We know, equation of ellipse is given by :
[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex]
Here,
(h,k) is centre of the ellipse = (0,0).
a = major axis = 8.
b = minor axis = 4.
Putting all given value in above equation, we get :
[tex]\dfrac{(x-0)^2}{8^2}+\dfrac{(y-0)^2}{4^2}=1\\\\\dfrac{x^2}{8^2}+\dfrac{y^2}{4^2}=1\\\\\dfrac{x^2}{64}+\dfrac{y^2}{16}=1[/tex]
Hence, this is the required solution.
[tex]f(x)=\sqrt{9+ln(x)[/tex] , find the domain
The domain of the function [tex]f(x) = \sqrt{9 + \ln(x)}[/tex] is [tex][e^{-9}, \infty)[/tex].
To find the domain of the function [tex]f(x) = \sqrt{9 + \ln(x)}[/tex], we need to determine the values of [tex]x[/tex] for which the function is defined.
The square root function [tex]\sqrt{x}[/tex] is defined only for non-negative values of [tex]x[/tex]. Therefore, in order for [tex]f(x)[/tex] to be defined, the expression [tex]9 + \ln(x)[/tex] inside the square root must be non-negative.
Let's solve this inequality:
[tex]9 + \ln(x) \geq 0[/tex]
To do this, we subtract 9 from both sides:
[tex]\ln(x) \geq -9[/tex]
Now, we can rewrite this inequality in exponential form:
[tex]x \geq e^{-9}[/tex]
For more such questions on function
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Help me with graphing
Answer:
option 3 I guess...isn't it..
If the figure has four side, opposite sides are congruent, and four right angles, then the
figure is a rectangle
True or False
Write the equation that can be used to solve for x.
7x + 7 + 4y = 112
-7 from both sides
A ball is thrown upward with an initial velocity of 60 mph. it is thrown from a height of 5 feet. what is the maximum height it reaches?
Answer:
h = 61.25 m
Step-by-step explanation:
It is given that,
The initial velocity of the ball, v = 60 m/s
It is thrown from a height of 5 feet, [tex]h_o=5\ ft[/tex]
We need to find the maximum height it reaches. The height reached by the projectile as a function of time t is given by :
[tex]h=-16t^2+vt+h_0[/tex]
Putting all the values,
[tex]h=-16t^2+60t+5[/tex] .....(1)
For maximum height, put
[tex]\dfrac{dh}{dt}=0\\\\\dfrac{-16t^2+60t+5}{dt}=0\\\\-32t+60=0\\\\t=\dfrac{-60}{-32}\\\\t=1.875\ s[/tex]
Put t = 1.875 in equation (1)
[tex]h=-16(1.875)^2+60(1.875)+5\\\\h=61.25\ m[/tex]
So, the maximum height reached by the ball is 61.25 m.
Expand and simplify the expression: 4u - 3 ( 2u - 5v) *
Answer: -2u + 15v
Step-by-step explanation:
Hey there!
Step 1: Expand by distributing terms.
4u - (6u - 15v)
Step 2: Remove parentheses.
4u - 6u + 15v
Step 3: Collect like terms.
(4u - 6v) + 15v
Step 4: Simplify.
-2u + 15v
~I hope I helped you! :)~
Answer:
Expanded: 4u-6u+15v Simplified: -2u+15v
Step-by-step explanation:
To expand, distribute the negative three to the terms in the parentheses by multiplying. Because a negative times a negative is a positive, it becomes plus 15v. To simplify, simply add like terms (the u variables).
Cory is building a model and needs 12 identical rods which are each 3/4 inch long. He wants to cut them all from the same rod. How long of a rod does he need?
What is the least number to be subtracted from 1690 to make it perfect square?
Answer:
90
Step-by-step explanation:
1600;is a perfect square as 40*40.
if we subtraction 90 from 1690 it is a perfect square..
Aaaaaaaaaaaaaaqqqqqqaaaaaaaaa help
Answer:
0.05?
Step-by-step explanation:
0.2 are taken by oarents
3/4 = 0.75 were taken by parents
0.20 + 0.75 = 0.95
1.00 - 0.95 = 0.05
Two angles are supplementary and one of them is 127° What is the size of
the other angle?
Answer:
53 degree
Step-by-step explanation:
i just subtracted it (linear pair axiom)
What is the measure of angle L?
J. 130
L.?
K.65
Answer:
m∠L = 65°
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the remote interior angles of the triangle.
130 = L + K
130 = L + 65
130 - 65 = L
65° = L
$20.80 → rounds to $
Answer:
$21.00
Step-by-step explanation:
$20.80 rounds off to $21
Let
с
be the function that gives the average cost per book
C (X)
in dollars, when using an online store to print
2x
copies of a self-published paperback book. Use the graph of
120 + 4x
C(x) =
to answer the following questions.
