Final answer:
To find the intersection points of the comet and the planet's orbits, we need to solve the system of equations formed by their respective path equations.
Explanation:
To find where the comet might intersect the orbiting planet, we need to find the common points between the equation of the planet's elliptical path and the equation of the comet's parabolic path.
By substituting the expression for y in the equation of the planet into the equation of the comet, we get 256x^2 + 16(x^2 - 16) = 4096.
Simplifying this equation and solving for x will give us the x-coordinates where the comet may intersect the planet's orbit. Substituting these x-values back into either the planet's or comet's equation will give us the corresponding y-coordinates.
A rectangle has a height of 7 and a width of 2x² –3. Expression should be expanded
14x^2 -21
[tex]width: 2x^2-3\\height:7\\S=7(2x^2-3)\\S=14x^2-21[/tex]
2 (r - 3) - 5(r + 2)
Answer:
-3r -16
Step-by-step explanation:
2 (r - 3) - 5(r + 2)
Distribute
2r-6 - 5r - 10
Combine like terms
-3r -16
what is the point-slope form of a line thats has a slope of-4 and passes through point (-3,1)
Answer:
y - 1 = -4(x+3)
Step-by-step explanation:
We will use the point slope form of a line
y-y1 = m(x-x1) where m is the slope and (x1,y1) is the point
y - 1 = -4(x--3)
y - 1 = -4(x+3)
Which two angles are supplementary?
There are only two angle measures here, an angle, a bunch of congruent copies, and its supplement, with a bunch of congruent copies.
∠1 ≅ ∠3 ≅ ∠5 ≅ ∠7 are all supplementary to ∠2 ≅ ∠4 ≅ ∠6 ≅ ∠8
When renting a limo for prom, the number of people varies inversely with the cost per person. Originally there were 12 people and the cost per person was $20. If the number of people changed to 6, what would be the new cost per person?
Answer:
40
Step-by-step explanation:
PLEASE help????????????
Answer:
A:(2m^4n^3)^3(5m^4n^3)^2
Step-by-step explanation:
The perimeter of a rectangle is represented by the expression 6x + 4. If the width of the rectangle is represented by the expression x – 1, which expression represents the length?
Divide the perimeter by 2:
6x + 4 / 2 = 3x+2
This is one length plus one width.
Now subtract the width to find the length:
3x +2 - x-1 = 2x+ 3
Length is 2x+ 3
Answer:
2x+3 or C
edge2021
1. In a small town, there are 83 clinics serving the population of 24,742. Each clinic serves
about __________ of the town’s population.
a. 200 b. 250 c. 300
Answer:
each clinic serves about 300 people
Step-by-step explanation:
Population of 24742 is served by 83 clinics
Then each clinic will serve
24742/83 =298.157
≈ 300
Answer:
c. 300
Step-by-step explanation:
24,742/83
298.0963855
Approximately 300
Ana's class packs lunches for the local shelter. They make the same number of sandwiches each minute. In 5 minutes, the class makes 20 sandwiches. At this rate, how many sandwiches does the class make in 32 minutes?
Answer: 128
Step-by-step explanation:
Part C: YX = 24 meters and mYX = 120 degrees , then determine the radius of circle H.
Answer: The radius is 11.5 meters (to the nearest tenth)
Step-by-step explanation: The circle with center H has an arc TX that measures 24 meters, and also the angle subtended by YX equals 120°.
The length of an arc is given b the formula;
Length of arc = (∅/360) x 2πr
Where the length of the arc is 24 and ∅ is 120, the formula becomes;
24 = (120/360) x 2(3.14) r
24 = (1/3) x 6.28 r
By cross multiplication we now have,
(24 x 3)/6.28 = r
72/6.28 = r
11.4649 = r
r ≈ 11.5
Therefore, the radius is approximately 11.5 meters
a triangle has an area of 16 feet squared and a height of 4 ft. finds its base
Answer:
Base = 8 feet
Step-by-step explanation:
[tex]area \: of \: \triangle = \frac{1}{2} \times base \times height \\ 16 = \frac{1}{2} \times base \times 4 \\ 16 = base \times 2 \\ base = \frac{16}{2} \\ base = 8 \: feet[/tex]
how to factor 15x-7x-2
Solve simultaneous equation
X-2y=1
2x-y=2
Answer: x=1,y=0
Step-by-step explanation:
X-2y=1.....equation 1
2x-y=2.....equation 2
X=1+2y.......equation 3
Substitute equation 3into 2
2(1+2y)-y=2
2+4y-y=2
2+3y=2
3y=2-2
3y=0
Y=0/3
Y=0
Substitute for y=0 in equation 1
X-2y=1
X-2(0)=1
X-0=1
X=1
X=1 & Y=0
Answer:
x=1
y=0
Step-by-step explanation:
On a map, 1 inch equals 5 miles. Two cities are 8 inches apart on the map.
