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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.
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.
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.
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If sec a = 5/4 and a is an angle in quadrant iv find the value of cos a
In two or more complete sentences, define the key features of the graph below and explain how to write its equation using function notation.
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.
CD←→ is tangent to circle A at point B.
What is the measure of ∠ABD?
45º
60º
90º
180º
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]
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What is the future value of $1,600 in 17 years assuming an interest rate of 10 percent compounded semiannually?
What is the value of n?
Enter your answer in the box.
n =
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
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
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.
How do you make 3ln2+2ln4 a single logarithm?
1.66666666667 rounded to the tenth
When a standard six sided die is rolled, what is the probability of getting a 9?
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
A species of catfish, can generate up to 350 voltsWrite an inequality to represent the amount of electricity generated by the catfish
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.
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.
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.
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.
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.
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.
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.
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.
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
find the value of x
What is the value of x in the triangle?
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.
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.
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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}
Answer:
The Answer is B
Step-by-step explanation:
If you do the math, this would be the conclusion you would come up with.
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.
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:
how are solutions, roots, and x-intercepts of a quadratic related?
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 .
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
Answer:
35 35 35 35
Step-by-step explanation:
it 35
Express 8.12 as a mixed number.