Answer:
[tex]x^2 = 2y[/tex] --- equation
[tex](x,y) = (0,\frac{1}{2})[/tex] --- focus
[tex]y = -\frac{1}{2}[/tex] --- directrix
[tex]Width = 2[/tex] ---- focal width
Step-by-step explanation:
Given
[tex]depth = 2[/tex]
[tex]diameter = 4[/tex]
Required
The equation of parabola
The depth represents the y-axis. So:
[tex]y = 2[/tex]
The diameter represents how the parabola is evenly distributed across the x-axis.
We have:
[tex]diameter = 4[/tex]
-2 to 2 is 4 units.
So:
[tex]x = [-2,2][/tex]
So, the coordinates of the parabola is:
[tex](-2,2)\ and\ (2,2)[/tex]
The equation of the parabola is calculated using:
[tex]x^2 = 4py[/tex]
Substitute (-2,2) for (x,y)
[tex](-2)^2 = 4p*2[/tex]
[tex]4 = 8p[/tex]
Divide by 8
[tex]p = \frac{4}{8}[/tex]
[tex]p = \frac{1}{2}[/tex]
So, the equation is:
[tex]x^2 = 4py[/tex]
[tex]x^2 = 4 * \frac{1}{2} * y[/tex]
[tex]x^2 = 2y[/tex]
The defining features
(a) Focus
The focus is located at:
[tex](x,y) = (0,p)[/tex]
[tex](x,y) = (0,\frac{1}{2})[/tex]
(b) Directrix (y)
[tex]y = -p[/tex]
[tex]y = -\frac{1}{2}[/tex]
(c) Focal width
[tex]Width = 4p[/tex]
[tex]Width = 4*\frac{1}{2}[/tex]
[tex]Width = 2[/tex]
which statements describe the procedure Dave used in this step and identifies the property that justifies the procedure?
9514 1404 393
Answer:
A
Step-by-step explanation:
The second equation differs from the first in that -9 is a term added to both sides of the equation. The addition property of equality tells you that doing this will not change the value of the variable.
_____
The reason (not justification) for doing this is that the sum of 9 and its additive inverse is 0, the additive identity element. This means the equation can be simplified to 3x = 12, which is the point of making that step (subtracting 9).
If my box plot is ranged from 60-64 in height and inches what is the data value is the upper quartile ( q3)
Answer:
[tex]Q_3 = 64[/tex]
Step-by-step explanation:
Given
Box of a box plot with the range: 60 - 64
Required
The upper quartile
To do this, we simply identify the endpoint of the range
Given that the range of the box is 60 to 64.
We have:
[tex]Start = 60[/tex]
[tex]End = 64[/tex]
Hence:
[tex]Q_3 = 64[/tex]
How did Progressives address the problems caused by industrialization?
You and your friend are selling magazine subscriptions for a fundraiser. After w weeks, you have sold (2w+9) subscriptions and your friend has sold (6w+3) subscriptions.
Answer:
3/2 weeks
Step-by-step explanation:
The question: find the number of weeks you and your friend sells equal number of magazine
You = 2w + 9
Your friend = 6w + 3
Equate both equations
2w + 9 = 6w + 3
Collect like terms
2w - 6w = 3 - 9
- 4w = - 6
w = -6/-4
w = 3/2 weeks
The question is in the screenshot
Answer:
D
Step-by-step explanation:
Here, we want to select the correct choice of answer
Looking at the two dot plots, we can see that for the class A, we have the clustering from 4-6 and from 10-12
With this, we can see that this clustering is essentially around two areas only
The beginning parts and the mid parts are left empty only for the two parts to be populated by data points
Write the system and
Brian sold fruit at his stand. Apples cost $0.40 and pears cost $0.50 each. In an afternoon he
sold 52 pieces of fruit and made $24. How many of each did he sell?
Answer:
20 apples, 32 pears
Step-by-step explanation:
Using a for number of apples and p for number of pears, you get a+p=52 (amount) and 0.4a+0.5p=24 (cost).
One way of solving simultaneous equations is using like terms and adding/subtracting them to remove a variable. There aren't any like terms here, but we can create some by multiplying terms.
