Answers
Answer: See the image below for the filled out table.
The other root is x = -2
===========================================================
Explanation:
The turning point is at (1, -45) which is the vertex. This is where the graph goes downhill, and then turns around to go uphill, or vice versa. Depending on the direction, the vertex is the lowest point or the highest point on the parabola.
We have (h,k) = (1,-45) as the vertex, so h = 1 and k = -45
y = a(x-h)^2 + k
y = a(x-1)^2 + (-45)
y = a(x-1)^2 - 45
Now plug in any other point from the table. You cannot pick (1,-45) or else you won't be able to solve for the variable 'a'. Let's go for (0,-40)
We'll plug x = 0 and y = -40 into the equation above to solve for 'a'
y = a(x-1)^2 - 45
-40 = a(0-1)^2 - 45
-40 = a(-1)^2 - 45
-40 = a - 45
a-45 = -40
a = -40+45
a = 5
Therefore, the equation for this parabola is
y = 5(x-1)^2 - 45
As a way to check, we can plug in something like x = -3 to find that...
y = 5(x-1)^2 - 45
y = 5(-3-1)^2 - 45
y = 5(-4)^2 - 45
y = 5(16) - 45
y = 80 - 45
y = 35
Which matches what the table shows in the first column. I'll let you verify the other columns. As you can probably guess at this point, we'll plug in the x values to get the corresponding y values.
So for x = -2, we get...
y = 5(x-1)^2 - 45
y = 5(-2-1)^2 - 45
y = 5(-3)^2 - 45
y = 5(9) - 45
y = 45 - 45
y = 0
The result of 0 here indicates we have a root at x = -2. This is the other x intercept. The x intercept already given to us was x = 4.
The rest of the table is filled out using the same idea. You should get what you see below.
Related Questions
Army needs to order a shade for a triangle-shaped window has a base of 6 feet and a height of 4 feet.what is the area of the shade
Answers
Answer:
The area of the shade is 12 feet
Step-by-step explanation:
To find the area you would do 6 * 4 which equals 24 but with every triangle you have to cut the area in half so the actual answer would be 12 feet
Directions: Find the odds and the probability of the event(s) occuring.
A bag contains three red marbles, four
blue marbles, and four yellow marbles.
You randomly pick a marble. The marble
is red or blue.
P(red or blue) =
Odds =
Answers
Answer:
red
Step-by-step explanation:
Answer:
Blue Oods=3 it because four marbles and yellow have four marbles if yellow are in there blue is picking up because blue are in the inside and out in this question
Explanation:Thanks me later and follow me rate my question..Hope its help...thanks
plz plz answer this 10pts:)
Answers
Answer:
8
Step-by-step explanation:
12-4=8
Answer:
12-4=8
8 more students
hope this helps
have a good day :)
Step-by-step explanation:
Triangle DEF has coordinates D(3, 4), E(4, 1), and F(1, -2). If the triangle is
dilated by a scale factor of 4, what are the coordinates of E?
Answers
Answer:
Hello! answer: coordinates of E' are (16, 4)
Step-by-step explanation:
4 × 4 = 16 4 × 1 = 4 therefore the new coordinates are (16, 4)
The coordinate of E after dilation is (16, 4).
What is a triangle?It is a two dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
Triangle DEF has coordinates:
D = (3, 4)
E (4, 1)
F = (1, -2)
The coordinates are dilated with a scale factor of 4.
This means,
Multiply all the coordinates by 4.
Now,
D = (3 x 4, 4 x 4) = (12, 16)
E (4 x 4, 1 x 4) = (16, 4)
F = (1 x 4, -2 x 4) = (4 , -8)
Thus,
The coordinate of E is (16, 4).
Learn more about triangles here:
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Lucy places five cards that are labeled 1 to 6 face down on the table and mixes them up.
What is the likelihood that her friend Harry will draw an even numbered card?
Answers
as likely as not
Can anyone answer ASAP
Answers
help:
Find LaTeX: (f-g)(x)(f−g)(x) if LaTeX: f(x) = \sqrt{4x}f(x)=4x and LaTeX: g(x) = \sqrt{16x}g(x)=16x.
Answers
Step-by-step explanation:
Simplify the matrix.
f
2
x
2
−
2
f
g
x
2
+
g
2
x
2
,
f
(
x
)
=
2
√
x
f
x
=
4
x
,
g
x
=
4
√
x
g
x
=
16
x
Is algebra.
PLEASE HELP NO LINKS OR FILES.
I don't want links.
I don't want links.
I don't want links.
I don't want links.
Answers
there are 60 inches in 5 feet.how many inches are in 8 ft?
Answers
Answer:
63in
Step-by-step explanation:
Jared places five cards that are labeled 1 to 5 face down on the table and mixes them up.
What is the likelihood that his friend Logan will draw an even-numbered card?
Answers
Answer: 2/5
Step-by-step explanation:
Answer:
2/5
Step-by-step explanation:{1,2,3,4,5}
even numbers among these numbers are {2,4}
likelihood of even numbers =number of even numbers/all numbers
2/5
Which of these symbols stands for less than or equal to?
Answers
Answer:
the far left one
Step-by-step explanation:
Please help me I’m stuck
Answers
Answer:
x = 3.2
Step-by-step explanation:
Apply pythagorean theorem, c² = a² + b²
Where,
c is the hypotenuse/longest side = √(10² - 9²) ≈ 4.4
a = x
b = 3
Substitute
4.4² = x² + 3²
19.36 = x² + 9
x² = 19.36 - 9
x² = 10.36
x = √10.36
x = 3.2 (nearest tenth)
PLS HELP I BEG YOUU!!!
Answers
Answer:
Step-by-step explanation:
the balloon starts at (10, 0 )
it ends at 16,0)
in the middle it's at between 10 and 16 , so say about 13, where it reaches 27
so in the middle it's (13,27)
so ( 11, 9)
(12, 18)
got 13
(14, 18)
(15, 9)
got 16
:P
Kelly drove 385 miles to visit her friend. She drove at an average rate of 55 miles per hour.
How long did it take her to drive to her friend's house?
A: 5 hours
B: 7 hours
C: 9 hours
D: 11 hours
Answers
Answer:
B. 7 hours
Step-by-step explanation:
The formula for time (in this scenario) is t = d/s.
t - time
d - distance
s - speed
For this problem, d - 385 mi and s - 55 mph. To find the time this trip took, you would solve 385/55=7. In the end, Kelly drove for 7 hrs. Hope this helps!!
Solve In(5x + 3) = 2.5
Answers
Answer:
[tex]x=\frac{e^{2.5}-3}{5}[/tex]
Step-by-step explanation:
Let y = 5x + 3
Then we get
㏑(y) = 2.5
Using exponentiation,
[tex]e^{lny} = e^{2.5}\\\textrm{But }e^{lny} \textrm{ is simply y (log rule)}\\\textrm{So we get}\\y = e^{2.5}\\\\\\\textrm{Substituting for y we get}\\\\5x + 3 = e^{2.5}\\x = (e^{2.5} - 3)/5\\[/tex]
This works out to x = 1.83649879
Mindy is the head cheerleader on her suad. She is making banners to place throughout the school for the first football game of the season. She used ⅔ cup of glitter to make 1 cup of glittery paint. Using this same proportion, how many cups of glitter will Mindy use to make 9 cups of glittery paint?
Answers
Answer:
[tex]6\:\text{cups}[/tex]
Step-by-step explanation:
Since the proportion is maintained, we can set up the following proportion:
[tex]\frac{2/3}{1}=\frac{x}{9}[/tex], where [tex]x[/tex] is the amount of glitter, in cups, Mindy will use to make 9 cups of glittery paint.
Cross-multiply to get:
[tex]1x=9\cdot \frac{2}{3},\\x=9\cdot \frac{2}{3}=\boxed{6\:\text{cups}}[/tex]
can you please solve this, the picture is in here
Answers
Answer:
no
Step-by-step explanation:
Which one of these is not congruent to angle 5?
Answers
Answer:
Step-by-step explanation:
The answer is 1 and 3
Solve the proportion.
Answers
Answer:
y = 5
Step-by-step explanation:
cross-multiply:
6y = 30
y = 5
2
Steven has 2 different spinners. He spun each spinner several times and recorded the
results in the tables below.
Spinner 1
Outcome Frequency
Red
8
Orange
4.
Yellow
2
Green
6
Spinner 2
Outcome Frequency
Blue
2
Purple
2
Black
1
White
5
Based on these results, if Steven spins each spinner 60 times, which of the following is
the best prediction of his results?
F Spinner 1 would land on orange 6 more times than Spinner 2 would land on purple.
G Spinner 1 would land on orange 10 more times than Spinner 2 would land on purple.
H Spinner 1 would land on orange twice as many times as Spinner 2 would land on purple.
3 Spinner 1 would land on orange the same number of times that Spinner 2 would land
on purple
Answers
Answer:
ok so the answer would be h
Step-by-step explanation:
so basically the ratio is 4:2 -1:2 so purple is 2 and orange is 4. meaning purple is half of the orange. that ratio stays the same. if you were to multiply puplr by 60 you get 120. and if you multiply 4 by 60 you get 240. which 240 divided by 120 is 2 meaning h is the right answer choice.
