Answer:
y=1/8(-x^2+4x+44
Step-by-step explanation:
In this question the given focus is (2,4) and a directrix of y = 8 and we have to derive the equation of the parabola.
Let (x,y) is a point on the given parabola.Then the distance between the point (x,y) to (2,4) and the distance from (x,y) to diractrix will be same.
Distance between (x,y) and (2,4)
= √(x-2)²+(y-4)²
And the distance between (x,y) and directrix y=8
= (y-8)
Now √(x-2)²+(y-4)² = (y-8)
(x-2)²+(y-4)² = (y-8)²
x²+4-4x+y²+16-8y = y²+64-16y
x²+20+y²-4x-8y = y²-16y+64
x²+20-4x-8y+16y-64=0
x²+8y-4x-44 = 0
8y = -x²+4x+44
In a herd of cattle, the ratio of the number
of bulls to cows is 1:6.
Find the number of bulls in terms of x.
Final answer:
The number of bulls in a herd with a bull-to-cow ratio of 1:6 is one-seventh of the total number of animals in the herd, represented as x/7.
Explanation:
In the scenario where the ratio of the number of bulls to cows is 1:6, we can express the number of bulls in terms of x, where x represents the total number of animals in the herd.
Let's define the number of bulls as B and the number of cows as C. Given the ratio B:C = 1:6, for every 7 animals in the herd (1 bull + 6 cows), there is 1 bull.
To find the number of bulls in terms of x, we divide the total number of animals by the sum of the parts of the ratio (1+6=7). So, the formula to find the number of bulls (B) is:
B = x / 7
Therefore, if x is the total number of animals in the herd, the number of bulls is one-seventh of x.
A rectangular cabinet is 5 feet long, 2 feet wide, and 3 feet tall. What is the surface area of the cabinet? Please help
Answer:
62 ft.
Step-by-step explanation:
Multiply 2(width)(length)+ 2(length)(height)+ 2(height)(width)
Simplify this expression with only positive exponents.
Answer:
[tex]\frac{2x}{y^{-1}}=2xy[/tex]
Step-by-step explanation:
To simplify the expression [tex]\frac{2x}{y^{-1}}[/tex] you must:
[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^{-1}=\frac{1}{a}\\\\y^{-1}=\frac{1}{y}\\\\\frac{2x}{y^{-1}}=\frac{2x}{\frac{1}{y}}[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{\frac{b}{c}}=\frac{a\cdot \:c}{b}\\\\\frac{2x}{\frac{1}{y}}=\frac{2xy}{1}[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{1}=a\\\\\frac{2xy}{1} = 2xy[/tex]
Therefore,
[tex]\frac{2x}{y^{-1}}=2xy[/tex]
What is the answer for 4t≤13
Step-by-step explanation:
4t < 13
t < 13/4
I think this should be the answer
Answer: T<13/4
Step-by-step explanation: See below
find the surface area of the square pyramid if the slant height is 13mm and the base length is 11mm
a) 264mm squared
b) 286mm squared
c) 335.5mm squared
d) 407mm squared
To find the surface area of a square pyramid, you need to calculate the lateral area and the area of the base. The lateral area can be found using the formula (1/2) × perimeter of the base × slant height. The base area is equal to the side length squared. To find the total surface area, you add the lateral area and the base area.
Explanation:Surface Area of Square PyramidTo find the surface area of a square pyramid, we need to calculate the lateral area and the area of the base.
Lateral Area
The lateral area of a square pyramid can be found using the formula:
Lateral Area = (1/2) × perimeter of the base × slant height
In this case, the slant height is given as 13mm and the base length is given as 11mm, so we have:
Lateral Area = (1/2) × 4 × 11mm × 13mm = 286mm2
Base Area
The base of the square pyramid is a square with side length 11mm. Therefore, the area of the base is:
Base Area = side length × side length = 11mm × 11mm = 121mm2
Total Surface Area
To find the total surface area, we add the lateral area and the base area:
Total Surface Area = Lateral Area + Base Area = 286mm2 + 121mm2 = 407mm2
Therefore, the surface area of the square pyramid is 407mm2.
