Answer:
3 months
Step-by-step explanation:
Let x be the number of months CDs are added at Tom and Nita's respective rates of 1 and 5 CDs/month.
Tom's collection after x months is = 30 + 1x
Nita's collection after x months is = 18 + 5x
At some point they will have equal numbers of CD's, so set the equations equal to each other:
30 + 1x = 18 + 5x
4x = 12
x = 3 months
At 3 months both Tom and Nita will have the same number of CDs.
Tom: 30 + 1*3 = 33 CDs
Nita: 18 + 5*3 = 33 CDs
x = 3
Step-by-step explanation:We can create a system of equations to represent the situation we have been given.
Creating the Equations
In this system, we can create an equation to represent both people's collections.
First, we can create Nita's.
To create the equation we can start with the constant. We are told she starts with 18 CDs. So, this will be one of the terms.Next, we can multiply x by 5. We can do this because x represents the number of months that have passed and 5 is the number of CDs she adds per month. This means 5x will be another term.Finally, the constant and variable will add up to the total number of CDs, which is represented by y. So, the expression will be set equal to y.All of this creates the equation: 5x + 18 = y.
Next, we can do the same to find Tom's equation.
Tom starts out with 30 CDs. So this will be the constant term.Each month he adds 1 CD. This means that we can multiply 1 by x to make the term 1x.Finally, like with Nita's this expression will be set equal to y.This creates the second equation: 1x + 30 = y.
The system is:
5x + 18 = y
1x + 30 = y
Solving the System of Equations
One method to solve a system of equations is substitution. Substitution is when you substitute an expression for a variable. Since both expressions are set equal to y, we can substitute the expressions for y and set them equal to each other.
This creates the new equation: 5x + 18 = 1x + 30. Then, solve normally.
First, subtract 1x from both sides4x + 18 = 30
Next, subtract 18 from both sides.4x = 12
Finally, divide both sides by 4x = 3
This means after 3 months the number CDs will be equal.
The perimeter of the rectangle below is 130 units. Find the length of side VY.
Write your answer without variables.
Y
4y
V
5y + 2
X
W
VY
Answer:
VY = 28 units
Step-by-step explanation:
the perimeter (P) of a rectangle is calculated as
P = 2 ( length + breadth )
given P = 130 , then
2(5y + 2 + 4y) = 130 ( divide both sides by 2 )
9y + 2 = 65 ( subtract 2 from both sides )
9y = 63 ( divide both sides by 9 )
y = 7
Then
VY = 4y = 4 × 7 = 28
3 quick algebra 1 questions for 50 points!
Only answer if you know the answer, shout-out to subtomex0, tysm for the help!
The range of the function across the domain is {18, 2, -6}
The range of the functionThe function is given as:
f(x) = -2x + 12
The domain is given as:
{-3, 5, 9}
So, we have:
f(-3) = -2*-3 + 12 = 18
f(5) = -2*5 + 12 = 2
f(9) = -2*9 + 12 = -6
Hence, the range of the function across the domain is {18, 2, -6}
The value of the functionThe function is
f(x) = 3x - 11
To calculate f(4), we have:
f(4) = 3 * 4 - 11
Evaluate
f(4) = 1
Hence, the value of f(4) is 1
The value of the functionThe function of the graph is given as:
w(x)
To calculate w(2), we check the corresponding point on the graph where x = 2
From the graph, we have:
w(2) = 5
Hence, the value of w(2) is 5
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Answer:
1. f(4) = 1
2. range: {18, 2, -6}
3. w(2) = 5
Step-by-step explanation:
Question 1
[tex]\textsf{Given}: \quad f(x)=3x-11[/tex]
To find f(4) substitute x = 4 into the given function:
[tex]\begin{aligned}\implies f(4) & = 3(4)-11\\& = 12-11\\& = 1\end{aligned}[/tex]
Question 2
Domain: set of all possible input values (x-values)
Range: set of all possible output values (y-values)
[tex]\textsf{Given}: \quad b(x)=-2x+12[/tex]
To find the range of the given function for the domain {-3, 5, 9} simply input these values of x into the function:
[tex]\implies b(-3)=-2(-3)+12=18[/tex]
[tex]\implies b(5)=-2(5)+12=2[/tex]
[tex]\implies b(9)=-2(9)+12=-6[/tex]
Therefore, the range of the given function is {18, 2, -6}.
