Person A buys 10 granola bars and 6 cups of yogurt for $18. Person B buys 5 granola bars and 4 cups of yogurt for $9.50. Find the cost of each item.
Answers
Answer:
granola bar: $1.50yogurt: $0.50Step-by-step explanation:
You want the cost of each item when person A buys 10 granola bars and 6 cups of yogurt for $18, and person B buys 5 granola bars and 4 cups of yogurt for $9.50.
EquationsThe equations describing the relations can be written ...
10g +6y = 18 . . . . . . . person A's purchase
5g +4y = 9.50 . . . . . . person B's purchase
SolutionSubtracting half of the first equation from the second, we find ...
(5g +4y) -1/2(10g +6y) = (9.50) -1/2(18)
y = 0.50 . . . . . . . . . . simplify
Substituting this into the first equation gives ...
10g +6(0.50) = 18
10g = 15 . . . . . . . . . . subtract 3
g = 1.50 . . . . . . . . . divide by 10
Each granola bar costs $1.50; each cup of yogurt costs $0.50.
__
Additional comment
The attachment shows the solution found using a calculator to find the reduced row-echelon form of the augmented coefficient matrix. The variable values are in the right column of the reduced matrix. This tells us granola bars are $1.50, and yogurt cups are $0.50, as we found above.
Related Questions
2x × 3y(4 - 8) + 8(4y - 2x)
Answers
Answer:
5.3
Step-by-step explanation:
Triangle EFG is dilated by a scale factor of 2/3 to form a triangle E'F'G'. What is the measure of side E'F'?
Answers
By using scale factor formula we can evaluate the measure of side EF.
What happens when we dilate a triangle?When a triangle is dilated by scale factors.The base and height change by the scale factor s while the area changes by a factor of s^2. While the scale distances between points dilations do not change angles.Dilation is used to make the objects larger or smaller.
How do you find scale factor?The scale factor can be calculated when the new dimensions and the original dimensions are given. The basic formula to find the scale factor of a figure is Scale factor = Dimension of the new shape ÷ Dimension of the original shape.
From the question ΔE'F'G' is the image formed by the dilation of preimage ΔEFG.
Therefore,
2/3 =[tex]E_{1}[/tex][tex]F_{1}[/tex]/EF
EF=3/2[tex]E_{1}[/tex][tex]F_{1}[/tex]
By substituting any value of F'G' given in the equation we can evaluate the measure of side FG.
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Solve 12 (10x + 3 -8y)
Answers
Answer:
120x - 96y + 32
Step-by-step explanation:
12 (10x + 3 -8y)
We use the distributive property to solve
120x - 96y + 32
One of the most important when writing the order of an equation is always written the number with the variable first; that is why the answer is
120x - 96y + 32
What will the width of the paper need to be ?
Answers
It would need to b D, 5 inches.
Uh please answer correctly I’ll mark you brainlist after I see if it’s correct!
Answers
Answer:
The equation for the volume of a rectangular prism is V=whl or width x height x length. The width is 7/2, the height is 7/5, and the length is 5. Multiply all of these numbers to get 49/2 or 24.5.
Answer:
24.5 cm cubed
(3.5 (7/2) times 1.4 (7/5) times 5)
Step-by-step explanation:
7/2cm multiplied by 7/5cm multiplied by 5cm
(3.5 times 1.4 times 5 = 24.5)
Piper has a coin collection. She keeps 12 of the coins in her box, which is 2% of the collection. How many total coins are in her collection?
Answers
The total number of coins Piper has in her collection is 100 coins.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, Piper has a coin collection. She keeps 12 of the coins in her box, which is 2% of the collection.
Let, The total number f coins in the box be 'x'.
Therefore, 2% of 'x' is 12 which can be numerically expressed as,
(2/100)×x = 12.
0.02x = 12.
x = 2/0.02.
x = 100.
So, She has 100 coins in her box.
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Please help me!
Will give you brainlist!!!!
Answers
2nd example- 5x, 2y to the third power, 7xy, x to the 5th power.
Example of binomial- x-2 x -2
2nd example- x-6 x negative 6 x negative 6 again.
Example of trinomial- x+y+z is a trinomial in three variables, x, y and z. 2a to the second power + 5a +7 is a trinomial in one variables. Xy+ x+2y to the second power is a trinomial in two variables x and y.
Examples of polynomial- 3x+2x-5
2nd example- 3x to the second power -2x -10.
11 in.
9 in.
4
8 in.
What is the volume of the figure above?
Answers
Answer:
Mizuki is here to help you! The volume of the figure above is 176[tex]in^2[/tex], but since you can only put numbers you need to put in 176.
Step-by-step explanation:
11 x 4 x 8 ÷ 2 =
44 x 8 ÷ 2 =
352 ÷ 2 =
176
Making connections between arithmetic sequences and linear function
Use the graph or the formula to write the equation of the line in a slope intercept form
Answers
on solving the provided question, we can say that - the graphs which is shown as the straight line graph.
What is graphs?Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph
here,
then line which is drawn is straright,
so the graph is straight .
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Answer ALL of the questions. LOOK AT ALL THE PICTUERS .Show your work. if you can show me a picture of your work and the step you did to complete it. HELP ME PLZZ.
BRAINLEST TO I GIVE BRAINLIEST
Answers
To swap a figure to 90 degrees counter clock wise turn the points from
(x,y) to (-y,x)
Let’s get your points
(-2,3) ; (-4,2) ; (-2,-4)
Swap the values and make the new x’s negotiate
(-3,-2) ; (-2,-4) ; (4,-2)
These should be the points of the new figure with is 90 degrees counterclockwise of the first one.
10.
To find x you can either:
Add 93 and 54
Or
Find the missing value of the triangle and subtract it from 180. Let’s do both
x = 93 + 54
x = 147
Or
180 - 93 - 54
33
180 - 33 = 147
x = 147
8.
First we dilate the coordinates by 0.5
(-4,6) ; (2,6) ; (2,-4) ; (-4,-4)
Basically divide each x and by by two
(-2,3) ; (1,3) ; (1,-2) ; (-2,-2)
Two units left would be to subtract two from the x values
(-4,3) ; (-1,3) ; (-1,-2) ; (-4, -2)
Add three to each y value
New coordinates:
(-4,6) (-1,6) (-1,1) (-4,1)
6.
Since these are the same circle, then we need to multiply the radius by 2 and then make the newly formed diameters equal to each other
2(6x) = 10x + 8
Multiply
12x = 10x + 8
Get x on one side
2x = 8
Divide
x = 4
Plug in 4 for an equation
2(6(4))
48
Circumference = pi * diameter
Unsure if you use 3.14 for pi
If you use 3.14 :
(3.14) (48) = 150.72
If you use pi :
Pi (48) (rounded) = 150.80
David launches a rock straight up over the edge of a 60-foot cliff and into the ocean. after 4 seconds, the rock reaches a maximum height of 108 feet. Six seconds later, the rock enters the ocean.
A) Write a function to model the scenario
B) Create a table of at least five values to represent the scenario
C) Identify how you see the X- and Y- intercepts in the table, graph, and equation.
Answers
Answer:
David launches a rock straight up over the edge of a 60-foot cliff and into the ocean. After 4 seconds, the rock reaches a maximum height of 108 feet. Six seconds later, the rock enters the ocean. . Create a graph to represent the scenario. The graph should include at least the x- and y-intercepts and the vertex. (A complete graph consists of axis labels and appropriate scales, ordered pairs for each identified point, the function, and appropriate domain/range.) . Write a function to model the scenario. Part C. Create a table of values to represent the scenario. Be sure to include at least five values. Values should include at least the x- and y-intercepts and the vertex. Part D. Identify how you see the x- and y-intercepts and vertex in the table, graph, and equation. (Hint: You may want to rewrite the equation in equivalent forms.)
Step-by-step explanation:
please help!!!!
Solving Systems of Linear Equations by Elimination
C.
0.6x = 1.2 +0.3y
2.2x-1.8y-1.6=0
Answers
By using systems of linear equations by elimination, it can be determined that x = 0.5 y +2 and 2.2x-1.8y-1.6=0 are equivalent to x=0.818182 and y+0.727273.
What do you meant by Systems of Linear Equations by Elimination ?Using elimination, let's fix your system. 0.6 x=1.2+0.3 y, 2.2 x-1.8 y-1.6=0 in the graph, and y=2 x-4, y=1.222222 x-0.88888
Step 1: Divide both sides by 0.6 to find the solution for x = 0.6 x=1.2 + 0.3 y.
[tex]$$\begin{aligned}& \frac{0.6 x}{0.6}=\frac{0.3 y+1.2}{0.6} \\& x=0.5 y+2\end{aligned}$$[/tex]
Let's figure out what x is, 2.2 x-1.8 y-1.6=0.
First, multiply both sides by 1.8 y.
[tex]$$\begin{aligned}& 2.2 x-1.8 y-1.6+1.8 y=0+1.8 y \\& 2.2 x-1.6=1.8 y\end{aligned}$$[/tex]
Add 1.6 to both sides in step two.
[tex]$$\begin{aligned}& 2.2 x-1.6+1.6=1.8 y+1.6 \\& 2.2 x=1.8 y+1.6\end{aligned}$$[/tex]
3. Multiply both sides by 2.2.
[tex]$\frac{2.2 x}{2.2}=\frac{1.8 y+1.6}{2.2}$[/tex]
x=0.818182 y+0.727273
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What are the opposites of 8, −3.5, 1.15, and 7/1/4
Answers
-8, 3.5, -1.15, and -7/1/4
Which of the following numbers is 90 divisible by?
2, 3, 4, 5, 6, 9, and 10 only
A. 2, 3, 4, 5, 6, 9, and 10 only B. 2, 3, 5, 6, 9 and 10 only
C. 2, 3, 6, 9, and 10 only D. 2, 5, 9, and 10 only
Answers
Answer:
B
Step-by-step explanation:
90/2= 45
90/3= 30
90/5= 18
90/6= 15
90/9= 10
90/10= 9
90/4= 22.5
Graph the line y=-2x-1
Answers
Answer:2024
Step-by-step explanation:
For the function
[tex]f(x)=x^2-2x-8\\[/tex]
Find the equation of the line of symmetry.
no links please and thank you! Please help ASAP! Will give Brainliest!
Answers
Answer:
x = 1
Step-by-step explanation:
For a quadratic function [tex]f(x)=ax^2+bx+c[/tex], the axis of symmetry is
[tex]x=-\frac{b}{2a}[/tex].
This comes from using part of the Quadratic Formula for finding zeros of the function:
[tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} = \frac{-b}{2a} \pm \frac{\sqrt{b^2-4ac}}{2a}[/tex]
See the -b/(2a) in the first term? That's the x-coordinate of the vertex (turning point) of the parabolic graph of the function. The axis of symmetry goes through the vertex.
if you are traveling at 60 mph you will travel almost the length of a football field in how many seconds
Answers
Time taken to cross the field will be 3.36 seconds.
What does physics mean by speed?Velocity is the rate and direction of an object's movement, whereas speed is the time rate at which an object is moving along a path. In other words, velocity is a vector, whereas speed is a scalar value. There are four different types of speed. constant speed, varying speed, an average rate, instantaneous speed.
Solution,
Given,
speed=60 mph
length of football field=0.056 miles
time taken to cross it = distance/speed
time=0.056/60=0.00093 hour = 3.36 seconds.
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HELPPPP!!! PLEASEEE!!! THANK U:)
Answers
Answer:
1st, 2nd, and 3rd options
Step-by-step explanation:
Some of the main properties of a kite:
It has no parallel sides
It has two pairs of congruent sides
It has two pairs of congruent angles
the diagonals are perpendicular
the longer diagonal bisects the other diagonal
opposite sides are not congruent
Answer:
hope this helps you bye..
3) Breanna thought of a number, subtracted 4 from it, and then multiplied her answer by 3. She got
a final number of 24. What was her starting number?
Answers
A student researcher compares the ages of cars owned by students and cars owned by faculty at a local state college. A sample of 224 cars owned by students had an average age of 5.06 years. A sample of 233 cars owned by faculty had an average age of 7.19 years. Assume that the population standard deviation for cars owned by students is 3.42 years, while the population standard deviation for cars owned by faculty is 2.81 years. Determine the 95% confidence interval for the difference between the true mean ages for cars owned by students and faculty. Step 2 of 3 : Calculate the margin of error of a confidence interval for the difference between the two population means. Round your answer to six decimal places.
Answers
The difference between the population means - 3.4 and -1.84 when calculated is found to be -2.62 years.
The 95% confidence interval for the difference in true mean ages of cars owned by students and faculty is between -3.4 and -1.84 years.
We know that the sample of 138 cars which belongs to the students have an average age of 5.13 years. The standard deviation = 3.45 years.
Then again,
A sample of 111 cars which belongs to the faculty have an average age of 7.75 years. The standard deviation= 2.08 years.
So the difference between them will be , s - f
= 3.45 - 2.08 = 1. 37
and the mean will be , mean of students - mean of faculty =
-2.62.
This is the point of difference between their means.
The SD is found to be as 0.3961.
and MOE is 0.78
with these details now we will calculate the required intervals,
The lower end is found to be as -2.62 - 0.78 = -3.4
The upper end is found to be as -2.62 + 0.78 = -1.84
Therefore, the mean difference between the cars is - 3.4 and -1.84.
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ILL BRAINLIEST YOU PLEASE HELP ME
Answers
Answer:
L = 40 The length is AC
W = 20 The width is AB
Step-by-step explanation:
Givens
P = 120
AB = 1/2 AC
Solution
P = L + L + W + W
W = 1/2 L
P = L + L + 1/2L + 1/2L Combine like terms
P = 3L
120 = 3L Divide by 3
3L/3 = 120/3
L = 40
W = 1/2 L
W = 1/2 * 40
W = 20
During a sale, a store offered a 20% discount on a tablet computer that originally sold for $490. After the sale, the discounted price of the tablet computer was marked up by 20%. What was the price of the tablet computer after the markup? Round to the nearest cent.
Answers
Step-by-step explanation:
I think you have to change 20% to a fraction
The table shows information about the masses of some dogs.
a) Work out the minimum number of dogs that could have a mass of more than
27 kg
b) Work out the maximum number of dogs that could have a mass of more than
27 kg
Answers
a) The minimum number of dogs that could have a mass of more than 27 kg is 6.
b) The maximum number of dogs that could have a mass of more than 27 kg is 18.
We have a table which shows information about the masses of some dogs.
Now , we need to determine the minimum number of dogs could have a mass more than 27 kg . Let us see dogs with mass of more than 27 kg present in the following intervals , 20≤x<30 and 30≤x<40 with 12 and 6 respectively.
But we wants minimum of 12 and 6 is 6 .
so, the minimum number of dogs with mass more than 27 kg is 6.
b) We need to determine maximum number of dogs with mass more than 27 kg ,so Maximum is equals to sum of number of dogs present in interval 20≤x<30 and in interval 30≤x<40 = 12+6 = 18. So, required maximum number of dogs are 18.
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Complete question:
The above table shows information about the masses of some dogs.
a) Work out the minimum number of dogs that could have a mass of more than 27 kg
b) Work out the maximum number of dogs that could have a mass of more than 27 kg
Wanda has 5 different fish in a small, crowded tank. She decides to randomly scoop up individual fish and transfer them to a new tank until a total of 4 fish have been moved. How many sequences of 4 fish are possible?
Answers
Answer:
64 sequences of 4 fish are possible.
Find the measure of the arc or angle indicated
Answers
Answer:
the term arc is used for a portion of a circle along its circumference. The size of the arc is usually given by the size of the angle subtended by the arc at the center or the length of the arc. The angle subtended at the center is also known as the angle measure of an arc or informally the arc measure.
Step-by-step explanation:
Answer:
A) 64°
Step-by-step explanation:
By intersecting secants theorem:
[tex] m\angle ACB = \frac{1}{2} (m\widehat {AS} - m\widehat {BD}) [/tex]
[tex] 35\degree = \frac{1}{2} (134\degree - m\widehat {BD}) [/tex]
[tex] 70\degree =134\degree - m\widehat {BD} [/tex]
[tex] m\widehat {BD} =134\degree - 70\degree[/tex]
[tex] m\widehat {BD} =64\degree[/tex]
Which of the following is a net?
Answers
Answer:
C.
Step-by-step explanation:
why?
a net spreads the actual look when it's open
HOPE IT HELPS
(FROM CROSS)
What does an inverse function look like?
Answers
Inverse functions are indicated by the symbol [tex]f^{-1}[/tex] and are functions whose inverse is the function itself (x).
A function takes in values, applies specific operations to them, and produces an output. The inverse function acts, agrees with the outcome, and returns to the initial function. The inverse function, which also returns the beginning value, returns the result of a function.
The relationship that results from swapping out an independent variable for a variable that depends on a given equation, and which may or may not be a function. Consider the inverse relationship between the functions f and g: f(g(x)) = g(f(x)) = x.
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I don't get this question can some one please help me solve it
Answers
Answer:
3, 2
Step-by-step explanation:
In order for the equation to be equal to zero, the following must be true:
x-3 = 0 or,
x-2 = 0
Therefore the 2 solutions are x=3, x=2
Write an equation for this situation: The cost of renting a car is $30 per day.
Answers
x: amount of days
y=30x
A spinner with equal sections numbered from 1 to 5 is spun twice. Raul is finding the probability that both spins will result in an even number. Find his mistake and explain what he should have done instead.
(2/5) x (1/4) =(2/10)
please help im really just about to cry myself to sleep and call it a day bcs im off the edge rn and i have to deal with school at the same time T_T
Answers
Answer:
his mistake is that he didn't need to remove one even number on the spinner so we just need to take 2/5x1/5equals2/25