Multiplying the second equation by 2 gives 0.8a+p=48, so that makes a like term.
Since the symbols are the same in front of the like term, we subtract the second term from the first one. This gives 0.2a=4.
Dividing by 0.2 gives a=20.
We can sub this into either equation to get the value of p.
a+p=52, so 20+p=52, meaning p=32.
**This content involves simultaneous equations, which you may want to revise. I'm always happy to help!
¿En cuál de los siguientes intervalos están solo los números reales que pertenecen a ] –3 , 5 ] y no pertenecen a [ –1 , 7 [?
Complete question:
¿En cuál de los siguientes intervalos están solo los números reales que pertenecen a ]- 3,5 ] y no pertenecen a [ –1 , 7 [ ?
A) ]-3, -1[
B) ]- 3, -1 ]
C) [-1,5]
D) ]- 3,7[
E) [5,7[
Answer:
A) ]-3, -1[
Step-by-step explanation:
El intervalo ]- 3,5 ] incluye a todos los números que se encuentran entre -3 y 5. Es decir,
...-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6...
El intervalo [–1 , 7[ excluye a los números que se encuentran entre -1 y 7, pero incluye a todos los números que sean menores a -1 y a todos los mayores a 7. Es decir,
...-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13...
Para responder el problema, debemos encontrar aquellos números reales que se incluyan dentro de ambos intervalos. Esto es,
]- 3,5 ] ...-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10...
]- ∞ , -1[ ∪ [7,∞[...-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10...
Es decir que el intervalo ]-3, -1[, corresponde a la intersección entre ambos conjuntos.
what are the roots of the quadratic equation below? 3x^2+15x-5=0
Answer:
X1 = [tex]\frac{=15+\sqrt{285} }{6}[/tex] and X2 = [tex]\frac{-15-\sqrt{285} }{6}[/tex]Step-by-step explanation:
To find the roots of a quadratic equation, you need to solve the quadratic equation by using the quadratic formula.
OR
You can use the (Equation/Function) mode on the calculator.
[tex]\frac{-b+-\sqrt{b^{2} -4ac } }{2a} x \neq 0[/tex]
For this equation,
a = 3
b = 15
c = -5
X1 = [tex]\frac{-15+\sqrt{15^{2} -4(3)(-5) } }{2(3)} x \neq 0[/tex]
X2 = [tex]\frac{-15-\sqrt{15^{2} -4(3)(-5) } }{2(3)} x \neq 0[/tex]
Solving this on the calculator and you should get
X1 = [tex]\frac{=15+\sqrt{285} }{6}[/tex] X2 = [tex]\frac{=15-\sqrt{285} }{6}[/tex]
a, b, c = constants, where a ≠ 0
x = the unknown
What is the degree of the monomial 4x^2y^5
Answer:
5
Step-by-step explanation:
The highest power is 5 so the degree of the monomial is also 5.
PLZ HELP!!!!! ASAP!!!!!!!!!!!! NO FILES!
Answer:
A' (1, -4)
B' (-4, -2)
C' (-5, 4)
D' (-2, 1)
Step-by-step explanation:
When reflecting a point across the x-axis, the x-coordinate remains the same, but the y-coordinate becomes its additive inverse.
The additive inverse of a number is simply the opposite of a number.
So, to reflect this quadrilateral across the x-axis, we must change the coordinates.
Remember: When reflecting a point across the x-axis, the x-coordinate remains the same, but the y-coordinate becomes its additive inverse.
Point A: (1, 4) ⇒ A' (1, -4)
Point B: (-4, 2) ⇒ B' (-4, -2)
Point C: (-5, -4) ⇒ C' (-5, 4)
Point D: (-2, -1) ⇒ D' (-2, 1)
The attachment will help as well.
If A = (7,9) and B = (3 , 12) what is the length of AB
Answer:
AB = 5 units
Step-by-step explanation:
Calculate the length using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+ (y_{2}-y_{1})^2[/tex]
with (x₁, y₁ ) = A(7, 9) and (x₂, y₂ ) = B(3, 12)
AB = [tex]\sqrt{(3-7)^2+(12-9)^2}[/tex]
= [tex]\sqrt{(-4)^2+3^2}[/tex]
= [tex]\sqrt{16+9}[/tex]
= [tex]\sqrt{25}[/tex]
= 5
What is the equation of the parabola, in vertex form, with vertex at (-2,-4) and
directrix x = -6?
