Find the equation of a line passing through the points (-1,5) and (3,17).
Answer:
y=3x+8
Step-by-step explanation:
First of all, remember what the equation of a line is:
y = mx+b
Where:
m is the slope, and
b is the y-intercept
you find the slope by using this formula:
then we figure out it is 3
then graph to find the y-intercept which is 8
Answer:
y = 3x + 8
Step-by-step explanation:
Below is the image for the formula of the slope.
1. Subtract y values:
17 - 5 - 12
2. Subtract x values:
3 - (-1) = 4
3. Divide y/x
12 / 4 = 3
Therefore, the slope is 3.
Next, you need to find the y-intercept. This is our equation so far:
y = 3x + b
We can substitute any of the points given to us from the problem. I will use the first point: (-1, 5).
When substituting, you get:
5 = 3 ( -1 ) + b
5 = -3 + b
b = 8
Therefore, the equation is y = 3x + 8
Does this relation represent a function?
Answer:
No
Step-by-step explanation:
There are multiple coordinates with the same x coordinate
Work out the bearing of D from C.
(Hint: bearings are written with three digits.)
Answer:
050°
Step-by-step explanation:
The bearing of D from C is the angle between the north pole and the line joining C and D when moving in a clockwise direction.
From the diagram, the angle is 050°
The sum of two numbers is 24
and their quotient is 3.
What are the two numbers?
In a board game, you gain 1.5x the number of coins in your purse every time you pass start. However, you max out at 300 coins. If you have 5 coins in your purse, how many times must you pass until you reach maximum?
Answer:
6
Step-by-step explanation:
The requried number of passes to reach the maximum is given as 10 passes.
What is an exponential function?The function which is in format f(x) =aˣ where a is constant and x is variable, the domain of this exponential function lies (-∞, ∞).
Here,
We have 5 coins in your purse,
We Gain 1.5x the number of coins in your purse every time you pass the start. The maximum number of coins is 300.
According to the quesiton,
5 . 1.5ˣ = 300
Where x is the number of passes,
1.5ˣ = 60
x ≈ 10
Thus, the requried number of passes to reach the maximum is given as 10 passes.
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ING DROPS
1. The total volume to be given is 30 ml.
The time over which this is to be given is 30 minutes.
The drop factor is 15.
How many drops per minute will be delivered ?
Answer:
15 drops per minute
Step-by-step explanation:
(drops per minute) flow/drip rate: volume ÷ time × drop factor
note:
volume (mL)
time (minutes)\
30 / 30 = 1
1 * 15 = 15
so, 15 drops per minute will be delivered
hope this helps!! have a lovely day :)
Answer:
15 drops/minute
Step-by-step explanation:
30 ÷ 30 = 1
1 · 15 = 15
hope this is helpful :)
What is the measurement of this angle?
F10) How many Solutions Does this
System Have?
y=2X
y = -x + 2
Answer:
See below.
Step-by-step explanation:
Problem:
Solve y=2x;y=−x+2
Steps:
I will solve your system by substitution.
y=2x;y=−x+2
Step: Solve y=2 x for y:
Step: Substitute 2x for y in y=−x+2:
y=−x+2
2x=−x+2
2x+x=−x+2+x(Add x to both sides)
3x=2
3x/3 = 2/3 (Divide both sides by 3)
x=2/3
Step: Substitute 2/3 for x in y = 2x
y=2x
y = 2(2/3)
y = 4/3 (Simplify both sides of the equation)
Answer:
x = 2/3 and y = 4/3
Answer:
only one at x = 2/3 y = 1 1/3
Step-by-step explanation:
At the same solution point Y = Y so
2x = -x + 2
3x = 2
x = 2/3
1-
-5-4-3-2-11₁
H
5
4
3
2
Mark this and return
-2+
-3+
AWN
-4
-5
]
[
C
1 2 3 4 5 x
]
What is the range of the function on the graph?
all the real numbers
O all the real numbers greater than or equal to 0
all the real numbers greater than or equal to 2
all the real numbers greater than or equal to -3
The range of the function on the graph is C. all the real numbers greater than or equal to –3 .
