Considering the definition of an equation and the way to solve it, the girls will both pay the same if they buy six pairs of pants and one sweater.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values appear.
The solution of a equation means determining the value that satisfies it. In this way, by changing the unknown to the solution, the equality must be true.
To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.This caseBeing "x" the number of pairs of pants, you know that:
Kelsey buys several pairs of uniform pants for $17.95 each, and a sweater for $24.Jeana shops at a different store and buys several pairs of uniform pants for $18.95 each, plus a sweater for $18.The equation in this case is:
17.95x + 24 = 18.95x + 18
Solving:
24 -18= 18.95x - 17-95x
6= x
Finally, this means that Kelsey and Jeana pay the same if they buy six pairs of pants and one sweater.
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You dilate the triangle below using a scale factor of 2.
Identify the new coordinates.
A' ( , )
B' ( , )
C' ( , )
Answer:
see explanation
Step-by-step explanation:
assuming the dilatation is centred at the origin
then multiply each of the original coordinates by the scale factor 2
A (1, 1 ) → A' (2(1), 2(1) ) → A' (2, 2 )
B (5, 2 ) → B' (2(5), 2(2) ) → B' (10, 4 )
C (3, 5 ) → C' (2(3), 2(5) ) → C' (6, 10 )
A music teacher charges $20 an hour but is willing to give a lesson on a different instrument for free to those students who are studying piano. He has 14 piano students and 11 saxophone students. He wants to know if he earns $500 on those days he gives lessons to both groups?
Draw a rectangle to represent the universal set,or all students in the class.
Make a circle inside the rectangle to represent the fourteen students in the class who take piano. The circle is R.
Draw another circle that partly overlaps circle R to represent the eleven students who play the saxophone. The circle is S. All of circle S is eleven.
The Venn diagram shows these groups overlap, and we need to know how many students are in this subgroup.
If there are 4 students taking saxophone for free, then this overlap ,T, equals 4.
Draw your Venn Diagram and use it to answer the following questions. Upload both your diagram and your answers.
How many students are in set R?
How many students in set R are not in S?
How many students are in set S?
How many total students are in R and S?
How many students are common to both R and S?
How much will the music teacher get for the piano students?
How much will the music teacher get for the saxophone students?
There are 14 students in set R.
There are 10 students in set R but not in set S.
There are 11 students in set S.
There are 21 total students in sets R and S.
There are 4 students common to sets R and S.
The music teacher will get $280 for the piano students.
The music teacher will get $140 for the saxophone students.
The amount charged by the music teacher is $20 per hour.The number of piano students is 14.The number of saxophone students is 11.The number of students who learn both instruments is 4.The set R represents piano students.The set S represents saxophone students.The number of students in set R is 14.The number of students in set R but not in S is 14-4 = 10.The number of students in set S is 11.The total number of students in sets R and S is 14 + 11 - 4 = 21.The number of students common to sets R and S is 4.The amount earned from the piano students is 14*20 = $280.The amount earned from the saxophone students is (11-4)*20 = $140.To learn more about sets, visit :
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Answer for this question
Answer:
Proofs provided below
Step-by-step explanation:
[tex]\bold {\text{Prove } (a + b)^2 = a^2 + 2ab + b^2}}[/tex]
