The focus of a parabola is (-6, -3). The directrix of the parabola is y =4.
What is the equation of the parabola?
o y = - a (x + 6)? +
o y = - (x + 6)+
o y = - + (x + 1)² +6
y = -5(x - ) - 6
14
2
1
2
Answers
well, we know the directrix is at y = 4 and the focus point is down below it at (-6 , -3), meaning is a downward opening vertical parabola, like the one you see in the picture below.
keeping in mind that the vertex is equidistant from the directrix and focus point by a distance "P", that puts this vertex at ( -6 , 1/2 ), and since the parabola is opening downwards, P is negative.
[tex]\textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex][tex]\begin{cases} h=-6\\ k=\frac{1}{2}\\[1em] P=-\frac{7}{2} \end{cases}\implies 4\left( -\cfrac{7}{2} \right)\left(y-\cfrac{1}{2} \right)=[x-(-6)]^2 \\\\\\ -14\left(y-\cfrac{1}{2} \right)=(x+6)^2\implies y-\cfrac{1}{2}=-\cfrac{1}{14}(x+6)^2 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=-\cfrac{1}{14}(x+6)^2+\cfrac{1}{2}~\hfill[/tex]
Related Questions
Reggie left a 15% tip for a meal that cost $51. What was the amount of the tip? $3. 40 $6. 60 $7. 65 $8. 15.
Answers
Answer:
7.65
Step-by-step explanation:
15% of 51$ is 7.65 for the meal tip!
Rational Functions
In 1918, women were allowed to join the Marine Corps to handle the clerical duties, while the men fought in World War I. Prior to World War II, the United States Marine Corps Women’s Reserve was formed. Eventually Congress passed the Women’s Armed Services Integration Act. Women could then join the regular component of the Marine Corps, but the number of women could not exceed 2% of the total number of Marines.
By 1965, during the Vietnam War, there were 2700 women in the Marines. Women could participate in a wider variety of duties including radio operator, parachute rigger, quartermaster, auto mechanic, telegraph operator, and aerial gunnery instructor. But it was not until 1967 that a law was passed removing the restriction on the number of women in the Marines. In addition, women could be promoted to the rank of colonel. Within the next ten years, women would be able to work in all aspects of the Marine Corps except the infantry, artillery, armor, and the pilot/air crew.
In 2008, there were 9782 women in the Marine Corps on active duty, or about 5% of the Marines on active duty. Currently, women now receive combat training and are accepted into special skill schools that were traditionally only available to the male Marines. Also, women are working in non-traditional jobs and in certain other areas that were previously restricted. Women in the Marine Corps serve proudly and honorably next to their male counterparts in any area the United States Marine Corps requires. The number of women in the United States Marine Corps can be modeled by:
W = 414x^2 - 3341x + 9403 / 0.04x^2 - 0.32x + 1
where x is the number of years since 2000
Graph the model to find the number of women in the Marine Corps between 2000 and 2009.
Use your graph to estimate the number of female Marines in 2006.
Identify the x-intercepts of this function, if any.
Identify the vertical and horizontal asymptotes of the graph of this function, if any.
Use the function to estimate the number of women in the Marine Corps in 2015.
Give two reasons why the number of women in the Marine Corps could exceed your answer from Exercise 5.
Answers
Answer:
see attached for a graph2006: 8,194no x-interceptshorizontal asymptote: y = 10,350; no vertical asymptotes2015: 10,084no information on Exercise 5Step-by-step explanation:
a)The graph is attached
__
b)The value for 2006 is shown in the table for x=6: 8,194.
__
c)The graph does not cross y=0. It has a minimum of about 7392.
__
d)The denominator is never zero, so there are no vertical asymptotes. The horizontal asymptote is the ratio of the x^2 coefficients, 414/0.04 = 10,350.
__
e)The value of the function for x=15 is 10,084. The number of women in the Marines in 2015 is modeled as 10,084.
__
f)No information is provided regarding Exercise 5 or its answer.
The price of a cup of coffee was $2.20 yesterday. Today, the price rose to $2.55 Find the percentage increase. Round your answer to the nearest tenth of a percent.