Answer:
The distance in miles that the cities are apart is 40 miles
Step-by-step explanation:
To get from 1 inch to 8 inches, you multiply by 8. This means you multiply 5 miles by 8 to get 40 miles.
Answer:40 miles
Step-by-step explanation:
because 1 inch is 5 miles and the cities are 8 miles apart so 8x5=40.
ILL MARK THE MOST BRAINLIEST!!!
Given the equation square root of quantity 3x minus 2 end quantity equals 4, solve for x and identify if it is an extraneous solution.
6; solution is extraneous
6; solution is not extraneous
two thirds; solution is extraneous
two thirds; solution is not extraneous
Answer:
6; solution is not extraneous
Step-by-step explanation:
[tex]\sqrt{3x-2} =4[/tex]
[tex](\sqrt{3x-2})^{2} = (4)^2[/tex]
[tex]3x-2= 16[/tex]
[tex]3x = 18[/tex]
[tex]x =6[/tex]
[tex]\sqrt{3(6)-2}=4[/tex]
[tex]\sqrt{18-2}=4[/tex]
[tex]\sqrt{16} =4[/tex]
[tex]4=4[/tex]
6; solution is not extraneous
because 4 is equal to 4, an extraneous answer would be the correct answer given, however when you plug it into the equation it is not equal
Which of the following is a solution to the inequality below?
10 − 12p > 41
A. p=12
B. p=7
C. p=11
D. p=-11
Answer:
The solution is D, -11.
Step-by-step explanation:
On Your Own
phone store makes $15 per hour plus a commission
cales This week she sold 40 phones averaging $450
4. An employee at a cell phone store makes $15
of 2.5% of her phone sales. This week she sold
each. What is her commission this week?
(i need the explanation)
An employee at a cell phone store sold 40 phones for $450 each, totaling $18,000 in sales. Based on her commission rate of 2.5%, she earns $450 in commission for the week.
Explanation:The subject of this question is how to calculate the employee's commission based on her sales. First, we need to calculate the total sales the employee made. She sold 40 phones at $450 each, so her total sales would be 40 * $450 = $18,000.
Next, we need to figure out what 2.5% of her total sales is because this is her commission rate. The calculation would be $18,000 * 2.5/100 = $450.
So, the employee's commission for this week is $450.
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find the missing angle. x=?
Answer:
Here we can see they are vertically opposite angles so x = 35°
x=35
bcoz they are vertically opposite angles.
As we know vertically opposite angles are equal.
A code on a student ID card begins with 3 letters and ends with 5 digits. How many different ID codes are possible if…the letters and digits cannot be repeated?
Answer:
The total number of combinations is 2,358,720,000
Step-by-step explanation:
For the letter part of the ID we have 3 letters out of a space of 26 possible letters (a-z), and they can't repeat. For the number part we want to group 5 numbers out of 10 possible algarisms (0-9).So we can make an arrangement for the letters and one for the numbers and multiply them. The arrangment can be done using the following formula:
A(n,k) = (n!)/(n-k)!
Where n is the total number of possibilities and k is the size of the group.
For the letters:
A(26,3) = (26!)/(26-3)! = (26!)/(23!) = (26*25*24*23!)/(23!) = 26*25*24 = 15600
For the numbers:
A(10,5) = (10!)/(10 - 5)! = 10!/5! = (10*9*8*7*6*5!)/(5!) = 10*9*8*7*6*5 = 151200
The total number of combinations is the product of both, so:
combinations = 15600*151200 = 2,358,720,000
2^5x=6 rounded to the nearest hundredth
I think that the answer would be 0.52 if you round it
Yo girl needs help please
Answer:
13
Step-by-step explanation:
f(x) = 10/2 + 8 = 5 + 8 = 13
Look at the attached picture⤴
Hope it will help u...
please help I am very confused xD
There are 3 red out of 7 total so red will be 3/7
There are 4 blue out of 7 total so blue will be 4/7
After he picks one he puts it back so every red will be 3/7 and every blue will be 4/7
B) multiply the probability of picking a red one by the probability of picking a red one again:
3/7 x 3/7 = 9/49 probability of picking 2 red ones.
A rectangle is dilated by a scale factor of n = 1. Which statement is true regarding the image of the dilation?
Answer:
The image will be congruent to the pre-image because n = 1.
Answer:
Awsner number 2
Step-by-step explanation:
Which of these equations have no solution? Check all that apply.
2(x + 2) + 2 = 2(x + 3) + 1
2x + 3(x + 5) = 5(x – 3)
4(x + 3) = x + 12
4 – (2x + 5) = (–4x – 2)
5(x + 4) – x = 4(x + 5) – 1
Answer: 2(x + 2) + 2 = 2(x + 3) + 1
Steps:
2x + 6 = 2x + 7
Subtract 6 from both sides
2x + 6 - 6 = 2x + 7 - 6
Simplify
2x = 2x + 1
Subtract 2x from both sides
2x - 2x = 2x + 1 - 2x
Simplify
0 = 1
The sides are not equal.
NO SOLUTION
Answer:
1, 2, and 5
Step-by-step explanation:
LAST PROBABILITY QUESTION!!:
Whoever gets correct, will get marked brainliest!
Answer:
7/21
Step-by-step explanation:
Answer:
1/729
Step-by-step explanation:
Just multiply 3 for the amount of rounds there are (6) so 3^6 is equal to 729
Express 80 as a product of prime numbers
Answer:
2 * 2 * 2 * 2 * 5
Step-by-step explanation:
Answer:
2^4*5 OR 2*2*2*2*5
Step-by-step explanation:
using prime factorization
factors of 80 are 10*8 then factor 8 and 10 and so on until you are left with all prime numbers.
Hope this helps!
A radioactive isotope, selenium, used in the creation of medical images of the pancreas,
has a half-life of 119.77 days. If 100 milligrams are given to a patient, how many milligrams
are left after 20 days?
7.
The Lualailua Hills Quadrangle of the East Maui (Haleakala) volcano on the island of
Maui in Hawaii is no longer active. To find out the date of the last eruption, scientists
conducted a chemical analysis of samples from the volcano area. The samples
contained approximately 62.31% of its original carbon-14. How long ago was the last
eruption of the volcano? (Use 5730 years for the half-life of carbon-14.)
Answer:
First problem: 89.07 grams
Second problem: 3910.15 days
Step-by-step explanation:
We can solve these problems with the exponencial equation:
P = Po * (1+r)^t
Where P is the final value, Po is the inicial value, r is the rate and t is the time.
In the first problem, the half-life is 119.77 days and Po = 100, so we have that:
P = 100 * (1-0.5)^(t/119.77)
So after 20 days, we will have:
P = 100 * (1-0.5)^(20/119.77) = 89.07 grams
For the second problem, we have the half-life of 5730 days, and the final value over the inicial value is 62.31%, so:
P/Po = (1-0.5)^(t/5730)
0.6231 = 0.5^(t/5730)
log(0.6231) = log(0.5^(t/5730))
-0.4730 = (t/5730)*log(0.5)
-0.4730 = (t/5730)*(-0.6931)
(t/5730) = 0.6824
t = 0.6824 * 5730 = 3910.15 days
Using the formula for half-life calculation, approximately 82.57 milligrams of Selenium left after 20 days. Based on the amount of Carbon-14 left, the last eruption of the volcano occurred approximately 3896 years ago.
Explanation:The calculation of remaining amount of a given isotope relies on the understanding of what is called a half-life. In the case of selenium, with a half-life of 119.77 days, we are looking at 20 days had passed. This would be a fraction of the half-life (20/119.77 = 0.167). The amount left can be calculated by the formula N = N0 * (1/2)^(t/T), where N is the final amount, N0 is the initial amount, t is the elapsed time, and T is the half-life. This becomes 100 * (1/2)^(0.167) which results in approximately 82.57 milligrams of Selenium left.
For the interval of carbon-14 relating to the volcano eruption using a half-life of 5730 years, we know from the sample that 62.31% of the original amount remains. This relates to 0.623 as the fraction of half life that has passed. Using the formula log2(1/0.623) we get approximately 0.68 half-lives. From this, we can find the time passed, which is half-life times the number of half-lives. This results in 5730 * 0.68 = approximately 3896 years ago for the last eruption.
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What is the exact area of a circle with a radius of 12 ft
Answer:
The area is approximately 453 ft²
Step-by-step explanation:
Area of a circle = [tex]\pi r^{2}[/tex]
If [tex]\pi[/tex] = 22/7, and r = 12 ft
Area = (22/7)×12²
= 3.143*144
= 452.592 ft²
≈ 453 ft²
1) If 3 out 5 students play sports at school, how many students play
sports if there are 720 students?
Answer:
432
Step-by-step explanation:
On a coordinate plane, a circle is centered at (5,5) and a triangle is centered at (-3,5). What is the distance between the centers of the circle and triangle?
The shapes don't really play a role in this story, do they. Both points are on the horizontal line y=5 so the distance between them is the absolute difference of the x coordinates, 5- -3 = 8
Answer: 8
The distance between the centers of the circle and triangle is 8.
What is the distance between two points of a line?The distance between two points of a line is given as:
Distance = [tex]\sqrt{(c - a)^2 + (d - b)^2}[/tex]
Where (a, b) and (c, d) are the two points.
We have,
The centre of a circle = (5, 5)
The centre of a triangle = (-3, 5)
Consider (a, b) = (5, 5) and (c, d) = (-3, 5)
The distance between the centre of a circle and the centre of the triangle.
= √(-3 - 5)² + (5 - 5)²
= √(64 + 0
= √64
= 8
Thus,
The distance between the centres is 64.
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