What is a reasonable domain for this context and explain your reasoning?
Answer:
hi or high
Step-by-step explanation:
so you right the world h and i and cobine them to make hi or high same thing
if one gallon of paint covers 825sq.ft how much paint is needed to cover 2640 sq.ft
Answer:
4 (3.2 exactly but you can't go to the store and say I want to buy 3.2 gallons of paint. They will look at you funny, So in this case you will by 4)
Step-by-step explanation:
2640/825 = 3.2 gallons
Answer:
Step-by-step explanation:
1 gallon = 825 square feet
x gallons = 2640 square feet
1/x = 825/2640 Cross multiply
825 x = 2640 Divide by 825
x = 2640/825
x = 3.2 gallons.
The 0.2 has to be rounded up (usually you would round down. That's because you have to get another gallon to paint the small area that is not covered.
So the rounded answer is 4 gallons.
pls help will give brainliest to the best answer
Answer:
x = -32/5
The equation has infinitely many solutions bc it can be rewritten as 0 = 0
Step-by-step explanation: dont forget the brainliest plz
A polynomial function g(x) with integer coefficients has a leading coefficient of 15 and a constant term of 3. According to the Rational Root Theorem, which of the following are possible roots of g(x)?
a. 1/3
b. -15
c. -5
d. 5
9514 1404 393
Answer:
a. 1/3
Step-by-step explanation:
The rational root theorem tells you possible rational roots will be of the form ...
±(factor of 3)/(factor of 15)
Which will be any of ±{1,3}/{1,3,5,15} = {±1/15, ±1/5, ±1/3, ±3/5, ±1, ±3}.
Of these, 1/3 is one of the available choices.
help. the choices are
A.y= 4x + 35
B.y= -4x - 35
C.y= -4x + 35
D.y= 4x - 35j
Answer:
so like A
he already has 35 employees which is (+35)
he gets 4 employees every month so (4x)
Out of the 20 students in Mrs. Green's class, 16 have a pet. What percent of the students in Mrs. Green's dass have a pet? The percent of students in Ms. Green's class that have a petis%.
Answer:
80%
Step-by-step explanation:
Step 1:
16 : 20 Ratio
Step 2:
16/20 Convert to a fraction
Step 3:
4/5 × 20 Simpify and Multiply
Answer:
80% Convert to percentage
Hope This Helps :)
A construction crew has just finished building a road. The crew worked for 8 days. If they built 3 5/6 kilometers of road each day, what is the total length of road they built?
Answer:
30 2/3 kmStep-by-step explanation:
Construction speed
3 5/6 km/dayTime
8 daysRoad length
8 * 3 5/6 =8 * 23/6 =92/3 = 30 2/3 kmWe are going to need to multiply to find the total length of road they built.
3 5/6 * 8
23/6 * 8/1
184/6
30.66.. or 30 2/3
Therefore, they built 30 2/3km of road.
Best of Luck!
selling price of a $17,100 truck with a 5% sales tax.
Answer:
17100 + 855tax = a total price of 17955
Step-by-step explanation:
We are required to find the selling price of a vehicle given the cost price and sales tax.
The selling price of the truck is $17,955
Given:
Cost price = $17,100
Sales tax = 5%
Amount of tax = 5% of $17,10
= 5/100 × 17,100
= 0.05 × 17,100
= $855
Selling price = cost price + amount of tax
= $17,100 + $855
= $17,955
Therefore, the selling price of the truck is $17,955
Read more:
https://brainly.com/question/19673462
How to find the inverse for f(x) = 2x-6
Answer:
The inverse is 1/2x +3
Step-by-step explanation:
f(x) = 2x-6
Replace f(x) with y
y= 2x-6
Exchange x and y
x = 2y-6
Solve for y
Add 6 to each side
x+6 = 2y-6+6
x+6 = 2y
Divide each side by 2
(x+6)/2 = 2y/2
1/2 x+3 = y
The inverse is 1/2x +3
Answer:
[tex]{f}^{ - 1} (x) = \frac{x + 6}{2} \\ [/tex]Step-by-step explanation:
[tex]f(x) = 2x-6[/tex]
To find the inverse of f(x) , equate f(x) to y that's
[tex]y = 2x - 6[/tex]
Next interchange the terms that's x becomes y and y becomes x
[tex]x = 2y - 6[/tex]
Next solve for y
Move 6 to the other side of the equation
That's
[tex]2y = x + 6[/tex]
Divide both sides by 2 to make y stand alone
[tex] \frac{2y}{2} = \frac{x + 6}{2} \\ \\ y = \frac{x + 6}{2} [/tex]
We have the final answer as
[tex] {f}^{ - 1} (x) = \frac{x + 6}{2} \\ [/tex]
Hope this helps you
A 3-column table with 3 rows. Column 1 is labeled Fraction with entries a, StartFraction 1 over 9 EndFraction, five-thirds. Column 2 is labeled Decimal with entries 1.2, b, 1.ModifyingAbove 6 with bar. Column 3 is labeled Percent with entries 120 percent, 11 and StartFraction 1 over 9 EndFraction percent, c.
Identify the values of the variables that complete the table to show the equivalent fractions, decimals, and percents.
a =
b =
c =
Answer:
A-10%
B-25/100
C-1/2
Step-by-step explanation:
i did it and got it right, hope this helps :D
8. AI, Bob, Carol, and Diane shared a $1000 prize. Bob got twice as much as AI,
Carol got 3 times as much as Al, and Diane got $100. How much, in dollars, did
Al get?
Answer:
Al got 150 dollars
Step-by-step explanation:
If we know for certain that Diane receives 100 dollars, than there is 900 left. If Al gets 150, then Bob, getting twice as much, would receive 300, and carol who gets three times as much would get 450. So 450+150+100+300=1000$
Find a solution to the following system of linear equations by using either 1 point
substitution or elimination:
y = 4x + 8
2x + 5y = 4
How to solve
2lb/wk equals lb/day
Answer:
2/7 lbs./day or 0.29 lbs./dayStep-by-step explanation:
2 lbs. x 1 wk.
wk. 7 days
= 2/7 lbs./day
or
= 0.29 lbs./day
2. Which of the following is equivalent to 8^3 x 8^7 ?*
O 1) 8^21
O2) 8^4
O 3) 8^10
O 4)1
Answer:
3) 8^10
Step-by-step explanation:
Use formula: (same base)
a^m × a^n = a^m+n
So,
8^3 × 8^7 = 8^3+7
= 8^10
Jacob is cutting a tile in the shape of a parallelogram. Two opposite angles have measures of (6 - 70)° and (2n + 10)°. What are the two different angle measures of the parallelogram-shaped tile? • 20° and 160° • 50° and 130° • 30° and 150° ( 70° and 110°
Answer:
50° and 130°
Step-by-step explanation:
Here are the steps to find the two different angle measures of the parallelogram-shaped tile:
Step 1:
Since opposite angles in a parallelogram are congruent, we can set the expressions for the two opposite angles equal to each other:(6n - 70 = 2n + 10) - 2n
(4n - 70 = 10) + 70
(4n = 80) / 4
n = 20
Thus, n = 20
Step 2:
We can substitute 20 for n in 6n - 70 and 2n + 10 to find their respective angle measures:Substituting 20 for n in 6n - 70:
6(20) - 70
120 - 70
50
Substituting 20 for n in 2n + 10:
2(20) + 10
40 + 10
50
So, the two different angle measures of the parallelogram-shaped tile are 50 degrees and 130 degrees (since the sum of two opposite angles in a parallelogram is 180 degrees).
Is there anything else you would like to know?
8
g
10
Which of the following is an even function?
Of(x) = (x - 1)
f(x) = 8x
f(x) = x2 - x
f(x) = 7
Answer:
f(x) = 7
Step-by-step explanation:
since an even function is defined as a function with the following rule. f(-x) = f(x) for all x in the domain of f(x). It would be odd if f(-x) = -f(x) for all x in the domain of f(x). If f(-x) ≠ -f(x), than it is neither. these are all known as the parity of a function.
you can apply these rules to all of given functions like this. (-x-1) ≠ -(x-1) so it is neither. 8(-x) = -(8x) so it would be odd. 2(-x)-(-x) = -(2x-x) so it is odd as well. This would make f(x) = 7 the only option, as there are no x variables in the equation so 7 = 7.
Use the following statement to answer the question.
If AB=CD, then AB+6=CD+6.
If the statement is used in a two-column proof, what is the correct reason for the statement?
Transitive Property of Equality
Transitive Property of Equality
Multiplication Property of Equality
Multiplication Property of Equality
Reflexive Property of Equality
Reflexive Property of Equality
Addition Property of Equality
Addition Property of Equality
It is 1,325 feet from Kinsey's house to her school. Kinsey walks to school each morning and gets a ride home each afternoon. How many feet does Kinsey walk to school in 5 days?
Answer: 6,625 feet
Step-by-step explanation:
Since she gets picked up in the afternoon, she's only walking one way. This means all you have to do is multiply 1,325 by 5 to get 6,625.
