Graph x2 + 9y2 = 25. What are the domain and range?
Someone please help me !
(Picture below)
Answers
x^2/5^2 + (3y)^2/5^2 = 1
This represent an equation of an ellipse with cente at the origin, the horizontal major axis running from -5 to 5 and vertical minor axis running from -5/3 to 5/3
The third graph is the correct answer.
Answer:
the third graph is correct.
Step-by-step explanation:
domain: -5 ≤ x ≤ 5
range: -1.67 ≤ y ≤ 1.67
Related Questions
Which number belongs to the solution set of the equation below? x - 7 = 35
A) 22
B) 28
C) 42
D) 41
Answers
A company introduces a new product for which the number of units sold S is
S(t)= 200 ( 5- 9/(2+t))
where t is the time in months
(a) Find the avg. value of S(t) during the first year.
(b) During what month does S'(t) equal the avg value during the first year? ...?
Answers
(1/(b-a)) times the integral of f from the limits x= a to x = b.
Now S = 200(5 - 9/(2+t))
The average value of S during the first year (from t = 0 months to t = 12 months) is then:
(1/12) times the integral of 200(5 - 9/(2+t)) from t = 0 to t = 12
or 200/12 times the integral of (5 - 9/(2+t)) from t= 0 to t = 12
This equals 200/12 * (5t -9ln(2+t))
Evaluating this with the limits t= 0 to t = 12 gives:
708.113 units., which is the average value of S(t) during the first year.
(b). We need to find S'(t), and then equate this with the average value.
Now S'(t) = 1800/(t+2)^2
So you're left with solving 1800/(t+2)^2 = 708.113
I'll leave that to you
Please help me
All of the following are equivalent except _____.
2%
0.2
1/50
0.02
Answers
Hope this helps
The difference between five times a number and twelve times the number is –35.
Answers
A student is running a 10-kilometer race. He runs 1 kilometer every 4 minutes. Select the function that describes his distance from the finish line.
f(x) = - 1 over 4x + 4
f(x) = - 1 over 10x + 4
f(x) = - 1 over 10x + 10
f(x) = - 1 over 4x + 10
Answers
f(
f(x) = - 1 over 4x + 10
Answer:
Option D is correct
[tex]y =-\frac{1}{4}x+10[/tex]
Step-by-step explanation:
Slope intercept form:
The equation of line is given by:
[tex]y=mx+c[/tex] .....[1]
where, m is the rate or slope and c is the y-intercept or initial value.
As per the statement:
Here, y represents the distance in kilometer and x represents the time in minutes.
A student is running a 10-kilometer race
⇒y(0) = b = 10 km
It is also given that he runs 1 kilometer every 4 minutes.
Now, with each passing minute the student is getting closer and closer to the finish line which was 10 kilometers away when the race started. Thus, as the race progresses, the distance between the student and the finish line will decrease.
[tex]m =-\frac{1}{4}[/tex]
Substitute these in [1] we have;
[tex]y = -\frac{1}{4}x+10[/tex]
Therefore, the function that describes his distance from the finish line is, [tex]y = -\frac{1}{4}x+10[/tex]
A piece of furniture has a retail price of $3,200 and is on sale at a 30% discount. how much money will be saved if the piece of furniture is purchased at the sale price?
Answers
$960 will be saved
The lengths of two sides of a triangle are 9 and 15. What can be said about the length of the third side?
It must be geater than or equal to 6 and less than 24.
It must be greater than or equal to 6 and at most 24.
It must be greater than 6 and less than 24.
It must be greater than 6 and at most 24.
Answers
Answer:
Your answer is B
As the sum of any 2 lengths of a triangle is always greater than the third length
Step-by-step explanation:
It must be greater than or equal to 6 and at most 24.
Given that
The lengths of the two sides of a triangle are 9 and 15.
We have to determine
What can be said about the length of the third side?
According to the question
The lengths of the two sides of a triangle are 9 and 15.
By the properties of the triangle, the sum of the square of two lengths is equal to the third side length of the triangle.
