Answer:
The equation of a parabola is
[tex]x = \frac{1}{4(f - h)} (y - k) ^{2} + h[/tex]
Step-by-step explanation:
(h,k) is the vertex and (f,k) is the focus.
Thus, f = 1, k = −4.
The distance from the focus to the vertex is equal to the distance from the vertex to the directrix: f - h = h - 2.
Solving the system, we get h = 3/2, k = -4, f = 1.
The standard form is:
[tex]x = - \frac{y ^{2} }{2} - 4y - \frac{13}{2} [/tex]
The general form is:
[tex]2x + {y}^{2} + 8y + 13 = 0[/tex]
The vertex form is:
[tex]x = - \frac{(y + 4) ^{2} }{2} + \frac{3}{2} [/tex]
The axis of symmetry is the line perpendicular to the directrix that passes through the vertex and the focus: y = -4.
The focal length is the distance between the focus and the vertex: 1/2.
The focal parameter is the distance between the focus and the directrix: 1.
The latus rectum is parallel to the directrix and passes through the focus: x = 1.
The length of the latus rectum is four times the distance between the vertex and the focus: 2.
The eccentricity of a parabola is always 1.
The x-intercepts can be found by setting y = 0 in the equation and solving for x.
x-intercept:
[tex]( - \frac{13}{2} \: ,0)[/tex]
The y-intercepts can be found by setting x = 0 in the equation and solving for y.
y-intercepts:
[tex](0, - 4 - \sqrt{3)} [/tex]
[tex](0, - 4 + \sqrt{3)} [/tex]
The length of a rectangle is triple the width. If the area of the rectangle is 75 square inches, then find the length and width
Answer:
W = 5
L = 15
Step-by-step explanation:
Formula for Area of Rectangle is L × W
Since stated triple;
L = 3W
Area = L×W = 3W² = 75
It'll be:
3W² = 75
Divide both sides with 3:
3W² = 75
3 3
W² = 25
Then square root both sides:
w = 5
Again stated that length is triple the width:
L = 5 × 3
L = 15
Therefore;
W = 5
L = 15
20 POINTS
Part E
How many of the 320 million Americans would you predict wear glasses?
The _____ of two sets X and Y is denoted by X-Y
Answer:
Cartesian product
Step-by-step explanation:
The Cartesian product of two sets, X and Y, denoted by X × Y, is the set of all ordered pairs (x, y), where x is an element of X and y is an element of Y: 8 (2.4.1) X × Y = { (x, y) ∣ x ∈ X ∧ y ∈ Y } For example, if Children = { Peter, Mark, Mary }, and Parents = { Paul, Jane, Mark, Mary }, then
I do not understand how they got this answer. I am stuck on the exponent party- Please see attached
Looking at the question, the answer gotten is:$4316.55. The question is related to compound interest.
What is compound interest?Compound interest is known to be the interest that is earned on a principal sum in addition to the accumulated interest previously. It is as a result of reinvesting interest.
To find the compound interest, the formula used is:
A= P(1+r/n)^nt.
Where
P is the principal sum= $3500
r is the rate = 0.035
n is the compounding period = 12 months.
t is the time = 6 years.
Substituting them in the equation, we have:
A = 3500 ( 1 + 0.035/12)^12×6
Working out the one in the bracket and multiplying the exponent, we have:
A = 3500 (1.00291667)^72
Note: We got 72 by multiplying 12 by 6.
1.00291667 raised to the power of 72 = 1.23330133
A = 3500× 1.23330133 = $4,316.55
Ans: $4,316.55
Learn more about compound interest on https://brainly.com/question/24274034
find the product 4 (-9 1/8)
Answer:
4/8=2
-91/2=-45.5
by eliminate 4 by dividing by 8
The longest worm is blank times as long as the shortest worm
If z varies directly with the square of x and inversely with the cube of y, when x = 8, y = 2, and z = 12, what is x when y = 1 and z = 24?
PLEASE HELP!!! :))))
Step-by-step explanation:
it just means
z = k×x²/y³
12 = k×8²/2³ = k×64/8 = k×8
k = 12/8 = 3/2
24 = k×x²/1³ = 3/2 × x²/1 = 3/2 × x²
24/(3/2) = x²
48/3 = x²
16 = x²
x = 4 or
x = -4
Help help help help ASAP apa
Answer:
A=49.12
Step-by-step explanation:
The area of the figure=
Area of the triangle + area of the semicircle.
Area of the triangle=
½×the base × the height=
½×6×8=
24ft.
Area of the semicircle=
½πr²=½×3.14×4²=
25.12ft.
Area of the figure=
24+25.12=
49.12ft
The length is :____ meters and the width is ____meters.
Answer:
Length= 8, Width= 4
Step-by-step explanation:
Say the length is l, and the width is w.
We can set l, the length as 2w, as it is double the length.
The perimeter= 2l + 2w= 24
Input l as 2w, get
4w+2w=24
6w=24, w=4.
Length is w*2, so length is 8.
The selling price for a classic speedboat is $20,000, which is $2000 less than two times its original price. What was the original price of the speedboat?
Answer:
$11,000
Step-by-step explanation:
let x = original price.
2x-2000=20000
2x=22000
x=11000
Please help! Consider the given circle with the shaded sector xy and central angle 225. The circumference is 30 units
[tex]\textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=30\pi \end{cases}\implies 30\pi =2\pi r\implies \cfrac{30\pi }{2\pi }=r\implies \boxed{15=r} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=15\\ \theta =225 \end{cases}\implies \widehat{XY}=\cfrac{(225)\pi (15)}{180}\implies \boxed{\widehat{XY}\approx 58.90} \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2\qquad \qquad A=\pi (15)^2\implies A=225\pi \implies \boxed{A\approx 706.86}[/tex]
FASTEST ANSWER WITH STESP FOR PROOF GETS BRAINLIEST
Answer:
314.16 m (if pi = 3.14) || 314π m (if (you may want to check the math yourself, just in case!)
Step-by-step explanation:
Step 1) Formula of a cone.
•volume = (1/3) * π * r² * h. [Or, if you prefer, volume = π * r² * h/3 ]
Step 2) Apply numbers.
•r = 1/2 * base diameter || r = 5 m
•height(h)= 12 m
Step 3) Apply formula.
V= (1/3) * π * 5² * 12
[Step 4 depends on how you learn, and this also dictates the answer, please read carefully.]
Step 4a) IF DEFINITE EXACT ANSWER (π = π), then V= 314.16
Step 4b) IF π = 3.14, then V= 314π
I was taught in a strange way where two different methods can be applied, so the answer depends on which one you've been taught!
(apologies if a mistake has been made)
Help help help help
What is the area of this shape?
Answer:
Area is 80[tex]m^{2}[/tex]
Step-by-step explanation:
Since the shape is a triangle, then the formula for area is: a = bh/2
Given values:
b = 20m
h = 8m
Substitute the given values into the equation
a = 20 x 8 / 2
a = 160/2
a = 80 meters squared
hope this helps and is right!! p.s. i really need brainliest :)
need help with geometry (number3)
Answer:
Step-by-step explanation:
If this is a parallelogram., this means that the opposite angles are congruent. Thus, the erasure of angle E is equal to the measure of angle G.
So, 10x-21=4x+27, meaning x=8.
Therefore, the measure of angle E is 10(8)-21=59 degrees
325.39 3.26.3 326.15 326.48 from greatest to least
Answer: 1)3.26.3
2)326.15
3)325.39
4)326.48
Step-by-step explanation: you want to start from the lowest number to get your answer
Why would it
be better to measure the length of your classroom with
meterstick instead of a centimeter ruler?
Answer:
Meterstick
Step-by-step explanation: A standard classroom is basically just a large open room, no rooms. So it is more straight than it is curved, and if you can cover a larger area in a shorter time, it is more effecient.
Which pair of segments must be parallel?
HELPP
Answer:
AB and GH
Step-by-step explanation:
Calculation of slope of each segment
AB = -1/4CD = -5/6EF = -5/5 = -1GH = -2/8 = -1/4Parallel lines have the same slope.
⇒ AB and GH are the pair of segments which are parallel
100+200x300=what is the answer
Answer:
100+200×300 = 60100
Step-by-step explanation:
According to the BODMAS, the order to solve any question is as follows
B - Brackets
O - Order
D - Division
M - Multiplication
A - Addition
S - Subtraction.
in the above expression Addition and multiplication two different operations are functioning. According to BODMAS the multiplication expression will be solved first, that outputs.
200×300 = 60000
after calculating correctly we have to operate second function i.e. addition and add 100 to the above result,
60000+100 = 60100
[tex]{Answer = 60100}[/tex]
Thanks for joining brainly community!
Award: 1.00 point Exercise 6-10A (Static) Why is it important to prepare the benefit analysis report or the total compensation report? [You may select more than one answer. Single flick the box with the question mark to produceea check marka forma correct answer and doubye-click the both with the question mark to empty the box for a wrong answer. Any boxes left with a question mark will be automatically graded as incorrect.) The reports may be used to accompany benefits billing. The reports may be used as employee contracts. The reports promote employee education about the total value of their salary and benefits. The reports inform labor planning and employer cost strategies. References Check All That Apply Difficulty: 1 Easy Exercise 6-10A (Static) Learning Objective: 06-06 Complete Benefit Analysis as a Function of Payroll
Answer:
i think its option one
Step-by-step explanation:
The data set below represents the different costs of a refrigerator at a local home improvement store.
$777, $498, $619, $379, $895, $1,256, $1,052
a. What is the median of the first half of the data? (first quartile)
The price of the refrigerators that is the median for the first half of the data is $498.
What is the median of the first half of the data?Median can be described as the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order
The prices arranged in ascending order is: $379, $498, $619, $777, $895, $1052, $1256
The first half of the prices are $379, $498, $619,
Median = $498
To learn more about median, please check: https://brainly.com/question/14746682
choco chip cookies cost $3.20 for the 15oz size . The 18oz size $3.75 Which is the better buy
Answer:
18 oz
Step-by-step explanation:
Choco Chip Cookies (15 oz): [tex]\frac{\$3.20}{15oz}=\frac{\$0.213}{oz}[/tex]
Choco Chip Cookies (18 oz): [tex]\frac{\$3.75}{18oz}=\frac{\$0.208}{oz}[/tex]
So, the 18oz package is the better buy by about [tex]\$0.005[/tex]
Convert the angle to radians: 85
Answer:
17pi/36 (PLATO answer)
Step-by-step explanation:
How can I find the value of X?
Answer:
D
Step-by-step explanation:
Remark
The first thing you must do is notice that <D = <BEA. Mark it that way on your diagram.
The Second thing you need to notice is that <BEA and <A are equal because <A and <D are marked as equal.
So both the large triangle and the small one are isosceles. because 2 of the 3 angles are equal.
Now are you ready for this? That means that BA = 10 because BA is opposite one of the 2 equal angles in the small triangle. So now you are ready to set up a proportion.
Proportion
AB / AC = AE/AD
Givens
AB = 10
AC = 18
AE = 8
AD = x + 8
Solution
Substitute the Givens into the Proportion.
10/18 = 8/(x + 8) Cross multiply
10(x + 8) = 8 * 18 Simplify both sides
10x + 80 = 144 Subtract 80 from both sides
10x + 80 - 80 = 144 - 80
10x = 64 Divide by 10
10x/10 = 64/10
Answer: x = 6.4
Expand to write an equivalent expression…
1/2(-4x + 2y)
Which of the following expressions are equivalent to 6 + (-4) - 56+(−4)−56, plus, left parenthesis, minus, 4, right parenthesis, minus, 5?
Choose 2 answers:
Choose 2 answers:
(Choice A)
A
-(-6+4)-5−(−6+4)−5minus left parenthesis, minus, 6, plus, 4, right parenthesis, minus, 5
(Choice B)
B
6-4-(-5)6−4−(−5)6, minus, 4, minus, left parenthesis, minus, 5, right parenthesis
(Choice C)
C
6-(4+5)6−(4+5)6, minus, left parenthesis, 4, plus, 5, right parenthesis
(Choice D)
D
6+4-56+4−56, plus, 4, minus, 5
(Choice E)
E
-(-6)+(-4)-(-5)−(−6)+(−4)−(−5)
Answer:
Step-by-step explanation:
−5+6−4
and
−4+(−5)+6
A triangular prism and its dimensions are shown in the diagram. What is the lateral surface area of this triangular prism in square feet?
Answer:
112 ft
Step-by-step explanation:
AL = (a+b+c)h
= (6+12+10) x 4
= 112 ft
PLEASE HELP ME WITH THIS !!
Answer: C
Step-by-step explanation:
When Flipped Down A is on the same point as D
Answer:
c
Step-by-step explanation:
because they are mirrored the only one that is equivilent is c
b doesnt corrospond to f it corrosponds to e
bc corrosponds to ef
ab corrosponds to ed.
In your own words describe how to find the perimeter of a shape with fractional sides used the rectangle below to example
Answer:
U add both side of the shape to get the fractional
Step-by-step explanation:
I just did this not to long ago
A bride wants to serve her 175 guests cheesecake instead of wedding cake. She purchases 14 cheesecakes that serve 12 people each. If each guest is served only one piece of cheesecake, how many guests will not get a piece? guests
Answer:
7 guest will not be served.
Step-by-step explanation: