7. Sketch the graph of f(x) = 2(x - 1.5)2 + 3, then state the domain and range of the function (show all your
work). (4 points)
8. Determine the value of a given that (7, 6) satisfies the quadratic function f(x) = a(x – 5)2 +6. (Show all your
work). (2 points)
9514 1404 393
Answer:
7. D: (-∞, ∞); R: [3, ∞); see attached for a graph (red)
8. a=0; see attached for a graph
Step-by-step explanation:
7. The function is a polynomial, so its domain is all real numbers.
The parabola opens upward. It has a minimum value of 3. The range is y ≥ 3.
__
8. Putting the given point coordinates in the equation, we can solve for a.
f(7) = 6
6 = a(7 -5)² +6
0 = a(2²)
0 = a
The value of a is zero.
(The given point has the same y-value as the vertex, but is not the vertex. The function can only go through that point if it is a horizontal line (not a parabola).) The attachment shows a graph.
A construction crew is lengthening a road that originally measured 45 miles. The crew is adding one mile to the road each day.
Let L be the length (in miles) after D days of construction.
Write an equation relating to . Then use this equation to find the length of the road after days.
Answer:
L = 45 + D
Step-by-step explanation:
Examples
D = 2
L = 47 miles
D = 5
L = 50 miles
D = 10
L= 55 miles
Kenneth's Tea Shop has caffeinated tea and decaffeinated tea. The tea shop served 63 caffeinated
teas and 7 decaffeinated teas. What percentage of the teas served were caffeinated?
Answer:
90%
90% of the teas were caffeinated.
Step-by-step explanation:
Total teas: 63+7= 70
63/70 x 100/1= 90%
90% of the teas were caffeinated.
Answer:
90%
Step-by-step explanation:
Which region indicates the intersection of the system 2x + 3y > 3 and y sx - 1?
Answer:
I think Region 1 is my answer, because the first equation is -1.1 and thats the closest point
Help please will mark brainliest
The half-life of Palladium-100 is 4 days. After 24 days a sample of Palladium-100 has been reduced to a mass of 7 mg.
A.) What was the initial mass (in mg) of the sample?
B.) What is the mass (in mg) 4 weeks after the start?
You may enter the exact value or round to 4 decimal places.
9514 1404 393
Answer:
A) 448 mg
B) 3.5 mg
Step-by-step explanation:
24 days is 24/4 = 6 half-lives. That is, the mass of 7 mg is 2^-6 times the initial mass.
A) The initial mass is 2^6×(7 mg) = 448 mg
__
B) 4 weeks is 28 days, or 7 half-lives. The remaining mass will be half the amount after 6 half-lives.
(7 mg)/2 = 3.5 mg . . . . remaining after 4 weeks
geometry I need help find the value of theta and round your answer to the nearest tenth.
Answer:
54deg
Step-by-step explanation:
We need to compute the inverse cosine of 10/17. I can't do it by hand, so I used a calculator and it arrived at ~53.97deg which is 54deg rounded to the nearest tenth.
Determine the missing side length:
Answer
35
Step-by-step explanation:
Using Pythagoras theorem since it's a right angle triangle,
The missing side, say h,is the hypotenuse
28²+21²= h²
784+441=h²
√1225=√h²
h=35
I really need help , Please help
Answer:
Step-by-step explanation:
Inpert
A circle has a diameter of 10 centimeters.
What is the best approximation of its area?
Use 3.14 to approximate for π.
Answer:
78.5
Step-by-step explanation:
hope i helped
What is 50π estimated? What is it exact?
