Maximum and Minimum Values of General Quadratic Functions
1. By expressing y = 2x^2 + 4x + 17 in the form y = a(x + b)^2 + C, where a, b, and c are constants, state the minimum value of y and the value of x at which this occurs. Hence, sketch the curve y = 2x^2 + 4x + 17
x =
y =
Answers
Answer:
x=-1
y=15
Step-by-step explanation:
This works because completing the square is essentially demonstrating what g(x) - where g(x) in this case = x^2 - would have to be translated by to give the function you have.
So by completing the square you have shown that the function you've been given has been shifted to the left by -1, stretched by a factor of 2 along the y axis and shifted up by 15.
Related Questions
An expression for the nth term of a sequence is
10-n^2
Find the third term of this sequence.
Answers
Answer:
1
Step-by-step explanation:
[tex] a_{n} = 10 - {n}^{2} \\ \\ \: plug \: n = 5 \\ \\ a_{3} = 10 - {3}^{2} \\ \\ a_{3} = 10 - 9 \\ \\ a_{3} = 1[/tex]
I got my ASVAB score back today... And I got a 21%... someone loves kill me now. But I didn't really have time to study for it, because my teachers offered for me to take it early and I did and now I have failed D:
Answers
Answer:
dang thats tough..
Step-by-step explanation:
idrk what an asvab is but it sounds horrible im
sorry that happened :(
0.74 x 0.422 =
Who ever answers will be brainiest
Answers
Answer:
0.30384
Step-by-step explanation:
uwu
Answer:
0.31228
Step-by-step explanation:
convert them into fractions: 74/100 * 422/1000simplify : 37/500 * 211/500multiply your answerYes i'm the brainiest
Tell me if i'm wrong
what is LCM of 2 and 5
Answers
Answer:
10
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
60 children go to a nursery. The ratio of girls to boys is 3 : 2
The children go to the nursery either in the morning or in the afternoon.
Three quarters of the children go to the nursery in the morning.
The rest of the children go to the nursery in the afternoon.
7 boys go to the nursery in the afternoon.
Work out how many girls go to the nursery in the morning.
Answers
Answer:
Girls (Morning) = 16
Step-by-step explanation:
60 children go to a nursery. The ratio of girls to boys is 3 : 2
Number of Boys = 3 / (3 + 2) * 60 = 3/5 * 60 =36
Number of Girls = 2 / (3 + 2) * 60 = 2/5 * 60 = 24
Three quarters of the children go to the nursery in the morning.
Number of children (Boys + Girls) = 3/4 * 60 = 45
The rest of the children go to the nursery in the afternoon.
Number of children (Boys + Girls) = 60 - 45 = 15
7 boys go to the nursery in the afternoon.
Boys + Girls = 15
Girls (Afternoon) = 15 - Boys = 15 - 7 = 8
Work out how many girls go to the nursery in the morning.
Girls (Morning) + Girls (Afternoon) = Girls (Total)
Girls (Morning) + 8 = 24
Girls (Morning) = 24 - 8
Girls (Morning) = 16
Answer:
The number of girls that go to the nursery in the morning are 28 girls
Step-by-step explanation:
The question is a word problem and the parameter given are as follows;
The number of children that go to the nursery, n = 60
The ratio of girls to boys = 3 : 2
The number of periods the children can attend the nursery = 2, morning or afternoon
The proportion of the children that go to the nursery in the morning = 3/4
The proportion of the children that go to the nursery in the afternoon = All those that do not go in the morning
The number of boys that go to the nursery in the afternoon = 7 boys
Let, 'x', represent the number of girls in the school, and let 'y', represent the number of boys in the school
Therefore, we have the following possible equations;
x + y = 60
x:y = 3:2
Therefore, the proportion of the total number of children that go to the nursery that are girls, x = 3/(3 + 2) = 3/5
The number of girls that go to the nursery, x = n × 3/5 = 60 × 3/5 = 36 girls
The number of girls that go to the nursery, x = 36 girls
∴ The number of boys that go to the nursery, y = 60 - 36 = 24 boys
The number of boys that go in the morning = y - (The number of boys that go to the nursery in the afternoon)
∴ The number of boys that go in the morning = 24 boys - 7 boys = 17 boys
The total number of children that go to nursery in the morning = 3/4 × (The number of children that go to the nursery, n)
∴ The total number of children that go to nursery in the morning = 3/4 × 60 = 45 children
The number of girls that go to the nursery in the morning = (The total number of children that go to nursery in the morning) - (The number of boys that go in the morning)
Therefore, the number of girls that go to the nursery in the morning = 45 children (girls + boys) - 17 boys = 28 girls
The number of girls that go to the nursery in the morning = 28 girls
The equation d = 3t represents the relationship between the distance in inches that a snail is from a certain rock and the time in minutes
Answers
Answer:
so would it be 3x 3 times pepepeppopo checkk
This coffee shop has on average 6 times more customers than the café down the street. Does the expression “x + 6” describe the situation? If not, write an expression that does and explain what the variable represents.
