The equation of line is y= 5/2x -7.
What is equation of line?The slope of the line and a point on the line may be used to create the equation of a line. To better comprehend how the equation for a line is formed. The slope of the line, which can be stated as a numeric integer, fraction, or the tangent of the angle it forms with the positive x-axis, is the line's inclination with respect to the positive x-axis. The coordinate system's point with the x coordinate and the y coordinate is referred to as the point.
One of the significant forms used to express a straight line algebraically is the two point form.
Written as, y- y1= m (x- x1), where m is slope.
Given:
a line passes through the point (2, -2) and parallel to 5x-2y = 4
Now, writing the given equation of line in the form of slope intercept form
5x- 2y=4
2y = 5x -4
y= 5/2x -2
Here the slope is 5/2 and the required line will also have the same slope as parallel line.
then, m=5/2
Now using y=mx +c
put y=-2 and x=2
-2 = 5/2(2) + c
-2 -5 = c
c=-7
Hence, the equation of line is y= 5/2x -7.
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If X=[tex]\frac{2a+3}{3a-2}[/tex] ,express [tex]\frac{x-1}{2x+1}[/tex] in terms of a
Expressing [tex]\frac{x-1}{2x+1}[/tex] in terms of a gives [tex]\frac{5-a}{7a+4}[/tex]
How to write the given expression in terms of aGiven that:
[tex]x=\frac{2a+3}{3a-2}[/tex]
[tex]\frac{x-1}{2x+1}[/tex]
The Knowledge required here is substitution, the value of x is given. Substitute [tex]x=\frac{2a+3}{3a-2}[/tex] in any place x is seen in the numerator and the denominator.
The numerator
x - 1
substituting the value of x
[tex]\frac{2a+3}{3a-2}-1[/tex]
[tex]\frac{(2a+3)-(3a-2)}{3a-2}[/tex]
[tex]\frac{2a+3-3a+2}{3a-2}[/tex]
[tex]\frac{5-a}{3a-2}[/tex]
The denominator
2x + 1
substituting the value of x
[tex]2*\frac{2a+3}{3a-2} +1[/tex]
[tex]\frac{4a+6}{3a-2} +1[/tex]
[tex]\frac{(4a+6)+(3a-2)}{3a-2}[/tex]
[tex]\frac{7a+4}{3a-2}[/tex]
combining the fraction
Here the numerator and the denominator is brought together and division of fraction is used to solve
[tex]\frac{\frac{5-a}{3a-2}}{\frac{7a+4}{3a-2}}[/tex]
[tex]\frac{5-a}{3a-2}}*\frac{3a-2}{7a+4}[/tex]
[tex]\frac{5-a}{7a+4}[/tex]
Using substitution as required, then expressing the equation in terms of a gives [tex]\frac{5-a}{7a+4}[/tex]
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Graph the function 6=3y
find the edge length of a cube whose volume is 1.728cubic cm is the edge length a rational number
The edge lengths of a cube that has a 1.728 cm³ volume is 1.2 cm
What is the volume of a cube?The volume of a cube is the given by the length of one edge raised to the power of 3
The volume of a cube, V = Length, L × Width, W × Height, H
Given that the lengths of the edges of a cube are equal, we have!
Length, L = Width, W = Height, H
Which gives;
The volume of a cube, V = L × L × L = L³
Therefore, for the given cube, we have;
L³ = 1.728 cm³
1.728 = 1728/1000
(a + b)³ = a³ + 3•a²•b + 3•a•b² + b³
Taking a = 10, and b = 3, we have;
(10 + 2)³ = 10³ + 3×10²×2 + 3×10×2² + 2³ = 1728
Therefore;
1728/1000 = (10 + 2)³/10³ = 12³/10³
Which gives;
L³ = 12³/10³
[tex] \displaystyle {L = \sqrt[3]{ \frac{{12}^{3} }{ {10}^{3} } } = 1.2}[/tex]
The edge lengths of the cube, L = 1.2 cm
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1 The parent function f(x) = x was shifted
7 units down to create function b. Which
represents function?
A
b(x) = -7f(x)
B b(x) = f(x) - 7
C
b(x) = f(x + 7)
D
b(x) = 7-f(x)
What is the answer ?
The answer is b(x)=f(x)-7, which is option B.
The function that represents the new function b will be b(x) = f(x) - 7. Then the correct option is B.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The parent linear function is given below.
f(x) = x
The function is shifted downward direction by 7 units. Then the function b(x) will be given as,
b(x) = f(x) - 7
The function that represents the new function b will be b(x) = f(x) - 7. Then the correct option is B.
