write equation of the line below
Hi there!
We are given two ordered pairs which are:
(0,0)(5,4)If you are curious how do I get these ordered pairs, they come from those two big circles or dots. x and y make relation and can be written as (x,y).
1. Find the slope
Yes, our first step is to find the slope of a graph if you want to find an equation. You may be curious how to find that right? No worries! We have got a special formula for you to find the slope![tex] \large \boxed{m = \frac{y_2 - y_1}{x_2 - x_1} }[/tex]
Since we have two given points, we can substitute them in the formula.
[tex] \large{m = \frac{4 - 0}{5 - 0} } \\ \large \boxed{m = \frac{4}{5} }[/tex]
2. Form an equation.
Since we have finally found, got or evaluated the slope. Next step is to find the y-intercept. Oh! Before we get to form an equation, do you know the slope-intercept form? We will be using that linear equation form since it is commonly used in the topic.[tex] \large \boxed{y = mx + b}[/tex]
Where m = slope and b = y-intercept. We substitute m = 4/5.
[tex] \large{y = \frac{4}{5} x + b}[/tex]
Next thing to remember is that when the graph intersects an origin point, b-term or y-intercept would be 0. Therefore b = 0 since the graph intersects (0,0).
[tex] \large \boxed{y = \frac{4}{5} x}[/tex]
3. Answer
Therefore the equation of the line is y = 4x/5.y = 2x - 3
y = -x + 3 solve for x and y
We are given the system of equations:
[tex] \large{ \begin{cases} y = 2x - 3 \\ y = - x + 3 \end{cases}}[/tex]
Since both are y-isolated equation, we can combine them together.
[tex] \large{2x - 3 = - x + 3}[/tex]
Isolate and solve for x-term.
[tex] \large{2x - 3 + 3 + x = - x + 3 + x + 3} \\ \large{2x + x = 6 \longrightarrow 3x = 6} \\ \large{ \frac{3x}{3} = \frac{6}{3} \longrightarrow \boxed{ \red{x = 2}}}[/tex]
Next, we find the value of y. Simply substitute x = 2 in one of these equations. The less coefficient values, the faster and better. I will substitute x = 2 in y = -x+3. You can substitute x = 2 in y = 2x-3 if you want but the result would be the same.
[tex] \large{y = - x + 3}[/tex]
Substitute x = 2 in the equation.
[tex] \large{y = - 2 + 3} \\ \large \boxed{ \blue{y = 1}}[/tex]
Therefore - when x = 2, y = 1. We can write in coordinate point or ordered pair as (2,1) from (x,y).
Answer
x = 2, y = 1(2,1) --- ordered pair
Write the expression. Then, complete the statements.
twice the difference of a number and seven
The word "twice" means multiplication by 2 v
The words "the difference of indicate
Find an equation for the line with the given property. (a) It passes through the point (2, −6) and is parallel to the line 4x + y − 10 = 0.
It has x-intercept 6 and y-intercept 4.
Answer:
[tex]y = -4x + 2[/tex]
Step-by-step explanation:
Required
Determine the equation
From the question, we understand that, it is parallel to:
[tex]4x + y -10 = 0[/tex]
This means that they have the same slope.
Make y the subject to calculate the slope of: [tex]4x + y -10 = 0[/tex]
[tex]y = -4x + 10[/tex]
The slope of a line with equation [tex]y =mx + c[/tex] is m
By comparison:
[tex]m = -4[/tex]
So, the slope of the required equation is -4.
The equation is then calculated as:
[tex]y = m(x - x_1) + y_1[/tex]
Where:
[tex](x_1.y_1) = (2,-6)[/tex]
So, we have:
[tex]y = -4(x - 2) -6[/tex]
Open bracket
[tex]y = -4x + 8 -6[/tex]
[tex]y = -4x + 2[/tex]
can anyone help please??
3.7 pounds of meat costs $20.35. What is the price per pound?
Answer:
$5.5 per pound of meat
Step-by-step explanation:
$20.35 ÷ 3.7 = $5.50
Hope this is helpful
If the distance from D to D' is 10 and the distance from A to D is 2 what is the scale factor?
Answer:
5
Step-by-step explanation:
10/2=5
The scale factor of the given case that the distance from D to D' is 10 and the distance from A to D is 2 will be 5.
What is the scale factor?
The ratio between comparable measurements of an object and a representation of that object is known as a scale factor in mathematics.
The scale factor is the ratio between two big and small figures and the ratio is called a scale for the given geometry.
For example, if we have a triangle with a side of 10 meters and another triangle with a side of 5 then the scale ratio will be 10/5 = 2.
