Answer:
The equation of the line is [tex]y=\frac{-1}{2}x+1[/tex]
Step-by-step explanation:
1. The equation of the line that passes through two points can be expresed as:
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex] (Eq.1)
where [tex]x_{1}[/tex], [tex]x_{2}[/tex], [tex]y_{1}[/tex] and [tex]y_{2}[/tex] are the given points.
2. Name the points:
[tex]x_{1}[/tex]=-6
[tex]x_{2}[/tex]=-2
[tex]y_{1}[/tex]=4
[tex]y_{2}[/tex]=2
3. Replace the points in the Eq.1:
[tex]\frac{y-4}{x-(-6)}=\frac{2-4}{-2-(-6)}[/tex]
[tex]\frac{y-4}{x+6}=\frac{2-4}{-2+6}[/tex]
[tex]\frac{y-4}{x+6}=\frac{-2}{4}[/tex]
[tex]\frac{4(y-4)}{x+6}=-2[/tex]
[tex]4(y-4)=-2(x+6)[/tex]
[tex]4y-16=-2x-12[/tex]
[tex]4y=-2x-12+16[/tex]
[tex]4y=-2x+4[/tex]
[tex]y=\frac{-2x+4}{4}[/tex]
[tex]y=\frac{-2x}{4}+\frac{4}{4}[/tex]
[tex]y=\frac{-1}{2}x+1[/tex]
point m lies between point L and N on LN
Answer:
64 units
Step-by-step explanation:
Segment addition holds, so we can write ...
LM + MN = LN
(10x +8) +(5x-4) = (12x +16)
15x + 4 = 12x + 16 . . . . . . . . collect terms
3x -12 = 0 . . . . . . . . . . . . . . subtract 12x+16
x-4 = 0 . . . . . . . . . . . . . . . . . divide by 3
x = 4 . . . . . . . add 4
LN = 12x +16 = 12·4 +16 = 48 +16 . . . . . substitute into the expression for LN
LN = 64 . . . . units
Antar is flying a triangular-shaped kite. it has a height of 41/2 feet and a base of 53/4 feet. what is the area of antar's kite?
Answer:
12.94
Step-by-step explanation:
2%2, percent of the students at Hamilton Middle School have red hair. There are 700700700 students at Hamilton Middle School. How many students at Hamilton Middle School have red hair?
Answer:
14 students have red hair.
Step-by-step explanation:
In Hamilton Middle School 2% of the students have red hair .
Total number of students in the school = 700
We have to calculate the number of students who have red hair.
2% of 700 students.
= [tex]\frac{2}{100}[/tex] × 700
= 0.02 × 700
= 14 students.
14 students have red hair in Hamilton Middle School.
Mitchell and Luke record the number of deliveries they each make for their family's restaurant. The results are shown in the box plots below.
Select the true statement.
The interquartile range of Mitchell's data is greater than the interquartile range of Luke's data.
Mitchell's data and Luke's data have the same interquartile range.
The median number of deliveries made by Mitchell each week is greater than the median number of deliveries made by Luke each week.
The median number of deliveries made by Mitchell each week is equal to the median number of deliveries made by Luke each week.
Answer:
A. The interquartile range of Mitchell's data is greater than the interquartile range of Luke's data.
Step-by-step explanation:
A box contains 3 blue and 2 red pens while another box contains 2 blue and 5 red pens. a pen drawn at random from one of the boxes turns out to be blue. what is the probability that it came from the first box
The probability of getting blue from the first box is 3/5.
Given that, a box contains 3 blue and 2 red pens while another box contains 2 blue and 5 red pens.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favourable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.
Probability(Event) = Favorable Outcomes/Total Outcomes = x/n.
The probability of getting blue from the first box:
The number of favourable outcomes = 3 and the number of total outcomes =5
So, P(E) = 3/5
The probability of getting blue from the second box:
The number of favourable outcomes = 2 and the number of total outcomes =7
So, P(E) = 2/7
Therefore, the probability of getting blue from the first box is 3/5.
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The length of a rectangle is 5 cm longer than its width. find the width given that the area is 36cm
what does 3P2 equal?
The height of a triangular road sign is 1 inch shorter than twice its base. if the area of the sign is 60 in.2, which equation could be used to find the base (b) of the sign?
The equation that can be used to find the base of the triangular road sign is 60 = (b * (2b - 1)) / 2.
Explanation:Let's assume that the base of the triangular road sign is represented by b. According to the problem, the height of the sign is 1 inch shorter than twice its base, which can be written as:
height = 2b - 1
The area of a triangle can be calculated using the formula Area = (base * height) / 2. Substituting the given values into the formula, we get:
60 = (b * (2b - 1)) / 2
This equation can be used to find the base, b, of the sign.
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What is a population?. a population is the set containing all the people or objects whose properties are to be described and analyzed by the data collector.
b. a population is a set of data.
c. a population is the set of all the properties that can be assigned to any people or objects in a given sample.
d. a population is a group that exhibits characteristics typical of those possessed by the target sample?
The term population is the set containing all the people or objects whose properties are to be described. Hence, option (a) is correct.
What is Population?A community is a distinct group of people, creatures, or other objects that can be recognized for the purposes of data gathering and analysis by at least one shared trait.
The majority of the time, data is collected from samples in order to learn more about huge populations. For instance, market researchers might randomly contact a small percentage of the town's subscribers to major carrier services who were born between 1980 and 2004 if they wanted to obtain representative statistics for Millennial consumers of mobile phones who did not have a landline in New York City (the population).
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i need help with number 2 please p
The Venn diagram represents the results of a survey that asked participants whether they would want a dog or a cat as a pet.
Enter your answers in the boxes to complete the two way table based on the given data.
Dog Not dog Total
Cat ___ ___ ____
Not
Cat ___ ____ ____
Total ___ ____ ____
Arrange the numbers shown on the diagram into the correct category:
Dog Not dog Total
Cat 31 10 41
Not Cat 24 7 31
Total 55 17 72
7^-5 times 7^3 equals what, I need help asap please
Solve the proportion. Show your work.
A bag contains 8 blue marbles 5 red marbles and 2 orange marbles , Carolina picks a marble from the bag at random and returns it to the bag and makes a second random selection . What is the probability that two blue marbles were selected
What is the answer to 5+14a=9a−5
1 and 2 are a linear pair, and 2 and 3 are vertical angles. m 2=(5+4 y) and m 3=(6 y-25). what is m 1
The equation for the line of best fit for a data set is y = 2x + 1.5. If the point (1, 4) is in the data set, what is the residual of 1? 0.5 3.5 4.0 7.5
Answer: First option is correct.
Step-by-step explanation:
Since we have given that
[tex]y=2x+1.5[/tex]
If the point (1,4) is in the data set.
we need to find the residual of 1.
At x = 1,
[tex]y=2x+1.5\\\\y=2\times 1+1.5\\\\y=2+1.5\\\\y=3.5[/tex]
So, At x = 1, the value of y = 3.5
As we know that
[tex]Residual\ value=Estimate\ value-Actual\ value\\\\Residual\ value=4-3.5\\\\Residual\ value=0.5[/tex]
Hence, The residual of 1 is 0.5.
Thus, First option is correct.
what is f(5) if f(x)=8x-3
Answer:
f(5)=37
Step-by-step explanation:
We have the function f(x)=8x-3,
f(5) is the value of the function f when x=5, then you have to replace f(x) with x=5,
f(x)=8x-3
f(5)=8.(5)-3
f(5)=40-3
f(5)=37
The width of a rectangle is 4 less than half the length. if l represents the length, which equation could be used to find the width, w?
The fractions of -42/-45 and 14/15 are equivalent
Answer:
True
Step-by-step explanation:
john buys a new bedroom set on credit for $2760 and no interest. he pays $115 per month. what is the equation that models the money john owes?
!!!!PLEASE HELP, WILL GIVE BRIANLIEST!!!!
Which three-dimensional figure is formed by the rotation given?
The first picture is the rotation, the rest are the choices.
Check out the Points Scored by Lebron James during his 2012 season: 10,11.15, 18, 20, 20, 21,23, 24, 24, 26
A sport Statistics Magazine said his Median Score was 21 is that True or False?
A. True
B. False
What do you call it when someone pays back a loan quickly
The side of a square measures 3mn^2. What is the area of the square if m=4 and n= -2
Which answer choice below correctly identifies the 202nd term in the sequence 5, 10, 15, 20, 25 …?
Answer:
answer is : A. 1010
Step-by-step explanation:
the weight of an object on mars varies directly as the weight of the object on earth a 90 pound object on earth weighs 34 pounds on mars.if an object weighs 135 pounds on earth how much does it weigh on mars
We have been given that the weight of an object on the mars varies directly as the weight of the object on earth.
Let y be weight of an object on Mars and x be weight of an object on Earth.
[tex]\\ y=kx[/tex]
We have been given that the weight of an object on Mars is 34 pounds and weight of the same object on Earth is 90 pounds.
Putting the given values in equation we get
[tex]\\ 34=k(90)\\ \\ k=\frac{34}{90}=\frac{17}{45}[/tex]
Therefore, our equation now becomes
[tex]\\ y= \frac{17}{45}x[/tex]
Now we have been given that the weight of an object on Earth is 135 pounds and we have to find the weight of the same object on Mars,
We have been given that [tex]\\ x=135[/tex]
Putting the given values in our equation we get
[tex]\\ y= \frac{17}{45}(135)=\frac{17\cdot 135}{45}=17\cdot 3 = 51[/tex]
Therefore weight of the object on Mars will be 51 pounds.
What is the recursive formula for the sequence 3, 12, 48, 192, 768...?
The given sequence is a geometric sequence. Each term in the sequence multiplies by 4 to obtain the next. Therefore, the recursive formula for the sequence is an = 4 * an-1.
Explanation:The given sequence is: 3, 12, 48, 192, 768, and so on. Looking at the sequence, we can see that each term is multiplied by 4 to get the next term. So, the sequence is a geometric sequence. The recursive formula for a geometric sequence is given by: an = r * an-1, where an is the nth term, r is the common ratio, and an-1 is the previous term. In this case, r equals 4 (since we are multiplying each term by 4 to get the next term). Thus, "the recursive formula for this geometric sequence is: an = 4 * an-1".
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what is the largest possible product of two odd integers whose sum is 42?
The largest possible product of two odd integers whose sum is 42 is 437, obtained from multiplying 19 by 23.
The question asks for the largest possible product of two odd integers whose sum is 42. To find this, we should split 42 into two odd numbers that are as close to each other as possible because the product of two numbers that are close together will be higher than the product of a pair that has a larger difference.
If we divide 42 by 2, we get 21, which is not an even integer, so we need to adjust the numbers by 1. So the two odd numbers closest to each half of 42 are 21 and 21. However, we can't have them both be the same number since we're looking for two integers, so we adjust one up and one down by 1, resulting in 20 and 22. To ensure both numbers are odd, we will subtract 1 from the first number and add 1 to the second number, giving us 19 and 23 as the two odd integers that sum to 42.
The product of 19 and 23 is 19 × 23 = 437, which is the largest possible product for two odd integers that add up to 42.
Must have third quartile of a data set be less than the maximum value? Explain.