Answer:
Among the four choices, [tex](x + 5)[/tex] is the only one that is not a linear factor of this polynomial function.
Step-by-step explanation:
Let [tex]a[/tex] denote some constant. A linear factor of the form [tex](x - a)[/tex] is a factor of a polynomial [tex]f(x)[/tex] if and only if [tex]f(a) = 0[/tex] (that is: replacing all [tex]x[/tex] in the polynomial [tex]f(x) \![/tex] with the constant [tex]a\![/tex] would give this polynomial a value of [tex]0[/tex].)
For example, in the second linear factor [tex](x - 2)[/tex], the value of the constant is [tex]a = 2[/tex]. Verify that the value of [tex]f(2)[/tex] is indeed [tex]0[/tex]. (In other words, replacing all [tex]x[/tex] in the polynomial [tex]f(x) \![/tex] with the constant [tex]2[/tex] should give this polynomial a value of [tex]0\![/tex].)
[tex]\begin{aligned}f(2) &= 2^3 - 5\times 2^2 - 4 \times 2 + 20 \\ &= 8 - 20 - 8 + 20 \\ &= 0 \end{aligned}[/tex].
Hence, [tex](x - 2)[/tex] is indeed a linear factor of polynomial [tex]f(x)[/tex].
Similarly, it could be verified that [tex](x - 5)[/tex] and [tex](x + 2)[/tex] are also linear factors of this polynomial function.
Rewrite the first linear factor [tex](x + 5)[/tex] in the form [tex](x - a)[/tex] for some constant [tex]a[/tex]: [tex](x + 5) = (x - (-5))[/tex], where [tex]a = -5[/tex].
Calculate the value of [tex]f(5)[/tex].
[tex]\begin{aligned}f(5) &= (-5)^3 - 5\times (-5)^2 - 4 \times (-5) + 20 \\ &= (-125) - 125 + 20 + 20 \\ &= -210\end{aligned}[/tex].
[tex]f(5) \ne 0[/tex] implies that [tex](x - (-5))[/tex] (which is equivalent to [tex](x + 5)[/tex]) isn't a linear factor of this polynomial function.
The IRS wants to develop a method for detecting whether or not individuals have overstated their deductions for charitable contributions on their tax returns. To assist in this effort, the IRS supplied data found in the file IRS.xlsx that accompanies this book listing the adjusted gross income (AGI) and charitable contributions for 11 taxpayers whose returns were audited and found to be correct.
Required:
a. Prepare a scatter plot of the data. Does there appear to be a linear relationship between these variables?
b. Develop a simple linear regression model that can be used to predict the level of charitable contributions from a return's AGI. What is the estimated regression equation?
c. Interpret the value of R2.
d. How might the IRS use the regression results to identify returns with unusually high charitable contributions?
Answer:
ŷ = 195.698X - 6169.941 ;
R² = 0.9224 ; About 92% variation in the value of Charitable contribution can be explained by the best fit line.
Step-by-step explanation:
The excel data:
AGI: (X) :
55
58
63
67
74
78
83
88
92
98
105
Charitable contribution Y:
4200
4800
6329
8017
7400
8600
12290
10406
11820
12090
14675
The scatter plot can b found in the picture attached below.
The estimated regression equation obtained is :
ŷ = 195.698X - 6169.941
Where ;
slope of the regression line = 195.698 ;
Intercept = - 6169.941
The R² value is called the Coefficient of determination which gives the proportion of variation due to the best fit line. Using the Coefficient determination calculator ; R² = 0.9224
About 92% variation in the value of Charitable contribution can be explained by the best fit line.
The table shows several points for function f(x).
A 2-column table with 8 rows. Column 1 is labeled x with entries negative 4, negative 2, 0, 2, 4, 6, 8, 10. Column 2 is labeled f (x) with entries 19, 15, 11, negative 6, negative 7, negative 8, negative 10, negative 14.
Which statement correctly identifies a point on the graph of f–1(x)?
A. The point (4, –7) is on the graph of f(x), so the point (7, –4) will be on the graph of f–1(x).
B. The point (–2, 15) is on the graph of f(x), so the point (2, –15) will be on the graph of f–1(x).
C. The point (–4, 19) is on the graph of f(x), so the point (–4, –19) will be on the graph of f–1(x).
D. The point (10, –14) is on the graph of f(x), so the point (–14, 10) will be on the graph of f–1(x).
Answer:
The answer is D.
Step-by-step explanation:
Just took the test. Got 100%.
when comparing data quickly, it’s best to use a
A. bar graph
B. pie graph
C. line graph
D. scatter plot
Answer:
line graph
Step-by-step explanation:
usa testprep
A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 6% vinegar, and the second brand contains 11% vinegar. The chef
wants to make 200 milliliters of a dressing that is 9% vinegar. How much of each brand should she use?
Answer:
The chef will use 120 milliliters of 11% vinegar, and 80 milliliters of 6% vinegar.
Step-by-step explanation:
Since a chef is going to use a mixture of two brands of Italian dressing, and the first brand contains 6% vinegar, and the second brand contains 11% vinegar, and the chef wants to make 200 milliliters of a dressing that is 9% vinegar, to determine how much of each brand should she use the following calculation must be performed:
100 x 0.11 + 0 x 0.06 = 11
90 x 0.11 + 10 x 0.06 = 10.5
80 x 0.11 + 20 x 0.06 = 10
70 x 0.11 + 30 x 0.06 = 9.5
60 x 0.11 + 40 x 0.06 = 9
200 x 0.6 = 120
200 x 0.4 = 80
Thus, the chef will use 120 milliliters of 11% vinegar, and 80 milliliters of 6% vinegar.
1. How would you describe your ability to apply rules for dividing powers ?
Find the midpoint of AB for: A(7,0)|and B(0,3)
Answer:
[tex]\boxed {\boxed {\sf (\frac {7}{2}, \frac{3}{2}) \ or \ (3,5, 1.5) }}[/tex]
Step-by-step explanation:
The midpoint is essentially a point with the average of the 2 x-coordinates and the 2 y-coordinates.
The formula is:
[tex](\frac {x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]
We are given two points: A (7,0) and B (0, 3). Remember points are written as (x, y).
Therefore,
[tex]x_1= 7 \\y_1=0 \\x_2=0 \\x_2=3[/tex]
Substitute the values into the formula.
[tex](\frac {7+0}{2}, \frac{0+3}{2})[/tex]
Solve the numerators first.
[tex](\frac {7}{2}, \frac{3}{2})[/tex]
The midpoint can be left like this because the fractions are reduced, but it can be written as decimals too.
[tex](3.5, 1.5)[/tex]
which statement best explains how Italian society was affected by the Renaissance?
italian society entered a new era of artistic and academic achievement
You don’t have to answer both. Will give brainliest if you help.
9514 1404 393
Answer:
15) 27
16) 6144
Step-by-step explanation:
15) Jill's sequence is exponential:
3 9 27 81 243
Marlando's sequence is linear:
15 21 27 33 39
The first number in both patterns is 27.
__
16) The number of cards ordered is ...
(256 pkgs)(24 cards/pkg) = 6144 cards
give the simplest ratio for 56 :7
Answer and Step-by-step explanation:
The simplest ration would be 8 : 1, because both numbers are divisible by 7.
56 divided by 7 is 8, and 7 divided by 7 equals 1.
#teamtrees #PAW (Plant And Water)
The question is in the graph. Please help.
Answer:
A I think
Step-by-step explanation:
because if you add them up.
Answer:
Aprox. 216 days
Step-by-step explanation:
Add the counts of the green bar(5-10mm) and the brown bar (0-5mm).
The brown is roughly 130 and the green is roughly 80, which is approx 216 days.
If i helped, a brainliest answer would be greatly appreciated!
6y-5=7 two step equations
Answer:
The answer is y = 2.
Step-by-step explanation:
1) Add 5 to both sides.
[tex]6y = 7 + 5[/tex]
2) Simplify 7 + 5 to 12.
[tex]6y = 12[/tex]
3) Divide both sides by 6.
[tex]y = \frac{12}{6} [/tex]
4) Simplify 12/6 to 2.
[tex]y = 2[/tex]
Thus, the answer is y = 2.
The value of y in 6y-5=7 is 2.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
6y-5=7
Now, solving for y
Add 5 both side
6y-5 + 5=7 +5
6y= 12
Now, divide both side by 6
6y/6 = 12/6
y= 2
Hence, the value of y is 2.
