Answers
Answer:
Option 2: y = a(x + 1)² - 9
Step-by-step explanation:
Given the graph of an upward-facing parabola, whose vertex occurs at point (-1, -9) as its minimum point.
Vertex FormUsing the vertex form of the quadratic equation, y = a(x - h)² + k:
where:
a = determines the wideness and the direction of where the graph opens.
(h, k) = vertex
h = determines the horizontal translation of the graph
k = determines the vertical translation of the graph
Using the vertex, (-1, -9), and another point from the graph, (2, 0), substitute these values into the vertex form to solve for the value of a:
y = a(x - h)² + k0 = a[2 - (-1)]² - 9
0 = a(2 + 1)² - 9
0 = a(9) - 9
Add 9 to both sides to isolate a:
0 + 9 = 9a - 9 + 9
9 = 9a
Divide both sides by 9 to isolate a:
[tex]\displaystyle\mathsf{\frac{9}{9}\:=\:\frac{9a}{9}}[/tex]
a = 1
Final answer:Therefore, the vertex form of the given parabola is: y = a(x + 1)² - 9.
Related Questions
A hybrid car can go 400 miles on 8 gallons of gas. How far can the car take you with 1 gallon of gas?
Answers
Answer:
50 miles
Step-by-step explanation:
Take the number of miles and divide by the number of gallons
400 miles / 8 gallons
50 miles per gallon
Answer:
50 miles
Step-by-step explanation:
if for each 8 gallons it can go to 400 miles
so the 8 will be divided to 8 and get 1
and also divide the 400 into 8 you will get 50 miles per 1 gallon
5. The combined perimeter of a circle and a square is 16. Find the dimensions of the circle and square
that produce a minimum total area.
Answers
The dimensions of the circle and square that produce a minimum total area are 1.12 and 2.24 respectively
Represent the side length of the square with s, and the radius of the circle with r.
So, the perimeter (P) and the area (A) of the shape are:
[tex]P =4s + 2\pi r[/tex]
[tex]A =s^2 + \pi r^2[/tex]
The perimeter is 16. So, we have:
[tex]4s + 2\pi r = 16[/tex]
Divide through by 4
[tex]s + 0.5\pi r = 4[/tex]
Make s the subject
[tex]s = 4 - 0.5\pi r[/tex]
Substitute [tex]s = 4 - 0.5\pi r[/tex] in [tex]A =s^2 + \pi r^2[/tex]
[tex]A = (4 - 0.5\pi r )^2 + \pi r^2[/tex]
Expand
[tex]A = 16 - 4\pi r + 0.25(\pi r)^2 + \pi r^2[/tex]
This gives
[tex]A = 16 - 4\pi r + (0.25\pi^2 + \pi )r^2[/tex]
Differentiate with respect to r
[tex]A' = 0 - 4\pi + 2(0.25\pi^2 + \pi )r[/tex]
[tex]A' = - 4\pi + 2(0.25\pi^2 + \pi )r[/tex]
Set to 0
[tex]- 4\pi + 2(0.25\pi^2 + \pi )r =0[/tex]
Add 4pi to both sides
[tex]2(0.25\pi^2 + \pi )r =4\pi[/tex]
Divide both sides by 2
[tex](0.25\pi^2 + \pi )r =2\pi[/tex]
Make r the subject
[tex]r =\frac{2\pi}{(0.25\pi^2 + \pi )}\\[/tex]
Factor out pi
[tex]r =\frac{2\pi}{\pi(0.25\pi + 1 )}[/tex]
Cancel out the common factors
[tex]r =\frac{2}{0.25\pi + 1 }[/tex]
Express pi as 3.14
[tex]r =\frac{2}{0.25\times 3.14 + 1 }[/tex]
[tex]r =\frac{2}{1.785}[/tex]
Divide
[tex]r =1.12[/tex]
Recall that:
[tex]s = 4 - 0.5\pi r[/tex]
This gives
[tex]s =4 -0.5 \times \pi \times 1.12[/tex]
This gives
[tex]s =4 -0.5 \times 3.14 \times 1.12[/tex]
[tex]s =2.24[/tex]
Hence, the dimensions of the circle and square that produce a minimum total area are 1.12 and 2.24 respectively
Read more about minimum areas at:
https://brainly.com/question/6427280
a pupil who scored 60 in her maths exam was absent and missed English exam use the line of best fit to predict what her English mark could be
Answers
Answer:
It's 48.
Hope that helped? Also, if you need anymore answers feel free to ask me as I had that assignment on Mathswatch.
Step-by-step explanation:
Answer:
i think it's 48 if i'm wrong i'm sorry
Is 6.32332333... a rational or irrational number? a Choose the correct answer below. O rational number O irrational number
Answers
Answer:
Irrational number because it cannot be written in fraction form a/b where b is not supposed to be 0
Harry has $10 in his bank account, and he adds $2 every week. based on this information, which representation best shows the relationship between the amount of money harry has in his bank account ,y, and the number of weeks that have passed, x? (im testing....)
Answers
Answer:
y= (2x)+10
Step-by-step explanation:
if harry has an initial balance of $10 in his bank account, he will have something +10 for the initial 10.
If he adds $2 to his bank account every week, then the amount of money in his bank account (y) can be modeled by the equation
y = (2x)+10
where y represents how much money he has in his bank account and x represents the amount of weeks he is adding $2.
John Marlow's total income last year was $31,300. Of that amount, he spent
$7,900 for food. What percent of Jon's total income did he spend for food? *
25%
40%
50%
85%
Answers
Based on the information given the percent of Jon's total income did he spend for food is 25%.
Using this formula
Percent of total income=Amount spent for food/Total income last year
Where:
Amount spent for food=$7,900
Total income last year=$31,300
Let plug in the formula
Percent of total income=$7,900/$31,300
Percent of total income=25%
Inconclusion the percent of Jon's total income did he spend for food is 25%.
Learn more about total income here:https://brainly.com/question/842469
Solve for x: x /6−y/3= 1
SHOW WORK
Answers
[tex]\dfrac x6 - \dfrac y3 =1\\\\\\\implies \dfrac x6 - \dfrac{2y}6 = 1\\\\\\\implies \dfrac{x-2y}6 =1\\\\\\\implies x -2y =6\\\\\\\implies x =6+2y\\\\\\\implies x = 2(3 +y)[/tex]
(100 points will award brainliest)
In the image below, the m
Answers
Answer: 67°.
Step-by-step explanation:
1) m∠PMR=m∠LMN=3x+19°;
2) m∠LMN+m∠LMP=180°, it can be written as 3x+19+9x-31=180;
3) if to solve the equation 3x+19+9x-31=180, then x=16;
4) m∠PMR=3x+19=48+19=67°.
Image attached giving 25 points please help
Answers
Solve the following compound inequality: 4 less-than-or-equal-to x + 4 less-than-or-equal-to 12. a. 0 less-than-or-equal-to x less-than-or-equal-to 8 c. 8 less-than-or-equal-to x less-than-or-equal-to 16 b. x less-than-or-equal-to 8 d. no solution Please select the best answer from the choices provided A B C D
Answers
Answer:
A. 0 <= x <= 8
Step-by-step explanation:
4 <= x + 4 <= 12
Remove 4 from all sides
4 - 4 <= x + 4 -4 <= 12 - 4
0 <= x <= 8
Apply Euclid algorithm to find HCF of number 4052 and 420
Answers
Answer:
ANSWER 4
Step-by-step explanation:
the hcf is 420 and then u say 2x2=4 simple
7 1/2 divided by 2 1/2
Answers
Answer:
3
Step-by-step explanation:
A birthday cake was cut into equal pieces, and 10 pieces were eaten. The
fraction below shows how much cake was left over. According to the fraction,
into how many pieces was the cake cut?
1
11
A. 1
B. 10
C. 21
D. 11
Answers
assuming the fraction is 1/11, the denominator shows how many parts the WHOLE was sliced into, namely 11 parts.
Pls help as soon as possible thank you
Answers
Answer:
D
Step-by-step explanation:
F(g) falls between 0 and 49.58
The dean of a business college in the Midwest claims that he can correctly identify whether a student is a finance major or a music industry management major by the way the student dresses. Suppose in actuality that he can correctly identify finance majors 84% of the time, while 16% of the time he mistakenly identifies a music industry management major as a finance major. Presented with one student and asked to identify the major of this student (who is either a finance or music industry management major), the dean considers this to be a hypothesis test with the null hypothesis being that the student is a finance major and the alternative that the student is a music industry management major. Which of the following statements illustrates a Type I error?
a. Saying that the student is a finance major when in fact the student is a music industry management major.
b. Saying that the student is a music industry management major when in fact the student is a music industry management major.
c. Saying that the student is a finance major when in fact the student is a finance major.
d. Saying that the student is a music industry management major when in fact the student is a finance major.
Answers
Using error concepts, it is found that the option that represents a Type I error is:
d. Saying that the student is a music industry management major when in fact the student is a finance major.The definitions of each type of error are as follows:
A Type I error happens when a true null hypothesis is rejected. A Type II error happens when a false null hypothesis is not-rejected.
In this problem, the Hypothesis are:
Null: Student is a finance major.Alternative: Student is a music industry management major.By the definition of a Type I error, in this problem, it would consist in saying that a finance major student is a music industry management major student, hence option d is correct.
You can learn more about Type I and II errors at https://brainly.com/question/25225353
Rick's Phone Service charges $12.52 for an activation fee plus $6 for every gigabyte (g) used.
Which of the following graphs models the situation?
(Please, help me I will do everything I can to boost you.. It's been a rough night of homework.)
Answers
Answer:
d
Step-by-step explanation:
same explanation as before just replace the current values with the previous explanation
Answer:
After a quick stint of attempting to read the graphs I would speculate D
guys pls ı need help really....
Answers
Answer:
Step-by-step explanation:
Calculus....finally something FUN to answer!
This is integration, but here you have the area under the curve, you just don't have the upper bound. Setting that problem up looks like this:
[tex]28=\int\limits^b_1 {7x} \, dx[/tex] and using the First Fundamental Theorem of Calculus, that will integrate to look like this:
[tex]28=\frac{7x^2}{2}[/tex] from 1 to b and applying the FTC:
[tex]28=\frac{7b^2}{2}-\frac{7}{2}[/tex] Multiplying everything by 2 to get rid of the denominators gives you:
[tex]56=7b^2-7\\\\56=7(b^2-1)\\8=b^2-1\\9=b^2\\b=3[/tex]
charles had a sheet cake for his birthday when 9/12 remained charles took 1/3 of the remaining cake to wrap and save for later what fraction of the original cake did he wrap
Answers
Answer:
He wrapped 3/4 of the cake.
Step-by-step explanation:
1/3 of 9/12 is 0.25 and 0.25 converted into a fraction is 3/4
- Hope this helps!
The function g(x) undergoes a vertical stretch of 2, a horizontal shift to the right 3 units, and a vertical shift up 1 to become f(x). Which equation describes f(x).
F(x) = 2|x + 3|- 1
F(x) = 2|x - 3| + 1
F(x) = 2|x - 3| + 1
F(x) = 2|x- 3| - 1
Answers
Answer:
NONE OF THE OPTIONS GIVEN
Step-by-step explanation:
F(x) = 2|x - 3| + 1 is close, but vertical bars in stead of parentheses completely changes the curve shape
I believe it should be f(x) = 2(x - 3) + 1
if g(x) = x
here are some plots to compare the possibilities. I've shifted the vertical of each to separate the blue and green lines slightly. If they were both true "1" values the lines would be colinear for x>3.
The red line has a slope of 1, stretching by a factor of 3 means the slope is now 3. The absolute value signs from the answer options makes f(x) have a sharp V shape whereas the parentheses creates a single line for all values of x as does g(x) = x.
The normal price of a television is reduced by 30% in a sale. The sale price of the television is £350 Work out the normal price of the television?
Answers
Answer:
$245
Step-by-step explanation:
0.7 * 350 = 245
The normal price of the television, if The normal price of a television is reduced by 30% in a sale, The sale price of the television is £350, is £500.
What is the sale price?The price at which something sells or is purchased following a price reduction. The cost that something is sold for. In other words, the price at which something is sold to a customer is called the sale price
Given:
The normal price of a television is reduced by 30% in a sale,
The sale price of the television is £350,
Write the equation of the above statement as shown below,
Normal price - 30% of normal price = Sale price
Substitute the value,
Normal price(1 - 0.30) = £350
Normal price = 350 / 0.7
Normal price = £500
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#SPJ2
A = 1011 + 337 + 337/2 +1011/10 + 337/5 + ... + 1/2021
Answers
The sum of the given series can be found by simplification of the number
of terms in the series.
