Answer: a = -2 and c = 7
Step-by-step explanation:
(this answer uses some basic calculus)
We know that [tex]f'(x) = 2ax + 4[/tex], and since [tex](1,9)[/tex] is a maximum of [tex]f[/tex], then [tex]f'(1) = 0[/tex]. That means [tex]2a + 4 = 0[/tex], so [tex]\boxed{a = -2}[/tex]. Then since [tex]f(1) = 9[/tex], we have [tex]-2(1)^2 + 4(1) + c = 9[/tex], so [tex]\boxed{c = 7}[/tex].
Answer:
a = -2
c = 7
Step-by-step explanation:
Given the quadratic function, f(x) = ax² + 4x + c, for which its vertex is the maximum point occurring at (1, 9), and b = 4.
Solve for the value of a:Since the x-coordinate of the vertex, x = 1, can be calculated using the formula, [tex]x = \frac{-b}{2a}[/tex]:
We can substitute the value of the x-coordinate and b = 4 into the formula, and solve for the value of a:
[tex]x = \frac{-b}{2a}[/tex]
[tex]1 = \frac{-4}{2a}[/tex]
Multiply both sides by 2a:
(2a) 1 = [tex]\frac{-4}{2a} (2a)[/tex]
2a = -4
Divide both sides by 2 to solve for a:
[tex]\frac{2a}{2} = \frac{-4}{2}[/tex]
a = -2
Therefore, the value of a = -2.
Solve for the value of c:Next, to solve for c, substitute the coordinate values of the vertex, (1, 9) into the given quadratic function:
f(x) = ax² + 4x + c
9 = -2(1)² + 4(1) + c
9 = -2 + 4 + c
9 = 2 + c
Subtract 2 from both sides to isolate c:
9 - 2 = 2 - 2 + c
7 = c
Double-check:In order to double-check the validity of our values for a and c, substitute a = -2, and c = 7 into the function, along with the coordinates of the vertex, (1, 9):
f(x) = -2x² + 4x + 7
9 = -2(1)² + 4(1) + 7
9 = -2 + 4 + 7
9 = 9 (True statement).
Therefore, the correct answers are: a = -2, and c = 7.
Find the number of integers between 1 and 1000 that are divisible by 12 or 15, but not by both 12 and 15.
Count the multiples of 12:
⌊1000/12⌋ = 83
(where ⌊x⌋ denotes the "floor" of x, or the largest integer that is less than or equal to x)
These are the integers
{12, 24, 36, 48, …, 996}
Count the multiples of 15:
⌊1000/15⌋ = 66
These are
{15, 30, 45, 60, …, 990}
Count the multiples of both 12 and 15; these are multiples of LCM(12, 15) = 60:
⌊1000/60⌋ = 16
These are
{60, 120, 180, 240, …, 960}
Now use the inclusion/exclusion principle to count the multiples of either 12 or 15, but not both:
83 + 66 - 2•16 = 117
Among the multiples of 12 and the multiples of 15, we count the numbers that are multiples of both 12 and 15. By subtracting the number of multiples of both (16), we get the count of integers that are either divisible by 12 or 15. We subract 16 again to remove those that are divisible by both 12 and 15.
Please take a look at the picture.
Answer:
B, and A
Step-by-step explanation:
big brain time
Which of the following statements are correct?
Please help
Answer:
True A. angles one and five are corresponding angles.
True B. angles three and six are alternate interior angles.
False C. angles two and seven are alternate interior angles.
Angles two and seven are alternate exterior angles.
False D. angles five and eight are alternate exterior angles.
Angles five and Eight are verticle angles.
False E. angles two and four are same-sided consecutive angles.
Angles two and four are supplementary angles
True F. angles four and six are same side consecutive angles.
True G. angles one and eight are alternate exterior angles.
What is sin 60°?
WA :)
an
2
90
30
5
A. I
оо
B.
-IS
o
C. 1
D.
