⦁ At store A, 3 pounds of apples cost $12. ⦁ At store B, the cost is given by y = 2x where y is the cost in dollars and x is the number of pounds of apples. ⦁ The cost of apples at store C is shown in the graph. Answer the questions to find out which store's apples are the least expensive. 1. What is the unit price of apples at store A? Explain how you found this unit price. (2 points) 2. What is the unit price of apples at store B? How did you use the equation to find the unit price? (2 points) 3. What is the unit price of apples at store C? How did you use the graph to find the unit price? (3 points) 4. Which store has the lowest unit price for apples? (3 points)
Answers
1. The unit price of apple in store A is $4
2. The unit price of apple in store B is $2
3. The unit price of apple in store C is $3
4. The store with the lowest unit price is store B
1. How to determine the unit price at store A
We can obtain the unit price at store A by doing the following:
3 pounds of apples cost $12.
Therefore,
1 pound will cost = (1 × pound $12) / 3 pounds = $4
Thus, the unit price is $4
2. How to determine the unit price at store B
We can obtain the unit price at store B by doing the following:
y = 2x
Number of pound (x) = 1Cost (y) = ?y = 2x
y = 2 × 1
y = $2
Thus, the unit price is $2
3. How to determine the unit price at store C
We can obtain the unit price at store C by obtaining the slope of the graph. This can be obtaioned as follow:
x coordinate 1 (x₁) = 1x coordinate 2 (x₂) = 3y coordinate 1 (y₁) = 3y coordinate 2 (y₂) = 9Slope (m) =?m = (y₂ – y₁) / (x₂ – x₁)
m = (9 – 3) / (3 – 1)
m = 6 / 2
m = 3
Thus, the unit price is $3
4.How todetermine the store with the lowest unit price
Unit price at store A = $4Unit price at store B = $2Unit price at store A = $3From the above, we can conclude that store B has the lowest unit price
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Related Questions
g(y)= y - 15/y
h(y) = − 3y
Evaluate.
h(g(5)) =
Answers
Answer: -6
Select all the lines that are perpendicular to 3x – y = 10. A. y = 3x + 5 B. y = –13x + 17 C. x + 3y = 27 D. y – 2 = 13(3x + 36) E. y = 13x + 2
Answers
From the list given, the line that is perpendicular to 3x – y = 10 is x + 3y = 27. (Option C)
What is a perpendicular line?It is to be noted that lines that intersect at a right angle (90 degrees) are considered perpendicular lines.
To justify the above results, we recall that when two lines are perpendicular then the product of their slope is -1.
The slope is given by y = mx + c where m is the slope.
Hence, the slope of the given equation 3x -y = 10 is arrived at by re-writing the expression as follows:
Y = 3x -10 where
slope m₁ = 3
given Lets attempt to derive the slope of the options given:
1) y = 3x + 5
m₂ = 3
The product of the slopes are:
= m₁ x m₂
= 3 x 3
⇒ 9 ≠ -1
Therefore, this is not a perpendicular line.
2) y = -13x + 17 our new m₂ = -13
m₁ x m₂
⇒ 3 x -13
⇒ -39 ≠ -1
Again, this is not the required line.
3) x + 3y = 27 [divide all sides by 3]
y = -1/3(x) + 9
The new m₂ = -1/3
Compute for slope:
= 3 x - (1/3)
= -3/3
= -1
Hence, x + 3y = 27 is the perpendicular line.
4) y -2 = 13(3x + 36)
y = 39x + 468 +2
y = 39x + 470
New Slope (m₂) = 39
Solving to check the slope, we have:
m₁ x m₂ = 3 x 39
⇒ 117 ≠ -1.
Thus, we have our final answer as option C.
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The required line which is perpendicular to the given line is x + 3y = 27. Option C is correct.
What is the slope perpendicular line?
The slope of the perpendicular lines is equal to the inverse and of the opposite sign.
Here,
Standard equation of the line,
y = mx + c
The property of the perpendicular line states that the product of their slopes is equal to -1.
So the slope of the given line is m = 3,
Let the slope of the perpendicular line that we have to determine, be x
According to the property,
The slope of line × slope of perpendicular line = -1
3 × x = -1
x = -1/3
So looking forward to the option, the line that has a slope of -1/3 is x + 3y = 27. because
x + 3y = 23
Transform the above equation to standard form,
y = -1/3x + 23
From the above equation, the slope of the above line is m = -1/3,
Thus, the required line which is perpendicular to the given line is x + 3y = 27. Option C is correct.
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13. Sofia's car can travel 228 miles on 6 gallons of gas.
a. Write an equation to represent the distance, y, in miles Sofia's
car can travel on x gallons of gas.
Answers
The most appropriate choice for unitary method will be given by-
y =38x is the equation to represent the distance, y, in miles Sofia's
car can travel on x gallons of gas.
What is unitary method?
Unitary method is the method in which the value of single unit can be calculated from the value of multiple unit and value of multiple unit can be calculated from the value of single unit.
Sometimes value of single unit is more than value of multiple unit
For example - Relationship between price of a commodity and quantity of a commodity
Sometimes value of single unit is less than value of multiple unit
For example - Relationship between number of men and number of days taken by those men to do a work
Here,
Let y be the distance travelled by Sofia's car in miles and let Sofia's
car can travel on x gallons of gas.
On 6 gallons of gas, Sofia's gas can travel 228 miles
On 1 gallon of gas, Sofia's car can travel [tex]\frac{228}{6}[/tex] miles
On 1 gallon of gas, Sofia's car can travel 38 miles
On x gallons of gas, Sofia's car can travel 38x miles
By the problem,
y = 38x
This is the equation to represent the distance, y, in miles Sofia's
car can travel on x gallons of gas.
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At a butcher shop, karl bought 2 7/20 lb of beef and some pork. he left with 14 14/25 lb of meat. Express the number of pounds of pork he bought using a decimal.
Answers
The number of pounds of pork he bought in decimal is 12.21 lb
Decimal:
A decimal is a number that consists of a whole and a fractional part. Decimal numbers lie between integers and represent numerical value for quantities that are whole plus some part of a whole.
For example 12.34 is a decimal.
Given,
At a butcher shop, karl bought 2 7/20 lb of beef and some pork. he left with 14 14/25 lb of meat.
Here we need to find the number of pounds of pork he bought using a decimal.
First, we have to convert the given fractions into decimal then we get,
Amount of beef = 2 7/20
Which is equal to,
=> 2 + 7/20
=> 2 + 0.35 = 2.35 lb
Similarly, total amount of meat = 14 14/25
=> 14 + 14/25
=> 14 + 0.56 = 14.56
Therefore, the amount of pork is,
=> total amount of meat - the amount of beef
=> 14.56 - 2.35
=> 12.21.
Therefore, the the number pounds of pork in decimal is 12.21 lb.
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A line through (-1,b) and (c,8) is parallel to a line through (-6,3) and (0,12). Find values of b and c that make the above statement true.
Answers
Answer:[tex]b=4, c=-7[/tex]
Step-by-step explanation:
Parallel lines have the same slope.
The slopes of the lines are [tex]\frac{8-b}{c+1}[/tex] and [tex]-\frac{3}{2}[/tex].
Therefore, [tex]\frac{8+b}{c+1}=-\frac{3}{2}[/tex], and one possible pair is [tex]b=4, c=-7[/tex].
Pat and Alex have a combined total of £63.
The ratio of Pat’s money to Alex’s money is 5 : 2
They each spend an equal amount on sweets.
The ratio of Pat’s money to Alex’s money is now 3 : 1
How much did Pat spend on sweets?
Answers
Answer:
£4.50
Step-by-step explanation:
ratio of Pat : Alex = 5 : 2 = 5x : 2x ( where x is a multiplier )
then
5x + 2x = 63
7x = 63 ( divide both sides by 7 )
x = £ 9
Pat has 5 × £9 = £45
Alex has 2 × £9 = £18
let the amount they spend on sweets be x , then ratio of money is 3 : 1
so 45 - x : 18 - x = 3 : 1
express the ratio in fractional form and equate proportionally
[tex]\frac{45-x}{18-x}[/tex] = [tex]\frac{3}{1}[/tex] ( cross- multiply )
45 - x = 3(18 - x)
45 - x = 54 - 3x ( add 3x to both sides )
45 + 2x = 54 ( subtract 45 from both sides )
2x = 9 ( divide both sides by 2 )
x = 4.5
Pat spent £4.50 on sweets
The average cost of producing x game disks for a computer is given by the function C(x)=2.6+5460/x. Find the number of game disks that must be produced for the average cost to be $4.70.
Answers
The number of game disks that must be produced for the average cost to be $4.70 is 2600.
Given:
The average cost of producing x game disks for a computer is given by the function C(x) = 2.6+5460/x
To determine the number of game disks that must be produced for the average cost to be $4.70.
Substitute the average cost in the equation and solve to find the value of x i.e. number of disks,
4.70 = 2.6 + 5460/x
4.70 - 2.6 = 5460/x
2.1x = 5460
x = 5460/2.1
x = 2600
Therefore, the number of game disks that must be produced for the average cost to be $4.70 is 2600.
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Which answer would be a sufficient counter example to the statement below? “Two angles that are supplementary are always different measures”
Answers
The counter example to the statement “Two angles that are supplementary are always different measures” is 90° and 90°.
What are supplementary angles?Supplementary angles are those angles that sum up to 180 degrees
In other words, two Angles are Supplementary when they add up to 180 degrees.
For example 130 degrees and 50 degrees are supplementary angles.
The statement says "two angles that are supplementary are always
different measures".
Therefore, the counter example to this statement is 90 degrees and 90 degrees. This is because they are the same and it still sum to 180 degrees.
In other words, the angles are supplementary and the same which is counter example to the statement.
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There are 100 students in Year 10.
Each student studies exactly one of French, German, and Spanish.
X girls study French and there are 3X girls in total.
2Y boys study German.
There are 35 students studying Spanish of which Y are boys.
Which of the following is an expression for the total number of students studying German?
Answers
The expression which correctly represents the number of students studying German as required is; 3y + 2x -35.
Which expression correctly represents the number of students studying German?It follows from the task content that the number of students studying German be determined from the given information.
Therefore since the total number of students is; 100.
35 students study Spanish of which y are boys, therefore, the number of girls studying Spanish is; (35 - y).
Also, since there are 3x girls in total and x of which study French, the remaining 2x study Spanish and German.
Hence, the number of girls who study German is; 2x - (35 - y).
Therefore, the total number of students (boys and girls) who study German is; 2y + 2x - (35 - y).
= 3y + 2x -35.
Ultimately, the total number of students who study German are; 3y + 2x -35.
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6.0 x 10^4 ÷ 4.0 x 10^8
Scientific Notation Please
Answers
Answer:
1.5x10^12
1500000000000
Step-by-step explanation:
Simplify the expression.
find equations of the lines that passe through the given point and are parallel to and perpendicular to the given line Y +4 =0 (-6,3)
Answers
Answer:
y = 3 and x = - 6
Step-by-step explanation:
y + 4 = 0 ( subtract 4 from both sides )
y = - 4
this is the equation of a horizontal line, parallel to the x- axis.
a parallel line will also be horizontal with equation
y = c ( c is the value of the y- coordinates the line passes through )
the line passes through (- 6, 3 ) with y- coordinate 3 , then
y = 3 ← equation of parallel line
a line perpendicular to the given line will be a vertical line with equation
x = c ( c is the value of the x- coordinates the line passes through )
the line passes through (- 6, 3 ) with x- coordinate - 6 , then
x = - 6 ← equation of perpendicular line
Use the information given to enter an equation in standard form.
Slope is 2, and (3, 5) is on the line.
Answers
Standard form of equation is 3x + 5y = 2.
Define equation.Ax+ By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y). When attempting to solve systems involving two linear equations, this form is also quite helpful. A linear equation has the conventional form Ax+ By=C. A slope-intercept form equation (y=mx+ b) must have the x and y on the same side of the equal sign and the constant on the opposite side in order to be converted to standard form. To relocate terms, use inverse operations.
Slope = 2
Points = (3, 5 )
Standard form of equation,
Ax + By = C
Equating,
3x + 5y = 2
Standard form of equation is 3x + 5y = 2.
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What is the slope of the line that passes through the points (-8, -1)(−8,−1) and (-8, -11)(−8,−11)? Write your answer in simplest form.
Answers
Answer:
Undefined slope
Step-by-step explanation:
Slope , m is equal to rise/run Or ( y1-y2) / ( x1 -x2)
This line is a vertical line at x = -8 And thus has undefined slope
(Because you cannot divide by zero)
Answer:
Undefined
Step-by-step explanation:
Hey! Let's help you with your question here! I am unsure if the points are correct cause you've written each one down twice. If it does change, I will change my answer accordingly.
We're looking for a slope of the line that passes through 2 points I see! Alright, so as you would recall, most equations of a linear line are described in the form of slope-intercept form. And that being this:
[tex]y=mx+b[/tex]
When we're finding for slope of the line, we're essentially just look for m. But how can we find m with only just 2 points? Well, we can! Using a formula that helps us find the slope using exactly 2 points! And that is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Now, all we have to do is plug in the values as such and solve:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{-11-(-1)}{-8-(-8)}[/tex]
From here, we come to a problem. If we were to solve this equation to find the slope, we will get an undefined value mainly because the denominator will equal 0 and we can't have it equal 0. So therefore, it is undefined.
Elizabeth is posting 12 flyers for the science club and 20 for the music club. She wants to make all the locations identical, with the same combination of science club flyers and music club flyers. In addition, she wants to make sure that no flyers are left over. What is the greatest number of locations that Elizabeth can post at?
Answers
we have the following:
in this case we must find the largest divisor between the numbers 12 and 20, this number is 4:
[tex]\begin{gathered} \frac{12}{4}=3 \\ \frac{20}{4}=5 \end{gathered}[/tex]Therefore 3 flyers for the science club and 5 flyers for the music club. And it would be 4 places
need asap pleaseeeeeeee
Answers
28 • 28 • 28 = 21,952
it’s 28 to the third power (aka “f^3”)
Answer:
c) f = 28
Step-by-step explanation:
Given problem,
→ f³ = 21952
Now the value of f will be,
→ f³ = 21952
→ f = ³√21952
→ [ f = 28 ]
Let's check the following,
→ 28³
→ (28 × 28) × 28
→ 784 × 28 = 21952
Hence, option (c) is correct.
Sandy Island Beach is building a new Snack Shack based on a scale drawing that is 60 centimeters by 20 centimeters and uses the scale 1 cm : 1.5 m.
Answers
A new Snack Shack is being constructed at Sandy Island Beach which dimensions are 90 centimeters by 30 centimeters.
What is a scale image?Scale image is defined as a ratio that represents the relationship between the shape and size of a figure and the corresponding dimensions of the actual figure or object
Sandy Island Beach is building a new Snack Shack based on a scale drawing that is 60 centimeters by 20 centimeters which are given in the question
Here the scale 1 cm : 1.5 m
As per the given scale, the dimensions would be as
60 centimeters :
⇒ 60 × 1.5 = 90
20 centimeters :
⇒ 20 × 1.5 = 30
Therefore, a new Snack Shack is being constructed at Sandy Island Beach which dimensions are 90 by 30 cm.
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Please tell me what −7 7/8+3.7−(−15.9) is...
Answers
That is your answer
Please tell me if it’s wrong
x+y-7
-2x - 2y = -14
What’s y and x ?
Answers
Answer:
Step by step solution of a set of 2, 3 or 4 Linear Equations using the Substitution Method x-y=7;2x-2y=14 Tiger Algebra Solver.
Step-by-step explanation:
5.
What is the LCD of 1, 3
4x x(x-4)
A. (x-4)(x+2)
B. 4x(x²+2x-8)
and
5?
x(x+2)
C. 4x(x-4)(x+2)
D.
x(x-4)(x+2)
4
Answers
B
Please help!! Name the reciprocals for the equations
In picture
1. 3
_ x = 9
4
4
2. -4 — x
7
Answers
If n is a real number, then its reciprocal will be 1/n.
1. If the equations be [tex]$\left(\frac{3}{4}\right) x=9$$[/tex] then the value of x = 12.
2. If the equations be [tex]$-4=\left(\frac{4}{7}\right) x$$[/tex] then the value of x = -7.
What is meant by reciprocals?The inverse of a value or a number is the definition of reciprocal in mathematics. If n is a real number, then its reciprocal will be 1/n. Reciprocals are used to convert division to multiplication when dividing fractions, which simplifies the division process.
1. Let the equations be [tex]$\left(\frac{3}{4}\right) x=9$$[/tex]
Multiply both sides by 4
[tex]$4 \cdot \frac{3}{4} x=9 \cdot 4$$[/tex]
Simplifying the above equation, we get
3x = 36
Divide both sides by 3
[tex]$\frac{3 x}{3}=\frac{36}{3}$$[/tex]
Simplify
Therefore, the value of x = 12.
2. Let the equations be [tex]$-4=\left(\frac{4}{7}\right) x$$[/tex]
Switch sides
[tex]$\left(\frac{4}{7}\right) x=-4$$[/tex]
Multiply both sides by 7
[tex]$7 \cdot \frac{4}{7} x=7(-4)$[/tex]
Simplifying the above equation, we get
4x = -28
Divide both sides by 4
[tex]$\frac{4 x}{4}=\frac{-28}{4}$$[/tex]
Therefore, the value of x = -7.
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F(11/10) if f(x) = 2x -7
Answers
PLUG IN
[tex] \frac{11}{10} [/tex]
in the place of x in the function and simplify.
[tex]f( \frac{11}{10} ) = 2( \frac{11}{10} ) - 7 \\ f( \frac{11}{10} ) = \frac{22}{10} - 7 \\ f( \frac{11}{10} ) = \frac{ - 48}{10} \\ f( \frac{11}{10} ) = \frac{ - 24}{5} [/tex]
ATTACHED IS THE SOLUTION
Hello!
To solve for f(11/10)
==> must simply plug '11/10' into x's position in the equation
[tex]f(\dfrac{11}{10} )=2(\dfrac{11}{10} )-7=\dfrac{11}{5} -7=\dfrac{11}{5} -\dfrac{35}{5} =-\dfrac{24}{5}[/tex]
Hope that helps!
The nth term of a sequence is 2n - 6
a) Work out the first three terms of the sequence.
b) Work out the tenth term of the sequence.
Answers
Answer:
a) do the first three terms
Answer: a) -4, -2, 0 b) 14
Step-by-step explanation:
To find any term, we plug the number into the equation for n.
a)
1st term => 2(1) - 6 = 2 - 6 = -4
2nd term => 2(2) - 6 = 4 - 6 = -2
3rd term => 2(3) - 6 = 6 - 6 = 0
b)
10th term => 2(10) - 6 = 20 - 6 = 14
Express in decimal notation. 5.51×10^-4
Answers
Step-by-step explanation:
Answer:
= 5.51 × 10⁻⁴
scientific notation
= 5.51e-4
scientific e notation
= 551 × 10⁻⁶
engineering notation
millionth; prefix micro- (u)
= 5.51 × 10⁻⁴
standard form
-4
Order of Magnitude
for scientific and standard forms
= 0.000551
(real number)
= five hundred fifty-one millionths
word form
The White family purchases a new pool table on a no-interest-for-one-year plan. The cost is $2,665. There is a d dollars down payment. If they make a minimum monthly payment of m dollars until the last month, express their last month’s payment algebraically.
Answers
The last month's payment for this family can be algebraically expressed this way: 2665 - d - 11m.
How can we algebraically represent the last month's payment?We can obtain an algebraic statement for the last month's payment when we assign alphabetic values to the variables provided.
First, the price is the primary figure that is = 2665
The down payment is represented with the alphabet d dollars.
The monthly payment is denoted by m dollars.
Since we are given a duration of one year or twelve months, we will have to subtract one month from 12 to give us, 11 months.
Given these substitutions, the algebraic statement can be represented thus:
2665 - d - 11m.
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The picture shows a triangular island:Which expression shows the value of q?s over sin 55 degreess over cos 55 degreesr sin 55°r cos 55°q?
Answers
A right triangle is a triangle with a right angle. The opposite side to the right angle is called the hypotenuse and the other sides are the legs. Given an angle in a right triangle, the ratio between the leg adjacent to the angle and the hypotenuse is equal to the cosine of the angle.
Using this relation in our problem, we have the following:
[tex]\cos(55^o)=\frac{s}{q}[/tex]Solving this expression for q, we have:
[tex]\begin{gathered} \cos(55^o)=\frac{s}{q} \\ q\cos(55^o)=s \\ q=\frac{s}{\cos(55^o)} \end{gathered}[/tex]And this is our answer.
[tex]\frac{s}{\cos(55^o)}[/tex]I'll send you the question
Answers
We know that
< means smaller than
≤ means smaller or equal to
> means greater than
≥ means greater or equal to
We want to find a number (let's call it x), greater than -34
Since, > means greater than, we use this symbol:
y > -34
Answer: DWhat is the slope of the line that passes through the points (-10, 9)
and (-10, 18)? Write your answer in simplest form.
Answers
Hello!
What is the equation for the slope:
[tex]\hookrightarrow \text{Slope}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
(x₁,y₁): a random point on the line ⇒ (-10,9) (x₂,y₂): another random point on the line ⇒ (-10,18)[tex]Slope =\dfrac{18-9}{-10-(-10)} =\dfrac{9}{0} \\[/tex]
Thus the slope is undefined:
Hope that helps!
Geometry Question on Foundations, Need Help.
Answers
Answer:
Plane RAT
Step-by-step explanation:
:]
can someone help me really quick
Answers
Answer:
21
Step-by-step explanation:
63 divided by 3 is 21
210 divided by 10 is 21
whats the anwser to 8ab - 5ab I want to know
Answers
Answer:
3ab
Step-by-step explanation:
i hope you don't want to know how i did this :)