A planet follows an elliptical path described by 256 x squared plus 16 y squared equals 4096.256x2+16y2=4096. A comet follows the parabolic path y equals x squared minus 16.y=x2−16. Where might the comet intersect the orbiting planet?
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.
triangle fgh is a right triangle? true or false
Answer:true
Step-by-step explanation:
Answer:
on ilearn i answered true and it was wrong. so the answer is false!
Step-by-step explanation:
ilearn
An album sells for $14.00 through an online music service. If the album is 30% off, and sales tax is 6%, what is the total price of the album including tax?
Answer:
10.39 dollars.
Step-by-step explanation:
14 times 0.7 equals 9.8 dollars. Then, multiply 9.8 with 1.06 and you get 10.388 or 10.39 Hope this helps!
The radius of a circle is 21 in. What is the precise distance around the circle?
Answer:
IT IS REALLY 31
Step-by-step explanation:
Find all real square roots of -121.
The real square roots of -121 are ±11i, where 'i' represents the imaginary unit.
Explanation:When dealing with square roots of negative numbers, it's important to recognize that the square root of a negative number is an imaginary number. In this case, the square root of -121 is found by taking the square root of the positive value of 121 and then multiplying the result by 'i'. The square root of 121 is 11, so the square root of -121 becomes ±11i.
In the context of real numbers, square roots of negative values do not exist. However, in the realm of complex numbers, the introduction of the imaginary unit 'i' allows for the representation of square roots of negative numbers. The number 'i' is defined as the square root of -1. When squared, 'i' multiplied by itself yields -1.
Hence, the square root of -121, which is a negative number, results in ±11i, representing two imaginary numbers with opposite signs. These imaginary square roots are crucial in various fields, including mathematics, physics, and engineering, where complex numbers play a significant role in modeling and solving problems involving quantities with both real and imaginary components.
A cylinder has a volume of 315x cubic meters and a height of 21 meters. What is the area of the base?
15x square meters
18x square meters
294x square meters
o 6,615x square meters
15x quare meters.
V = π r2 h
2.1857 as r
21 Goves about 315 x cubic meters.
Area of a circle with 2.1857 as radius is around 15.
Which gives you 15x square meters.
Please halp me with both!
Answer:
See below
Step-by-step explanation:
I see the term 2x being repeated 5 times, and repeated addition is multiplication, so we can do 5(2x) to get 10x, and we can set that equal to 11 to get 10x=11. Dividing both sides by 10 gets us x=11/10 or x=1.1
An experiment consists of randomly drawing a cube from a bag containing three red and two blue cubes What is the sample space of this experiment
Answer:
{Red,Blue}
Step-by-step explanation:
Since the experiment consists of randomly drawing just a cube from a bag containing three red and two blue cubes, the outcome could be either a red or blue cube. Therefore the sample space is:
{Red,Blue}
Find the volume of the composite figure. Round to the nearest tenth. The base of each pyramid is a square with a side length of 5 inches and each pyramid has a height of 9 inches.
Answer:
[tex]75[/tex] cubic inches
Step-by-step explanation:
Given:
The base of each pyramid is a square with a side length of 5 inches
Height of of pyramid is 9 inches.
To find: volume of the pyramid
Solution:
As the base of each pyramid is a square with a side length of 5 inches,
length of the pyramid (l) = base of the pyramid (b) = 5 inches
Height of of pyramid (h) = 9 inches
Volume of the pyramid [tex](V)=\frac{lbh}{3}[/tex]
On putting values of l, b and h, we get
[tex]V=\frac{5\times 5\times 9}{3}=75[/tex] cubic inches
Given that the measure of ∠x is 73°, and the measure of ∠y is 40°, find the measure of ∠z.
Hi,
In a triangle, all angles must add up to 180*.
73 + 40 = 113
180 - 113 = 67
Thus, the measure of Z is equal to 67
A certain television is advertised as a 45-inch TV (the diagonal length). If the width of the TV is 36 inches, how many inches tall is the TV?
The TV is 27 inches tall.
Step-by-step explanation:
Given,
The diagonal length of the TV = 45 in
The width of the TV = 36 in
To find the length the the TV.
Formula
By Pythagoras theorem,
h²=l²+b², where h be hypotenuse, b be base and l be height.
