Since the focus is at (-5, -2) and the directrix is the line y = 1, we know that the vertex of the parabola lies halfway between them, which is at (-5, -0.5).
Since the directrix is a horizontal line, the parabola opens downward. Let (x, y) be a point on the parabola, and let d be the distance from (x, y) to the directrix (which is y - 1). Then the distance from (x, y) to the focus is d + 0.5 (half the distance between the focus and directrix).
Using the distance formula, we have:
√[(x - (-5))² + (y - (1))²] = d + 0.5
Simplifying, we get:
(x + 5)² + (y - 1)² = (d + 0.5)²
Since the point (x, y) lies on the parabola, its distance to the directrix is equal to its distance to the focus:
d = |y - 1 - (-0.5)| = |y - 0.5|
Substituting this into the equation above, we get:
(x + 5)² + (y - 1)² = (|y - 0.5| + 0.5)²
Expanding and simplifying, we get:
x² + 10x + y² - 2y - 12|y - 0.5| - 12 = 0
To put this in standard form, we need to eliminate the absolute value. We consider two cases:
Case 1: y ≥ 0.5
In this case, |y - 0.5| = y - 0.5, so we have:
x² + 10x + y² - 2y - 12y + 6 - 12 = 0
Simplifying, we get:
x² + 10x + y² - 14y - 18 = 0
Completing the square, we get:
(x + 5)² + (y - 7/2)² = 99/4
This is the standard form of the equation of the parabola.
Case 2: y < 0.5
In this case, |y - 0.5| = -(y - 0.5) = 0.5 - y, so we have:
x² + 10x + y² - 2y - 6(0.5 - y) - 12 = 0
Simplifying, we get:
x² + 10x + y² - 2y + 3 = 0
Completing the square, we get:
(x + 5)² + (y - 1)² = 21
This is also the standard form of the equation of the parabola, but it corresponds to a different part of the curve than the previous equation (since it has a different sign for the y-term).
To know more about parabola refer here:
https://brainly.com/question/31142122
#SPJ11
[tex] - \sqrt{49 {x}^{2} } [/tex]
simplify expression
Step-by-step explanation:
Given
[tex] - \sqrt{49 {x}^{2} } \\ = - \sqrt{ {7}^{2} {x}^{2} } \\ = - 7x[/tex]
Hope it will help :)
I need help my brain is too small to answer this
Answer:
5/6 or 0.83
Step-by-step explanation:
5 ÷ 6 = 0.83 or 5/6
Factor completely
1/25-25z^2
Answer:
1/25(1-25z)(1+25z)
Step-by-step explanation:
your welcome : )
Which of the following angles DO NOT have equal measure when a pair of parallel lines is crossed by a transversal?
HELP HELP ME PLSS!! Please I really need help....
The sum of the measures of the interior angles of a decagon (10 sided polygon) is 1,440
Suppose we know that the birth weight of babies is Normally distributed with a mean 3500g and a standard deviation of 500g. What is the probability that a baby is born that weighs less than 3100g?
Answer:
0.21186
Step-by-step explanation:
We solve the above question using the z score formula.
z = (x-μ)/σ, where
x is the raw score = 3100g
μ is the population mean = 3500g
σ is the population standard deviation = 500g
z = 3100 - 3500/500
z = -0.8
Probability value from Z-Table:
P(x<3100) = 0.21186
The probability that a baby is born that weighs less than 3100g is 0.21186
he equation shows the relationship between x and y:
y = −7x + 9
What is the slope of the equation?
−7
−2
7
9
Answer:
-7
Step-by-step explanation:
y=-7x+9
y=mx+b
m=slope
y=y-intercept
Which term has the definition "The value that is half way between the minimum and the median
It’s sad when I help people because they don’t do the same thing to so please please please... answer me once :((((((((((((((((((((((((((((((((((((((((((((((
Step-by-step explanation:
Equation = 4m=16
Answer= 4m=16
m=16/4 = 4
So Tyrone has 4 model planes.
Don't know if its correct
is 14.16 or 14.6 the higher number
Answer:
14.6 because 14.6 is equivalent to 14.60
Step-by-step explanation:
Answer:
14.6
Step-by-step explanation:
It would be 14.6 because 14.6 is basically 14.60
So you would compare 14.16 to 14.60
I need help I don’t wanna failed this class:(
Factorise : x³ + x - 3x² -3
Answer:
(x²+1)(x-3)
Step-by-step explanation:
Factorize x³ + x - 3x² -3
x³-3x²+x-3
Factorize
x²(x-3)+1(x-3)
= (x²+1)(x-3)
Hence the factorized form is (x²+1)(x-3)
one answer question
Answer:
c is the answer you will get you answer as a rational number (hope I'm not wrong)
How do i learn this subject easily?
Answer:
try to download app that can help you, watch videos on how to do the problems or ask help with someone you know or just take notes that makes you understand better
Step-by-step explanation:
I WILL MARK BRAINIEST PLEASE HELP
Answer: do you still need help
Step-by-step explanation:
One number exceeds another by 5. The sum of the numbers is 89. What are the numbers ?
Answer:
42
Step-by-step explanation:
89-5=84
84÷2=42
and reverse it to check
(42+5)+(42)=89
PLS HELP! i rly need help on this. it’s hard for me.
1: what is the name of that figure??
2: what would be the cross section from a vertical slice of the figure??
Answer:
The 3D solid shown in the image is a hexagonal pyramid. If we made a cross section with a vertical slice (top to bottom), we would have an isosceles triangle.
Useful Extra Knowledge:
However—and this isn't a question here, but just useful knowledge—if we made a cross section with a horizontal slice (left to right or right to left), we would have a regular hexagon. If it were a diagonal cross section, we would have an irregular hexagon.
Step-by-step explanation:
First, what's the difference between a sphere, a cylinder, a pyramid, a cone, and a prism? These are all 3D solids, but in your case, an explanation of what they are may be a good refresher:
A sphere is a 3D solid where every point is equidistant from the center point. Basically, it's a 3D circle. It's completely round.A prism is a 3D solid with straight, parallel sides and a polygonal base.A cylinder is a 3D solid with straight, parallel sides and a circular baseA pyramid is a 3D solid with sides that converge at a common vertex and a polygonal base.A cone is a 3D solid with sides that converge at a common vertex and a circular base.We definitely know this shape can't be a sphere! It's not completely round! Actually, take a closer look: there's no hint of a circle anywhere in the figure. It can't be a cylinder nor a cone.
This means it's either a pyramid or a prism. But, going back to the definitions above, let's redefine the difference between the two: pyramids have only one base and only triangular faces, while prisms have two bases and rectangular faces.
How many bases does this figure have? It has one base. And what shape are its faces? They're all triangles! This means we have to be looking at a pyramid.
So, you may think, that solves it. We're looking at a pyramid.
Sorry, buddy. It's not that easy. We can classify this figure even further. How do we do this? We use its base! And what type of polygon is the base? When we count the sides of the base, we find six sides, which means this shape is a hexagon. So this is a hexagonal pyramid, right?
Actually, there's one more specification we could give this. That hexagon has sides that are all equal to each other. That may not seem special to you, but there's a special term given to polygons who have equal sides and equal inner angles: they are called regular polygons.
That description matches the base of our shape, right? So, now we have the name of the figure: it's a regular hexagonal pyramid.
Now, what about the cross section? This means we're taking a piece of that solid, like cutting into a cake with a knife. Who likes cake here?
I digress. This piece, the cross section of the 3D solid, becomes a 2D shape. Now, the question asks for the shape of a vertical cross section, which means up and down, like the y-axis on the coordinate plane/Cartesian plane.
So, imagine taking a butter knife and slicing right down the middle of that bad boy. If you get the middle point exactly, you'll have two equal halves which would look like triangles with two equal sides: an isosceles triangle.
That's assuming you look straight on at them. If you veered to the side a little, you'd find a scalene triangle (a triangle with no equal sides).
But, should you miss the center a little, you'd get a trapezoid instead, because part of the top would be missing.
But I'm assuming the question is asking about a vertical slice exactly down the middle and viewed straight on. In that case, your answer is an isosceles triangle.
I droned on for a bit, I know. But hopefully this helps you understand the concept better! Have a great day!
between which two consecutive integers does the square root of 830 lie
28^2=784
29^2=841
784<830<841
therefore sqrt784<sqrt830<sqrt841
therefore 28<sqrt830<29
Done!
The sum of two integers is - 5 and their difference is 11.
What are the two numbers
Sung loo worked 54 hours during a special sale at the store. 10 hours was time and a half, and 4 hours were at double time. Her regular rate is $6.86. How much would Sung Loo make?
Answer:
$432.18
Step-by-step explanation:
Time and a half = 50% more pay rate / 1.5*6.86 = $10.29 per hour
Double time = 2*6.86 = $13.72 per hour
Rest of the time => At regular rate
Total Amount = 10(10.29) + 4(13.72) + (54 - 10 - 4)(6.86)
= 10(10.29) + 4(13.72) + (40)(6.86)
= $ 432.18
Answer:
so 10 hours was 1,5 time and 4 hours was 2 (double) time Her regular rate is $6,86/h so 10 h with 1,5 time make 10*1,5 = ? and 4 h with 2 time make 4*2 = ? total how much you get multiplie by 6,86 and will get in this way easy sure the correct answer.
Find the height of a cone that has a radius of 3 in and a volume of 96.91 in.
Answer:
thank you lil shawty
Step-by-step explanation:
Use the original price and the markup to find the retail price.
Original price $68; Markup 15%
The retail price is $________?
how I did it 68 x .15= 45.33333 rounded = 4.53
68 + 4.53 = 72.5 then I added a 0, 72.50
is 72.50 the answer?
Answer:
15% of $68 is $10.2
$68 + $10.2 = $78.2
The retail price is $78.20
yooooo please help lol
Answer:
You first want to divide 210 by 50 2/3. once you do that you will get 35/251 or 0.13944
Now you should be able to make about $44 dollars
Step-by-step explanation:
Are the ratios 2:4 and 5:6 equivalent? yes or no
Answer:
No
Step-by-step explanation:
If you try to multiply the 2:4 to change it to 5:6 , you can't because 5 is an odd number and 2 is and even
The difference of a number and seven
Answer: x-7
Step-by-step explanation:
Answer:
x -- 7
Step-by-step explanation:
help and i’ll give extra pounts
Answer:
C
Step-by-step explanation:
ZPRS and ZSRQ are supplementary angles.
85
Р
R
Q
What is the measure of ZSRQ?
O 5
O 15
O 95
O 105
Answer: 95
Step-by-step explanation: All supplementary angles always have to equal 180 degrees which means that you have to only do 180-85 and boom- 95- that is ur answer. Plz mark Brainliest:).
Help Please!? Thank You!
how to find LCM of 58??
Answer:
Find the prime factorization of 58. 58 = 2 × 29.
Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM: LCM = 2 × 2 × 2 × 2 × 2 × 2 × 29.
LCM = 1856.
Step-by-step explanation:
What is the interest rate in A = 12,000(1 + 0.07/4)^(4)(4)