The equation of the line passing through the points (-2,9) and (1,3) is
y = -2x + 11 where the slope is -2 and the y-intercept is +11
What is the Equation of a Line?The equation of a line can be formed with the help of the slope of the line and a point on the line. The slope of the line is the inclination of the line with the positive x-axis and is expressed as a numeric integer, fraction, or the tangent of the angle it makes with the positive x-axis. The point refers to a point in the coordinate system with the x coordinate and the y coordinate.
m = (y2 - y1) / (x2 - x1)
y1 = 9
y2 = 3
x1 = -2
x2 = 1
m = (3 - 9) / (1 - (-2))
m = - 6 / 3
m = - 2
The equation of the line;
m = (y - y1) / (x - x1)
-2 = y - 9 / x - 1
y - 9 = -2(x - 1)
y - 9 = -2x + 2
y = -2x + 11
Therefore the y-intercept is +11.
Learn more about equation of a line here: brainly.com/question/3493733
#SPJ1
How do you find the discrminant?
The discriminant is calculated using the formula b squared minus 4ac.It reveals how many possible answers there are to a quadratic problem.
what is discriminant ?The section of the quadratic formula following the square root symbol, b2-4ac, is the discriminant. If there are two solutions, one solution, or no solutions, the discriminant informs us of this. There are two solutions if the discriminant is bigger than zero. The square root's input (i.e., its contents), which is the phrase b2 4ac, is known as the "discriminant" because using its value, you may "discriminate" between (i.e., be able to distinguish between) the different solution types.
here
Keeping in mind that a, b, and c are the coefficients of your quadratic in standard form,
the discriminant is calculated using the formula b squared minus 4ac.
It reveals how many possible answers there are to a quadratic problem.
To know more about discriminant visit :-
https://brainly.com/question/15884086
#SPJ1
Equations of Exponential Functions
The Shop and Save is starting their annual clearance and the store has sent out to all their customers a coupon book offering a variety of saving on their products. The LCD television that you have wanted was reduced by 35% prior to the annual clearance. In addition, the coupon book has a 10% off coupon for the LCD television. Determine what you would pay after applying the discounts given that the price of the LCD television was $1,325. Round your answer to the nearest cent.
a. $728.75 c. $596.25
b. $775.13 d. $46.38
Please select the best answer from the choices provided
Answer:
B. $775.13
Step-by-step explanation:
I calculated it logically
The volume of a cylinder is 8281 cm?. The height of the cylinder is 23 cm.
What is the radius of the cylinder?
Answer:
V = πr²h
r = √V/πh
r = √8281 cm³/(3.14)(23 cm)
r = √8281 cm³/72.22 cm
r = √114.66 cm²
r = 10.71 cm
LINE GRAPH EASY PLEASE HELP!!
x -10 -3 4 11
y 1 6 30 120
Is the relationship linear, exponential, or neither?
Choose 1 answer:
Choose 1 answer:
A
Linear
B
Exponential
c
Neither
Answer:
Option C, neither.
Step-by-step explanation:
Here we have the table:
x: -10 -3 4 11
y: 1 6 30 120
This means that if our function is f(x), then:
f(-10) = 1
f(-3) = 6
f(4) = 30
f(11) = 120
We want to know if this represents a linear equation or an exponential equation or neither.
First, let's try with a linear equation.
We know that a linear equation can be written as:
f(x) = a*x + b
Then let's input the known values and let's see if this equation works.
We can use two of the known points to get:
f(-10) = 1 = a*-10 + b
f(4) = 30 = a*4 + b
With these equations, we can find the value of a and b, once we find these values, we can see if the equation also works for the other two points.
1 = a*-10 + b
30 = a*4 + b
First, we need to isolate one of the variables in one of the equations.
I will isolate b in the first one:
b = 1 + a*10
Now we can replace this in the other one to get:
30 = a*4 + 1 + a*10
30 = 1 + a*14
30 - 1 = a*14
29 = a*14
29/14 = a = 2.07
and using the equation b = 1 + a*10 we can find the value of b:
b = 1 + 2.07*10 = 1 + 20.7 = 21.7
Then the equation we get is:
f(x) = 2.07*x + 21.7
Now we need to see if this works for the other two points:
for x = -3, we need to get: f(-3) = 6
f(-3) = 2.07*-3 + 21.7 = 15.49
We did not get the value we expected, then we already know that the relationship is not linear.
