Answers
Answer:
Second Choice
Step-by-step explanation:
The vertex form can be expressed as:
[tex] \displaystyle \large{f(x) = a {(x - h)}^{2} + k}[/tex]
We know that the vertex is (h,k) which we are given (-3,-1). Substitute h = -3 and k = -1 in:
[tex] \displaystyle \large{f(x) = a {(x - ( - 3))}^{2} - 1} \\ \displaystyle \large{f(x) = a {(x + 3)}^{2} - 1}[/tex]
Now we know that the parabola passes through (-2,1). Substitute x = -2 and f(x) = 1 then solve for a.
[tex] \displaystyle \large{1= a {( - 2 + 3)}^{2} - 1} \\ \displaystyle \large{1= a {(1)}^{2} - 1} \\ \displaystyle \large{1= a - 1} \\ \displaystyle \large{1 + 1= a } \\ \displaystyle \large{2 = a}[/tex]
Therefore a = 2.
Hence:-
[tex] \displaystyle \large{f(x) = 2{(x + 3)}^{2} - 1}[/tex]
Related Questions
Answer the question below, and then fill in the blanks if necessary.
Can the distributive property be used to rewrite
3 x (8 + 4) ?
Yes
No
If yes, fill in the blanks below.
3 x (8 + 4) - (0 * D + xD
X 5
?
Answers
Answer:
yes
Step-by-step explanation:
3(8+4)
(3×8)+(3×4)
24+12
36
(1 point) Use the graph below to find exact values of the indicated derivatives, or state that they do not exist. If a derivative does not exist, enter dne in the answer blank. The graph of f(x) is black and has a sharp corner at x = 2. The graph of g(x) is blue.
Let h(x) = f(g(x)). Find
A. h'(1) =
B. h'(2) =
C. h'(3) =
Answers
Derivatives can be calculated from graphed functions.
The values of the derivatives are:
The given parameter is:
[tex]\mathbf{h(x) = f(g(x))}[/tex]
Start by calculating the equations of f(x) and g(x)
Graph f(x)
The slopes of f(x) are: 3/2 and -3/2
So, the equations are:
[tex]\mathbf{f(x) = \frac{3}{2}x,\ 0 \le x \le 2}[/tex]
[tex]\mathbf{f(x) = -\frac{3}{2}x,\ x \ge 2}[/tex]
Graph g(x)
The slope of g(x) is: -1/2
So, the equation is:
[tex]\mathbf{g(x) = -\frac 12x}[/tex]
For x = 1 and x = 2, we have:
So, we have:
[tex]\mathbf{h(x) = f(g(x))}[/tex]
Where:
[tex]\mathbf{f(x) = \frac{3}{2}x\ 0 \le x \le 2}[/tex] and [tex]\mathbf{g(x) = -\frac 12x}[/tex]
[tex]\mathbf{h(x) = f(g(x))}[/tex] becomes
[tex]\mathbf{h(x) = \frac{3}{2}(-\frac{1}{2}x)}[/tex]
Open brackets
[tex]\mathbf{h(x) = -\frac{3}{4}x}[/tex]
Differentiate
[tex]\mathbf{h'(x) = -\frac{3}{4}}[/tex]
So:
[tex]\mathbf{h'(1) = -\frac{3}{4}}[/tex]
[tex]\mathbf{h'(2) = -\frac{3}{4}}[/tex]
For x = 3, we have:
[tex]\mathbf{h(x) = f(g(x))}[/tex]
Where:
[tex]\mathbf{f(x) = -\frac{3}{2}x\ x \ge 2}[/tex] and [tex]\mathbf{g(x) = -\frac 12x}[/tex]
[tex]\mathbf{h(x) = f(g(x))}[/tex] becomes
[tex]\mathbf{h(x) = -\frac{3}{2}(-\frac{1}{2}x)}[/tex]
[tex]\mathbf{h(x) = \frac{3}{4}x}[/tex]
Differentiate
[tex]\mathbf{h'(x) = \frac{3}{4}}[/tex]
Substitute 3 for x
[tex]\mathbf{h'(3) = \frac{3}{4}}[/tex]
Hence, the values of the derivatives are:
[tex]\mathbf{h'(1) = -\frac{3}{4}}[/tex], [tex]\mathbf{h'(2) = -\frac{3}{4}}[/tex] and [tex]\mathbf{h'(3) = \frac{3}{4}}[/tex]
Read more about graphed functions at:
https://brainly.com/question/11804653
james likes to make sculptures. First he makes a scale and then he blows it up to normal size. The height of the scale model is 3 inches. The scale he is using is 1inch = 3 feet. How tall is the sculpture?
Answers
Evaluate 2x2y3 when x=2\3 and y=1\2
Answers
Answer:
The answer is 4
Step-by-step explanation:
2(2/3)2(1/2)3
Lisa bought a refrigerator on sale for 50% off the original price, for $235. What was the original price before the sale?
Answers
Answer:
470$Step-by-step explanation:
50% = 1/2
235 * 2 = 470
Write the converse inverse and contrapositive of the statement below
Answers
Answer:
c because if the converse is true then the inverse is also logically through
help me with this math question WILL GIVE BRAINLIEST
Answers
Step-by-step explanation:
all such triangles inscribed into a circle with their baseline being the diameter of the circle, must be right-angled. the 90 degree angle is at C.
the other thing is that the sum of all angles in a triangle is always 180 degrees.
so,
B = 180 - 90 - 20 = 70 degrees
Which represents the solution to the inequality 4x + 7(3x - 3) ≤ 9 - 5x in interval notation
Answers
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form:
x < 1
Interval Notation:
( − ∞, 1)
Need help with number 31
Answers
Answer:
Kelly's wrong, because 97/1000 can be written as 0.097 not 0.97.
Step-by-step explanation:
you would get 0.97 by dividing 97 by 100.
20 points fast plzz!!! Bob fenced in his backyard. The perimeter of the yard is 22 feet, and the length of his yard is 5 feet. Use the perimeter formula to find the width of the rectangular yard in inches: P = 2L + 2W.
6 in.
12 in.
72 in.
144 in.
Answers
Answer:
The width of the rectangular yard is 72 inches
Step-by-step explanation:
Let
L -----> the length of the yard
W ----> the width of the yard
we know that
The perimeter is equal to
we have
substitute in the formula and solve for W
Divide by 2 both sides
Subtract 5 both sides
Convert feet to inches
Remember that
1 ft= 12 in
Step-by-step explanation:
The width of the rectangle is 6 feet or 72 inches if the perimeter of the yard is 22 feet, and the length of his yard is 5 feet.
What is rectangle?It is defined as the two-dimensional geometry in which the angle between the adjacent sides are 90 degree. It is a type of quadrilateral.
Perimeter of the rectangle :
P = 2L + 2W
L = 5 feet
22 = 2(5) + 2W
After calculating:
W = 6 feet
1 feet = 12 inches
6 feet = 72 inches
Thus, the width of the rectangle is 6 feet or 72 inches if the perimeter of the yard is 22 feet, and the length of his yard is 5 feet.
Learn more about the rectangle here:
https://brainly.com/question/15019502
#SPJ2
4. 4^6x4^3
4^9 4^18 12^9 64^9
Answers
Final answer: 4^9
Please mark brainliest, thanks
Can someone help me on this question! It’s really confusing
Answers
is that all of the question?
Please help me 4⅗ ÷ ⅕ =
Answers
Answer:
23
Step-by-step explanation:
just used a calculator
Let’s start by making the mixed number an improper fraction. To do this you multiply the whole number by the denominator and add the numerator.
4 x 5 + 3 = 23
No we have 23/5 divided by 1/5
We have common denominators but you don’t need them for multiplying and dividing fractions. To discuss fractions you just go across, but there’s a thing. You have to flip the second fraction then you can multiply instead of divide.
So
23/5 x 5/1
23 x 5 = 115
5 x 1 = 5
115/5
This can be simplified to 23 because 5 divided by 115 is 23.
Hope this helps
What is the slope of the line?
Answers
Answer:
-3
Step-by-step explanation:
we take two points to find slope m
lets take ( 1, 4) and ( 2, 1)
then m=(1-4)/(2-1)
m=(-3)/(1)
m= -3
How to Reduce -2/-6 to its lowest form?
Answers
Answer:
1/3. To reduce a fraction, divide both the numerator and denominator by the GCF.
ANSWER THE QUESTION. THE IMAGE IS THE QUESTION.
Answers
Answer:
18, because the number of catalogs is 72/5 ÷ 4/5
Step-by-step explanation:
The answer is the last option because in total, the shelf is 72/5 inches wide. Given each catalog is 4/5 inch wide, and we want to find how many catalogs can fit in the shelf, we have to divide 72/5 by 4/5. When we divide 72/5 by 4/5, we get 18.
Answer:
18
Step-by-step explanation:
Because 72/5 by 4 over 5
72/4
= 18
Hope this helps :) Pls mark brainliest if you want
Solve for X
Marking you the brainliest provided you got it right and with step by step explanation
Answers
Answer:
260°Step-by-step explanation:
We need to find the value of angle x:
x = m∠BCG + m∠DCGFind the angles BCG and DCG, considering BA, CG and DE are parallel lines:
m∠DCG = 180° - m∠CDE = 180° - (360° - 312°) = 132°m∠BCG = 180° - m∠ABC = 180° - 52° = 128°Find x:
x = 132° + 128°x = 260°each big square below represents one whole. What percent is represented by the shaded area
Answers
Please answer, I will mark BRAINELIST!
Answers
Answer:
answer is c
Step-by-step explanation:
3x (x-3)=0
than 3x=0 or x-3=0
x=0 or x=3
Answer:
HMMMMMMMMMMMMMMMMMMMMMMMM
Step-by-step explanation:
HMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
Anything would help :))
Answers
Step-by-step explanation:
1.
x = number
x/4 = x/3 - 1
x/3 - x/4 = 1
4x/12 - 3x/12 = 1
x/12 = 1
x = 12
2.
the numerator is the top (it gives the number of the parts of the whole that are combined in the fraction).
the denominator is the bottom (it says in how many and therefore how small parts we split the whole).
x = numerator
y= denominator
fraction is x/y
y = x + 2
(x+3)/(y+3) = 23
x + 3 = 23(y + 3) = 23y + 69
x = 23y + 66
now we use the first equation (y = x + 2) and substitute it into the last equation :
x = 23(x + 2) + 66 = 23x + 46 + 66 = 23x + 112
x = -112/22 = -56/11
y = -68/22 = -34/11
the original fraction is
x/y = -56/11 / -34/11 = -56/11 × -11/34 = 56/34 = 28/17
3.
in 1 hour the large pipe has done 1/3 of the work. and the small pipe 1/6 of the work.
so, in total in 1 hour we get (1/3 + 1/6) done.
what factor do we need to multiply (1/3 + 1/6) to get 1/1 (the whole work) ?
x(1/3 + 1/6) = 1
x(2/6 + 1/6) = 1
x(3/6) = 1
x × 1/2 = 1
x = 2
it takes both pipes together 2 hours to empty the pool.
4.
very similar to 3.
we are just using days instead of hours.
in 1 day Erwin gets 1/2 of the work done and Ana 1/5 of the work. so, together, 1/2 + 1/5 of the total work in one day.
so, how many days to get 1/1 (the whole work) done ?
x(1/2 + 1/5) = 1
x(5/10 + 2/10) = 1
x(7/10) = 1
7x = 10
x = 10/7
it takes them together 10/7 days to mow the whole lawn.
Michael wants to save $46,000.00 for a down payment on a home. How much will he need to invest in an account with 6.1% APR, compounding daily, in order to reach his goal in 7 years? Round the answer to the nearest cent
Answers
Step-by-step explanation:
Simple Interest
Discussing interest starts with the principal, or amount your account starts with. This could be a starting investment, or the starting amount of a loan. Interest, in its most simple form, is calculated as a percent of the principal. For example, if you borrowed $100 from a friend and agree to repay it with 5% interest, then the amount of interest you would pay would just be 5% of 100: $100(0.05) = $5. The total amount you would repay would be $105, the original principal plus the interest.
four rolled-up dollar bills seeming to grow out of dirt, with a miniature rake lying in between them
SIMPLE ONE-TIME INTEREST
I
=
P
0
r
A
=
P
0
+
I
=
P
0
+
P
0
r
=
P
0
(
1
+
r
)
I is the interest
A is the end amount: principal plus interest
P
0
is the principal (starting amount)
r is the interest rate (in decimal form. Example: 5% = 0.05)
EXAMPLES
A friend asks to borrow $300 and agrees to repay it in 30 days with 3% interest. How much interest will you earn?
Show Solution
The following video works through this example in detail.
One-time simple interest is only common for extremely short-term loans. For longer term loans, it is common for interest to be paid on a daily, monthly, quarterly, or annual basis. In that case, interest would be earned regularly.