O A. (x+2) = 8(y+4)
B. (y+4)2 = - 8(x+6)
O c. (y+4)2 = 16(x+2)
O D.(x+4)² = 8(y+2)
Answer:
Step-by-step explanation:
The distance between the vertex and the directrix is 4 units, that means that p = 4 in the equation
[tex](y-k)^2=4p(x-h)[/tex] and h and k are the coordinates of the vertex. Filling in:
[tex](y+4)^2=4(4)(x+2)[/tex] which simplifies to
[tex](y+4)^2=16(x+2)[/tex] choice C
Option C is correct, (y+4)² = 16(x+2) is the the equation of the parabola, in vertex form, with vertex at (-2,-4) and directrix x = -6
What is Parabola?A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.
The focus of the parabola is at a point that is equidistant to the vertex and the directrix.
Since the directrix is x = -6, the focus is at (-2+4,-4) = (2,-4).
The vertex form of the equation of a parabola is given by:
(y - k)² = 4p(x - h)
where (h, k) is the vertex and p is the distance between the vertex and focus.
In this case, (h, k) = (-2,-4) and the focus is at (2,-4). Therefore, p = 4.
Substituting the values into the vertex form equation, we get:
(y + 4)² = 4(4)(x + 2)
Simplifying, we get:
(y + 4)² = 16(x + 2)
Hence, (y+4)² = 16(x+2) is the the equation of the parabola, in vertex form, with vertex at (-2,-4) and directrix x = -6
To learn more on Parabola click:
https://brainly.com/question/31142122
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Figure ABCD is rotated clockwise about the origin through 360 degrees. Identify the transformed figure.
Answer: 360 is a complete circle meaning the figure will be back where it was originally
Step-by-step explanation:
ASAP what is the answer?
Answer: The ASAP Math program provides an opportunity for additional small group instruction for students who find the math program challenging. Students in grades 1 to 4 will come to the ASAP room two to three times a week during the math block.
I AM GOING TO FAIL THIS EXAM L M A F O
Answer:
x = 4
Step-by-step explanation:
The line in the triangle is an angle bisector and divides the opposite sides into segments that are proportional to the other 2 sides, that is
[tex]\frac{x+6}{20}[/tex] = [tex]\frac{x}{8}[/tex] ( cross- multiply )
20x = 8(x + 6) = 8x + 48 ( subtract 8x from both sides )
12x = 48 ( divide both sides by 12 )
x = 4
HCF of smallest 2 digit composite number and smallest 3 digit prime number is?
Answer:
HCF = 1
Step-by-step explanation:
Smallest 2 digit composite number = 10
Smallest 3 digit prime number = 101
Factors of 10 = 1 , 2 , 5
Factors of 101 = 1 , 101
HCF = 1
One afternoon, Olive, who is 2 feet 3 inches tall, casts a shadow that is 6 feet 1 inch long. At the same time of
the day, a nearby tree casts a shadow that is 12 feet long. Olive reasons she can figure out the height of the
tree.
What is the height of the tree in feet?
Answer:
4.5 feet
Step-by-step explanation:
Line AB || Line CD {sun height are parallel}
Angle ACB parallel to Angle DEC = 90°
Triangle ABC is parallel to Triangle DCE
12/61 * 2.5
=4.5 feet
Help!!!!!! I Don’t Know The Answer It’s Hard
Answer:
D
Step-by-step explanation:
Have a great summer :)
Answer:
C
Step-by-step explanation:
The slope is negative, so we can exclude the graph A and D
If we substitute y with 2 and x with -3 we have
2 = -4/3 (-3) -2
2 = 4 - 2
2 = 2
the equality is verified so C is the answer
Solve for x. Round to the nearest tenth, if necessary.
=======================================================
Explanation:
We use the cosine ratio here. Make sure your calculator is in degree mode.
cos(angle) = adjacent/hypotenuse
cos(69) = x/10
10*cos(69) = x
x = 10*cos(69)
x = 3.583679495453 which is approximate
x = 3.6
How do i get the answer I don’t understand what it’s asking me to do
Answer:
the answer is 6
Step-by-step explanation:
ans:g(9)=6
Answer:
g(9)=6
Step-by-step explanation:
if you look at the green table to the right, you can see that when t is 9, g(t) is 6. Therefore, g(9)=6
Maria rolls a six sided die. What is the possibility that she rolls a prime number?
1/6
1/3
1/2
2/3
Answer:
1/2
Step-by-step explanation:
2, 3, and 5 are the prime numbers. Therefore, it would be 3/6 or 1/2 chance she rolls a prime number.
What is the slope of a line that passes through (8,0) and (0,8).
Answer:
slope is 0
Step-by-step explanation:
use the formula y2 - y1 / x2 - x1
I need help with it one plz
Answer:
- 2/5
Step-by-step explanation:
(3/5 + 1/5) + (4/5 - 2/5) = 6/5
6/5 - (9/5-1/5) = - 2 /5
If 7 - y = 6, then y =
A. -29
B. -5
C. 1
D. 29
Answer:
C. 1
Step-by-step explanation:
7 - y = 6
-y + 7 = 6
-y - + 7 - 7 = 6 - 7
-y = -1
(-y=-1)/-1
y = 1
Hope this helps.
[tex]\sf \bf {\boxed {\mathbb {\: C.\:1}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex]7 - y = 6[/tex]
[tex]➺ \: - y = 6 - 7[/tex]
[tex]➺ \: - y = - 1[/tex]
[tex]➺ \: y = 1[/tex]
Therefore the value of [tex]y[/tex] is 1.
[tex]\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}[/tex]
[tex]7 - y = 6[/tex]
[tex]➼ \: 7 - 1 = 6[/tex]
[tex]➼ \: 6 = 6[/tex]
➼ L. H. S. = R. H. S.
Hence verified.
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35♨}}}}}[/tex]
r=x(a+b) solve for A
Answer:
Step-by-step explanation:
r=x(a+b)/x
r/x=a+b-b
r/x-b=a
What is 21-21+21-21-31-7877
Answer:
- 7,908
Step-by-step explanation:
Have a nice day :)
Answer:
-7,908
Step-by-step explanation:
help help help :)))))))
Answer:
✓✓ Area of traingle = 1.2 cm^2 ✓✓
Step-by-step explanation:
Hello mate (◕ᴗ◕✿)
=>> In above traingle, height and hypotenuse are given
=> height = 12 cm
=> Hypotenuse = 14 cm
✓✓ Area of traingle = 1/2(base*height) ✓✓
we need to find base of above traingle
Base = √Hypotenus - √Perpindicular
Base = √14 - √12
Base = 3.7 - 3.4
Base = 0.2 cm
Now, we can find area of traingle
Area of traingle = 1/2(Base*Height)
Area of traingle = 1/2(0.2*12)
Area of traingle = 6*0.2
Area of traingle = 1.2 cm^2
Hope it helps you mate (. ❛ ᴗ ❛.)
Answer :
➢ 43.3 cm²
Explanation :
let the missing side be c
a = 12 cm
b = 14 cm
Pythagoras theorem :
➢ a² + c² = b²
➢ 12² + c² = 14²
➢ 144 + c² = 196
➢ c² = 196 - 144
➢ c² = 52
➢ c = √52
➢ c = 7.21
Area = 1/2 × a × c
➢ 1/2 × 12 × 7.21
➢ 6 × 7.21
➢ 43.26 cm²
➢ 43.3 cm² [ round off to 1 decimal place ]
cual es la distancia entee los siguientes puntos R ( 6,-10) M (5,4) C(7,3) H (8,6) M (-4,9)
Answer:
M ( -4,9)
Step-by-step explanation:
Write all subsets of set {1, 2, 3}
The set {1, 2, 3} has 8 subsets.
A set with 'n' elements in it can have 2n subsets.
Please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!
Answer:
The answer is C≈49.64
Answer:
C=2πr=2·π·7.9≈49.63716
Step-by-step explanation:
brainliest??
