Compare the y-intercepts and the rates of change of the following items. A. The y-intercepts are the same, but the rates of change are different. B. The items have different y-intercepts and different rates of change. C. The items have the same y-intercept and the same rate of change. D. The rates of change are the same, but the y-intercepts are different.
Answers
The y-intercept tells us where a line intersects the y-axis and the rate of change (slope) shows how much 'y' changes for a unit change in 'x'. Given these, we can identify different line characteristics based on whether the lines have the same or different y-intercepts and slopes.
Explanation:Let's start by understanding the concepts of y-intercepts and rate of change. The y-intercept describes where a line intersects the y-axis. For example, in Figure A1, the y-intercept is 9, which means the line crosses the y-axis at y=9. Similarly, the rate of change, also known as the slope, indicates how much 'y' changes for each change in 'x'. A straight line will have the same slope at all points along the line, as illustrated in the example of Figure A1 where the slope is 3.
Now, let's compare the items:
A. When the y-intercepts are the same but the rates of change are different, the lines start at the same point on the y-axis, but diverge as 'x' increases because the slope of each line is different.
B. Different y-intercepts and different rates of change means that the lines start at different points on the y-axis and vary in how steeply they climb or fall.
C. When items have the same y-intercept and the same rate of change, these lines are coincident; they will overlap perfectly because they have the same starting point on the y-axis and ascend or descend at the same rate.
D. When the rates of change are the same but the y-intercepts are different, the lines are parallel. They rise or fall at the same rate, but they do not start at the same point on the y-axis.
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The y-intercepts are the same, but the rates of change are different. The option (C) is correct.
To compare the y-intercepts and the rates of change of the given linear equation and the data in the table, we need to first understand each component:
- The slope (rate of change) is the coefficient of [tex]\( x \),[/tex] which is [tex]\( 2 \).[/tex]
- The y-intercept is the constant term, which is [tex]\( -4 \).[/tex]
Let's find the rate of change (slope) and the y-intercept for the data in the table.
The slope [tex]\( m \)[/tex] between two points [tex]\((x_1, y_1)\) and \((x_2, y_2)\)[/tex] is calculated as:
[tex]\[m = \frac{y_2 - y_1}{x_2 - x_1}\][/tex]
We'll calculate the slope using the points [tex]\((x, y)\)[/tex] from the table:
Using the points [tex]\((-4, -6)\) and \((-2, -5)\):[/tex]
[tex]\[m = \frac{-5 - (-6)}{-2 - (-4)} = \frac{-5 + 6}{-2 + 4} = \frac{1}{2}\][/tex]
Using the points [tex]\((-2, -5)\) and \((0, -4)\):[/tex]
[tex]\[m = \frac{-4 - (-5)}{0 - (-2)} = \frac{-4 + 5}{0 + 2} = \frac{1}{2}\][/tex]
We can see the rate of change is consistently [tex]\( \frac{1}{2} \).[/tex]
We can use the slope-intercept form [tex]\( y = mx + b \)[/tex]. We know [tex]\( m = \frac{1}{2} \)[/tex] and we can use any point from the table to find [tex]\( b \).[/tex]
Using the point [tex]\((0, -4)\):[/tex]
[tex]\[y = \frac{1}{2}x + b \\-4 = \frac{1}{2}(0) + b \\-4 = b\][/tex]
So the y-intercept [tex]\( b \)[/tex] is [tex]\( -4 \).[/tex]
Rate of change (slope):
- Equation [tex]\( y = 2x - 4 \)[/tex] has a slope of [tex]\( 2 \).[/tex]
- Table data has a slope of [tex]\( \frac{1}{2} \).[/tex]
Y-intercept:
Both the equation and the table data have a y-intercept of [tex]\( -4 \).[/tex]
Therefore, the correct comparison is (C) The y-intercepts are the same, but the rates of change are different.
The complete question is:
Compare the y-intercepts and the rates of change of the following items.
(A) The items have different y-intercepts and different rates of change.
(B) The rates of change are the same, but the y-intercepts are different.
(C) The y-intercepts are the same, but the rates of change are different.
(D) The items have the same y-intercept and the same rate of change.
Related Questions
a wallet that holds $25 contains the same number of $1 bills, $5 bills, and quarters. how many of each type of bill or coin does the wallet contain?
Answers
4 quarters = $1
4 dollars = $4
4 five $5 = $20
So 20+4+1 = 25
There for the answer is 4
The number of each type of bill or coin the wallet contains is:
4
Step-by-step explanation:It is given that:
A wallet holds $ 25 in total.
Also, the number of $ 1 bills,$ 5 bills and qaurters are present in equal number in the wallet.
Let the number of each coin or bill in the wallet be: x
Also, we know that:
1 quarter= 1/4 dollar
i.e.
1 quarter= 0.25 dollar
Hence, we get:
x+5x+0.25x=25
i.e.
6.25 x=25
On dividing both side of the equation by 6.25 we get:
x=25/6.25
i.e.
x=4
Hence, the number of each kind of coin or bill are: 4
lisa wants to make at least $300.00 selling candy. Hard candy cost $3.00 per piece and chocolates cost cost $6.00 per piece. How many pieces of each type of candy could Lisa sell in order to make at least $300.00
Answers
Hard candy = x
Chocolate = y
3x+6y=300
To find y, x=0
3(0)+6y=300
6y=300
y=50
To find x, y=0
3x+6(0)=300
3x=300
x=100
Lisa can either sell 100 hard candies or 50 chocolate to make $300.
What is an equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, Lisa wants to make at least $300.00 selling candy. Hard candy cost $3.00 per piece and chocolates cost $6.00 per piece.
Establishing the equation for this problem.
Let,
Hard candy = x
Chocolate = y
Therefore,
3x+6y=300
To find y, let x=0
3(0)+6y =300
6y = 300
y = 50
Similarly,
To find x, put y=0
3x+6(0)=300
3x=300
x=100
Hence, Lisa can sell 100 hard candies or 50 chocolate to make $300.
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Can someone please help me
Factor completely
9-6a-24a^2
Answers
You don't want a negative in front of the variable that is being squared.
-1(24a^2 + 6a - 9)
-3(8a^2 + 2a - 3)
now we use the A C method. what two numbers multiply to equal A×C (8×-3) and add to be B (2)?
6 and -4
-3(8a^2 + 6a - 4a - 3) factor by grouping
-3(2a(4a + 3) -1(4a + 3))
-3(2a - 1)(4a + 3)
hope this helped C:
Answer:
3(3+4a)(1-2a)
Step-by-step explanation:
If events X and Y are independent, what must be true? Check all that apply.
Answers
1) The occurrence or lack of event X does not influence the occurrence of event Y, and the occurrence or lack of event Y does not influence the occurrence of event X.
2) P(X∩Y) = P(X) * P(Y)
3) P(X | Y) = P(X).... this is the probability of X given Y is equal to the probability of X.
4) P (Y | X) = P(Y)
5) P(A∪B) = P(A) + P(B) - P(A∩B)
3. P(Y | X) = P(Y) and 6. P(X | Y) = P(X)
Bethany's family can eat (13h + 6) hotdogs. Clark's family can eat (10h + 3) hotdogs. Which expression shows the difference between the number of hotdogs Bethany's family can eat and the number of hot dogs Clark's family can eat?
A.3h - 9
B.3h + 3
C.-3h + 9
D.-3h + 3
Answers
use multiples to write two fractions equivalent to 7/9
Answers
Answer:
[tex]\displaystyle\frac{35}{45}, \frac{49}{63}[/tex] are two equivalent fractions of the given fraction.
Step-by-step explanation:
We are given the following information in the question:
We are given the fraction:
[tex]\displaystyle\frac{7}{9}[/tex]
We have to find an equivalent fraction. This could be done by multiplying both the numerator and the denominator by the same number.
Equivalent fraction:
Multiplying both numerator and denominator by 5
[tex]\displaystyle\frac{7\times 5}{9\times 5} = \frac{35}{45}[/tex]
Multiplying both numerator and denominator by 7
[tex]\displaystyle\frac{7\times 7}{9\times 7} = \frac{49}{63}[/tex]
Hence, [tex]\displaystyle\frac{35}{45}, \frac{49}{63}[/tex] are two equivalent fractions of the given fraction.
Which of the following inequalities is equivalent to -6 > x?
Answers
Which expression is undefined
A. -8÷(-8)
B. -8÷8
C. 0÷8
D. 8÷0
Answers
Suppose a fair coin is flipped and a fair six-sided die is rolled. list the members of the event "the die does not land on 5"
Answers
100 envelopes cost $0.70 how much would it be for 250
Answers
The cost of 250 envelopes would then be 0.007 × 250, which is $1.75
If 100 envelopes cost $0.70 then it would cost $1.75 for 250 envelopes.
If 100 envelopes cost $0.70, we can set up a proportion to determine the cost of 250 envelopes:
100 envelopes / $0.70 = 250 envelopes / x
Cross-multiplying:
100 × x = 250 × $0.70
Simplifying:
100x = 175
Dividing both sides by 100:
x = 175 / 100
x = $1.75
Therefore, it would cost $1.75 for 250 envelopes.
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Of 50 students surveyed, 19 said they had soda for breakfast. write a portion in fraction, decimal, percent
Answers
___________________________
In fraction: [tex] \frac{19}{50}[/tex] .
___________________________
In decimal: 0.38 .
_________________
In percent: 38 % .
_________________
Explanation:
_________________
19/50 = (19*2)/(50*2) = 38/100 .
38/100 = 38 ÷ 100 = 0.38 .
38/100 = 38 % .
___________________________
How many different sums of money can be formed from penny and half a dollar?
Answers
starting with your 51 pennies you can get rid of every 5 pennies and replace them with a nickel so say you get rid of 10 pennies you would have 2 nickels
so 51/5= 10.2
or 10 nickels
so that is ten combos right there along side 51 pennies
so no you do the dimes witch for every 10 pennies you get rid of is = to 1 dime so 51/10=5.1 or 5 dimes so that gives you 5 more combos
so now its 1 penny combo with 10 nickel combos with 5 dime combos
now for quarters for every 25 pennies you get rid of is = to 1 quarter so
51/25=2.04 or just 2 and with half dollars ( they do make thoses ) it is for every 50 pennies you get rid of is = to one half dollar ( which is 50 cents) so 51/50= 1.02 or 1 so it is
1 penny combo + 10 nickels combos + 5 dime combos + 2 quarter combos + 1 half dollar combo =
1+10+5+2+1=19 different sums of money
What is the reason for each step in the solution of the equation? −5(x−6)=10x
−5(x−6)=10x
−5x+30=10x
30=15x
2=x
Division Property of Equality
Commutative Property
Addition Property of Equality
Given
Distributive Property
Answers
Statement Reason
−5(x−6)=10x Given
−5x+30=10x Distributive Property
30=15x Addition Property of Equality
2=x Division Property of Equality
Consider the statement 4-3+5=-6+8+4 this mathematically correct sentence is the sentence true or false? Explain how you know
Answers
4-3+5=6
(-6)+8+4=6
They both equal 6
Suppose that hot dogs come in packs of 9 and buns come in packs of 12 . kareem bought the same number of hot dogs as buns. it was the least number of each for which this was possible.
Answers
36 is least number of each for which this was possible.
what is Least common multiple?The smallest positive integer that is divisible by both a and b is known as the least common multiple, lowest common multiple, or smallest common multiple of two integers, or lcm(a, b), in mathematics and number theory.
4 is the LCM of 2 and 4. To get the smallest multiple that is exactly divisible by 2 and 4, i.e. 4, we must first determine the multiples of 2 and 4 (multiples of 2 = 2, 4, 6, 8; multiples of 4 = 4, 8, 12, 16).
Given:
Hot dogs cam in pack of 9.
Buns came in pack of 12.
Now, to find least number of each bought the same number of hot dogs as buns.
So, LCM(9, 12)
9= 3x 3
12= 2 x2 x 3
Thus, LCM(9, 12) = 3 x 3 x 2 x 2 = 36
Hence, 36 is least number of each for which this was possible.
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Express 275% as a decimal number
Answers
Alright so, 100% is equal to 1, because think about it as a fraction, 2/3 is 66%, because it's not full, and 2/3 is 66%, but it's also .66(etc). So, in order to get 100% you'd have to have a 3/3.
I'm going to use 4/4. so in order to go above 100% you'd have to add more.
8/4 is 200% because it divides to 2.00
So now just add 3 more because 3/4 is 75%
11/4 is 275%
Which also divides to 2.75
2.75 is your answer, hope this helped!
The conversion of a percentage to a decimal number, divide the percentage by 100 it means that 275% represents 2.75 times the original quantity.
To convert a percentage to a decimal number,
divide the percentage value by 100.
Here's the step-by-step explanation for converting 275% to a decimal:
Take the percentage value (275%) and divide it by 100.
275 ÷ 100 = 2.75
So, 275% as a decimal is 2.75.
It means that 275% is equal to 2.75 times the whole quantity.
For example, if you have 100 dollars and increase it by 275%, you will end up with 100 + (2.75 × 100) = 375 dollars.
Therefore, the 275% as a decimal number is equal to 2.75.
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All the angles are measured in degrees, show that the triangle is isosceles.
Answers
n ==> number of sides
∴ (3 - 2) × 180° = 180°
(4x + 8°) + (5x + 2°) + (6x - 10°) = 180°
Remove the parenthesis
4x + 8° + 5x + 2° + 6x - 10° = 180°
Simplify
15x = 180°
x = 12°
An isosceles triangle has 2 equal angles and sides.
In this case, we check them by the angle.
Substitude x into 4x + 8, 5x + 2 and 6x - 10
1. 4(12°) + 8° = 56°
2. 5(12°) + 2° = 62°
3. 6(12°) - 10° = 62°
Notice 2 and 3 have the same angular value.
∴ ∆ is an isosceles ∆.
The triangle is isosceles.
What is a triangle?A triangle is a polygon that has three vertices on each of its three sides. The angle that is created within the triangle is 180 degrees. It indicates that the sum of a triangle's interior angles is 180 degrees. This is a polygon with the fewest sides. At the end of the day, a triangle is characterized as a three-sided two-layered figure whose inside points are equivalent to 180°.
Given a triangle let the triangle be ΔABC
given angles (4x + 8), (5x + 2) and (6x - 10)
let ∠A = (4x + 8), ∠B = (5x + 2) and ∠C = (6x - 10)
we know that sum of angle of triangle is 180⁰
∠A + ∠B + ∠C = 180
4x + 8 + 5x + 2 + 6x - 10 = 180
15x = 180
x = 180/15 = 12
∠A = 4x + 8 = 4(12) + 8 = 56⁰
∠B = 5x + 2 = 5(12) + 2 = 62⁰
∠C = 6x - 10 = 6(12) - 10 = 62⁰
since ∠B = ∠C
it is the property of an isosceles triangle, An isosceles triangle is a triangle with any two sides that are the same length and angles on opposite sides that are the same size.
Hence the Given triangle is isosceles.
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What is the minimum value for p=x-2y over the feasibility region defined by the constraints shown above?
x <= 8
y>= 0
y<= 3x+2
y<= -x+10
a. 8
b. -2
c. -16
d. -14
Answers
The fact that x ≤ 8 and y ≥ 0 means we are free to set x as low and y as high as possible, as long as they agree with the other constraints.
Graphing the inequalities helps to see the optimum point. It is where 3x +2 and -x +10 intersect, at (2,8). This is the greatest point for y that agrees with our inequality.
Remember that the function we are minimizing is p = x - 2y
The value for p at this point is 2 - 2(8) = 2 - 16 = -14
Answer is D)
what are two decimals that have square root between 3 and 4
Answers
1.86^2 = 3.4596
1.78^2 = 3.1684
The center of a circle is at the origin. An endpoint of a diameter of the circle is at (-3, -4). How long is the diameter of the circle?
5
10
25
Answers
hope this helps you
You plan to take $450 u.s. on a trip to south africa. how many rands is this if one u.s. dollar equals 3.70 rands?
Answers
$450 is simply 450 times $1, so multiply the conversion equation above by 450 on both sides.
450 * $1 = 450 * 3.70 rands
$450 = 1665 rands
Jason draws a line in the sand at the beach. The line is 78 ft long. He wants to divide the line into sections that are each 1/8 ft long.
How many sections will the line be divided into?
Enter your answer in the box.
Answers
If m∠APW = 20°, then the measure of ∠WPZ is
20
70
90
160
Answers
Answer:
It is 70
Step-by-step explanation:
Both angles have to add up to 90 and I did the lesson ight
What is the probability that it lands on heads at least 5 times?
Answers
4nm - 4m = 8. Solve for m
Answers
4m(n - 1) = 8
4m = 8 / (n - 1)
m = [8 / (n - 1) / 4
m = 2 / (n - 1) answer
Suppose you traveled 84 in 1.5h moving at the same speed, how many mi would you cover in 3 1/4? & can someone answer number 45 also?
Answers
43. To solve this, we can find the unit rate by dividing the amount traveled by the amount of time. 84/1.5 is 56. You are traveling at 56 mph. 3 1/4 is equivalent to 3.25. We can multiply that by 56 to find the amount traveled in 3 1/4 hours. 56 * 3.25 is 182. There. You would cover 182 miles in 3 1/4 hours.
44. To find the amount of heart beats in 50 seconds, we can set up a proportion like this: 130/12 = x/50. You set this up, because we’re looking for the amount of heartbeats, but we know the time frame. Cross multiply the values to get 6,500 = 12x. Now, divide each side by 12 to isolate the “x”. 6,500/12 is 541.6666 (541 2/3) or 542 when rounded to the nearest whole number. The heart beats about 542 times in 50 seconds.
45. Okay. Gas costs $1.85 per gallon and there is 18 miles per gallon. To find the cost per mile, we can divide the price for a gallon of gas by 18. 1.85/18 is 0.102777 and 7’s repeating or 0.10 when rounded to the nearest hundredth. The cost for gas per miles is approx. 10 cents.
Note: You didn’t ask for question #44 to be answered, but I solved it for you anyway to help you out.
Divide: 1,485 ÷ 0.09
Answers
hoped this helped
just use a calculator then you wont have to spend your points here
What is 0.72 written as a simplified fraction? (1 point) seventy-two over one hundred one hundred over seventy-two thirty-six over fifty eighteen over twenty-five 4. ms. johnson's class is having a pizza party. if there are 14 students and 7 pizzas cut into 8 slices, what answer choice represents the fraction of one pizza that each student receives? (1 point) one-third one-fourth one-half one-eighth?
Answers
Determine the x- and y-intercepts of the graph of y = 1/4x - 2
Then plot the intercepts to the graph the equation
Answers
Answer:
The y-intecept is [tex](0,-2)[/tex], and the x-intercept is [tex](8,0)[/tex].
Step-by-step explanation:
The interception points with the axes can be foun by making zero one variable.
If you wanna find y-interception, we must make x = 0.
If you wann find x-interception, we must make y = 0.
The given function is
[tex]y=\frac{1}{4}x-2[/tex]
For [tex]x=0[/tex], we have
[tex]y=\frac{1}{4}(0)-2\\y=-2[/tex]
For [tex]y=0[/tex], we have
[tex]y=\frac{1}{4}x-2\\0=\frac{1}{4}x-2\\2=\frac{1}{4}x\\x=8[/tex]
Therefore, the y-intecept is [tex](0,-2)[/tex], and the x-intercept is [tex](8,0)[/tex].
The image attached show this.
A cab ride from the airport to your home costs $19.50. If you want to tip the cab driver close to 10 percent of the fare, how much should you tip?
$1
$2
$3
Answers
The tip for the cab is close to 10 percent is around $2.
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, A cab ride from the airport to your home costs $19.50.
Now, The tip given is 10% of the fare so,
= (10/100)×19.50.
= 0.1×19.50.
= 1.95.
So, The exact tip would be $1.95 which is approximately $2.
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