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Dividing polynomials
(12x5+4x4-24x²-8x) + (3x + 1)
Answer:
Any quotient of polynomials a(x)/b(x) can be written as q(x)+r(x)/b(x), where the degree of r(x) is less than the degree of b(x). For example, (x²-3x+5)/(x-1) can be written as x-2+3/(x-1).
Properties of equality can be used to justify steps in solving an equation.
Equation is 4x-1 =27. that means the correct answer is 27
The equals sign is used in mathematical formulas to show that two expressions are equal. In contrast to English, where an equation is defined as any well-formed formula that consists of two expressions joined by the equals sign, French defines an equation as containing one or more variables. The first stage in resolving a variable equation is determining the values of the variables that lead to equality.
Here, 4x-1 =27
We know that x=7
4x=27+1
4x= 28
Therefore x = 28÷4 = 7.
Hence, 4x-1 =27
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Dilations and Partitions
A segment AB is partitioned as shown.
A
P
Complete the statement.
Answer:
3:7
Step-by-step explanation:
AR has 3 spaces while AB has 7 means its 3:7
Discussion Topic Ratios and rates are ways to relate different quantities. For example, for every 1 car, there are 4 tires. This is a ratio. What other examples of ratios can you think of? A rate is similar to a ratio. Rates usually include the word per. One example of a rate is a car driving 60 miles per hour. What other examples of rates can you come up with?
Some examples of ratios are:
There are 20 passengers on each bus
There are 2 red and 3 black balls in each box.
Some examples of unit rates are:
The man can run 10 miles in one hour.
I can type 100 words in 30 minutes.
What is ratio and unit rate?A unit rate means a rate for one of something.
We write this as a ratio with a denominator of one.
The ratio is the comparison of two quantities of the same units.
We have,
Ratio:
For every 1 car, there are 4 tires.
We can have some examples of ratios as:
1 - There are 20 passengers on each bus
2 - There are 2 red and 3 black balls in each box.
Unit rate:
Car driving 60 miles per hour.
We can have some examples of unit rates:
1 - The man can run 10 miles in one hour.
2 - I can type 100 words in 30 minutes.
Thus,
Some examples of ratios are:
There are 20 passengers on each bus
There are 2 red and 3 black balls in each box.
Some examples of unit rates are:
The man can run 10 miles in one hour.
I can type 100 words in 30 minutes.
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What is an equation of the line that passes through the point (-1, 5) and is parallel
to the line x - y = 6?
Answer:
Step-by-step explanation:
An equation of the line that passes through the point (−4,8) and is parallel to the line x+y=6 could be y = - x + 4 .What is the Point-slope form?The equation of the straight line has its slope and given point.If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equationy-y₁ = m(x-x₁)Which is the required equation of a line in a point-slope form.WE havex + y = 6y = - x + 6Slope= -1Now, Use the same slope since the two lines are parallel to each other.Point-slope formula:y - 8 = -1 (x - - 4)y - 8 = -1 (x + 4)y - 8 + 8 = -x - 4 + 8y = - x + 4 (Slope-intercept form)Hence, an equation of the line that passes through the point (−4,8) and is parallel to the line x+y=6 could be y = - x + 4 .Learn more about slope here: brainly.com/question/2503591#SPJ2
⇒Parallel lines have equal gradients . It means that to obtain the gradient of the new equation we should first find the gradient of the given equation by writing the given equation in the form y=mx+c
[tex]x-y=6\\y=x-6[/tex]
⇒The gradient of the given equation is 1 as we know that the gradient of the equation is the coefficient of the variable x
This means the equation of the new equation is also going to be 1 since I explained above why. to find the value of c in the new equation we will substitute the known values in the general equation including the point.
[tex]5=1(-1)+c\\6=-1+c\\c=5+1\\c=6[/tex]
This means that the new equation is going to be:
[tex]y=x+6[/tex]
Please HELP ME!!! due at 8pm tonight 10/12/22
Answer:
y=2x+4
Step-by-step explanation:
get x is get two point let’s say (-2,0) and (0,4)
The 4-0/0-(-2)=4/2=2 so 2 is x and (0,4) is where it hit the y axis so 4 is b plug in
Y=2x+2
there are 10 questions on a discrete mathematics exam. how many ways are there to assign scores to the problems if the sum of the scores is 100 and each problem is worth at least 5 points?
There are 12,565,671,261 ways to assign scores to the problems in discrete mathematics exam.
What is meant by the term combination?A combination is a set of n items taken k at a time with no repetition. The conditions k-selection, k-multiset, and k-combination to repetition are frequently used to refer to combinations wherein repetition is permitted.In this case, we must employ the combination as well as repetition formula.