Sample response: Start by calculating the volume of the original prism. The area of the base, B, is 4(6) = 24 m2. Multiply that by the height to get the volume: 24(10) = 240 m3. Now, if you double all of the dimensions, you would have a rectangular prism with a base that is 8 m by 12 m and a height of 20 m. The area of the base, B, is 8(12) = 96 m2. Multiply that by the height to get the volume: 96(20) = 1,920 m3. To compare, look at the ratio of the original prism to the new prism: 96/1,920 = 1/8. The volume increases by 8 times the original volume.
Check all that you included in your response.
Find the original volume. The area of the base, B, is 4(6) = 24 m2. Multiply that by the height to get the volume: 24(10) = 240 m3.
If you double all of the dimensions, you would have a rectangular prism with a base that is 8 m by 12 m and a height of 20 m.
Find the new volume. The area of the base, B, is 8(12) = 96 m2. Multiply that by the height to get the volume: 96(20) = 1,920 m3.
The volume increases by 8 times the original volume.
Answer:
Step-by-step explanation:
What is the surface area of a sphere with a diameter of 4?*
O
57.63 u2
87.6 u2
50.2 u2
63.9 u2
Answer:
50.2 u²
Step-by-step explanation:
SA = 4 pi r²
SA = 4 × 22/7 × 2 × 2
SA = 50.2 u²
solve for x.
A. x = √55
B. x = √73
C. x = 4√7
D. x = √130
Answer:
C. x = 4√7
Step-by-step explanation:
This is a right triangle
The hypotenuse is 3+8 (the radius is 3 and the exterior length is 8)
We can use the Pythagorean theorem
a^2 +b^2 = c^2
3^2 + x^2 = 11^2
9+x^2 = 121
Subtract 9 from each side
9-9 + x^2 = 121-9
x^2 = 112
Take the square root of each side
sqrt(x^2) = sqrt(112)
x = sqrt(16*7)
x = 4 sqrt(7)
What’s the missing length
Answer:
a=9in
Step-by-step explanation:
Pythagoreans Theorem
a^2+5.6^2=10.6^2
a^2+31.36=112.36
a^2=81
(take square root of both sides)
a=9
Which of the following equations matches the graph above?
A.
y=2x-1
B.
y=2/5x-1
C.
y=2/5x+1
D.
y=5x-1
it will be A. y=2x-1
hope this helps
how to find volume of the cylinder
Answer:
cbjkjcghuugchbcguygcbvyc
create a story problem for 1/2 × 6
Answer: Mary had six pieces of candy but her mother didn’t want her having too much sugar. She took away half of her candy. How many pieces does she have now?
Step-by-step explanation:
Answer:
I had 6 dollars. you stole half. How much do I have left
Step-by-step explanation:
6 x 1/2 = 3
I want brainliest :)
write the following expression in the form of 4^n
4^4 times 4^3 is equal to?
this is exponets.
Answer:
4^7
Step-by-step explanation:
4 * 4 * 4 * 4 = 256
4 * 4 * 4 = 64
Since the number is the same, another way to write the expression is 4^7.
256 * 64 = 16,384
Hope I helped! Please give me brainliest!
Y varies inversely with x, when y is 48 when x is 1/3 .which equation represents this situation?
a) Y=16/x
b) Y=16x
c) Y=144x
d) Y= 144/x
Answer:
A
Step-by-step explanation:
Given that y varies inversely with x then the equation relating them is
y = [tex]\frac{k}{x}[/tex]
To find k use the condition y = 48 when x = [tex]\frac{1}{3}[/tex], thus
k = yx = 48 × [tex]\frac{1}{3}[/tex] = 16
y = [tex]\frac{16}{x}[/tex] ← equation of variation
A projectile with an initial velocity of 48 feet per second is launched from a building 190 feet tall. The path of the projectile is modeled using the equation h(t) = –16t2 + 48t + 190. What is the maximum height of the projectile? 82 feet 190 feet 226 feet 250 feet
Answer:
226 feet
Step-by-step explanation:
The maximum height of the projectile is 226 feet
How to calculate the maximum height of an object?Given the equation of the height modelled as h(t) = –16t^2 + 48t + 190
The ball reaches the maximum height at the point where v = dh/dt = 0
dh/dt = -32t + 48
32t = 48
t = 1.5s
Get the maximum height;
h(1.5) = –16(1.5)^2 + 48(1.5) + 190
h(1.5) = -36 + 72 + 190
h(1.5) = 226 feet
Hence the maximum height of the projectile is 226 feet
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Which of the following is a geometric sequence?
0, 2, 6, 12, 72,
0 1 2 3 4 5
23'4'5'6
4.9, 14, 19, 24,..
1.3. 9. 27. 81
Answer:
1, 3, 9, 27, 81, ...
Step-by-step explanation:
right on edg
what is two times 57 plus two raised to the power of 63?
Answer:
1.150411783 E130
Step-by-step explanation:
Kira attempts to write the word divisibility in cursive, but she mistakenly writes one of the letters incorrectly. What is the probability that Kira wrote a letter i incorrectly? Assume each letter of the alphabet is equally difficult to write.
A. 5/12
B. 6/15
C. 1/2
D. 1/6
The probability that Kira wrote a letter i incorrectly in cursive in the word divisibility is 5/12.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that Kira wrote a letter i incorrectly = number of i / total number of letters
5/12
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Colin & Brian share a lottery win of £2100 in the ratio 4 : 1. Colin then shares his part between himself, his wife & their son in the ratio 2 : 5 : 3. How much more does his wife get over their son?
Answer:
His wife gets $336 more than his son.
Step-by-step explanation:
Colin and Brian:
Ratio of 4:1.
So Colin gets [tex]\frac{4}{4+1} = \frac{4}{5}[/tex] of the prize.
[tex]\frac{4*2100}{5} = 1680[/tex]
Colin got $1680. Dividing between himself, his wife and their son:
Ratio of 2:5:3.
So Colin gets [tex]\frac{2}{2+3+5} = \frac{2}{10}[/tex], his wife gets [tex]\frac{5}{2+3+5} = \frac{5}{10}[/tex] and his son gets [tex]\frac{3}{2+3+5} = \frac{3}{10}[/tex]
Wife:
[tex]\frac{5*1680}{10} = 840[/tex]
His wife got $840.
Son:
[tex]\frac{3*1680}{10} = 504[/tex]
His son got $504.
How much more does his wife get over their son?
840 - 504 = 336
His wife gets $336 more than his son.
PLEASE HELP ME :(
Find the surface area of the cone. *
Answer:
A≈597.62
Step-by-step explanation:
A=π r l + π [tex]r^{2}[/tex]
l=[tex]\sqrt{r^{2} +h^{2} }[/tex]
Which equation can be used to find the unknown length, b, in this triangle?
Answer:
use pythagorean theorem
Step-by-step explanation:
a^2+b^2=c^2
Answer:
4²+b² = 5²
Step-by-step explanation:
got it right on edge
Simplifty (x - 4)(x +8)
Answer: x² + 4x - 32
Step-by-step explanation: So to multiply these two binomials together, let's use the F.O.I.L. method.
Remember, F.O.I.L. stands for First, Outter, Inner, Last.
This is because we start with the product of the first terms which is x², then we add the product of the outer terms which is 8x, then we add the middle terms which is -4x, and then we add the product of the last terms which is -32.
So we have x² + 8x + -4x + -32.
Combining the like terms 8x + -4x, our final answer is x² + 4x - 32.
A bag contains 4 red marbles, 3 blue marbles and 2 green marbles. If two marbles are drawn out of the bag, what is the probability, to the nearest 10th of a percent, that both marbles drawn will be red?
The probability of drawing two red marbles is approximately 16.7%.