O
E. 5
o
OF
PREVIOUS
Answer:
F
Step-by-step explanation:
If you look at that triangle and do trigonometry with sin, you would have to do opposite/hypotenuse. This would be (square root of 3)/2
Ms. April likes for the twenty students in her
class to have a carton of milk each day at break
time. She sends three of her students down to
the cafeteria to ask for the cartons of milk, but
she likes to mix things up a bit and wants to
send a different group of students down every
day. Will she have enough different groups of
three students in her class of twenty students to
send a different group every day of the school year? (There are 180 days in the school year)
9514 1404 393
Answer:
yes
Step-by-step explanation:
There are 20 ways to choose the first student, 19 ways to choose the second student, and 18 ways to choose the third student. Chosen this way, the same three students can be chosen 3×2×1 = 6 different ways. So, the number of different choices of 3 students will be ...
(20×19×18)/(3×2×1) = 1,140
There are easily enough different combinations of 3 students to have a different combination each day.
_____
Additional comment
The number found above is the number of combinations of 20 students taken 3 at a time: 20C3 or C(20, 3). The value can be computed from ...
nCk = n!/(k!(n-k)!)
At a cafe, the Bishop family pays $12 for a salad, a fruit bowl, and two sandwiches. The Cortez family pays $14 for two salads and two sandwiches. The Donovan family pays $14 for a salad and three fruit bowls. What is the price of a fruit bowl at the cafe?
$2
$3
$4
$5
Answer:
$3
Step-by-step explanation:
https://brainly.com/question/16432745
[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right][/tex]
[tex]\huge{\underline{\underline{\boxed{\sf{\purple{Answer}}}}}}[/tex]
Since column 3 of the given matrix consists of numbers which are all constant multiples of each other, there is a theorem which states that the determinant of this matrix is 0 .However, I will prove it from calculation just to verify and show how you would calculate such determinants should you not be aware of the theorems of linear matrix algebra.Use co-factor expansion along any row or column of your choice.This involves adding the products of the entries in each row with their co-factors[tex] { - 1}^({i + j} )[/tex]for an entry in row I and column j, multiplied by the minor of the entry, formed by evaluating the resulting determinant when you delete row I and column j.In this case, since the given matrix is 3x3 indimension, it will result in three 2×2 determinants which we can find from definition[tex] \binom{a \: b}{c \: d} [/tex] = ad-bc
I will take co-factor expansion along row 1 as an example to find the determinant of the given matrix as :
∆=[tex] 1( - 1) {}^{1 + 1} {} \binom{56}{8 \: 9} + 2( - 1) {}^{1 + 2} \binom{4 \: 6}{7 \: 9} + 3( - 1) {}^{1 + 3} \binom{4 \: 5}{7 \: 8} \\ = 1(45 - 48) +( - 2)(36 - 42) + 3(32 - 35) \\ = - 3 + 12 - 9 \\ = 0 [/tex]
Find the slope of the line that passes through:
(6,7) and (4,2)
Answer:
5/2
Step-by-step explanation:
Slope = Change in y/Change in x
Slope = 2 - 7/4 - 6
Slope = -5/-2
Slope = 5/2
-Chetan K
I need to know the answer
Answer:
2 x 6 = 12
6 x 2 = 12
12 ÷ 6 = 2
12 ÷ 2 = 6
Step-by-step explanation:
If it takes you 2 1/2 hours to assemble one unit, how many units will you complete in 15 hours? (Change 2 1/2 to improper fraction first)
Answer:37.5
Step-by-step explanation:
2 1/2 as an improper fraction is 5/2
If i'm wrong tell me please i hope this helped you
If 10 candy cost $35. How much candy can I buy with $20
Answer:
6 candies
Step-by-step explanation:
(find unit rate, cost / quantity)
35/10 = 3.5
20/3.5 = = 5.7142857142857
candies cannot be in decimal so you must round to the nearest whole
Simplify the following expression
3x + 2(x +6) -4 -2x
A. 3x + 2
B. 7x + 8
C. 3x + 8
D.7x + 10
Answer:
C
Step-by-step explanation:
3x+2(x+6)-4-2x.
First, we do the parenthesis.
This gives us: 3x+2x+12-4-2x.
Then, we reorder so like terms are together.
This gives us: 3x+2x-2x+12-4.
Then, we combine like terms.
This gives us: 3x+8, which is C.