Now let's see if the relationship can be exponential.
An exponential function is written as:
f(x) = A*(r)^x
Let's do the same as above, let's use two of the known points to find the values of A and r
f(-3) = 6 = A*(r)^(-3)
f(4) = 30 = A*(r)^4
Now we have the system of equations:
30 = A*(r)^4
6 = A*(r)^(-3)
If we take the quotient of these two equations, we get:
(30/6) = (A*(r)^4)/( A*(r)^(-3))
5 = (r^4)*r^3 = r^(4 + 3) = r^7
(5)^(1/7) = r = 1.258
And the value of A is given by:
30 = A*(1.258)^4
30/( (1.258)^4 ) = 11.98
Then the exponential equation is something like:
f(x) = 11.98*(1.258)^x
Now let's see if this equation also works for the other two points:
for x = -10, we should get f(-10) = 1
Let's see that:
f(-10) = 11.98*(1.258)^(-10) = 1.2
And for x = 11 we should get f(11) = 120
f(11) = 11.98*(1.258)^(11) = 149.6
So we get values closer to the ones we should get, but not the exact ones, so this is not an exponential relation.
Then the correct option is C, neither.
What is 70% of 400??
Answer: 280
Step-by-step explanation:
change 70 into a decimal, by moving the period 2 times the the left etc. and multiply it by 400 to get the answer.
0.70 x 400 = 280
mmmmmmmmm,mmmmmmmmmmmmmmmmmmm
Answer:
2 1/6
Step-by-step explanation:
Answer:
11
Step-by-step explanation: says it
what is this I need the answer
Answer:
104
Step-by-step explanation:
Elizabeth is 7 years older than her sister
Lauren. Five years ago, Elizabeth was twice
Lauren's age. How old is Lauren now?
Answer:
Lauren is now 12 years old.
Step-by-step explanation:
Lauren is now 12 years old, and Elizabeth is 19.
5 years ago, when Lauren was 7 years old, Elizabeth was twice her age, so she was 14.
✅
An equation is formed when two equal expressions. Lauren is currently 12 years old.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the present age of Elizabeth be represented by E, while the present age of Lauren is represented by L.
Given that Elizabeth is 7 years older than her sister Lauren.
Therefore, we can write the relation between their age as,
E = L + 7
Also, it is given that Five years ago, Elizabeth was twice Lauren's age.
(E - 5) = 2(L - 5)
E - 5 = 2L - 10
Substitute the value of E from the first equation,
L + 7 - 5 = 2L - 10
7 - 5 + 10 = 2L - L
L = 12
Hence, Lauren is currently 12 years old.
Learn more about Equation here:
https://brainly.com/question/14686792
#SPJ2
Use Vocabulary to Describe a Graph
What is the domain of the relation?
✓ -4
5x56
COMPLETE
What is the range of the relation?
-4 ≤ys
DONE ✔
-4
+y
4
2
-2
-4
X
For the given graph, the domain and range of the relation equals [-4, 6].
What in mathematics is a relation?A collection of ordered pairs having one item from each set makes up a relation between two sets. If the ordered pair (x,y) is present in the relation and the objects x and y come from different sets, then the objects are said to be connected. One kind of relation is a function.
In other words, the ordered pair collection, where the ordered pair is made up of an object from each set, is used to define the relationship between the two sets. As an illustration, consider the set notation symbols (-2, 1), (4, 3), and (7, -3) with curly brackets.
To learn more about relations from given link
https://brainly.com/question/29236632
#SPJ1
If the line y=4x+2 passes through the point (0,2), what other point will it pass through? There is more than one right answer.
Select one or more:
a. (1,6)
b. (4,14)
c. (3,12)
d. (2,10)
Answer:
A and D
I graphed the equation on desmos
Answer:
A,D
Step-by-step explanation:
2. According to the law of supply, if the price of a good or service increases:
Answer:
There is a negative relationship between the price of a good or service and the quantity producers will supply.
Step-by-step explanation:
The question is in the picture. pls help
Answer:
f=1 e=2 d=3
Step-by-step explanation:
Find the measurement of the angle I dictated for each trapezoid.