Question 3
Given: The graph of function w(x)
To find w(2) simply find the y-value of the point on the graph where x = 2:
Find x = 2 on the x-axis. Trace vertically until you meet the line. Trace horizontally to the y-axis to find the corresponding value of y.Therefore, w(2) = 5
Find the measure of the angle indicated in bold
Answer:
60 for both
Step-by-step explanation:
Since these angles are parallel, they are equal to each other :
6x = 5x + 10
Subtracting 5x from both sides gives us :
x = 10
Substituting this value back into both angles gives us
6x = 60
5x+10 = 60
A math teacher randomly assigns seats in the classroom to students each quarter. Each student randomly chooses their row number out of a hat. In the classroom, there are 4 desks in each row and 27 students in your class. What is the probability that you and your 3 friends will get to sit together in the same row?
Using the combination formula, it is found that the probability that you and your 3 friends will get to sit together in the same row is given by:
[tex]p = \frac{1}{17550}[/tex].
We do not consider the order, hence the combination formula is used to solve this question.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
4 students will be taken from a set of 27, hence the number of ways they can sit is given by:
[tex]C_{27,4} = \frac{27!}{4!23!} = 17550[/tex]
Only one outcome is desired, hence the probability is given by:
[tex]p = \frac{1}{17550}[/tex].
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The height of an
equilateral triangle is
11√12. What is a side
of the triangle?
Answer:
I don't know the answer
Step-by-step explanation:
it's hard solve it for me
As strange as it may seem, it is possible to give a precise-looking verbal definition of an integer that, in fact, is not a definition at all. The following was devised by an English librarian, G. G. Berry, and reported by Bertrand Russell. Explain how it leads to a contradiction. Let [tex]n[/tex] be “the smallest integer not describable in fewer than [tex]12[/tex] English words.” (Note that the total number of strings consisting of [tex]11[/tex] or fewer English words is finite.)
Worth 10 points.
YOUR ANSWER MUST BE UNIQUE
The statements hold the contradiction, just by confusion in keep meaning of statements and get confused with "12" which is string in quotes
Let be “the smallest integer not describable in fewer than English words.” (Note that the total number of strings consisting of or fewer English words is finite.)
What do you mean by contradiction?
Contradiction means that couple of statements that opposes each other.
Here,
The statement says let n be “the smallest integer not describable in fewer than English words.” which implies that n is connected with string mentioned in "" quotes, which is not a definition but contain 11 words in the quotes.
and another statement - Note that the total number of strings consisting 11 or fewer English words is finite which implies that:
the limit of words inside the quotes ≤ 11 words
Thus, strings implies in quotes is simple meaning with 11 word in it
While in statement in brackets implies the limit of words as a string should be ≤ 11. the string "12" create the contradiction in minds.
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Evaluate the expression for x = 6.
12 + 2x - 5
A. 19
B. 79
C. 14
D. 54
Answer:
A. 19
Step-by-step explanation:
Slove this expression using the order of operation PEMDAS.
12 + 2x -5
Replace x with 6
12 + 2(6) - 5
12 + 12 - 5
24 -5
19
Therefore the answer is the first option A.19 .
On his first day of school, Kareem found the high temperature in degrees Fahrenheit to be 76.1°. He plans to use the function C of F = five-ninths (F minus 32) to convert this temperature from degrees Fahrenheit to degrees Celsius. What does C(76.1) represent?
the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius
the temperature of 76.1 degrees Celsius converted to degrees Fahrenheit
the amount of time it takes a temperature of 76.1 degrees Fahrenheit to be converted to 32 degrees Celsius
the amount of time it takes a temperature of 76.1 degrees Celsius to be converted to 32 degrees Fahrenheit
The function is C(F) = (F-32) * 5/9
This means the function C, is using variable F to get the output.
C is Celsius, F is Fahrenheit, so the answer is "the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius"
Answer:
a
Step-by-step explanation:
What is the domain of function m based on the graph?
Answer:
let why is equal to FX b and function with an independent variable X and dependent variable y if a function of f provide a way to successfully produced the single value using for the prepos a value of x then the chosen X value is called belong to domain f
please help!!!!!!!!!!!!
Answer: $233
Step-by-step explanation:
- A flat fee is an amount that is charged or paid that doesn’t account for hourly use or work
- Then, you must pay by the hour for use
- So you would use the equation:
(22 • 9) + 35
- 22 is the maximum hours and 9 is the hourly rate
- 35 is your flat fee
- So, (22 • 9) + 35 = $233
hope this helps :)
Answer:
$233
Step-by-step explanation:
We can make up a linear equation. We already know that it costs $35 to rent a small auger.
Every hour there is a extra fee of 9$.
So, 9 can be the slope, while 35 can be the x intercept.
y=9x+35
x=22; maximum hours
y=9(22)+35
y=198+35
y=$233
Here is a more simple way
multiply 22 hours with 9 dollars, =$198
then add the 35 dollars; 198+35=$233
Look At The Graph. How many nails are less than 1 1/2 inches long?
A)7
B)17
C)6
D)15
Answer:
D 15
Step-by-step explanation:
Count all of the x's less than 1 1/2 = 15
In GeoGebra, display the slope of AB and the slope of the perpendicular line passing through C. Use this to verify your responses in parts B and C. Then move points A, B, and C on the grid to several different locations, and record the slopes of the two lines and the coordinates of A, B, and C.
The slope of the perpendicular line passes through C in GeoGebra.
What is GeoGebra?GeoGebra is the software for the mathematical question for all levels of academics.
GeoGebra brings many mathematical problem solutions like geometry, algebra, spreadsheets, graphing, statistics, and calculus in one search engine.
Display the slope of and the slope of the perpendicular line passing through C.
Hence, the slope of the perpendicular line passes through C in GeoGebra.
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A number of friends decided to go on a picnic and planned to spend rs. 96 on eatables. four of them, however, did not turn up. as a consequence, the remaining ones had to contribute rs. 4 each extra. the number of those who attended the picnic was
The number of those who attended the picnic was 8.
Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = [tex]ax^{2} + bx + c[/tex] = 0 where a, b, c, ∈ R and a ≠ 0.
Such questions are best examples of quadratic equations where the unknown is simply assumed to be a variable which when substituted according to the conditions yield a quadratic equation which can easily be solved.
Let x represent the whole population.
Total Spending = Rs. 96
Thus, each individual's contribution is equal to 96/x.
Four people did not show up causing
others to contribute Rs. 4 extra.
So the given condition can be written as
96/(x-4) – 96/x = 4
=>96x – 96(x-4) = 4x(x-4)
=> 96x -96x + 384 = 4x2 – 16x
=> 4x2 – 16x – 384 = 0
=> x2 – 4x – 96 = 0
=> (x – 12)(x + 8) = 0
=> x = 12 or x = -8 (neglect)
So x = 12
x-4 = 8 ( because four of them did not turn up)
∴ The number of those who attended the picnic was 8.
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In the following exercises, multiply the binomials. Use any method.
254. (10a − b)(3a − 4)
Answer:
Hence the expression [tex]$$(10a-b)(3a-4)=30a^2-3ab-40a+4b$$[/tex]
Step-by-step explanation:
Explanation
The given expression is (10a-b)(3 a-4).We have to multiply the given expression.Multiply the (10a-b) by -4, multiply the (10 a-b) by 3a then add like terms.[tex]$$\begin{matrix}{} & {} & {} & {} & 10a & - & b \\ \times & {} & {} & {} & 3a & - & 4 \\ \end{matrix}$$[/tex]
___________________
[tex]$$\begin{matrix}{} & {} & {} & - & 40a & + & 4b \\ 30{{a}^2} & - & 3ab & {} & {} & {} & {} \\ \end{matrix}$$[/tex]
___________________
[tex]$$\begin{matrix}30{{a}^2} & - & 3ab & - & 40a & + & 4b \\ \end{matrix}$$[/tex]
Help Pls! I need this fast!
Answer: 36
Step-by-step explanation:
[tex]\overline{AB} \cong \overline{BC}[/tex] (Triangle ABC is isosceles)
[tex]m\angle CAB=m\angle CBA=30^{\circ}[/tex] (base angles of an isosceles triangle are congruent)
[tex]\angle MCB=90^{\circ}[/tex] (In triangle CMB, angles in a triangle add to 180 degrees)
[tex]\angle ACM=30^{\circ}[/tex] (triangle sum theorem)
[tex]MB=24[/tex] (30-60-90 triangle CMB)
[tex]AB=12[/tex] (sides opposite congruent angles in a triangle are congruent)
[tex]AB=36[/tex] (segment addition postulate)
Find the tangent of angle Θ in the triangle below.
Answer: 4/3
Step-by-step explanation:
[tex]\tan \theta=\frac{20}{15}=\boxed{\frac{4}{3}}[/tex]
Can someone give me the answer to this?