URGENT, WILL GIVE BRAINLIEST!!
In △ABC, A=27∘, a=27 and c=24. Which of these statements best describes angle C?
C must be acute.
C must be obtuse.
C can be either acute or obtuse.
△ABC cannot be constructed.
Answer:
C must be acute, and ABC cannot be constructed
Step-by-step explanation:
24 degrees is under 90 degrees making angle c an acute angle.
ABC cannot be contructed because a triangle makes up of 180 degrees, and ABC does not make up 180 degrees.
Have a great day friend! :D
Answer:
C must be acute.
Step-by-step explanation:
The smaller the length of the side, the smaller is the angle opposite it, so C must be < 27.
x – 1= 4x + x - 8+ 3x
Answer:
1
Step-by-step explanation:
Add one on both sides, combine like terms and solve.
Explain how you can write 4.1 as a/b
Answer:
ax + by
Step-by-step explanation:
i hope its correct
if its wrong then im sorry :)
Five tickets numbered 1, 2, 3, 4, and 5 are placed in a box, and three are selected at random. Determine the probability of obtaining a 1 or a 2 or both.
Answer:
the probability is 1 and 2
Find the equation of the line.
Answer:
Step-by-step explanation:
(-4,-5) and (6,4)
Slope: (4 - - 5) / ( 6 - - 4) = 9/10
y-intercept= - 5 - (9/10)(-4)
= - 5 + 36/10 = -7/5
y = 9/10x - 7/5
The equation of the line is x + 10y -19 = 0.
We are given that;
The points of line segment= (6,4) and (-4,5)
Now,
To find the equation of a line given two points, we can use the two-point form formula:
y − y 1 = y 2 − y 1 x 2 − x 1 ( x − x 1)
where (x 1, y 1) and (x 2, y 2) are the two given points and (x, y) is any point on the line.
We have:
(x 1, y 1) = (6,4)
(x 2, y 2) = (-4,5)
Substituting these values into the formula, we get:
y − 4 = 5 − 4 -4 − 6 ( x − 6)
Simplifying and rearranging, we get:
y = -1/10 x + 19/10
This is the equation of the line in slope-intercept form. We can also write it in standard form by multiplying both sides by 10 and moving all terms to one side:
x + 10y -19 = 0
Therefore, by equation the answer will be x + 10y -19 = 0.
Learn more about equation;
https://brainly.com/question/10413253
#SPJ2
what is the sum of 6/12 and 1/2
A.3/12
B.9/12
C.12/12
D.13/12
PLZZZZ HELP I WILL GIVE BRAINLIST
Answer:
1/2
Step-by-step explanation:6/12 is 1/2 of the fraction meaning that 6/12 is = to 1/2.
Answer:
12 / 12
Step-by-step explanation:
LCM of 12 and 2 = 12
1 / 2
= ( 1 / 2 ) x ( 6 / 6 )
= ( 1 x 6 ) / ( 2 x 6 )
= 6 / 12
6 / 12 + 1 / 2
= 6 / 12 + 6 / 12
= ( 6 + 6 ) / 12
= 12 / 12
Suppose you are reviewing your cell phone bill on Friday and you notice you go over your data limit 49% of the time. You
review the weather forecast for tomorrow that says there is a 11% chance of rain. Assuming rain and going over in data are
independent events, what is the probability that it rains and you go over in data tomorrow? Give your answer as an exact
fraction and reduce the fraction as much as possible.
Probability that it rains and you go over in data tomorrow = 0.0539
Percentage of time it takes to go over your data limit = 49%
Probability that you go over your data limit, P(data) = 49/100
P(data) = 0.49
The chance that it rains tomorrow = 11%
Probability that it rains tomorrow, P(rain) = 11/100
Probability that it rains tomorrow, P(rain) = 0.11
Probability that it rains and you go over your data tomorrow = P(rain) x P(data)
Probability that it rains and you go over in data tomorrow = 0.11 x 0.49
Probability that it rains and you go over in data tomorrow = 0.0539
Learn more here: https://brainly.com/question/25537557
Here is another one if anyone can help me out
Answer:
1. 3 × Equation [A2] --> Equation [B2]
2. 4 × Equation [B1] + Equation [B2] --> Equation [C2]
Step-by-step explanation:
1. 3 × Equation [A2] --> Equation [B2]
Technically 1 x equation [A1] --> equation [B2] works, but I doubt you're meant to do that lol
Instead, this works:
4x × 3 = 12x
-7y × 3 = -21y
8 × 3 = 24
2. 4 × Equation [B1] + Equation [B2] --> Equation [C2]
(-3x × 4) + 12x = -12x + 12x = 0x
(2y × 4) + -21y = 8y - 21y = -13y
(7 × 4) + 28 = 28 + 24 = 52
=========================
I'll try to explain my process a little this time.
From A to B, you can see that equation 2 changed. Looking at the first term, 4x changed to 12x. Thats a multiplier of 3, and you can check that on the rest. In this case, that works.
Then from B to C, equation 2 changed again. This time, I noticed that x was canceled out. That means -12x had to have been added to 12x. In equation 1, theres a -3x. 4 times that is -12, and adding -12x to equation 2 works. Check that with the rest, and they all work.
1. The method of substitution is likely the best method for which system?
−8x−2y=18x−2y=5
2x+y=103x+2y=5
5x−2y=32x+2y=1
−3x+2y=93x−5y=4
2. Solve the system of equations using the substitution method.
5x−4y=−15x−3y=−3
(3, 0)
(0, -4)
(-3, 0)
(0, -3)
Answer:
2.) x=−3 and y=0
Step-by-step explanation:
im still tryna figure out answer to number 1. sorry
show that √20 = 2√5
hence , 2√5 = √20
What is the sum of the two expressions? (3/7x+4)+(1/7x-2)
Combine the like terms:
3/7x + 1/7x = 4/7x
4 + -2 = 4-2 = 2
Answer: 4/7x + 2
the given number line shows the solutions to which inequality
A)x + 4 ≥ 5
B)x – 2 > 7
C)x – 3 ≥ 6
D)x – 1 ≥ 8
—————————-
C) x – 3 ≥ 6
Solving this inequality by adding 3 on both sides, we get
x ≥ 9 which is shown on the number line
Jorge wants to find the height of the house, help him find it.
1) The temperature in Chicago is 42°F and the temperature in
Dayton is 19° cooler. What is the temperature in Dayton?
A. 25°F B. 61°F C. 23°F D. 58°F
what is the trend of the graph of the equation y = 3x + 10
Answer:
3x+y-10
Step-by-step explanation:
please Mark my answer in brainlist
Find the value of x in each case.
Answer:
Step-by-step explanation:
To find x
Â= 180⁰-8x (angle on a straight line)
B= 180- 9x (angle on a straight line)
:. G + Â + B = 180⁰ ( sum of angles in a triangle)
5x + 180⁰ - 8x + 180⁰ - 9x = 180⁰
5x -8x - 9x + 180⁰ +180⁰ = 180⁰
-12x + 360⁰ = 180⁰
360⁰ - 180⁰ = 12x
180⁰ = 12x ( divide both sides by 12)
x = 15⁰
answerrrrrrrrrrrr plssssssssssssssssssssssssssssssss
1. Complete the problem by using your calculator. Round your answer to three decimal places.
If f(x)=x^3– 7x^2+ 3 find f(-2) and f(3/4)
a. f(-2) = 3 and f(3/4)= 2.728
b. f(-2)= 3 and f(3/4)= 10
c. f(-2)=-33 and f(3/4)=-0.516
d. f(-2)= 7 and f(3/4)= 21
e. f(-2)= 10 and f(3/4)=-0.968
nhing utility Round
Answer:
c.
Step-by-step explanation:
Plug in -2 for x ....
f(x) = -2^3 - 7(-2)^2 + 3
= -8 - 28 + 3
= -36 + 3
= -33
Plug in 3/4 for x ....
f(x) = 3/4^3 - 7(3/4)^2 + 3
= 27/64 - 63/16 + 3
The put in decimals ....
27/64 = .422
63/16 = 3.938
Put the decimals back into the equation ....
= .422 - 3.938 + 3
= -3.516 + 3
= -.516