
Probability that the first marble is Blue
First, the total number of marble has to be calculated;
[tex]Total = Red\ Marble + Blue\ Marble + Orange\ Marble[/tex]
[tex]Total = 5 + 3 + 2[/tex]
[tex]Total = 10[/tex]
The probability of Blue being the first is calculated as thus;
[tex]P(Blue) = \frac{n(Blue)}{Total}[/tex]
[tex]P(Blue) = \frac{3}{10}[/tex]
[tex]P(Blue) = 0.3[/tex]
Hence, the required probability is 0.3
Select the appropriate technique with the problem you are looking for.
a. Checking the equal variance assumption
b. Checking the normal assumption
c. Check for model misspecification
d. Check for dependent errors
1. Create a scatterplot of hat versus your QN X's
2. Create a stem-and-leaf display of the zresiduals
3. Create a scatterplot of the residuals versus time period collected
4. Create a scatterplot of the residuals versus yhat
5. Create a scatterplot of the residuals versus your QN X's
Answer:
A, B, C, D
Step-by-step explanation:
(A) Checking the Equal Variance Assumption, the appropriate technique to use is:
- The ANOVA (Analysis of Variance) F test
- Plot residuals against fitted values
(B) Checking the Normal Assumption, the appropriate techniques to use are:
- Test for Kurtosis & Skewness
- Kolmogorov-Smirnov Test
- Q-Q Plots (the graphical method) also known as Quantile Plot
- Do not use a histogram; it is not advisable
(C) Checking for Model Misspecification, the appropriate techniques to use are:
- The Ramsey Regression Specification Error Test; also called RESET
- The Davidson & MacKinnon J. Test
(D) Checking for dependent errors, the appropriate technique to use is:
- Plot residuals against time variables
the supplement of a 45 degree angle is
Answer:
135°
Step-by-step explanation:
The supplement of an angle is the measure in which, when combined with the previous angle, will total up to 180°. Since we already know the measure of 1, we can easily find the supplement, assuming [tex]x[/tex] is the supplement of 45.
[tex]45 + x = 180\\\\x = 180-45\\\\x=135[/tex]
Hope this helped!
Graph the image of the given segment under a di6with scale factor -1/3 and center of dilatation (0,0). Line on graph is A (-6,9) B (-3,3) please explain to me how I solve this.
Answer:
A ' = (2, -3)
B ' = (1, -1)
See attached image below for the diagram
========================================================
Explanation:
Point A is originally at (-6, 9). It moves to A ' (2,-3) after applying the scale factor. This is because we basically multiply the scale factor (-1/3) by each coordinate of point A
-6 * (-1/3) = 2
9 * (-1/3) = -3
The negative scale factor is like a mirror in a way. Points in negative regions move to positive regions, and vice versa. Since |-1/3| = 1/3 is less than 1, this means the new point (2,-3) is closer to (0,0) compared to its original counterpart.
Point B follows the same idea
B(-3,3) moves to B ' (1, -1) after multiplying each coordinate by -1/3
-------------
Side note: The segment A'B' is 1/3 as long compared to segment AB.
Simplify (5ab4c)(-abc2)
Answer: -5a²b⁵c³
Step-by-step explanation: 5ab⁴c can be thought of as 5a¹b⁴c¹ and in the second part of the problem, since there is no coefficient on -a¹b¹c², we can give it a coefficient of 1.
Now simply multiply the coefficients
and add the exponents to get -5a²b⁵c³.
Kate is making a pasta salad for her family party. She has 3 pounds of pasta salad to serve 12 people. She wants to give an equal amount of pasta salad to each person in her family. How much pasta salad should Kate put in each person’s bowl?
Answer:
0.25 of a pound, 1/4
Step-by-step explanation:
3 divided by 12 = 0.25
make h the subject A=1/2(a+c)h
Answer:
h = [tex]\frac{2A}{a+c}[/tex]
Step-by-step explanation:
Given
A = [tex]\frac{1}{2}[/tex](a + c)h
Multiply both sides by 2 to clear the fraction
2A = (a + c)h ( divide both sides by (a + c) )
[tex]\frac{2A}{a+c}[/tex] = h
Answer:
[see below]
Step-by-step explanation:
[tex]a = 1/2(a+c)h\\\\1/2(a+c)h = a\\\\2 * 1/2(a+c)h = a * 2\\\\h(a+c)=2a\\\\\frac{h(a+c)}{a+c}=\frac{2a}{a+c}; a \neq -c\\\\\boxed{h=\frac{2a}{a+c}; a \neq -c}[/tex]
Hope this helps.