How to get the range?We can see by the graph maximum value of y of function is -3 and the graph continues to extend upward .
So, the range contain all the real numbers greater than or equal to –3 .
Therefore, the range contain all the real numbers greater than or equal to –3 .
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What is the initial value of the sequence? Please help
The initial value of the sequence is 1
How to determine the initial value?From the graph, we have the following ordered pairs
(x, y) = (1, 1), (2, 4) and (3, 8)
Remove the x values
y = 1, 4, 8
The first value in the above sequence is 1
Hence, the initial value of the sequence is 1
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PLS HELP PLS In the diagram below, ΔABC ≅ ΔDEF. Complete the statement ∠A ≅
Answer:
∠A ≅ ∠D
Step-by-step explanation:
When writing a triangle congruency like ΔABC ≅ ΔDEF, the angles are congurent based on the orders listed. For example the first angle A is congruent with the first angle of the other triangle D.
∠A ≅ ∠D
∠B ≅ ∠E
∠C ≅ ∠F
Choose the letter of the equation for
the graph.
Using translation concepts, the equation for the graph is given as follows:
b. [tex]y = \cos{\left(x + \frac{\pi}{2}\right)} + 1[/tex].
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, we have a cosine function(zero at pi/2, this is zero at the origin), shifted pi/2 units to the right and 1 unit up(as the standard amplitude is between -1 and 1, here is between 0 and 2).
Hence the rule is given by:
b. [tex]y = \cos{\left(x + \frac{\pi}{2}\right)} + 1[/tex].
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Find the area of the triangle.
Answer:
take 1/2 multiply by sin 91°×2×8
What is the inverse of the function f(x) = 2x + 1?
Answer:
[tex]h(x)=\frac{1}{2}x -\frac{1}{2} .[/tex]
Step-by-step explanation:
if the initial function is f(x)=2x+1, then
x=2*h(x)+1;
2h(x)=x-1;
[tex]h(x)=\frac{x}{2} -\frac{1}{2}.[/tex]
PS. change design according the local requirements.
Answer:
[tex]y^{-1} =\frac{1}{2} x-\frac{1}{2}[/tex]
Step-by-step explanation:
To find the inverse, you want to swap the inputs with the outputs, which is why you have the swapped domain and range between a function and its range.
So, given f(x)=2x+1, its inverse would give,
x=2y+1.
Solve for y,
2y=x-1 -> y=(x-1)/2 -> y=[tex]\frac{1}{2} x-\frac{1}{2}[/tex]
Therefore, [tex]y^{-1} =\frac{1}{2} x-\frac{1}{2}[/tex]
Please help me find the area of this trapeziod.
Answer:
37.5 m
Step-by-step explanation:
Since the trapezoid area formula is ((base 1+base 2)/2)*height, we can plug in the values.
((8+7)/2)*5
(15/2)*5
7.5*5=37.5
Now we add the unit, "m" to get 37.5 m!
Polygon ABCDE is the first in a pattern for a high school art project. The polygon is transformed so that the image of A' is at (−2, 2) and the image of D' is at (−3, 0). Which transformation can be used to show that ABCDE and its image are congruent?
The transformation that can be used to show that ABCDE and its image are congruent is a 90° counterclockwise.
How to depict the transformation?It should be noted that when we rotate a point through 90° counterclockwise, the mapping will be: (x, y) to (-y, x).
In this situation, it van be deduced that the x and y coordinates swapped positions. This illustrates a 90° counterclockwise rotation about the origin..
In this situation, since the rotation is a rigid motion, the two shapes are congruent.
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Simplify 2√2-√3
---------------
√2+√3
Step-by-step explanation:
[tex] = \frac{2 \sqrt{2} - \sqrt{3} }{ \sqrt{2} + \sqrt{3} } [/tex]
[tex] = \frac{2 \sqrt{2} - \sqrt{3} }{ \sqrt{2} + \sqrt{3} } \times \frac{ \sqrt{2} - \sqrt{3} }{ \sqrt{2} - \sqrt{3} } [/tex]
[tex] = \frac{ 2( \sqrt{2} - \sqrt{3} )( \sqrt{2} - \sqrt{3} )}{ { \sqrt{2} }^{2} - { \sqrt{3} }^{2} }[/tex]
[tex] = \frac{2(2 - \sqrt{6} - \sqrt{6} - 3) }{2 - 3} [/tex]
[tex] = \frac{2( - 1 - 2 \sqrt{6} )}{ - 1} [/tex]
[tex] = \frac{ - 2(1 + 2 \sqrt{6} )}{ - 1} [/tex]
[tex] = 2(1 + 2 \sqrt{6} )[/tex]
[tex] = 2 + 4 \sqrt{6} [/tex]
The graph displays the relationship between the length of time an employee works at a company and the number of the employee's monthly customers.
y intercept is 2, which shows while changing the jobs employees bring two customers.
What is linear equation?A linear equation is in the form, y = mx + b where m is the rate of change (slope) and b is the y intercept (initial value of y).
The complete question is:
The graph displays the relationship between the length of time an employee works at a company and the number of the employee's monthly customers.
Time Employed (Month)
If the equation for the line of best fit is y = 4.5x + 2, which of the following can be used to interpret the y-intercept in context?
Employee training takes 2 months.
Employee training takes 4.5 months.
Employees are likely to bring 2 customers with them when changing jobs.
Employees are likely to bring 4.5 customers with them when changing jobs.
As, linear equation is
y = mx + b
Let y be the number of customers and x be the length of time.
Then, y = 4.5x + 2
As, y intercept is 2, which shows while changing the jobs employees bring two customers.
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a. What are the distances in feet covered in 4 steps, 6 steps, 12 steps, and 30 steps?
The distances in feet covered in 4 steps, 6 steps, 12 steps, and 30 steps are 10 feet, 15 feet, 30 feet and 75 feet.
Missing informationWhen you walk with a normal stride, the average distance covered in 2 steps is about 5 feet
How to determine the distances?From the question, we have:
Rate = 5 feet per 2 steps
This gives
Rate = 5/2 feet per step
So, we have:
Rate = 2.5 feet per step
The distance is then calculated as:
Distance = Rate * Steps
This gives
Distance = 2.5 * Steps
So, the distances in feet covered in 4 steps, 6 steps, 12 steps, and 30 steps are
Distance = 2.5 * 4 = 10 feet
Distance = 2.5 * 6 = 15 feet
Distance = 2.5 * 12 = 30 feet
Distance = 2.5 * 30 = 75 feet
Hence, the distances in feet covered in 4 steps, 6 steps, 12 steps, and 30 steps are 10 feet, 15 feet, 30 feet and 75 feet.
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Round 7,485 to the nearest hundred.
Answer:
7,500
Step-by-step explanation:
When you round you automatically round up unless told otherwise
so find the hundredth, which is 485 and you round that to 500
then put the 7 back → 7,500
This year, a teacher graded 83 more final exams than last year. If the teacher graded 625 final exams this year, how many final exams did the teacher grade last year?
Answer:
542
Step-by-step explanation:
So X is the number of finals graded by teacher last year
she graded 83 more finals than the last year
and the total number of finals she graded this year is 625 so we have an equation
X + 83 = 625
and as you solve it for X
X = 625-83
x = 542
Answer:
542,
Step-by-step explanation:
You could solve these types of problems with inverse operations, so if you subtract 83 from 625, you'd get 542.
Need help with this geometry question
Answer: B
Step-by-step explanation:
In triangles ABC and CED, CE=AC and AB=ED, but CD>BC, meaning the angle E is smaller than angle A.
A woman passed gas silently. I said "it stinks", and she said "I apologize. Excuse me". Why did she say both of those things?
That's because there's this thing called polite people
Answer:
Because she is nice unlike me
Step-by-step explanation:
give me brainiest pls
see? I am not nice :) But seriously can I get brainliest?
Lily pads increase by 25% every 10 days.lf a pond starts with 22 lily pads,how many will there be after 50 days?
We conclude that after 50 days, there will be 67 lily pads.
how many will there be after 50 days?
We know that the number increases by 25% every 10 days.
In 50 days we have 5 groups of 10 days, so there will be five increases of 25%.
We know that the initial number is 22 lily pads, if we apply five consecutive increases of the 25% we get:
N = 22*(1 + 25%/100)*...*(1 + 25%/100%)
( the factor (1 + 25%/100%) appears five times)
So we can rewrite:
N = 22*(1 + 25%/100%)⁵
N = 22*(1 + 0.25)⁵ = 67.1
Which can be rounded to the nearest whole number, which is 67.
So we conclude that after 50 days, there will be 67 lily pads.
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Work out the height of this triangle with base, b = 4.7mm and area, A = 137.475mm2.
Step-by-step explanation:
hope you can understand
The height of the triangle will be;
⇒ 58.5 mm
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The base of the triangle = 4.7 mm
The area of triangle = 137.475 mm²
Now,
We know that;
⇒ The area of triangle = 1/2 × Base × Height
Substitute all the values, we get;
⇒ 137.475 = 1/2 × 4.7 × h
⇒ 137.475 = 2.35 × h
⇒ h = 137.475 / 2.35
⇒ h = 58.5 mm
Thus, The height of the triangle = 58.5 mm
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Please explain and i need it urgently... One fifth of marked price of a watch is given as discount. What is the discount percent?
Answer:
1/5 times 100= 20%
Step-by-step explanation:
brainliest????????!!!!!!!
Graph the following non-linear system of equations and identify the two solutions. y=2x −7x+3y=3 What type of function is the equation y=2x ? Linear [ ] Quadratic [ ] Exponential [ ] What type of function is the equation −7x+3y=3 ? Linear [ ] Quadratic [ ] Exponential [ ] Use your graph below to identify the two solutions to this non-linear system of equations. Note: All solutions to this problem are whole numbers. None of the answers are decimals or fractions. List the solution, (x,y), with the smallest x value below. x= __________ y= __________ List the solution, (x,y), with the largest x value below. x= __________ y= __________
The solution to the given non linear system of equation is smallest x value , x = 0 , y = 1 , largest x value x = 3 , y = 8 .
What is a Equation ?An Equation is a mathematical statement which relates two algebraic expression with an equal sign in between.
The equations given in the question is
y = 2ˣ
This is an exponential function
-7x +3y = 3
This is a linear function
The equations have been plotted and the solution to the non linear system of equation has been determined
The point at which the graphs intersect is the solution to the system of non -linear equations.
(0,1) and (3,8)
x = 0 , y = 1 ; x = 3 , y = 8
The solution to the given non linear system of equation is smallest x value , x = 0 , y = 1 , largest x value x = 3 , y = 8 .
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If
5 , 3 = 28
9 , 1 = 810
8 , 7 = 115
6 , 2 = 48
then
7 , 5 = ?
Answer:
212
Step-by-step explanation:
Simple addition and subtraction is to be used here.
5, 3 = 28
5-3 = 2 , 5+3 = 8
9 , 1 = 810
9-1 = 8 , 9+1 = 10
8 , 7 = 115
8-7= 1 , 8+7 = 15
6 , 2 = 48
6-2 = 4 , 6+2 = 8
7 , 5 = 212
7-5 = 2 , 7+5 = 12
Answer:
212
Step-by-step explanation:
Rule
Subtract the 2nd number from the first to obtain the first digit(s) of the answer.Add the 2nd number to the 1st to obtain the last digit(s) of the answer.5 - 3 = 2
5 + 3 = 8
Therefore: 28
9 - 1 = 8
9 + 1 = 10
Therefore: 810
8 - 7 = 1
8 + 7 = 15
Therefore: 115
6 - 2 = 4
6 + 2 = 8
Therefore: 48
7 - 5 = 2
7 + 5 = 12
Therefore: 212
find the probability of obtaining two digit number which is divisible by either of the two consecutive odd numbers whose product is 15
if you put 25ml of concentration in a glass, how much water should be added
Answer:
50 ml
Step-by-step explanation:
50 ml