Answers
Hello,
We need first to know what's a gradient. The Gradient (also called Slope) of a straight line shows how steep a straight line is.
But how do we find the slope (or Gradient) from two points ?
For exemple, let's find the gradient of the two points PQ...
Method
1. We need the coordinates of the point P, and the point Q :
P = (6 ; -11)
Q = (k ; -9)
2. The slope is the change in height divided by the change in horizontal distance.
In other words we :
a) subtract the x values
b) subtract the y values
c) divide
Application for PQ
subtract x values : xQ - xP = k - 6
subtract the y values : yQ - yP = -9 - (-11) = -9 + 11 = 2
divide : (k-6) / 2
That is the gradient of PQ.. Now let us find the gradient of PR
Application for PR
subtract x values : xR - xP = 2k - 6
subtract the y values : yR - yP = -3 - (-11) = -3 + 11 = 8
divide : (2k-6)/8
That is the gradient of PR.
We know that by assumption, gradient of PQ = gradient of PR, what is the value of k ? Well, we simply need to solve an equation here :
gradient of PQ = gradient of PR
(k-6) / 2 = (2k - 6) / 8
k-6 = (4k - 12)/8 (we have multiplied by 2 on each sides of the equation)
8k - 48 = 4k - 12 (we have multiplied by 8 on each sides of the equation)
8k - 4k = - 12 + 48
4k = 36
k = 36 / 4 = 9
So the value of k in order for the two gradients to be equals needs to be equal to 9
Good luck
Related Questions
i’m not sure how to do this question could some help me as soon as possible
Answers
Answer: 729
Step-by-step explanation:
d+(-9)=-5
i need to solve for d. thank u
Answers
Answer:
4
Step-by-step explanation:
d - 9 = -5
Add 9 to -5, and you will get 4.
4 - 9 = -5
Answer:
d=4
Step-by-step explanation:
d+(-9)=-5
d=-5+9
d= 4
-2(x-2) - 4x = 3 (x + 1) - 9x
Answers
Answer:
No solution :(
Step-by-step explanation:
-2(x-2)-4x=3(x+1)-9x love these problems.
-2x+4-4x=3x+3-9x<-- I first multiplied the number outside of the parentheses to the numbers inside. Keep in mind that when a negative time a negative, it equals a positive, in the case of -2*-2.
-6x+4=-6x+3<-- I then combined like terms.
Right away I see that -6 and -6 would cancel out if i just added it to the other side. Thus this equation has no solution.. sorry.
6. A pollster reports, with 95 percent confidence, that between 55 and 61 percent of all Americans favor mandatory drug testings for employees in positions of public trust (bus drivers, airline pilots, etc). The point estimate for the unknown population proportion (who favor mandatory drug testing) equals a) 55 percent. b) 58 percent. c) 61 percent. d) some unknown percent.
Answers
Answer:
b
Step-by-step explanation:
karl is 4 years older than danny. eigt years ago carl was twice as old as danny. How old is danny now
Answers
Answer:
Karl is 16 and Danny is 12
Step-by-step explanation:
What is the idea of factoring by grouping?
Answers
Answer:
When factoring by grouping also called factoring in pairs, we should split the expression into two pairs that have something in common. The idea is that after we factor each pair, we get a binomial common factor.
Step-by-step explanation:
solve pls brainliest
Answers
what is the equation of a line that passes through the points (6,9) and is perpendicular to the line
Answers
Answer:
the line is perpendicular to what line you didn't mention that
Step-by-step explanation:
Write the exponential function for the values in the table below.
Answers
Answer:
f(x) = [tex]8^{x}[/tex]
Step-by-step explanation:
[tex]\sqrt[3]{512} = 8\\\sqrt[4]{4096} = 8\\\sqrt[5]{32768} = 8[/tex]
which means 8 to the power of 3 will give you 512, to the fourth power will give you 4096.
So the exponential function is f(x) = [tex]8^{x}[/tex]
Which of these are a multiple of 12? 2,8,16,24
Answers
Answer:
Step-by-step explanation:
24 is the multiple of 12
24 is a multiple of 12, so 24 is the correct answer of this question
Why is all the answers on this website saying my work is wrong.
Answers
Answer:
you're wrong
Step-by-step explanation:
should have been "Why are all the answers on this website saying my work is wrong?"
Two legs of a right triangle are each 70 cm. If one leg grows at the rate of 5cm/min and the oth
shrinks at the rate of 5 cm/min.
A)how fast is the hypotenuse of the triangle changing 2 minutes later?
Answers
The rate of change of the hypotenuse after 2 minutes is 0.505 cm/min
Let L be the length of one leg and D be the length of the other leg of the right triangle and y its hypotenuse
Since it is a right angled triangle, we have that, using Pythagoras' theorem
y² = L² + D²
Since the length of sides are the same, L = D = 70 cm.
So, y² = L² + D²
y² = 70² + 70²
y² = 2(70²)
y = 70√2
y = 98.99 cm
Also, one side increases at a rate of 5 cm/min and the other side decreases at a rate of 5 cm/min.
The increase in length of one side after 2 min is 5cm/min × 2 min = 10 cm.
So, it new length is L' = 70 + 10 = 80 cm
The decrease in length of the other side after 2 min is -5cm/min × 2 min = -10 cm.
So, it new length is D' = 70 + (-10 cm) = 60 cm
So, the new hypotenuse length is y' = √(L'² + D'²)
= √(80² + 60²)
= √(6400 + 3600)
= √10000
= 100 cm
Now, the change in length of the hypotenuse side in 2 minutes is Δy = 100 cm - 98.99 cm = 1.01 cm
So, rate of change of the hypotenuse after 2 minutes is 1.01 cm/2 min = 0.505 cm/min
The rate of change of the hypotenuse after 2 minutes is 0.505 cm/min
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Name Performance Task Write and Solve Equations Account Mario received his most recent bank statement and is planning what to do with his finances. He wants to be responsible with his money and save as much as he can for the future. The table shows the current balance of his 3 bank accounts.
Checking Account: 7,456.43
Savings Account: 2,010.55
Money Market Account: 2,378.09
Write your answers on another piece of paper. Show all your work to receive full credit.
Part 4 Mario wants the total of the 3 accounts to be at a minimum of $13,000 after his next paycheck. His next paycheck will be worth $1,200. He thinks that he will reach this goal if he deposits his entire paycheck to his accounts. Is Mario correct? Use an equation to support your answer.
Answers
Answer:
13000
Step-by-step explanation:
PLS ANSWER IM BEGGING PLS
Answers
Answer:
x = 3
Step-by-step explanation:
This is an isosceles triangle. Two angles (D and F) are equal because the sides opposite them are equal (or vice versa).
Thus, side DE = side EF, or
12x - 8 = 4x + 16
Combining like terms: 8x = 24
Thus, x = 24/8 = 3
x = 3
Consider the equation 12x - 15y = 70
Solve for x (in terms of y)
Solve for y (in terms of x)
PLEASE HELP MEEEE IM IN A TEST!
Answers
y = (12x-70) / 15
Zachary wants to ride his bicycle 26.8 miles this week. He has already ridden 8 miles.
If he rides for 4 more days, write and solve an equation which can be used to
determine m, the average number of miles he would have to ride each day to meet his
goal.
Answers
Answer:
4.7 ~~~ :D
Step-by-step explanation:
t = total...i = initial amount ridden......d = days..... m = average amount of miles
---------------
t = i +dm
26.8 = 8 + 4m
----------------- solve -----------------
26.8 = 8 + 4m ----> 18.8 = 4m ----> 4.7 = m
The expression is 26.8 = 8 + 4m and the average number of, miles he would have to ride each day to meet his goal is 4.7.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Let the attributes be, t = total, i = initial amount ridden, d = days, and m = average amount of miles.
The required expression can be written as below:-
t = i +dm
26.8 = 8 + 4m
The value of average miles will be calculated by solving the expression:-
26.8 = 8 + 4m
18.8 = 4m
4.7 = m
Therefore, the expression is 26.8 = 8 + 4m and the average number of, miles he would have to ride each day to meet his goal is 4.7.
To know more about expression follow
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the cost of cookies at store A are shown in the graph. The cost y for x cookies at store B is represented by the equation y=o.30x. which of the following statements are true? F. the cookies at store A cost more G. the cookies at store A cost $0.50 each H. the cookies at store B cost $0.15 each I. the cookies at store B cost more I need help ASAP please
Answers
Answer:
I
Step-by-step explanation: pick I because The cookies at store B cost more
find the 10th term
FORMULA: Tn=a+d(n-1)
Answers
Answer:
T₁₀ = 23
Step-by-step explanation:
The nth term of an arithmetic sequence is
[tex]T_{n}[/tex] = a + (n - 1)d
where a is the first term and d the common difference
Here a = - 4 and d = T₂ - T₁ = - 1 - (- 4) = - 1 + 4 = 3 , then
T₁₀ = - 4 + (9 × 3) = - 4 + 27 = 23
Answer:
-4,-1,2,5 turn into consecutive terms
d=-1-(-4)
d=2-(-1)
d=5-2
d=-1-(-4) calculate the value
d=3
d=2-(-1)
d=5-2
So it is a Arethmetic Sequence
That's my answer hope it helps
Which equations are true equations?
Select all correct answers.
54 ÷ 6 + 3² = 4 + 4²
8042=10−22−1
62−22=4+7⋅22
19−2⋅5=9⋅73−9
Answers
Answer:
B and C
Step-by-step explanation:
Took the test and 80/4^2 = 10 - 2^2 - 1 and 6^2−2^2=4+7⋅2^2 are the answers. Hope this helps :D
None of the equations is true.
What is an equation?Two or more expressions with an equal sign are defined as an equation.
The first equation is 54 ÷6 + 3² =4 + 4².
Simplify the equation:
54 ÷6 + 3² =4 + 4²
9 + 9 = 4 + 16
18 = 20
The left side and the right side of the equation are not equal, hence the first equation is not true.
Simplify the second equation:
8042 = 10-22-1
8042 = -13
The second equation is also false.
Simplify the third equation:
62−22=4+7⋅22
40 = -11
The third equation is also false.
Simplify the fourth equation:
19−2⋅5=9⋅73−9
16.5 = 0.73
The fourth equation is also false.
Hence, none of the equations is true.
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7. Which three lengths could be the lengths of the sides of a triangle
O 11 cm, 11 cm, 24 cm
O 18 cm, 12 cm, 9 cm
O9 cm,
19 cm,
10 cm
O4 cm, 7 cm, 23 cm
Answers
The sum of the lengths of two sides of a triangle cannot be less than the length of the third side.
So,
3.9cm, 19cm, 10cm
the total of this is 297197401415÷842035
Answers
Answer:
Approximately 352,951.36
Answer:
Step-by-step explanation:
= 297197401415+842035
= 297198243450
=297197401415/842035
=352951.363
Comparing credit and debit cards
Answers
Answer:
When you use a debit card, the funds for the amount of your purchase are taken from your checking account in almost real time. When you use a credit card, the amount will be charged to your line of credit, meaning you will pay the bill at a later date, which also gives you more time to pay.
Naomi's square bedroom
has an area of 90 square feet. What is
the length of one of the walls? Round to the nearest tenth if
necessary. ( The answer is 9.5 but how to you get there ?)
Answers
Think of a number, that when multiplied with itself, will get you 90.
We could try something like 7. So 7*7 = 49, but it's too small.
How about 10? Well we get 10*10 = 100 which is too big. The answer is between 7 and 10.
Let's try 8. So we get 8*8 = 64 which is too small.
This process is repeated until you determine that the answer is somewhere between 9 and 10
9*9 = 81
10*10 = 100
----------------
From here, we can try 9.5 since it's right between 9 and 10
9.5*9.5 = 90.25
close but not quite there. It's a bit too large. So the actual value is somewhat smaller than 9.5
Let's try 9.4
9.4*9.4 = 88.36
That seems even worse off compared to 90.25, so 9.5 is the better answer.
-----------------
As a shortcut, you can use the square root on your calculator
[tex]\sqrt{90} \approx 9.4868 \approx 9.5[/tex]
You are paid 82.50 for 7 1/2 what is ur rate of par
Answers
82.50/7.5= 11
hope this helps
A-project-of-construction-of-a-building-can-be-completed-by-150-workers-in-40-days-But-project-manager-brought-30-more-workers-after-16-days-In-how-many-days-will-the-remaining-work-be-finished
Answers
Answer:
In the second scenario after 16 days, 150 workers would have completed 150*16=2400 worker days. That leaves 6000-2400=3600 worker days remaining. If you add 30 workers, it would take 3600/180=20 days longer to complete. So, the entire project would take 16+20=36 days to complete.
three friends are playing a card game. to start each player draws four cards. the player with the largest sum goes first. which player goes first?
Deena:
6, -9, 7, -5
Cory:
5, 3, 0, -6
Malcom:
11, -12, -3, 4
Answers
Answer:
cory
Step-by-step explanation:
brainliest plz!!! :) have a good day
HELP ME PLSSSSSSSSSSSSSSSSSSSS
Answers
can someone please help me out with this as ive tried to put everything to solve it but im still wrong.
kind regards
Franklin
Answers
Divide 180 by 3 and you get 60.
You want an exterior angle so you cut the angle in half ( it is now 30 )
Because the base and the line are parallel (form right angle if drew line connecting them) x is equal to
90-30=60
which is the largest ratio? 5/36, 2:9, 3 to 18, 1:3
Answers
ashtons containor of water holds 80 milliliters. nelsons container holds 9/16 of that amont. how many milliniters of water do the two containors hokd together
Answers
Answer: Neither
Step-by-step explanation: Technically the containers hold no water at all as they hold only the bottles in which the water is actually contained. So the answer I suppose is 'Neither'.