50 POINTS
Use the function f(x) to answer the questions.
f(x) = −16x2 + 22x + 3
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)
work and answers below
Answer:
[tex]\text{Part A.}\\(-\frac{1}{8},0),\\(\frac{3}{2},0)\\\\\text{Part B.}\\(\frac{11}{16},\frac{169}{16})\\\\\text{Part C.}[/tex]
Draw a parabola concave down with vertex at [tex](\frac{11}{16},\frac{169}{16})[/tex]. Since the leading coefficient of the equation is -16, the parabola should appear thinner than its parent function [tex]y=x^2[/tex]. Ensure that the parabola passes through the points [tex](\(-\frac{1}{8},0)[/tex] and [tex](\frac{3}{2},0)[/tex].
Step-by-step explanation:
Part A:
The x-intercepts of a function occur at [tex]y=0[/tex]. Therefore, let [tex]y=0[/tex] and solve for all values of [tex]x[/tex]:
[tex]0=-16x^2+22x+3[/tex]
The quadratic formula states that the real and nonreal solutions to a quadratic in standard form [tex]ax^2+bx+c[/tex] is equal to [tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex].
In [tex]-16x^2+22x+3[/tex], assign:
[tex]a\implies -16[/tex] [tex]b\implies 22[/tex] [tex]c\implies 3[/tex]Therefore, the solutions to this quadratic are:
[tex]x=\frac{-22\pm\sqrt{22^2-4(-16)(3)}}{2(-16)},\\x=\frac{-22\pm 26}{-32},\\\begin{cases}x=\frac{-22+26}{-32}=\frac{4}{-32}=\boxed{-\frac{1}{8}},\\x=\frac{-22-26}{-32}=\frac{-48}{-32}=\boxed{\frac{3}{2}}\end{cases}[/tex]
The x-intercepts are then [tex]\boxed{(-\frac{1}{8},0)}[/tex] and [tex]\boxed{(\frac{3}{2},0)}[/tex].
Part B:
The a-term is negative and therefore the parabola is concave down. Thus, the vertex will be the maximum of the graph. The x-coordinate of the vertex of a quadratic in standard form [tex]ax^2+bx+c[/tex] is equal to [tex]x=\frac{-b}{2a}[/tex]. Using the same variables we assigned earlier, we get:
[tex]x=\frac{-22}{2(-16)}=\frac{-22}{-32}=\frac{11}{16}[/tex]
Substitute this into the equation of the parabola to get the y-value:
[tex]f(11/16)=-16(11/16)^2+22(11/16)+3,\\f(11/16)=\frac{169}{16}[/tex]
Therefore, the vertex of the parabola is located at [tex]\boxed{(\frac{11}{16},\frac{169}{16})}[/tex]
ESSE
Combine these radicals.
27-3
O √24
O 23
O-23
0 -3/2
here's the answer to your question
Which equation does the graph represent?
A. x^2 + y^2 = 4
B. x^2/3^2 + y^2/4^2 = 1
C. (X - 1)^2 / 3^2 + y^2/4^2 = 1
D.X^2 / 4^2 + (y + 1)^2 / 3^2 = 1
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Answer:
B. x^2/3^2 + y^2/4^2 = 1
Step-by-step explanation:
The graph looks like a circle, but is not. It is a unit circle scaled by a factor of 3 in the x-direction and a factor of 4 in the y-direction. Thus, its equation is ...
(x/3)^2 +(y/4)^2 = 1
x^2/3^2 +y^2/4^2 = 1
I need help with the question below
Answer:
a: 1/12
b: 1/6
c: 1/2
d: 1/2
e: 1/12
f: 1/3
Step-by-step explanation:
Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x=t−t−1, y=1+t2, t=1
Answer:
Step-by-step explanation:
First, I would find the point on the curve. By substituting t=1, I get (x, y). Next, I will try to eliminate the t and make a xy equation. In this case, the t's will cancel out in 'x=t-t-1" which wouldnt make this a curve. To find the equation of the tangent line, find the deretitave of the xy equation, and subsitute x in to find the slope at that point. Next, use point slope form to find the equation at the point.
If an orange seller bought 5 dozen oranges at the rate of tk.60 per four and sold them at the rate of tk50 per four,how much did he lose
Answer:
tk 30
Step-by-step explanation:
5 dozen = 5 * 12 = 60 oranges
12/4 = 3
total cost = 60 * 3 = tk.180
total sell = 50 * 3 = tk 150
total lose = 180 - 150 = tk 30
Add O used 6 cups of whole wheat flour and eggs we flower and ax cups of white flour in the recipe what is the equation that can be used to find the value of Y the total amount of flour that adult used in the recipe and what are the constraints and the values of X and Y
Answer:
6x+y
Step-by-step explanation:
write your answer in simplest radical form
Answer:
3 =f
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp/ adj
tan 60 = f/ sqrt(3)
sqrt(3) tan 60 = f
sqrt(3) * sqrt(3) = f
3 =f
My flvs teacher said that she was asked to hold off on grading my assignment. She will give me a call back when when gets more information. Anyone have the same problem?