Always remember that when you add two sides to a triangle, the sum will come out to be higher than the third side’s length.
Hence, It must be greater than or equal to 6 and at most 24.
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7.What are the steps that you would follow to recreate a triangle using a protractor, a string, and the AAS Congruence Theorem?
Answers
ANSWER:
To construct a triangle given one side and the angle at each end of it with compass and straightedge or ruler. It works by first copying the line segment to form one side of the triangle, then copy the two angles on to each end of it to complete the triangle. Follow these steps to draw the recreate a triangle using a protector, a string and angle, angle side congruence theorem.
STEP-BY-STEP EXPLANATION:
Step 1: You will need to choose two angle and one length for both triangle. Noted that the two angle and one length must be the same for both triangle.
Step 2: Draw a long line on a paper
Step 3: Use a ruler to measure the length ,and then make a mark on the string.
Step 4: Use the string to mark on the long line.
Step 5: Use a protractor to measure
Step 6: Use AAS Congruence Theorem to prove that both triangle are congruent.
Write the trigonometric expression in terms of sine and cosine, and then simplify.
csc2 x − cot2 x
Answers
=1−cos^2(x)/sin^2(x)
=sin^2(x)/sin^2(x)
=1
your new cell phone plan charges $50 per month for 400 minutes of talk time. the plan charges $0.10 for each additional minute you talk. you use 50 additional minutes this month. what is your bill for the month?
Answers
Answer:
$55
Step-by-step explanation:
To cover A rectangle region of her yard penny needs atleast 170.5 square feet of sod. The length of the region is 15.5 feet. What are the possible widths of the region?
Answers
5,893,402 + 19,392,009 =
Answers
What is 4/5 4/5 as a mixed number fraction?
Answers
Jared wrote an equation for the perimeter of an equilateral triangle as 3x = 20. What does x represent in his equation?
Answers
x must represent the legnth of 1 side
x=20/3
Answer:
The length of a side of the triangle.
Step-by-step explanation:
An equilateral triangle has 3 equal sides so the x would be equal to one side of the triangle.
A class of 18 students took a math test. Seven students had an average of 90. The other students had an average of 82.
What is the average for the whole class? Round to the nearest whole percent.
A) 80
B) 83
C) 85
D) 87
Answers
Answer: C- 85%
Step-by-step explanation:
7x11=630
Remaining Students: 18-7=11
11x82=902
Aveage:
630+902=1532
1532/18=85.1111
77 decreased by twice of a number
Answers
The algebraic expression for '77 decreased by twice of a number' is 77 - 2x, where x is the unknown number.
Explanation:The question '77 decreased by twice of a number' involves creating an algebraic expression. This expression will have the form 77 - 2x, where x represents the unknown number. To decrease 77 by twice a number means to subtract two times that number from 77.
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which is greater 14 ounces or 0.4 kilograms
Answers
After converting 0.4 kilograms to ounces using the appropriate conversion factors, it is determined that 0.4 kilograms is slightly greater than 14 ounces.
Explanation:To determine which is greater, 14 ounces or 0.4 kilograms, we first need to use the appropriate conversion factors to compare the two measurements in the same unit. Since 1 pound is equivalent to 0.4536 kilograms, and 1 pound is also equal to 16 ounces, we need to convert one of the measures so that both are in either ounces or kilograms for a direct comparison.
Converting 0.4 kilograms to ounces:
1 kilogram is approximately 2.20462 pounds (since 1 pound is 0.4536 kg).So, 0.4 kilograms is 0.4 * 2.20462 pounds, which is approximately 0.882 pounds.Next, we convert 0.882 pounds to ounces by multiplying by the conversion factor of 16 ounces per pound: 0.882 * 16 = 14.11 ounces (approximately).Now we have both weights in ounces, and we can see that 14.11 ounces is slightly more than 14 ounces. Therefore, 0.4 kilograms is greater than 14 ounces.
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Find the number of years it would take for $1,200 to earn simple interest of $324 at an annual interest rate of 6% per year.