Explanation:To find the probability of drawing two red marbles from the bag, we need to find the probability of drawing one red marble and then, given that the first marble was red, drawing another red marble. The probability of drawing a red marble on the first draw is 4/9 (since there are 4 red marbles out of a total of 9 marbles). After the first marble is drawn, there are now 8 marbles left in the bag, including 3 red marbles.
Therefore, the probability of drawing a red marble on the second draw, given that the first marble was red, is 3/8. To find the probability of both events occurring, we multiply the probabilities: (4/9) × (3/8) = 1/6, or approximately 16.7%.
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The probability of drawing 2 red marbles without replacement from a bag containing 4 red, 3 blue, and 2 green marbles is 16.7%.
Explanation:The question is asking for the probability of drawing two red marbles from a bag that contains 4 red marbles, 3 blue marbles, and 2 green marbles, without replacing the first one drawn.
Firstly let's figure out the total number of ways to draw 2 marbles from a bag of 9 marbles. Using combination formula, the total number of possible ways is: 9C2 = 36.
Now, how many ways can you draw 2 red marbles from 4? That will be: 4C2 = 6 ways.
So the probability of drawing 2 red multiplies, without replacement, is therefore 6 / 36 = 0.167 or 16.7% when rounded to the nearest tenth of a percent.
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Find the volume. *
30 ft
.
24 ft
Volume =
Trevor spent $27 and now has no money left. He had ____ before his purchase
Answer:
%27
Step-by-step explanation:
Answer:
27%
Step-by-step explanation:
-8x - 1= -25 Thanks for the help guys!
Answer:
x=3
Step-by-step explanation:
-8x - 1= -25
Add 1 to each side
-8x-1+1 = -25+1
-8x = -24
Divide each side by -8
-8x/-8 = -24/-8
x = 3
Answer:
X=3
Step-by-step explanation:
-8x-1=-25
-8x =-24
-24/-8=3
What is the value of k for the inverse variation
function?
k=
DONE
Answer:
19,800
Step-by-step explanation:
Answer:
k=19800
k represents the number of gallons of water needed to fill the pool
third is y=19800/x
Step-by-step explanation:
The circumference of a great circle of a sphere is 44π. Find the Surface Area of the sphere.
Answer:
1936 π square units
Step-by-step explanation:
Given the information:
The circumference of a great circle of a sphere is 44π.
As we know the formula used to find a circle's circumference is:
C = 2πr , where r is the radius of the circle
In this situation, we know C = 44π
<=> 2πr = 44π
<=> r = 22 units
Hence, the Surface Area of the sphere
S.A = 4π[tex]r^{2}[/tex]
= 4π[tex]22^{2}[/tex]
= 1936 π square units
What is the third quartile of this data set?
20, 21, 24, 25, 28, 29, 35, 37, 42, 43, 44
Answer:
You should get 42
Step-by-step explanation:
In the picture I sent you, to find quartile 1 and 3 and the median use the order you have and slash out from the left and the right, if you don't get 2 numbers that you have to add and divide by 2 for the median you have to make lines outside of the middle number and slash on each side to get quartile 1 and quartile 3. Quartile 2 is the median.
The third quartile of the data set is, 42.
What is Ascending order?The numbers arrange in order to least to greatest number is called Ascending order.
Now, For the third quartile of the data set, we first need to find the median, which is the second quartile.
Hence, We can ordering the data set in ascending order:
20, 21, 24, 25, 28, 29, 35, 37, 42, 43, 44
Here, The median is the middle number or the average of the two middle numbers if the data set has an even number of values.
In this case, we have 11 values, so the median is the 6th value, which is 29.
And, we need to find the third quartile, which is the median of the upper half of the data set. The upper half of the data set includes the values:
35, 37, 42, 43, 44
The median of these values is the third quartile.
Hence, take the middle value or the average of the two middle values if there is an even number of values in the upper half.
In this case, there are 5 values in the upper half,
Hence, the median is the 3rd value,
⇒ 42.
Therefore, the third quartile of the data set is, 42.
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What is bigger 0.2 or 0.125
Answer:
0.2 is bigger than 0.125.