Answers
Answer:
Step-by-step explanation:
No the expression "x+6" does not describe the situation. The expression 6x describes the situation. "x" represents the number of customers in the coffee shop.
Answer:
X= number of people in the coffe shop
Step-by-step explanation:
Hope this helps :)
which of the following statements is not true
Answers
Answer:
2nd option is the answer
Step-by-step explanation:
Work out
m
and
c
for the line:
y
=
9
x
Answers
Answer:2
Step-by-step explanation:
2
For line y = 9x, m = 9 and c = 0
What is the slope-intercept form of the line?"y = mx + c, where m is the slope of the line and c is the y-intercept of the line."
What is slope of the line?"It is the change in y coordinate with respect to the change in x coordinate."
What is y-intercept?"It is a point at which a line intersects the Y-axis."
For given question,
We have been given an equation of line y = 9x
By comparing above equation of line with the slope-intercept form of line,
m = 9 and c = 0
This means the slope of the line y = 9x is 9 and the y-intercept is 0
Therefore, for line y = 9x, m = 9 and c = 0
Learn more about the slope and y-intercept of the line here:
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Julie has 5 yards of fabric to make doll outfits. Each outfit requires 3/4 yards of fabric. What is the maximum number of outfits Julie can make with her fabric?
Answers
Answer:
6
Step-by-step explanation:
well 5 divided by 3/4 is 6.66666666667 which you can say is 6
Please help me!!! This is due in an hour!!!
Answers
You would multiply 12 x 5 then divide that by 2
In a lab experiment, 130 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 8 hours. How many bacteria would there be after 24 hours, to the nearest whole number?
Answers
Answer:
1040
Step-by-step explanation:
8 hours = 260
16 hours = 520
24 hours = 1040
Find cos x and cos y! Please help me out! You don’t need to answer all just what you can :)
Answers
Answer:
7. cos(X) = 3/5 = 0.6
cos(Y) = 4/5 = 0.8
8. cos(X) = 15/17 ≈ 0.8824
cos(Y) = 8/17 ≈ 0.4706
9. cos(X) = 1/2 = 0.5
cos(Y) = (√3)/2 ≈ 0.8660
Step-by-step explanation:
The trigonometric ratio for cosine is given as follows;
[tex]Cos(\theta) = \dfrac{Adjacent\, side \, to\, angle}{Hypothenus\, side \, length \ of\, the \ triangle}[/tex]
7. The adjacent leg length to ∠X = 27
The length of the hypotenuse side of the triangle = 45
∴ cos(X) = 27/45 = 3/5 = 0.6
Cos(X) = 3/5 = 0.6
The adjacent leg length to ∠Y = 36
∴ cos(Y) = 36/45 = 4/5 = 0.8
cos(Y) = 4/5 = 0.8
8. The adjacent leg length to ∠X = 15
The length of the hypotenuse side of the triangle = 17
∴ cos(X) = 15/17 ≈ 0.8824
The adjacent leg length to ∠Y = 8
∴ cos(Y) = 8/17 ≈ 0.4706
9. The adjacent leg length to ∠X = 13
The length of the hypotenuse side of the triangle = 26
∴ cos(X) = 13/26 = 1/2 = 0.5
Cos(X) = 1/2 = 0.5
The adjacent leg length to ∠Y = 13·√3
∴ cos(Y) = 13·√3/26 = (√3)/2 ≈ 0.8660
cos(Y) = (√3)/2 ≈ 0.8660.
Determine the number of decimals places in each decimal
1. 0.378
2. 8.1867
3. 9419.4
4. 77.64
5. 9.05072
Answers
1)3
2)4
3)1
4)2
5)5
the spinner shown is
Answers
Answer:
where is the spinner
Step-by-step explanation:
Ms. Durand has an obsession with Christmas. She is standing 8ft away from a 20ft Christmas Geometree. She wonders, "hmmm, what is the angle of elevation from myself to the star on the top of the tree?"
Answers
Answer:
68.20°
Step-by-step explanation:
Using Pythagoras rule :
Tanθ = opposite / adjacent
Adjacent = 8ft
Opposite = 20
Tanθ = 20 / 8
θ = tan^-1(20/8)
= 68.198590
Hence, angle of elevation = 68.2°
The number of miles that regular tires last has a Normal
distribution with a mean of 50,000 miles and a standard
deviation of 8,200 miles.