The measures of missing angles in trapezoids are listed below:
Case 5: m ∠ J = 75°, Case 7: m ∠ T = 118°
How to determine the measures of missing angles
In this question we must determine the measures of missing angles in trapezoids. There are two hints to determine the values of the missing angles:
Any pair of angles along one of the two parallel lines and between the other two congruent sides have the same measure. Any pair of angles between two parallel lines are supplementary angles. Two angles are supplementary when the sum of their measures equals 180°.Now we proceed to determine the missing angles in every trapezoid:
Case 5
m ∠ K + m ∠ J = 180°
21 · x + 15 · x = 180°
36 · x = 180°
x = 5
m ∠ J = 15 · x
m ∠ J = 15 · 5
m ∠ J = 75°
Case 7
m ∠ U = m ∠ T
m ∠ T = m ∠ U
m ∠ T = 118°
To learn more on trapezoids: https://brainly.com/question/12623349
#SPJ1
12 cups to 2 pints ratio
please help will give brainliest
Answer:
c
Step-by-step explanation:
10 times 8 = 80
80 times 3 = 240
Answer:
A
Step-by-step explanation:
length times width times height will give you volume
Just before a referendum on a school budget, a local newspaper polls 417 voters to predict whether the budget will pass. Suppose the budget has the support of 54% of the voters. What is the probability that the newspaper's sample will lead it to predict defeat?
Answer:
The probability here is 62%
The probability that the newspaper's sample will lead it to predict defeat is approximately 0.0495, or about 5%.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
Let X be the number of voters in the sample who do not support the budget (i.e., who will vote against it). Then X follows a binomial distribution with parameters n = 417 (the sample size) and p = 1 - 0.54 = 0.46 (the probability that a voter does not support the budget).
The probability that the sample will lead the newspaper to predict defeat is the probability that X is greater than half the sample size (since the budget will be defeated if more than half of the voters in the population vote against it). In other words, we need to calculate:
P(X > 0.5n) = P(X > 0.5 × 417) = P(X > 208.5)
We can use a normal approximation to the binomial distribution to estimate this probability. The mean of the binomial distribution is np = 417 × 0.46 = 191.82, and the standard deviation is √(np(1-p)) = √(417 × 0.46 × 0.54) = 10.04.
To apply the normal approximation, we standardize the random variable X as follows:
Z = (X - np) / √(np(1-p))
Then we can use a standard normal distribution table or calculator to find the probability:
P(X > 208.5) = P(Z > (208.5 - 191.82) / 10.04) = P(Z > 1.65) ≈ 0.0495
Therefore, the probability that the newspaper's sample will lead it to predict defeat is approximately 0.0495, or about 5%.
Learn more about probability here:
brainly.com/question/11234923
#SPJ2
Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 12 feet and a height of 20 feet. Container B has a diameter of 16 feet and a height of 12 feet. Container A is full of water and the water is pumped into Container B until Container A is empty.
Answer:
After the pumping, Container B is 11.8\%11.8% empty.
Step-by-step explanation:
The volume of water inside Container B equals the entire volume of Container A. The empty portion of Container B is equal to the entire volume of Container B minus the volume of water inside Container B. So the volume of empty space inside Container B is equal to 1570.7963-1385.44241570.7963−1385.4424 which equals 185.3539. The percent of Container B that is empty can be found by setting up a proportion with the entire volume of Container B: 11.8 %
HELP ASAP!!!! I will mark Brainlist!!! Thank you!!
Step-by-step explanation:
These triangles are similar (SAS)24m>21mSo<1 is greater than <2Solve the system:
y = x2 + 3x
y = 12x2 + 3x
Question 4 options:
A)
(12, 1)
B)
(0, 0)
C)
(1, 12)
D)
No solution
Answer:
B) (0, 0)
Step-by-step explanation:
It is where the two figures intersect on the graph!
Hope this Helps!! :))
The value of z varies inversely with the value of w. The constant of variation is 2. Which are possible values for z
3
and w? Check all that apply.
Oz=.
z = 1+₁ w = 2/1/201
O z = 2, w = 3
O z=
z = -1/₁w=2
O z
4,
= 1/5, w = 2/1/201
z = 1/2/3₁, w = 2/1/201
Answer:A,C,D
As a result of the inverse relationship between z and w, their product is constant.
What does "inverse connection" actually mean?There is an inverse relationship between two parameters when they are connected, where the value of one parameter tends to decrease as the value of the other parameter increases. It's often described as a "bad friendship" in conversation.
According to the information:z * W is equal to 1.
