Answer:
[tex]a=6[/tex]
Step-by-step explanation:
We have been given coordinates of three points on the same line and we are asked to find the value of 'a'.
First of all, we will find the equation of the line in slope-intercept form of equation [tex]y=mx+b[/tex].
Let us find slope of our given line using coordinates of point [tex](2,-2)[/tex] and [tex](-6,2)[/tex].
Upon substituting the coordinates of the given points in slope formula we will get,
[tex]m=\frac{2--2}{-6-2}[/tex]
[tex]m=\frac{2+2}{-8}[/tex]
[tex]m=\frac{4}{-8}[/tex]
[tex]m=-\frac{1}{2}[/tex]
Now, we will substitute [tex]m=-\frac{1}{2}[/tex] and coordinates of point [tex](2,-2)[/tex] in slope-intercept form of equation to find the y-intercept.
[tex]-2=-\frac{1}{2}*2+b[/tex]
[tex]-2=-1+b[/tex]
[tex]-2+1=-1+1+b[/tex]
[tex]-1=b[/tex]
Therefore, the equation of line passing through the given points is [tex]y=-\frac{1}{2}x-1[/tex].
To find the value of 'a' we will substitute coordinates of point [tex](a,-4)[/tex] in our equation as:
[tex]-4=-\frac{1}{2}*a-1[/tex]
[tex]-4+1=-\frac{1}{2}*a-1+1[/tex]
[tex]-3=-\frac{1}{2}*a[/tex]
Upon multiplying both sides of our equation by -2, we will get
[tex]-3*-2=-\frac{1}{2}*a*-2[/tex]
[tex]6=a[/tex]
Therefore, the value of a is 6.
Answer:
A = 6
Step-by-step explanation:
I think this is late but i got this right hope this helps :D
Average speed of Car 1 = 45 mph.
Average speed of Car 2 = 65 mph.
Time elapsed between start of Car 1 and start of Car 2 = 18 minutes.
how long until the cars lapse
It will take 40.5 minutes for Car 2 to catch up to Car 1 after its 18-minute head start.
To find out how long it will take for Car 2 to catch up to Car 1, we first need to determine the distance Car 1 travels during the 18-minute head start.
Convert 18 minutes to hours.
18 minutes ÷ 60 minutes/hour = 0.3 hours
Calculate the distance Car 1 travels during the 18-minute head start.
Distance = Speed × Time
Distance = 45 mph × 0.3 hours
Distance = 13.5 miles
Now that we know Car 1 has traveled 13.5 miles when Car 2 starts, we need to find out how long it takes for Car 2 to catch up, which is essentially the time needed to cover this distance at the speed difference between the two cars.
Calculate the relative speed of Car 2 compared to Car 1.
Relative Speed = Speed of Car 2 - Speed of Car 1
Relative Speed = 65 mph - 45 mph
Relative Speed = 20 mph
Calculate the time it takes for Car 2 to catch up.
Time = Distance ÷ Relative Speed
Time = 13.5 miles ÷ 20 mph
Time = 0.675 hours
Convert the time from hours to minutes for better understanding.
0.675 hours × 60 minutes/hour = 40.5 minutes
So, it will take 40.5 minutes for Car 2 to catch up to Car 1 after its 18-minute head start.
rewrite the following fractions as division problems 7/11 5/2 9/10 7/15
We are given some fractions and we need to write these fractions in terms of division problem.
a)
7/11
There are 7 chocolates and a total of 11 children present at a party.If the chocolates are to be distributed equally among all, then how many chocolates does each get?
b)
5/2
The distance traveled by Xavier is 5 km and the time taken by him is 2 hours.Then find his speed?
c)
9/10
If there are a total of 19 students in a class and the number of girls are 1 more than the number of boys then find the ratio of number of boys to number of girls?
d)
7/15
The are 7 red balls, 2 green balls and 6 yellow balls in a bag.One ball is drawn at random.What is the probability of getting a red ball?
Another tent has the perimeter of 7.2 metres. If the width is 1.3 meters, what is the length?
21.95 with a 4.25% sales tax
show the zero property of multiplication using the number 25
If g is an odd function, which pair of points could be found on the graph of g?
A) (-1,16) and (1,16)
B) (3,-5) and (-3,-5)
C) (4,28) and (4,-28)
D) (-2,32) and (2,-32)
Answer:
D is the only option that satisfies this. f(x)=-32 and f(-2)=-f(x)=32.
Step-by-step explanation:
Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. Round to three decimal places. n = 4, x = 3, p =
Final answer:
To find the probability of x successes in a binomial distribution, use the binomial probability formula. Substituting the given values into the formula will yield the probability.
Explanation:
To find the probability of x successes in a binomial distribution with n trials and probability of success p, we use the binomial probability formula. The formula is:
P(x) = (nCx) * p^x * (1-p)^(n-x)
Using the given values n = 4, x = 3, and p = ..., we can substitute these values into the formula to calculate the probability.
For example, if p = 0.5, the probability is:
P(3) = (4C3) * 0.5^3 * (1-0.5)^(4-3) = 4 * 0.125 * 0.5 = 0.25
In general, the air temperature decreases 12 degrees for every 4,000 feet increase in altitude. If a hiker climbs 3,000 feet by how much can she expect the temperature to decrease?
find the (f of f) (0) f(x)=3x-2
To find (f of f)(0), substitute the value of f(0) into the function and evaluate.
Explanation:To find (f of f)(0), we need to first find f(f(0)). Given that f(x) = 3x - 2, let's substitute f(0) into the function.
Therefore, (f of f)(0) is equal to -8.
If 5+6i is a root of the polynomial function f(x),which of the following must also be a root of f(x)
Answer:
5 - 6i must also be a root of f(x)
Step-by-step explanation:
Complex conjugates states that the two complex numbers are conjugates of each other if they have the same real part and their imaginary parts are negatives of each other i.e, the complex conjugate of a + bi is a - bi where i is imaginary.
Conjugate root theorem states that if the complex number a + bi is a root of a polynomial P(x) in one variable with real coefficients, then the complex conjugate a-bi is also a root of that polynomial.
Given: if 5+ 6i is a root of the polynomial function f(x).
then,
by the conjugate root theorem;
5 - 6i is also be a root of the polynomial f(x).
7.5% of what number is 12?
How you could use the numerical value of slope to describe the slant and steepness of a line?
Mr. Henderson did not realize his checking account had a balance of $200 when he used his debit card for a $317.25 purchase. What is his checking account balance after the purchase?
record the product. use expanded form to help. 5×162=
WORTH 20 POINTS
Which functions are equivalent to f(x)= 4√162? Check all that apply
Answer:
1,2,5
Step-by-step explanation:
How do you represent any number in an equation?
A film shop carrying black and white film and color film has $4000 in inventory the profit on black and white film is 12% and the profit on color film is 21% if all the film is sold and if the profit on color film is $150 less than the profit on blavk and white film how much was invested in each type of film
To solve this problem, set up a system of linear equations based on the total investment and profit conditions given. Solve for the variables representing investment amounts in black and white film and color film. This process demonstrates practical application of algebra in finance.
Explanation:Let's find how much was invested in black and white film and color film at a film shop with a total inventory of $4000, knowing that the profit on black and white film is 12%, the profit on color film is 21%, and the profit on color film is $150 less than the profit on black and white film.
Let x represent the amount invested in black and white film, and y represent the amount invested in color film. According to the problem, we have two equations:
First, rearrange Equation 2 to isolate y: 0.12x - 150 = 0.21y. Then, convert it to y = (0.12/0.21)x - (150/0.21).
Next, substitute the value of y from Equation 2 into Equation 1: x + ((0.12/0.21)x - (150/0.21)) = 4000. Solve this equation for x to find the amount invested in black and white film, then substitute x back into either equation to find y, the amount invested in color film.
This problem involves forming and solving a system of linear equations based on the given profit percentages and the condition that profit on color film is $150 less than the profit on black and white film, demonstrating application of algebra in financial contexts.
What is 1/7^9 × 1/7^-6
Need help on question 30 please
Imagine two lines intersect. How can the properties of linear pairs and vertical angles help to determine the angle measures created by the intersecting lines? Explain.
If you know the measure of one angle in a linear pair, you can find the measure of the other because the sum of the measure of the two angles is 180 degrees. If you know the measure of one angle in a pair of vertical angles, you can find the measure of the other because they are congruent.
Final answer:
Properties of vertical angles and linear pairs allow us to find unknown angles when two lines intersect by employing the facts that vertical angles are equal and linear pairs sum up to 180 degrees.
Explanation:
When two lines intersect, they form two pairs of vertical angles and two pairs of linear pairs. Vertical angles are opposite angles made by intersecting lines and are always equal. So, if one of the vertical angles is known, the opposite angle can be determined because it is congruent. Linear pairs are adjacent angles whose outer arms form a straight line. These linear pairs are supplementary, meaning their sum is 180 degrees. Therefore, if we know one angle of a linear pair, we can find the other by subtracting the known angle from 180 degrees. Understanding these properties allows us to solve for unknown angle measures around the intersection of two lines. For example, if one angle measure in a linear pair is given, we can find the measure of the adjacent angle. Knowing the measure of this adjacent angle, which is also a vertical angle, allows us to determine the measure of the angle vertical to it, as they are equal.
there are 220 calories in 4 ounces of beef. how many calories are there in 5 ounces
Final answer:
To find the number of calories in 5 ounces of beef, divide 220 calories by 4 ounces to find the per ounce calorie count and then multiply by 5. The answer is 275 calories for 5 ounces of beef.
Explanation:
To determine the number of calories in 5 ounces of beef, we will first calculate the calories per ounce. Given that there are 220 calories in 4 ounces of beef, we can divide 220 calories by 4 to find the number of calories in 1 ounce.
220 calories ÷ 4 ounces = 55 calories per ounce.
Now, if one ounce of beef has 55 calories, then 5 ounces of beef would have:
55 calories/ounce × 5 ounces = 275 calories.
Therefore, 5 ounces of beef contains 275 calories.