The correct observation is Spinner 1 would land on orange the same number of times that Spinner 2 would land on purple.
What is Fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
Total times spined = 60
Spinner 1 land on orange out 60 times
= 4/20 x 60
= 1/5 x 60
= 12
Spinner 2 land on Purple out 60 times
= 2/10 x 60
= 1/5 x 60
= 12
Hence, Spinner 1 would land on orange the same number of times that Spinner 2 would land on purple.
Learn more about Fraction here:
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Help me please and explain for me
Answers
Answer:
1.575 × 10^6 gallons
Step-by-step explanation:
1.25 × 10^6 = 1.25 × 1,000,000 = 1,250,000 gals.
Dolphin tank = 325,000 gals.
total vol. = 1,250,000 + 325,000 = 1,575,000 gals.
scientific notation = 1.575 × 10^6 gallons
The parent teacher association is raising money for a new swing set. They need $682.56 to purchase the swing set and receive a $200.00 donation. The remaining amount will be equally divided among 8 different student groups to raise. How much money will each student group need to raise in order to purchase the swing set?
Answers
Answer:
Each student will raise $60.32
Step-by-step explanation:
682.56-200.000 = 482.56
482.56/8 = $60.32
17, 24, 31, 38, ... common diffrence Arithmetic Sequences
Answers
Ans: 10+7n
Step-by-step explanation: there you go
Answer:
d=7; equation=17+(n-1)7
Step-by-step explanation:
I dont know what your question is but it goes up by 7
How can you tell if these are greatest common factor or difference of squares questions?
Answers
Answer:
When an expression can be viewed as the difference of two perfect squares, i.e. a²-b², then we can factor it as (a+b)(a-b). For example, x²-25 can be factored as (x+5)(x-5). This method is based on the pattern (a+b)(a-b)=a²-b², which can be verified by expanding the parentheses in (a+b)(a-b).
Help me with this one. I’m stuck with it since an hour and a bit more.
Answers
Answer:
1) 5 : 7 : 8.75
2) Happy = 168 . Juma = 210
3) Rima = 17800 . Happy = 24920 . Juma = 31150
Step-by-step explanation:
1) 5 : 7 : 8.75
Ratio Rima to Happy = 5:7
Ratio Happy to Juma = 4:5
7/4 = 1.75
1.75 x 5 = 8.75
Ratio = 5 : 7 : 8.75
2) Happy = 168 . Juma = 210
Ratio = 5 : 7 : 8.5
120 / 5 = 24
Happy = 24 x 7 = 168
Juma = 24 x 8.75 = 210
3)17800 : 24920 : 31150
5 + 7 + 8.75 = 20.75
73870 / 20.75 = 3560
3560 * 5 = 17800 = Rima
3560 * 7 = 24920 = Happy
3560 * 8.75 = 31150 = Juma
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Can someone please help me with this?? i will mark brainliest!
Answers
Answer:
cos angle = 12/17
angle = cosine inverse (0.70588)
angle = 50.110
Determine which sides/angles need to be congruent in order to prove the triangles are congruent by the desired theorem
PLEASE GIVE THE ANSWER
Answers
I don't understand this problem
Answers
Answer:
45%
Step-by-step explanation:
Step-by-step explanation:
It's asking you what the probablitiy of a red car is.
Since this looks like a test/homework, I'll give some hints.
Let's say that SUV's and car's are x.
Out of x, 60 percent is cars.
Let's call the amount of cars we have y.
Out of y amount car's, 15 percent is red.
It's asking that if you randomely chose a car, what the probability would be if you got a non-red car.
Of course, this problem only needs one variable, but for the sake of simplicity, I added 2.
Hope this helps!
An 8-ft ladder leans against the side of a house. How far is the bottom of the ladder from the side of the house when the angle of elevation of the ladder is 75 7 Round your answer to the nearest tenth.
Answers
Answer:
Step-by-step explanation:
Use SOH CAH TOA to recall how the trig functions fit on a triangle
SOH: Sin(Ф)= Opp / Hyp
CAH: Cos(Ф)= Adj / Hyp
TOA: Tan(Ф) = Opp / Adj
the side "?" is the Adjacent side (Adj) and we are given the angle and the Hypontenuse ( long side) (Hyp) of this triangle
so use CAH
cos(75) = Adj / 8
algebra to solve for the Adj side (which is the "?" for this problem )
8*cos(75) = Adj
2.07055 = Adj
so the "?" is 2.1 ft ( rounded to the nearest 10th )
what's the answer ?
[tex] \sqrt{25 \times 9} [/tex]
Answers
Answer:
[tex] \sqrt{25 \times 9} [/tex]
[tex] \sqrt{5² \times 3²} [/tex]
±(5*3)
±15 is a required answer.