1. Let f(x) be defined by the linear function graphed below and
g(x) = x2 - 9x + 14.
I
A. Describe the right end behavior of g(x).
Answers
Answer:
Step-by-step explanation:
A). g(x) = x² - 9x + 14
Since coefficient of highest degree term (x²) is positive, parabola will open upwards.
For any parabola opening upwards,
Right end behavior,
y → ∞ as x → ∞
B). Let the equation of the linear function is,
f(x) = mx + b
Where m = slope of the function
b = y-intercept
From the graph attached,
Slope 'm' = [tex]\frac{\text{Rise}}{\text{Run}}=\frac{-(2+1)}{(0+1)}[/tex]
m = -3
b = -1
Therefore, function 'f' will be,
f(x) = (-3)x - 1
f(x) = -3x - 1
g(x) = x² - 9x + 14
= x² - 7x - 2x + 14
= x(x - 7) - 2(x - 7)
= (x - 2)(x - 7)
If h(x) = f(x)g(x)
h(x) = -(3x + 1)(x -2)(x - 7)
For h(x) ≥ 0
-(3x + 1)(x - 2)(x - 7) ≥ 0
[tex]x\leq -\frac{1}{3}[/tex] Or 2 ≤ x ≤ 7
Therefore, for 2 ≤ x ≤ 7, h(x) ≥ 0
C). If k(x) = [tex]\frac{h(x)}{(x-2)}[/tex]
k(x) = [tex]\frac{-(3x+1)(x-2)(x-7)}{(x-2)}[/tex]
k(x) = -(3x + 1)(x - 7)
For k(x) = -56
-(3x + 1)(x - 7) = -56
3x² -20x - 7 = 56
3x² - 20x - 63 = 0
3x² - 27x + 7x - 63 = 0
3x(x - 9) + 7(x - 9) = 0
(3x + 7)(x - 9) = 0
[tex]x=-\frac{7}{3},9[/tex]
Related Questions
A normal population has mean =μ7 and standard deviation =σ5. (a) What proportion of the population is less than 18?
Answers
Answer:
P(x< 18) = 0.986
Step-by-step explanation:
Step 1: find the z-score using the formula, z = (x - µ)/σ
Where,
x = randomly chosen values = 18
µ = mean = 7
σ = standard deviation = 5
Proportion of the population that is less than 18 = P(x < 18)
Plug in the values into z = (x - µ)/σ, to get z-score.
z = (18 - 7)/5
z = 11/5 = 2.2
Step 2: Find P(x< 18) = P (z<2.2) using z-table.
The probability that corresponds with z-score calculated is 0.986.
Therefore,
P(x< 18) = 0.986
You choose a card from a deck of 52 cards. Without replacing the card, you choose a second card. What is the probability of choosing two red cards?
Answers
Answer: 13/51
Step-by-step explanation: After shuffling there are 52 permutations of 52 cards. Each has the probability of occurrence equal to another, that is the probability of any sequence of cards is 1/52.
Let's count only those where there is a red card on the first place and black card on the second. There are 26 red and 26 black cards. Therefore, we have 26 ⋅26 choices for a pair of two first cards. The sequence of other 50 cards in unimportant and any permutation among them is fine for us since we fixed the first two.
Therefore, we have 26 ⋅ 26 ⋅50 different permutations when the first card is red and the second is black.
Therefore, we have 26 ⋅ 26 ⋅50 different permutations when the first card is red and the second is black.
The final probability, therefore, is
26 ⋅26 ⋅50 / 52 = 26 ⋅26 / 52 ⋅ 51 = 13 / 51
13/51 is the final answer
A scanner can scan 20 pages and 120 seconds. How many pages can scan in 4 minutes?
Answers
Answer:
40 pages
Step-by-step explanation:
120 or 2 min x 2 = 4
20 x 2 = 40
Sorry I couldn't explain more, but I hope this helps!
Answer:
40 pages
Step-by-step explanation:
convert 4 mins -> 240 secs
then cross multiply 20/120 and x/240 (x represents the pages scanned)
u then get 120x=4800
simplify(divide)-> x=40
Evaluate each expression.
b)
d)
169 cm2:13x13=169 13cm by cm
2500 cm2:50x50=2500 50cm by cm
/8
a) 2 + (10 − 3) =2+(10-3)
c)
(4 + 3)2 − (3 − 1)3 =
= 2+(7)=10
=
=
11.
b) (3 + 5) × 6 ÷ 3 + (8 + 52)
d)
18 + (4 + 5)2 × 2
=
=(7)x6/3+(177)
=
=(42/30
=
=
=
=
=
Answers
Answer:
atleast 1
Step-by-step explanation:
78 billion scientific notation
Answers
Answer:
78 x 10^9
Step-by-step explanation:
Hope this helps!
Answer:
7.8 x
Step-by-step explanation:
Scientific notations are being used to write very large or very small numbers. In line with this, the other details regarding 78 million in scientific notation are indicated above.
Assuming part a is correct, how do you do b and c?
Answers
Step-by-step explanation:
B. Yes, we are 99% confident that the population mean is within the interval.
C. Yes, 225 is below the interval minimum, so it is reasonable to conclude the average cholesterol level is greater than 225 mg/dl.
D. No. Increasing the sample size would decrease the margin of error, so the ends of the interval would move closer to the sample mean of 251.9. So the interval minimum would still be higher than 225.
Shelly's pet food store sold one costumer 5 peanut butter biscuits for $3. She sold another costumer 7 beef treats for $4.20.
Answers
How many kilograms of potatoes will each person get if 5 people share 1/3 of a kilogram of potatoes equally?
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Answer:
1/15 kg
Step-by-step explanation:
Divide by 5 can be written as multiply by 1/5
1/3 * 1/5 = 1/15
adult men weights mean of 190 30 3 random men mean weight
Answers
Answer:
is this the question ?
Step-by-step explanation:
Just one more question I need this in a step by step please
Answers
Answer:
2x+20+3x+40=90
5x+60=90
5x=30
x = 6
2x+20 = 2(6)+20
12+20
=32
3x+40 = 3(6)+40
18+40
=58
Answer:
Here we can first find the value of x simply by using the concept of corresponding angles.
As we know that angle with measurement 2x+20Degree and the right angle below are corresponding as we can consider the line (underlined in red) as a transversal intersecting lines underlined in green. {PLEASE SEE THE ATTACHMENT TO SEE THE HIGHLIGHTED LINES}
So, we get 2x+20 degree = 90 degree.
= 2x+20=90
= 2x=90-20
= 2x=70
= x= 70/2
= x=35 degree.
Now as we know the value of x we can find the other unknown angle by substituting it in the equation for the other angle.
Therefore, 3x+40degree= 3*35+40
105+40
= 145 degrees.
The nth term of an AP is given by 2n +9 find the first term
Answers
PLEASE HELP ME ON ALL ASAP!!!! I WILL GIVE BRAINLIEST!!!
Answers
Answer:0=16 1=23 2=30 3=37 4=44
Step-by-step explanation:
What is the value of a in the proportion???? need help!!!
Answers
Answer:
90
Step-by-step explanation:
90-15/90= 5/6
90-15= 75
75/90= 83.3333 or 5/6
What digit is in ten thousands place 983,471?
Answers
7
The digit in ten thousandths place is 7 as it is the fourth digit to the right of decimal point.
Answer:
8
Step-by-step explanation:
9= one hundred thousands
8= ten thousands
3= one thousands
4= one hundreds
7= tens
1= ones
The last school year enrollment of Genoa Middle school was 465 students. This year the enrollment is 525.
Answers
Answer:
465 to 525
Step-by-step explanation:
60 difference
Which line is perpendicular to y=2x-7
Answers
Answer:
y=-1/2x−5/2
Step-by-step explanation:
The equation of a line perpendicular to given line is y=-x/2.
The given equation of a line y=2x-7 and passes through the point (0, 0).
What is slope of an equation?The slope formula is used to calculate the inclination or steepness of a line. It finds application in determining the slope of any line by finding the ratio of the change in the y-axis to the change in the x-axis.
The standard form of equation of a line is y=mx+c, where m=slope and c=y-intercept.
So, slope of a given equation is y=2x-7
m=2
Now, slope of a line perpendicular to given line is -1/m = -1/2
Put m= -1/2 and (0, 0) in y=mx+c and simplify.
That is, 0=0+c
c=0
Then, the equation of a line is y=-x/2
Therefore, the equation of a line perpendicular to given line is y=-x/2.
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"Your question is incomplete, probably the complete question/missing part is:"
Which line is perpendicular to y=2x-7 and passes through (0, 0).
Which point is on Analyn's graph
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The sign of the leading coefficient for the polynomial equation of the graph is negative positive zero
Answers
Answer:
The sign of the leading coefficient for the polynomial equation of the graph is NEGATIVE
Hope this helps!
Answer: 1 turning point
Step-by-step explanation:
What do u think the answer is !!
Answers
Answer:
Yeah
Step-by-step explanation:
Just swiss cheese ngl
Answer:
cheddar + turkey
Step-by-step explanation:
.........mmmm....mm..mm.mm.mm
NEED HELP WITH MATH! Will Give Brainliest! Image is below.
Answers
Answer:
#2
Even though the graph dips down, x is still increasing, and y will increase as will .
As x is decreasing, y is also decreasing.
the value of x in logx(9/63)=1/2 is
Answers
Answer: x = 7/2
Step-by-step explanation: u juss simplify 1/2 x 7 to 7/2 so x = 7/2
The value of x in logarithmic equation [tex]log_{10}x(\frac{9}{63} )=\frac{1}{2}[/tex] is [tex]1000\sqrt{10}[/tex].
What is a logarithmic equation?
"A logarithmic equation is an equation that involves the logarithm of an expression containing a variable."
Given logarithmic equation
[tex]log_{10}x(\frac{9}{63} )=\frac{1}{2}[/tex]
⇒ [tex]log_{10}x(\frac{1}{7} )=\frac{1}{2}[/tex]
⇒ [tex]log_{10}x=\frac{1}{2}({7} )[/tex]
⇒ [tex]log_{10}x=\frac{7}{2}[/tex]
⇒ [tex]x = 10^{\frac{7}{2} }[/tex]
⇒ [tex]x = 10^{3+\frac{1}{2} }[/tex]
⇒ [tex]x = 10^{3}[/tex] × [tex]10^{\frac{1}{2} }[/tex]
⇒ [tex]x = 1000\sqrt{10}[/tex]
The value of [tex]x = 1000\sqrt{10}[/tex]
Hence, the value of x in logarithmic equation [tex]log_{10}x(\frac{9}{63} )=\frac{1}{2}[/tex] is [tex]1000\sqrt{10}[/tex].
Learn more about logarithmic equation here
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HELP ME ASAP!!! I WILL MARK BRAINLIEST!!
Answers
Answer:
Brand A ($2) is more expensive than Brand B ($1.50) (see below)
Step-by-step explanation:
First, you will have to find the slopes of both lines. Slope is y/x, which is the cost/meter or cost per meter.
Using the slope formula:
y2 — y1
m = ---------------
x2 — x1
Plug in any two points from both lines:
y2 — y1
m = --------------- = graph 1 (0, 0), (1,2)
x2 — x1
2 — 0
m = ---------------
1 — 0
2
m = --------------- = $2/m
1
_______graph 2_______
y2 — y1
m = --------------- = graph 2 (0, 0), (4, 6)
x2 — x1
6 — 0
m = ---------------
4 — 0
6 3
m = --------------- = ----------- = $3/2 m
4 2
Because you are unable to have an exact cost per meter of Brand B, you can use a ratio:
$3 = $x
2m = 1m
Cross multiply:
3 (1) = 2x
3 = 2x
x = (3 ÷ 2)
x = 1.5
So Brand B is $1.50 per meter while Brand A is $2.00 per meter. Brand B is cheaper.
a chemical change creates a new
Answers
Answer:
A new substance with new and different physical and chemical properties.
Step-by-step explanation:
Chemical reactions involve combining different substances. The chemical reaction produces a new substance with new and different physical and chemical properties. Matter is never destroyed or created in chemical reactions. The particles of one substance are rearranged to form a new substance.
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Help!!!!
Which of the following is a condition for the figure below that will not prove /1 // 12?
Answers
Answer:
option D , <a +<c = 180
Step-by-step explanation:
please mark brainlist
Mr.Watts is a famous motivational speaker. He travels across the country by jet and gives an average of seven presentations a week. He gives his
speeches in auditoriums that are always full and hold an average of 1000 people each. He charges $40 per person at each of these speeches. His
average expenses for each presentation, including renting the auditorium, are about $20,000. The cost of meals, motels, jet travel, and support
personnel total $60,000 per week. How many weeks will Mr. Watts need to travel if he wants to earn $560,000 per year?
Answers
Answer:
Mr watts needs 7 weeks
Step-by-step explanation:
The average expense per presentation = $20,000
Since Mr. Watts can give about 7 presentations per week, hence the average expense per presentation for a week = $20000 × 7 = $140000
Also the cost of meals, motels, jet travel, and support personnel total $60,000 per week. Hence the total cost per week is:
Total cost = $140000 + $60000 = $200000
The revenue gotten is $40 per person and can take 1000 people per each presentation. Hence:
Revenue per week = $40 per person × 1000 people × 7 days = $280000
Let assume the number of weeks needed to earn $560000 be x. Hence:
280000x - 200000x = 560000
80000x = 560000
x = 7
what is 0.067 reccuring as a fraction
Answers
Answer:
67/1000
Step-by-step explanation:
How to translate 0.067 to a fraction:
So you can there is the tenths place (which is considered 0 on the decimal behind the point.) The hundredths place (where the 6 is placed), and the thousandths place (where the 7 is placed.)
Since the 7 is placed at the thousandths place, that means the denominator would be 1000. The number behind the point is .067.
So the fraction would be this:
67/1000
(Also it's at it's simplest form.)
HEY I NEED HELP ASAP!!!!!!!!!!!!!
this is the problem I need help with
n - 25/4 =3
Answers
Answer:
n = 37/4
Step-by-step explanation:
that's the answer to you question
solve the following inequality.
6.3r < -45.36
which graph shows the correct solution?
A) Open circle pointing to the right, starting from -72 to infinity
B) Open circle pointing to the left, starting from -72 to infinity
C) Open circle pointing to the right, starting from -7.2 to infinity
D) Open circle pointing to the left, starting from -7.2 to infinity
Can u help please??
Answers
Answer:
D. Open circle, point is at -7.2 pointing to the left.
Step-by-step explanation:
Got it right on Edge 2021! Hope I helped <3
Does anyone know the answer?
Answers
Answer:
20 i think
Step-by-step explanation:
Which of the following statements describes the value of the expression 35 – 2x, when x = 6?
A) It is a prime number
B) It is a composite number
C) It is a whole number that is neither prime nor composite
D) It is not a whole number.
Answers
Answer: B
Step-by-step explanation: 3x3=9 1x9 equals 9 if a number has 2 or more sets, it's a composite number. It would not become prime because 9 does not have 1 set.
Answer:
Step-by-step explanation:
b