[tex]\frac{FI}{IG}=\frac{14}{28}=\frac{1}{2}\\\\\frac{FE}{EH}=\frac{12}{26}=\frac{6}{13}[/tex]
So, IE is not parallel to GH.
Write as an equation: The product of a number and 12 is 78.
A. 12n=78
12
n
=
78
B. n+12=78
n
+
12
=
78
C. 12−n=78
12
−
n
=
78
D. 12=78n
This table shows the scores that Mario had on his last five math tests.
Which statement does NOT describe this set of data?
A. The mode is 85.
B. The mean is greater than the median.
C. The median is 81.
D. The mode and the median are equal.
Answer:
Step-by-step explanation:
its A i just did it lol
Suppose the round-trip airfare between Philadelphia and Los Angeles a month before the departure date follows the normal probability distribution with a mean of $387.20 and a standard deviation of $68.50. The interval around the mean that contains 95% of the airfares is ________.
The interval around the mean that contains 95% of the airfare is (250.2,524.2).
Normal Distribution is bell shaped and symmetrical in nature.
We use standard normal to find probabilities of normal distribution
Normal distributions have key characteristics that are easy to spot in graphs: The mean, median and mode are exactly the same. The distribution is symmetric about the mean—half the values fall below the mean and half above the mean. Diagram below shows standard normal figure.
In a normal distribution, 95% of the values fall between mean±2*sd
Give: mean=387.20
sd=68.50
So the interval around the mean that contains 95% of the airfare is (250.2,524.2).
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Anthony is planning a trip using a map with the scale of 1 cm to 15 miles it’s a destinations 15 cm away on the map how far away in Miles as the destination
The distance of Miles' destination is 225 miles.
What is the distance of the destination?A scale drawing is a reduced form in terms of dimensions of an original image / building / object. The map is a scale drawing of a larger town. The scale drawing is reduced by constant dimensions.
Actual distance = (15 x 15) / 1 = 225 miles
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(bus, cab, or train) to school, and in the evening he has the same 333 choices for his trip home.
The probability that he will use both bus and the train among bus, cab, train is 0.11.
Given There are 3 choices to people each among bus, cab, train for his trip home.
Probability is the likeliness of happening an event among all the events possible. The value of probability lies between 0 and 1. The formula to calculate probability is as under:
Probability= number of things/ total things.
The value of probability cannot be negative.
Number of buses=3
Number of cab=3
Number of train=3
Probability that he will go through train and bus is 3/9*3/9
=9/81
=1/9
=0.11
Hence the probability that he will travel with bus and train is 0.11.
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Question is incomplete as it includes:
What is the probability that he will use both train and bus?
If two triangles are congruent which of the following statements must be true
The statement which must be true are Options B, C and D
which are the triangles have the same size and shape, the corresponding sides of the triangles are congruent and the corresponding angles of the triangles are congruent.
What are congruent triangles?Congruent triangles are triangles that have corresponding sides, angles which are all equal in measure.
They can be rotated and turned to be look be identical.
Thus, the statement which must be true are Options B, C and D
which are the triangles have the same size and shape, the corresponding sides of the triangles are congruent and the corresponding angles of the triangles are congruent.
The complete question is
If two triangles are congruent which of the following statements must be true? CHECK ALL THAT APPLY
A. The triangles have the same size but not the same shape.
B. The triangles have the same size and shape
C. The corresponding sides of the triangles are congruent.
D. The corresponding angles of the triangles are congruent.
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32. Find the ratio of the side lengths of the small triangle to the large
triangle.
3/10
6/20
3/2
2/3
Answer:
2/3
Step-by-step explanation:
that the ratio of that number
Use the inverse variation equation to fill in the table.
p =
8.31
V
Volume
(Liters) Pressure
(kilopascals)
83.1 a
b 0.4
415.5 c
a =
4.17
⇒ 0.1, b =
⇒ 20.775, c =
8.31
⇒ 0.02
The value of a is 0.10.
The value of b is 20.78.
The value of c is 0.02.
What are the missing values?
When two variables have inverse variation, the two variables move in opposite directions. If one variable increases, the other decreases.
p = 8.31 / V
V = 8.31 / p
a = 8.31 / 83.1 = 0.10
b = 8.31 / 0.4 = 20.78
c = 8.31 / 415.5 = 0.02
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Answer:
a= 0.1
b=20.775
c=0.10
Step-by-step explanation:
edge 2023
From the diagram below, if the sides AD = 3 and DC = 27, and BD = X + 3, find x.
Select one:
a.
36
b.
9
c.
16
d.
6
Answer: d. 6.
Step-by-step explanation:
AD=3 DC=27 BD=x+3 x>0 x=?
1. Consider triangle ABD:
It's rectangular (∡ADB=90°). ⇒
AB²=(x+3)²+3²=(x+3)²+9.
2. Consider triangle BDC:
It's rectangular (∡BDC=90°). ⇒
BC²=(x+3)²+27²=(x+3)²+729.
3. Consider triangle ABC:
It's rectangular (∡ABC=90°).
AC=AD+CD=3+27=30. ⇒
AC²=AB²+BC²
(x+3)²+9+(x+3)²+729=30²
2*(x+3)²+738=900
2*(x²+6x+9)+738=900
2x²+12x+18+738=900
2x²+12x-144=0 |:2
x²+6x-72=0
D=324 √D=18
x₁=-12 ∉ 'cause x>0
x₂=6.
Solve for x in the equation x squared 20 x 100 = 36. x = –16 or x = –4 x = –10 x = –8 x = 4 or x = 16
Possible values of x is -4 or -16
How to solve?
[tex]{x}^2[/tex] + 20x +100 = 36
[tex]\\{x}^2[/tex] + 20x + 100-36 = 0
[tex]\\{x}^2[/tex] + 20x + 64 = 0
Using middle term split
In this method splitting of middle term in to two factors, In Quadratic Factorization using Splitting of Middle Term which is x term is the sum of two factors and product equal to last term.
[tex]{x}^2[/tex] + 4x + 16x + 64 = 0
x(x+4) + 16(x+4) = 0
taking common (x+4)
(x+4)(x+16) = 0
Either
x+4 = 0
⇒ x = -4
or (x+16) = 0
⇒ x = -16
Thus possible values of x is -4 or -16
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Answer: A
Step-by-step explanation:
Please help me!!
Find the value of x:
Answer:
x = 34 degrees
Step-by-step explanation:
Corresponding Angles Theorem: If 2 parallel lines are cut by a transversal, their corresponding angles are congruent.
Angle RNM = 78 degrees
Triangle RMN = 180 degrees
180 = 78 + 2x + x
102 = 3x
x = 34
17-19, deal with the ambiguous SSA. For each, find all possible solutions and sketch the triangle(s) in each case
The possible solutions using the Sine Law are given as follows:
Triangle A:
B = 50.26°
C = 79.74°
Triangle B:
B = 62.79°
C = 70.21°
What is the sine Rule?
The sine law asserts that the ratio of a triangle's side length to the sine of the opposing angle is the same for all three sides. The sine rule is another name for it.
What is the explanation for the above solution?Triangle A
Given the sine law:
a/SinA = b/SinB
Hence
Sin B = (b/a) SinA
Sin B = 15/10 (Sin 50)
Sn B = (15/10) * 0.766
Sin B = 1.5 * 0.766
B = Sin⁻1 (1.14)
B = 50.26°
Hence, C =
180 - B - A
= 180 - 50.26 - 50
C = 79.74°
Solution B
Given the sine law:
a/SinA = b/SinB
Hence
Sin B = (b/a) SinA
Sin B = 2/1.6 (Sin 47)
Sn B = 1.25 * 0.73
Sin B = 0.9125
B = Sin⁻1 (0.9125)
B = 62.79°
Hence,
C = 180 - 62.79 - 47
C = 70.21°
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calls arrive at lynn ann fish's hotel switchboard at a rate of 2.0 per minute. the average time to handle each is 10 seconds. there is only one switchboard operator at the current time. the poisson and negative exponential distributions appear to be relevant in this situation. what is the probability, as a percent, that the operator is busy
The probability that the operator is busy is 33.33% if the call rate is 2 per minute and average time to handle is 10 seconds.
Given rate of calls 2 per minute and average time to handle a call is 10 seconds.
We have to find the probability that the operator is busy.
Probability is the chance of happening an event among all the events possible. The value of probability lies between 0 and 1.
Probability= number of items/ total items
If rate is 2 per minute then the customers handled in 1 hour=2*60=120
The average time to handle a call=10 seconds.
Therefore customers to be handled in 1 hour=360 (10*6*60)
Probability that the operator is busy is as under:
Probability=λ/μ
=120/360
=1/3
=1/3*100
=33.33%
Hence the probability that the operator is busy is 33.33%.
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