A student wrote three papers in mathematics examination marks for two papers we're 77and 72 respectively.to obtain grade A, an average of not less than 75marks is required for the three papers
Answer:
The student must score at least 76 in the third subject
Step-by-step explanation:
Given
Scores in 2 subjects = 77 and 72
Number of subjects = 3
Required
Determine the scores in the third subject to get an average of 75
Represent the score in the third subject with y
Average in 3 scores is calculated as thus;
[tex]Average = \frac{Sum\ of\ 3\ scores}{3}[/tex]
Substitute 75 for Average
[tex]75 = \frac{Sum\ of\ 3\ scores}{3}[/tex]
Multiply both sides by 3
[tex]3 * 75 = \frac{Sum\ of\ 3\ scores}{3} * 3[/tex]
[tex]3 * 75 = Sum\ of\ 3\ scores[/tex]
[tex]225 = Sum\ of\ 3\ scores[/tex]
Substitute (77 + 72 + y) for Sum of 3 scores
[tex]225 = 77 + 72 + y[/tex]
[tex]225 = 149 + y[/tex]
Subtract 149 from both sides
[tex]225 - 149 = 149 - 149 + y[/tex]
[tex]225 - 149 = y[/tex]
[tex]76= y[/tex]
[tex]y = 76[/tex]
Hence, the student must score at least 76 in the third subject
y=3/2x+5 in standard form
Answer:
3x -2y = -5
Step-by-step explanation:
Standard form is ...
ax +by = c
where the leading coefficient (a, or b if a=0) is positive and a, b, c are mutually prime.
Multiplying the equation by 2 gives ...
2y = 3x +5
We can subtract 2y+5 to get standard form:
3x -2y = -5
Which are vertical angles?
O AFE and BFD
O BFC and DFE
O AFE and CFD
O BFC and EFA
Answer:
✔️AFE AND BFD
Step-by-step explanation:
vertical angles are angles are formed from a pair of intersecting lines. The vertical angles are angle AFE and BFD
What are vertical angles?These angles are formed from a pair of intersecting lines, The meet at a point X in a figure.
from the given figure, we need to find which of the angles are vertical angles. Since vertical angles are equal, hence the measure of this angles must be equal.
From the diagram, the vertical angles are angle AFE and BFD
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Hurry Please!!! Which two numbers on the number line have an absolute value of 4 Select the location of both numbers on the number line.
Answer:
-4 and 4
Step-by-step explanation:
Hello!
An absolute value is a number regardless if it is negative or positive
For example, the absolute value of -6 is 6, -3 is 3 and 5 is 5
So numbers that have an absolute value of 4 are 4 and -4
Hope this Helps!
Evaluate the expression shown below and write your answer as a fraction in simplest form. 3 (-20 8 Answer: Submit Answer attempt 1 out of 2 O
Answer:
[tex] -\frac{1}{40} [/tex]
Step-by-step explanation:
To evaluate [tex] -\frac{3}{8} - (-\frac{7}{20}) [/tex], start by opening the bracket.
When opening the bracket, we would be multiplying negative sign by negative sign, which equal positive sign.
Thus,
[tex] -\frac{3}{8} + \frac{7}{20} [/tex]
Solve further by performing addition operation to make both fractions one
The common denominator of 8 and 20 is 40,
[tex] \frac{5(-3) +2(7)}{40} [/tex]
[tex] \frac{-15 + 14}{40} [/tex]
[tex] \frac{-1}{40} = -\frac{1}{40} [/tex]
The answer of given expression in simplest form is: [tex]\dfrac{-1}{40}\\[/tex]
The given expression is:
[tex]-\dfrac{3}{8} - (-\dfrac{7}{20})[/tex]
Multiplying negative sign with negative sign will result in positive sign of the latter term.
The simplification will be done as follows:
[tex]\\-\dfrac{3}{8} - (-\dfrac{7}{20})\\\\= -\dfrac{3}{8} + \dfrac{7}{20}\\\\=\dfrac{-3 \times 5 + 7 \times 2}{40}\\\\= -\dfrac{1}{40}\\[/tex]
In the above process, we the lcm of 8 and 20 was taken which is equal to 40.
Thus, the simplest form of the given expression is [tex]\dfrac{-1}{40}\\[/tex].
Learn more here:
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10y-3(y+5) what’s the answer
Answer:
7y-15
Step-by-step explanation:
10y-3(y+5)
=10y-3y-15
=7y-15
Hope it helped :)
Write the rule that transforms p(x) into q(x), where q(x)=2p(x+3)−6
Answer: - A horizontal shift of 3 units to the left.
- A vertical dilation of factor 2.
- A vertical shift of 6 units down.
Step-by-step explanation:
Here we have 3 transformations:
I will start giving general cases for each transformation:
Horizontal shift.
When we have a function f(x), an horizontal shift to the right of N units (N positive) is written as:
g(x) = f(x - N)
So in our case, we have a shift to the LEFT of 3 units.
Vertical dilation/contraction.
A vertical dilation/contraction of factor A, is written as:
g(x) = A*f(x)
if A > 1, this is a dilation, if A < 1, this is a contraction.
In the case of our problem, we have A = 2.
Vertical shift:
A vertical shift is written as:
g(x) = f(x) + N.
If N is positive, we have a shift of N units up, if N is negative, we have a shift of N units down.
in this case, N = -6.
Then the transformations are:
q(x) = 2*p(x -(-3)) - 6
- A horizontal shift of 3 units to the left.
- A vertical dilation of factor 2.
- A vertical shift of 6 units down.
Find x. Assume that segments that appear tangent are tangent.
Answer:
27
Step-by-step explanation:
FE is tangent to the circle with center D at point E and DE is radius.
[tex] \therefore FE \perp DE \implies m\angle FED = 90\degree [/tex]
DE = x
DF = x + 18
FE = 36
By Pythagoras theorem:
[tex] DF^2 = DE^2 + FE^2 [/tex]
[tex] (x+18)^2 = x^2 + 36^2 [/tex]
[tex] x^2 + 36x + 324= x^2 + 1296[/tex]
[tex] 36x + 324= 1296[/tex]
[tex] 36x = 1296-324[/tex]
[tex] 36x = 972[/tex]
[tex] x = \frac{972}{36}[/tex]
[tex] x =27[/tex]
The value of x from the given figure, which is radius of a circle is 27 units.
From the given figure, FE=36 units, DE=x units and FD=x+18 units.
What is the angle formed with tangent and radius?Tangent and radius of a circle meet at 90°. If we draw a radius that meets the circumference at the same point, the angle between the radius and the tangent will always be exactly 90°.
Using Pythagoras theorem, we have
FD²=FE²+DE²
⇒ (x+18)²=36²+x²
⇒ x²+36x+324=1296+x²
⇒ 36x=1296-324
⇒ 36x=972
⇒ x=972/36
⇒ x=27 units
Hence, the value of x from the given figure, which is radius of a circle is 27 units.
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Find the greatest common factor of 16 and 36
Answer:
GCF= 4
Step-by-step explanation:
A factor is a number that evenly divides into another number.
First, list the factors of 16.
1 , 2, 4, 8, 16
Next, list the factors of 36
1 , 2 , 3, 4, 6, 9, 12, 18, 36
Now, find the GCF, or greatest common factor. The GCF is the largest factor that both numbers share.
16 : 1 , 2, 4, 8, 16
36 : 1 , 2 , 3, 4, 6, 9, 12, 18, 36
When we compare the lists, we see the biggest number that appears in both lists is 4.
The Greatest Common Factor of 16 and 36 is 4.
Answer: 4
Step-by-step explanation: The Greatest Common Factor of two
numbers is the largest factor shared by both numbers.
As a review in case you didn't know, a factor of a
number divides into that number without a remainder.
To find the greatest common factor of 16 and 36,
we begin by finding all of the factors of each number.
Let's start by finding the factors of 16.
16 ÷ 1 = 16
16 ÷ 2 = 8
16 ÷ 4 = 4
We can stop here because if we continue
dividing, we won't find any new factors.
So the factors of 16 are 1, 2, 4, 8, and 16.
Now let's find the factors of 36.
36 ÷ 1 = 36
36 ÷ 2 = 18
36 ÷ 3 = 12
36 ÷ 4 = 9
36 ÷ 6 = 6
So the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
Now find the largest number shared by the two lists.
In this case, the largest number is 4.
So the greatest common factor of 16 and 36 is 4.