Answer:
y=-37
Step-by-step explanation:
A perpendicular line has a negative reciprocal slope to the original line. We will use the slope formula to find the slope of line m, then take the negative reciprocal for the slope of line n which will reveal the value of y.
Slope:[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We substitute [tex]x_1=6\\y_1=8[/tex] and [tex]x_2=-1\\y_2=2[/tex]
[tex]m=\frac{2-8}{-1-6}[/tex]
[tex]m=\frac{2-8}{-1-6}=\frac{-6}{-7} =\frac{6}{7}[/tex]
[tex]m\neq \frac{6}{7}[/tex] for line n because it is perpendicular to it. This means we will need to change it into its negative reciprocal which is [tex]m=-\frac{7}{6}[/tex].
We will substitute [tex]m=-\frac{7}{6}[/tex] into the slope formula to find line n's coordinate value y. We will also substitute [tex]x_1=-1\\y_1=5[/tex] and [tex]x_2=5\\y_2=y[/tex] .
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]-\frac{7}{6}=\frac{y-5}{5-(-1)}[/tex]
[tex]-\frac{7}{6}=\frac{y-5}{6)}[/tex]
[tex]6(-\frac{7}{6})=y-5[/tex]
[tex]-42+5=y-5+5[/tex]
[tex]-37=y[/tex]
The value of y that makes Line n perpendicular to Line m is 59/6. This is found by first calculating the slope of Line m and then finding the negative reciprocal (since perpendicular lines have negative reciprocal slopes), and using this new slope to solve for y in Line n.
Explanation:To solve this problem, we first need to understand that the slopes of two perpendicular lines are negative reciprocals of each other. This means that if Line m has a slope of a, then Line n will have a slope of -1/a.
First, let's find the slope of line m which contains the points (6,8) and (-1,2). The formula for slope is (y2-y1)/(x2-x1). This gives us (2-8)/(-1-6) = -6/-7 = 6/7.
Because line n is perpendicular to line m, its slope will be the negative reciprocal of 6/7, which is -7/6. We can then use this slope and the point (-1,5) to find the value of y when x=5 on line n. We use the equation y-y1 = m(x-x1), and substitute the values in: y - 5 = -7/6 * (5 - (-1)), which simplifies to y = -7 + 5 + 35/6 = 29/6 + 30/6 = 59/6.
Learn more about Slope of Perpendicular Lines here:https://brainly.com/question/35632758
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BRAINLIEST AND 60 POINTS!!!!!!!
1.) A coin is flipped. What is the theoretical probability that the coin lands on tails?
2.) A six sided number cube is rolled. What is the theoretical probability that a number greater than 4 is rolled?
3.) 2 six-sided number cubes are rolled. What is the theoretical probability that the sum of the number cubes is 8?
Answer:
1. P ( tails) = 1/2
2.P (number greater than 4) = 1/3
3. P (2 die sum to 8) = 5/36
Step-by-step explanation:
A coin only has 2 possibilities, head or tails, and they are equally likely
So the probability of getting a tails is 1/2
P ( tails) = 1/2
A die has the numbers 1,2,3,4,5,6 . There are 2 numbers greater than 4. They are 5 and 6. So there are 2 of the 6 choices that work.
P (number greater than 4) = 2/6 = 1/3
See the dice chart
There are 36 possibilities when you roll the die.
There are 5 that sum to 8
P (2 die sum to 8) = 5/36
Answer:
Guy above is correct
Step-by-step explanation:
Find all real numbers X such that 4x+2≥14 and -21x+1<22
[tex]\begin{cases}4x+2\ge14\\-21x+1<22\end{cases}[/tex]
In the first inequality, we have
[tex]4x+2\ge14\implies4x\ge12\implies x\ge3[/tex]
In the second, we have
[tex]-21x+1<22\implies-21x<21\implies x>-1[/tex]
The solution to the system is the intersection of these two intervals, which would be [tex]x\ge3[/tex].
Find f(4) for f(x)=-1/2x+5
Answer:
HELLO :
f(4) = -1/2(4)+5 = -2+5=3
A knife is three times the cost of a spoon. 9 spoons and 12 knifes cost ?82.80 workout the cost of 1 knife.
Let S = spoon
Let K = knife
1 knife is thee times the cost of a spoon, so it would be 3S
Now you have 9S + 12K = 82.80
We can replace the K with 3S:
9S +12(3S) = 82.80
Simplify the left side:
9S + 36S = 82.80
Add:
45S = 82.80
Divide both sides by 45"
S = 82.80 / 45
S = 1.84
One spoon cost $1.84
We know one knife cost 3 times as much, so multiply the cost of a spoon by 3:
Knife = 1.84 x 3 = $5.52
Answer:
1.84 x 3 = $5.52
The earth travels one full rotation around the sun 365.25. Ow many minutes does it take for the earth to travel one full rotation?
Angles 1 and 2 are supplementary.
Which equation represents the relationship between their measures?l?
Answer:
m∡1 + m∡2 = 180
Step-by-step explanation:
m∡1 + m∡2 = 180
This is because supplementary means they add up to 180°.
Saul in third in line. Enid is last in line. There are 3 children between them. What position is Enid in line?
The top three corn producers in the world - country A, country B, and country C - grew a total of about 664 million metric tons (MT) of corn in 2014. The country A produced 82 million MT more than the combined production of country B and country C. Country B produced 177 million MT more than country C. Find the number of metric tons of corn produced by each country.
Answer:
Number of metric tons of corn produced by country A = 373 million MT
Number of metric tons of corn produced by country B = 234 million MT
Number of metric tons of corn produced by country C = 57 million MT
Step-by-step explanation:
From the given information we have
A+B+C = 664 ____equation(1)
A = B+C+82 ____equation(2)
B = C + 177 ____equation(3)
1) Plugging in B=C+177 into equation 2, we get
A = B+C+82
=> A = (C+177) + C +82
=> A = C+177+C+82
=> A = C +C +177+82
=> A= 2C + 259 ____let it be equation (4)
2) Plugging in A=2C+259 from equation 4 and B=C+177 from equation 3 into the equation 1, we get
A+B+C = 664
=> (2C+259)+(C+177)+C = 664
=> 2C+C+C+259+177 = 664
=> 4C + 436 = 664
3) Subtracting 436 from both the sides, we have
4C + 436 - 436 = 664 - 436
4) Cancelling out +436 and -436 from the left side, we get
4C = 228
5) Dividing both the sides by 4, we get
[tex]\frac{4C}{4} = \frac{228}{4}[/tex]
6) Cancelling out the 4's from the left, we get
C = 57
7) Plugging in C=57 into the equation 3, we get
B = C + 177
=> B = 57+177
=> B = 234
8) Plugging in B=234 and C=57 into the equation 1, we get
A+B+C = 664
=> A+234+57=664
=> A + 291= 664
9) Subtracting 291 from both the sides, we get
A + 291 - 291 = 664 - 291
10) Cancelling out +291 and -291 from the left side, we get
A = 373
So, A = 373, B= 234, C=57
Jordan needs 6 3/10 gallons of milk to make 4 1/2 gallons of ice cream. How much gallons of milk will Jordan need to make one gallon of ice cream.
Answer:
45/63
Step-by-step explanation:
6 3/10=63/10, 4 1/2=45/10,
(45/10)/(63/10)=45/63
Shemar tips at the rate of 75:5 waiters. How many waiters will he be tipping, if he can afford a $90 tip?
Justin and Mike are learning how to ski. Justin falls down every 30 feet. Mike falls down every 25 feet. If they both start skiing from the same point, how far is the first point where they will both fall down?
Answer:
150 feet
Step-by-step explanation:
in order to find the solution we have to take the L.C.M of 25 and 30
L.C.M of 25 and 30 is 150
so after 150 feet , they will both fall down
Answer: They will both fall down after 150 feet.
Step-by-step explanation:
Hi, to answer this question we have to find the least common multiple (LCM)
of 30 and 25:
To obtain the multiple of a number we have to multiply that number by another number (not zero) in the multiplication table order (by 1,by 2,by 3,etc)
Multiples of 30:30,60,90,120,150
Multiples of 2525,50,75,100,125,150
The LCM is a number that appears on both lists, and is the smallest.
They will both fall down after 150 feet.
Feel free to ask for more if needed or if you did not understand something.
Adriano runs a website that helps writers write better stories. Every month, Adriano receives a subscription fee of $5 from each of the subscribers to his website.The website had 200 subscribers last month. This month 40 new members joined the website and 10 members cancelled their subscription. How much money will Adriano's online business earn this month?
Answer:
Adriano's this month earning is $1150
Step-by-step explanation:
Adriano's existing customers =200
Every customer Pays subscription fee = $5 per month
This month number of customers joined =40
And number of number of customers cancelled subscription =10
So this month addition of new customers = 40-10 =30
Therefore total numbers of subscribers =200+30 =230
And money earned this month = 230× $5
= $1150
What value in the replacement set is a solution to this equation? 3(n+7)=48 Replacement set: {8, 9, 10} Drag the solution into the box.
Answer:
n = 9 is the value in the replacement set is a solution to the equation [tex]3(n+7)=48[/tex]
Step-by-step explanation:
Given an equation: [tex]3(n+7)=48[/tex] .....[1]
Replacement set: {8, 9, 10}
For n = 8
Substitute in equation [1], we get;
[tex]3(8+7)=48[/tex]
[tex]3(15)=48[/tex]
[tex]45=48[/tex] False.
Similarly, For n = 9
Substitute in equation [1], we get;
[tex]3(9+7)=48[/tex]
[tex]3(16)=48[/tex]
[tex]48=48[/tex] True.
for n = 10
Substitute in equation [1], we get;
[tex]3(10+7)=48[/tex]
[tex]3(17)=48[/tex]
[tex]51=48[/tex] False.
Therefore, the value in the replacement set is a solution to this equation [tex]3(n+7)=48[/tex] is, 9
Answer:
9
Step-by-step explanation:
Jack wants to buy a Ford F150 Supercab with a base MSRP of $28,882.00. He wants the V8 Engine for an extra $1,379.00 and 4wd for an extra $3,215.00. What is the total price of the truck with the options Jack wants?
Answer:
$33,476.00
Step-by-step explanation:
Just add them all together
In 1992, the population in a town was 8,000 people. In 1997, the population was 14,000. What was the percent increase in the population?
Answer:
75%
Step-by-step explanation:
To calculate the percent increase or decrease, we:
Find the difference between the new value and the originalDivide the number by the originalMultiply by 100 and the % symbol.The population of the town originally had 8,000 in 1992. In 1997, the population is 14,000.
14000-8000=60006000/8000=0.750.75(100)=75%The towns population increase by 75%
To find the percent increase in the population from 1992 to 1997, subtract the initial population from the final population, divide by the initial population, and multiply by 100, resulting in a 75% increase.
To calculate the percent increase in the population of the town from 1992 to 1997, follow these steps:
Subtract the initial population in 1992 from the final population in 1997 to find the absolute increase: 14,000 - 8,000 = 6,000 people.Divide the absolute increase by the initial population to get the increase relative to the initial population: 6,000 \/ 8,000 = 0.75.Multiply the result by 100 to convert it to a percentage: 0.75 * 100 = 75%.Therefore, the percent increase in the population from 1992 to 1997 was 75%.
Please answer this question! 15 points and brainliest!
Answer:
-1< x< 3 x is an integer
Step-by-step explanation:
There are the dots on the number line. Three points are represented
x= 0,1,2
We want an inequality
-1< x< 3 x is an integer
The distance between the cities Chicago and Toronto is 540 miles. A motorcycle's speed is 48 mph. For a car, it takes 2.25 hours less to cover the same distance than for the motorcycle. How long does it take them to meet, if they start moving towards each other simultaneously?
