One month Yoko rented 3 movies and 5 video games for a total of $40. The next month she rented 9 movies and 7 video games for a total of $74. Find the rental cost for each movie and each video game.
Answers
Answer:
movie: $3.75video game: $5.75Step-by-step explanation:
Two equations in two unknowns can be written:
3m +5v = 40
9m +7v = 74
These can be solved a variety of ways. One of them is using Cramer's rule. It tells you the solution to
ax +by = cdx +ey = fis given by ...
∆ = bd -eax = (bf -ec)/∆y = (cd -fa)/∆For the numbers above,
∆ = 5·9 -7·3 = 24m = (5·74 -7·40)/24 = 90/24 = 3.75v = (40·9 -74·3)/24 = 138/24 = 5.75The rental cost for each movie is $3.75; for each video game, it is $5.75.
___
The attached graph shows a graphing calculator solution to these equations.
Related Questions
which is the best first step and explanation for solving this system of equations?
2x + 3y = 7
2x = 4y - 5
A ) subtract the second equation from the first equation
B ) add the two equations to one another
C ) Multiply both sides of the first equation by 3
D ) Subtract an equal amount from both sides of the first equation
Answers
Answer:
A ) subtract the second equation from the first equation
Step-by-step explanation:
2x + 3y = 7
2x - 4y = -5
subtracting the second equation from the first equation we get,
7y = 12
y=12/7
This is the correct option
Answer:
A ) subtract the second equation from the first equation
Step-by-step explanation:
Let's consider the following system of equations.
2x + 3y = 7
2x = 4y - 5
If we subtract the second equation from the first equation, we get:
2x + 3y - 2x = 7 - (4y - 5)
3y = 7 - 4y + 5
7y = 12
y = 12/7
Then, we can use any of the original equations and solve for x.
2x = 4y - 5
2x = 4(12/7) - 5
x = 13/14
This rectangular tank is filled with water to a height of 4 centimeters. How much more water is needed to fill the tank completely? the width is 18 cm,length 12 cm,and height 6 cm.
Answers
so calculate the Volume of the water that is already in the tank
so l x w x h
4 x 18 x 12
=864cm^3 is in the tank
find the total volume of the tank:
6 x 18 x 12
=1296cm^3
and subtract the current from the total to find what you need:
1296cm^3 - 864cm^3
= 432 cm^3
you can also find how much you need by using the remaining 2cm from the height (6-4=2) and use the volume formula with 2 substituted as the height and you’ll get the same answer
The amount of water needed to fill the tank is 432 cm³.
What is Volume?Volume is a three-dimensional quantity used to calculate a solid shape's capacity. That means that the volume of a closed form determines how much three-dimensional space it can fill.
Volume of cuboid = lwh
The tank is filled with water to a height of 4 centimeters.
The dimension of the tank is width is 18 cm, length is 12 cm, and height 6 cm.
So, the Volume of water present in the tank
= l x w x h
= 4 x 18 x 12
= 864 cm³
Now, the total Volume of tank
= 6 x 18 x 12
= 1296 cm³
So, the amount of water needed to fill the tank
= 1296 - 864
= 432 cm³
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An equal number of students from two Algebra 1 classes at Bozeman School were randomly selected and asked how many hours per week they spend studying algebra.
The class with the largest median for hours spent studying is
-Mrs. Castro’s class
-Mr. Philippe’s class
-The medians are the same
The class with the largest range of hours spent studying is
-Mrs. Castro’s class
-Mr. Philippe’s class
-The ranges are the same
The class with the largest IQR for hours spent studying is
-Mrs. Castro’s class
-Mr. Philippe’s class
-The IQRs are the same
Answers
Answer:
Largest Median: Same
Largest Range: Castro
Largest IQR: Castro
Step-by-step explanation:
With a box-and-whisker plot, the box represents the upper and lower quartiles, the vertical line inside the box represents the median, and the lines on either side of the box show the high and low of the range.
Largest Median: Medians are the same because the verticle line inside the boxes is at 7 for both
Largest Range: Ms Castro's Class- the lines on either side of the box for Ms Castro go from 1-10 while the other class only goes from 4-10.
Largest IQR (interquartile range) Ms. Castro's class: their IQR goes from 5-8 while the other class only goes from 6-8
Answer:
same median and CASTRO CASTRO just took the TYS on algebra nation
Step-by-step explanation:
Please help ASAP
(k+5)(k−5)=k^2 −25
Eleanor says that k+5 is a factor of k^2-25
Isabel says that k^2 -25 is divisible by k+5
Who is correct?
Answers
Answer:
both are
Step-by-step explanation:
A number, or a polynomial, is "divisible" by a "factor." Since (k+5) is a factor of (k^2-25), (k^2-25) is divisible by (k+5). Both Eleanor and Isabel are correct in their description.
Which are the maximum values ? I will add a picture please help
Answers
Answer:
58 at the point (9,8)
7 at the point (1, 1)
Step-by-step explanation:
The maximum points will be found in the vertices of the region.
Therefore the first step to solve the problem is to identify through the graph, the vertices of the figure.
The vertices found are:
(1, 10)
(1, 1)
(9, 5)
(9, 8)
We look for the values of x and y belonging to the region, which maximize the objective function [tex]f(x, y) = 2x + 5y[/tex]. Therefore we look for the vertices with the values of x and y higher.
(1, 10), (9, 5), (9, 8)
Now we substitute these points in the objective function and select the one that produces the highest value for f (x, y)
[tex]f(1, 10) = 2(1) + 5(10) = 52\\\\f(9, 5) = 2(9) + 5(5) = 43\\\\f(9, 8) = 2(9) + 5(8) = 58[/tex]
The point that maximizes the function is:
[tex](9, 8)[/tex] with [tex]f(9, 8) = 58[/tex]
Then the value that produces the minimum of f(x, y) is (1, 1)
[tex]f(1, 1) = 2(1) + 5(1) = 7[/tex]
What is the sum of the series? 5∑i=1 4i
Answers
Answer:
60
Step-by-step explanation:
∑[i=1,5] 4i = 4·1 + 4·2 + 4·3 + 4·4 + 4·5
= 4 + 8 + 12 + 16 + 20
= 60
micah has 10 more fish than cella has. together, micah and cella have 34 fish. how many fish does micah have
Answers
Answer:
22 fish
Step-by-step explanation:
cella has 12 fish. micheal has ten more 12+10=22. combind 22+12=34
Answer:
22 fish
Step-by-step explanation:
Abdul's gas tank is 1/5 full. After he buys 7 gallons of gas, it is 7/10 full. How many gallons can Abdul's tank hold?
Answers
Answer: 14 gallons
Step-by-step explanation:
Let's call the total gallons of gas Abdul's tank can hold x.
Then, based on the information given in the problem, you can write the following expression:
[tex]\frac{1}{5}x+7=\frac{7}{10}x[/tex]
Therefore, when you solve for x, you obtain the following result:
[tex]\frac{1}{5}x+7=\frac{7}{10}x\\\\\frac{1}{5}x-\frac{7}{10}x=-7\\\\-\frac{1}{2}x=-7\\\\-x=(-7)(2)\\x=14[/tex]
Find the area between 1.10 and 1.60 standard deviation above the mean.
Answers
Answer:
about 0.08087
Step-by-step explanation:
The statistics functions of your graphing calclulator can help you with that. It is a good idea to learn to use them.
I need help on this problem. I don’t understand it at all. Please help me.
Answers
When dealing with numbers, we find the LCM by factoring the numbers, and then choosing all the primes appearing, with the highest exponent possible.
Similarly, we will factor the polynomials first:
[tex] x^4+3x^3 = x^3(x+3)[/tex]
[tex]x^2-9 = (x+3)(x-3)[/tex]
[tex]x^3+6x^2+9x = x(x^2+6x+9) = x(x+3)^2[/tex]
The following factors emerged:
[tex]x,\ x^3[/tex] We will choose [tex]x^3[/tex] because it has the higher exponent[tex]x-3[/tex][tex]x+3,\ (x+3)^2[/tex] We will choose [tex](x+3)^2[/tex] because it has the higher exponent.So, the LCM is
[tex]x^3(x-3)(x+3)^2[/tex]
which of the following could be side lenths of a right triangle? A.) 0.9cm, 1.2cm, 1.5cm B.) 0.9cm, 1.5 cm, 1.5cm C.) 0.9 cm, 1.2cm, 1.8cm D.) 0.9cm, 0.6cm, 1.5cm
Answers
Answer:
The answer A
Step-by-step explanation:
B: You need a side that is longer than 2 equal sides. B is incorrect.
A: Try
9^2 + 12^2 = 15^2 if that works, A will work.
81 + 144 = 225
This works. I used these numbers because they were easier to see.
0.9^2 + 1.2^2 = 1.5^2
0.81 + 1.44 = 2.25
2.25 = 2.25
That is the answer A
But we have to check the other two.
C:
0.9^2 = 0.81
1.2^2 = 1.44
1.8^2 = 3.24 This won't work. 3.24 is just too big.
D:
0.9^2 = 0.81
0.6^2 = 0.36
1.5^2 = 2.25 It's too far away.
In a function, each x-value has ________ y-value.
Answers
Explanation:
In a function, each x-value has one y-value.
___
That is the definition of a relation that is a function.
Final answer:
Each x-value in a function has exactly one corresponding y-value. Functions map elements of the domain to unique elements in the range, which can be represented graphically and must pass the vertical line test. The derivative in calculus, such as dy/dx, reflects the rate of change between these variables.
Explanation:
In a function, each x-value has one corresponding y-value. This is a foundational concept in mathematics that defines a relationship whereby each input (or x-value) in the function produces exactly one output (or y-value). Essentially, a function maps each element of the domain to exactly one element in the range.
An example of a function is y = f(x), which could represent a linear function like y = 3x + 2. In this case, for every x-value, there is a specific y-value determined by the function's formula. So if x were 1, then y = 3(1) + 2 = 5. The graphical representation of a function, such as its curve or line on a coordinate plane, must pass the vertical line test. That means if you draw a vertical line through any point on the graph, it should intersect the graph at no more than one point, confirming that each x-value has only one y-value.
Understanding functions is pivotal in different areas of mathematics, including calculus where the derivative of a function represents the rate of change of the y-value with respect to the x-value. In the case of the linear function y = 6+3x, the derivative dy/dx is constant at 3, implying that for every unit increase in x, y will increase by 3 units.
Can someone help me...
Answers
Answer:
48.3 cm^2
Step-by-step explanation:
The area of the enclosing square is that of a square 15 cm on a side, so is ...
square area = (15 cm)^2 = 225 cm^2
The white area is that of a quarter-circle of radius 15 cm, so that area is ...
quarter-circle area = (1/4)πr^2 = (π/4)·(15 cm)^2 = 56.25π cm^2 ≈ 176.7 cm^2
Then the yellow area is the difference ...
yellow area = square area - quarter-circle area
= (225 cm^2) - (176.7 cm^2)
yellow area = 48.3 cm^2
An animal shelter spends $4.50 per day to care for each bird and $6.50 per day to care for each cat. Kaylee noticed that the shelter spent $96.00 caring for birds and cats on Thursday. Kaylee found a record showing that there were a total of 16 birds and cats on Thursday. How many birds were at the shelter on Thursday
Answers
Answer:
4
Step-by-step explanation:
Let b represent the number of birds. Then the cost of care for b birds and 16-b cats was ...
4.50b +6.50(16-b) = 96.00
-2.00b = -8.00 . . . . . . . . . . . . simplify, subtract 104
b = 4 . . . . . . . . . . . . . . . . . . . . .divide by -2
The number of birds at the shelter on Thursday was 4.
write the equation 2x-3y=6in slope -intercept form
Answers
Answer:
y = 2/3 x -2
Step-by-step explanation:
Slope intercept form is y = mx+b where m is the slope and b is the y intercept
We need to solve for y
2x-3y = 6
Subtract 2x from each side
2x-2x-3y=-2x+6
-3y = -2x+6
Divide by -3
-3y/-3 = -2/-3x+6 /-3
y = 2/3 x -2
The slope is 2/3 and the y intercept is -2
The coordinates A(0,0), B(0,3), C(4,3) and D(4,0) are graphed and connected together. What 3 dimensional shape will be created when this shape is rotated about the y-axis?
Answers
a cube would be formed as ABCD form a square when graphed
tabia stores her hair bands in a cube shaped container. the cube has a volume of 64 cubic inches. What is the lenght of the edges of the cube?
Answers
Answer:
The length of the edge of the cube = 4 inches
Step-by-step explanation:
* Lets describe the cube
- It has 6 faces all of them are squares
- It has 8 vertices
- It has 12 equal edges
∵ The volume of any formal solid = area of the base × height
∵ The base of the cube is a square
∴ Area base = L × L = L² ⇒ L is the length of the edge of it
∵ All edges are equal in length
∴ Its height = L
∴ The volume of the cube = L² × L = L³
* Now we have the volume and we want to find the
length of the edges
∵ Its volume = 64 inches³
∴ 64 = L³
* Take cube root to the both sides
∴ ∛64 = ∛(L³)
∴ L = 4 inches
* The length of the edge of the cube = 4 inches
The length of the edges of the cube is 4 inches.
Given that the volume V is 64 cubic inches, we can set up the equation:
[tex]\[ a^3 = 64 \][/tex]
To solve for a , we take the cube root of both sides:
[tex]\[ a = \sqrt[3]{64} \][/tex]
The cube root of 64 is 4, since [tex]\( 4^3 = 4 \times 4 \times 4 = 64 \).[/tex]
Therefore, the length of the edges of the cube is 4 inches.
Adriana collects rainwater in a large barrel that weights 10 pounds. When there are 10 gallons of water in the barrel, the total weight of the barrel and the water is 93.4 pounds. When there are 20 gallons of water, the total weight is 176.8 pounds. Which equation and graph match this situation?
Answers
Answer:
A. y = 8.34x + 10
Step-by-step explanation:
The first choice is appropriate to the situation where y=10 when x=0 and where y increases by 83.4 when x increases by 10.
___
The equation of selection D is the same and is also appropriate, but the graph does not match the equation. The equations of the other choices are incorrect, as are the graphs.
The linear equation which represents the data is : y = 8.34x + c. Hence, correct option is A.
The linear equation for the graph can be expressed in the form :
y = bx + c b = slope ; c = interceptb = change in y / change in x
Change in y :
176.8 - 93.4 = 83.4Change in x :
20 - 10 = 10Hence , slope , b = (83.4 /10) = 8.34
The value of the intercept, c ;
93.4 = 8.34(10) + c
93.4 = 83.4 + c
c = 10
Hence, the linear equation is :
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marcia is placing a fence around the circular flower bed in her garden. the diameter of the flower bed is 3 feet. how much fencing should marcia use? Use 3.14 for \pi. Round to the nearest tenth if necessary.
Answers
Answer:
9.4 ft
Step-by-step explanation:
The formula for the circumference of a circle is ...
C = πd . . . . . where d represents the diameter
Putting your numbers into this equation gives ...
C = 3.14·(3 ft) = 9.42 ft
Rounding as required gives the length of fence as 9.4 ft.
To find the length of fencing needed for a circular flower bed, use the formula C = π * d, where C is the circumference and d is the diameter of the circle.
Explanation:To find the length of fencing needed to go around a circular flower bed, we need to calculate the circumference of the circle. The circumference can be found using the formula C = π * d, where π is approximately 3.14 and d is the diameter of the circle. In this case, the diameter of the flower bed is 3 feet, so the circumference is 3.14 * 3 = 9.42 feet.
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Please help! The following three shapes are based only on squares, semicircles, and quarter circles. Find the perimeter and the area of each shaded part.
Answers
Answer:
perimeter = (18 +9π) cm
area = (81 -20.25π) cm^2
Step-by-step explanation:
The perimeter of the shaded area is the circumference of the circle added to two sides of the square. The circumference of the circle is π times the diameter, so the perimeter is ...
p = 2(9 cm) + π(9 cm) = (18 +9π) cm
___
The area of the shaded portion is the difference between the area of the square and the area of the circle. The area of the square is the square of the diameter. The area of the circle is π/4 times that value.
A = (9 cm^2) + (π/4)(9 cm^2) = (81 +20.25π) cm^2
_____
Comment on circle area
The formula you often see is ...
A = πr^2 . . . . r is the radius
since r = d/2, where d is the diameter, this can also be written as ...
A = π(d/2)^2 = (π/4)d^2
Here, the diameter of the circle is the same as the side length of its enclosing square, so the area of the circle is π/4 times the area of the enclosing square.
Answer:
Area= [tex]81-\frac{81}{4}\pi[/tex]
Perimeter= [tex]9\pi +18[/tex]
1. A claim states that a specific crimes occurs in the given proportions shown in the table for October through March. Use the frequencies from randomly selected crimes to find the test statistic using a 0.01 significance level needed to test the claim.
A. 15.086
B. 9.843
C. 6.683
D. 749.500
(plus other questions in attached)
Answers
Answer:
C. 6.683
Step-by-step explanation:
If $389 is invested @ 3.9% interest compounded monthly for 6 years what would be the total in the account?
Answers
Answer:
$491.37
Step-by-step explanation:
The appropriate formula for the future value of a single investment is ...
A = P(1 +r/n)^(nt)
where P is the principal invested (389), r is the annual rate (0.039), n is the number of compoundings per year (12), and t is the number of years (6).
Putting the given numbers into the formula, you get ...
A = 389·(1 +.039/12)^(12·6) = 389·1.00325^72 ≈ 491.37
The total in the account after 6 years will be $491.37.
which number is an irrational number
Answers
I’m pretty sure it’s A
Answer: A
Step-by-step explanation:
Find the vertex of the given function. f(x) = |x + 1| - 7
Answers
Vertex is at (-1,-7), because the |x+1| moves the graph left 1 and -7 moves the graph down 7.
Answer:
the second answer is a
Step-by-step explanation:
edge 2020
help please, anyone thank you
Answers
Answer:
Part A: A (6 , 11) , B (5 , 6) , C (7 , 1) , D (0 , 8)
Part B: A (-6 , -11) , B (-5 , -6) , C (-7 , -1) , D (0 , -8)
Step-by-step explanation:
* Lets study the reflection about the two axes X and Y
- The distance between the point and the axes of reflection =
the distance between its image and the axes
- The point and the its image are on opposite sides of the axes
- If a point (x , y) reflected about x axis, that means the point
will move vertically
- Moving vertically means we will change the sign of the y-coordinates
∴ The image of (x , y) after reflection about x-axis is (x , -y)
- If a point (x , y) reflected about y axis, that means the point
will move horizontally
- Moving horizontally means we will change the sign of the x-coordinates
∴ The image of (x , y) after reflection about x-axis is (-x , y)
* Now lets use the explanation above to solve our problem
- At first lets right the original point of the quadrilateral ABCD
∵ A (-6 , 11) , B (-5 , 6) , C (-7 , 1) , D (0 , 8)
Part A: The y-axis is the line of reflection
- Lets change the signs of x-coordinates in all points
∴ The new points after reflection about y-axis is:
A (6 , 11) , B (5 , 6) , C (7 , 1) , D (0 , 8)
- Note: The point D does not change because x-coordinate is 0
and there is no sign for the 0
Part B: The x-axis is the line of reflection
- Lets change the signs of y-coordinates in all points
∴ The new points after reflection about x-axis is:
A (-6 , -11) , B (-5 , -6) , C (-7 , -1) , D (0 , -8)
Consider the two way table.
Answers
➷ Find the total data in the first row:
90 + 30 = 120
Now divide each of these values by the total:
(30/120) = 0.25
(90/120) = 0.75
It would be 0.25 in the first box and 0.75 in the second.
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
Answer:
Group1 .18
Group2 = .54
Step-by-step explanation:
To find the relative frequency, you divide the number by the total number
The total number is 30+90+14+32 = 166
Category 1 Group 1 has 30 in it
The relative frequency is 30/166 = .180722892 = .18
Category 1 Group 2 has 90 in it
The relative frequency is 90/166 =.542168675=.54
Please hurry I will mark brainliest and 20 points
simplify sqrt0.08^12
a.(0.08)^6
b.(0.8)^6
c.(0.16)^6
d.(0.12)^8
Answers
Answer:
a) (0.08)^6
Step-by-step explanation:
Given in the question,
[tex]\sqrt{0.08^{12} }[/tex]
As we know that
[tex]\sqrt{x} = x^{1/2}[/tex]
So,
[tex]\sqrt{0.08^{12}[/tex] = [tex]0.08^{12(1/2)}[/tex]
[tex]0.08^{12/2}[/tex]
[tex]0.08^{6}[/tex]
Create a second equation so the system has no solution. y=3/4x-4
Answers
Answer:
y=3/4 *x
Step-by-step explanation:
1. the given equation is the equation of line in slope-interception form (y=kx+b), where 3/4 is 'k' and (-4) is 'b'.
2. if the system of the two equations has no solution, it means, the 2d line is parallel to the given one, then 'k' of the 2d line is the same value.
3. common view of the equation of the 2d line is y=3/4 *x+b, where 'b' is number. For example, y=3/4x; y=3/4 *x+1; y=3/4 *x-5/8, etc.
One example of a linear function that generates a system without a solution is given by:
[tex]y = \frac{3}{4}x + 5[/tex]
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.If two equations have the same slope but different intercepts, they never intersect each other, that is, a system without solutions is generated. Hence, one possible example in this problem is given by:
[tex]y = \frac{3}{4}x + 5[/tex]
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Write 765,056 in word form
Answers
Seven thousand sixty-five fifty six
Answer:
seven hundred sixty-five thousand fifty-six
Step-by-step explanation:
Your Welcome
The difference between simple and compound interest in a savings account is that ______________.
Answers
Answer:
The difference is that the simple interest gives you interest only on the deposited amount in the account while the compound interest is calculated over the deposited amount and the previous interest amount added to the deposited amount.
Step-by-step explanation:
The difference between simple and compound interest is that simple interest is calculated only on the principal amount, while compound interest is earned on past interest.
Explanation:The difference between simple and compound interest in a savings account is that simple interest is an interest rate calculation only on the principal amount, while compound interest is interest that is earned on past interest. This means that with compound interest, the total amount of savings will grow dramatically over time. To illustrate this, consider the example of putting $1,000 in a savings account with 10% interest. With simple interest, after one year, you will have $1,100. But with compound interest, if you leave the $1,100 in the account and continue to earn 10% interest, you will have $1,210 at the end of year two.