The statement indicates that the constant's value is 2/3, so:
z * w = 2/3
The result of solving for any of the variables is:
either w = (2/3) / z or z = (2/3) / w
The following values fit that relation:
z w = (2/3) / z
-8/9 (2/3) / (-8/9)
= - (2/3) * (9/8) = -3/4
- 4/9 (2/3) / (-4/9)
= - (2/3) * (9/4) = - 3/2
- 2/9 (2/3) / (-2/9)
= - (2/3) * (9/2) = - 3
2/9 (2/3) / ( 2/9)
= (2/3) * (9/2) = 3
4/9 (2/3) / (4/9)
= (2/3) * (9/4) = 3/2
To know more about inverse relationship visit:-
https://brainly.com/question/28628342
#SPJ1
Given points A (1, 5) and B (-7, -5), which of the following coordinates is the midpoint of AB? (-3, 0) (-4, 0) (-2, 0) (4, 0) (2, 0)
Using formula of midpoint of a line, the coordinate of the midpoint is (-3, 0)
What is Midpoint of LineThe midpoint of a line is a point that is equidistant from both endpoints of the line. It can be found by taking the average of the x-coordinates of the two endpoints, and then taking the average of the y-coordinates of the two endpoints. For example, if the two endpoints of a line are (x₁, y₁) and (x₂, y₂), then the midpoint of the line is:
Midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
The formula of midpoint of a line is given as;
M(x, y) = (x₂ + x₁) / 2, (y₂ + y₁) / 2
Substituting the values into the formula;
M(x, y) = (-7 + 1) / 2, (-5 + 5) / 2
M(x , y) = -6/2, 0/2
M(x, y) = -3, 0
The coordinate of midpoint is (-3, 0)
Learn more on midpoint of line here;
https://brainly.com/question/24778489
#SPJ1
the total cost for 5 adult tickets and 18 student tickets at a local theater is $98. The total cost was 98. The total cost for 4 adult tickets and 22 student tickets at the theater is $105. What’s the cost for one adult ticket and one student ticket? PLEASEE BRO
The cost of one adult ticket is 3.6 and cost of one student ticket is 4.3
Tickets for a school talent show cost $2 for students and $3 for adults. If Chris spends at least $11 but no more than 14 on x student tickets and 1 adult ticket, what is one possible value of x?Either 4 or is the appropriate response.
Chris spends a total of 2 x + 3 dollars on x student tickets and a total of x adult tickets because each student ticket costs $ 2 and each adult ticket costs $ 3.
Because Chris spends at least $ 11 but no more than $ 14 on the tickets, the entire inequality 2 x + 3 1 can be written.
x = 4 and x = 5.5 are obtained by subtracting 3 from each side of both inequalities and then dividing each side of both inequalities by 2.
A number higher than or equal to 4 and less than or equal to 5.5 must both be integers in order for x to have a value.
Therefore, either x = 4 or x = 5.
To be learn more about integers refer to:
https://brainly.com/question/15276410?referrer=searchResults
#SPJ1
Which expression best estimates 6 3/4 ÷ 1 2/3?
7÷2
6=1
8÷3
3÷2
Answer:
7÷2
Step-by-step explanation:
6 3/4= 6.75
1 2/3= ~1.67
round up 6.75 to 7 and 1.67 to 2
7÷2
The location of a monkey in its coordinate space enclosure is expressed as the ordered triple M (−8, 0, 0). A treat has been hidden in the same enclosure at a location expressed as T (0, 0, 6).
If each unit on the graph measures 1 foot, how far is the monkey from the treat? (Hint: The Pythagorean theorem can be used because the x-axis, y-axis, and z-axis each intersect at a right angle.)
2 ft
6 ft
10 ft
14 ft
Answer: I believe it’s 10 ft
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
Help me please trig hw
Answer:
44.044 is your answer dude
Sawyer picks a negative number. What is true about the opposite of his number?
Answer: the opposite number will be positive
Step-by-step explanation:
Using the following equation, find the center and radius of the circle. You must show and explain all work and calculations to receive credit. Be sure to leave your answer in exact form.
x^2 + y^2 - 8x + 2y + 13 = 0
Thank you!
Answer:
radius = 2 center = (4,1)
16.) true or false The absolute value of a number and the opposite of a number
will always be different.
Answer
false
Step-by-step explanation:
the absolute value of -1 is 1, and the opposite of -1 is also 1, so it would be false since these are the same
Someone please help me please don’t answer if you don’t know ..
the answer would be 7/8
Step-by-step explanation: