[tex]\text{Given that,}\\\\f(x) = x^3+ax^2-7x+b \\\\\text{Since}~ (x+2)~ \text{and}~ (x-3)~ \text{are factors of f(x),}\\\\f(-2) = 0 ~ \text{and}~ f(3)=0\\\\\\ \text{Now,}\\\\f(-2)=0\\\\\ \implies (-2)^3+a(-2)^2-7(-2)+b =0\\\\\implies -8 +4a +14+b =0\\\\\implies 4a +b +6 =0~~~....(i)\\\\\\f(3) = 0\\\\\implies 3^3+a(3^2) -7(3) +b =0\\\\\implies 27 +9a -21 +b =0\\\\\implies 9a +b +6 =0~~....(ii)\\\\\\(ii)-(i):\\\\9a+b+6 - 4a-b - 6 = 0\\\\\implies 5a =0\\\\\implies a = 0\\[/tex]
[tex]\text{Substitute a=0 in equation (i):}\\\\4(0) +b +6 =0\\\\\implies b+6 =0\\\\\implies b =-6\\\\\text{Hence, a = 0 and}~ b =-6[/tex]
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Every week a company provides fruit for its office employees. They can choose from among five kinds of fruit. What is the probability distribution for the 30 pieces of fruit, in the order listed?
Answer:
it is A bacause the fractions for that one are correct
Step-by-step explanation:
Which of the following is not a factor of 9 ?
Answer:
2, 4, 5, 6, 7, 8
Step-by-step explanation:
The number 2 is not a factor of 9. The correct option is D.
What is factor?A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor in mathematics.
The given number is 9.
To find the factor of 9:
Number m that evenly divides another number 9.
In simple words, when we divide the number 9 by a number m.
We should get a whole number.
From the options,
9/1 = 9
9/3 = 3
9/9 = 1
9/2 = 4.5
Therefore, the number 2 is not the factor of 9.
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The complete question is:
Which of the following is not a factor of 9?
Options:
1 , 3, 9, 2.
What of the following exponential functions is represented by the data in the table?
A) f(x)=(1/3)^3
B) f(x)=3^x
C) f(x)=x^3
D) f(x)=x1/3
Answer:
f(x) = ( 1/3) ^ (x)
Step-by-step explanation:
The function is
f(x) = (1/3) ^ (x)
When x = 1 f(x) = 1/3
when x=2 f(x) = 1/9
When x = -1 f(x) = ( 1/3) ^ -1 = 3/1 =3
Answer:
f(x)=(1/3)^x
Step-by-step explanation:
Plug in the given values of x in the function above and match the answers with f(x) which is y.
Find the allowable height for the hypotenuse if the hypotenuse catheters are 4 cm and 9 cm
Answer:
L = 9.85 cm
Step-by-step explanation:
I guess you meant length for the hypotenuse. We just apply the pythagorean theorem:
L = [tex]\sqrt{(4 cm)^2 + (9 cm)^2} = \sqrt{16 cm^2 + 81 cm^2} = \sqrt{97 cm^2} = (circa) 9.85 cm[/tex]
Answer:
solutions given;
base:9 cm
perpendicular: 4 cm
hypotenuse:?
By using pythagorus law
hypotenuse^2: perpendicular^2+base^2
hypotenuse:[tex]\sqrt {4^2+9^2}[/tex]
hypotenuse:9.84cm
Try changing these improper fractions to mixed numbers.
16/5?
( teach me how to solve this please!)
Answer:
3 1/5
Step-by-step explanation:
The improper fraction 16/5 is called improper because the top number(the numerator) is bigger than the bottom number(the denominator) we "fix" this by dividing and creating a mixed number (it is called mixed because there is a whole part and a fraction part):
As 16÷5 >>> doing this division gives you 3 wholes and 1/5 leftover. We write this as
3 1/5 (in handwriting the three is big and the 1/5 is a fraction, it is the mixed number they are asking you for)
Which inequality matches the graph?
Answer:
x < 2/3 y + 2 1/3
Step-by-step explanation:
put it in a graphing calculator and they matched, I do not know
You have two right triangles that are similar. The base of the first is 8 and the height is 12.
If the base of the second triangle is 22, what is the height of the second triangle?
A. 33 units
B. 26 units
C. 14.7 units
D. 4.4 units
Let the height be x
[tex]\\ \sf\longmapsto \dfrac{8}{12}=\dfrac{22}{x}[/tex]
[tex]\\ \sf\longmapsto 12x=22(8)[/tex]
[tex]\\ \sf\longmapsto 12x=176[/tex]
[tex]\\ \sf\longmapsto x=14.7units[/tex]
Step-by-step explanation:
X :8/12 = 22/x
x • 12 = 22 • 8
12x = 176
x = 14.7units (C.)
f(x) = {(1,0),(2,1),(3,-1),(4, -2),(-1,-2)
Find the inverse of the function
LAST ATTEMPT IM MARKING AS BRAINLIEST!! (Draw a dilation of the figure using the given scale factor )
how many more seconds does it take to drive 1 mile at 40 miles per hour than 60 miles per hour
Answer:
165 seconds
Step-by-step explanation:
If you were going steadily 60 miles per hour, you would go one mile in one minute. So, if you were going steadily 40 miles per hour, without your speed going up or down, you would get through one mile in 3 3/4 minutes (which is 165 seconds more than 1 minute).
Hope this helps. Pls give brainliest! Also, pls sub to kgirl633 on yt!
Find the slope of the line on the graph. Write your answer as a fraction or whole number, but a mixed number or decimal.
Answer:
-1/4
Step-by-step explanation:
Rise over run
Rises -1 runs 4
slope = -1/4
A triangle and a square are drawn on dotty paper with dots 1 cm apart. What is the area of the region coloured red?
Answer:
≈ 0.9 cm²
Step-by-step explanation:
I don't know if there is any easier way to solve this, I use 8th grade slope and line method to solve. suppose A is on origin, then the coordinates of triangle ABC are (0,0) (1,3) (4,1) and polygon DEFGH intersect line BC at F and G.
F is the intersect of y=2 and line BC, while G is intersect of x=3 and line BC.
Line BC: pass (1,3) and slope (m) = (1-3)/(4-1) = - 2/3,
F(x,2)
(2-3) / (x-1) = -2/3
2x-2 = 3 x = 2.5
*F (2.5 , 2)
G (3,y)
(y-3) / (3-1) = -2/3 y = 5/3
*G (3 , 5/3)
*point I (3 , 2)
segment FI = 3-2.5 = 0.5 = 1/2
segment GI = 2 - 5/3 = 1/3
area ΔFIG = (1/2 * 1/3) / 2 = 1/12 = 0.083
area of polygon DEFGH (region colored RED) = 1 - 0.083 = 0.917 ≈ 0.9 cm²
4/7 divided by 1 1/3 =
Answer:
i think probably 3/7 is answer
Describe the functions plz and thank u<3also 50pts
Answer:
See belowStep-by-step explanation:
Given function:
y = 1/2|x + 3| + 2This is a transformation of the absolute value function y = |x|.
The transformations are:
1. Dilation by a scale factor of 1/22. Translation left by 3 units3. Translation up by 2 pointsThe locator point is the vertex: (-3, 2)
Domain is any value: x = (- ∞, + ∞)
Range is anything not less than 2: y ≥ 2 or y = [2, + ∞)
See the graph attached
6. Rachael is married with 2 dependents. Her salary as a dental hygienist is $47,650 paid
in 26 pay periods. Find the state tax withheld per pay period.
Answer:1.2389 million US$
Step-by-step explanation:
Which value of a makes the equation true?
Answer:
a = -2
Step-by-step explanation:
3(a + 1.5) = -1.5
3a + 4.5 (-4.5) = -1.5 (-4.5)
3a = -6
a = -2
help me plssssss
ssssssssss
Answer:
The answer is going to be A
Step-by-step explanation:
Which inequality represents the graph? x ≥ (y + 3)2 + 1 x ≤ (y + 3)2 + 1 x ≥ (y – 3)2 + 1 x ≤ (y – 3)2 + 1
The graph of each of the inequalities are created using a graphing tool as follows;
Graph 1; x ≥ (y + 3)² + 1
The domain = 1 ≤ x ≤ ∞
The range = -∞ < y < ∞
Graph 2; x ≤ (y + 3)² + 1
The domain = -∞ ≤ x ≤ ∞
The range = -∞ < y < ∞
Graph 3; x ≥ (y - 3)² + 1
The domain = 1 ≤ x ≤ ∞
The range = -∞ < y < ∞
Graph 4; x ≤ (y - 3)² + 1
The domain = -∞ ≤ x ≤ ∞
The range = -∞ < y < ∞
Learn more about graph of inequalities here:
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Answer:
c or x ≥ (y-3)^2+1
Step-by-step explanation:
sixty students at gillette road middle school play a winter modified sport. if there are 500 students in the middle school, what percent of students play a sport
Answer:
60/500=0.12
so 12%
Hope This Helps!!!
Question
Triangle ABC is similar to triangle XYZ. Find side a.
13
39
Y
5
Z
B
Provide your
Answer:
Step-by-step explanation:
There are two great ways to set up this problem and they both get you the same answer. First you know that the triangles are similar, this means they are the same shape, but not necessarily the same size. You can use ratios to compare the sizes of the sides. Just be sure to compare like things to like things.
One way: compare the small triangle's long side to short leg with the big triangle's long side to short leg. Like this:
13/5 = 39/a
OR...compare long side(sm) to long side(big) compared to short leg(sm) to short leg(big). Like this:
13/39 = 5/a
Amazingly, these equations will give you the same answer.
13a = 39*5
13a = 195
13a/13 = 195/13
a = 15
You can maybe see that the big triangle's side is 3 times bigger than the small one (13 times 3 is 39) So it works out that the 5 on the little triangle is 3 times bigger--15--on the large triangle!
A sweatshirt was on sale for 32% off and cost $40.80 without tax. What was the original price of the sweatshirt?
Answer:
The original price of the sweatshirt was $127.50
Step-by-step explanation:
$40.80 / .32(32%) = $127.50
What is the next number
3, 4, 7, 16, 11, 64, …
Answers:
A) 55
B)14
C)39
D)15
the answer is c) 39 according to the sequence
The next number 3, 4, 7, 16, 11, 64, is: 55.
What is the number pattern?A number pattern is a pattern in a series of numbers that represents the common relationship between the numbers.
When all the terms of a geometric sequence are added, then that expression is called geometric series.
We are given the series as;
3, 4, 7, 16, 11, 64, …
If we separate the numbers that in order are in the even place of the odd ones, we would have :
3, 4, 7, 16, 11, 64,..
If we finish in 1 then they increase by 1 in 1, while in 2.- they increase in odd numbers, the following number is: 55
The correct option is A.
Learn more about a number pattern:
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Sammy factored the polynomial x2 + x - 6. She came up with the factors of
(x-3) and (x-2). Describe and correct the error.
Answer:
(x+3) and (x-2) are the correct factors
Step-by-step explanation:
If we expand (x-3)(x-2), we see that it equates to x²-5x+6, which is not what we want. The correct factors would be (x+3)(x-2) since the middle term's coefficient becomes 1 as 3-2=1 whereas -3-2=-5.
Angles A,D and G are congruent, and angles c, f and j are congruent. What is the mesure of angle E?
Answer:
60
Step-by-step explanation:
Since the angles A, D, and G are congruent then sum of given angles is eaqual to 180 degrees
x + 20 + 2x + x = 180 add like terms
4x + 20 = 180 subtract 20 from both sides
4x = 160 divide both sides by 4
x = 40
Angles B, E, and H are congruent so E is also = x + 20 and x = 40 so angle E = 60
help I suck at math..
Answer:
The correct answers are:
B
D and
F
Step-by-step explanation:
Hope it can help you lovelots
#LEARN WITH BRAINLY
Pls help as soon as possible thank you
Answer:
answer is b
Step-by-step explanation:
6x+10
6*-3+10=-8
4x+4
4*-3+4=-8
Sam saved $40 each month for 3 years. Then, he spent 65% of his savings on a cruise. How much of his savings was left? A. $420 B. $588 C. $1,092 D. $1,260
Answer:
$588 was left
Step-by-step explanation:
Since it was $40 for 3.5 years, and there are 12 months in a year, we do: (3*12+6)*40=168065%= 13/2013/20 * 1680Sam paid $10921680 - 1092 = 588how do i get the answer for this problem. 2x+2x+2=4x+2
Let f(x) = x+2/x+6
f^-1(-6) =
We can explicitly find the inverse. If [tex]f^{-1}(x)[/tex] is the inverse of [tex]f(x)[/tex], then
[tex]f\left(f^{-1}(x)\right) = \dfrac{f^{-1}(x)+2}{f^{-1}(x)+6} = x[/tex]
Solve for the inverse :
[tex]\dfrac{f^{-1}(x) + 2}{f^{-1}(x) + 6} = x[/tex]
[tex]\dfrac{f^{-1}(x) + 6 - 4}{f^{-1}(x) + 6} = x[/tex]
[tex]1 - \dfrac4{f^{-1}(x) + 6} = x[/tex]
[tex]1 - x = \dfrac4{f^{-1}(x) + 6}[/tex]
[tex]f^{-1}(x) + 6 = \dfrac4{1-x}[/tex]
[tex]\implies f^{-1}(x) = \dfrac4{1-x} - 6[/tex]
Then when x = -6, we have
[tex]f^{-1}(-6) = \dfrac4{1-(-6)} - 6 = \dfrac47-6 = \boxed{-\dfrac{38}7}[/tex]
Alternatively, we can first solve for x such that [tex]f(x) = -6[/tex]. Then taking the inverse of both sides, [tex]x = f^{-1}(-6)[/tex]. (The difference in this method is that we don't compute the inverse for all x.)
We have
[tex]\dfrac{x+2}{x+6} = -6[/tex]
[tex]x + 2 = -6 (x + 6)[/tex]
[tex]x + 2 = -6x - 36[/tex]
[tex]7x = -38[/tex]
[tex]\implies x = \boxed{-\dfrac{38}7}[/tex]
Wildcat Pizza, Inc. is trying to decide whether to revise its target capital structure. Currently, it targets a 50-50% mix of debt and equity, but it is considering a target capital structure with 70% debt. Wildcat currently has 6% after-tax cost of debt and a 12% cost of common stock. The company does not have any preferred stock outstanding