What is the domain of the graphed function?
A) y ≥ 4
B) x ≥ -2
C) y ≥ -2
D) x ≤ -2
Answers
Related Questions
A theater charges $25 for adults and $15 for children. When the price of a child's ticket increases to $18 next year,the cost for a dance club to attend the theater will increase from $450 to $480. Write and solve a system of equations to find how many adults are in the dance club.
Answers
tickets for adults - 25
tickets for kids - 15
initial cost - 450
increase in tickets for kids to - 18
cost after increase - 480
let x be number of adults and y be number of kids
25x + 15y = 450
25x + 18y = 480
subtraction:
25x + 15y = 450
-25x - 18y = -480
0 - 3y = - 30
y = -30/-3
y = 10
There are 10 kids.
25x + 15y = 450
25x + 15(10) = 450
25x + 150 = 450
25x = 450 - 150
25x = 300
x = 300/25
x = 12
There are 12 adults.
All in all there are 12 adults and 10 kids.
to check:
25x + 15y = 450
25(12) + 15(10) = 450
300 + 150 = 450
450 = 450
25x + 18y = 480
25(12) + 18(10) = 480
300 + 180 = 480
480 = 480
Jorge and Mary are both filling cups with fruit punch in preparation for a party. After 3 minutes, Jorge had 53 cups left to be filled, and after 5 minutes, he had 25 cups left to be filled. Mary’s progress is shown in the table of values below. Assuming that both Jorge and Mary are filling cups at a constant rate, which statement is correct?
Mary’s Cup-Filling Progress
Time (minutes)
0.5
1
1.5
2
2.5
Cups Remaining
99
81
63
45
27
Jorge is filling 14 cups per minute, which is faster than Mary.
Jorge is filling 28 cups per minute, which is faster than Mary.
Mary is filling 18 cups per minute, which is faster than Jorge.
Mary is filling 36 cups per minute, which is faster than Jorge.
Answers
Answer:
Mary is filling 36 cups per minute, which is faster than Jorge.
Step-by-step explanation:
Lets get Jorge's time :
As the rate is constant, we can find the slope to know the number of cups he is filling per minute.
Slope is found using: [tex]\frac{y2-y1}{x2-x1}[/tex]
= [tex]\frac{53-25}{5-3}[/tex]
= [tex]\frac{28}{2}=14[/tex]
From the table lets get Mary's time:
[tex]\frac{99-81}{1-0.5}[/tex]
= [tex]\frac{18}{0.5}=36[/tex]
Another data: [tex]\frac{63-45}{2-1.5}[/tex]
= [tex]\frac{18}{0.5}=36[/tex]
Therefore, we can see that Mary is filling 36 cups in a minute and Jorge is filling 14 cups.
Hence, the correct answer is : Mary is filling 36 cups per minute, which is faster than Jorge.
Answer:
Mary is filling 36 cups per minute, which is faster than Jorge.
Step-by-step explanation:
Perpendicular lines AB and CD intersect at point E. If m∠AED = x + 20, what is the value of x?
A.) 160
B.) 110
C.) 90
D.) 70
Answers
Find the retail price of a backpack that has a wholesale price of $25 and is marked up 40%. Multiply $25 and 40% in decimal form to find the markup amount. 25(0.40) = $10 Add the wholesale price to the markup amount. What is the selling price? $10 $15 $35 $65
Answers
Answer:
35 35 35 35
Step-by-step explanation:
it 35
Each of two trapezoidal prisms has a volume of 120 cubic centimeters. the prisms have no dimensions in common. give possible dimensions for each prism.
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If the height of one trapezoid is 4, the area would need to be 30. I wrote out the formula for area of a trapezoid (h (b1+b2)/2) and solved for 30. I multiplied both sides by 2 and saw that I needed a 60 from the sun of my 2 bases and the height of the trapezoid base. I used 2 for the height and 20 and 10 as the 2 bases.
For the second trapezoid, I used 6 as the height of the prism. This left me with 20 as the area. I used the same formula above and found that I needed to get 40. I used 5 as the height of the trapezoid and 1 and 7 as the two base lengths. Hope this helps!!
Let a(−9, 4) and b(3, −12) be points in the plane. (a) find the slope of the line that contains a and
b.
Answers
Slope of the line = -4/3
What is slope?The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line. The net change in y coordinate is Δy, while the net change in the x coordinate is Δx. So the change in y coordinate with respect to the change in x coordinate can be written as,
The slope of line is the measure of steepness or the direction of line the coordinate plane.
m = Δy/Δx
where, m is the slope
Given,
A = (-9,4)
B = (3, -12)
Slope of line AB = (y - y')/(x-x')
= -12-4/3 - -9
= -16/12
Slope of line AB = -4/3
Hence, -4/3 is the slope of the line.
Learn more about slope of the line here:
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How do you make 3ln2+2ln4 a single logarithm?
Answers
2ln 4 = ln 4² = ln 16
Sum means it is a product:
ln (8 × 16) = ln 128
Or ln (2³×4²)
3ln2 + 2ln4 = ln 2^3 + ln 4^2 = ln 8 + ln 16 = ln 128
What is the value of x in the triangle?
Answers
We’re going to use Cosine because the angle and sides given are Adjacent and Hypotenuse- which goes with the CAH part of SOH CAH TOA.
Cos(18) = x/25
Multiply both sides by 25
25cos(18) = X = 23.776
So x = 23.776 cm
I hope this Helps!
And that gives you... x = 23.776 cm
A rectangular solid is dilated by a factor of 0.5.
How many times larger is the volume of the resulting solid than the volume of the original solid?
Enter your answer as a decimal in the box.
Answers
Answer:
0.125 took test
Step-by-step explanation:
Volume of the resultant solid will be 0.125 times of the original solid.
Volume scale factor of a rectangular solid:If the sides of a rectangle solid is dilated by a scale factor 'k',Volume of the solid will be given by the expression,
Volume = (k)³(Volume of the original solid)
If a rectangular solid is dilated by a scale factor 'k' = 0.5
Volume of the resultant solid = (0.5)³(Volume of the original solid)
= 0.125(Volume of the original solid)
Therefore, volume of the resultant solid will be 0.125 times of the original solid.
Learn more about the dilation of a rectangular solid here,
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OUCH MY BRAIN IS HURTING AFTER TRYING TO SOLVE THIS QUESTION
Answers
The 3rd selection is appropriate.
What is the future value of $1,600 in 17 years assuming an interest rate of 10 percent compounded semiannually?
Answers
F--------------------> future value
P--------------------> present value
r --------------------> interest rate per year
m ------------------ > number of compounding periods per year
t --------------------> time in years.
we know that
P=$1,600
t=17 years
m=2
r=10%------> 0.10
F=P(1+i)^n
where
i=r/m ---------> 0.10/2=0.05
and
n=m*t------------> 2*17=34
F=1600*(1+0.05)^34=8405.36
the answer is $8405.36
A species of catfish, can generate up to 350 voltsWrite an inequality to represent the amount of electricity generated by the catfish
Answers
The inequality to represent the amount of electricity generated by the catfish, which can generate up to 350 volts, is: [tex]\[ 0 \leq E \leq 350 \][/tex] where [tex]\( E[/tex] represents the amount of electricity in volts.
This inequality indicates that the electricity generated by the catfish is at least 0 volts and at most 350 volts. The lower bound of 0 volts is included because the catfish cannot generate negative voltage, and the upper bound of 350 volts is the maximum it can generate.
how are solutions, roots, and x-intercepts of a quadratic related?
Answers
You can solve a quadratic equation by factoring by applying a equation called "Quadratic formula", which is usually used when you can't factorize it. This formula is:
x=(-b±√(b^2-4ac))/2a
Answer:
Step-by-step explanation:
The quadratic equation [tex]ax^2+bx+c=0[/tex]
The roots of quadratic equation is defined as that value when we substitute in the quadratic equation then we get zero.
Solution of quadratic equation is defined as that value of roots which substitute in the equation then we get zero.
x-intercept of the quadratic equation is defined as that real value of x on the x- axis when we substitute in the equation then the value of equation becomes zero.
From the above definitions we can see that roots of quadratic equation can be imaginary or real but x- intercept value of equation is always a real value.
Solution is also called the value of roots but x- intercept is equal to roots when the value of roots is real.
Now, we can says that roots and solutions of quadratic equation are same when values of roots are real. But when the roots are imaginary then we can not find x- intercept in cartesian coordinate plane .
Noah was asked to find the median of the following numbers.
115, 109, 117, 136, 127, 131
Noah’s work is shown below.
109, 115, 117, 127, 131, 136
mc006-1.jpg
What error, if any, did Noah make?
A)He forgot to put the numbers in order first.
B)He crossed off the high/low number pairs incorrectly.
C)He left out a number when putting the numbers in order.
D)He did not make any error.
Answers
1. he makes the numbers in order
2. he didn't cross off the high/low number pairs incorrectly
3. he didn't leave out a number
CD←→ is tangent to circle A at point B.
What is the measure of ∠ABD?
45º
60º
90º
180º
Answers
The measure [tex]\angle ABD[/tex] is C. [tex]90^{\circ}[/tex]
Given,CD is tangent to the circle A at point B.
We have to find the measure of [tex]\angle[/tex][tex]ABD[/tex].
Tangent:We know that,
Tangent to a circle is the line that touches the circle at only one point. There can be only one tangent on a point to circle. The Tangent makes an angle of [tex]90^{\circ}[/tex] with the radius of the circle at the point of contact.Hence [tex]\angle ABD[/tex] is [tex]90^{\circ}[/tex].The correct option is C. [tex]90^{\circ}[/tex]
For more details about tangent, follow the link:
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Write a two-column proof
it says Given: the top number is 2x+6 and the bottom number is 96. Prove: x = 45
It's a little blurry sorry. Please help me I have never understood two-column proofs and they don't make sense to me
Thank you
Answers
You just have to solve the equation and justify each step along the way:
2x + 6, 96 Given
96 = 2x + 6 Vertical angles are congruent
90 = 2x Subtraction Property of Equality
45 = x Division Property of Equality
And that's all there is to it! I hope this helps you. (:
If f(x)=x+7 and g(x)=1/x-13 what is the domain of (f*g)(x)
A. {x| x = 6}
B. {x| x = -6}
C. {x| x = -13}
D. {x| x = 13}
Answers
Answer:
The Answer is B
Step-by-step explanation:
If you do the math, this would be the conclusion you would come up with.
If sec a = 5/4 and a is an angle in quadrant iv find the value of cos a
Answers
sec a = 5/4
sec(a)=1/cos(a)
then
cos (a)=1/sec(a)
cos (a)=1/(5/4)=4/5---> is positive because the function cos is positive in IV quadrant
the answer is cos(a)=4/5
This is the first part of a three-part problem. express $18\sqrt 8$ in the form $a\sqrt b$, where $a$ and $b$ are integers and $b$ is as small as possible.
Answers
Answer:
[tex]18\sqrt{8}=36\sqrt{2}[/tex]
Where a=36 and b=2 with b is small.
Step-by-step explanation:
Given problem [tex]18\sqrt{8}[/tex]
We have to write the given problem in form of [tex]a\sqrt{b}[/tex], where a and b are integers and b is as small as possible.
Consider the given problem [tex]18\sqrt{8}[/tex]
8 can be written in factored form as 2 × 2 × 2
Substitute, in given problem, we have
[tex]18\sqrt{8}=18\sqrt{2 \times 2\times 2}[/tex]
This can be written as,
[tex]18\sqrt{2 \times 2\times 2}=18(\sqrt{4}\sqrt{2})[/tex]
We know [tex]\sqrt{4}=2[/tex] , thus,
[tex]18(\sqrt{4}\sqrt{2})=18\cdot 2\sqrt{2}=36\sqrt{2}[/tex]
Thus,[tex]18\sqrt{8}=36\sqrt{2}[/tex]
Where a=36 and b=2 with b is small.
6 cards are drawn from a standard deck without replacement how many different 6 card hands are possible if the drawing is done without replacement
Answers
14658134400 / 720
20358520
1.66666666667 rounded to the tenth
Answers
The tenth place is where the first 6 is, so:
1.666666666667=
1.7 because 6>5
I hope this helps!
~kaikers
So, the number after the tenths place is a 6 which is greater than 5, so you would round up.
So, your answer would be 1.7
find the value of x
Answers
Since angle 130° and angle A are on the same straight line, they are supplementary angles; therefore:
[tex]130+A=180[/tex]
[tex]A=180-130[/tex]
[tex]A=50[/tex]
Next, angle B and angle 134° are also on the same straight line, so they are supplementary as well, which means:
[tex]B+134=180[/tex]
[tex]B=180-134[/tex]
[tex]B=46[/tex]
Now, to find angle C remember that the sum of the interior angles of a triangle is 180°; therefore:
[tex]A+B+C=180[/tex]
[tex]50+46+C=180[/tex]
[tex]C=180-50-46[/tex]
[tex]C=84[/tex]
Finally, we also know that angle [tex]x[/tex] and angle C are on the same line, so they are supplementary angles just like before; therefore:
[tex]x+C=180[/tex]
[tex]x+84=180[/tex]
[tex]x=180-84[/tex]
[tex]x=96[/tex]
We can conclude that the measure of our angle [tex]x[/tex] is 96°.
In two or more complete sentences, define the key features of the graph below and explain how to write its equation using function notation.
Answers
This means that for each value of f (x) there are two possible values of x.
The absolute value function is:
f (x) = lxl
y = f (x) - 2 shifts the graph 2 units down.
y = f (x + 3) moves the graph 3 units to the right.
Finally:
The function that best fits this graph is:
f (x) = l-x + 3l-2
Answer:
The function notation of the graph is f(x) = |x-3| - 2
Step-by-step explanation:
From the graph it is evident that it is the graph of the absolute value of the function i.e. f(x) = |x| and we know that 'Translation' is a transformation that shifts the graph of a function in any direction.
Now, as we can see that the graph is shifted towards the right of the y-axis at point x=3, this means that it is translated by 3 units to the right of y-axis.
Therefore, the function becomes f(x) = |x-3|.
Furthermore, it is also shifted downwards at the point x= -2, this means that it is translated by 2 units downward from the x-axis.
Hence, the new function is f(x) = |x-3| - 2.
It can also be seen from the figure below that the graph of above f(x) is same as that of the provided image.
An initial deposit of $5325 was made into an account that compounds interest semi-annually. No other deposits were made. At the end of 13 years, the balance in the account had doubled. Find the interest rate on this account.
Answers
Formula: Where: r = n[(A/P)^1/nt - 1]
What is the value of n?
Enter your answer in the box.
n =
Answers
18(n+1) = 9(n+7)
18n + 18 = 9n + 63
18n - 9n = 63 - 18
9n = 45
n = 45/9
n = 5
Answer:
n = 5
Step-by-step explanation:
This problem follows the theorem "If two chords intersect each other inside a circle, the products of their segments are equal."
To follow this theorem, you must multiply both segments of the chord with each other.
Do it to both chords.
The two chords are equal to each other. It should look like:
18*(n+1) = 9*(n+7)
[distributive property]
18n + 18 = 9n + 63
9n = 45
n = 5
Express 8.12 as a mixed number.
Answers
Let's keep our goal in mind. A mixed number is a whole number and a fraction together. SInce we already have our whole number, 8, we need to make .12 a fraction.
If we look at .12, we see that that 12 is in the hundredths place. When you go to whole numbers, you have tens, hundreds, and so on. When you go to fractions, it goes tenths, hundredths and so on.
That means that since the 12 is in the hundredths, it's 12 hundredths, or 12/100.
That means our mixed number is 8 12/100
Hope this helps
When a standard six sided die is rolled, what is the probability of getting a 9?
Answers
Nina has $5 bills and $10 bills in her wallet. she has a total of 7 bills with a value of $55. how many of each type of bill does she have? show all work to justify your answer.
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helppppppppppppppppppppppppppppppp
Answers
a (x) = 3x + 1
b (x) = root (x-4)
Making the composition
b (a (x)) = root ((3x + 1) -4)
Rewriting:
b (a (x)) = root (3x-3)
b (a (x)) = root (3 (x-1))
Answer:
The domain of the function is:
x> = 1
Equivalently:
[1, inf)
PLEASE HELP ASAP!!!
The first figure is dilated to form the second figure.
Which statement is true?
The scale factor is 0.8.
The scale factor is 1.25.
The scale factor is 2.0.
The scale factor is 18.0.
Answers
10/8=1.25.
Answer: The answer is (a) The scale factor is 1.25.
Step-by-step explanation: We are given two figures in the question, where the second one is dilated from the first one. We are to find the scale factor here.
One side of the dilated figure is of length 10 inch and the original figure has a side of length 8 units.
Therefore, the scale factor is given by
[tex]S.F.=\dfrac{10}{8}=1.25.[/tex]
Therefore, the scale factor is 1.25 and (B) is the correct option.