Now,
Putting, h=45, b= 36 we get,
45²=l²+36²
or, l²= 45²-36²
or, l²= 729
or, l = √729
or, l = 27
Hence,
The TV is 27 in tall.
what's the answer to this ?
Answer:
x = 13.1°
A is correct answer
Step-by-step explanation:
Given Data:
Angle = ∅ = 24°
Base = b = 12
To find out:
Hypotenuses = x = ?
Formula:
Cos∅ = Base/Hypotenuses
Cos∅ = b/x
x = b/Cos∅
Solution:
x = b/Cos∅
x = 12/Cos(24°)
x = 12/0.91
x = 13.1°
4. At the grocery store, Terry weighed his
apples on the scale. They weighed 4.3
pounds. When he went to the register, he
was charged $8.56. How much did Terry
pay per pound of apples?
A $0.99 per pound
B $1.49 per pound
C, $2.09 per pound
D $1.99 per pound
Answer:
D.$1.99 per pound
Step-by-step explanation:
$8.56 ÷ 4.3= 1.990697674
round answer to 1.99
Answer:
D. $1.99 per pound
Step-by-step explanation:
Divide the price of the apples by how much they weigh to find the unit price
price/weight
8.56/4.3=1.99069767
So, he paid about $1.99 per pound of apples
Hope this helps!
Sammy is laying brick in his front walkway. The rectangular path measure 3/5 of a foot by 4/9 of a foot. What is the area of space that will be covered with bricks
Answer: 4/15ft2
Step-by-step explanation:
Area of a rectangle is
Length ×breadth
Length is 3/5
Breadth is 4/9
Area = length × breadth
Area= 3/5×4/9
Area=12/45
Divide both the numerator and denominator by 3
We have
Area= 4/15ft2
Mr. Z constructs a cube with 512 magnetic blocks. Students in his two classes will each make an identical cube. There are 28 students in one class and 25 students in the other class. How many blocks does he need for all his students?
Need help and steps
Write the sentence as an equation. The product of r and 338 plus 97 is the same as r.
Answer:
Step-by-step explanation:
To write this sentence as equation
We get
r×338+97=r
338r+97=r
To solve further
r-338r=97
-337r=97
r=-0.2878
The given sentence can be written as the equation: 338r + 97 = r. By following the steps to identify the product, add 97, and set the expression equal to r, we achieve the correct equation. This equation can now be solved for r.
To translate the sentence into an equation, follow these steps:
Identify the key components: product of r and 338 can be written as 338r.Add 97 to this product, which gives 338r + 97.This expression is the same as r, yielding 338r + 97 = r.Therefore, the equation representing the given sentence is 338r + 97 = r.
Find the volume of the sphere.
Either enter an exact answer in terms of r or use
for T.
unite 3
Answer:
[tex]\frac{1}{48} \pi[/tex] units cubed
Step-by-step explanation:
The volume of a sphere is: [tex]\frac{4}{3}\pi r^{3}[/tex]
We know the radius r = 1/4, so we just plug this into the equation:
(4/3)*[tex]\pi[/tex]*(1/4)^3 = (4/3)*[tex]\pi[/tex]*(1/64) = [tex]\frac{1}{48} \pi[/tex]
So, the answer is [tex]\frac{1}{48} \pi[/tex] units cubed.
Answer:
Step-by-step explanation:
[tex]volume=\frac{4}{3} \pi r^3\\=\frac{4}{3}\pi (\frac{1}{4} )^3\\=\frac{\pi }{48} ~units^3[/tex]
Thomas wrote the expanded form of (Five-halves) Superscript 4 below.
Five-halves + five-halves + five-halves + five-halves
Which statement is true?
Thomas wrote the expanded form correctly.
Thomas should have multiplied 5 times 4.
Thomas should have multiplied the base by itself four times.
Thomas should have multiplied the exponent by 5.
The answer is Thomas should have multiplied the base by itself four times
Answer:
c
Step-by-step explanation:
i did it on my test and got it correct
What method would you choose to solve the equation 2x^2-7=9? Explain why you chose this method
Answer:
PEMDAS
Step-by-step explanation:
parenthesis, exponents,multiplication,division,additon,substraction, these are the steps in order to follow when solving equations.
What information did Sebastian use in his deduction?