Answers
Answer:
%15.9 increase
Step-by-step explanation:
Solve for X round to the nearest tenth if necessary
Answers
Answer:
the answer is 6.9
the answer is.... 6.9
Step-by-step explanation:
to get 6.9 you have to divide 69 by 10
Sine rule
[tex]\tt \dfrac{US}{sin\:T}=\dfrac{ST}{sin\:U}[/tex]
U = 180 - (69+90)=21°
Input the value:
[tex]\tt \dfrac{10}{sin\:90}=\dfrac{X}{sin\:21}\\\\X=35.8^o[/tex]
Finn bought a 2-liter bottle of soda. If he poured 4 cups of soda filled with 350 milliliters each, how many milliliters of soda are left in the bottle?
Answers
Answer: 1000 ml to a liter so that gives 2000 350 ml x 4 = 1400ml
2000 -1400= 600
600 ml left in the soda bottle
Step-by-step explanation:
1. What is the slope of the line that passes through the points (-2, -3), and (5, 4)?
-1
3
1
-3
60 points if you give me the answer with an explanation, please!
Answers
Hi!
I can help you with joy!
We are given 2 points: (-2, 3) and (5, 4), so we can easily calculate the slope of this line using this formula:
[tex]\displaystyle\frac{y2-y1}{x2-x1}[/tex]
[tex]\displaystyle\frac{4-(-3)}{5-(-2)}[/tex]
[tex]\displaystyle\frac{4+3}{5+2}[/tex]
[tex]\displaystyle\frac{7}{7}[/tex]
[tex]1[/tex] (Answer)
I hope it helps!
Ask if you have any queries.
~Misty~
[tex]\bf{GracefulTeen[/tex]
Enjoy your day!
48 is 80% of what amount?
Answers
Answer:
The answer is 60 just divide 80/48.
Help quick I don’t know if it’s C
Answers
Answer:
You got it bro. its 12:30
Step-by-step explanation:
Answer:
yes it's correct.It's 12.30pm
Miguel paid a total of $12,000 for stock that was $8 per share. If he sold all his shares for $15,000, how much profit on each share did he make? a. $2 b. $8 c. $10 d. $12 Please select the best answer from the choices provided A B C D.
Answers
Explanation: He paid $12000 total, at a rate of $8 per share. This means he bought 12000/8 = 1500 shares.
He sells these 1500 shares for $15000; this means he received 15000/1500 = $10 per share.
This means he made 10-8 = $2 profit per share.
Answer: 10
Step-by-step explanation:
Miguel paid a total of $12,000 stock that was $8 per share. That's $1,500 you make. 15,000 that was $8 per share. That's $1,875. I dont know if the answer is right, but I wish you well
Help pls!
The sum of -9 and a number
A) -9-x
B)-9/x
C) 9 + x
D) -9x
Answers
Answer:
C) 9 + x is the answer
Step-by-step explanation:
sum means to add
Hey there!
Guide:
• Sum means add/addition
• Difference means subtract/subtraction
• Product means multiply/multiplication
• Quotient means divide/Division
So, let’s answer your given question.
Key terms in your word problem
“The SUM of -9 and a NUMBER”
Sum is to add and Number is to unknown so we can label it as “x”
Your equation/answer should be:
-9 + x
Because you’re adding -9 to your unknown number (x)
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
May you please help me
I will give you 50 points plus an brainliest
God bless you
Answers
Answer:
140
Step-by-step explanation:
the triangle is 180 degrees
Answer:
Below.
Step-by-step explanation:
Below
The answer is A Rectangle. Or (Wrecked angle) Shortened up.
1-119.
2:135
3:45
4:22
5:60
6:A
7 10
8:143
9:62
Which number is farthest from 2 on the number line?
Answers
Answer:
StartRoot 2.1 EndRoot
Step-by-step explanation:
hope this helps
I need help stuck on the last question
Answers
Answer:
5x + 4 = 14
Step-by-step explanation:
expand the brackets: 2 ((5x + 4)/2) = 5x + 4
and 7(2) = 7 x 2 = 14
⇒ 5x + 4 = 14
Riley has 300 stamps. 20% are from Russia 18% are for Europe 38% are from Australia the rest are from North America. How many of his stamps are from North America
Answers
Answer: 135%
Step-by-step explanation: Given
Europe = 35%
Asia = 10%
Australia* = 20%
North America = ?