Use multiples to write two fractions equivalent 3/8
Answer:
its 3
Step-by-step explanation:
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When going more than 38 miles per hour, the gas mileage of a certain car fits the model y = 43.81 - .395x where x is the speed of the car in miles per hour and y is the miles per gallon of gasoline. Based on this model, at what speed will the car average 15 miles per gallon? (Round to nearest whole number.)
Answer:
d. 73
The car will average 15 miles per gallon at the speed 73 miles per hour
Step-by-step explanation:
Your equation is: y = 43.81 - 0.395x
We need to solve for x if y = 15
So plug 15 into your equation: 15 = 43.81 - 0.395x
Then rearrange your equation to get the variable by itself and change the sign: 0.395x = 43.81 - 15
Subtract 43.81 - 15 = 28.81
0.395x = 28.81
Then divide both sides of the equation by 0.395
0.395x/0.395 = 28.81/0.395
x = 72.9367088608
Then (Round to nearest whole number.)
Giving you your solution of 73
To Conclude:
The car will average 15 miles per gallon at the speed 73 miles per hour
Women's shoe size follow a normal distribution with a mean of size 7.5 and a standard deviation of 1.5 sizes. Using the 68-95-99.7 rule, if a store owner wants to stock shoe that fit. 68% of women, what range of sizes should the owner order
To fit 68% of women, the store owner should stock shoe sizes between 6 and 9.
Explanation:To determine the range of shoe sizes that the store owner should order in order to fit 68% of women, we can use the 68-95-99.7 rule, which states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean.
In this case, the mean shoe size is 7.5 and the standard deviation is 1.5. So, we can calculate the range by adding and subtracting one standard deviation from the mean:
Lower Bound = Mean - Standard Deviation
Upper Bound = Mean + Standard Deviation
Therefore, the owner should stock shoe sizes between 6 and 9 to fit 68% of women.
Theoretically, what would happen if a nation had an unlimited supply of a certain resource?
Convert 0.5% to a decimal. 0.5 0.05 0.005 5.0
Answer:
the answer is o.oo5
Step-by-step explanation:
Sarah started 3 miles below the rim of the canyon and hiked until she was 8 miles above the rim. Her brother Sam said she hiked 5 miles. Sarah said she hiked 11 miles.
Who is correct and why?
A. Sam is correct because |3 – 8| = 5.
B. Sam is correct because |–3 – 8| = 5.
C. Sarah is correct because |–3 + 8| = 11.
D. Sarah is correct because |–3 – 8| = 11.
-3 to 0 would be 3 then add 8 = 11 miles.
Sarah is correct
answer is D. Sarah is correct because |–3 – 8| = 11.
Sarah is correct because |–3 – 8| = 11, answer is option D. using number line concept.
What is number line geometery?A number line is a horizontal line that has numbers in equal intervals.The numbers included on the line can be negative or positive taking zero as a reference point at the center called the origin.
The horizontal straight lines in which the integers are placed in equal intervals increase as we go right.The horizontal straight lines in which the integers are placed in equal intervals decreases as we go left.
A vector is an object that has both a magnitude as wel as direction. direction. It is represented by an arrow (head) and the tail which indicates the direction.The length is proportional to the quantity's magnitude.The resultant vector can be calculated using vector addition, and vector subtraction.Unit vector always has a magnitude of one and tells about the direction
explanation:- using number line concept.
-3 to 0 would be 3 then add 8 = 11 miles.
⇒Sarah started 3 miles below the rim = -3
⇒ initially she was above 8 miles
⇒ total distance first from -3 to 0 and than from o to 8
Therefore total distance = |–3 – 8| = 11.
Hence the answer is option D. Sarah is correct because |–3 – 8| = 11.
Learn more about Number line here:-https://brainly.com/question/25748640
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One card is drawn at random from the deck of cards shown. Which of the following probabilities is equal to one?
P(even or odd)P(even and odd)P(not yellow)
Answer:
P(Even or ODD) ( .Y .)
Step-by-step explanation:
A statistics class at wilmington college has 25 students of which 15 are math majors and 10 are business majors. the professor randomly selects five students to work together on a group project. what is the mean of this probability distribution if selecting a business major is defined as a success?
Final answer:
The mean of this probability distribution is 2.
Explanation:
To find the mean of the probability distribution, we need to calculate the expected value. In this case, the random variable is selecting a business major as a success. So, the probability of selecting a business major is 10/25, or 0.4. The number of successes (business majors) in the group project can range from 0 to 5. Using the formula for expected value:
E(X) = p1 * x1 + p2 * x2 + ... + pn * xn,
where pi is the probability of xi occurring, we can calculate the mean as:
E(X) = (0.4 * 0) + (0.4 * 1) + (0.4 * 2) + (0.4 * 3) + (0.4 * 4) + (0.4 * 5)
E(X) = 2
Therefore, the mean of this probability distribution is 2.
True or false: the mean of a normal distribution has no effect on its spread. explain your answer. choose the correct answer below.
a. false. the spread of a normal distribution is completely determined by its mean.
b. true. the spread of a normal distribution is completely determined by its standard deviation.
c. true. the spread of a normal distribution is completely determined by its median.
d. false. the spread of a normal distribution is determined by both its mean and standard deviation.