Answer:
(x - 5)² -121 = 0
Step-by-step explanation:
if you need to find the roots you can take the square root of each side:
(x-5)² = 121
(x-5)² = 121
square root of (x-5)² is x-5
square root of 121 is ±11
first root: x-5 = 11
x = 16
second root: x-5 = -11
x = -6
Answer:
[tex]f(x) = (x - 5)^{2} - 121[/tex].
Step-by-step explanation:
The goal is to rewrite [tex]f(x)[/tex] in the vertex form [tex]a\, (x - h)^{2} + k[/tex] by completing the square (where [tex]a[/tex], [tex]h[/tex], and [tex]k[/tex] are constants.)
Expand the vertex form expression:
[tex]\begin{aligned}& a\, (x - h)^{2} + k\\ &= a\, (x - h)\, (x - h) + k \\ &= a\, \left(x^2 - h\, x - h\, x + h^2\right) + k \\ &= a\, \left(x^2 - 2\, h\, x + h^2\right) + k\\ &= a\, x^2 - 2\, a\, h\, x + \left(a\, h^2 + k\right) \end{aligned}[/tex].
Compare this expression to [tex]f(x) = x^2 - 10\, x - 96[/tex] and solve for the constants [tex]a[/tex], [tex]h[/tex], and [tex]k[/tex]. Make sure that the coefficient of each term matches:
Coefficient for the [tex]x^2[/tex] term: [tex]a[/tex] in the expanded expression and [tex]1[/tex] in the expression for [tex]f(x)[/tex]. Hence, [tex]a = 1[/tex].Coefficient for the [tex]x[/tex] term: [tex](-2\, a\, h)[/tex] in the expanded expression and [tex](-10)[/tex] in the expression for [tex]f(x)[/tex]. Hence, [tex]-2\, a\, h = -10[/tex].Coefficient for the constant term: [tex]\left(a\, h^2 + k\right)[/tex] in the expanded expression and [tex](-96)[/tex] in the expression for [tex]f(x)[/tex]. Hence, [tex]a\, h^{2} + k = -96[/tex].Substitute [tex]a = 1[/tex] into the second equation, [tex]-2\, a\, h = -10[/tex], and solve for [tex]h[/tex].
[tex]-2 \, h = -10[/tex].
[tex]h = 5[/tex].
Substitute both [tex]a = 1[/tex] and [tex]h = 5[/tex] into the third equation, [tex]a\, h^{2} + k = -96[/tex], and solve for [tex]k[/tex].
[tex]5^2 + k = -96[/tex].
[tex]k = -121[/tex].
Therefore, [tex]a\, (x - h)^{2} + k[/tex] becomes [tex](x - 5)^2 + (-121)[/tex].
Hence, the vertex form of the parabola [tex]f(x)[/tex] would be:
[tex]f(x) = (x - 5)^{2} - 121[/tex].
-6x+5y=1 and 6x+4y=10.substitution
Answer:
(23/27, 11/9)
Step-by-step explanation:
Given the simultaneous equation;
-6x+5y=1..... 1
6x+4y=10.... 2
Add both equations
5y + 4y = 1+10
9y = 11
y = 11/9
Substitute y = 11/9 into 1;
From 1;
-6x+5y=1.
-6x + 5(11/9) = 1
-6x + 55/9 = 1
-6x = 1- 55/9
-6x = (9-55)/9
-6x = -46/9
x = -46/-54
x = 23/27
The solution to the system of equation is (23/27, 11/9)
Part B: Which of the following statements
accurately describes the shape, center, and
spread of the data?
O A. The range is 9, there is a gap at 94, the
distribution is skewed right, and there is a peak
at 96.
o B. The median is 96, there is a gap at 92, a peak
at 96, and the distribution is symmetrical.
O C. The mode is 96, there are gaps at 92 and 94,
the distribution is skewed left, and 90 and 91
are outliers.
D. The mean is about 95.5, there are no gaps, the
distribution is symmetrical, and 90 is an outlier
Answer:
c
Step-by-step explanation:
because that would be the wrong one
Please give a solution
Answer:
x-3<10 is solution and 6y>12 is not a solution
Step-by-step explanation:
Which graph represents exponential decay?
Answer:
1000x4=4000
Step-by-step explanation:
there is no graph
Answer:
C
Step-by-step explanation:
What is the volume of this composite solid?
6 m
5 m
12 m
9 m
Answer:
864 my brother
Step-by-step explanation:
A shirt boutique purchased 100 new shirts for $1072. The short-sleeved shirts cost $10 each and the long-sleeved shirts cost $12 each. How many short-sleeved shirts were purchased?
Answer:
one equation would be S+ L=36for the number of shirts sold.
Answer: 64 short-sleeved shirts were purchased.