To find
Europe + Asia + Australia =
35% + 10% + 20% = 65%
Then the total subtracted from the given
200 - 65 = 135
Therefore,
North America = 135%
Confirm
To make sure that is the correct answer, add it all together.
35 + 10 + 20 + 135 = 200
Which means it is correct.
Trisha had the following seven distances (in feet) in the triple jump.
29, 30, 28, 32, 28, 31, 27
What was the interquartile range of her distances?
1
2
5
3
Answers
Answer:
5 is your answer sweetheart
Step-by-step explanation:
We know that the range to a data set is the difference between the maximum data value and the minimum data value .
The given data set : 29, 30, 28, 32, 28, 31, 27
Maximum value = 32
Minimum value = 27
Then , the range the given data set would be :-
\begin{gathered}\text{Range = Maximum-Minimum}\\\\\Rightarrow\text{Range}=32-27=5\end{gathered}Range = Maximum-Minimum⇒Range=32−27=5
Hence, the range of her distances = 5
Answer:
5
Step-by-step explanation:
f(131) = -131 - 5
f(131) =
Answers
Answer:
f ( 131 ) = - 136
Step-by-step explanation:
1- Factor out the negative sign
2- Calculate
The two triangles are similar.
What is the value of x?
Enter your answer in the box.
X=
Answers
Answer:
x = 5
Step-by-step explanation:
Looking at the ratios of height to base:
Smaller triangle 3x + 1 : 12
Larger triangle 4x : 3 + 12 = 4x : 15
Therefore as triangles are similar:
3x + 1 : 12 = 4x : 15
Write as fractions:
⇒ [tex]\dfrac{3x+1}{12}=\dfrac{4x}{15}[/tex]
Cross multiply and solve for x:
⇒ 15(3x + 1) = 12 · 4x
⇒ 45x + 15 = 48x
⇒ 15 = 3x
⇒ x = 5
Ratio remains same
[tex]\\ \tt\Rrightarrow \dfrac{3+12}{4x}=\dfrac{12}{3x+1}[/tex]
[tex]\\ \tt\Rrightarrow \dfrac{15}{4x}=\dfrac{12}{3x+1}[/tex]
[tex]\\ \tt\Rrightarrow 15(3x+1)=12(4x)[/tex]
[tex]\\ \tt\Rrightarrow 45x+15=48x[/tex]
[tex]\\ \tt\Rrightarrow 3x=15[/tex]
[tex]\\ \tt\Rrightarrow x=5[/tex]
HELP PLEASE! Find the area of the figure.
Answers
Answer: 36 square units.
Step-by-step explanation:
First, you can separate the figure into a 4x6 rectangle and a 6x4 isosceles triangle. You can find the area of the rectangle by using the rectangle area formula, A = l x w .
4 x 6 = 24 units
Then, to find the area of the triangle, you can use the triangle area formula, A = [tex]\frac{1}{2}[/tex] b x h .
1/2 x 4 x 6 = 12 units
Finally, you can simply add 24 + 12 to get the total area of 36 units. Since the area is the measure found, you would use the square symbol (²) at the end of the units:
36 units²
I hope this helps!
Carbon-14 has a half-life of approximately 5,730 years. This exponential decay can be modeled with the function N(t) = N0.
If an organism had 200 atoms of carbon-14 at death, how many atoms will be present after 14,325 years? Round the answer to the nearest hundredth.
Answers
[tex]\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &200\\ t=\textit{elapsed time}\dotfill &14325\\ h=\textit{half-life}\dotfill &5730 \end{cases} \\\\\\ A=200\left( \frac{1}{2} \right)^{\frac{14325}{5730}}\implies A=200\left( \frac{1}{2} \right)^{\frac{5}{2}}\implies A\approx 35.36[/tex]
Ferb wanted to measure the height of a tree. They walk exactly 37 feet from the base of the tree and look
up. The angle of elevation from the ground to the top of the tree is 46º. To the nearest whole number, how
tall is the tree?
