Answer:
[tex]\displaystyle y=-\frac{1}{10}x^2-\frac{4}{5}x-\frac{11}{10}[/tex]
Step-by-step explanation:
By definition, any point (x, y) on the parabola is equidistant from the focus and the directrix.
The distance between a point (x, y) on the parabola and the focus can be described using the distance formula:
[tex]d=\sqrt{(x-(-4))^2+(y-(-2))^2[/tex]
Simplify:
[tex]d=\sqrt{(x+4)^2+(y+2)^2}[/tex]
Since the directrix is an equation of y, we will use the y-coordinate. The vertical distance between a point (x, y) on the parabola and the directrix can be described using absolute value:
[tex]d=|y-3|\text{ or } |3-y|[/tex]
The two equations are equivalent. Therefore:
[tex]\sqrt{(x+4)^2+(y+2)^2}=|y-3|[/tex]
Solve for y. We can square both sides. Since anything squared is positive, we can remove the absolute value:
[tex](x+4)^2+(y+2)^2 = (y-3)^2[/tex]
Expand:
[tex](x^2+8x+16)+(y^2+4y+4)=(y^2-6y+9)[/tex]
Isolate:
[tex]x^2+8x+11=-10y[/tex]
Divide both sides by -10. Hence, our equation is:
[tex]\displaystyle y=-\frac{1}{10}x^2-\frac{4}{5}x-\frac{11}{10}[/tex]
1. What is the equation of the vertical line that passes through the point (3, 4)?
2. What is the equation of the horizontal line that passes through the point (3,4)?
Answer:
1. the Equation of vertical line=> x=3
2. the Equation of horizontal line
=> y = 4
Answer:
y=4
Step-by-step explanation:
Please help me with this
A mathematics teacher wanted to see the correlation between test scores and homework. The homework grade (x) and test grade (y) are given in the accompanying table. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth. Using this equation, find the projected test grade, to the nearest integer, for a student with a homework grade of 34.
SOMEONE HELP ME WITH THIS RIGHT NOW. please
Answer:
23
Step-by-step explanation:
Using an online calculator and plugging the values in, we get our equation of y=mx + b to become y = 1.2x - 17.8 .
Plugging 34 in for x, we get 1.2(34) - 17.8 = 23 for their projected test grade
A shop keeper buys a pair of shoes for birr 180 and sells it for birr 225 what is the percentage profit
Answer:
Percentage profit = 20%
Step-by-step explanation:
Given the following data;
Cost price = birr 180
Selling price = birr 225
To find the percentage profit;
First of all, we would determine the profit;
Profit = selling price - cost price
Profit = 225 - 180
Profit = birr 45
Next, we would determine the percentage profit;
[tex] Percentage \; profit = \frac{profit}{selling \; price} * 100[/tex]
[tex] Percentage \; profit = \frac{45}{225} * 100[/tex]
[tex] Percentage \; profit = 0.2 * 100[/tex]
Percentage profit = 20%
100 points and brianllest for whoever answer first
Answer:
5/12 hour or 25 minutes
Step-by-step explanation:
The formula is
distance = rate * time
changing minutes to hours (50 * 1 /60 ) = 5/6 hours
distance = 20 mph * 5/6 hours
distance = 50/3 miles
We need to go the same distance at 40 mph
50/3 = 40 mph * time
Multiply each side by 1/40
50 /3 * 1/40 = 40 * 1/40 *t
50/3 *1/40 =t
5/12 of an hour
Changing back to minutes
5/12 * 60 =25
Which of the following graphs represents the equation below?:y=−9x−2
Answer:
C
Step-by-step explanation:
y intercept of the graph is -2
-9x is a very steep gradient
PLEASE HELP Which composition of similarity transformations
maps ALMN to A L'M'N'?
a dilation with a scale factor less than 1 and then a
reflection
a dilation with a scale factor less than 1 and then a
translation
a dilation with a scale factor greater than 1 and then
a reflection
a dilation with a scale factor greater than 1 and then
a translation
Answer:
a dilation with a scale factor greater than 1 and then a translation (the last option)
The composition of transformation is a dilation with a scale factor greater than 1 and then a translation.
What is Translation?A translation only moves a shape up, down, or from side to side; it has no effect on how it appears.
We have a transformations maps LMN to L'M'N'.
As the size of Triangle L'M'N' is larger as compared to LMN.
The compression is represented by a scale factor with an absolute value between 0 and 1, while the enlargement is represented by a scale factor with an absolute value greater than 1.
Thus, dilation with a scale factor greater than 1 and then a translation.
Learn more about Translation here:
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Tres amigos obtienen un premio de $1000.00 en la lotería, ¿cómo deben repartirlo si uno de ellos aportó $12.00, el otro $8.00 y el tercero $15.00?
Ayudeeen es para hoyyyy
Answer:
hii
Step-by-step explanation:
follow me please gugs
Someone help me with this one
Answer:
p' (4,-2)
Step-by-step explanation:
P is at ( -1,5)
We are moving it 5 units to the right so add 5 to the x
We are moving it 7 units down so subtract 7 from the y
p'( -1+5, 5-7)
p' (4,-2)
number 1 and 2 pls help me
what is the distributive property of 6(14+7)
Answer:
126
Step-by-step explanation:
6 (14 + 7)
6 (21)
126
Find the volume. Whoever answers I will reward the brainliest please help
Answer:
A. 900 un³
Step-by-step explanation:
Volume = Area triangle x height
Area triangle = 1/2 (15 x 8) = 1/2(120) = 60
60 x 15 = 600 + 300 = 900 un³
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Use the Distributive Property to find 1/3×6 1/2.
ILL MARK YOU SOMETHING LIKE BRAINY GENIUS
Answer:
2 1/6 or 13/6
Step-by-step explanation:
Equation: [tex]\frac{1}{3}[/tex] × 6[tex]\frac{1}{2}[/tex]
Distribute: (1/3) ( 6 + 1/2)
(1/3)(6) + (1/3)(1/2)
2 + 1/6
2 1/6 or 13/6
1. State whether the following sets of lines
are parallel, perpendicular, or neither.
A y=5 and y = -2
B y=8 and x = 8
C y = 4x + 8 and y = -4x - 2
D y=-X+6 and y = x + 1
E y = 6x + 2 and y = 6x
Which equation could generate the curve in the graph below?
Answer:
Your answer is DDDDDDDDD
Step-by-step explanation:
where is the sand dollar
Answer:
maybe the palm tree is at 5 the rock at -2 and the sand dollar at 0?
or, somthing like that
Step-by-step explanation:
The sand dollar is at zero which is 2 units away from rock and five units away from palm tree
What is Number system?A number system is defined as a system of writing to express numbers.
A sand dollar is 2 units away from rock and five units away from palm tree, We have to find the location of the sand dollar
Let the rock is at -2 on number line
The palm tree is at 5 on number line
So the sand dollar is at 0, as zero is two units away from rock and tree is five units away
Hence, the sand dollar is at zero which is 2 units away from rock and five units away from palm tree
To learn more on Number system click:
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Brainliest goes to whoever answers correctly and explains also if you want extra points answer my other questions
Answer:
isn't that the same as before? :D
Cual es el cociente y el resto de la siguiente división? 64:5= *
a) El cociente es 4 y el resto 5
b) El cociente es 12 y el resto 0
c) El cociente es 4 y el resto 12
d) El cociente es 12 y el resto
Answer:
D
Step-by-step explanation:
el cociente es 12 y el resto es 4, porque 12 por 5 es 60. 60 es el cociente. y 64-60 = 4 por lo tanto 4 es el resto
I need help thank you
Answer:
9 is the answer
Step-by-step explanation:
You will multiply 3x3 and 9x1 it will have the least common denominator
Can someone help me please TwT
Each week, Morgan walks a total of 5 miles to and from school, and Whitney walks a total of 6 miles to and from school. Part A Enter a number in each box to complete the ordered pairs showing the total number of miles that Morgan and Whitney will have walked after each week. The first term of each ordered pair is the number of miles Morgan will have walked. The second term is the number of miles Whitney will have walked.
Answer: (5,10) (6,12) (15,18) (20,24) (25,30)
Step-by-step explanation:
All you have to do is read the question carefully, and if you don’t understand than, keep doubling each number. Example: 5, 10 then you do whitneys part, which is 6,12 than you keep adding 5 and 6
I can't remember how to do this. I need help with this.
How many roots do the functions have in common?
f(x)=x^2-9
one root common that's -3
Step-by-step explanation:
use desmos
The number of pages in an Algebra book is 99 less than the number of pages in a geometry book.
Write and solve an equation to find the number n of pages in the geometry book.
Answer: An equation is *629 = n - 99. The geometry book has 728 pages*
Step-by-step explanation: The Algebra book has 99 pages LESS than the geometry book, in other words, the geometry book has 99 pages MORE than the Algebra book. This equation can be used to find the answer. I’m afraid 530 is not the answer.
Hope this helps! :)
Divide using long division! Show your work. As soon as possible!
Answer:
Step-by-step explanation:
if you've any doubt just ask :)
Solve for x and show your work.
• GIVING BRAINLIEST!
Integer x is evenly divisible by 3. Which expression below is also evenly divisible by 3?
A. 2x+ 1
B. 3x-5
C. 4x-1
D. 4x+6
help pleaseee
find the equation of the line passing through (-5, -4) and (13, 5)
Answer:
y = 1/2x - 3/2
Step-by-step explanation:
y2 - y1 / x2 - x1
5 - (-4) / 13 - (-5)
9 / 18
1/2
y = 1/2x + b
-4 = 1/2(-5) + b
-4 = -5/2 + b
-3/2 = b
Liam spent $4.76 on a salad bowl, and $3.81 on a cup of coffee. He paid using TWO ten dollar bills. What was Liam's change?
Answer:
11.43
Step-by-step explanation:
You can start this by adding the total cost of the salad and the coffee.
4.76 + 3.81 = 8.57
Then you have the paid amount of 20 bucks because there was two tens.
20 - 8.57 = 11.43.
What’s the Missing Side?
PLEASEEE HELPP
Answer:
11 km
Step-by-step explanation:
34.1 = 3.1x
solve for x
x=11 km
A line is parallel to 5x+2y-8-0 and has the same y-intercept as x+4y-12-0.
Find the equation for the line in slope y-intercept form
Answer:
y=(-5/2)x+3
Step-by-step explanation:
5x+2y-8=0
2y=-5x+8 Divide with 2
y=(-5/2)x+4
Slope is dy/dx
dy/dx=-5/2
x+4y-12=0 for x=0
4y-12=0
4y=12 Divide with 4
y=3 y-intercept
Line equation:
y = mx + b
This is called the slope-intercept form because "m" is the slope and "b" gives the y-intercept.
m-5/2 b=3
Euation for the your line:
y=(-5/2)x+3