Given that
distance from D to D' is 10
distance from A to D is 2
So the scale ratio will be
DD'/AD = 10/2 = 5 hence scale ratio will be 5 for the given
geometry.
For more about scale ratio,
https://brainly.com/question/13770371
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Which shows the following expression after the negative exponents have been eliminated?
Step-by-step explanation:
The given expression is :
[tex]\dfrac{a^3b^{-2}}{ab^{-4}}[/tex]
We need to simplify the above expression.
a³ is in numerator and a is in denominator. It gts cancelled.
[tex]\dfrac{a^3b^{-2}}{ab^{-4}}=\dfrac{a\times a\times a\times b\times b\times b\times b}{a\times b \times b}\\\\=\dfrac{a^2\times b^{-2}\times b^4}{1}\\\\=\dfrac{a^2}{b^{-2}}[/tex]
Hence, this is the required solution.
If a normal distribution has a mean of 154 and a standard deviation of 15,
what is the value that has a z-score of 1.6?
Answer:
The correct answer is - 178.
Step-by-step explanation:
The standard deviation is a measure of the amount of dispersion in a set of values.
Given:
Mean of a normal distribution (m) = 154
Standard deviation (s) = 15
z-score = 1.6
Solution:
To find: value (x) that has a z-score of 1.6
z-score is given by = x-u/15
1.6*15 = x-154
=> 154+24 = x
x = 178
Pls help I’ll brainlest
In a bread recipe, the ratio of milk
to flour is 5 to 4. If 7 cups of flour
are used, how many cups of milk
are used?
If f(x) is an exponential function where f(-2,5) = 9 and f(7) = 91, then find the value of f(12), to the nearest hundredth.
Answer:
[tex]f(12) = 323.02[/tex]
Step-by-step explanation:
Given
[tex]f(-2.5) = 9[/tex]
[tex]f(7) = 91[/tex]
[tex]f(12) = 16.7 * 1.28^{12[/tex]
Required
[tex]f(12)[/tex]
An exponential function is:
[tex]f(x) = ab^x[/tex]
[tex]f(-2.5) = 9[/tex] implies that:
[tex]9 = ab^{-2.5}[/tex]
[tex]f(7) = 91[/tex] implies that:
[tex]91 = ab^7[/tex]
Divide both equations
[tex]91/9 = ab^7/ab^{-2.5}[/tex]
[tex]91/9 = b^7/b^{-2.5}[/tex]
Apply law of indices
[tex]91/9 = b^{7+2.5}[/tex]
[tex]10.11 = b^{9.5}[/tex]
Take 9,5th root of both sides
[tex]b = 1.28[/tex]
So, we have:
[tex]9 = ab^{-2.5}[/tex]
[tex]9 = a * 1.28^{-2.5}[/tex]
[tex]9 = a * 0.54[/tex]
[tex]a = 9/0.54[/tex]
[tex]a = 16.7[/tex]
f(12) is calculated as:
[tex]f(x) = ab^x[/tex]
[tex]f(12) = 16.7 * 1.28^{12[/tex]
[tex]f(12) = 323.02[/tex]
3+5 plz help will gibe brain
Answer:
8
Step-by-step explanation:
Convert the following improper fraction to a whole number or a mixed number: 41/6
Answer:
6 and 5 over 6
6 5/6
Step-by-step explanation:
it would be a mixed fraction because 6 can't go into 41 evenly
Answer:
6
Hope that this helps!
order of operation problem who two operations inside parentheses and two ex outside ( using all add, subtract, multiply and divide)
PLEASE SHOW ALL WORK
Answer:
17 + 123 (4 - 1) + (36 / 18) 52 =
17 + 123 x 3 + 2 x 52 =
17 + 369 + 104 =
17 + 473 =
490
Step-by-step explanation:
hope this helps! i made up everything so i hope its okay!
What is the slope of the line that passes through the points (10, 5) and (15,20)? Write your answer in simplest form.
Answer:
3
Step-by-step explanation:
(10, 5) and (15,20)
m = rise/run
m = ∆y/∆x
m = (y₂ - y₁) / (x₂ - x₁)
m = (20 - 5) /(15 - 10)
m = 15/5
m = 3
Need help on this question been stuck on it
Answer:
Exponential Function
Step-by-step explanation:
y values increase by x4
Answer:
exponential function
the ans is b
Find the equation of the line with Slope = 3 and passing through (4, 10) .write your equation in the form y=mx+b
Please tell me how to do it thank you
Answer:
First set: 0.95. Second set: 0.86. Third set: 0.88.
Step-by-step explanation:
Imagine that these are not decimals, they are regular numbers (for example: 0.88 is turned into 88). You would determine which one is the greatest depending on which one is higher (like 44 is higher than 32). Therefor the first set: 0.95 the second set: 0.86 the third set: 0.88.
Please help!! First person gets award or whatever it is!! Awarding 10 points
Which function is shown in the graph below?
Answer:y=log1x
Step-by-step explanation:
please help meeeeeeee
pt 4
Answer:
The answer is
[tex]2 {x}^{2} + 3x - 1 = 0[/tex]
Why? Below I explain
Step-by-step explanation:
That formula has three variables a, b and c.
So, a = 2, b = 3 and c = -1
Because the formula is written like
[tex] \frac{ - b + - \sqrt{ {b}^{2} - 4 \times a \times c} }{2 \times a} [/tex]
If P = (7,-4), Find:
(180° (P)
([?], []
Enter
Step-by-step explanation:
the answer is in the above image
peter bought 3 suits and 3 pairs of jeans and paid $2397. James bought 8 suits and 11 pairs of jeans and paid $6989. What is the price of each?
Answer:
Therefore each suit cost $600 and each jean cost $199
Step-by-step explanation:
Let x represent the price of each suit and let y represent the price of each jeans.
Since 3 suits and 3 pairs of jeans cost $2397, this can be represented by the equation:
3x + 3y = 2397
Dividing through by 3:
3x/3 + 3y.3 = 2397/3
x + y = 799 (1)
Also, 8 suits and 11 pairs of jeans cost $6989, this can be represented by the equation:
8x + 11y = 6989 (2)
To find x and y, solve equation 1 and 2 simultaneously. Multiply equation 1 by 8 and subtract from equation 2 to get y:
3y = 597
y = $199
Put y = $199 in equation 1:
x + 199 = 799
x = $600
Therefore each suit cost $600 and each jean cost $199.
Rationalize the denominator of the fraction and enter the new denominator below.
Answer:
7/19
Step-by-step explanation:
7/19=square root of 11=22-3 19
The table shows a linear relationship between x and y.
х
у
-20
96
-12
60
-6
33
-2
15
What is the rate of change of y with respect to x?
Answer:
[tex] -\frac{9}{2} [/tex]
Step-by-step explanation:
Rate of change of x and y can be calculated using the following formula and using any two given pair of values from the table:
Rate of change = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Using (-12, 60) and (-6, 33).
Where,
[tex] (-12, 60) = (x_1, y_1) [/tex]
[tex] (-6, 33) = (x_2, y_2) [/tex]
Plug is the values
Rate of change = [tex] \frac{33 - 60}{-6 -(-12)} [/tex]
Rate of change = [tex] \frac{-27}{6} [/tex]
Simplify
Rate of change = [tex] \frac{-9}{2} [/tex]
Rate of change = [tex] -\frac{9}{2} [/tex]
The graph of the function f(x)=4/5 sqrt x is shown.
What is the domain of the function?
Answer:
All real number greater than equal to zero.
Step-by-step explanation:
The function is given by
[tex]f(x) = \frac{4}{5}\sqrt x[/tex]
The domain is defined as the input values so that the function is well defined.
here, the values of x should be all real number and zero also.
So, the correct option is (d).
Answer:
D
Step-by-step explanation:
It costs $21.50 to enter an amusement park and $0.50 to ride a ride. You have $24. Write an equation that represents the number r of rides you can ride.
Answer:
$24.00=$21.50+r*$.50
Step-by-step explanation:
total cost= entrance fee + r (number of rides) * $0.50 (cost of rides)
$24.00=$21.50+r*$.50
2.50=r*.50
2.5/.5=r
r=5
Examine the geometric relationships in the diagram below which option shows the correct value of x and y?
Answer:all of them
Step-by-step explanation:
In the questions below suppose the variable x represents students and represents courses, and:
•M(y): y is a math course F(x): x is a freshman
•B(x): x is a full-time student T(x,y): x is taking
•Write the statement in good English without using variables in your answers.
Answer:
Here the answer is given as follows,
Step-by-step explanation:
The last three parts are coming with a question mark, so can't answer those parts. post the image or write it properly
a) Every student is taking at least one course.
[tex]\forall x \exists y T(x,y)[/tex]
So for all x, there is a y such that T(x,y) is a true will be given by the above statement
b) There is a part-time student who is not taking any math courses.
[tex]\exists x \forall y [A(x) \Lambda (M(y) \rightarrow ~T(x,y))][/tex]