[tex]\\\\\implies (a + b)^2 = (a+b) \times (a+b)\\\\\implies (a + b)^2 = a \times (a+b) +b \times (a+b)\\\\\implies (a + b)^2 = a \times a + a \times b + b \times a + b \times b\\\\\implies (a + b)^2 = a^2+ab+ba+b^2\\\\\implies (a + b)^2 = a^2+ab+ab+b^2 \;\;\;\;\text{ since ab = ba}\\\\\implies (a+b)^2 = a^2+2ab+b^2\\\\[/tex]
[tex]\bold{\text{Prove } a^2-b^2 \,=\, (a+b)(a-b)\\\\}[/tex]
1. Add and subtract ab to LHS
[tex]\implies a^2-b^2 = a^2-b^2-ab+ab\\\\\implies a^2-b^2 = a^2-ab+ab-b^2\\\\[/tex]
2. Factorize the above expression
[tex]\implies a^2-b^2 = a(a-b)+b(a-b)\\\\\implies a^2-b^2 = (a-b)(a+b) \;\;\;\; \text{since (a-b) is a common factor in RHS }[/tex]
∴ (a² - b²) = (a - b) (a + b)
[tex]\bold{\text{Prove $\dfrac{\sqrt{3}+1}{\sqrt{3}-1}$= $2+\sqrt{\ensuremath{3}}$}}\\[/tex]
[tex]\text{1. Multiply LHS by $\dfrac{\sqrt{\text{}3}-1}{\sqrt{3}-1}$}\\\\\implies $\dfrac{\sqrt{\text{}3}+1}{\sqrt{3}-1}$ \times $\dfrac{\sqrt{\text{}3}-1}{\sqrt{3}-1}$ \\\\[/tex]
[tex]\implies \dfrac{ (\sqrt{3} + 1)(\sqrt{3}-1) }{(\sqrt{3} - 1)(\sqrt{3}-1) }\\\\[/tex]
Numerator is
[tex](\sqrt{3} + 1)(\sqrt{3}-1) = (\sqrt{3})^2 - 1^2 = 3 - 1 = 2\\\\[/tex]
Denominator is
[tex](\sqrt{3}-1)^2 = (\sqrt{3})^2 - 2\cdot \sqrt{3} \;\cdot 1 + (-1)^2\\\\= 3 - 2 \sqrt{3} + 1\\\\= 4 - 2 \sqrt{3}\\\\[/tex]
So LHS becomes
[tex]\dfrac{2}{4 - 2\sqrt{3}} \\\\[/tex]
Dividing numerator and denominator by 2 yields
[tex]\dfrac{2}{4 - 2\sqrt{3}} = \dfrac {1}{2 - \sqrt{3}}[/tex]
Multiply numerator and denominator by [tex]{2-\sqrt {3}}[/tex]
[tex]$\dfrac{1\cdot(2+\sqrt{3})}{(2-\sqrt{3})(2+\sqrt{3)}}$[/tex]
[tex]=$\dfrac{\ensuremath{2}+\sqrt{3}}{2^{2}-(\sqrt{3)^{2}}}=$$\dfrac{\ensuremath{\ensuremath{2}+\sqrt{3}}}{4-3}=\ensuremath{2}+\sqrt{3}$[/tex]
Hence Proved
Does the frequency distribution given appear to be normal?
Score Frequency
65-69 4
70-74 5
75-79 6
80-84 4
85-89 6
90-94 4
95-99 5
Yes, the frequencies preceding the maximum are roughly a mirror image of those that follow the maximum
No, there is not a concentration of frequencies in the middle
Yes, there is symmetry in the distribution THIS ONE
No, the frequencies increase, reach a maximum, then decrease
The verdict on whether the frequency distribution given appears to be normal is; No, there is not a concentration of frequencies in the middle.
It follows from the task content that it is required to determine if the frequency distribution as given appears to be normal.On this note, since a major distinctive feature of a normal distribution is that; there is a concentration of frequency in the middle and additionally, a normal distribution infers symmetry in the frequency distribution.
Therefore, since the middle data value in this scenario is; (80 - 84) which has a frequency of; 4 which is not the highest.
On this note, the frequency distribution is not a normal distribution and this is because there is not a concentration of frequencies in the middle.
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Maria has $5.05 in quarters and dimes. The number of quarters is exceeds twice the number of dimes by 1. Find the number she has of each kind.
The number of quarters and dimes with Maria are 17 and 8 respectively.
Linear equations in mathematics are ones where the greatest power of the variable is one. A linear equation can only have one possible solution: a straight line. Thus, a simultaneous linear equation is a system of two linear equations in two or three variables that are solved concurrently to get a shared answer. Three methods are frequently used to solve simultaneous linear equations: substitution method, elimination method, and graphic method.
Let q be the number of quarters.
Let d be the number of dimes.
Given that the total amount is 5.05 in quarters and dimes
Therefore, 0.25 q + 0.10d = 5.05;
I once more, q = 2d + 1. — (ii) (ii)
Inferring from I and (ii), d = 4.80/0.60 = 8 and 0.25(2d + 1) + 0.10d = 5.05 and 0.60d = 4.80 respectively.