Answer:
yeah, teachers kinda suck
What is the value of 3?
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Answer:
3 ⇒ 12
Step-by-step explanation:
Apparently "a = b" in this case is used to mean f(a) = b. It appears as though the function is ...
f(x) = x(x+1)
Then f(3) = 3(3+1) = 3·4 = 12
_____
Additional comment
IMO this is a poor use of the equal sign, which should be reserved for situations where the left side expression has the same value as the right side expression.
Write an equivalent expression to 1/2 (2n+6).
Answer:
n+3
Step-by-step explanation:
1/2 × 2(n+3)=n +3
I hope this helps
The figures to the right are similar. Compare the first figure to the second. Give the ratio of the perimeters and the ratio of the areas
(integer or a simplified fraction)
Thank you!
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Answer:
perimeter: 3 : 4area: 9 : 16Step-by-step explanation:
The perimeter ratio smaller : larger is the same as the side length ratio.
18 : 24 = 3 : 4 . . . smaller : larger perimeter ratio
The area ratio is the square of this.
3^2 : 4^2 = 9 : 16 . . . smaller : larger area ratio
A quality control inspector has drawn a sample of 18 light bulbs from a recent production lot. If the number of defective bulbs is 1 or more, the lot fails inspection. Suppose 30% of the bulbs in the lot are defective.
Required:
What is the probability that the lot will pass inspection?
Answer:
0.0016 = 0.16% probability that the lot will pass inspection.
Step-by-step explanation:
For each bulb, there are only two possible outcomes. Either it is defective, or it is not. The probability of a bulb being defective is independent of any other bulb, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Sample of 18 light bulbs
This means that [tex]n = 18[/tex]
30% of the bulbs in the lot are defective.
This means that [tex]p = 0.3[/tex]
What is the probability that the lot will pass inspection?
It will pass inspection if there are no defective bulbs, that is, we have to find P(X = 0). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{18,0}.(0.3)^{0}.(0.7)^{18} = 0.0016[/tex]
0.0016 = 0.16% probability that the lot will pass inspection.
a yogurt shop offers 7 different flavors of frozen yogurt and 11 different toppings. How many choices are possible for a single serving of frozen yogurt with one topping
answer: 77
Step-by-step explanation:
7×11=77
sorry if I'm wrong
Answer:
fijatebie nl aperguntaa
Step-by-step explanation:
Rationalize the denominator and simplify
Answer:
x² - √3x / x² - 3
Step-by-step explanation:
To Do :-
To rationalize the denominator .Solution :-
We need to rationalize ,
x/ x + √3Multiply numerator and denominator by x-√3 :-
x( x - √3 ) / ( x +√3)( x -√3) x² - √3x / (x)² - (√3)² x² - √3x / x² - 3What is the slope of the line that contains these points? xxx 454545 494949 535353 575757 yyy 101010 555 000 -5−5minus, 5 slope:
Answer:
-5/4
Step-by-step explanation:
Given :
x : 45, 49, 53, 57
y : 10, 5, 0, - 5
The slope of the line :
Slope = Rise / Run
y2 = - 5, y1 = 10
x2 = 57, x1 = 45
Rise = y2 - y1 = - 5 - 10 = - 15
Run = x2 - x1 = 57 - 45 = 12
The slope = Rise / Run = - 15 / 12 = - 5/4
Answer:
-1
Step-by-step explanation:
i brought the answer correct
Your calculator is showing a result of 248.592.
What is this to the nearest whole number?
Use the definition of a Taylor series to find the first four nonzero terms of the series for f(x) centered at the given value of a. (Enter your answers as a comma-separated list.)
f(x) = 7/1+x a=2
If f(x) = 7/(1 + x), then
f (2) = 7/3
f '(x) = -7/(x + 1)² ==> f ' (2) = -7/9
f ''(x) = 14/(x + 1)³ ==> f '' (2) = 14/27
f '''(x) = -42/(x + 1)⁴ ==> f ''' (2) = -14/27
Then the Taylor series of f(x) about a = 2 is
7/3 + 1/1! (-7/9) (x - 2) + 1/2! (14/27) (x - 2)² + 1/3! (-14/27) (x - 2)³
= 7/3 - 7/9 (x - 2) + 7/27 (x - 2)² - 7/81 (x - 2)³
How many of 320 million Americans would you predict wear contact lens
Answer:
I think 40 - 60 Million Americans would wear contact lenses.
Determine the area of the given parallelogram with length 11 and altitude five
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Answer:
55 square units
Step-by-step explanation:
The area of a parallelogram is the product of base length and height:
A = bh
A = (11)(5) = 55 . . . area of the given parallelogram in square units
Find the length of BC
A. 6.81
B. 7.64
C. 13.37
D. 29.44
Answer:
13.37 = BC
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = opp / hyp
cos 27 = BC / 15
15 cos 27 = BC
13.36509 = BC
Rounding to the nearest hundredth
13.37 = BC
d) A product contains three lasers, and the product fails if any of the lasers fails. Assume the lasers fail independently. What should the mean life equal for 99% of the products to exceed 10000 hours before failure
Solution :
Let the probability laser works = p
The probability that the system works = [tex]$P(\text{all three component works}) = p^3 $[/tex]
= 0.99
Therefore, p = 0.9967
Now for the above probability critical z = -2.72
Hence, the mean life is equal to = [tex]10,000 + 2.72 \times 600[/tex]
= [tex]10,000+1632[/tex]
[tex]=11,632[/tex]
Rewrite the function f(x)=16^x in four different ways, using a different base in each case.
Answer:
X=1
f(x)=16^1
=16
X=2
f(x)=16^2
256
X=3
f(x)=16^3
=4096
X=4
f(x)=16^4
=65536
Here are four different ways to rewrite the function f(x) = 16^x, using a different base for each case:
Using base 2:
f(x) = (2^4)^x = 2^(4x)
Using base 3:
f(x) = (3^2)^x = 3^(2x)
Using base 10:
f(x) = (10^(log10(16)))^x = 10^(log10(16) * x)
Using base e (natural logarithm):
f(x) = (e^(ln(16)))^x = e^(ln(16) * x)
How to explain the functionIn these rewritten forms, the exponentiation of the base is expressed as a simpler expression.
This involves the new base, which helps to illustrate the relationship between the original function and the different bases used.
Learn more about functions
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Question 4 please provide explanation for question
Answer:
A
Step-by-step explanation:
We need to find a equation that is where the domain is all real numbers and the range is all real numbers greater than -3
A square root function cannot equal to all real numbers because we cant take the square root of a negative number. so B and C are already wrong.A cubic function range is all real numbers. so y can be greater than -3 but it would also include. values lesser than -3. so D is Wrong.A is right, the domain of a absolute value function is all real numbers. The range of a absolute value is all numbers greater than or equal to zero but if we subtract 3, it changes into all real numbers greater than or equal to -3
Helpekksdjfkfodldkdkdodidididisj Help
Answer:
The answers to your questions are given below.
Step-by-step explanation:
1. m∠1 and m∠2 are complementary. This statement was given from the question.
2. m∠1 + m∠2 = 90°. Complementary angles add up to give 90°.
3. m∠2 = 74°. This was given in the question.
4. m∠1 + 74 = 90°. Since m∠1 and m∠2 are complementary. Their sum will add up to give 90°
5. m∠1 = 16°
We can prove m∠1 = 16° as shown below:
m∠1 + m∠2 = 90° (complementary angles)
m∠2 = 74°
m∠1 + 74 = 90°
Collect like terms
m∠1 = 90 – 74
m∠1 = 16°
Think of a two-digit number. What is the probability that it has different digits?
Answer:
9/10
Step-by-step explanation:
The first two digit number is 10 and the last is 99. That's a total of 99-10+1 numbers in all. That simplifies to 90. (Just like if we wanted to see how many numbers was 3,4,5, we would do 5-3+1=3 to get the total number.
Anyways, let's consider first how many 2 digjt numbers whose digits are equal. You have 11 22,33,44 55,66,77,88,99 which is 9 numbers total.
So the amount of 2 digits number whose digits differ is 90-9=81.
The probability that a 2 digit number have different digits is 81/90.
This can reduce. Divide top and bottom by 9 giving 9/10.
what is x divided by one
Answer:
[tex] x \div 1[/tex]
[tex] = x[/tex]
Answer:
[tex]x\div 1=x[/tex]
Step-by-step explanation:
When x is divided by one it is called reciprocal.
reciprocal is the inverse of a number or a value.
examples: The reciprocal of 3 is 1/3, and the reciprocal of 5 is 1/3.
OAmalOHopeO
An item is regularly priced at$15.It is now priced at a discount of55%off the regular price
Answer:
$6.75
Step-by-step explanation:
The regular price is $15 dollars. The discount is 55% off the $15.
15 * 0.55 = 8.25
15 - 8.25 = 6.75
Hope this helps.
Answer:
discount =8.25
New price 6.75
Step-by-step explanation:
15 is the regular price
The discount is 55%
15*.55
8.25
The new price is the regular price minus the discount
15-8.25
6.75
The population of a strain of bacteria doubles in a culture. At noon there were 80 bacteria present and by 4:00 PM there were 20 480 bacteria. Determine algebraically the doubling period. Hint: You DO NOT need to use systematic trials.
Answer:
t = 1/2 hour
Step-by-step explanation:
20480 = 80[tex]x^{t }[/tex]
20480 = 80[tex]x^{4 }[/tex]
20480/80 = [tex]x^{4 }[/tex]
256 = [tex]x^{4 }[/tex]
x = 4
doubling period
2 = [tex]4^{t}[/tex]
t = 1/2 hour
round 3/5 to 3 decimal points
Answer:
3/5=0.600
Step-by-step explanation:
I hope this answer helps
The answer is 0.6.
Upto 3 decimal places it is 0.600.
