The vertex of a parabola is (-2,6), and its focus is (-5,6).
What is the standard form of the parabola?
Enter your answer by filling in the boxes.
The equation of the parabola is:
(y - 6)² = -12(x +2)
Parabola is the locus of a point such that its distance from a fixed point (called the focus) and a given line (called the directrix) is always the same.
The equation of a parabola is given by:
(y - k)² = 4p(x - h)
Where (h, k) is the vertex, (h + p, k) is the focus
Given the vertex of a parabola is (-2,6), and its focus is (-5,6).
Hence, k = 6, h = -2;
h + p = -5
-2 + p = -5
p = -3
Hence the equation of the parabola is:
(y - 6)² = -12(x +2)
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Susan's checkbook had a balance of $422.05 on April 1. On April 5, she wrote a check for $106.30 to the auto repair shop. On April 7, she
wrote a check in the amount of $310.00 for rent. On April 9, her dad sent her $95.00 to deposit into her account. What is the balance of
Susan's account after this deposit?
Answer: 422.05-106.30-310.00+95.00=100.75
Step-by-step explanation:
your subtracting the 422/106/310 while you adding the $95
The seventh grade class is raising money to have a class trip at the end of the year. They began the year with $2,500. Now they have 54.750 in the account. What is the percent increase for the money the
dass has raised? The dass figured out that if there is a percent increase of 99% from the beginning of the year, they will have enough to pay for every student. How much money wil they need to pay for every student?
The percent increase is
They will need to pay for every student?
Answer:
21.6%
Step-by-step explanation:
PLS HELP!!! I WILL GIVE BRAINLIEST!!!!!!!!!!!
Which transformation of f(x) will produce the same graph as g(x)?
Answer:
A. [tex]h(x)=f(x+1)[/tex]
Step-by-step explanation:
Let's start doing exactly what each function says.
[tex]g(x) = 3x+3[/tex]
At this point, let's see what the various h-s do. Let's call each [tex]h_A... h_D[/tex] to understand which flavor of it we're talking about.
[tex]h_A(x)=f(x+1) = 3(x+1)=3x+3 = g(x)\\h_B(x)=2f(x)=2\cdot3x= 6x \ne g(x)\\h_C(x)=f(x-1)=3(x-1)=3x-3\ne g(x)\\h_D(x)= f(x)+1= 3x+1\ne g(x)[/tex]
A small business has 50 total employees, 15 of which are full-time. What percent of the employees are part-time?
Answer:
70%
Step-by-step explanation:
50-15 =35
35/50 = 70/100
Select the correct answer.
Which statement best describes the solution to this system of equations?
3x + y= 17
x+2y= 49
OA. It has no solution.
OB.
It has infinite solutions.
OC. It has a single solution: x= 15, y= 17.
OD. It has a single solution: x= -3, y = 26.
Reset
Next
Answer:
D. (-3, 26)
Step-by-step explanation:
The ratios of x- and y-coefficients are different in the two equations, so there will be a single solution. (Different ratios mean the slopes are different. Lines with different slopes must intersect in exactly one point.)
We can rearrange the first equation to give an expression for y:
y = 17 -3x
This can be substituted into the second equation to give ...
x +2(17 -3x) = 49
-5x +34 = 49 . . . . . . simplify
-5x = 15 . . . . . . . subtract 34
x = -3 . . . . . . divide by -5
Then the value of y is ...
y = 17 -3(-3) = 26
The single solution is (x, y) = (-3, 26).
5x=4y make x the subject
Answer:
[tex]x = \frac{4y}{5}[/tex]
Step-by-step explanation:
[tex]5x = 4y\\\rule{150}{0.5}\\\frac{5x=4y}{5}\\\\\boxed{x = \frac{4y}{5}}[/tex]
Hope this helps.
c) 2 x x 3 x y
Please help
100 points yes i said 100 no links
Answer:
None
Step-by-step explanation:
A rational number can never be changed into irrational
Answer:
The answer to your question is None
Step-by-step explanation:
A rational number can never be changed into irrational.
In mathematics, the irrational numbers are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers.
I hope this helps and have a wonderful day!
How to do multiplication with decimals.
Answer: just line up the decimals.
Step-by-step explanation:
is there a specific question I can help you with?
PLS HELP ASAP ITS FOR MY ASSIGNMENT DUE RN!!! WHOEVER ANSWERS FIRST GETS BRAINLIEST, 5 STARS, AND A THANKS!!!!
[tex]\\ \sf\longmapsto 9\dfrac{7}{11}-(5+1\dfrac{1}{2})[/tex]
[tex]\\ \sf\longmapsto4 \dfrac{7}{11}-1\dfrac{1}{2}[/tex]
[tex]\\ \sf\longmapsto 4\dfrac{14}{22}-1\dfrac{11}{22}[/tex]
[tex]\\ \sf\longmapsto 3\dfrac{3}{22}[/tex]
m-2/3<-4 OR 3m -8>4
Pls help ⚠️
Answer:
-10 OR 4
Step-by-step explanation:
What is the solution to this system of equations?
x − 2y = 15
2x + 4y = -18
A. x = 1, y = -6
B. x = 1, y = -7
C. x = 3, y = -6
D. x = 3, y = -7
Answer:
C. x = 3, y = -6
Step-by-step explanation:
You can divide the second equation by 2. Then you have ...
x +2y = -9
This gives you a couple of choices for solution. The x-coefficients match, so subtracting one equation from the other eliminates x:
(x +2y) -(x -2y) = (-9) -(15)
4y = -24 ⇒ y = -6
Adding the two equations eliminates y:
(x -2y) +(x +2y) = (15) +(-9)
2x = 6 ⇒ x = 3
The solution is (x, y) = (3, -6).
_____
Additional comment
I find it quick and easy to use a graphing calculator to find the solution. Many graphing calculators also make it simple to solve systems of equations in matrix form. Either way, you can obtain a solution in little more than the time it takes to enter the equations (or their coefficients).
A candle is 14 inches tall. Once the candle is lit, it burns at a rate of 0.8 inches per hour. How many hours will the candle last?
Answer:
about 14 to 15 hours if it burns at that speed while it is burning
Answer:
17.5
Step-by-step explanation:
what are equivalent ratios for 5:4here are the options: 5:4 10:4 15:12 10:8 5:8 4:5
15:12 is the equivalent ratio of 5:4
Determine the domain of each graph:
Answer:
The 1st
Domain is (1,-3)
The second
Domain is (R)
The 3rd
Domain = (R)
The 4th
Domain =(-1,+infinity )
Respectively
Below are two parallel lines with a third line intersecting them.
A class has 30 students. 10 students take the bus. What percentage of students take the bus?
Answer:
33.3%
Step-by-step explanation:
10/ 30= 0.3(3 would be a reoccurring decimal)
0.3*100=33.3
10% of students take the bus
|2x + 6| = 16
plsss helppp
Answer:
x = 5
Step-by-step explanation:
|2x + 6| = 16
=> 2x + 6 = 16
=> 2x = 16 - 6
=> 2x = 10
=> x = 5
Hoped this helped.
expand and simplify
(x +3)(x+5)
Answer:
x² + 8x + 15
Step-by-step explanation:
(x +3)(x+5)
=> x² + 5x + 3x + 15
=> x² + 8x + 15
So, after simplifying, we can conclude that x² + 8x + 15 is our answer. Hoped this helped.
A cylinder has a base radius of 8 meters and a height of 19 meters. What is its
volume in cubic meters, to the nearest tenths place?
Answer:V≈3820.18m3 the best i got
Step-by-step explanation: V=πr2h=π·82·19≈3820.17667m³ i hope this helps
Can somebody solve this question?
Answer:
3 is the answer because it's value only add by the 3
Find the angle measure.
The measure of the angle is ?
Answer:
133°
Step-by-step explanation:
The angle X is the same as the given.
[tex]\mathbb{ANSWER:}[/tex]
⇒ The two parallel lines are cut by a transversal so the interior angles on the same side of a transversal are congruent. This means that the measurement of the second angle is also 133 degrees.
Hence, the measurement of the angle is also 133 degrees.
Which is the best example of anticipating a potential accident in a science lab? A student skips the instructions because she has performed the lab before. A student checks for flammable liquids before lighting the Bunsen burner. A student keeps a glass of water on her lab bench in case she gets thirsty. A student works quickly so that she can be on time for her next class
Answer: C
Step-by-step explanation:
i took the test
Last week it snowed 4.32 inches on Monday and 6.86 inches on Tuesday. It Snowed 7.89 inches this week.
How much more did it snow last week than this week?
01.03 inches
O 2.54 inches
0 3.29 inches
O 3.57 inches
Answer:
3.29
Step-by-step explanation:
4.32+6.86=11.18
11.18-7.89=3.29
ANSWER PART B
Sia designs a board game in which a card is drawn on each turn.
• A blue card means move forward 4 squares.
• A red card means move back 6 squares.
Liam suggests adding some other cards to Sia's game
Part A
Liam explains that drawing a yellow card is equivalent to drawing a blue card followed by a red card. How many spaces forward or backward does a player move after drawing a yellow card? Justify your answer.
ANSWER PART B
How could Liam use red, blue, and yellow cards to describe each of the following motions? Write equations to support your answer. • A green card means move forward 2 spaces. • An orange card means move 8 spaces backward. • A purple card means move forward 10 spaces.
Answer:
Answer:Back 2
Step-by-step explanation:Blue + Red=-2
Step-by-step explanation:
Ingrid is 3 times as old as Ernest. The sum
of their ages is 24. This is represented by the
equation e + 3e = 24, where e is Ernest's age.
How old is Ernest?
-
D. 21
C. 12
A. 3.
B. 6
Answer:
Ernest is six (B)
Step-by-step explanation:
e + 3e = 24
4e=24
[tex]\frac{4e}{4} =\frac{24}{4}[/tex]
e= 6
Substitution Property of Equality
Reflexive Property of Equality
Addition Property of Equality
Division Property of Equality
Symmetric Property of Equality
Transitive Property of Equality
Angle Addition Postulate
Pick 1 for each blank PLS HURRY!!!!
The path of a large arrow fired from a catapult can be modeled by y= -0.0044x^2+1.68x, where x is the distance the arrow traveled (in yards) and y is the height of the arrow (yards).
Give the height of the castle wall, find the safest distance from the wall to launch an arrow over the wall.
1. the height of the wall is 120 yards
2. the height of the wall is 100 feet.
Answer:
Step-by-step explanation:
Wwe can solve this in either of two ways: Differentiation or graphing.
Differentiation
y= -0.0044x^2+1.68x
y' = -0.0088x + 1.68
y' is an equation that tells us the slope of the line for any point x. We want to know when the arrow begins it's descent. That is the point of maximum height, and the slope of the line through that point will be zero. Set y' = 0 and solve for x:
0 = -0.0088x + 1.68
0.0088x = 1.68
x = 191
The maximum height is when the arrow has travelled 191 feet. Now put 191 feet into the equation to find the maximum height:
y= -0.0044x^2+1.68x
y(191) = feet
The maximum height is 160 feet
--
Graphing
See attachment.
Admission to a science museum is $22 for an adult. The cost for a child is $5 less than the cost for an adult. What would be the total cost of admission for 12 adults and 15 children? Explain.
Answer:
The total cost is 519
Step-by-step explanation:
22x12=264 and 22-5=17 so 17x15=255
264+255= 519