Step-by-step explanation: (x = short-sleeved shirts. y = long-sleeved shirts.)
x + y = 100
10x + 12y = 1072
—12(x + y = 100) >>> -12x - 12y = -1200 10x + 12y = 1072 (add the equations and cancel out the 12y)
-2x/-2 (-2 cancels out) = -128/-2 (divide both by -2)
x = 64 shirts purchased for $10 each. (Hope this helped!)
(vvvThis next part doesn’t answer the question, but I should finish the equation.)
(Plug in 64 for x)>>> 64 + y = 100 (then, subtract 64 from both sides) >>> 64 - 64 = 0 (they cancel out) and 100 - 64 = 36
y = 36 shirts purchased for $12 each.
I really hope this helped! :)
( The answer is a response, Not multiple Choice )
Can anyone help!!!! Please!!!?
Answer:
384
Step-by-step explanation:
A=[tex]6_{2}[/tex]a=6·82=384
What is the slope of the line below? If necessary, enter your answer as a
fraction in lowest terms, using the slash (/) as the fraction bar. Do not enter
your answer as a decimal number or an equation.
(6,6) (1,-4)
Answer:
Hope this helps! let me know
A company sells widgets. The amount of profit, y, made by the
company, is related to the selling price of each widget, x, by the given
equation. Using this equation, find out the maximum amount of profit
the company can make, to the nearest dollar.
y = -4x^2 + 183x – 1247
Answer:
846.06 units
Step-by-step explanation:
The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation as follows :
[tex]y = -4x^2 + 183x- 1247[/tex] ...(1)
We need to find out the maximum amount of profit the company can make.
For maximum profit put dy/dx = 0
So,
[tex]\dfrac{d}{dx}(-4x^2 + 183x- 1247)=0\\\\-8x+183=0\\\\x=\dfrac{183}{8}\\\\x=22.87[/tex]
Put x = 22.87 in equation (1). So,
[tex]y = -4(22.87)^2 + 183(22.87)- 1247\\\\=846.06[/tex]
So, the maximum profit is 846.06 units.
2,200 people enter an amusement park every hour. How long will it take for 6,000 people to enter the park?
P= Total # of people who entered the park
t= The time in hours
P=2200t
6600 = 2200t
Divide both sides of the equation by 2200:
3=t
answer : 3 hours
9515 1404 393
Answer:
2 8/11 hours ≈ 2.73 hours
Step-by-step explanation:
Assuming a constant rate, entries are proportional to time.
time/people = 1 h/(2200 people) = t/(6000 people)
t = (1 h)(6000/2200) = 2 8/11 h ≈ 2.73 h
It will take about 2.73 hours for 6000 people to enter.
PLZ HELP EM ASAP PLSSSZZZ
Answer:
You will need 800 [tex]ft^{3}[/tex] of water to fill the pool.
Step-by-step explanation:
The amount of cubic that we need is equal to the volume of the pool therefore we just have to find the volume of the pool by using the following formula...
Volume = (Length)(Width)(Height/Depth) = (20)(10)(4) = 800
Therefore you will need 800 [tex]ft^{3}[/tex] of water to fill the pool.
Complete the table below to find solutions to the linear equation 4x + y = -40.
Answer:
(1,-44), (2,-48),(3,-52).......
Step-by-step explanation:
4(1)+y=-40
4+y=-40
y=-40-4
y=-44
(1,-44)
.
.
.
(x,y)
(0,−40)
(2,−48)
(−10,0)
Figure ABCD is a rectangle. Find the
value of x.
С
B
2x + 4
E
7X-1
А
D
x = [?]
PLEASE HELP‼️
The value of x for the two lengths of the diagonals is 1.
What is a diagonal?A diagonal in geometry is a line segment that connects two polygonal or polyhedral vertices when they are not on the same edge. Any sloping line is known as a diagonal informally.
Geometry is the area of mathematics that deals with the characteristics of space and the shapes of particular things as well as the interactions between them in space.
Given that the two segment values are 2x + 4 and 7x - 1. The value of x will be calculated as,
2x+4 = 7x-1
5x = 5
x = 1
Hence, the value of x is 1.
To know more about geometry follow
https://brainly.com/question/16967799
#SPJ2
X = {a, c, d, e, f, g,I}
Y = {b, c, d, e, h, i, k, l, m}
Z = {c, f, i, j, m}
Represent the above information on a Venn diagram.
Help
Answer: sorry but i need points
Answer:
Step-by-step explanation:
me too^^
Classify the data of the number of customers at a restaurant
Answer:
we need a picture or screenshot to answer this correctly, but i would think it would be consumer growth per time unit that the graph is based on
Answer:
we would need a question like a picture or some thing else.
The chance of rain is 20%, the chance of it being sunny is 60%, and the chance of it
being sunny and rainy at the same time is 10%. Calculate, the probability that it is
either sunny or rainy.
Answer:
0.6 = 60% probability that it is either sunny or rainy.
Step-by-step explanation:
We solve this question treating these events as Venn probabilities.
I am going to say that:
Event A: Rain
Event B: Sun
The chance of rain is 20%
This means that [tex]P(A) = 0.2[/tex]
The chance of it being sunny is 60%
This means that [tex]P(B) = 0.6[/tex]
The chance of it being sunny and rainy at the same time is 10%.
This means that [tex]P(A \cap B) = 0.1[/tex]
Calculate, the probability that it is either sunny or rainy.
This is:
[tex]P = P(A) + P(B) - 2P(A \cap B) = 0.2 + 0.6 - 0.2 = 0.6[/tex]
0.6 = 60% probability that it is either sunny or rainy.
Enter your answer
24. If you invest $4000 in an account that gains 7% interest each year, how long will it take for there
to be $9000 in the account?
(5 Points)
Answer:So, since it is continuously, we need to think of PERT
A=P\times e^{rt}
So, we just plug our numbers in to solve for T
8000=4000e^{.07t}\\\ln(8000)=\ln(4000e^{.07t})\\\ln(8000) = \ln(4000) + \ln(e^{.07t})\\\ln(8000)=\ln(4000)+.07t\ln(e)\\\ln(8000)=\ln(4000)+.07t\\\frac{\ln(8000)}{\ln(4000)}=.07t\\\frac{\ln(8000)}{.07\ln(4000)}=t\\ 15.479=t
It will take 15.479 years
Step-by-step explanation:
3. The table below lists the colored marbles in a bag. Match the theoretical probabilities for drawing a single marble with the correct marble color. Marble Color Number of Marbles blue 12 red 6 yellow 21 black 8 green 11 1. 19% 2. 14% 3. 36% 4. 21% 5. 10% a.red b.black c.green d.red e.yellow
Answer:
Blue = 12/58 * 100% = 20.68 = 21%
Red = 6/58 * 100 = 10.34 = 10%
Yellow = 21/58 * 100 = 36.20 = 36%
Black = 8/58 * 100 = 13.79 = 14%
Green = 11/58 * 100 = 18.96 = 19%
Step-by-step explanation:
Given the table :
Marble_color ____ Number of marbles
Blue ___________ 12
Red ___________ 6
Yellow _________ 21
Black __________ 8
Green _________ 11
Theoretical probability % = (number of favorable outcome / number of total possible outcomes)
Total possible outcomes = (12+6+21+8+11) = 58
Blue = 12/58 * 100% = 20.68 = 21%
Red = 6/58 * 100 = 10.34 = 10%
Yellow = 21/58 * 100 = 36.20 = 36%
Black = 8/58 * 100 = 13.79 = 14%
Green = 11/58 * 100 = 18.96 = 19%
will you please help me with this question?
Answer:
i can't see it make it more noticeable
HELP PLEASE !! .................................................................................................................................................................
Answer:
15
Step-by-step explanation:
Substitute a and b then
Follow PEMDAS
Hope this helps! :)
The reflection of point s across the y-axis is point_ the reflection of point
Answer:
Point V
Step-by-step explanation:
i think
Find the value of x and y that makes the quadrilateral a parallelogram
Answer:
x=25
y=15
Step-by-step explanation:
hope it helps bye :]
Albert has $150 in his bank account. If he plans to add $25 a week, if represents weeks, how long would it take Albert to save $1340. A 32 weeks
B
40 weeks
C
48 weeks
D
60 weeks
Answer:
C
Step-by-step explanation:
( it think you meant to put 1350 because theres no way to get 1340)
Brandon measured the length of a pencil to be 18cm. The actual length of the pencil is 21cm. What is the percent error for Brandon’s measurement? (Round to the nearest tenth).
Answer:
14.2% error
Step-by-step explanation:
21-18 = 3
3/21 = 14.2
Answer:
14.2%
Step-by-step explanation:
21-18 = 3
3/21 = 14.2
Find (f+g)(x) for the function.
f(x) = x2 + x
g(x) = x + 2
3)
2(34 + 12) > 50
This inequality contains a variable, b. Choose ALL numbers that make this inequality true.
A)
16
B)
18
19
D
20
E)
22
Answer:
a and c
Step-by-step explanation:
alguien que me ayude con esto
Answer:
Triangulo: A= h(subindice b)b/2
Cuadrado: A= L×L o A=L^2
Rectangulo: A= b×a
Rombo: A= D×d/2
Romboide: A= b×h
Trapecio: A= (B×b)h/2
Trapezoide: A= b+B/2(h)
What is the inverse of f(x)=3x+14
Answer:
f^-1(x)=x/3-14/3
Step-by-step explanation:
what if i clapped ya moms cheeks?
Answer:
If you do you nasty
Smh why would you say thaaaaaat
Answer:
where ya mom at homie :smirk:
Step-by-step explanation: