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 set A′ ∩ B′
U={a, b, c, d, e, f, g}
A={b, c, e, g}
Answer:
i dont know
Step-by-step explanation:
i dont know
There are 10 girls in the class. This is three less thank half the number of boys . How many boys are in the class?
Answer:
there are 6 boys
Step-by-step explanation:
the price of broccoli is $1.25 per pound. let y be the total cost in dollars of buying x pounds of broccoli
which equation represents this situation
a, x=y+1.25
b. y= 1.25x
c. y= x+1.25
d. x= 1.25y
Match the dimensions of each rectangle with its corresponding area.
3 feet by 8 feet
90 square feet
5 feet by 7 feet
24 square feet
9 feet by 10 feet
64 square feet
13 feet by 2 feet
26 square feet
8 feet by 8 feet
35 square feet
Answer:
3x8= 24sf
5x7= 35sf
9x10= 90sf
13x2= 26sf
8x8= 64sf
Step-by-step explanation:
Find the missing length of each triangle and round to the nearest tenth.
Answer: 5 inches
Step-by-step explanation: We must use the Pythagorean theorem to solve this. Since the hypotenuse is always opposite of the right angle, we know that the hypotenuse is 13 and we can substitute the values into this formula: a^2 + b^2 = c^2
12^2 + b^2 = 13^2
144 + b^2 = 169
169 - 144 = 25 (this is b^2)
[tex]\sqrt{25}[/tex] = 5
Thus, the value of x is 5 inches.
Would appreciate brainliest <3
Use the clues and each of the numbers on the sign to complete the grid.
Clues
. All four numbers in a row must have a common factor greater than 1.
. Pairs of numbers in a column must have a common factor greater than 1.
Answer:
prayers lang po katapat nyan
(4+6)/(2•1) simplified
Answer:
5
Step-by-step explanation:
trust
Answer:
(4+6)/(2•1)
(4+6=10)/(2×1=2)
10÷2
5
A textbook store sold a combined total of 209 history and math textbooks
in a week. The number of math textbooks sold was 75 less than the
number of history textbooks sold. How many textbooks of each type
were sold?
Answer:
67 math, 142 history
Step-by-step explanation:
lets say the number of math textbooks was x and the number of history textbooks is y. we have x+y=209 and x=y-75. we can plug the second equation into the first to get y-75+y=209. simplfy to get 2y=284 so y=142. since x=y-75, x=67
Consider the function f(x) = 3x4 − 5x2. This function is (even, odd, neither) because [ f(x) = -f(x), f(x) = f(-x), -f(x) = f(-x) ]
Answer:
odd
Step-by-step explanation:
cuz it can't be neither or even
Look at the angle Z that is marked on the shape. Is this angle less than, more than or equal to a right angle?
Answer:
Less then a right angle
Step-by-step explanation:
It’s can’t be equal (looks at other examples of a right angle)
It can’t be more since that would bve more then a right angle and it certainly isnt more
it can only be less
FedEx will ship the Olympic medals from the producer to Japan. Each medal weighs 0.5 kilograms. A box carries 6 medals. If FedEx charges $28 per every 10 kilograms, how much will cost to ship 30 medals ?
A. $280
B. $168
C. $42
Answer:
42
Step-by-step explanation:
weight of medals:
30 (0,5) = 15 kg
cost of 5 kg:
28/2 = 14
cost of shipping:
14+28=42
$112,500 is the price of 75 towels, how much does 1 cost?
Answer:
1500
Step-by-step explanation:
112500/75=answer
answer=1500
Answer: 1 towel cost 1,500
Step-by-step explanation: When you divide $112,500 by 75 you get 1,500.
4
b(x) = 16.22 – 25
bx)
Use the drop-down menus to factor the expression and find the zeros of b(x).
Answer:
1) (4x)² - (5)²
2) (4x + 5) (4x -5)
3) Zeros of b are [tex]\frac{5}{4}[/tex] and [tex]\frac{-5}{4}[/tex] (can also be 1.25 and -1.25)
PLS HELP I NEED THIS DONE TODAY PLSSS WILL GIVE BRAINLY
Answer:
You need 6 lbs of red potatoes
32oz of cream cheese
43oz cream of potatoe soup
Step-by-step explanation:
Multiply all by 4
4. How long would it take sound waves traveling through air that is 68°F to
travel 1,372 meters? Use an equation to solve the problem.
Answer:
2.7 seconds
Step-by-step explanation:
[] Temp of air: 68°F -> 20°C
[] Velocity of sound in air:
[tex]v=331.3\sqrt{1+\frac{T}{273.15} }[/tex]
[tex]v=331.3\sqrt{1+\frac{68}{273.15} }[/tex]
v ≈ 370.25 m/s
[] Last,
t = [tex]\frac{d}{v}[/tex]
t = [tex]\frac{1,372}{370.25}[/tex]
t ≈ 3.7056 ≈ 2.7 seconds
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Estimate the difference of $19 320 and $9 876?
Answer:
$9444 Is the difference
Step-by-step explanation:
$19,320 - $9876 = 9444$
(Hope this helps can I pls have brainlist (crown)☺️)
Use the drawing tools to form the correct answer on the graph. What is the inverse of the function shown? (4,-2)
well, keeping in mind that to draw a line all we need is two points, now, the one drawn already has many points let's pick two off of it, hmmm (-1,4) and (-6,-2).
Now, let's recall that for inverse functions, the domain of the original is the range of the inverse and the range of the original is the domain of the inverse, what does that mean? heheh, well, it simple means that for any point on the original that is say (a , b), the inverse will have a point at the flipped version of it of (b , a). So if the orginal has the points aforementioned above, then the inverse will surely have the points of (4 , -1) and (-2 , -6), and we can just draw a line through those. Check the picture below.
Measure E is equal to?
Answer:
E =114
Step-by-step explanation:
The two base angles are equal to 33 since it is an isoscles triangle. We know that because the two sides are equal. That means D and F are equal to 33. The sum of the angles of a triangle are 180.
D+E+F = 180
33+E +33=180
66+E = 180
E = 180-66
E =114
Question 10 of 10 According to this diagram, what is tan 62°? 62 i 7 28° tra OA. A. 15 B. 0 O C. OD D8 O E 17 F
9514 1404 393
Answer:
B. 15/8
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that the tangent relation is ...
Tan = Opposite/Adjacent
The side opposite the 62° angle is marked 15.
The side adjacent the 62° angle is marked 8.
Then the tangent ratio for 62° is ...
tan(62°) = 15/8
what is the percent of change from 5 to 7
Answer: 40
Step-by-step explanation:
If a ≠ 0 and b ≠ 0 which of the following is equivalent to 2/3a 1/b?
Answer:
58
Step-by-step explanation:
If u=log(x3+y3+z3-3xyz)show that d2u/dx2+d2u/dy2+d2u/dz2=-3/(X+y+z)^2
PLEASEEEE HELP! MY MOM IS GONNA KILL ME
Answer:
16
Step-by-step explanation:
Since the perimeter of the rectangle is 80, we can set up the perimeter formula:
80=2L+2W=2(3x+3)+2(2x+2)=6x+6+4x+4=10x+10
10x=70
x=7
AB=2x+2=2(7)+2=14+2=16
Answer:
AB= 16
Step-by-step explanation:
2x+2+3x+3=40
Add like terms: 2x+3x= 5x and 2+3=5
New equation: 5x+5=40
Solve: 40-5= 35
35 divided by 5= 7Now we know that x is equal to 7.
2(7)+2= 16
Side DC equals 16.
Side AB has the same length as side DC since it's a rectangle.
Side AB equals 16.
Let's check: 16+16=32 (side DC and side AB)
80-32=483(7)+3= 2424 must be the length of the other sides.
24+24= 48So, when you add all the sides together...
16+16+24+24= 80
You get 80, the perimeter!
I hope this helped!
show how to find slope of a line that passes through the points in the table
Answer:
Step-by-step explanation:
here you go m = (y2-y1)/(x2-x1)
= (11-(-9))/(3-(-1))
= 20/4
= 5
Your cousin opened a bank account with a deposit of $256 dollars. After one week, she had $280 in her account. After two weeks, she had $304, and after three weeks she had $328. If this pattern continues, how much money will your cousin have in her account after 18 weeks?
Answer:
dont waste your money... go and play free fire.. open play stire and downlod freefire. and waste your money in freefire by doing topup..
Question 3 What is the equation of the parabola that opens up, has a vertex V(5,0), and a y-intercept of 50?
Answer:
y=2(x-5)^2
Step-by-step explanation:
Vertex form:
y=a(x-p)^2+q
(p,q) = (5,0)
y=a(x-5)^2
y-intercept has coordinates (0,50) so, substitute x=0 and y= 50 in the above equation to find "a"
50=a(0-5)^2
50=25a
a=2
equation
y=2(x-5)^2
Not sure how to do this.
Answer:
5ft into 7ft
Step-by-step explanation:
(2,-6); m= -1/4
(Write an equation in point-slope form of the line that passes through the given point and has the given slope)
Answer:
y + 6 = -1/4(x - 2)
Step-by-step explanation:
Point slope form: [tex]y - y_{1} = m(x - x_{1} )[/tex]
[tex]y - y_{1} = m(x - x_{1} )[/tex] Substitute slope = -1/4 and point (2, -6)
[tex]y - (-6) =\frac{-1}4} (x - 2)\\[/tex]
y + 6 = -1/4(x - 2)
Given m\parallel nm∥n, find the value of x. n m (8x+19)° 59°
what is the measure of x?
Answer:
Hello!
After reviewing the problem you have provided I have come up with the correct solution:
x= 9
Step-by-step explanation:
To come up with this solution you have to first realize that the smaller triangle is a proportionally scaled down version of the entire larger triangle! (I will show what I mean in a linked picture)
So after we have realized that the smaller triangle is a scaled down version of the larger one, we can then create a formula or ratio to calculate the value of the missing side of the larger triangle (being x+6=??).
To create the formula/ratio I divided 10inches by 4inches. Thus the larger triangle is 2.5 times larger than the smaller one.
I then use this ratio to figure out the missing length of the larger triangle by doing:
6inches x 2.5 = 15inches.
I then inputed the 15inches into the formula of the missing side:
x+6=15
Subtracted 6 from both sides to simplify, and came up with the solution!
x=9
Let me know if this helps!