Answer:
Step-by-step explanation:
If you plot the vertex and the directrix, you'll see that the directrix is a horizontal line above the vertex. That means that the parabola opens upside down and has the standard equation:
[tex](x-h)^2=-4p(y-k)[/tex] where h and k are the coordinates of the vertex and p is the number of units between the directrix and the vertex. From the vertex we determine that h = 6 and k = 2. And by counting, we determine that p = 2. Filling in the equation then gives us:
[tex](x-6)^2=-4(2)(y-2)[/tex] and simplifying just a tiny bit will get us what we need:
[tex](x-6)^2=-8(y-2)[/tex] which is the second choice down.
The equation of this parabola in standard form is (x - 6)² = -8(y - 2) if the vertex of a parabola is (6,2) option (C) is correct.
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
(x - h)² = 4a(y - k)
(h, k) is the vertex of the parabola:
a = √[(c-h)² + (d-k²]
(c, d) is the focus of the parabola:
It is given that:
The vertex of a parabola is (6,2), and the equation of its directrix is y = 4.
The standard form of the parabola:
y = a(x - h)² + k
y = a(x - 6)² + 2
As the directrix is y = 4
The equation of the parabola becomes:
(x - 6)² = -8(y - 2)
Thus, the equation of this parabola in standard form is (x - 6)² = -8(y - 2) if the vertex of a parabola is (6,2) option (C) is correct.
Learn more about the parabola here:
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#SPJ5
Juliette gagne 1500 € par mois. Elle est augmentée de 2%
a) calculer le montant de son augmentation en euro
b) déterminer le taux d'évolution : t=
c) calculer le coefficient multiplicateur de l'augmentation: C=
d) calculer son nouveau salaire en euro
Pouvez vous m'aider, je ne comprend pas
The table below shows some inputs and outputs of the invertible function fff with domain all real numbers. xxx 555 333 111 1 81818 000 999 f(x)f(x)f, left parenthesis, x, right parenthesis 999 -2−2minus, 2 -5−5minus, 5 -1−1minus, 1 111 111111 Find the following values: f^{-1}(f(58))=f −1 (f(58))=f, start superscript, minus, 1, end superscript, left parenthesis, f, left parenthesis, 58, right parenthesis, right parenthesis, equals f(f(5))=f(f(5))=f, left parenthesis, f, left parenthesis, 5, right parenthesis, right parenthesis, equals
Invertible functions are functions whose inverse can be calculated.
The values of the expressions are: [tex]f^{-1}(f(5)) = 5[/tex] and [tex]f(f(5)) = 11[/tex]
The table entry is given as:
x | 5 | 3 | 1 | 18 | 0 | 9
f(x) | 9 | -2 | -5 | -1 | 1 | 11
(a) Calculate f^-1(f(5))
Start by calculating f(5).
From the table, we have:
[tex]f(5) = 9[/tex]
Take inverse function of both sides
[tex]f^{-1}(f(5)) = f^{-1}(9)[/tex]
From the table, the inverse value of 9 is 5.
i.e. [tex]f^{-1}(9) = 5[/tex]
So, we have:
[tex]f^{-1}(f(5)) = 5[/tex]
(b) Calculate f(f(5))
In (a) above, as have:
[tex]f(5) = 9[/tex]
So, the function becomes
[tex]f(f(5)) = f(9)[/tex]
From the table, the value of f(9) is 11.
So, we have:
[tex]f(f(5)) = 11[/tex]
Read more about invertible functions at:
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Please solve it quickly! thanks!
Answer:
2a - 8
General Formulas and Concepts:
Algebra I
Combining Like TermsStep-by-step explanation:
Step 1: Define
(a - 3) + (a - 5)
Step 2: Simplify
Combine like terms (a): 2a - 3 - 5Combine like terms (Z): 2a - 8The formula f(x + 1) = Two-thirds(f(x)) defines a geometric sequence where f(1) = 18. Which explicit formula can be used to model the same sequence?
f(x) = (18)(two-thirds)(x – 1)
f (x) = 18 (x minus 1) Superscript two-thirds
f (x) = 18 (two-thirds) Superscript x minus 1
f(x) = (18)x – 1
Answer:
Its C, f(x)=18[2/3]x-1
Step-by-step explanation:
yep
Answer:
Correct!!!