HELP PLEASE
Answer:
Motorcycle will complete the 540 mile trip in 11.25 hr.
The car will complete it 2.25 hours less, or 9 hours.
The speed of the car therefore is 540/9 = 60 mph.
60t + 48t = 540
108t = 540
t = 5
So they will meet in 5 hours, after which time the motorcycle will have traveled 48*5 = 240 miles
and the car will have traveled 60*5 = 300 miles.
Hope this help
Step-by-step explanation:
Lynn has 8.58 in quarters and pennies. If she has eight times as many pennies as quarters, how many of each does she have
Answer:
10.82 is the answer
Step-by-step explanation:
If triangle ABC is similar to triangle DEF, which statement is true about the two triangles?
A.)Segment AB is congruent to segment DE, and angles C and F are congruent.
B.)Segment BC is proportional to segment EF, and angles A and D are congruent.
C.)Segment AB is congruent to segment DE, and angles C and F are proportional.
D.)Segment BC is proportional to segment EF, and angles A and D are proportional.
Answer:
B.)Segment BC is proportional to segment EF, and angles A and D are congruent.Step-by-step explanation:
If ΔABC and ΔDEF are similar, then
AB is proportional to DE
BC is proportional to EF
CA is proportional to FD
and
angles A and D are congruent
angles B and E are congruent
angles C and F are congruent
Answer:
B.)Segment BC is proportional to segment EF, and angles A and D are congruent.
Step-by-step explanation:
Help me please Algebra Two!!
Answer:
a. -2, even mult. and 1, odd mult.
b.[tex](x+2)^2(x-1)[/tex]
c. Odd degree of 3 or higher, likely higher due to the turns in the graph.
Step-by-step explanation:
A polynomial graph has several features we look for to determine the equations.
The zeros of the function are the x-intercepts. If the x-intercepts touch but do not cross then the intercepts have an even multiplicity like 2, 4, 6, etc. If the x-intercepts cross over then they have an odd multiplicity. Degree is the exponent or multiplicity of each zero. Therefore if we know the multiplicity of each zero we can add them together to find or make an educated guess for the degree of the entire polynomial. The shape of the graph tells us what type of polynomial. Odd degrees have a backwards S shape. Even degrees have a W shape. The shape can even tell us the if the equation has a positive or negative leading coefficient. Upside down W or an M shape is negative. While a sideways S shape is negative.In this graph, there are two real zeros: -2,1
We can write them in intercept or factored form as (x-1) and (x+2).
Because the graph never crosses the x-axis at x=-2 the zero has an even multiplicity of at least 2. The opposite is true for x=1 because it crosses. Therefore it has an odd multiplicity of at least 1.
The graph is a sideways s shape and ends up so is positive.
This means the function has a degree of 3 or higher with the degree being odd.
Which inequality is true?
Answer:
∠6 > ∠3 is TRUE.
Step-by-step explanation:
We know that acute angle is less than 90 degree while obtuse angle is more than 90 degree. By looking at the given angles, we can easily determine which angle is obtuse or acute. then we can decide which angle is bigger to find the answer.
∠10 > ∠7
FALSE;
Because∠10 is acute while ∠7 is obtuse.
------------
∠6 > ∠3
TRUE;
Because∠3 is acute while ∠6 is obtuse.
------------
∠9 > ∠11
FALSE;
Because∠9 is acute while ∠11 is obtuse.
------------
∠8 > ∠11
FALSE;
Because∠8 is acute while ∠11 is obtuse.
------------
I need HELP ASAP
Mrs. Hool is planning on grading tests over the weekend. The number of tests that she has left to grade after each hour can be modeled by the equation = 78 − 15ℎ, where is the number of tests left to grade and ℎ is the number of hours she has worked on grading. What is the meaning of the values 78 and −15 in this equation?
Answer:
-15 is how many tests per hour i think, and 78 is how many tests total
Step-by-step explanation:
= 78 − 15ℎ
1 hour would be
78-(15x1)=63
2 hours would be
78-(15x2)=48
and so on.
Final answer:
The value 78 represents the initial number of tests Mrs. Hool has, while -15 represents the rate at which she grades tests per hour.
Explanation:
The values 78 and -15 in the equation represent the initial number of tests that Mrs. Hool has and the rate at which she grades the tests per hour, respectively.
The value 78 is the initial number of tests that Mrs. Hool has left to grade. This means that when she starts grading, she has 78 tests remaining.
The value -15 represents the rate at which Mrs. Hool grades the tests per hour. It indicates that for every hour she works on grading, she is able to complete 15 fewer tests than what she started with. In other words, the number of tests she has left decreases by 15 for every hour she works.
A runner, training for a competition, ran on a track every day for 10 weeks. The first week he ran 8 kilometers each day of the week. The second week he increased his daily run by one lap (400 meters). The third week he increased again his daily run by one lap and so on. What is total distance he ran in 10 weeks?
Answer:
Total = 686000 meters for 10 weeks 7 days a week.
Step-by-step explanation:
Let's solve this by doing the increase on just 1 training day per week. Then we can find the grand total for 7 days a week by multiplying by 7
a = 8000
n = 10
d = 400
Sum = (a + L)*n/2
L = a + (n - 1)*dL = 8000 + (10 - 1)*400L = 8000 + 9*400L = 8000 + 3600L = 11600 metersSum = (8000 + 11600)*10/2
Sum = 19600 * 10/2
Sum = 98000 meters.
This total represents 1 training day a week.
The total amount is 7 times this figure.
Total = 7 * 98000 = 686 000 meters.
A plane flies at an average speed of 300 miles per hour the expreesion 300t gives the distance traveled by the plane in t hours find the distance traveled by the plane in 8 hours
It costs 3.24 for a pack of 12 pens. Find the unit price in dollars per pen. Round your answer to the nearest cent
Terry has 3 gallons of fruit punch to serve at a party right and solve a proportion to determine how many quarts are in 3 gallons
Please help me out!!!!!!!!!!
than anwser is 22% or 0.22
Which inequality corresponds with the graph?
A) x > -2
B) x < -2
C) x ≤ -2
D) x ≥ -2
Answer:
D
Step-by-step explanation:
An inequality is an expression which means more than one number is a solution. We graph the solutions on a number line to show all possible values. We graph using circles and arrows.
Equal to and less/greater than are graphed with filled in circles on the value.Only less/greater than (not equal to) are graphed with open (not filled in) circles on the value.We draw an arrow the direction the solutions satisfy the inequality. Generally this is the direction the inequality itself points.This is a filled in circle on -2 so this is [tex]\leq or \geq[/tex]. This means only answers C and D are options.
Answer D points to the right.
Answer:
The answer is D
Step-by-step explanation:
MrsStrong was correct!!!! Thank you
What is the equation of a line that is perpendicular to 4x-3y=12 and passes through (-8,1)?
Answer:
y=-(3/4)x-5
Step-by-step explanation:
First we must write our equation in slope intercept form:
[tex]y=mx+b[/tex]
Where m is slope and b is the y-intercept.
[tex]4x-3y=12\\\\-3y=-4x+12\\\\y=\frac{4}{3}x-4[/tex]
Now we will find a line that is perpendicular to [tex]y=\frac{4}{3}x-4[/tex]
To do this we will get the negative inverse of our original slope which is 4/3 and the negative inverse is: [tex]-\frac{3}{4}[/tex].
Now we must determine our y-intercept for the perpendicular line by using the slope calculated above and plugging it in to the following equation:
[tex]y=m(x-x_1)+y_1[/tex]
Where m is the slope, x1 = -8 and y1=1 and so:
[tex]y=-\frac{3}{4}(x-(-8))+1\\\\y=-\frac{3}{4}x-\frac{24}{4}+1\\\\y=-\frac{3}{4}x-6+1\\\\y=-\frac{3}{4}x-5[/tex]
Over the course of a year, a company goes from 115 employees to 124 employees. What equation do you use to solve this equation
Answer:
115+9=124 employees