Answer:
The statements that can be made about the parabola are;
The parabola opens towards the right
The equation of the parabola is (y - 1)² = 16 × (x + 1)
The parabola has a vertex at (-1, 1)
Step-by-step explanation:
The given focus of the parabola is (3, 1)
The directrix of the parabola, x = -5
Therefore, from the location of the directrix (on the x-axis) and the location of the focus relative to the directrix towards the positive direction of the x-axis relative to the directrix, the parabola opens towards the left of the coordinate chart
The general equation of the focus = (h + p, k)
The general equation of the directrix, x = h - p
Comparing with the values of the focus and the directrix of the given parabola, we have;
(3, 1) = (h + p, k)
-5 = h - p
Therefore, we get;
k = 1
h + p = 3...(1)
h - p = -5...(2)
Adding equation (1) to equation (2) gives;
h + h + p - p = 3 + (-5)
2·h = -2
h = -2/2 = -1
h = -1
From equation (1), we get;
h + p = -1 + p = 3
∴ p = 3 + 1 = 4
p = 4
The vertex of the parabola, (h, k) = (-1, 1)
The equation of the parabola in the form (y - k)² = 4·p·(x - h) is therefore, presented as follows;
The equation of the parabola = (y - 1)² = 4 × 4 × (x - (-1))
(y - 1)² = 16 × (x - (-1))
The equation of the parabola is (y - 1)² = 16 × (x + 1).
Which expressions below are equivalent to
2(2x + 1)?
Select all that apply.
0 A. 4x + 2
O B. 2(1 + 2x)
C. 2(2x) + 1
0 D. 2x + 1 + 2x + 1
E. x + x + x + x + 1 + 1
Which expression is equivalent to the
Vesa
Answer:
A.4x+2
Step-by-step explanation:
distrubuve property,u multiply the numbers in the bracket by two.so,2x2=4 and 2x1=2 so 4x+2
beth ran 1 1/2 and 2 1/8 and 1/32 during the week how many miles did beth run
I need help fast please and no fies
Answer:
x=-16
Step-by-step explanation:
from x=-3 to get to y=12 u need to multiply x=-3 by -4 to get to 12 so for y=64 u need to divide by -4 which equals x=-16
Answer:
x is (-16)
Hope it helps!!!
The perimeter of a rectangle is the same as the
perimeter of a square. If the area of this rectangle
is x^2 + 4x – 21 and the side lengths are integers,
find:
a. the perimeter of the rectangle
b. the area of the square
Answer:
a. 20
b. 25
Step-by-step explanation:
Let find the side lengths of the rectangle,
We can complete the square.
[tex] {x}^{2} + 4x - 21[/tex]
[tex] {x}^{2} + 4x = 21[/tex]
[tex] {x}^{2} + 4x + 4 = 25[/tex]
[tex](x + 2) {}^{2} = 25[/tex]
[tex](x + 2) = 5[/tex]
[tex]x = - 7[/tex]
or
[tex](x + 7)[/tex]
[tex]x = 3[/tex]
or
[tex](x - 3)[/tex]
This means the perimeter of is
2 times -7 equal 14
2 times 3 equal 6
14+6=20.
The side lengths of the square is equal so each side length will measure 5.
[tex] {5}^{2} = 25[/tex]
Find the number that is exactly half way between -4 and 10
Answer:
7 as a halfway of a line
3 if you were using points on a graph
Step-by-step explanation:
10--4/2=7
use midpoint formula for 3
The number that is exactly halfway between -4 and 10 is 3
The distance between two point is the amount of length between the two points.
Midpoint of -4 and 10 is 10 - (-4) gives 10 + 4
The distance between -4 and 10 is 14 units
Halfway of the length between -4 and 10 is 14 /2 (7)
The number that is exactly halfway between -4 and 10 = -4 + 7 or 10 - 7 = 3
The number that is exactly halfway between -4 and 10 is 3
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Find the solution to the following system using substitution or elimination:
Answer:
B) (3,1)
Step-by-step explanation:
y = -2x + 7
y = 3x - 8
3x - 8 = -2x + 7
combine like terms:
5x = 15
divide both sides of the equation by 5:
x = 3
y = 3(3) - 8 = 1
The diameter of a circle is 18 cm. Find its area in terms of pi
Answer:
I love algebra anyways
the ans is in the picture with the steps
(hope it helps can i plz have brainlist :D hehe)
Step-by-step explanation:
Translate this phrase into an algebraic expression.
17 increased by twice Malik's score
Use the variable m to represent Malik's score.
Answer:17+2m
Step-by-step explanation:
I think its angle bisector but want to make sure.
Answer:
Yes, that's an angle bisector.
You are correct in saying that this is a bisector.
Slope of the line pls helpppppp
Answer:
[tex] slope(m) = \frac{3}{2} [/tex]
Step-by-step explanation:
Slope (m) = change in y / change in x = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Use any two pairs of values to find the slope. Thus, let's use (-14, 3) and (-12, 6):
Where,
[tex] (-14, 3) = (x_1, y_1) [/tex]
[tex] (-12, 6) = (x_2, y_2) [/tex]
Plug in the values
[tex] m = \frac{6 - 3}{-12 -(-14)} [/tex]
[tex] m = \frac{3}{2} [/tex]
Your teacher has told you that she will drop your "worst" test.
On Test 1 you scored 90 (mean=88, SD = 4)
On Test 2 you scored 88 (mean=79, SD=3)
Which test was "worse"?
Test one would be the worst one
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!
Answer:
5: 113.1 cm^3
6: 7238.23 cm^3
Step-by-step explanation:
The formula is V=4/3(pi)r^3, so just plug in values for R.
Volume for 8 x 2 x 4
A garden is in the shape of a square with a perimeter of 68 feet. The garden is surrounded by two fences. One fence is around the perimeter of the garden, whereas the second fence is 2 feet from the first fence on the outside. If the material used to build the two fences is $1.37 per foot, what was the total cost of the fences?
Answer:
$197.28
Step-by-step explanation:
perimeter of a square = 4 x length
length = perimeter / 4 = 68/4 = 17 ft
Price of the first fence = perimeter x price per foot
68 x 1.37 = 93.16
Perimeter of the second fence = (17 + 2 ) x 4 = 76
total price = sum of the price of the two fences
Price = 76 x 1.37 = 104.12
total price = 197.28
What are all of the steps to get 17=5y-3
Answer:4
Step-by-step explanation: 17 = 5y-3
Add 3 to both sides
17 turns into 20
3 is gone
20=5y
Divide by 5 on both sides
20 divided by 5 =4
5 crossed out
4=y
SECTION C
11. UNE PISCINE
L'opération consistant à vider une piscine débute à 8 h du matin. À 10 h du matin, la
piscine contient 80 000 litres d'eau et à midi elle contient 64 000 litres.
Si la piscine se vide à un débit constant, à quelle heure la piscine sera-t-elle vide?
HURRY!!!!! Hey guys help me with this PI question. Pi = 3.14
Thank you!
Answer:19.625in
Step-by-step explanation:
Answer: 19.625 inches is the answer
Step-by-step explanation:
Which is the area of the parallelogram
Answer:
96
Step-by-step explanation:
formula is simple
just base times height
so 12 × 8 which is 96
96m² is your Answer:
Solution given:
base[b]=12m
height[h]=8m
we have
Area of parallelogram=b×h=12×8=96m²
The formula for determining the pressure, p, exerted
on an object at a depth, h, below the surface of a
liquid is p = s + dgh, where s is the atmospheric
pressure, d is the density of the liquid, and g is the
acceleration due to gravity. Which formula
represents h in terms of p, s, d, and g?
Answer:
p = s + dgh
p - s = dgh
(p - s) / dg = h
Answer = h= p-s/dg
The formula that represents the height "h" in terms of p, s, d, and g is expressed as (p - s)/dg
Given the formula for determining the pressure, p, exerted on an object at a depth, h, below the surface of a liquid expressed as p = s + dgh where:
s is the atmospheric pressure,
d is the density of the liquid, and;
g is the acceleration due to gravity
We are to make h the subject of the formula;
p = s + dgh
Subtract s from both sides
p - s = dgh
dgh = p - s
Divide both sides by dg
dgh/dg = (p - s)/dg
h = (p - s)/dg
Hence the formula that represents the height "h" in terms of p, s, d, and g is expressed as (p - s)/dg
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The velocity of a ball thrown upward into the air is given by v(t)= -32t+96 where t is measured in seconds and velocity v in feet per second calculate the displacement of the ball between t=1 and t=4
Answer:
The displac ment between t = 1 and t = 4 is 272 feet
Step-by-step explanation:
To get the displacement of the ball, we first need to get the equation for the position of the ball with respect to time.
We can do this by differentiating the velocity equation given:
v(t) = -32t +96
integrating between the limits of t = 1 and t = 4, we have
[tex]s = \int\limits^4_1 {-32t +96} \, dt[/tex]
[tex]s(t) = -32t^2/2 +96t[/tex]
[tex]s =[ -16t^2 +96t] t = 4, t =1[/tex]
where t = 4.
s = 256 + (96) =352 feet
Where t = 1
s = 80
Displacement of the ball = 352 -80 = 272ft
The displac ment between t = 1 and t = 4 is 272 feet
I need HELP ASAP! It’s due today
Answer:
28 cubs
Step-by-step explanation:
Since one and a half bear produces one and a half cub, then 6 bears will produce 6 cubs in one and a half days.
We need to find 7 days, though but we have the rate for six bears for 1.5 days which 6 bears one a half day.
What is the rate for a day?
6/1.5 =
6 bears produce 4 cubs a day.
Now just do 4 x 7
4 x 7 = 28
Therefore, 6 bears produce 28 cubs in 7 days.
Someone please help me
Answer:
a=17 angles= each other = 64
Step-by-step explanation:
Carmen has 2.4% as much money as Anna. How much money does Anna have a Carmen has $846?
Answer:
$20.30
Step-by-step explanation:
Anna has 846 dollars
Carman has 2.4% the amount that Anna has.
2.4% = 2.4 / 100
2.4/100 * 846 = 20 dollars and 30 cents. You lose the 0.004
PLEASE HELP! This problem contains Algebra which I am super bad at!
Answer:
c
Step-by-step explanation:
because the i just worked it out
What is the midpoint of the segment shown below? (-3, 4) (-6, -1)
A. (-9,3) O B.(-9/2, 3/2) C. (-9, 3/2) D. (-9/2,3)
Answer:
B) -9/2 , 3/2
That's the correct answer
The midpoint of the given segment is (-9/2, 3/2), so the correct option is b.
Where is the midpoint of the segment?For a segment whose endpoints are (a, b) and (c, d), the midpoint of that segment is given by the point:
( (a + c)/2, (b + d)/2).
In this case the endpoints are (-3, 4) and (-6, -1), using the above formula, we get that the midpoint is:
( (-3 - 6)/2, (4 - 1)/2) = (-9/2, 3/2)
We can see that the correct option is B.
If you want to learn more about midpoints:
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What steps to get the answer for -4x+7=11
Answer:
-4x=4
Step-by-step explanation:
-4x+7=11 subtract 7 add to the 11 answer-4x=4
Answer:
x=-1
Step-by-step explanation:
Move all terms not containing x to the right side of the equation.
Subtract 7 from both sides of the equation
-4x=11-7
Subtract 7 from 11
-4x=4
Divide each term and simplify
x=-1.
Hope this helps :)
Plz mark brainiest!
The values of several terms in a sequence are shown in the table.
Second=5
Fourth=12
Seventh=22.5
Find the first term, f (1).
Answer:
1.5
Step-by-step explanation:
You divide and stuff. Then you subtract 3.5 from 5 to get 1.5 and bam answer.
Margo wants new carpet and a new wallpaper border for her bedroom. The room is 5.7 yards long and 6 7 8 yards wide. About how many square yards of carpet will she need? About how many yards of wallpaper border will she need?
Answer:
39.19 yards^2
25.15 yards
Step-by-step explanation:
To determine the squares square yards of carpet needed, we have to determine the area of the room
The room is shaped like a rectangle
area of a rectangle = length x breadth
5.7 x 6 7/8
To multiply, convert 6 7/8 to a decimal
to do this, divide 7 by 8. Add the value gotten to 6
5.7 x 6.875 =39.19 yards^2
To determine the yards needed for the border, calculate the perimeter of the room
Perimeter = 2 x (length + breadth)
2 x(5.7 + 6.875) = 25.15 yards
A computer programmer worked for 5 hours and earned $25, which is a rate of $_ Per hour
Answer:
They earned 5 dollars per hour
Step-by-step explanation:
Take the amount earned and divide by the number of hours
25/5
5
They earned 5 dollars per hour
Russ plants seeds in 1/2 of his garden. If he planted sunflower seeds in 1/4 of that section, what part of the total garden should grow sunflowers?
Answer:
1/8
Step-by-step explanation:
part of the garden that is sunflowers=1/4 of 1/2=1/2*1/4=1/8 (in math of usually means multiplication ex. 50% of 100=0.50*100=50)
Answer:
1/8
Step-by-step explanation:
Ik im late but- Yeah its that