Guided Practice
Write the equation of the parabola in vertex form. The vertex is (−3, 3) and the parabola passes through the point (4, 150). Create a rough sketch of the graph to use as a visual aid.
A.
y = 3(x + 3)^2 + 3
B.
y = 4(x − 3)^2 + 3
C.
y = 50(x + 3)^2 + 4
D.
y = 3(x − 3)^2 + 3
Answer:
A.
y = 3(x + 3)^2 + 3
Step-by-step explanation:
The vertex form of the equation is y=a(x-h)2 + k
You know that the vertex (h,k) is (-3,3) and a point on the parabola is (4,150). So what you’re needed ing to find is a bc all of the other letters can be replaced into the equation.
First I would put the equation into vertex form using the vertex given in the problem. : y= (x - (-3))2 + (3). Then I would use the ordered pair (4,150) and replace the x and y with those values
150 = a(4 + 3)2 + 3
Now simplify
150 = a (7)2 + 3
150 = 49a + 3 Important: please be sure to square.
147 = 49a
3= a
Next replace a into the formula now leaving x and y alone.
y = 3 (x+3)2 + 3 [Vertex form]
I hope this helps. Have a great day!
Answer:
A. [tex]y = 3(x + 3)^2 +3[/tex]
Step-by-step explanation:
The vertex form is:
[tex]y = a(x - h)^2 + k[/tex]
Where [tex]a[/tex] is the variable that determinate if the parabola is facing up or facing down and [tex]h[/tex] is the [tex]x[/tex] coordinate of the vertex and [tex]k[/tex] is the [tex]y[/tex] coordinate of the vertex.
So with the given values we have:
[tex]150 = a(4 + 3)^2 + 3[/tex]
Then isolate [tex]a[/tex] for find the missing value.
[tex]147 = a49\\\frac{147}{49} = a\\3 = a[/tex]
Then the final answer is [tex]y = 3(x + 3)^2 +3[/tex]
Someone plsss help with this one
Answer:
B) The amount of service fee, in dollars
Step-by-step explanation:
Look for words relating to "one time," as that indicates the constant
The area of a triangle is 30sq. the perimeter of the triangle is 10in. write an inequality that represents the missing side of the triangle.
Is it supposed to be 30 divided by 10?
HELP
express \sqrt{3} - \frac{2}{\sqrt{3} } [tex]\sqrt{3} - \frac{2}{\sqrt{3} }[/tex]
[tex]\sqrt{3} - \frac{2}{\sqrt{3} } = \frac{3}{\sqrt{3} } - \frac{2}{\sqrt{3} } = \frac{1}{\sqrt{3} } = \frac{\sqrt{3} }{3}[/tex]
ok done. thank to me :>
2.3/2.4 representing slope in proportional relationships
Answer:
Ok
Step-by-step explanation:
Ok
Answer this middle school math equation for 30 points lol
Answer:
n
Step-by-step explanation:
Answer:
[tex]x=14[/tex]
Step-by-step explanation:
Multiply both sides by -5:
[tex]-\frac{1}{5} (x-4)=-2[/tex]:
[tex]-\frac{1}{5} (x-4)*-5=-2*-5[/tex]
[tex]1(x-4)=10[/tex]
[tex]x-4=10[/tex]
Add 4 to both sides:
[tex]x-4+4=10+4[/tex]
[tex]x=14[/tex]
g/(g ^ 2 + 4g) - g/((g + 4) ^ 2) =?
Simplify.
Answer:
[tex] \frac{4}{(g + 4) ^{2} }[/tex]
Step-by-step explanation:
Factor the expressions that are not already factored in g/g² + 4g.[tex] \frac{g}{g(g + 4)} - \frac{g}{(g + 4) ^{2} } [/tex]
Cancel out g in both numerator and denominator.[tex] \frac{1}{g + 4} - \frac{g}{(g + 4) ^{2} } [/tex]
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of g+4 and (g+4)² is (g+4)². Multiply 1/g + 4 times g + 4/g + 4.[tex] \frac{g + 4}{(g + 4) ^{2} } - \frac{g}{(g + 4) ^{2} } [/tex]
Since g + 4/(g + 4)² and g/( g + 4)⁴ have the same denominator, subtract them by subtracting their numerators.[tex] \frac{g + 4 - g}{(g + 4) ^{2} } [/tex]
Combine like terms in g+4−g.[tex] \frac{4}{(g + 4) ^{2} } [/tex]
Expand (g + 4)².[tex] \frac{4}{g^{2} + 8g + 16 } [/tex]
Hope It's Help
A farmer has two tractors. The probability that
tractor 1 will break down is 3% and the
probability that tractor 2 will break down is
5%. What is the probability that both tractors
will break down on a given day? Give your
ansineras
Step-by-step explanation:
the break down probabilities are for the same given day ? one day ?
if that is so, then the expected value for a break down day for tractor 1 will be 34 days (rounded up 100%/3%), and for tractor 2 20 days (100%/5%).
that would be horrible. a tractor would only work for about a month without major repair.
because normally such probabilities are given for a warranty period like 1 or 3 or 5 years.
but the description does not say anything about that. so, we have to go with the primary assumption.
so, the question is about the probability that both things happen at the same time (the same day).
this is like asking for the probability of rolling a double 6 with two dice - both events (a 6 on a die) have to happen "together". so it is the probability of one event multiplied by the probability of the second event : 1/6 × 1/6 = 1/36
5% = 0.05 (5% is 5 hundredths) = 5/100
3% = 0.03 (3% is 3 hundredths) = 3/100
now both events (break-down of both tractors) happen together means 5/100 × 3/100 = 15/10000 = 0.0015
that means the probability in % is 0.15%
that means in other words, this event (both tractors breaking down on the save day) is expected to happen 15 times in 10000 days, or once every 667 days (or roughly every 2 years).
Find the perimeter. Simplify your answer.
Answer:
2p -2
Step-by-step explanation:
To find the perimeter, add up all the lengths of each side of the rectangle.
Perimeter
= 2 +2 +p -3 +p -3
= 2 +2 -3 -3 +p +p
= -2 +2p
= 2p -2
Use the solution for the system to find x - y
3x - 2y = 10
2x + 3y = -2
Answer:
solution is (3,-1/2)
Step-by-step explanation:
pLS pls pls pls help me with this:((((((((((((
pls pls:((((((
Answer:
4 = a
5 = a
hope this answer helps you dear!
Find the solution set of this inequality. Enter
your answer in interval notation using grouping
symbols.
| 2x+3 | <= 3
Answer:
-3 ≤ x ≤ 0
Step-by-step explanation:
2x + 3 ≤ 3
2x ≤ 0
x ≤ 0
-2x - 3 ≤ 3
-2x ≤ 6
x ≥ -3
terrell is going to the salem fair. it costs $5 to get into the fair and $.75 per ride. if he only has $20, how many rides can terrell ride?
An advertisement for a box of crackers says that the new box has 20% more crackers than the original box. If the weight of the original box was 12 ounces, what is the weight of the new box of crackers?
Based on the weight of the old box of crackers, we can infer that the weight of the new box is 14.4 ounces.
The old box weighed 12 ounces and the new box has 20% more than the old box had.
The new box should therefore weigh 20% more than the old box which means that it weighs:
= Weight of old box x ( 1 + increase in new box)
= 12 x (1 + 20%)
= 14.4 ounces
In conclusion, the new box weighs 14.4 ounces.
Find out more at https://brainly.com/question/2051201.
Can someone double-check this to see if it's right?
Answer:
yea it is
Step-by-step explanation:
if 9^x = 1/27, find the value of x
[tex]9^x = \dfrac 1{27}\\\\\implies (3^2)^x = \dfrac{1}{3^3}\\\\\implies 3^{2x} = 3^{-3}\\\\\implies 2x = -3 \\\\ \implies x = -\dfrac 32[/tex]
the shown bellow question answer
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
Are of the given figure is ~
[tex] \boxed{ 50.28 \: \: cm {}^{2} }[/tex]
[tex] \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}[/tex]
The area of the compound shape is equal to ~
Area of rectangle + Area of semi - circle
let's find the Area of rectangle ~
[tex]length \times width[/tex][tex]11 \times 4[/tex][tex]44 \: \: {cm}^{2} [/tex]now, let's find the Area of Semicircle ~
[tex] \dfrac{ \pi{r}^{2} }{2} [/tex][tex] \dfrac{3.14 \times 2 \times 2}{2}[/tex][tex]6.28 \: \: c {m}^{2} [/tex]So, Area of the given figure is equal to ~
[tex]44 + 6.28[/tex][tex]50.28 \: \: cm {}^{2} [/tex]Ethan sold 2/3 gallon of lemonade. Kayla sold some lemonade too. Together, they sold 1 1/4 gallons. how much did Kayla make
Answer:
7/12
Step-by-step explanation:
Are the line y=x+3 and y=x-3 perpendicular
Answer:
no
Step-by-step explanation:
to be perpendicular the second equation would have to be -x (the opposite of x)
these lines are parallel
Answer:
No, not perpendicular
Step-by-step explanation:
Compare the slopes of the two lines. In each case the slope is 1. Therefore the slopes are not negative reciprocals of one another, and the lines are NOT perpendicular.