C- f (x) = 18 (two-thirds) Superscript x minus 1
:)
find two numbers a and b for which a+2b=100 and the product ab is maximized
1. Which of the following situations could be represented by the equation y 1 point
= -2x + 88?
a. The temperature in Williamsburg is 88° and increases about 2 each hour.
b. Trey has traveled 2 miles and continues to travel at a speed of 88 miles per hour.
c. Priscilla is grading her homework and has an 88 so far. She will lose 2 points for
each additional question she misses.
d. Greg has $88 in a short-term savings account, and he deposits $2 each day.
Answer:
2( x + 4)
Step-by-step explanation:
2
x
+
8
Factor
2
out of
2
x
.
2
(
x
)
+
8
Factor
2
out of
8
.
2
x
+
2
⋅
4
Factor
2
out of
2
x
+
2
⋅
4
.
2
(
x
+
4
)
WILL MARK BRAINLIEST! What are the coordinates of point P?
A. (Negative 4.5, negative 2)
B. (Negative 2, negative 4.5)
C. (2, negative 4.5)
D. (4.5, negative 2)
Points on number line
Answer:
-22 or -2
Step-by-step explanation:
Understanding size
If RS is 10, it does not matter where they are. As long as they are 10 units apart, it works.
However, we already know S lies at -12 so we only have 2 choices for R.
Check the picture I uploaded for better understanding.
This is because RS doesn't mean that R has to be before S. It just means that they are a segment. This means that RS and SR are the same segments.
Suppose that A is inversely proportional to B. If A = 4 when B = 9, find A when B = -72.
Step-by-step explanation:
A 1 / A 2 = B2 / B1
4 / A 2 = - 72 / 9
A 2 = - I / 2
Answer:
-1/2
Step-by-step explanation:
i got the same question and found the answer
Sebastian's friend gives him 4 special-edition baseball cards to start his own collection. Sebastian then buys 6 new baseball cards for his collection every month.
If x is the number of months, what is the linear function, f (x), that represents the total number of baseball cards in Sebastian's collection as a function of the number of months?
A: f(x) = 4x
B: f(x) = 6x
C: f(x) = 4x + 6
D: f(x) = 6x + 4
Answer:
D
Step-by-step explanation:
its 6x + the 4 he gave him
Answer:D
Step-by-step explanation:
took the test
273+147+325 how much is it all together
Answer:
745
Step-by-step explanation:
Answer:
745.
Step-by-step explanation:
Next time you can use a calculator so you don't use up your points if you want.
I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!
a^3=4a^2+21a
need help please
Hello!
[tex]\large\boxed{a = 0, -3, 7}[/tex]
a³ = 4a² + 21a
Move all "a" to one side:
0 = -a³ + 4a² + 21a
Factor out "-a" from the equation:
0 = -a(a² - 4a - 21)
Solve for a by factoring:
0 = -a(a - 7)(a + 3)
Solve for the roots by setting each factor equal to 0:
-a = 0
a = 0
a - 7 = 0
a = 7
a + 3 = 0
a = -3
Solutions: a = 0, -3, 7
I have a past due balance of $87.50 and my new charges are $75.00. I was also charged a late fee of 15% of my past due balance. What is my new total? Your new total is
Answer:
$186.30
Step-by-step explanation:
87 + 75 = 162
162 + 15% = 186.3
Answer: your new total is $162.65
Step-by-step explanation:
it added 87.50 + 75.00 + 15% and got $162.65
Aimee's garbage disposal has 7/8 horse power. Vincent's garbage disposal has 3/5 horse power. How much more power does aimee's garbage disposal have?
Answer:
Aimee's garbage disposal has 11/40 more power than Vincent's garbage disposal.
Step-by-step explanation:
Aimee's garbage disposal horse power = 7/8
Vincent's garbage disposal horse power = 3/5
All we need is to subtract Vincent's power from Aimee's power.
i.e.
[tex]\frac{7}{8}-\frac{3}{5}[/tex]
Thus,
[tex]\frac{7}{8}-\frac{3}{5}\:=\frac{35}{40}-\frac{24}{40}[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{c}-\frac{b}{c}=\frac{a-b}{c}[/tex]
[tex]=\frac{35-24}{40}[/tex]
[tex]=\frac{11}{40}[/tex]
Thus, Aimee's garbage disposal has 11/40 more power than Vincent's garbage disposal.
En una baraja de 52 cartas, donde hay 13 cartas de trébol. 13 cartas de
corazones, 13 cartas de espadas y 13 cartas de rombos. Si sacamos dos
cartas con reemplazo. ¿Cuál es la probabilidad de que sean de
corazones?