O
The table does not show a vertical asymptote.
The table shows two y-intercepts and it changes from increasing to decreasing,
The table shows one x-intercept and one y-intercept.
The table shows two x-intercepts and it changes from increasing to decreasing.
The correct option is D.
Sebastian use in his deduction the table shows two x-intercepts and it changes from increasing to decreasing.
CONCULSION-The curve is definitely not logarithmic because it has two x-intercepts.The curve will cut the x-axis at two points and hence, it will have two x-intercepts.There is no sign of any y-intercept based on the data available in the table.
Therefore, the conclusion is made using the information "the table shows two x-intercepts and it changes from increasing to decreasing".
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Sebastian used the information 'The table shows two x-intercepts and it changes from increasing to decreasing' for his deduction. This could suggest that he might be dealing with a quadratics or an inverted expressive function.
Explanation:Based on the choices provided, it appears that Sebastian used the information that 'The table shows two x-intercepts and it changes from increasing to decreasing' in his deduction. An x-intercept in a function table happens where the y-value equals zero. Two x-intercepts imply that there are two points where the function crosses the x-axis. A function's pattern shifting from an increasing pattern to a decreasing pattern is indicative of a maximum point. This suggests that Sebastian may be working with a quadratics or an inverted expressional function.
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While at a bakery, Chad decides to purchase some cupcakes and brownies to share with his friends. He can spend no more than $13, and the bakery charges $3 for a cupcake and $2 for a brownie. Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.
x = the number of cupcakes
y = the number of brownies
Answer:
13 divided by 6
Step-by-step explanation:
Final answer:
The situation where Chad is buying cupcakes and brownies with a budget of $13 is represented by the inequality 3x + 2y ≤ 13, where x is the number of cupcakes and y is the number of brownies.
Explanation:
To express Chad's purchasing situation at the bakery within his budget constraint in inequality form, we need to consider the cost per cupcake and brownie and how many of each he can buy without exceeding his budget of $13. Given that a cupcake costs $3 and a brownie costs $2, the inequality in standard form will reflect the price of each item multiplied by the quantity purchased.
The inequality representing this situation is 3x + 2y ≤ 13, where 'x' is the number of cupcakes and 'y' is the number of brownies. This inequality means that the total cost of cupcakes and brownies combined must not exceed $13, which corresponds to Chad's budget constraint.
An empty lot is being covered into a park with a playground area. The shape of the playground is shown below. This area will be covered with recycled rubber chips. Find the area of the figure given to determine how many square feet of rubber chips will be needed.
**SEE ATTATCHED DIAGRAM***
To solve for the area, find the area of an entire theoretical parallelogram. Then subtract the difference (the small triangle added).
Area = 1020 centimeters squared
If you need the answer in square feet, you have to convert.
(1 cm)^2 = (0.3937008 inches)^2
1 cm ^2 ≅0.155 in ^ 2 (or square inches)
A = 1020 * 0.155 ≅ 158.1 square inches
1 square inch = 0.006944444 square feet
158.1 square inches ≅ 1.097 square feet
Terry is going to make some concrete mix. He needs to mix
cement, sand and gravel in the ratio 2 . 3 : 5 by weight. He
estimates he needs to make 220 kg of concrete mix.
Terry has:
• 50 kg of cement
• 90 kg of sand
• 100 kg of gravel
Does Terry have enough cement, sand and gravel to make the
concrete mix?
Answer:
No
Step-by-step explanation:
Sum the parts of the ratio, 2 + 3 + 5 = 10 parts
Divide 220 Kg by 10 to find the value of one part of the ratio.
220 Kg ÷ 10 = 22 Kg ← value of 1 part of the ratio, thus
2 parts = 2 × 22 = 44 Kg ← quantity of cement needed
3 parts = 3 × 22 = 66 Kg ← quantity of sand needed
5 parts = 5 × 22 = 110 Kg ← quantity of gravel needed
He has the required amounts of cement and sand but not of gravel.
Thus he cannot mix the concrete
Terry requires 44 kg of cement, 66 kg of sand, and 110 kg of gravel for the concrete mix. He has enough cement and sand but is short of gravel by 10 kg, so he cannot make the complete mix with the materials he currently has.
Explanation:First, we calculate the total parts of the mix by adding the ratio numbers: 2 (cement) + 3 (sand) + 5 (gravel) = 10 parts in total. Next, we find out how much each part weighs: 220 kg ÷ 10 parts = 22 kg per part. Then we multiply the number of parts for each material by the weight per part: Cement needed = 2 parts × 22 kg/part = 44 kg, Sand needed = 3 parts × 22 kg/part = 66 kg, Gravel needed = 5 parts × 22 kg/part = 110 kg. Now, let's compare these requirements with what Terry has:
Cement: needs 44 kg, has 50 kg — enoughSand: needs 66 kg, has 90 kg — enoughGravel: needs 110 kg, has 100 kg — not enoughIn conclusion, Terry does have enough cement and sand, but he does not have enough gravel for the mix.
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What is the median for the given set of data?
{40, 54, 22, 30, 55, 13, 33}
A) 32
B) 33
C) 40
D) 42
Step-by-step explanation:
Arranging in ascending order, we get
13 , 22 , 30 , 33 , 40 , 54 , 55
no of data (N) = 7
Now Position of Median
= {(N +1 ) / 2}th item
= {(7+1) / 2 } that item
= 4 that item
So now exact median = 33
Answer:
The answer is 33
Step-by-step explanation:
By arranging the numbers in order of smallest to largest you get: ----------------> 13, 22, 30, 33, 40, 54, 55. Cross off a number from each side until you get one or two left in the middle. Cross out 13 and 55 then 22 and 54 then 30 and 40. Now you have 33 left in the middle, that is your median
calculate the shaded area circle a radius=6.5 circle b radius 2.3
Answer:
shaded part = 116cm² (3sf)
Step-by-step explanation:
area of larger circle:
a = πr²
= π x 6.5cm²
= 132.7322896cm²
area of smaller circle:
a = πr²
= π x 2.3cm²
= 16.61902514cm²
132.7322896 - 16.61902514 = 116.1132645
shaded part = 116cm² (3sf)
Hope this helps. :)
The shaded part of the circle is 116cm² (3sf)
How to find the shaded region?
To find a shaded region, First, take the area of the larger circle and the area of the smaller circle. Then subtract to find the shaded region.
Area of a larger circle:
a = πr²
= π x 6.5cm²
= 132.7322896cm²
Area of a smaller circle:
a = πr²
= π x 2.3cm²
= 16.61902514cm²
= 132.7322896 - 16.61902514 = 116.1132645
Shaded part = 116cm²
The area of a circle is pi times the radius squared (A = π r²).
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A certain company's main source of income is selling cloth bracelets.
The company's annual profit (in thousands of dollars) as a function of the price of a bracelet (in dollars) is modeled by:
P(x)=-2x^2+16x-24P(x)=−2x
2
+16x−24P, left parenthesis, x, right parenthesis, equals, minus, 2, x, squared, plus, 16, x, minus, 24
What bracelet price should the company set to earn this maximum profit?
Answer:8
Step-by-step explanation:
.
Answer:
2 or 6, you can type in either one.
Step-by-step explanation:
What is the difference in LATERAL surface area of the prisms shown?
Answer:
.
Step-by-step explanation:
.
Please answer this question
Answer:
A is closer to 1/2
Step-by-step explanation:
2/15 + 1/3 = ?
Make the denominator equal
2/15 + 5/15 = 7/ 15
6/7 - 1/3
MAke the denominator equal
18/21 - 7/21 = 11/21
MAke the denominator equal
147/315
165/315
Exactly half is 157.5 / 315
165 - 157.5 = 7.5
157.5 - 147 = 10.25
That means that A is closer to half
PLEASE HELP 15 POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Which set of three angles could represent the interior angles of a triangle?
A. 19 degrees, 70 degrees, 91 degrees
B.47 degrees, 12 degrees, 31 degrees
C. 50 degrees, 20 degrees, 20 degrees
D. 25 degrees, 25 degrees, 100 degrees
Answer:
(: Hey I got the answer for you its pretty simple. Its A 19, 70, 91
Step-by-step explanation:
Its A because if you add 19 + 70+ 91 you will get 180.
Answer:
A
Step-by-step explanation:
just add all the numbers together and you get 180
Find the sum of the following series
Answer:
it is 40
Step-by-step explanation:
mark brainliest?