Answers
________
rate x principal
There are five seniors in a class. For each situation, write how the binomial formula is used to calculate the probability.
a) In how many ways can I choose one senior to represent the group?
b) In how many ways can I choose two seniors to represent the group?
c) In how many ways can I choose three seniors to represent the group?
d) In how many ways can I choose four seniors to represent the group?
e) In how many ways can I choose five seniors to represent the group?
Answers
nCr = n! / (r! (n - r)!)
n - number of things to be chosen from
r - number of chosen things
There are five seniors in a class: n = 5
I choose one senior: r = 1
nCr = n! / (r! (n - r)!)
5C1 = 5! / (1! (5 - 1)!)
= (5 * 4 * 3 * 2 * 1) / (1 * 4!)
= 120 / (4 * 3 * 2 * 1)
= 120 / 24
= 5
b) The answer is 10.
nCr = n! / (r! (n - r)!)
n - number of things to be chosen from
r - number of chosen things
There are five seniors in a class: n = 5
I choose two seniors: r = 2
nCr = n! / (r! (n - r)!)
5C2 = 5! / (2! (5 - 2)!)
= (5 * 4 * 3 * 2 * 1) / ((2 * 1) * 3!)
= 120 / (2 * (3 * 2 * 1))
= 120 / (2 * 6)
= 120 / 12
= 10
c) The answer is 10.
nCr = n! / (r! (n - r)!)
n - number of things to be chosen from
r - number of chosen things
There are five seniors in a class: n = 5
I choose three seniors: r = 3
nCr = n! / (r! (n - r)!)
5C3 = 5! / (3! (5 - 3)!)
= (5 * 4 * 3 * 2 * 1) / ((3 * 2 * 1) * 2!)
= 120 / (6 * (2 * 1))
= 120 / (6 * 2)
= 120 / 12
= 10
d) The answer is 5.
nCr = n! / (r! (n - r)!)
n - number of things to be chosen from
r - number of chosen things
There are five seniors in a class: n = 5
I choose four seniors: r = 4
nCr = n! / (r! (n - r)!)
5C4 = 5! / (4! (5 - 4)!)
= (5 * 4 * 3 * 2 * 1) / ((4 * 3 * 2 * 1) * 1!)
= 120 / (24 * 1)
= 120 / 24
= 5
e) The answer is 1.
nCr = n! / (r! (n - r)!)
n - number of things to be chosen from
r - number of chosen things
There are five seniors in a class: n = 5
I choose five seniors: r = 5
nCr = n! / (r! (n - r)!)
5C5 = 5! / (5! (5 - 5)!)
= (5 * 4 * 3 * 2 * 1) / ((5 * 4 * 3 * 2 * 1) * 1!)
= 120 / (120 * 1)
= 120 / 120
= 1
Solve for x.
x/7 = -3
1,) x = -21
2.) x = -10
3.) x = 4
4.) x = 21
Answers
There are 13 fish in an aquarium. seven of the fish are guppies. how many non-guppies are in the aquarium
Answers
Karina uses the system of equations below to compare the monthly utility costs in July and December for electricity, x, and natural gas, y.
750x + 17y = 141.61
300x + 30y = 75.90
Karina solves the system using linear combination and arrives at the equation 116y = 96.28. She then solves this equation for y. Which statement explains Karina’s solution?
a. The cost of electricity is $0.17 per unit.
b. The cost of natural gas is $0.20 per unit.
c. The cost of electricity is $0.72 per unit.
d. The cost of natural gas is $0.83 per unit.
Answers
D: The cost of natural gas is $0.83 per unit.
Answer:
Option d is correct
The cost of natural gas (y) = $0.83 per unit
Step-by-step explanation:
Given the system of equation:
750x + 17y = 141.61 ......[1]
300x + 30y =75.90 ......[2]
where x is the cost of electricity and y is the costs of natural gas.