This is put into (ii), and the result is q = 2d + 1 = 2*8 + 1 = 17.
As a result, q = 17 and d = 8
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HELP PLEASE!!!!!!!!
To rent a certain meeting room, a college charges a reservation fee of $13 and an additional fee of $4 per hour. The chemistry club wants to spend at most $33 on renting the room. What are the possible numbers of hours the chemistry club could rent the meeting room?
Use t for the number of hours.
Write your answer as an inequality solved for t.
The inequality that represents the possible number of hours the chemistry club could rent the meeting room is 13 + 4t ≤ 33 or t ≤ 5.
The possible numbers of hours the chemistry club could rent the meeting room are 1, 2, 3, 4 and 5 hours.
Given that:-
Reservation fee charged to rent the meeting room by college = $ 13
Additional fee per hour charged by the college = $ 4
The maximum amount the chemistry club want to spend on meeting room = $ 33
Let t be the number of hours.
Hence,
13 + 4t ≤ 33
4t ≤ 33 - 13
4t ≤ 20
t ≤ 5 hours.
Hence, the possible number of hours the meeting room can be booked by chemistry club are 1, 2, 3, 4 and 5 hours.
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n(x) = -1 -1/3x + 1 2/3 given x = -2, 0, 5
The solution to the equations are n(-2) = 4/3, n(0) = 2/3 and n(5) = -1
How to solve the equation using the replacement sets?The equation of the function is given as:
n(x) = -1 -1/3x + 1 2/3
The replacement set is given as
x = -2, 0, 5
So, we replace the variables using the elements in the replacement set
When x = -2, we have
n(-2) = -1 -1/3 x -2 + 1 2/3
Evaluate the equation
So, we have the following equation
n(-2) = 4/3
When x = 0, we have
n(0) = -1 -1/3 x 0 + 1 2/3
Evaluate the equation
So, we have the following equation
n(0) = 2/3
When x = 5, we have
n(5) = -1 -1/3 x 5 + 1 2/3
Evaluate the equation
So, we have the following equation
n(5) = -1
Hence, the values of the functions are 4/3, 2/3 and -1
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the depth of water d in a swimming pool increases and decreases by 3% over a one-month period. Match each verbal description of the greatest and least water depths with all equivalent expressions.
The least water depth and greatest depth will be 0.97d and 1.03d.
How to illustrate the expression?An expression is used to show the relationship between the variables.
In this case, the depth of water d in a swimming pool increases and decreases by 3% over a one-month period.
The least water depth will be:
= d - (3% × d)
= d - 0.03d
= 0.97d
The greatest water depth will be:
= d + (3% × d)
= d + 0.03d
= 1.03d
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In a lottery, the top cash prize was $632million, going to three lucky winners. Players pick four different numbers from 1 to 57 and one number from 1 to 44. A player wins a minimum award of $100 by correctly matching two numbers drawn from the white balls (1 through 57) and matching the number on the gold ball (1 through 44). What is the probability of winning the minimum award?
The probability of winning the minimum award of $100 in the lottery is [tex]\frac{113}{140448}[/tex]
The probability of picking first winning number (out of 57 white balls) is [tex]\frac{1}{57}[/tex]
Now, out of the remaining 56 white balls, the probability of picking second winning number is [tex]\frac{1}{56}[/tex]
So total probability of the correctly matching two numbers drawn from the white balls is [tex]\frac{1}{57} + \frac{1}{56}[/tex]
Next, to match the winning number on the gold ball, probability of this event is [tex]\frac{1}{44}[/tex]
Thus overall probability of winning the minimum award is calculated by multiplying the individual probabilities of aforesaid two independent events as follows:
[tex](\frac{1}{44}) (\frac{1}{57}+\frac{1}{56})[/tex]
= [tex]\frac{113}{140448}[/tex]
Above value is the probability of winning the minimum award of $100.
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Given the following preimage and image coordinates, what is the line of reflection?
The given coordinate's line of reflection is the x-axis, Option D.
After intersecting the co-ordinates A(-3,5), B(2,8) and C(-4,-5) of line 1 and co-ordinates A'(-3,-5), B'(2,-8) and C'(-4,5) of line 2. It is deduced that both lines are similar.