The height in feet, h, of a model rocket t seconds after launch is given by the equation h(t) = 3+70t - 16t^2. The average rate of change in h(t) between t = 1 second and t = 3 second is 6. What does the average rate of change tell you about the rocket?
Answer:
The average rate of change
[tex]\frac{dh}{d t} = 70 (1) - 16(2t)[/tex]
At t = 1
[tex]\frac{dh}{d t} = 70 (1) - 16(2t) = 38[/tex]
at t=3
Step-by-step explanation:
Step(I):-
The given function h(t) = 3+70t - 16t²
[tex]\frac{dh}{d t} = 70 (1) - 16(2t)[/tex]
The [tex]\frac{dh}{d t} = 70 (1) - 16(2t) =0[/tex]
70 - 32 t = 0
⇒ 70 = 32 t
⇒ [tex]t = \frac{70}{32} = \frac{35}{16}[/tex]
Step(ii):-
The average rate of change in h(t) between t = 1 second and t = 3 second
[tex]\frac{dh}{d t} = 70 (1) - 16(2t)[/tex]
At t = 1
[tex]\frac{dh}{d t} = 70 (1) - 16(2t) = 38[/tex]
At t = 3
Geometry. Attached photo. PLEASE FOR THE LOVE OF GOD.
Answer:
m<C = 42°
Step-by-step explanation:
Given:
m<A = (2x - 2)°
m<C = (4x - 6)°
m<DBC = (5x + 4)°
Thus:
m<DBC = m<A + m<C (exterior angle theorem of a triangle)
(5x + 4)° = (2x - 2)° + (4x - 6)°
Solve for x
5x + 4 = 2x - 2 + 4x - 6
Collect like terms
5x + 4 = 6x - 8
5x - 6x = -4 - 8
-x = -12
Divide both sides by -1
x = 12
✔️m<C = (4x - 6)°
Plug in the value of x
m<C = 4(12) - 6 = 48 - 6
m<C = 42°
Step-by-step explanation:
[tex]\angle{DBC }[/tex]=(5x+4)°
[tex]\angle{ A }[/tex]=(2x-2)°
[tex]\angle{C }[/tex]=(4x-6)°
we know that,
[tex]\angle{DBC}[/tex]=[tex]\angle{A}[/tex]+[tex]\angle{C}[/tex]
According to the question,
[tex]\tt{ 5x+4=2x-2+4x-6 }[/tex]
[tex]\tt{ 5x+4=6x-8 }[/tex]
[tex]\tt{ 6x-5x=4+8 }[/tex]
[tex]\bold{x=12 }[/tex]
so,
[tex]\angle{C }[/tex]=(4x-6)°=(4×12-6)°=(48-6)°=42°
What is the length of the line segment that joins (3, -2) and (3, 9)
Step-by-step explanation:
[tex] \sqrt{3 - 3} + \sqrt{9 - - 2} [/tex]
[tex] \sqrt{0} + \sqrt{11} [/tex]
[tex] \sqrt{11} [/tex]
Thats the answer of distance
In a fruit punch drink, the 3 ingredients are apple juice, orange juice and cranberry juice. If 2/7 of
the drink is apple juice and 1/2 is orange juice then write the ratio of cranberry juice to apple
juice to orange juice in its simplest form,
Answer:
3 : 4 : 7
Step-by-step explanation:
apple juice - 2/7 = 4/14
orange juice - 1/2 = 7/14
AJ + OJ = 11/14
this means that 3/14 of the punch is cranberry juice.
cranberry : apple : orange
3 : 4 : 7
2. O
Mia buys ink at the office supply store for a business.
She buys 3 printer cartridges, and the sales tax is 7%. Write an expression
to represent the total cost of ink supplies in two different ways.
Answer:
The total cost of the ink supplies can be represented in two different ways, as follows:
a. 3p (1+r)
b. p * (1+ r) * 3
Step-by-step explanation:
a) Data and Calculations:
Number of printer cartridges bought = 3
Sales tax rate = 7%
The total cost can be represented as:
Total cost = 3p (1+r)
where p = the price of a printer cartridge
and r = the sales tax rate
Alternatively, the total cost can be represented as:
Total cost = p * (1+ r) * 3
b) Whichever expression is used, the total cost derived will remain the same. The first expression includes the sales tax in the total cost, while the second expression includes the sales tax in the cost of the unit before arriving at the total cost.
Answer:
3c+3c(0.07)
Step-by-step explanation:
can every one just ask questents and not commet s brainly is for questions!!!!!!!!!!!!!!!!!!