For example, bonds are essentially a loan made to the bond issuer (a company or government) by you, the bond holder. In return for the loan, the issuer agrees to pay interest, often annually. Bonds have a maturity date, at which time the issuer pays back the original bond value.
EXERCISES
Suppose your city is building a new park, and issues bonds to raise the money to build it. You obtain a $1,000 bond that pays 5% interest annually that matures in 5 years. How much interest will you earn?
Show Solution
Further explanation about solving this example can be seen here.
solve pls brainliest
Answers
In coordinates, the first number is the x and the second one is y. In (4,2), 4 is the x and 2 is the y. The x axis goes from left to right and the y axis goes from up to down.
if x=-y+3 and 3x-2y=-1 what is the value of x and y
Answers
Answer: x=1, y=2
Step-by-step explanation:
3(1) - 2(2)=-1
I NEED A 100% ACCURATE ANSWER FOR THIS QUESTION ASAP NO LINKS !!!
Answers
Answer:
y = 5
Step-by-step explanation:
Group all y terms on the left side of the equation
Subtract 3y from both sides: 3-y-3y=3y+10-3y
Group like terms: -y-3y+30=3y+10-3y
Simplify the arithmetic: -4y+30=3y+10-3y
Group like terms: -4y+30=3y-3y+10
Simplify the arithmetic: -4y+30 = 10
Group all constants on the right side of the equation
Subtract 30 from both sides: -4y+30-30=10-30
Simplify the arithmetic: -4y=10-30
Simplify the arithmetic: -4y=-20
Isolate the y
Divide both sides by-4: -4y/-4 = -20/-4
Cancel out the negatives: 4y/4 = -20/-4
Find the greatest common factor of the numerator and denominator: y = 5·4/1·4
Factor out and cancel the greatest common factor:
y=5
UWUWUWUWIWUWUWUUWWUWUWUUWWUUWUWWUUWUWUWWUUWU2UWUWUWUWUWUWUWUWUWUUWUWUWU
Answers
Answer:
UWUWUWUUWUWUWUWUUWUWUW
Step-by-step explanation:
UwU OwO
solve pls brainliest
Answers
1/4 - 1/8 = 2/8 - 1/8 = 1/8
Answer:
1) 2
2) 1
3) 8
Step-by-step explanation:
brainliest plz
The average person’s speed when riding a bike along a street is 18 kilometers per hour. What conversion factor can be used to convert this speed to meters per hour?
StartFraction 1 kilometer Over 1,000 meters EndFraction
StartFraction 1 meter Over 1,000 kilometers EndFraction
StartFraction 1,000 meters Over 1 kilometer EndFraction
StartFraction 1,000 kilometers Over 1 meter EndFraction
Answers
Answer:
The given average speed = 18 km per hour
Now, as we know from the conversion parameters:
1000 meters = 1 km
or 1 meter = ( 1/ 1000) kilometer
So, we can use the above information to convert average speed into meters per hour.
The given speed = 18 km / hr = 18 x (1000) meters /hr
= 18,000 meters / hr
Step-by-step explanation:
A truck can be rented from Company A for $110 a day plus $0.50 per mile. Company B charges $80 a day plus $0.75 per mile to rent the same truck. Part A: Write an equation to find the number of miles in a day at which the rental costs for Company A and Company B are the same. Part B: Solve the equation.
Answers
m=number of miles
A=$110+$0.50m
B=$80+$0.80m
$110+$0.50m=$80+$0.80m Subtract ($80+$0.50m)
$30=$0.30m Divide each side by $0.30
100=m ANSWER: More than 100 miles must be driven per day to make Company A a better deal.
-2,-6,-18,-54....n equals 11
What is the Geometric series!
Formula:Sn=a1(1-r^n) over(1-r)
PLEASE ANSWER I WILL GIVE U BRANLIEST ANSWER if correct¡!!¡
Answers
9514 1404 393
Answer:
-177146
Step-by-step explanation:
The given formula is useful. The first term is a1 = -2. The common ratio is r = -6/-2 = 3. For n = 11 terms, the sum is ...
S11 = -2(1 -3^11)/(1 -3) = -2(-177146/-2) = -177146
The sum of 11 terms of the series is -177146.
solve each system by substitution.
-x + 4y = 6
y = -2x + 6
Answers
Answer:
(x,y)+(2,2)
Step-by-step explanation: