This graph shows the cost of buying dried fruit.
What is the slope of the line and what does it mean in this situation?
Select from the drop-down menus to correctly complete each statement.
The slope of the line is ____. This means that every of dried fruit costs $____.
Answers
the correct answer is =
The slope of the line is 3.5
This means that every pound
of dried fruit cost $3.50
Slope of the line is 3.5. This means that every of dried fruit costs $3.5 per lb.
From the graph attached,
Points shown on the graph are (4, 14) and (8, 28).
Since, slope of a line passing two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Therefore, slope of the line passing through (4, 14) and (8, 28) will be,
Slope = [tex]\frac{28-14}{8-4}[/tex]
= [tex]\frac{14}{4}[/tex]
= 3.5
This means that every of dried fruit costs $3.5 per lb.
Therefore, slope of the line is 3.5. This means that every of dried fruit costs $3.5 per lb.
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Related Questions
Functions f(x) and g(x) are shown below:
f(x) = -4(x - 6)^2 + 3
g(x) = 2 • cos(2 • x - pi) + 4
Using COMPLETE SENTENCES, explain how to find the maximum value for each function and determine which function has the largest maximum y-value.
Answers
This is a parabola with vertex at (6, 3).
Because the leading coefficient of -4 is negative, the curve opens downward, and the vertex is the maximum value.
Answer: Maximum of f(X) = 3
Consider the function g(x) = 2 cos(2x - π) + 4
The maximum value of the cosine function is 1.
Therefore the maximum value of g(x) is
2*1 + 4 = 6
Answer: Maximum of g(x) = 6
What is the slope ? Simplify your answer and write it as a proper fraction improper fraction or integer
Answers
1) which expression forms an equation with the given expression?
18-4•3=______
A. 8•4÷4
B. 14-11•2
C. 3(12-9)
D. 12÷3+3
2) choose the expression that completes the equation
24÷6+20=_____
A. 3(7+1)
B. 2(7+10)
C. 4(4+3)
D. 3(7+7)
HELP PLEASEEE
Answers
A. 8*4/4= 8
B. 14-11*2= -8
C. 3(12-9)= 9
D. 12/3+3= 7
The answer for (1) is none of the above, is there a problem with the question?
2)24/6+20= 24
A. 3(7+1)= 24
B. 2(7+10)= 34
C. 4(4+3)= 28
D. 3(7+7)= 42
The answer for (2) is A. 3(7+1)
What is a quick way to determine which savings account will pay the most interest?
Answers
A family is comparing different car seats. One car seat is designed for a child up to and including 30 lb. Another car seat is designed for a child between 15 lb and 40 lb. A third car seat is designed for a child between 30 lb and 85 lb, inclusive. Model these ranges on a number line. Represent each range of weight using interval notation. Which car seats are appropriate for a 32-lb child?
Answers
The interval notation is:
0 < x ≤ 30; 15 < x < 40; 30 ≤ x ≤ 85;
The second and third car seats are suitable.
The number lines shows the weights of the car seats which is designed for in comparison the weight of the 32lb child.
Three car seats are designed as follows:
The car seat made for children upto 30lb. The seat for children between 15lbs and 40lbs andThe seat designed for a child between 30 lb and 85 lbAs the seat designed for a child upto and including 30 lb would not be suitable for 32 lb child. Because 32lb is more than the 30 lb.
Now, the seat designed for a child between 30 lb and 85 lb, 30lbs and 85lbs would be suitable as the child is within these weight ranges that is 32lb.
The interval notation is:
0 < x ≤ 30; 15 < x < 40; 30 ≤ x ≤ 85;
The second and third car seats are suitable.
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"you buy a baseball bat and a ball for $1.10. the baseball bat costs $1.00 more than the ball. how much did the ball cost?"
Answers
If (1, 2) and (3, 4) lie on the same line, give the slope-intercept equation of the line.
Answers
y - y1 = x - x1
here x1 = 1 and y1 = 2 :-
y - 2 = x - 1
y = x + 1 <---- Answer
Final answer:
The slope-intercept equation of the line that passes through (1, 2) and (3, 4) is y = x + 1, with a slope of 1 and a y-intercept of 1.
Explanation:
To find the slope-intercept equation of a line that passes through the points (1, 2) and (3, 4), we first need to determine the slope of the line. We use the formula for the slope (m) given by the change in y over the change in x, or Δy/Δx. Calculating the slope, we get:
m = (4 - 2) / (3 - 1) = 2 / 2 = 1.
Now we have the slope, we can use the slope-intercept form of the line, which is y = mx + b, where m is the slope and b is the y-intercept. Plugging in one of the points, say (1, 2), into this equation gives us:
2 = (1)(1) + b
Which simplifies to:
b = 2 - 1 = 1
So the y-intercept (b) is 1. Therefore, the slope-intercept equation of the line is:
y = x + 1
If George received $ 78.00 for his work at Weaver's Store, and he was paid $ 6.00 per hour, how many hours did he work?
Answers
78.00 ÷ 6.00 equals 13 hours
6×13 equals 78
78 / 6 = 13
He worked 13 hours to get paid $78.00
Hope this helps!
How would you graph the solution set of ≤ -18?
closed circle on -3 and shaded to the right
closed circle on -3 and shaded to the left
closed circle on -108 and shaded to the right
closed circle on -108 and shaded to the left
Answers
Faith xoxo
Answer:
Closed circle on -108 and shaded to the left, I took the same lesson and got 100%
Step-by-step explanation:
But your missing part of the question, it's how would you graph the solution set of x/-6 ≤ -18?
Which irrational number can be multiplied by negative square root of 41 to get a product that equals 1?
Answers
-√41 * -1 / √41 = √41 / √41 = 1
For this case we define the following variable:
x: unknown number
We then have the following equation:
[tex]- \sqrt {41} x = 1[/tex]
From here, we clear the value of x.
We have then:
[tex]x = - \frac {1} {\sqrt {41}}[/tex]
Answer:
An irrational number that can be multiplied by negative square root of 41 to get a product that equals 1 is:
[tex]x = - \frac {1} {\sqrt {41}}[/tex]
what is 6 divided by 46.8
Answers
Which of the following statements describes the process for solving 4x ≥ -24?
Divide both sides of the inequality by -24 and flip the symbol.
Divide both sides of the inequality by -24 but don't flip the symbol.
Divide both sides of the inequality by 4 and flip the symbol.
Divide both sides of the inequality by 4 but don't flip the symbol.
Answers
You only flip the inequality symbol if you divide by a negative number.
If you’re solving for x (which you are), you want to get x by itself. The only way to do that is to divide by 4.
Answer:
Your answer would be D.
Step-by-step explanation:
2x to the fourth power + 5x squared + 3, factored
Answers
[tex]2x^4+5x^2+3[/tex]
This may seem tricky because of the high powers, but remember that [tex]x^4=(x^2)^2[/tex]. Then we can factor it as:
[tex]2x^4+5x^2+3=(2x^2+3)(x^2+1)[/tex]
Circle J and circle K are shown in the diagram below.
What is the total number of lines of tangency that are common to circle J and circle K?
3
2
4
1
Thank you!
Answers
Answer: 4
Which will result in a difference of squares? (–7x + 4)(–7x + 4) (–7x + 4)(4 – 7x) (–7x + 4)(–7x – 4) (–7x + 4)(7x – 4)
Answers
a^2 – b^2 = (a + b)(a – b)
in this case
(–7x + 4)(–7x – 4)
answer
(–7x + 4)(–7x – 4)
Answer:
(–7x + 4)(–7x – 4) Sign changes in the middle of both parenthesis , so this will result in difference of squares
Step-by-step explanation:
The formula for difference of squares
[tex]a^2 - b^2 =(a+b)(a-b)[/tex]
(–7x + 4)(–7x + 4) both parenthesis having same terms so this will not result in difference of squares
(–7x + 4)(4 – 7x) both parenthesis having same terms so this will not result in difference of squares
(–7x + 4)(–7x – 4) Sign changes in the middle of both parenthesis , so this will result in difference of squares
(–7x + 4)(7x – 4) sign changes for both terms in both parenthesis so this will not result in difference of squares
Describe which of the two points lies on the graph of the line
Y-x=4
A. 9,5
B. 5,9
Answers
x = 5
y = 9
y - x = 4
(9) - (5) = 4
True
hope this helps
Which property can be used to remove the parentheses in the expression 1.7(x+9)
Answers
The m6 = (11x + 8)° and m7 = (12x – 4)° What is the measure of 4? m4 = 40° m4 = 48° m4 = 132° m4 = 140°
Answers
m6 = m7
It tells us what m6 and m7 are in the problem, so we can replace m6 with "11x + 10" and m7 with "12x - 4." From there, we can solve for x and find out what the angles are in degrees.
m6 = m7
Replace m6 and m7.
11x + 8 = 12x - 4
Subtract 11x from both sides.
11x + 8 - 11x = 12x - 4 - 11x
8 = x - 4
Add 4 to both sides.
8 + 4 = x - 4 + 4
12 = x
Now that we have x, we can find m6 and m7.
m6 = 11x + 8
m6 = 11(12) + 8
m6 = 132 + 8
m6 = 140
And for m7.
m7 = 12x - 4
m7 = 12(12) - 4
m7 = 144 - 4
m7 = 140
From here, we can find m8 because m8 and m6 together are a straight line. Straight lines have an angle of 180 degrees.
m6 + m8 = 180
Replace m6 with 140.
140 + m8 = 180
Subtract 140 from both sides.
140 + m8 - 140 = 180 - 140
m8 = 40
Now that we have m8, we can find m4.
Because of the properties of parallel lines and transversals, we know that
m1 = m5
m2 = m6
m3 = m7
m4 = m8
Since we know m8 = 40 and m4 = m8, we can replace m8 with 40 to get m4 = 40.
The measure of angle 4 is 40°. That is, m4 = 40°. The correct option is the first option m4 = 40°
From the diagram, we can observe that angles 6 and 7 are vertically opposite angles.
From one of the angle theorems, we have that vertically opposite angles are equal
That means,
measure of ∠ 6 = measure of ∠ 7
From the question,
we have that, m6 = (11x + 8)° and m7 = (12x – 4)°
Since, the measures of angles 6 and 7 are equal, then we can write that
(11x + 8)° = (12x – 4)°
Now, determine the value of x, we will solve the equation
11x + 8 = 12x – 4
First, subtract 11x from both sides
11x - 11x + 8 = 12x - 11x - 4
8 = x - 4
Now, add 4 to both sides
8 + 4 = x -4 +4
12 = x
∴ x = 12
Now, we will determine the measure of ∠6
m ∠6 = (11x + 8)°
Put x = 12
∴ m ∠6 = (11(12) + 8)°
m ∠6 = (132 + 8)°
m ∠6 = 140°
To determine the measure of ∠4, m4, we will first determine the measure of ∠8.
From the diagram,
m ∠6 + m ∠8 = 180° (Sum of angles on a straight line)
∴ 140° + m ∠8 = 180°
Then,
m ∠8 = 180° - 140°
m ∠8 = 40°
From the diagram, we can observe that angles 4 and 8 are corresponding angles.
Also, from one of the angle theorems, we have that corresponding angles are equal.
Hence, the measure of ∠ 4 equals the measure of ∠ 8.
From above, m ∠8 = 40°
∴ m ∠4 = 40°
Hence, the measure of angle 4 is 40°. That is, m4 = 40°. The correct option is the first option m4 = 40°
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Kate earns $8.50 per hour. How much money will she earn after working 8 hours? She will earn $.
Answers
relative maxima and relative minima are called relative_____.
Hint: first 2 letters are ex
Answers
Relative maxima and relative minima are called relative extrema.
Given:
The given statement is:
Relative maxima and relative minima are called relative_____.
To find:
The correct word to fill the given blank.
Explanation:
Relative maxima: If the function changes from increasing to decreasing, then the turning point is known as relative maxima.
Relative minima: If the function changes from decreasing to increasing, then the turning point is known as relative minima.
Relative extrema: The turning points relative maxima and relative minima are known as relative extrema.
Therefore, the relative maxima and relative minima are called relative extrema.
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after 5 years what is the total amount of a compound interest investment of 32,000 at 3% interest, compounded quarterly
A.57.795.56
B.32,426.67
C.43,099.36
D.37,157.89
Answers
if f(x)=2x-4 find f(q+1)
Answers
The value of f(q+1) is 2(q-1).
What is a function?A relation or expression involving one or more variables.
Given that, f(x) = 2x - 4
When x = q+1
f(q+1) = 2(q+1) - 4
f(q+1) = 2q + 2 - 4
f(q+1) = 2q - 2
f(q+1) = 2(q-1)
Hence, the value of f(x) when x = (q+1) is 2(q-1)
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Determine whether 2y=3x-1 represents a direct variation. if it does, find the constant of variation.
Answers
The equation 2y=3x-1 does not represent a direct variation in its strict definition, as it includes a y-intercept. If the y-intercept is ignored, the constant of variation would be k = 3/2.
The equation 2y=3x-1 represents a direct variation if it can be written in the form y = kx, where k is the constant of variation. To determine if this equation represents a direct variation, we can solve it for y:
Divide both sides of the equation by 2 to isolate y:
y = (3/2)x - 1/2.
Since we can express y as an equation of the form y = kx + b, with b being a constant, it does not represent a pure direct variation, as direct variation should have a form y = kx without the constant term.
However, if the question is interpreted to include such linear relationships as direct variations despite the y-intercept, then the constant of variation would be k = 3/2.
Which equation is the inverse of y = x2 – 36?
Answers
i hope that helps
Answer:
The given equation of the curve is
y= x² - 36
To find it's inverse we have to convert y in terms of x.
So, adding 36 to both sides of equation
→ y + 36=x² -36 + 36
→ y + 36 = x²
→ x² = y+ 36
→ x =[tex]\pm[/tex][tex]\sqrt{y+36}[/tex]
Now, to find inverse you can replace x by y, so by replacing x by y, the above equation becomes
y =[tex]\pm\sqrt{x+36}[/tex]
Second option is correct.
What's the ordered pair ?
Answers
We clearly see that for ever point in terms of CHOICE C the value of x is different.
Answer: Choice C
PLEASE HELP ASAP!!!!!
Carl, Brian, Dave, and Ashley want to attend the same university. Unfortunately only two spots remain and these four friends have the same GPA, as well as virtually identical community service and leadership experiences. Therefore, the two spots will be determined by their SAT and ACT scores. Carl scored 1,280 on the SAT, while Brian scored 1,325. Dave scored 28 on the ACT, while Ashley scored 30. Use z-scores to determine which two students should be admitted. The mean SAT score was 1,000 with a standard deviation of 175 and the mean ACT score was 20.6 with a standard deviation of 5.2 Both tests are normally distributed.
Answers
28-20.6
For Dave: z = ---------------- = 1.42
5.2
Find the z scores for the other 3 students. Rank your results in ascending order. Take the 2 students whose z scores are greater than the remaining z scores.
Carl:
z = (x - μ)/σ
z = (1280 - 1000)/175
z = 1.6
Brian:
z = (x - μ)/σ
z = (1325 - 1000)/175
z = 1.9
Dave:
z = (28 - 20.6)/5.2
z = 1.42
Ashley:
z = (x - μ)/σ
z = (30 - 20.6)/5.2
z = 1.81
Using the z-scores for each student above, the following two students should be admitted into the university:
Brian based on his SAT score and Ashley based on her ACT score.
Pleaseeee help!!!!!!!!!
Answers
Add -12+20, Then divide the sum by -4
Answers
divide 8 by -4 and get -2
Use two or three unit fractions to convert. 1515 daysdaysequals=_______ secondsseconds
Answers
It is found that Fifteen days is equivalent to 1,296,000 seconds, Or we can say one million two hundred ninety-six thousand seconds.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We need to find the unit fractions to convert 15 days into seconds.
1 day = 24 hour
1 hour = 60 minutes.
1 minutes = 60 seconds
Therefore, 24 hours = 24 x 60 x 60 = 86400 seconds
There are 86400 seconds in one day.
Then 15 days = 15 x 86400 = 1,296,000
Hence, It is found that Fifteen days is equivalent to 1,296,000 seconds, Or we can say one million two hundred ninety-six thousand seconds.
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Write the equation of the function whose graph is shown.
Answers
Answer:
[tex]y=1(x-5)^2 + 3[/tex]
Step-by-step explanation:
Given : from the graph vertex is (5,3)
Also graph passes through point (8,12)
We use vertex form of quadratic equation
General vertex form is
[tex]y=a(x-h)^2 + k[/tex]
vertex is (5,3)
h= 5 and k =3
So equation becomes [tex]y=a(x-5)^2 + 3[/tex]
Now we need to find out 'a'
We use (8,12) to find out 'a'
Plug in x=8 and y = 12
[tex]12=a(8-5)^2 + 3[/tex]
[tex]12=a(3)^2 + 3[/tex]
12= 9a + 3
subtract 3 on both sides
9 = 9a
divide both sides by 9
so a=1
Final equation is
[tex]y=1(x-5)^2 + 3[/tex]
An equation of the function of this graph is equal to [tex]y=1(x-5)^2 + 3[/tex]
Given the following data:
Points on the x and y-axis = (8, 12).Vertex (h, k)= (5, 3).How to write a function.The vertex form of a quadratic equation can be used to write an equation of the function of a graph.
Mathematically, the vertex form of a quadratic equation is given by this formula:
[tex]y=a(x-h)^2 + k[/tex]
Substituting the given parameters into the formula, we have;
[tex]12=a(8-5)^2 + 3\\\\12=(3a)^2+3\\\\9a^2=12-3\\\\9a^2=9\\\\a^2=1[/tex]
a = 1.
For the equation:
[tex]y=a(x-h)^2 + k\\\\y=1(x-5)^2 + 3[/tex]
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