Answer:
Calm down jamal. dont pull out the nine
Step-by-step explanation:
Can anyone please helping me out with question 3 it’s my last question and I can’t get it!!!
Answer:
x=1, y= -1
Step-by-step explanation:
x = 2y +3
3x -y = 4
Use the substitution method because we have x= something in terms of y
3 (2y+3) -y = 4
6y + 9 -y = 4 subtract 9 from both sides
6y -y = 4-9 combine like terms
5y = -5 divide both sides by 5
y = -1
x= 2*(-1) +3 = -2+3 = 1
Since 20% of 950 is
students can use
?
square feet of the courtyard.
190 square feet.
Step-by-step explanation:
In this problem, we assume that the courtyard measures 950 square feet.
So, 20% of 950 is
That is, the 20% of the courtyard is 190 square feet.
Therefore, the complete statement is
Since 20% of 950 is 190 , students can use 190 square feet of the courtyard:
190 square feet.
Step-by-step explanation:
In this problem, we assume that the courtyard measures 950 square feet.
So, 20% of 950 is
20 \%(950)=\frac{20}{100}950=\frac{1}{5}950= 190ft^{2}20%(950)=
100
20
950=
5
1
950=190ft
2
That is, the 20% of the courtyard is 190 square feet.
Therefore, the complete statement is
Since 20% of 950 is 190 , students can use 190 square feet of the courtyard
if f is a signum function then f(100) =
Answer:
787
Step-by-step explanation:
i took the test
To help with her retirement savings, Donna has decided to invest. Assuming an interest rate of 3.59% compounded quarterly, how much would she have to invest to have $117,300 after 18 years?
Answer:
We get the value of Principal amount i.e initial investment = $61640
Step-by-step explanation:
Interest rate r = 3.59% or 0.0359
Compounded quarterly n = 4
Future Amount A = 117,300
Time t = 18 years
We need to find initial investment i,e Principal Amount P
The formula used is: [tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Putting values and finding P
[tex]A=P(1+\frac{r}{n})^{nt}\\117300=P(1+\frac{0.0359}{4})^{4*18} \\117300=P(1+0.008975)^{72}\\117300=P(1.008975)^{72}\\117300=P(1.903)\\P=\frac{117300}{1.903}\\P=61640[/tex]
So, We get the value of Principal amount i.e initial investment = $61640
how to solve 52/48 in the form of hcf
HCF is 4
Step-by-step explanation:
factors of 52 are: 2x2x13
factors of 48 are:2x2x2x2x3
common factors of 52%48 are: 2
hence, = 2x2
=4
hope it helps
name the property
cx1=c
83+(52+17)=(83+52)+17
22+b+18=b+22+18
Answer:
distributive property :)
Brian is skateboarding at 8 kilometers per hour. How long will it take Brian to travel 12 kilometers?
Answer:
An hour and 30 minutes.
Step-by-step explanation:
In one hour, they travel 8 kilometers. They then have 4 kilometers left. 4 is half. of 8, so I would possibly take half the time it would to travel 8, making it 30 minutes for the other 4 kilometers.
Finish the following table for the given function with x as the independent variable. x 10 10 15 10 15 Ax) = V100- x
a. 95, 90, 85
b. 9.75, 9.49, 9.22
C. 9.75, 9.22, 9.49
d. 10, 9,8
Answer:
Option (b) is true.
Step-by-step explanation:
Given the function
[tex]f\left(x\right)=\sqrt{100-x}[/tex]
plug in x = 5 in the function
[tex]f\left(5\right)=\sqrt{100-5}[/tex]
[tex]\:f\left(5\right)=\sqrt{95}\:\:\:\:[/tex]
[tex]f(5) = 9.75[/tex]
plug in x = 10 in the function
[tex]f\left(10\right)=\sqrt{100-10}[/tex]
[tex]\:f\left(10\right)=\sqrt{90}\:\:\:\:\:[/tex]
[tex]\:f\left(10\right)=9.49[/tex]
plug in x = 15 in the function
[tex]f\left(10\right)=\sqrt{100-15}[/tex]
[tex]\:f\left(10\right)=\sqrt{85}\:\:\:\:\:[/tex]
[tex]\:\:f\left(15\right)=9.22[/tex]
Thus, the table will be:
x f(x)
0 10
5 9.75
10 9.49
15 9.22
Therefore, option (b) is true.
Ill give 15 points to whoever answers and I’ll make the branniest