A is approximately 2020.022Reasons:
The given sequence is presented as follows;
A = 1011 + 337 + 337/2 + 1011/10 + 337/5 + ... + 1/2021
Therefore;
[tex]\displaystyle A = \mathbf{1011 + \frac{1011}{3} + \frac{1011}{6} + \frac{1011}{10} + \frac{1011}{15} + ...+\frac{1}{2021}}[/tex]The n + 1 th term of the sequence, 1, 3, 6, 10, 15, ..., 2021 is given as follows;
[tex]\displaystyle a_{n+1} = \mathbf{\frac{n^2 + 3 \cdot n + 2}{2}}[/tex]Therefore, for the last term we have;
[tex]\displaystyle 2043231= \frac{n^2 + 3 \cdot n + 2}{2}[/tex]2 × 2043231 = n² + 3·n + 2
Which gives;
n² + 3·n + 2 - 2 × 2043231 = n² + 3·n - 4086460 = 0
Which gives, the number of terms, n = 2020
[tex]\displaystyle \frac{A}{2} = \mathbf{ 1011 \cdot \left(\frac{1}{2} +\frac{1}{6} + \frac{1}{12}+...+\frac{1}{4086460} \right)}[/tex]
[tex]\displaystyle \frac{A}{2} = 1011 \cdot \left(1 - \frac{1}{2} +\frac{1}{2} - \frac{1}{3} + \frac{1}{3}- \frac{1}{4} +...+\frac{1}{2021}-\frac{1}{2022} \right)[/tex]
Which gives;
[tex]\displaystyle \frac{A}{2} = 1011 \cdot \left(1 - \frac{1}{2022} \right)[/tex]
[tex]\displaystyle A = 2 \times 1011 \cdot \left(1 - \frac{1}{2022} \right) = \frac{1032231}{511} \approx \mathbf{2020.022}[/tex]
A ≈ 2020.022Learn more about the sum of a series here:
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A is equal to 1,685.00049.
Given that A = 1011 + 337 + 337/2 +1011/10 + 337/5 + ... + 1/2021, the following calculation must be performed to determine the result of this operation:
337/2 = 168.5 1011/10 = 101.1 337/5 = 67.4 1/2021 = 0.00049 1011 + 337 + 168.5 + 101.1 + 67.4 + 0.00049 = A 1685.00049 = A
Therefore, A is equal to 1,685.00049.
Learn more about maths in https://brainly.com/question/25273534
V is themidpoint of UW. If UV = x + 8 and VW = 9x, what is VW?
Answers
Answer:
x=1
Step-by-step explanation:
If V is the midpoint of the line UW, that would mean that there's an equal distance between UV and 9x. So, the value of UV and VW would eed to be the same.
x+8=9x
8=8x
x=1
(3v^5-34v^4+79v^3+5v^2+21v+19)\(v-8)
Answers
Answer:
3 big guys
Step-by-step explanation:
Answer:
Step-by-step explanation:
we find by synthetic division.
v-8=0
v=8
8 | 3 -34 79 5 21 19
| - 24 -80 -8 -24 -24
|----------------------------------
3 -10 -1 -3 -3 |-5
Quotient:-3v^4-10v³-v²-3v-3
Remainder:- -5
Write five demicals that round to 0.96?
Answers
Answer:
0.964
0.959
0.961
0.958
0.963
Step-by-step explanation:
Anything below 5 can be rounded down, anything above 5 can be rounded up.
You can have a decimal after 0.96 to be less than 5, or a decimal after 0.95 to be greater than 5.
Here's some I picked:
0.964
0.959
0.961
0.958
0.963
Solve for x&y using substitution but do it step by step
Answers
Answer:
x +2y = 2 ...... 1
7x + 10y = 2 ..... 2
x = 2 - 2y ..... 3
substitute 3 in 2
7(2 - 2y) + 10y = 2
14 - 14y + 10y = 2
14 - 4y = 2
- 4y = 2 - 14
- 4y = - 12
divide by - 4 on both sides
y = 3
substitute the value of y in 3
× = 2 - 2(3)
x = - 4
(x ; y )
(- 4 ; 3)
Show all work to solve 2x2 +7x - 4 = 0
Answers
Heyy!!
2x2 + 7x - 4 = 0
4x + 7x - 4 = 0
11x - 4 = 0
11x = 4
x = 4/11
ANSWER: x = 4/11HELP ILL MARK BRAINLIEST ANSWER THIS QUESTION IN THE PIC
Answers
Median: outdoor group, 7
Mean: outdoor, 7 (rounded up 6.93)
Larger: outdoor group
I think these are right, good luck!
HELP PLEASE!!! 50 POINTS INCORRECT ANSWERS WILL BE REPORTED.
Answers
5x+24=9x-17
Subtract 5x on both sides
24=4x-17
Add 17 to both sides
41=4x
Divide by 4
10.25
If [tex]x^{2} + y^{2} = 6[/tex] and [tex]x + y = \sqrt{7}[/tex], then what is [tex]x-y[/tex]?
Answers
Recall that
(x + y)² = x² + 2xy + y²
Then if x + y = √7 and x² + y² = 6, we have
(√7)² = 6 + 2xy ⇒ 2xy = 1
We also have
(x - y)² = x² - 2xy + y²
so that
(x - y)² = 6 - 1 ⇒ (x - y)² = 5
which means x - y has two possible values, √5 or -√5.
I need help on math true and false please
Answers
Answer:
Step-by-step explanation:
1. False
2. False
3. True
4. True
5. True
6. True
7. True
8. True
9. True
10. False