If a random sample of 4 tires are selected, the probability
that the mean number of miles they last is more than
60,000 miles is 0.0075.
Is there convincing evidence that the mean number of
miles for all regular tires is greater than 60,000 miles?
___,it is,____ to randomly select 4 tires and
obtain a sample mean of greater than 60,000 miles if
the true mean of the population is 50,000 miles.
Answers
Answer:
1. 0.0075 or B
2. Yes and unlikely
Step-by-step explanation:
can someone help me with this question?
Answers
Answer: the answer is b,
Step-by-step explanation:
the girls are longer cause their shoes combined is 12 and 3/8
Answer:
Both daughters shoes combines
Step-by-step explanation:
8 5/8 plus 3 6/8 = 12 3 /8
"The combines length of the daughters shoes are longer since they are 12 and 3/8"
5/8 plus 6/8 = 11/8
11/8= 1 3/8
11+ 1+ 3/8 = 12 3/8
261, 256,251,... what would be the 46th term
Answers
Answer:
36
Step-by-step explanation:
Subtract: 3g - 1/g - 2g -4 /g+1
A. g - 5/ g - 1
B. g + 3/ 2g + 1
C. 5g^2 - 4g -1/ g^2 + 1
D. g^2 + 6g - 1/ g^2 + g
Answers
Answer:
D on edge
Step-by-step explanation:
Answer:
d is right on edge
Step-by-step explanation:
What is the value of x
in the equation 3=2x
?
A
23
B
1
C
112
D
5
Answers
Answer:
its 3/2
Step-by-step explanation:
Answer:
none x= 3/2
Step-by-step explanation:
Write each ratio as a fraction in simplest form.
9:4
Answers
Answer: 2 and 1/4
Step-by-step explanation: You make the fraction 9/4 then simplify.
5/7x - 14 = -22. Find x.
Answers
Answer:
x = -56/5, -11 1/5, or -11.2
Step-by-step explanation:
5/7x - 14 = -22
5x -98 = -154
5x = -154 + 98
5x = -56
x = -56/5, -11 1/5, or -11.2
Answer:
x= -11.2
Step-by-step explanation:
5/7x-14=-22
+14 +14 Add 14 on both sides
5/7x = -8
(7/5)*5/7x = -8*(7/5) Multiply by the reciprocal on both sides to leave x alone
x= -11.2 Answer
neda sells televisions she earns a fixed amount for each television and an additional $15 if the buyer gets an extended warranty. If neda sells 19 televisions with extended warranties, she earns $1,425. How much is the fixed amount neda earns for each television?
Answers
Answer:
$5
Step-by-step explanation:
15x18=270
1170-270=900
900/18=50
Answer:
$60
Step-by-step explanation: This helpful but I can not step by step
Help please! See attached photo
Answers
Hope this helps :)
Please help!!! What type of transformation is shown from Triangle P to Triangle Q?
A. Reflection across the y axis
B. Rotation
C. Translation
D. Reflection across the x axis
Answers
Answer:
D
Step-by-step explanation:
Reflection across the x axis
This is your answer because it is reflection on the x axis
Hope this helps u :)
Pls mark brainlist
The transformation shown from Triangle P to Triangle Q is Translation.
What is a transformation?
A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.
Given that, Triangle P is transformed to Triangle Q.
The transformation shown is a translation transformation, because in a translation transformation, all the points in the object are moved in a straight line in the same direction.
Hence, The transformation shown from Triangle P to Triangle Q is Translation.
For more references on transformation, click;
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At Summer camp, 62 percent of the campers decide they want to go swimming instead of hiking. If there are 200 kids at the camp, how many go swimming?
Answers
Answer:
124
Step-by-step explanation:
9 over 16 times x over 12
Answers
Answer:
x=6.75
Step-by-step explanation:
9/16x x/12
cross multiply
16 times x equals 16x 9 times 12 equals 108
16x=108
16/16=108/16
x=6.75
pls brainliest hope this helps
Which expressions are equivalent to 6 ^ 16? Check all that apply.
Answers
Answer:
the first one -4 and -4
Step-by-step explanation:
-4 times -4 is 16 because the negatives cancel out
The recipe uses 1/2 cup of sugar for 1 cup of flour...how much flour should there be if there is 2 cups of sugar? *
Answers
Answer:
4 cups
Step-by-step explanation:
2 divided by 1/2 is 4 so there are 4 half cups of sugar.
Since the sugar is multiplied by 4 you have to multiply the flour by 4.
1*4=4