Answer:
157.079632679
Garland put 2b + 3 dollars in the bank in the first week. The following week he doubled the first week’s savings and put that amount in the bank. The next week he doubled what was in the bank and put that amount in the bank. If he now has $477 in the bank, how much did he put in the bank the first week
Answer:
1st week deposit= 2b+3
2nd week deposit=2(2b+3)
3rd week deposit=4(2b+3)
Total deposit=2b+3+2(2b+3)+6(2b+3)
=9(2b+3)
=18b+27
18b+27=477
18b. =477-27=450
18b. =450
;
b=450/18=25
Therefore 2b+3=2(25)+3 =50+3=53
PLEASE GIVE BRAINLIEST
Assuming that the drug has no effect, so that the probability of nausea was 0.0124, find the mean and standard deviation for the numbers of people in groups of 828 that can be expected to experience nausea.
Answer:
11.
Step-by-step explanation:
Given that the drug has no effect and that the probability of nausea was 0.0124, to find the mean and standard deviation for the numbers of people in groups of 828 that can be expected to experience nausea, the following calculation must be performed:
828 x 0.0124 = X
10.26 = X
Thus, the number of people who may feel nauseous after using the drug in question is 11 individuals.
6) How many solutions does the system have? y = 5x + 3 and y = -2x + 3
Step-by-step explanation:
5x + 3 = -2x + 3
7x = 0
x = 0
y = 0 + 3
y = 3
(0, 3)
one solution
Can you solve these trapezoid areas please?
Thank you
the first one is 3.15 and the second one is 630
It's Friday afternoon and six fraternity brothers at UNC have just attended their last class of the semester. To unwind before the final exam Monday morning, they decide to spend the weekend at the beach. After a weekend of immature, irresponsible behavior, they oversleep Monday morning and miss the final exam. Later that day they go to their professor (who received her Ph.D. from NC State) and explain that they went to the beach and were on the way back for the final exam but their car (a BMW of course) had a flat tire. The professor says that they can come back the next morning and she will give them a make-up final exam consisting of one short-answer question! The students are ecstatic and high-five each other all the way back to the frat house. The next morning the professor puts each student in a different room and hands them their one-question test. The question: Which tire?
Required:
What is the probability that all 6 students will say that the same tire was flat?
If 6 times a certain number is added to 8, the result is 32. Which of the following equations could be used to solve the problem? 6 x = 8 + 32 6 x+8 = 32 6 x= 32 61 X + 8) = 32
Answer:
6x + 8 = 32
6(x + 8) = 32
Step-by-step explanation:
Hope this helps
please answer! will give brainliest
Answer:
9.5 I think
STEPS-
9+4+11+14=38
38/4=9.5
how much interest does $1,000 earn at an interest rate of 6% compounded semi annually? what is the balance after 2 years
Answer:
Interest = A - P = 1015 - 1000 = $15
Step-by-step explanation:
1 Gabriel and his mom have jars of apple sauce stored in boxes in their pantry. Each box contains 12 jars of
apple sauce. Gabriel's mom uses 3 jars from 1 of the boxes,
Which function shows the relationship between y, the total number of jars of apple sauce remaining in the
pantry, and x, the number of boxes in the pantry
A. y = 9x
B. y = 11x +9 C. y = 12x
D. Y = 12x - 3
Answer:
D. y = 12x - 3
Step-by-step explanation:
We know that the number of boxes is x and that each box contains 12 jars