Decide which of the following numbers does not belong in the group.
108
502
603
360
And why does it not belong?
Answer:
502
Step-by-step explanation
108 has the numbers 0, 1, and 8 which added together totals 9
603 has the numbers 0, 3, and 6 which added together totals 9
360 has the numbers 0, 3, and 6 which added together totals 9
502 has the numbers 0, 2, and 5 which equal 7
502 is the odd one out
For what value of the variable will the expression 8b-27 be equal to the following? -11
100 POINTS
BRAINLIEST IF CORRECT
Answer:
2
Step-by-step explanation:
8b - 27 = -11
8b = 16
b = 2
The variable b will equal 2
Let's check
8b-27=-118b=-11+278b=16b=2-28- 15 + 3
_________
8-(-2)
Answer:
-4
Step-by-step explanation:
First, you want to solve each equation.
-28-15+3
-43+3
-40
8-(-2)
8+2
10
Then divide.
-40÷10=-4
Plzzzz help meeee plzzzz
Answer:
i. 2040 ii.1632
Step-by-step explanation:
I think i did this right..
I do this do y'all can get extra point and complete challenges!
What is 1 + 1
(hey, it's 100 points, you can do it)
Answer:
1 + 1 is 2
Step-by-step explanation:
very hard question
Answer:
Step-by-step explanation:
1+1= 2
Describe a pattern in the sequence then figure out the next 2 terms.
3, 11, 19, 27, ..., ...
Answer:
35, 43
Step-by-step explanation:
The pattern is that to obtain a term in the sequence , add 8 to the previous term, then
27 + 8 = 35
35 + 8 = 43
35 and 43 are the next 2 terms in the sequence
Answer:
35,43
Step-by-step explanation:
add 8 k so ya but ya and so on
Given: Circle A externally tangent to Circle B.
How many possible common tangents to circles A and B can exist?
2
3
4
there are only 2 possible common tangents to circles A and B can exist
ok done. Thank to me :>
Answer:
3
Step-by-step explanation:
After substituting, what is the first operation performed when evaluating 5 + (9 x minus 3) divide 2 for x = 5?
Answer:
After substituting We multiply 5 with 9.
Step-by-step explanation:
Given Expression 5 + ( 9x - 3 ) ÷ 2
5 + ( 9 × 5 - 3 ) ÷ 2
5 + ( 45 - 3 ) ÷ 2
5 + ( 42 ) ÷ 2
5 + 21
26
8.If one sheet of paper is 2/5 cm thick, how thick is a packet containing 180 sheets of paper ?
A aluminum bar 4 feet long weighs 24 pounds. What is the weight of a similar bar that is 3 feet 3 inches long?
A. 29.54 LBS
B. 3 LBS
C. 19.50 LBS
D. 78 LBS
Answer:
C. 19.50 lbs
Step-by-step explanation:
3 feet 3 inches is nearly 4 feet, but is a little shorter. That means the weight of the bar will be nearly 24 pounds, but a little less.
It cannot be 29 or 78 pounds, because those weights are more than 24 pounds. It cannot be 3 pounds, because that weight is significantly less. The only viable answer choice is 19.50 pounds.
__
We assume the weight is proportional to the length. Then the weight (w) of the shorter bar will be ...
w/39 = 24/48 . . . . . weight in pounds/length in inches
w = 39(24/48) = 39/2 = 19.5
The weight of the shorter bar is 19.5 pounds.
7th grade math
3/4 times 1/2
Answer:3/8
Step-by-step explanation: 3/4 x 1/2 = 3/8