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.
If a ≠ 0 and b ≠ 0 which of the following is equivalent to 2/3a 1/b?
Answer:
58
Step-by-step explanation:
The lines shown below are parallel. If the green line has a slope of 5, what is
the slope of the red line?
A. 5
O B. //
1
C.
091
D. -5
Answer:
its C. 1/5
Mark me BRAINLIEST9/10 - _ = 1/5 mathematics
Answer:
x=7/10
Step-by-step explanation:
1/5=2/10
9/10- =2/10
Substitute the blank with X
9/10- X =2/10
x=7/10
Answer:
7/10
Step-by-step explanation:
9/10 - _ = 1/5
Let's represent the unknown as x
Therefore,
9/10 - x = 1/5
9/10 - 1/5 = x
x = 9/10 - 1/5 = 7/10
100 points! show work or else i report
A certain microwave requires 1200 watts. How much would it cost to run the microwave for a total of 30 minutes (defrosting chicken) at a cost of $0.20 per kilowatt hour?
[tex]\boxed{\sf E=Pt}[/tex]
E is energy
P is power
t is time in hours
E=1200(0.5h)E=600WhE=0.6KwhCost
0.6(0.2)$0.12Answer:
$0.12
Step-by-step explanation:
Conversions
1000 watts = 1 kilowatt-hour
⇒ 1200 watts = 1.2 kilowatt-hour
60 minutes = 1 hour
⇒ 30 minutes = 0.5 hour
A microwave requiring 1200 watts will use 1.2 kilowatts per hour.
If the microwave is used for a total of 30 minutes, it will use:
⇒ 1.2 × 0.5 = 0.6 kWh
If the cost is $0.20 per kWh, the cost of running the 1200 watt microwave for 30 minutes is:
⇒ 0.6 × $0.20 = $0.12
Dr. Brennen donated 49 duffle bags of First-aid kits to the Bahamas Red Cross. Each bag
contained 604 First-aid kits. How many First-aid kits did the Red Cross receive in all?
Answer:
29,596 first aid kits
Step-by-step explanation:
This is a multiplication problem. There are 604 kits in each duffle bag, and there are 49 duffle bags, so the equation is 604 x 49.
In the first step, we multiply 604 by 9 to get 5,436. In the second, we multiply 604 by 40 to get 25,160. Then we add the two numbers together to get 29,596.
Hope this helped :)
can find anything to answer this
Answer:
where?
Step-by-step explanation:
maybe I can help to your question
please give explanation and answers for brainlist
Answer:
y - (-1) = 6/15 (x - 4)
(y + 1) 15 = 6 (x - 4)
15y + 15 = 6x - 24
15y = 6x -24 -15
15y = 6x - 39
Step-by-step explanation:
try hard
Helps plz and no links
Answer:
1+2+3- -9+236359
Step-by-step explanation:
Answer:
y=-4x-7
Step-by-step explanation:
if you use the slope formula, y2-y1 over x2-x1 using any two points from the grid, you get a slope of -4.
if you use the slope intercept form, y=mx+b, and plug in y, m the slope, and x, you get -3=-4(-1)+b
if you solve that, you get -3=4+b
and if you isolate 4 by subtracing 4 from both sides, b=-7.
then you plug slope and y intercept into formula, and get y=-4x+b
4. A) Joe types 200 words in 12 minutes, how many does he type per minute?
Answer:
Step-by-step explanation:
So, we divide 1200 by 25 to find out how many words per minute he types.
1200 / 25 = 48
So, he types 48 words per minute.
Now, we multiply this by 45 to find out how many words he can type in 45 minutes.
48 x 45 = 2,160
Joseph can type 2,160 words in 45 minutes!
i will mark as brainliest PLZ HELPPPPPP
Find the inverse function of f informally.
Answer:
What is f?
Step-by-step explanation:
la quinta parte de 20
Answer:
4
Step-by-step explanation:
20/5 = 4
If f(x)=8-5x, what is f(4p+3)
Answer:
-20p - 7
Step-by-step explanation:
f(x)=8-5x
f(4p+3) = 8 - 5(4p + 3)
= 8 - 20p - 15
= -20p -7
An octopus weighed 3 5/6 kilograms.After two weeks,its weight was increased by 1 4/5 kilgrams.But afterwards,it got sick and lost 2 7/15 kilograms.what is the current weight?
I think it's 3 1/6 kilograms
Step-by-step explanation:
3 5/6 + 1 4/5 since it increased
find the LCD (Least Common Denominator)
that would be 30
3 25/30 + 1 24/30
=4 49/30
= 5 19/30
Then we do subtraction since it lost some weight
5 19/30 - 2 7/15
find LCD again
5 19/30 - 2 14/30
=3 5/30
simplify
3 1/6 kilograms. That's what I think.
Write an equation in slope-intercept form that has a y-intercept at (0, -3) and also contains the point
(4, 5).
Write your answer as an equation with numbers, letters, and symbols - no spaces.
Answer: y = (1/2)x + 3
Step-by-step explanation:
The equation in slope-intercept form y = (1/2)x+3
How do you write an equation in slope-intercept?To determine how to write an equation from two points, we must determine the value of the slope and the yy-intercept. First, we will calculate the slope. This will be the value of mm in the slope-intercept form equation:
y=mx+b
Let’s answer the question, “What is the slope-intercept form of a line going through the points (1,5)(1,5) and (-4,7)(−4,7)?”
Remember, to calculate the slope we use the equation:
y2-y1/x2-x1
Therefore, the slope of the line is
-2/5
We can substitute
-2/5 for m.
To learn more about equation in slope-intercept refer to:
https://brainly.com/question/1884491
Use the Distributive Property to expand 3(6x-4y)-8
Answer:
[tex]18x - 12y -8[/tex]
Step-by-step explanation:
Distribute property means that [tex]a(b+c)=ab+ac[/tex]
Meaning that you will have to multiply 3(6x) and 3(-4y)
3(6x) = 18x and 3(-4y) = -12y and because -8 isn't inside the parenthasis we don't multiply 3 and -8
Solve the problem using a system of equations: The difference of the squares of two numbers is 15. The difference of twice the square of the first number and the square of the second number is 30. Find the numbers.
(__,__),(__,__)
The numbers which hold true for the situation modelled in the task content are; (-√15, 0) and (+√15, 0).
Which numbers hold true for the situation?The system of equations which model the situation is;
x²- y² = 15
2x² - y² = 30.
Hence, by subtracting equation 1 from 2; we have;
x² = 15
x = ±√15.
and hence by substitution; the value of y is;
(√15)² + y = 15
y = 0.
Hence, the required values of the numbers are;
(-√15, 0) and (+√15, 0).
Read more on system of equations;
https://brainly.com/question/14323743
#SPJ1
When the input of the function is -1, What is the output of the function?
Answer:
2
Step-by-step explanation:
The graph clearly shows that when x = -1, y = 2.
Thus, the output of this function is 2.
Use a calculator to solve the following equation for θ on the interval [−π2,π2]. csc(θ)=−5 Select all correct answers.
[tex]csc(\theta )=-5\qquad -\frac{\pi }{2}<\theta <\frac{\pi }{2} \\\\[-0.35em] ~\dotfill\\\\ csc(\theta )=-5\implies \stackrel{\textit{using the reciprocal of } csc(\theta )}{\cfrac{1}{sin(\theta )}=-5}\implies \cfrac{1}{-5}=sin(\theta ) \\\\\\ sin^{-1}\left( -\frac{1}{5} \right) = sin^{-1}[sin(\theta )]\implies sin^{-1}\left( -\frac{1}{5} \right) = \theta \implies \begin{array}{llll} -11.54^o\\ ~\hfill or\\ 348.46^o \end{array} \approx \theta[/tex]
The value of θ is -11.54⁰ or 348.86⁰ for cosec(θ)=−5 for interval [−π/2,π/2].
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given,
cosec(θ)=−5 for interval [−π/2,π/2].
We know Sinθ=1/cosecθ
Cosecθ=1/sinθ
Now cosec(θ)=−5
-5=1/sinθ
sinθ=-1/5
θ=sin⁻¹(1/5)
θ=sin⁻¹(1/5)
θ=-11.54⁰ or 348.86⁰
Hence the value of θ is -11.54⁰ or 348.86⁰ for cosec(θ)=−5 for interval [−π/2,π/2].
To learn more on trigonometry click:
https://brainly.com/question/25122835
#SPJ2
The hypotenuse of a right triangle is three times the length of one of its legs. The length of the other leg is four feet. Find the lengths of the three sides of the triangle. For non-integer answer(s), round your answer(s) to the nearest tenth.
___feet, ___feet, ___feet
then then then
okokokokokokok
Which expression has the same value as − 4 1/5 + 9 3/5?
Answer:
27 / 5
Step-by-step explanation:
− 4 1/5 + 9 3/5 = 5.4 or 5 2/5
27/5 = 5.4 or 5 2/5
Simplify (-2)^4(-2) =
(3st)^2 =
7^0=
Answer:
-32
Step-by-step explanation:
What is the solution set for this inequality?
- 6x + 30 < -18
0x<-2
0x<&
Ox>-2
Ox>8
Answer:
x>8
Step-by-step explanation:
[tex]- 6x+ 30 < - 18 \\ - 6x < - 18 - 30 \\ - 6x < - 48 \\ \frac{ - 6x}{ - 6} < \frac{ - 48}{ - 6} \\ x > 8[/tex]
Help please Its about functions
I only got the first one, but i hope this helped :/
Find the measure of
Answer:
∠ A = 43°
Step-by-step explanation:
Since the triangles are similar then corresponding angles are congruent, so
∠ B = ∠ T = 55°
The sum of the 3 angles in a triangle = 180°
sum the 3 angles in Δ ABC and equate to 180
2x - 9 + 3x + 4 + 55 = 180 , that is
5x + 50 = 180 ( subtract 50 from both sides )
5x = 130 ( divide both sides by 5 )
x = 26
Then
∠ A = 2x - 9 = 2(26) - 9 = 52 - 9 = 43°
Whose statement is correct based on the expected value?
Step-by-step explanation:
only Hadley. and even that is not fully correct.
the expected value here gives us the overall most likely outcome of the scenario when throwing 2 balls.
and not ball by ball. and not directly a probability.
like rolling a die : the expected value of rolling a 6 in 6 attempts is 1 due to the individual roll probability of 1/6.
but the probabilty is NOT 1 or 100% (a guaranteed 6 in 6 attempts).
and that brings me to my concern with Hadley's statement. it says with conviction "the player will make ...". no, only "... will likely make ..." or "... on average".
Answer:
Step-by-step explanation:
neither statement is correct. right answer on khan
A father wants to buy a total of five milk drinks for his son and spend $7.95. Eggnog costs $1.55 and a peanut punch costs $1.65. Determine the number of each milk drink bought
Answer:
2
Step-by-step explanation:
$ 1.55 + $1.65 = $3.11
the budget is $7.95
$7.95 ÷ $3.11 = 2.5 but since you can't get half a milk it's 2
Which of the following expenses would be considered a “need” instead of a “want”?
Answer:
There are no options but what they are trying to say is which is more a need then a want. so a need is something like i broke my foot i "NEED" a docter fast. Want is like I just ate dinner and I "WANT" dessert. You can survive without that dessert.
Step-by-step explanation:
Find the equation of the line with slope −7 which goes through the point (−5,5).
Give your answer in slope-intercept form y=mx+b.
Answer:
[tex]\boxed {\boxed {\sf y= -7x -30}}[/tex]
Step-by-step explanation:
We are asked to find the equation of a line, given a point and a slope.
We can use the point-slope formula:
[tex]y-y_1= m(x-x_1)[/tex]
In this formula, (x₁, y₁) is the point and m is the slope. This line has a slope of -7 and passes through the point (-5,5). Therefore:
x₁ = -5 y₁= 5 m= -7Substitute the values into the formula.
[tex]y-5= -7 (x- -5)[/tex]
[tex]y-5= -7(x+5)[/tex]
We want to give the answer in slope-intercept form, or y=mx+b. We must isolate the variable y.
First, distribute the -7 on the right side of the equation. Multiply each term inside the parentheses by -7.
[tex]y-5= (-7*x) + (-7*5)\\y-5 = (-7x) + (-35) \\y-5= -7x -35[/tex]
5 is being subtracted from y. The inverse operation of subtraction is addition. Add 5 to both sides of the equation.
[tex]y-5+5 =-7x -35 +5 \\y= -7x -35 +5 \\y= -7x +30[/tex]
The equation of the line is y= -7x+30.
Solve for the missing variable
Answer:
x = 7.5.
The two lines on the side of the triangle in the screenshot show us that the two lines made are the same length. So the difference between the first two values, i.e. 22.3 and 14.9 is the same difference between 14.9 and x.
Step-by-step explanation:
hope this helps. . .<3
good luck! uωu
Answer:
Step-by-step explanation:
14.9 is the middle value of x and 22.3. So your formula looks like this.
(x + 22.3) / 2 = 14.9 Multiply both sides by 2
2(x + 22.3) / 2 = 14.9*2 Remove the brackets.
x + 22.3 = 29.8 Subtract 22.3 from both sides
x = 29.8 - 22.3
x = 7.5