Answers
Please help me I’m giving 20 points
Answers
Answer:
The answer is B
Step-by-step explanation:
Find the axis of symmetry
Use the formula -b/2a
2x^2-8x+6
- (-8)/2(2)
8/4
2
The axis of symmetry is at x=2, which means that the vertex is at x=2
Substituting x=2 into the quadratic:
2(2)^2-8(2)+6
2*4-16+6
8-16+6
-2
The vertex is at (2,-2)
The graph where this applies is B.
Therefore, the answer is B.
Ratio of girls to boys is 2:3. How many boys if there are 56 girls?
Answers
Answer:
78 boys
Step-by-step explanation:
If the ratio is 2:3 that means there are 5 equal parts
56/2= 28
3 x 28 = 78
Therefore there are 78 Boys
56:78
[RevyBreeze]
what is the volume of his figure
Answers
Answer:
216 cm3
Step-by-step explanation:
the sum of all of the sides of a stop sign is 96 inches a stop sign is an octagon with all side equal. what is the area of the stop sign?
Answers
Answer:
44498.78 in²
Step-by-step explanation:
A=2(1+2)a2=2·(1+2)·962≈44498.78 in²
12. A triangle has side lengths of 13 inches and 35 inches. What are the possible sidelengths for the third side of the triangle? Is a side length of 4 feet possible? Why or why not?
Answers
Answer:
22 in < third side < 48 inches
48 inches is not a possible side length
Step-by-step explanation:
The triangle inequality allows the third side to range between the difference and the sum of the two given sides:
(35 -13) < s < (35 +13)
22 < s < 48 . . . . . . inches
A side length of 4 feet (48 inches) does not satisfy the triangle inequality.
_____
Additional comment
Some authors allow the "or equal to" case in the triangle inequality. When the sum of the shortest sides is equal to the longest side, the triangle looks like a line segment: it has an area of zero. Other authors prefer a strict inequality, so the triangle has non-zero area. That is the version we have used to answer this question. YMMV
Graph -9x+6y=18−9x+6y=18minus, 9, x, plus, 6, y, equals, 18.
Answers
find the measure of angle A of the following triangle
Answers
Answer:
θ ≈ 48.2°
Step-by-step explanation:
The trig function that relates the angle, adjacent side, and hypotenuse is ...
Cos = Adjacent/Hypotenuse
This tells you ...
cos(θ) = 6/9
The angle is found from the cosine value using the inverse cosine function.
θ = arccos(6/9) ≈ 48.2°
Angle A is about 48.2°.
WILL CHOOSE BRAINLIEST
Without solving, identify whether this equation has a solution that is positive, negative, or zero:
3 x − 5 = - 3
Solve the equation.
x − 5 ( x − 1 ) = x − ( 2 x − 3 )
Answers
x - 5 (x - 1) = x - (2 x - 3) is x= 2/3
JOSHUA ORDERED A NEW PAIR OF NIKES ONLINE FOE $168 AND 2 HATS FOR $39 EACH HIS SHIPPING FEE IS 10% OF HIS TOTAL PURCHASE RICE HOW MUCH WILL JOSHUA PAY ALTOGETHER
Answers
Answer:
Joshua is paying a total of $270.60.
Step-by-step explanation:
Info that we have:
Pair of Nikes is $168.
2 hats for $78. (Not 39 because the question said $39 for each).
Shipping fee is 10% of total purchase.
We need to add up the cost.
168 + 78 = $246
Find how much is 10%.
10% of 246 = 24.6
Add the shipping fee to the total.
246 + 24.60 = 270.60
Answer:
Joshua is paying a total of $270.60.
Info that we have:
Pair of Nikes is $168.
2 hats for $78.
Shipping fee is 10% of total purchase.
need help with simplify root square
Answers
Answer:
Step-by-step explanation:
[tex](\sqrt{24b^{3} } )(\sqrt{40b^{2} } )(\sqrt{b^{2} } )=(2b\sqrt{6b})(2b\sqrt{10} )(b)[/tex]
[tex]=4b^{3} (\sqrt{6b})(\sqrt{10} )[/tex]
Hope this helps