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Related Questions
Holding the price level constant, we would expect that if the multiplier is 1.5, the cumulative effect of this change in M on AD will be: $ billion
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The quadratic function f(x)=ax^2+4x+c has a maximum at the point (1, 9) . What are the values of a and c?
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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.
In 2011 online sales were $192 billion and in 2014 they were $243 billion
(a) Find a linear function S that models these data, where S is the sales in billions of dollars and is the year Write S(x) in slope-intercept form
(b) Interpret the slope of the graph of S
(c) Determine when online sales were $226 billion
(a) Write S(x) in slope-intercept form S(x)=
(b) Interpret the slope of the graph of S Choose the correct answer below
A .Sales increased on average by $17 billion/yr B .Sales increased by $17 billion in next 3 years C. Sales decreased an average by $17 billion/y D.Sales decreased by $17 billion in next 3 years
(c) Online sales were 5226 billion in the year ___
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A) S(x) = 18x + -36005
B) 18
C) 2013
b) 18
c) 2013
Can someone help me on theses?
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Simplify the linear expression.
−2x+3(−5x+1)
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[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
Let's simply the given expression ~
[tex] - 2x + 3( - 5x + 1)[/tex][tex] - 2x - 15x + 3[/tex][tex] - 17x + 3[/tex]For one English test jason correctly answered 22 questions these correct answers gave him a percent score of 50% In total how many questions were on this English test
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Can someone give more explanation
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You just have to underline the word that connects two sentences .
for example: In number 2. Sophia ate a lot. She is still hungry. These are two sentences the word 'yet' connects two sentences. that is called conjunction.
1.= under line so
2.= under line yet
3.= under line but
4.= under line so
Please need answer now will mark brainliest and no files please What is the slope of this line?
Enter your answer as a whole number or a fraction in simplest form in the box.
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6/6, simplified to 1,
negative slope so -1
2
Select the correct answer.
Which equation represents the vertical line passing through (7,-3)?
Α.x= -3
B. y=-3
C.x= 7
D.y=7
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Answer:
x=7
Step-by-step explanation:
because the x equals 7 and then the line would pass through (7,-3)
What is the area of a square if the Perimeter is 36 inches and each side is X -1
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Answer:
Area= 100 inches square.
Step-by-step explanation:
4(x-1)=36
4x-4=36
4x=40
x=10
10×10=100
I need help I been here all day trying to solve this I'm good I reading not math
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32,760 is the answer!!
Anna can jump 35 times in one minute. This is
70% as many as Alexander can jump in one
minute. How many times can Alexander jump in
a minute?
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Answer:
Alex can jump 50 times in one minute.
Step-by-step explanation:
1.) Start off by creating your equation.
It says that Anna can jump 35 times in one minute. It continues to say, that this value IS 70% as many as Alexander can jump in one minute. Thus, your equation should look like this:
x represents the number of jumps Alexander can do in one minute
35 = 0.70x
2.) Solve for x
35 = 0.70x
35/0.70 = x
50 = x
I hoped this helped. Good luck!
A researcher claims that 89% of people sleep with a pillow. In a random sample of 1000 people, 825 say that they sleep with a pillow
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Find the surface area of the sphere.
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Answer:
R is 4*Pi*R2
Which term from the drop-down menu makes the statement true?
Select Choice triangles are similar.
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A list of choices that appears on a computer screen when a person clicks on the menu title To print the document click on print in the file drop down menu
Find (a) the axis of symmetry and (b) the vertex of the graph of the function.
Ax) = 4x² - 8x
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Step-by-step explanation:
I am not sure, what is the level of math for you currently.
do you do differentiation and derivatives already ?
because that is how I find "extreme points" and "turning points" of a function right away.
the vertex is the turning point for a quadratic parabola.
that means the point where the slope (= the first derivative) of the function is 0.
and that is also where the axis of symmetry is.
8x - 8 = 0
8x = 8
x = 1 (axis of symmetry).
y = 4×1² - 8×1 = 4 - 8 = -4
so, the vertex is (1, -4)
in case you don't understand derivatives yet, there is a shortcut for this for quadratic equations (fyi - in fact, the generic result of the first derivative) :
y = ax² + bx + c
the x value for the axis is then
x = -b/(2a)
in our case
a = 4
b = -8
x = - -8/8 = 8/8 = 1
and then y is calculated as above.
Glve the position of E on this number line. -- 1 Write a fraction for your answer. 昌 口号 Х ?
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Answer:
3/8
Step-by-step explanation:
Shirley is making a map of Main Street, which runs west to east through town. She used the number line shown, where each unit on the number line represents a block of main street and town hall was placed at zero.
After walking Main Street, she noted the following statements in her notebook. The flower boutique is five blocks west of the pet store. The pet store is four blocks east of the bank. The bank is eight blocks west of the hardware store. The hardware store is three blocks east of the bookstore. The bookstore is two blocks east of town hall.
Shirley also made a note to place an empty store in the opposite location of the bank on the number line.
Where should Shirley plot the empty store?
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Answer:
3
Step-by-step explanation:
bookstore is two blocks east of town hall: 0+2=2
the hardware store is three blocks east of the bookstore: 2+3=5
the bank is eight blocks west of the hardware store: 5-8=-3
place an empty store in the opposite location of the bank: opposite of -3 is 3
A banker estimated a customer's worth to be $127,000. The customer was actually worth $120,000.
Find the percent error.
A. 5.5%
B. 5.6%
C. 5.7%
D. 5.8%
Please explain and get 100 points+ Brainlyist
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Answer:
the answer is
5.6 I think
Please someone help
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Answer:
E=10.353
Step-by-step explanation:
First plug in all the numbers: 1.960(31.25/[tex]\sqrt{35}[/tex])
solve: E=10.353
2. Write an equation of the line that passes through (-2,3) and is parallel to the line y=2x-1.
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Hello there! :)
Parallel lines have identical slopes.
So if one line has a slope of 2, then the line parallel o it would have the same slope.
Now, use the Point-Slope form:
y-y1=m(x-x1)
y-3=2(x-(-2)
y-3=2x+4
y=2x+4+3
y=2x+7
Therefore, the equation of the line is: y=2x+7Hope this helps!
~Just a cheerful gal
#CarryOnLearning
[tex]SilentNature :)[/tex]
a number divided by 5 increased by 4
Answers
Answer:
(n/5)+4
Step-by-step explanation:
I think you were asking for the equation?
Answer:
X/5 + 4
Step-by-step explanation:
X is the “number”
Juan is paid a salary of $2400 biweekly. Find Juan's earnings per year. (use only numbers) $
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Therefore to find Juan’s earnings, you multiply 26 by $2400
26 x 2400 = $62,400
Juan’s earnings per year is $62,400
April took out a $600 loan from the
bank. At the end of 5 years, she pays
back the principal, plus $60 simple
interest. What was the interest rate?
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Answer:
2%
Step-by-step explanation:
Answer:
I don’t know
Step-by-step explanation:
What is the solution to the system graphed?
A. (2,-1)
B.(1,-2)
C.(-1,2)
D.(-2,1)
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Answer: C. (-1, 2)
Explanation: The two lines intersect at this point. This point satisfies both equations at the same time.
unicorn a is 4 times older than unicorn b.The sum of their ages is 1.450.
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Answer:
Unicorn a : 1,160, and Unicorn b : 290
Step-by-step explanation:
We can make this an equation
Unicorn a is 4x
Unicorn b is x
4x + x = 1,450
x = 290
Unicorn a : 4•290= 1160 years old
Unicorn b : is 290 years old
16. In April, Harry received his phone bill and found that he was charged $40 for 120
minutes of talking. In May, Harry received his phone bill and found that he was
charged $50 for 140 minutes of talking
Part A: Find the rate that Henry is charged for each minute of use.
a. $2 per minute
b. $1 per minute
C. $5 per minute
d. $0.50 per minute
Part B: Describe an equation in point slope form for calculating the cost (y) based on
minutes of use (x)
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Step-by-step explanation:
A. Take two pairs of points:
(120, 40) and (140, 50)Find the rate of change:
(50 - 40)/(140 - 120) = 10/20 = 0.5This is the rate, $0.50 per minute
B. Take one pair of points (120, 40) to show the relationship between number of minutes and the cost:
y - 40 = 0.5(x - 120)Fluffy the bunny ate 1 4 of a carrot in the morning, and he ate some more at night. By the end of the day, he still had 1 3 of the carrot left to eat. How much of the carrot did Fluffy the bunny eat at night?
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Answer:
She ate 5/12 of carrot hope it's help
Which of the following is the perimeter of a triangle with side lengths of 8 in, 9 in, and 11 in?
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Answer:
show the question
Step-by-step explanation:
Complete the statement:
If AB, CD, then
a. AB - CD
b. AB = CD
C. ABCD
d. AB - CD
-