A few points (co-ordinates) for the given equations are :
(1,-1/2),(-1,1/4),(0,1),,(2,-1/4)
What are the points on the graph called?These points are called Coordinates, where the horizontal line denotes the x-axis and the verticle line is the y-axis.
Each point is identified by both x and y coordinates. A point's x-coordinate is a value that indicates how far the point is from the horizontal or x-axis origin.
According to the given information:y denotes the distance of the point on the vertical line from the origin
x denotes the distance of the point on the horizontal line from the origin
In the given equation y=-1/3x-1
We can substitute x with any integer (i.e any number among the positive or negative numbers)
Putting, x=1 in the given equation we get
y=-1/(3x1)-1
⇒ y=-1/3-1
⇒y=-1/2
Thus the coordinate when x=1 is (1,-1/2)
Similarly by putting x=0, 1, 2, -1 ;we get the following co-ordinates respectively
(0,1), (1,-1/2), (2,-1/4),(-1,1/4)
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Researchers claim that 60 tissues is the average number of tissues a person uses during the course of a cold. The company that makes Kleenex brand tissues thinks that fewer of the tissues are needed. What are their null and alternative hypotheses?
The null and alternative hypotheses for the research will be H0: µ ≥ 60 vs Ha: µ < 60
What are null and alternative hypothesis?In statistical hypothesis testing, null and alternative hypotheses are utilized. A test's null hypothesis always predicts that there will be no effect or relationship between variables, whereas the alternative hypothesis outlines your research prediction of an effect or link.
A null hypothesis is a straightforward contradiction of an alternative hypothesis. This implies that if one of the two hypotheses is correct, the other is incorrect.
The null and alternative hypotheses are two claims about a population that are mutually exclusive. In this case, the hypothesis are illustrated above.
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how many groups 1/4 are in 3/4
There are 3 1/4's in 3/4, hope this helps.
Answer: 3
Step-by-step explanation: since they are the same denominator it is basically asking how many 1s go in 3
Find the values of x and y
X= 20 & Y= 70 in right-angled triangle .
What is right angle triangle?
A right-angled triangle is a particular kind of triangle in which one of the angles is 90 degrees. The combined angles of the other two are 90 degrees. Perpendicular and the triangle's base make up the sides that the right angle is formed from. The longest of the three sides, known as the hypotenuse, is the third side.2X + 140 = 180
2X = 40°
X = 20°
X + Y = 90°
Y = 70°
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bag has 5 red beads 3 Blue, 4 green random probability a single picked bead is blue
Answer:
1/4
Step-by-step explanation:
add all of them to get the sum which is 12. Since he asked for the blue which are 3. You put the 3/total which is 3/12. Then simplify. Which is equal to 1/4
Please HELP 7 B(x)*C(x)
Answer: dont be rude
Step-by-step explanation:
Young Frankenstein has two brothers, Pugsley and Gomez. The sum of their ages is 34. Frankenstein is older than Pugsley, but Pugsley is not the youngest. Gomez is 8 years younger then Frankenstein and Pugsley and Gomez’s ages differ by 5 years. How old are the three brothers?
The age of the three brothers, based on the relationship between the ages of Frankenstein, Pugsley, Gomez, is:
Frankenstein - 15 years Pugsley - 12 years Gomez - 7 yearsHow to find the ages?Frankenstein is older than Pugsley and so is not the youngest. Pugsley is not the youngest according to the question so Gomez must be the youngest.
Assuming Gomez's age is x, the relationship between their ages is:
Gomez age + Pugsley age + Frankenstein age = 34
x + x + 5 + x + 8 = 34
3x + 13 = 34
x = (34 - 13) / 3
x = 7 years
Pugsley's age is:
= x + 5
= 7 + 5
= 12 years
Frankenstein's age is:
= x + 8
= 7 + 8
= 15 years
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Movies at the rental store are $3.75 each. Snacks and drinks are $1.89 each. Round each amount to the nearest dollar to estimate the cost to rent 3 movies and buy popcorn, a soda, and a candy bar.
Answer: List all of the solutions.
3.75
=
1.89
=
dollar
=
3
=
Step-by-step explanation:
The table shows a proportional relationship between x and y.
x 3.6 12.2 2.1
y 14.4 48.8 8.4
Which of the following correctly describes the graph of the relationship?
OA line that goes through (3.6, 14.4) and (48.8, 12.2)
OA line that goes through (14.4, 3.6) and (12.2, 48.8)
OA line that goes through (0, 0) and (3.6, 14.4)
OA line that goes through (0, 0) and (14.4, 3.6)
The correct answer which define proportional relationship between x and y is OA line that goes through (0, 0) and (3.6, 14.4)
What does proportionality mean to you?
Any relationship that has a constant ratio is said to be proportionate. For instance, the ratio of proportionality is the average number of apples per tree, and the amount of apples in a crop is proportional to the number of trees in the orchard.
As we can see that in the given question [tex]\frac{x}{y} =\frac{1}{4}[/tex]
and there is only one option which fits this ratio is third one
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Answer:
to simplify the dude aboves' answer its C
Step-by-step explanation:
A line that goes through (0, 0) and (3.6, 14.4)
Use PMT=
nearest dollar.
-nt
to determine the regular payment amount, rounded to the
The price of a home is $210,000. The bank requires a 15% down payment and one
point at the time of closing. The cost of the home is financed with a 30-year fixed-
rate mortgage at 6.5%.
a. Find the required down payment.
b. Find the amount of the mortgage.
c. How much must be paid for the one point at closing?
d. Find the total cost of interest over 30 years, to the nearest dollar.
B)
OA) a. down payment: $31,500
b. amount of mortgage: $178,500
c. points paid at closing: $2100
d. total cost of interest over 30 years: $196,167
a. down payment: $31,500
b. amount of mortgage: $178,500
c. points paid at closing: $1785
d. total cost of interest ver 30 years: $227,667
Oc) a. down payment: $31,500
b. amount of mortgage: $178,500
c. points paid at closing: $2100
d. total cost of interest over 30 years: $227,667
OD) a. down payment: $31,500
b. amount of mortgage: $178,500
c. points paid at closing: $1785
d. total cost of interest over 30 years: $406,167
Answer:
B
a. down payment: $31,500b. amount of mortgage: $178,500c. points paid at closing: $1785d. total cost of interest over 30 years: $227,667Step-by-step explanation:
You want to know the 15% down payment, the mortgage amount, the value of 1 point, and the total interest cost for a 6.5% 30 year loan on a $210,000 home.
Look at the Answer ChoicesThe answer choices all have the down payment as $31,500 and the loan value as $178,500. A "point" is one percent of the loan value (not the home value), so ...
1 point = 0.01 × $178,500 = $1785 . . . . . . eliminates choices A and C
The difference between choices B and D is in the value of the interest paid. Your experience with 30-year loans in this interest rate range tells you that the interest paid is between 1 and 2 times the loan value. That is, the chice $227,667 is more likely correct than the choice $406,167.
Comparing these two numbers, we see they differ by 178,500, which is the value of the loan. That is, we can guess that 406,167 is the total amount repaid, not just the interest.
Answer choice B is the only one that makes sense.
Work the problemIf you like, you can work the problem.
down payment = 15% × $210,000 = $31,500
loan amount = $210,000 -31,500 = $178,500
one point = 0.01 × $178,500 = $1785
The monthly payment is found using the amortization formula:
A = P(r/12)/(1 -(1 +r/12)^(-12t))
A = 178500(0.065/12)/(1 -(1 +0.065/12)^(-12·30)) ≈ 1128.24
The monthly payment amount is about $1128.
So, the total repaid is 360 payments of $1128.24, or $406,167.
The interest paid is this amount less the principal:
interest paid = $406,167 -178,500 = $227,667
If a cone has a volume of 100 cubic inches, what is the length of the radius? Round your answer to the nearest tenth.
The radius of the cone is 10√(3/πh) inches when the volume of the cone is 100 cubic inches.
According to the question,
We have the following information:
Volume of cone = 100 cubic inches
We know that the following formula is used to find the volume of cone:
Volume of cone = π[tex]r^{2}h/3[/tex] where r is the radius of the cone and h is the height of the cone
π[tex]r^{2}h/3[/tex] = 100
Now, using the cross multiplication method:
π[tex]r^{2}[/tex]h = 100*3
Dividing both sides of the equation by πh:
[tex]r^{2}[/tex] = 300/πh
r = 10√(3/πh) inches
We can also solve it further by putting the value of π.
Hence, the radius of the cone is 10√(3/πh) inches when the volume of the cone is 100 cubic inches.
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If you borrow $28 000 to buy a car and repay it over 5 years with a fixed interest rate of 9.8% p.a., how much simple interest will you pay?
Answer:
$13,720.00
Step-by-step explanation:
Calculate simple interest using the equation A = P(1 + rt)
Convert 9.8% to a decimal for ease (0.098)Solve: A = 28000(1 + (0.098 × 5)) = $41720.00A = $41,720.00
Interest = total repayment - original cost
$41,720.00 - 28,000 = $13,720.00
I need help on this question and it is the last one please help!
Both function in item I is decreasing, and the function in item II is increasing.
What is function?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.
What is domain?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
What is range?
The difference between the lowest and highest values in a list or set is known as the range. Put all the numbers in order before determining the range. The lowest number should then be subtracted from the highest. The range of the list is provided in the response.
1) As shown in the I that the function is in 3rd quadrant so thats why it decreases.
2)As show in II figure if ;
x1 = -1 ,y1 = -1
x2 = 0 , y2 =2
x3 = 1, y3 = 5
from the above observation it is clear that ;
x1<x2, y1<y2, x2<x3, y2<y3
So, the II item is increases (monotone increasing)
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The ratio of teachers to students is 1 to 26. Find an equivalent ratio
Answer:
2:52
Step-by-step explanation:
Multiply by 2
Let's play a game where I flip a coin. If the coin lands on Heads you win a $1, if it lands on Tails you lose a $1. I flip a coin 8 times and here is the results Tails Tails Tails Tails Tails Tails Tails Tails So you lost 8 times in a row and thus lose $8.00.
Part1: Would you like to continue this game. Why or why not.
Part 2: Calculate the P-value of getting 8 tails in a row assuming the coin is fair. Is it a big number or small?
Part 3: Based on the P-value you got above what would you conclude about your initial hypothesis that the coin is fair.
Using the z-distribution to test the hypothesis, it is found that:
1. You would not like to continue the game, as in each trial you are losing.
2. The p-value is of 0.0023.
3. The low p-value means that there is enough evidence to conclude that the coin is biased.
What are the hypothesis tested?At the null hypothesis, it is tested if there is not enough evidence that the coin is biased, that is, the proportion of heads is of 0.5, hence:
[tex]H_0: p = 0.5[/tex]
At the alternative hypothesis, it is tested if there is enough evidence that the coin is biased, that is, it has a proportion of heads lower than 0.5, hence:
[tex]H_1: p_1 < 0.5[/tex]
What is the test statistic?The test statistic is given by the equation as follows:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which the variables are listed and explained as follows:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.The values of these parameters are given as follows:
[tex]\overline{p} = \frac{0}{8} = 0, n = 8, p = 0.5[/tex]
Hence the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0 - 0.5}{\sqrt{\frac{0.5(0.5)}{8}}}[/tex]
z = -2.83.
P-value and conclusionUsing a z-distribution calculator, and considering a left-tailed test, as we are testing if the proportion is less than a value, with z = -2.83, the p-value is of 0.0023.
Since this p-value is less than the standard significance level of 0.05, it means that there is enough evidence to conclude that the coin is biased towards tails.
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A die is continuously rolled until the total sum of all rolls exceeds 150 What is the probability that at least 40 rolls are necessary?
The probability that at least 40 rolls are necessary is 4/15.
What is probability?
Probability shows the likelihood of an event happening. it can be calculated by dividing the number of outcomes of an event by the total number of possible outcomes or sample space. Probability is equal to '1' when the event is certain to occur. i.e P =1. It is less than '1' when it is not likely to occur. i.e P< 1
Probability P=no. outcomes/total no. of the possible outcomes
From the question;
No of out comes=40
No. of total possible outcome=150
Therefore probability P= 40/150
P=4/15
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Hello, I need help with this math exercise.
John buys 7 apples and 4 pears for $7.25. At the same prices, Hayley buys 5 apples and 9 pears for $10.40. What is the price of one pear? Use Cramer’s Rule to solve.
The price of one pear is $0.85
How to use Cramer’s Rule to solve the price of one pear?
Cramer's rule is one of the useful methods used for solving a system of equations. In this method, the values of the variables in the system are to be calculated using the determinants of matrices. Thus, Cramer's rule is also known as the determinant method.
Given that: John buys 7 apples and 4 pears for $7.25 and at the same prices, Hayley buys 5 apples and 9 pears for $10.40
We will use this given information to form equations in matrices form. Let a and p represent the prices of one apple and one pear respectively.
The equation is:
7a + 4p = 7.25
5a + 9p = 10.40
The matrix formed is:
[tex]C=\left[\begin {array}{ccc}7&4\\5&9\end{array}\right][/tex] , [tex]b=\left[\begin {array}{ccc}7.25\\10.40\end{array}\right][/tex]
Find the determinants,
D = (7 x 9) - (5 x 4) = 43
Da = (7.25 x 9) - (10.40 x 4) = 23.65
Dp = (7 x 10.40) - (5 x 7.25) = 36.55
a = Da/D = 23.65/43 = 0.55
p = Dp/D = 36.55/43 = 0.85
Since p = 0.85. Therefore, the price of one pear is $0.85
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If you roll a die 75 times. How many 1's should you expect to roll?
The graph of the absolute value parent function, f(x) = |x), is stretched
horizontally by a factor of 3 to create the graph of g(x). What function is g(x)?
OA. g(x)= x+3|
OB. g(x) = 31x1
C. g(x) = 13x1
OD. g(x)= |||
Answer:
OB. g(x) = 31x1
C. g(x) = 13x1
Step-by-step explanation:
Screenshot included in this work
The two blanks on the left side of the equation and the solution blank should be completed with the following ratios:
2050 kg/1 m³ × 2.2 lb/1 kg × 1 m³/35.3 ft³ = 127.76 lb/ft³.
What is a conversion factor?In Mathematics, a conversion factor simply refers to a number that is typically used to convert a number in one (1) set of units to another, either by dividing or multiplying.
Generally speaking, an appropriate conversion factor to an equal unit of value must be chosen and used when it is necessary to perform any mathematical conversion.
Conversion:
2050 kg/1 m³ × 2.2 lb/1 kg = 4,510 lb/1 m³
4,510 lb/1 m³ × 1 m³/35.3 ft³ = 4,510 lb/35.3 ft³
4,510 lb/35.3 ft³ = 127.76 lb/ft³.
Additionally, take note of the following units of conversion:
kg = kilograms.m³ = cubic meter.lb = pounds.ft³ = cubic foot.In conclusion, we can logically deduce that the crate's density is equal to 127.76 pounds per cubic foot.
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The Top-Notch Middle School had athletes from all the grades playing on a sports team.
6th grade 7th grade 8th grade
Basketball 2 4 7
Baseball 1 6 5
Soccer 7 4 4
Football 8 15 10
Explain what the ratio 8:73 represents.
A: The ratio 8:73 represents the ratio of total athletes to 7th grade football players.
B: The ratio 8:73 represents the ratio of 6th grade football players to total athletes.
C: The ratio 8:73 represents the ratio of 8th grade baseball players to total athletes.
D: The ratio 8:73 represents the ratio of 6th grade athletes to total athletes.
The ratio 8:73 represents B: The ratio 8:73 represents the ratio of 6th grade football players to total athletes.
What is a ratio?It should be noted that ratio demonstrates how many times one number can fit into another number as they contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point to another data point.
In this case, the football players for 6rh grade is 8 and the total number of athletes is 73.
Therefore, the ratio that illustrates this is 8:73.
In conclusion, the correct option is B.
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Answer:
b
Step-by-step explanation:
i took the test and its right :)
A postage stamp has a mass of 2 cg. How many of these stamps would have a total mass of 1 kg?
Total number of postage stamp having total mass 1 kg = 50000 stamps
Unitary Method: What is it?
The unitary method involves first establishing the value of a single unit, followed by the value of the required number of units. What can be numbers and units?
Let's say you go to the store to purchase six apples. You are told by the shopkeeper that he is selling 10 apples for Rs 100. In this example, the value and the units are the cost of the apples. Understanding the units and values is crucial when using the unitary technique to a problem.
Always write the things that need to be estimated on the right side and the variables that are known on the left side to simplify the task. In the important in the current, the number of apples is known, but it is unclear what they are worth. It should be highlighted that issues with this method are addressed using the concepts of ratio and proportion.
Given That :
1 postage stamp is = 1 cg
now we will convert cg into g
1 cg = 0.01g
1 postage stamp is = 0.02g
now we will convert g into kg
1 g = 0.001 kg
0.01g = 0.00001kg
1 postage stamp is = 0.00002kg
so now
total number of stamp in 1 kg = 1/0.00002 = 50000
Hence the ans is 50000 stamps
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sin cos tan
( )
0
7
ans
Submit Question
I
+
One side of a rectangle is 24 m longer than four times another side. Find the length of the sides, given that
the area of the rectangle is 1408 m². Enter both sides, separated by a comma.
Length of the sides:
Question Help: D Post to forum
1
m
Length= 80 and width = 16 cm in the rectangle .
What is rectangle?
A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.let side = x cm
= x( 24 + 4x) = 1408
= 24x + 4x² = 1408
⇒ 4x² + 24x - 1408 = 0
4 ( x² + 6x - 352 ) = 0
x² + 6x - 352 = 0
x² + 22x - 16x - 352 = 0
x( x + 22 ) - 16 ( x + 22) = 0
( x - 16 ) ( x + 22 ) = 0
x= 16 , -22
we take x = 16 because distance never be negative
length = 16 + 4 * 16 = 80 cm
width = 16 cm
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The price of a new car was £12,500
It is reduced to £11,625
Work out the percentage reduction.
well, the reduction in value is £12500 - £11625 = £875.
if we take 12500 to be the 100%, what is 875 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 12500 & 100\\ 875& x \end{array} \implies \cfrac{12500}{875}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{100}{7}=\cfrac{100}{x}\implies 100x=700\implies x=\cfrac{700}{100}\implies x=7[/tex]
Answer: El porcentaje de reducción exacto es de: 7%, con esto el precio de descuento es de €875.
What is the end behavior of the graph?
Responses
As x approaches infinity, f(x) approaches negative infinity.
As x approaches negative infinity, f(x) approaches negative infinity.
As x approaches infinity, f open argument x close argument approaches negative infinity., , As x approaches negative infinity, f open argument x close argument approaches negative infinity., , ,
As x approaches infinity, f(x) approaches infinity.
As x approaches negative infinity, f(x) approaches infinity.
As x approaches infinity, f open argument x close argument approaches infinity., , As x approaches negative infinity, f open argument x close argument approaches infinity., , ,
As x approaches infinity, f(x) approaches negative infinity.
As x approaches negative infinity, f(x) approaches infinity.
As x approaches infinity, f open argument x close argument approaches negative infinity., , As x approaches negative infinity, f open argument x close argument approaches infinity., , ,
As x approaches infinity, f(x) approaches infinity.
As x approaches negative infinity, f(x) approaches negative infinity.
The end of the graph is
As x approaches infinity, f open argument x close argument approaches negative infinity., , As x approaches negative infinity, f open argument x close argument approaches infinity
as x tends to ∞, f(x) tends to -∞as x tends to -∞, f(x) tends to ∞What is end behavior?The end behavior of function typically says the characteristics of the function at the ends
How to find the end behavior of polynomial functionThis is determined by examining the graph and the coordinates.
The graph shows as at the positive side of the x coordinate, as x tends to ∞ the curve is pointing down - ∞The graph shows as at the negative side of the x coordinate as x tends to - ∞ the curve is pointing up ∞The end behavior is can be written as
x ⇒ ∞ f(x) ⇒ -∞
x ⇒ -∞ f(x) ⇒ ∞
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In the first five math quizzes, Patty had an average score of 8. She got a 7 and a 5 on the next two quizzes. After the eighth quiz, her
average stood at 7.5. What was her score on the eighth quiz?
*
Answer:
SHe got a 8 on the 8th quiz
Step-by-step explanation:
The score for eighth quiz is 8.
What is Algebra ?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
The average for 5 quiz marks is 8.
So, total quiz point = 8 x 5
= 40
Now, for next two the score are 7 and 8
The Total quiz point= 40 + 7+ 8= 55
let x be score on the 8th quiz
55+ x /8= 7.5
52 + x = (7.5)(8)
x = 60 - 52
x= 8
Hence, the score for eighth quiz is 8.
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Solve for j.
–3(j − 8) + –6 = –9
Answer:
j=3
Step-by-step explanation:
distribute
-3(j-8)+-6=-9
-3j+24-6=9
-3j+18=9
-3j=-9
j=3
Hopes this helps pleae mark brainliest
Answer:
j = 9
Step-by-step explanation:
Let's solve for the value of j,
→ -3(j − 8) + (-6) = -9
→ -3j + 24 - 6 = -9
→ -3j + 18 = -9
→ -3j = -9 - 18
→ j = (-27)/(-3)
→ j = 27/3
→ [ j = 9 ]
Hence, the value of j is 9.
If it takes 1 printer 14 minutes to print a batch of leaflets, how long would it
take 2 printers to print the same number of leaflets?
2 printers takes 7 minutes to print the same number of leaflets.
From the question, we have
1 printers takes 14 minutes to print the leaflets.
2 printers takes = 14/2 = 7 minutes to print the leaflets.
Divide:
Divide, in its simplest form, means to divide into two or more equivalent portions, spaces, groups, or divisions. Divide, in plain English, means to provide the entire thing to a group in equal portions or to divide it into equal pieces. Let's say a square is divided into two triangles with equal areas by a diagonal. A division operation may or may not provide an integer as the outcome. The outcome may occasionally take the form of decimal numbers.
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Answer: 7
Step-by-step explanation: because 1 printer takes 14 mins but if u have 2 u half the 14 it gives you 7 so it will take 2 printers 7 mins to print the same amount of leaflets. hope this helps.
What is the equation of the line that passes through the point (8, 2) and has a slope of -3/4
The equation of the line that passes through the point (8, 2) and has a slope of -3/4 is y = -3/4(x-8)+2.
In the given question we have to find the equation of line that passes through the point (8, 2) and has a slope of -3/4.
The given points are (8, 2).
The slope(m) = -3/4
The standard equation of slope intercept form is
y-y(1) = m(x-x(1))
From the question; x(1) = 8 and y(1) = 2.
Putting the value
y-2 = -3/4(x-8)
Add 2 on the both side, we get
y = -3/4(x-8)+2
Hence, the equation of the line that passes through the point (8, 2) and has a slope of -3/4 is y = -3/4(x-8)+2.
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Please Help me its a hard ;--;
Answer: y intercept: (0, -1/7)
Step-by-step explanation:
First you start with y = 10x - 1/7
Since your finding the y-intercept, you turn the 10x into a 0
So you would have y = -1/7
So y = -1/7
is your answer!
4. The distance needed to stop a car varies directly as the square of its speed. It
requires 120 m to stop a car at 70 km/h. What distance is required to stop a car
at 80 km/h?
Answer:
156.7 m (nearest tenth)
Step-by-step explanation:
Define the variables:
Let d = distance in meters.Let v = speed in kilometers per hour.If the distance needed to stop a car varies directly as the square of its speed:
[tex]\boxed{d \propto v^2 \implies d=kv^2}[/tex]
where k is the constant of proportionality.
Given:
d = 120 mv = 70 km/hTo find the constant of proportionality, k, substitute the given values into the equation:
[tex]\begin{aligned}\implies 120&=k(70)^2\\k&=\dfrac{120}{70^2}\\k&=\dfrac{6}{245}\end{aligned}[/tex]
Substitute the found value of k back into the formula to create an equation for the given relationship:
[tex]\implies d=\dfrac{6v^2}{245}[/tex]
To find the distance (in meters) required to stop a car at 80 km/h, substitute v = 80 into the equation:
[tex]\implies d=\dfrac{6(80)^2}{245}[/tex]
[tex]\implies d=\dfrac{6\cdot 6400}{245}[/tex]
[tex]\implies d=\dfrac{7680}{49}[/tex]
[tex]\implies d=156.73469...\; \sf m[/tex]
[tex]\implies d=156.7\; \sf m\; (nearest \;tenth)[/tex]
Therefore, the distance required to stop a car at 80 km/h is:
156.7 m (2 d.p.).