C(n + r-1, r) = (n + r -1)!/ r! (n - 1) !
n = 10 is provided (The number of questions)
Every question is worth a minimum of 5 points.
For 10 question = 10×5 = 50 points.
The total are 100 (sum of the scores)
r = 100 - 50
r = 50
Applying the formula.
C(10 + 50 - 1 , 50) = (10 + 50 - 1)!/ 501 (10 - 1)!
C(59, 50) = 59!/50!9!
We get by clarifying the above factorial.
C(59, 50) = 12,565,671,261
Thus, there are 12,565,671,261 ways to assign scores to the problems in discrete mathematics exam.
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please help me to find x,y and z
suppose that a certain college class contains students. of these, are juniors, are chemistry majors, and are neither. a student is selected at random from the class. (a) what is the probability that the student is both a junior and a chemistry major? (b) given that the student selected is a junior, what is the probability that she is also a chemistry major?
The answer will be .25 and .25 for both set of question. using probablity.
What is Probability ?
Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities.
Total number of students =1-juniors+chemistry+neither+both
(a) For both a junior and chemistry major =1/4 =. 25
(b) probability that she is also a chemistry major will be 1/4 =. 25
Hence The answer for the above two set of qustion will be .25 and .25.
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Safara wants to rent a bicycle the graph shows the cost for renting a bicycle for different lengths of time. What is the slope of the line?
The slope of the line will be equal to 30.
Slope of a line may be defined as the steepness of a curve. Slope of line can be positive, negative or zero. Slope of a line is used to determine the equation of the line which is given as y = mx + b where m is the slope, b is y intercept and x and y are independent and dependent variables respectively. The slope of a line on points (x₁, y₁) and (x₂, y₂) is given by the formula, m = y₂ - y₁/x₂ - x₁.
According to the question the value of points is (x₁, y₁) = (0, 0) and (x₂, y₂) = (2, 60).
Now, the slope can be calculated as
m = (60 - 0)/(2 - 0)
=> m = 60/2
=> m = 30 which is the required slope.
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There were 450 travelers on a flight to Orlando, and 80% of them checked luggage. How many travelers checked luggage?
Answer:
5.625
Step-by-step explanation:
450÷80 I hope I'm right and it helps if not I'm sorry.
Trey is driving to Philadelphia. Suppose that the distance to his destination (in miles) is a linear function of his total driving time (in minutes). Trey has 49 miles
to his destination after 37 minutes of driving, and he has 37.8 miles to his destination after 51 minutes of driving. How many miles will he have to his
destination after 57 minutes of driving?
distance (in miles)
Driving time(in minutes)
As per the linear function, the destination after 57 minutes of driving is 1055 miles.
Linear function:
The linear equation is defined as an algebraic equation of the form
y = mx + b.
involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
Given,
Trey is driving to Philadelphia. Suppose that the distance to his destination (in miles) is a linear function of his total driving time (in minutes).
Trey has 49 miles to his destination after 37 minutes of driving, and he has 37.8 miles to his destination after 51 minutes of driving.
Here we need to find his destination after 57 minutes of driving.
In this one, first we have to find the linear equation for the situation.
For that, we need the slope and the intercept.
So, here we consider the distance as y axis and the corresponding time as x axis. then we get the points as,
(x1. y1) => (37, 49)
(x2, y2) => (51,37.8)
Then the slope of the line is calculated as,
m = (37.8 - 49) / (51 - 37)
m = -11.2/14
Now, the intercept is calculated using the point (37,49) and the slope m = -11.2/14 is,
49 = -11.2/14(37) + b
686 = -414.4 + b
b = 1100.4
So, the linear equation of the function is
y = -11.2/14x + 1100.4
Here we need to find the distance when the time is 57 minutes,
For that, we have to apply the value of x as 57, to get the value of y,
Therefore,
y = -11.2/14 (57) + 1100.4
y = -45.6 + 1100.4
y = 1055
Therefore, the destination after 57 minutes of driving is 1055 miles.
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for every integer m, 7m 4 is not divisible by 7. construct a proof for the statement by selecting sentences from the following scrambled list and putting them in the correct order.
Answer: CAELYNN YOU WWELCOME
Step-by-step explanation:
7 +7+7+7+7+7
7y - 14 factor please ..
Answer:
2
Step-by-step explanation:
7y-14=0
7y=14
7y/7=14/7
y=2
Name the property illustrated.
(7 + 8) + 9 = 7 + (8 + 9)
answer: associative property
Step-by-step explanation:
Given the line segment AB with endpoints (-10,0) and (6,8). Find the approximate value of AB, round the answer to the nearest tenth if necessary. Then find the exact coordinates of its midpoint.
The line segment AB with endpoints (-10,0) and (6,8). The equation of the line segment is x-2y+10=0.
Given that,
The line segment AB with endpoints (-10,0) and (6,8).
We have to find the equation of the line segment.
The equation of the line formula is y-y₁=m(x-x₁).
Here we don't know the m value that is nothing but slope of the line.
First we have to find the slope of the line segment.
Slope of the line m=[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
m=(8-0)/(6+10)
m=8/16
m=1/2
Now,
We know the equation of line is y-y₁=m(x-x₁)
y-0=1/2(x+10)
2y=x+10
x-2y+10=0
Therefore, The equation of the line segment is x-2y+10=0.
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2 × 10 + 8 × 1 + 1 × 0.1 unit form
Answer: 20 x 1 x 0.1 + 8 + 1
2 + 8 = 10
d = 4n-2 solve for n
The value of the equation d = 4n - 2 for n is (d + 2) ÷ 4.
Given data, d = 4n - 2
For finding the value of n first add 2 to both the side,
d + 2 = 4n - 2 + 2
d + 2 = 4n
Now, divide 4 into both sides of the equation:
(d + 2) ÷ 4 = 4n ÷ 4
(d + 2) ÷ 4 = n
∴ The value of n after solving the equation d = 4n - 2 is (d + 2) ÷ 4.
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9th term of 25,150,900
Answer: The 9th term is 41990400
Step-by-step explanation:
As we can see here 25, 150, 900 to find the common ratio i'll divide 150 by 25 which gives me 6
to 25 times 6 is 150
150 times 6 is 900
T=Term
1t=25 2t=150 3t=900 4t=5400 5t=32400 6t=194400 7t=1166400 8t=6998400 9t= 41990400
900*6= 5400
5400*6=32400
32400*6= 194400
194400*6= 1166400
1166400*6= 6998400
6998400*6=41990400
22 is what percent of 110?
Answer:
22 is 20% of 110
Step-by-step explanation:
22 of 110 can be written as:22/110To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100 22/110 * 100/100=[22*100] /110 *1/100=20/100Therefore, the answer is 20%Need help with math question
Answer:
3/2
Step-by-step explanation:
XY/Z
-2×-3/4
6/4
3/2
e function.
f(x) = -4x² + 3x − 11
Find f(-4)
Answer:
-87
Step-by-step explanation:
-4x^2 + 3x - 11
-4(-4)^2 + 3(-4) - 11
-4 * 16 + 3(-4) - 11
-4 * 16 - 12 - 11
-64 - 12 - 11
-76 - 11
-87
Hope this helps! :)
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Brianna is very good at keeping her school binder organized. Every time her teacher returns
an assignment, Brianna puts it in the right section. Brianna has 113 assignments in the
history, science, and art sections combined. The rest of her assignments are in the math
section. Brianna has 182 assignments in total.
Use an equation to find the number of assignments in the math section of Brianna's binder.
assignments
You
The number of mathematics assignments are 69.
How to form an equation?Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y). When attempting to solve systems involving two linear equations, this form is also quite helpful.
Given : Brianna has 113 assignments in history, science and art.
Let x be the number of assignments that are in math section. There are 182 assignments in total.
The equation to represent this is
113 + x = 182
x = 182 - 113 = 69.
So the number of math assignments are 69.
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Graph this line using the slope
and y-intercept:
y= 1/6x + 4
Answer: See attached.
Step-by-step explanation:
To graph this, we will look at the pieces they gave us. Slope-intercept form equations are written in y = mx + b.
➜ The slope, m, is the pitch of the line. It's "rise over run" and helps us know where the plot points. For this problem, we will rise one value and move 6 values right to the next point.
➜ The y-intercept, b, is where the line intercepts the y-axis. It helps us know where the first point goes (0, y). For this problem, we will graph (0, 4).
Using these details, we will graph the line. View attached.
-3( v + 2) - 2v simplify use distributive property
NOTE -3 MUST MULTIPLY EVERYTHING IN THE BRACKETS.
[tex] = - 3(v) - 3(2) - 2v \\ = - 3v - 6 - 2v \\ = - 3v - 2v - 6 \\ = - 5v - 6[/tex]
GOODLUCK.
Jenna is now x years old and Amy is 3 years younger than Jenna. In terms of x, how old will Amy be in 4 years?
Answer:
x-3+4 = x+1
Step-by-step explanation:
x-3+4 = x+1.