This means that:
Total number of jars = number of boxes * number of jars in each box
Total number of jars = 12x jars
Now, Gabriel's mum used 3 jars
This means that, the number of remaining jars (y) can be calculated by removing 3 from the total number of jars (12x)
Based on the above:
Remaining jars = Total number of jars - Number of used jars
Y = 12x - 3
Hope this helps :)
if you answer all the questions I will give you 80 points and brainliest
Answer:
1) SA = 2(wl + hl + hw) = 2(12*2 + 12*6 + 6*2) = 2(24 + 72 + 12) = 2(108) = 216
2) SA = (6*4)/2 + 6*11 + 2(5*11) = 12 + 66 + 110 = 188
3) SA = 2(6*12 + 14*12 + 6*14) = 648
4) (9*12)/2 + 15*6 + 9*6 + 12*6 = 54 + 90 + 54 + 72 = 270
5) 2(16*9 + 4*9 + 16*4) = 488
6) SA = 2πrh+2πr^2 = 2*3.14*10*16 + 2*3.14*10^2 = 1004.8 + 628 = 1632.8
7) SA = 2(7*7 + 14*7 + 7*14) = 490
8) SA = 2πrh+2πr^2 = 2*3.14*7*11 + 2*3.14*7^2 = 483.56 + 307.72 = 791.28
9) (12*10)/2 + 2(14*13) + 14*10 = 60 + 364 + 140 = 564
Answer:Answer:
1) SA = 2(wl + hl + hw) = 2(12*2 + 12*6 + 6*2) = 2(24 + 72 + 12) = 2(108) = 216
2) SA = (6*4)/2 + 6*11 + 2(5*11) = 12 + 66 + 110 = 188
3) SA = 2(6*12 + 14*12 + 6*14) = 648
4) (9*12)/2 + 15*6 + 9*6 + 12*6 = 54 + 90 + 54 + 72 = 270
5) 2(16*9 + 4*9 + 16*4) = 488
6) SA = 2πrh+2πr^2 = 2*3.14*10*16 + 2*3.14*10^2 = 1004.8 + 628 = 1632.8
7) SA = 2(7*7 + 14*7 + 7*14) = 490
8) SA = 2πrh+2πr^2 = 2*3.14*7*11 + 2*3.14*7^2 = 483.56 + 307.72 = 791.28
9) (12*10)/2 + 2(14*13) + 14*10 = 60 + 364 + 140 = 564
Step-by-step explanation:
4) Find a solution to the following system of equations by graphing
X-y = 11
X-y = 5
!SHOW WORK PLEASE!
Answer:
No solution
Step-by-step explanation:
Given
[tex]x - y = 11[/tex]
[tex]x - y = 5[/tex]
Required
Solve by graph
See attachment for graph.
From the attachment, lines [tex]x - y = 11[/tex] and [tex]x - y = 5[/tex] do not intersect. This implies that, no solution exist
Find the quotient 3/4÷1 1/10
Answer:
15/22
Step-by-step explanation:
Pls help, my address is 123 help
Answer:
y=2x
Step-by-step explanation:
First you find out what times what equals 2 and that's it
The graph shows the relationship between the
cups of water and pounds of beef needed for a
beef casserole.
Poop
Answer:
Step-by-step explanation:
12x = 3y - w, solve for x
Answer:
[tex]x = \frac{3y - w}{12} [/tex]
Step-by-step explanation:
[tex] \frac{12x}{12} = \frac{3y - w}{12} [/tex]
[tex]x = \frac{3y - w}{12} [/tex]
mr miller bought 1/3 pounds of nuts he divided the nuts equally among his three children how much did each child get
Answer:
1/9
Step-by-step explanation:
1/3 ÷ 3 = 1/9
People use the KCF method for this kind of solution.
At first it is 1/3 ÷ 3/1, after that you need to flip the 2nd fraction. For example, to be able to flip the fraction to find the answer, the equation your supposed to get after flipping the 2nd fraction is 1/3 x 1/3 which makes 1/9.
Simplify the expression 9+2y+3y squared -2y squared
Answer:
[tex]y^{2}[/tex] + 9
Step-by-step explanation:
To simplify, combine like terms:
3[tex]y^{2}[/tex] - 2[tex]y^{2} = y^{2}[/tex]
9 = 9
Set it up:
[tex]y^{2} + 9[/tex]
Find the product or type
"impossible"
[6 ]I-1
1 11
(-5
-5 3
Answer:
the answer is -58
Step-by-step explanation:
you factor out the negitive sign and calcuate.
Answer: [1/10 9/6]
Step-by-step explanation:
Write the first five terms of the geometric sequence.
an= - 4an-1; a1= 5
Answer:
don't know only
Step-by-step explanation:
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