The point of intersection of lines 1 and 2 is on the X-axis as the reflection of the coordinate,
A(-3,5) on the negative x-axis and positive y-axis is A'(-3,-5) on the negative y-axis and the negative x-axis.
B(2,8) on the positive x-axis and positive y-axis is B'(2,-8) on the negative y-axis and the positive x-axis.
C(-4,-5) on the negative x-axis and negative y-axis is C'(-4,5) on the positive y-axis and the negative x-axis.
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Mrs. Kwan is packaging apples in paper
bags. She needs to package 30 red apples
and 24 green apples so that there is the same
number of apples in each bag. But she
cannot mix the different apples, and there
can be no apples left over. What is the
greatest number of apples she can package
In each bag?
If 1/4 of the box is green apples, then 3/4 of the box is red apples. Thus, 3 times the number of green apples is equal to the number of red apples, which would give 3 * 5 = 15 red apples.
Solve for .
5x - 4 ≥ 12 OR 12x + 5 < -4
Answer: That is the answer
Step-by-step explanation:
Divide 8 1/2 by the positive difference between 4 4/5 and 7 7/10
The division of 8 1/2 by the positive difference between 4 4/5 and 7 7/10 is 85/29.
How can we make the division?We can find the difference between 4 4/5 and 7 7/10, but we will need to convert the mixed number into the improper fraction as
Then we have 24/5 and 77/10, then the difference between the values are:(77/10 - 24/5) = 29/10
Then we can proceed to find the division of this number that we got from the difference as ( 29/10)/ 8 1/2
But we can make the 8 1/2 as improper fraction from the mixed fraction it was 17/2
Then the division of the values will be ( 17/2)/ ( 29/10) = 85/29
Therefore the division is 85/29.
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Solve each system of equation using substitution show you work
Please help mee :(
Answer:
wouldn't y=8?
Step-by-step explanation:
if x is 3
-5(3)+2y=1
-15+2y=1
2y=16
y=8
I cant find the answer [2-|-2/3-2(-1/5)|] divided
by 13
The answer to the expression [2-|-2/3-2(-1/5)|] divided by 13 is 2/15 .
In the question ,
the expression is given as
=[2-|-2/3-2(-1/5)|] divided by 13
which means
= [2-|-2/3-2(-1/5)|] ÷ 13
Solving the terms inside [ ] first , we have
-2*(-1/5) = 2/5
Substituting the value of -2*(-1/5) in the expression , we get
= [2-|-2/3+2/5|] ÷ 13
Solving the norm(modulus) first
|-2/3+2/5| = |-10/15+6/15| = |-4/15| = 4/15
Substituting the value of |-2/3+2/5| in the expression , we get
= [2-4/15] ÷ 13
Simplifying further we get ,
= [30/15-4/15] ÷ 13
= [26/15] ÷ 13
= [tex]\frac{\frac{26}{15} }{13}[/tex]
= [tex]\frac{26}{15} \times \frac{1}{13}[/tex]
= 2/15
Therefore , the answer to the expression [2-|-2/3-2(-1/5)|] divided by 13 is 2/15 .
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Please help me with this problem
[tex]x^{2} +5x-3=-4x-3\\x^{2} +5x+4x-3+3=0\\x^{2} +9x=0\\\\x(x+9)=0\\x=0 or x+9=0\\x= -9[/tex]
I hope this helps.
Answer:
x = 0
or
x = (-9)
Step-by-step explanation:
[tex] {x}^{2} + 5x - 3 = - 4x - 3[/tex]
transfer like terms to the same side of the equation
[tex] {x}^{2} + 5x + 4x = - 3 + 3[/tex]
Add/subtract like terms
[tex] {x}^{2} + 9x = 0[/tex]
Now we can factor terms
[tex] {x}^{2} = x \times x \: and \: 9x = 9 \times x[/tex]
we can write them with their common divisor
x*(9+x) = 0 for this equation to be correct either x = 0 or (9+x) = 0
if x = 0 well then that's the first value of x
if (9+x) = 0 then x = -9 and this is the second value of x
How do you do this question
Given the triangle LMN and the line (n)
We will find the image of the triangle LMN after the reflection over the line (n)
So, from each point, construct a line segment perpendicular to the line (n)
Then make sure the distance between the point and the line is the same as the line and the image point.
the reflection of the triangle will be as shown in the following figure:
f(x) = -4/3 (-x+5)^3 +12
X Y
3 1.333
4 10.667
5 12
6 13.333
8 48
Find all x-intercepts of the function. Express your answer as a list of x-values.
f(x) = 5x¹ - 80
The x-intercept of the function is found to be x = (y + 80)/5 and the values of x calculated are 17,18,19 and so on.
What is an illustration of intercept?Given, the x-axis and y-axis are intersected by two intercepts, P(2,0) and Q(0,3). => 3x + 2y – 6 = 0, Consequently, the line's equation is 3x + 2y - 6 = 0. Figure.
How do x and y intercept work?A line's x-intercept and y-intercept are the points at which the x- and y-axes, respectively, are crossed.
The given function is:
f(x) = 5x¹ - 80
Let,
y = f(x)
∴ y = 5x – 80
y + 80 = 5x
(y + 80)/5 = x
∴ x = (y + 80)/5
If y = 5,
x = (5 + 80)/5 = 17
If y = 10,
x = (10 + 80)/5 = 18
If y = 15,
x = (15 + 80)/5 = 19
Thus, by substituting y values in multiples of 5, we can get x values as 17, 18, 19 and so on.
Thus, the x-intercept of the function is found to be x = (y + 80)/5 and the x values calculated are 17,18,19 and so on.
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In 3 billion repetitions of an experiment, a random event occurred in 500 million cases.
The probability of the event is 1.
The probability of the event is 0.
What is the expected probability of this event?
What is the expected probability of the complement of the event?
A shelf has 20 bags of potatoes. Two of the bags have potatoes starting to go bad.
The probability of drawing a bag with bad potatoes is less than 1.
The probability of drawing a bag with good potatoes is greater than 0.
What is the probability of drawing a bag with bad potatoes?
What is the expected probability of the complement of the event?
Answer:
The correct answer is 1/6 for the question, "In 3 billion repetitions of an experiment, a random event occurred in 500 million cases..."
The correct answer is 1/10 for the question, "A shelf has 20 bags of potatoes. Two of the bags have potatoes starting to go bad."
Hope this helps you! May I please get brainliest if I'm correct?
A forest fire leaves behind an area of grass burned in an expanding circular
pattern. If the radius of the circle of burning grass is increasing with time
according to the formula r(t) = 2t + 1, express the area burned as a function of
time.
The function of the area of the forest in terms of time is A(t) = π(2t + 1)²
How to determine the area function?The given parameters are
Radius function, r(t) = 2t + 1
From the question, we understand that:
The pattern is circular
The area of a circle is
A = πr²
Express as a function
A(r) = πr²
Substitute r(t) = 2t + 1
A(t) = π(2t + 1)²
Hence, the area function in terms of time is A(t) = π(2t + 1)²
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the graph shows then number of possible passengers for a given number of roller coasters cars that leave the platform
oluition
or this case we have the folllowing:
Part a
e select (0,0) and (3,24)
the slope would be:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{24-0}{3-0}=8[/tex]then the equation for this case would be:
y= 8x +b
Using (0,0) we can find b:
0 ) 8*0 +b
b= 0
Then the equation is:
y= 8x
Part b
or this case we can conclude that for each n8 passengers is required a new car for the rooller coaster
Using the measurements shown, which of these parallelograms is it
possible to work out the area of?
Answer:
B, D, E
Step-by-step explanation:
We can find the area of B since the height and lengths is known, so the area is just 2*4 = 8 cm^2
D also has the height and length given, it is 4*3 = 12 cm^2
E gives 3 values, but only focus on the height and length, which are 2 and 5 respectively. 3 is also a side length, but there is no height to match that length. The area of E is 2*5 = 10 cm^2
The reasons A, C, and F don't work:
A seems like it would work, until you realize that 5 is a height, not a length, and so is 2. They are both heights, and multiplying heights together won't usually get you an accurate area unless the shape is a rectangle.
C has a length, but no height. the 3 cm is pretty much an arbitrary measurement.
F has two lengths, which would only give the area if the shape was a rectangle, which it is not.
find the median of the numbers 34, 48, 52, 61, 76, 76, 61, 84, 61, 39, 83, 61, 79, 81, 56, and 88.
Answer:
61
Step-by-step explanation:
A figure is dilated by a factor of 3. Which of following statements about the image of the figure is true?
When a figure is dilated by a factor of 3, the statement about the image of the figure that is true is C Both the area and the perimeter decrease.
What is dilation?Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original.
The x and y coordinates of the original figure are multiplied by the scale factor to discover spots on the dilated image when a dilation in the coordinate plane has the origin as the center of dilation. The algebraic representation of the dilation is (x, y) for scale factor k. (kx, ky).
In this situation, since the figure is dilated by a factor of 3, there will be a reduction. In conclusion, the correct option is C.
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A figure is dilated by a factor of 3. Which of the following statements about the image of the figure is true?
A The perimeter decreases.
B The area decreases.
C Both the area and the perimeter
decrease.
D Both the area and the perimeter
increase.
We can find the remainder for the quotient using either substitution or synthetic division as discussed in class. Using either method, explain whether or not we can conclude that x - 5 is a factor of the polynomial
(Your answer must include what that remainder value is and what it indicates.)
Using either method, we can conclude that x - 5 is a factor of the polynomial
This is further explained below.
What is the polynomial?Explain, based on the fact that, using either approach, whether or not we can consider x-5 to be a factor in the polynomial.
Generally, the equation for the problem is mathematically given as
f(x)=x^3-x^2-17 x-15
Therefore, If (x-5) is factor of f(x) then at x=5 ,f(x)=0 then apply this
[tex]\begin{aligned}f(x) &=5^3-5^2-17 \times 5-15 \\&=125-25-85-15 \\&=0\end{aligned}[/tex]
In conclusion,Since f(x) is equal to 0 when x = 5, the factor of f is (x-5) (x).
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Find the area of the figure. 16cm 9cm
area: cm2
The area of the figure is 144 square centimeters
What are areas?The area of a shape is the amount of space on the shape
For most regular quadrilaterals, you multiply the side lengths to determine the area
How to determine the area of the shape?The given parameters are
Shape = parallelogram
Base = 9 cm
Height = 16 cm
The area of a parallelogram shape is
Area = Base * Height
So, we have
Area = 9 * 16
Evaluate the expression
Area = 144
Hence, the area is 144 square centimeters
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The carnival spinner shown below is divided into equal sections. On every spin, each outcome is equally likely.
If the spinner lands on a number less than 10 on its next spin, what is the probability that it is a multiple of 4?
a. 1/5
b. 2/9
c. 1/4
d. 1/3
Answer:
2/9
Step-by-step explanation:
The possibilities that satisfy the condition are 4 and 8.
This is 2 numbers out of the possible 9, so the probability is 2/9.
Solve the equation using the Quadratic Formula. 2x² + 5x = 3
Answer:
x = (1/2)
x = -3
Step-by-step explanation:
Quadratic:
2x² + 5x = 3
-3 -3
----------------------
2x² + 5x - 3 = 0
-b ± √b² - 4(a)(c)
-------------------
2(a)
-5 ± √5² - 4(2)(-3)
---------------------------
2(2)
-5 ± √25 + 24
---------------------------
4
-5 ± √49
----------------
4
-5 ± 7
----------
4
-5 + 7 2 1
---------- = ------- = ------
4 4 2
-5 - 7 -12
---------- = --------- = -3
4 4
----------------------------------------------------------------------------------------------------------
Factored (for fun):
(2x² + 6x) (-1x - 3) = 0
2x(x + 3) -1 (x + 3)
(2x - 1)(x + 3) = 0
2x - 1 = 0, x + 3 = 0
+1 +1 -3 -3
--------------- ------------------
2x = 1 x = -3
÷2 ÷2
-------------
x = (1/2)
I hope this helps!
A dolphin swims at a depth of 13.5 meters below sea level while a seagull flies 10 meters above sea level. How far apart are they? Write and evaluate an expression to answer this question.