Learn more about Equation here:
https://brainly.com/question/10413253
#SPJ2
Given the quadratic function
The vertex is (-4,-3)
The axis of symmetry is x=-4
and the transformations are:
please hurry.-. and if u can give all answers to the lesson
i don’t know how , help me pleaseeeee
Answer:
-3
Step-by-step explanation:
hopes that it helps you out
Grade 12 Number Patterns:
The first, third and thirteenth terms of an arithmetic sequence are the first 3 terms of a geometric sequence. If the first term of both sequences is 1, determine:
1.) the first three terms of the geometric sequence if r > 1
2.) the sum of 7 terms of the geometric sequence if the sequence is 1, 5, 25
Answer:
1. The first three terms of the geometric sequence are 1, 5, 25
2. Sum of the 7th terms of the geometric sequence is 19531
Step-by-step explanation:
We'll begin by calculating the common ratio (r). This can be obtained as follow:
For Arthmetic sequence:
First term (a) = 1
3rd term (T₃) = a + 2d
3rd term (T₃) = 1 + 2d
13th term (T₁₃) = a + 12d
13th term (T₁₃) = 1 + 12d
For Geometric sequence:
First term (a) = 1
2nd term (T₂) = ar
2nd term (T₂) = 1 × r
2nd term (T₂) = r
3rd term (T₃) = ar²
3rd term (T₃) = 1 × r²
3rd term (T₃) = r²
From the question given above,
The first term of the arithmetic sequence is also the first term of the geometric sequence.
The 3rd term of the arithmetic sequence is the 2nd term of the geometric sequence i.e
3rd term (T₃) = 2nd term (T₂)
1 + 2d = r
The 13th term of arithmetic sequence is the 3rd term of the geometric sequence i.e
13th term (T₁₃) = 3rd term (T₃)
1 + 12d = r²
SUMMARY:
1 + 2d = r .... (1)
1 + 12d = r²..... (2)
Substitute value of r from equation 1 into equation 2
1 + 12d = (1 + 2d)²
1 + 12d = 1 + 2d + 2d + 4d²
1 + 12d = 1 + 4d + 4d²
Rearrange
1 – 1 + 4d – 12d + 4d² = 0
–8d + 4d² = 0
4d² – 8d = 0
4d(d – 2) = 0
d = 0 or 2
Since the common difference (d) can not be 0, thus, is 2
Substitute the value of d into equation 1
1 + 2d = r
d = 2
1 + 2(2) = r
1 + 4 = r
r = 5
Thus, the common ratio (r) is 5
1. Determination of the first three terms of the geometric sequence.
First term (a) = 1
Common ratio (r) = 5
2nd term (T₂) = ar
2nd term (T₂) = 1 × 5
2nd term (T₂) = 5
3rd term (T₃) = ar²
3rd term (T₃) = 1 × 5²
3rd term (T₃) = 1 × 25
3rd term (T₃) = 25
Thus, the first three terms of the geometric sequence are 1, 5, 25
2. Determination of the sum of 7th terms of the geometric sequence .
1, 5, 25
First term (a) = 1
Common ratio (r) = 5
Number of term (n) = 7
Sum of the 7th term (S₇) =?
Sₙ = a[rⁿ – 1]/r – 1
S₇ = 1[5⁷ – 1]/5 – 1
S₇ = [78125 – 1]/4
S₇ = 78124 / 4
S₇ = 19531
Thus, sum of the 7th terms of the geometric sequence is 19531
Im a game with 10 floating ducks,there are 2 ducks with a green dot on the bottom,3with a blue dot and 5 with a red dot.What is the probability of selecting a green duck
Answer:
2/10 or 1/5
Step-by-step explanation:
There are a total of 10 ducks, and only 2 have green dots.
So the probability would be 2 / 10, which simplifies to 1 / 5.
Greatest common factor of 2 and 10: 2
So: 2 ÷ 2 = 1
10 ÷ 2 = 5
pls help!!
Find h. 10 cm h h = ✓ [?] cm .... 6 cm Enter
Answer:
h = √91 cm
Step-by-step explanation:
Apply pythagorean theorem, a² + b² ° c².
Where,
a = ½(6) = 3 cm
b = h
c = 10 cm
Plug in the values
3² + h² = 10²
9 + h² = 100
9 + h² - 9 = 100 - 9
h² = 91
h = √91 cm
Answer:
Step-by-step explanation:
Find the area of the parallelogram below by decomposing into two triangles. The figure is not drawn to scale.
Answer:
Step-by-step explanation:
area of a triangle = (½)(base)(height)
You can divide the parallelogram into two congruent triangles with base = 8 mi and height = 10 mi.
area of each triangle = (½)(8)(10) = 40 mi²
area of parallelogram = 2(40) = 80 mi²
Review Fractions:
1) 1/2x7/10
2) 2/4x2/3
3) 1/10x1/2
4) 1/10x1/2
5) 1/2x6/10
Answer:
1) 7/20
2) 1/3
3)1/20
4)1/20
5) 3/10
Step-by-step explanation:
Answer: 1) 7/20
2) 1/3
3) 1/20
4) 1/20
5) 3/10
Step-by-step explanation: 1) because we are multiplying fractions all we have to do is multiply the fractions numerator by numerator and denominator by denominator so 1x8=7 and 2x10=20 so 1/2x7/10=7/20
2) 2x2=4 4x3=12 so 2/4x2/3=4/12 now we can simplify so 4 divided by 4=1 and 12 divided by 4=3 so 1/3
3) 1x1=1 10x2=20 so 1/10x1/2=1/20
4) 1x1=1 10x2=20 so 1/10x1/2=1/20
5) 1x6=6 2x10=20 so 1/2x6/10=6/20 so now we have to simplify so 6 divided by 2=3 and 20 divided by 2=10 so 3/10
plz mark me brainliest
Find the distance d. Assume that the ratio of d to 60 ft is the same as the ratio of 40 ft to 30 ft.
Answer:
If [tex]\frac{d}{60} = \frac{40}{30}[/tex] then [tex]d = 2\cdot40 = \boxed{80}[/tex].
Hope this helps!
Work out m and c for the line:
y = 2 x + 1
Answer:
m=2
c=1
Step-by-step explanation:
y=mx+c
m=slope
c=y-intercept
y=2x+1
An escalator lifts people to the second floor of a building, 21 ft above the first floor. The escalator rises at a 30° angle. To the nearest foot, how far does a person travel from the bottom to the top of the escalator?
Answer:
42
Step-by-step explanation:
Sin 30=21/H
H=21/sin 30
H= 42
PLEASE HELP ITS AN EMERGENCYYYYYYYYYY!!!
Given f(x) = 3x^3 - 4x + k, and x – 1 is a factor of f(x), then
what is the value of k?
Answer:
The value of k is 1.
Step-by-step explanation:
x – 1 is a factor of f(x)
This means that:
x - 1 = 0
x = 1
That means that when [tex]x = 1, y = 0[/tex]. We use this to find the value of k.
f(x) = 3x^3 - 4x + k
[tex]3*1^3 - 4(1) + k = 0[/tex]
[tex]3 - 4 + k = 0[/tex]
[tex]k = 1[/tex]
The value of k is 1.
Which expression is equal to x−5x2+3−x2−x+4x2+3 ?
the third option. I think
HELP PLSSSSSS ITS TIMED
Determine any data values that are missing from the table, assuming that the data represent a linear function.
can someone one example please?
Answer:
A. 4 and 5
Step-by-step explanation:
You know that 4^2 is 16 and 5^2 is 25. [tex]\sqrt{16}[/tex] is 4 and [tex]\sqrt{25}[/tex] is 5, so [tex]\sqrt{20}[/tex] must be somewhere in between 4 and 5.
Which equation could have been used to create the function table?
Answer:
y=x+6
if im not mistaken
Step-by-step explanation:
use y=m×+b
so get ur two points (2,8) (5,11)
then divide them where they supposed to be the y-coordinates on the top and the x-coordinates on the bottom so like
8-11/2-5 and that equals 1
sense you have ur M well ur slope use y=m×+b
so its going to be (8=(1(2)+b) which equals 6 so ur b will be 6
Whoever solves this correctly will get the brainiest
Answer:
43
Step-by-step explanation:
The lengths of the sides of a triangle are 12,6 V3 and 6. Classify this triangle,
A)
right, scalene triangle
B)
acute, scalene triangle
o
obtuse, scalene triangle
D)
right, isosceles triangle
Answer:
right,scalene triangle
Cual es el decimal del 3%
Answer:
0.03
Step-by-step explanation: