Jeremy claims that if a linear function has a slope of the same steepness and the same y-intercept as the linear function in the graph, then it must be the same function. On a coordinate plane, a line goes through points (0, negative 1) and (2, 0). Which equation is a counterexample to Jeremy’s argument? y = negative one-half x minus 1 y = negative one-half x + 1 y = one-half x minus 1 y = one-half x + 1
Answers
Answer: It is only the 3rd equation that is a good example to Jeremy's argument. Others are counter examples to Jeremy's argument.
Step-by-step explanation:
Let us consider the general linear equation
Y = MX + C
On a coordinate plane, a line goes through points (0, negative 1) and (2, 0).
Slope = ( 0 - -1)/( 2- 0) = 1/2
When x = 0, Y = -1
Substitutes both into general linear equation
-1 = 1/2(0) + C
C = -1
The equations for the coordinate is therefore
Y = 1/2X - 1
Let's check the equations one after the other
y = negative one-half x minus 1
Y = -1/2X - 1
y = negative one-half x + 1
Y = -1/2X + 1
y = one-half x minus 1
Y = 1/2X - 1
y = one-half x + 1
Y = 1/2X + 1
It is only the 3rd equation that is a good example to Jeremy's argument. Others are counter examples to Jeremy's argument.
Final answer:
Jeremy's claim that if a linear function has the same steepness (slope) and the same y-intercept, it must be the same function is not correct. A counterexample is y = negative one-half x + 1, which has the same steepness and y-intercept but is a different function.
Explanation:
The line going through points (0, negative 1) and (2, 0) can be expressed in slope-intercept form (y = mx + b) where the slope m can be calculated as (y2-y1)/(x2-x1) and the y-intercept b is the y-value when x=0. For this line, we have m = (0 - (-1))/(2-0) = 1/2 and b = -1. Hence, the equation for this line is y = one-half x - 1.
However, we can prove Jeremy's claim wrong with a counterexample. Even if a function has the same slope and y-intercept, it doesn't necessarily mean they represent the same function. A counterexample is y = negative one-half x + 1. This line has the same steepness (slope -1/2) but a different direction (its slope is negative, unlike the other line), and the same y-intercept (y=1 when x=0) but it's not the same function.
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Answer:
The height of the hovercraft at the time of takeoff is 33 meters.
Step-by-step explanation:
Height of hovercraft x seconds after takeoff = h(x) = -(x - 11)(x + 3)
Height after takeoff is = h(0) = -(0 - 11)(0 + 3) = -(-11)(3) = 33
So the correct answer is 33 meters. The height of the hover craft at the time of the takeoff is 33 metres.
Answer: 33 meters.
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Hope this helps
Answers
The word form of the decimal number 0.76 is, Zero point seven six.
What is the standard decimal form of numbers?
The standard decimal form of numbers is written in base 10 as there are 10 different numbers from 0 to 9.
Each digit has a face value and a place value.
Given, A decimal number 0.76.
Now, If it was just 76 we could pronounce it as seventy-six.
But it is decimal form and we know each digit after the decimal we pronounce it as a single digit.
Therefore, 0.76 in terms of words is, zero point seven six.
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Answers
Answer:
They sold 182 sandwiches all together.
Step-by-step explanation:
We now that the sell ratio is 4:7:3, where 4 represents Adam, 7 represents Ming, and 3 represents Clinton.
An important characteristic of ratios is that they have a constant of change, which we can calculate using Ming's sandwiches sold and his ratio. If we divided these facts, we have:
This means that the constant of change is 13, now, if Ada and Clinton are in the same ration, the must also have the same constant of change, this means that we can multiply 13 in each case to get the total amount of sandwiches sold:
Therefore, they sold 182 sandwiches all together.
Answers
The inequality that represents the number of toll passes without having to add any value to the toll pass is 18.
What is inequality?
It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
Toll pass accountvalue = $32
Amount deducted with each toll pass = $1.25
The amount in the account after which value is added to the account.
= below $10
The inequality that represents the number of toll passes.
32 - 1.25x < 10
Solve for x.
32 - 1.25x < 10
32 - 10 < 1.25x
22 < 1.25x
1.25x > 22
x > 22/1.25
x > 17.6
Thus,
The number of tollpasses is 18.
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deducted=amount deducted each time times number of times
amount deducted each time =1.25
x=number of times
so
32=amount now
1.25x is deducted
so the amount left has to be greater than or equal to 10
32-1.25x≥10
minus 1.25x both sides
32≥10+1.25x
minus 10 both sides
22≥1.25x
divide both sides by 1.25
17.6≥x
you can't pass through 0.6 times so 17 times is max
the inequality is
32-1.25x≥10 whre x is the number of times that he passes
B 0.3
C 3
D 30
Answers
0.3% => 0.003
A 0.003 is the answer.
Answer:
0.003%
Step-by-step explanation:
you have to multiply this number by 100 which makes 0.3%
Answers
Lenny = 3/4 yds = 6/8
6/8>4/8
The answer is no because 6/8 is 1/4 greater than 4/8
3/4 = 0.75 yards
0.75 is greater than 0.5 therefore, no.