Multiply equation [1] by 30 and equation [2] by 75 we get;
[tex]30 \cdot (750x + 17y) = 30 \cdot 141.61[/tex]
Simplify:
22500x + 510y = 4248.3 ......[3]
[tex]75 \cdot (300x + 30y) = 75 \cdot 75.90[/tex]
Simplify:
22500x + 2250y = 5692.5 .......[4]
Subtract equation [3] from [4] we get;
1740 y = 1444.2
Divide by 15 both sides, we get
116 y = 96.28
Since, Katrina solves the above system using linear equation and arrives at the equation :
116 y = 96.28
Division property of equality states that divide the same number to both sides of an equation:
Divide by 116 to both sides of an equation, to solve for y;
[tex]\frac{116 y}{116} =\frac{96.28}{116}[/tex]
Simplify:
y = 0.83 where y represents the cost of natural gas
Therefore, the cost of natural gas y ,is, $ 0.83 per unit.
What is the unit rate of 50.4 feet in 14 years?
Answers
A rectangle's length is 4 feet more than its width. If the area of the rectangle is 396 square feet, what is its width, in feet?
Answers
l = w + 4
Area = length x width
396 = (w + 4)w
w² + 4w - 396 = 0
w = 18, w = -22
Negative width not possible so answer discarded.
Width = 18 feet.
After 3 years, what is the total amount of a compound interest investment of $5,000 at 4% interest, compounded quarterly?
$5,203.71
$5,360.68
$20,480,000
$5,634.13
Answers
Given that f(x) = 6x 2 and g(x) =2x=4/5 , solve for g(f(1))
Answers
Answer:
The answer would be 4.
Step-by-step explanation:
What you have to do here is you have to substitute
So the problem told you the f(x) = 1. So what you want to do is plug that into the function f(x).
So:
f(x) = 6(1)2
= 8
Now we know that f(x) = 8, so what we going to do now is plug f(x) into g(x).
So:
g(f(8)) = 2(8) + 4/5
= 4
The value of g(f(1)) is 4.
Composite function -Composition of functions is the process of plugging one function into another, and simplifying or evaluating the result at a given x-value. Another way to read it is "f circle g of x." It is a process that joins two functions to create a third, unique function.Given ,
f(x) = 6x + 2
g (x) = 2x + 4 /5
To get value of g(f(1)) first we have to solve f(x).
f(x) = 6x + 2 .......................(1)
We simply put x = 1 in equation 1 .
Then, F(1) = 6 × 1 + 2 ⇒ 8
Now , we put value of f(1) in g(f(1)) ,
So, g(f(1)) = [tex]\frac{2x + 4}{5}[/tex]
= [tex]\frac{2 * 8 + 4}{5}[/tex]
= [tex]\frac{16 + 4}{5}[/tex]
= 20/5 ⇒ 4
Therefore, the value of g(f(1)) is 4 .
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21. The Johnsons framed a family picture to hang on the wall. The perimeter of the frame is 72 inches. Use the formula P = 2 l + 2 w to find the length of the frame if the width is 14 inches. 21. The Johnsons framed a family picture to hang on the wall. The perimeter of the frame is 72 inches. Use the formula P = 2 l + 2 w to find the length of the frame if the width is 14 inches.
Answers
72 = 2l + 2(14) = 2l + 28
2l = 72 - 28 = 44
l = 44/2 = 22 inches.
Given that the perimeter of the frame is 72 inches and the width is 14 inches, we are going to look for the length. The formula for perimeter is 2L + 2W.
So let us substitute the values.
P = 2L + 2w
72 = 2L + 2(14)
72 = 2L + 28
72 -28 = 2L
44 = 2L <<<divide both sides by 2
22 = L
So the length of the picture frame is 22 inches.
To check, 22 in x 2 is 44 inches + 14 x 2 is 28 inches. 28 + 44 is 72 inches.
Hope this answer helps. Thanks for posting your question.
simplify please I need help don't get it
Answers
How many times does 59 go into 295?
Answers
Then answer equal 5
5
So 59 goes into 295 5 times.
How many regions would a net for a three-dimensional solid like the one shown have?
Answers
Which brings us with total of 8 regions. 2 bases and 6 sides
Answer:
A
Step-by-step explanation: