Answer:
parallel line: a(x-h) +b(y-k) = 0, or y-k = m(x -h); same slopeperpendicular line: b(x-h) -a(y-k) = 0, or y-k = (-1/m)(x -h); opposite reciprocal slopeStep-by-step explanation:
You want the steps to writing the equation of a line parallel or perpendicular to a given line through a given point.
EquationsGiven line ax+by=c and point (h, k), you can write equations for the desired lines using the forms:
a(x -h) +b(y -k) = 0 . . . . . . parallel line
b(x -h) -a(y -k) = 0 . . . . . . . perpendicular line
If you eliminate parentheses and collect terms, you will have the general form equation of the desired line(s). If you solve for y, you will have the slope-intercept form of the equation.
To use these forms, it is helpful to start with the equation of the given line in standard form, as shown. (It could also be in general form ax+by-c=0.)
StepsUsing the above solution, the steps are ...
Write the equation of the given line in standard form or general form.Identify the coefficients 'a' and 'b'.Fill in the coefficients and given point coordinates in the relevant equation above.Rearrange the result to whatever form you need.You will note that the same coefficients are used on the same variables for a parallel line. This is because parallel lines have the same slope.
The coefficient of the variables are swapped, and one of them is negated in the equation for the perpendicular line. This is because perpendicular lines have opposite reciprocal slope.
Slope-intercept formWhen the given line is in slope-intercept form, y = mx +b, the slope is readily identified as m, the coefficient of x. For the parallel line, this slope can be used directly in the point-slope equation for a line through a given point:
y -k = m(x -h) . . . . . . . line with slope m through point (h, k)
This can be rearranged to the slope-intercept form:
y = mx +(k -mh)
The perpendicular line has opposite reciprocal slope. The line perpendicular to the given line with slope m will have slope -1/m. Then the two forms of equation are ...
y -k = -1/m(x -h) . . . . . . . . . point-slope form
y = (-1/m)x +(k +h/m) . . . . . slope-intercept form
__
Additional comment
A standard form equation (ax +by = x) has mutually prime integer coefficients, with a positive leading coefficient. When you have written your equation, you may find it necessary to multiply the equation by some value to put it in this form. For example, -2x +4y = -8 must be multiplied by -1/2 to get the standard form equation x -2y = 4.
You need to be aware of the form required by your grader. The wording "the equation" often means slope-intercept form, or the form matching the given equation or the answer box format.
Solve the following equation in the picture....thanks:)
The Verdicts on each value of u according to the given inequality are as follows; 11, 13 and 8.
What values ares solutions to the inequality; u ≤ 13?It follows from the task content that the values which are solutions to the inequality; u ≤ 13 are to identified.
To determine the solution of an inequality on a number line, the number line representation of such inequality is very pivotal.
Therefore, the inequality given; u ≤ 13 simply implies that; the solution set of u includes 13 and all numbers to the left of 13 on the number line.
Hence, by considering each of the given values of u; we have;
11 ≤ 13?; Yes.13 ≤ 13?; Yes.8 ≤ 13?; Yes.18 ≤ 13?; No.Ultimately, the solutions to the inequality among the answer choices are; 11, 13 and 8 respectively.
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a shop has a sale microwave oven
Answer:
good i will buy
Step-by-step explanation:
I will name you the Brainliest if you answer!
Choose the ordered pair that is a solution of the inequality y ≤ −3x − 5.
(2, 3)
(0, 0)
(−1, −3)
(0, −1)
Answer:C. (1,-3)
E. (2,5)
Step-by-step explanation:
Select ALL the correct answers.
Observe the expression below and select the true statement(s).
The "3y" in the first term is a factor.
The "(7 + 2x)" in the first term is a factor.
The "10" in the third term is a coefficient.
The "x" in the second term is an exponent.
The "2" in the first term is a constant.
The "9" in the second term is a coefficient.
The correct statements are
The 3y in the first term is a factor The (7 + 2x) in the first term is a factor The 9 in the second terms is a coefficientThe expression is
3y(7 + 2x) + 9xy -10
The expression is the mathematical statement that consist of different variables, numbers and mathematical operators. The mathematical operators are addition, subtraction, division and multiplication
The expression is
3y(7 + 2x) + 9xy -10
From the expression 3y is the first term is a factor and (7+2x) is also the first term is a factor
Therefore,
The 3y in the first term is a factor.
The (7 + 2x) in the first term is a factor.
Consider the second term
The 9 in the second terms is a coefficient
Last term 10 is a constant, but there is not suitable statement is given
Hence, the correct statements are
The 3y in the first term is a factor The (7 + 2x) in the first term is a factor The 9 in the second terms is a coefficientLearn more about expression here
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In a class of 80 students, 40 study physics, 48 study mathematics and 44 study chemistry. 20 study physics and mathematics, 24 study physics and chemistry and 32 study only two of the three subjects. If every student studies at least one of the three subjects, find : a. The number of students who study all the three subjects. b.The number of students who study only mathematics and chemistry.
1. The number of students who study all three subjects is 10.
2. The number of students who study only mathematics and chemistry is 8
What are set operations?Set operations are the operations that are applied on two or more sets to develop a relationship between them.
Let mathematics = M, physics = P, chemistry = C.
n(M∪P∪C) = 80
n(M) = 48
n(P) = 40
n(C) = 44
n(M∩P) = 20
n(M∩C) = ?
n(C∩P) = 24
n(M∩P) + n(M∩C) + n(C∩P) - 3n(C∩P∩M) = 32
20 + n(M∩C) + 24 - 3n(C∩P∩M) = 32
n(M∩C) = 3n(C∩P∩M) - 12 - *
We know,
n(M∪P∪C) = n(M) + n(P) + n(C) - n(M∩P) - n(M∩C) - n(C∩P) + n(C∩P∩M)
80 = 48 + 40 + 44 - 20 - n(M∩C) - 24 + n(C∩P∩M)
n(M∩C) = n(C∩P∩M) + 8 -
Equating
n(C∩P∩M) + 8 = 3n(C∩P∩M) - 12
2n(C∩P∩M) = 20
n(C∩P∩M) = 10
Putting the value of n(C∩P∩M) in *
n(M∩C) = 18
n(M∩C) - n(C∩P∩M) = 8
Therefore, eight students study mathematics and chemistry.
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Find the slope and y-intercept of the graph of the linear equation. Write your answers in simplest form.
y=9.5
Slope: ?
y-intercept: ?
Answer:
0, 9.5
Step-by-step explanation:
We can rewrite the equation as [tex]y=0x+9.5[/tex].
Comparing this to slope-intercept form, the slope is 0 and the y-intercept is 9.5.
Write an expression for the area of the following figure.
The expression for the area of the given figure is: 18x
Given, figure:
we are asked to determine the area of the expression of the given figure.
Label the given figure and join the points G and C
Draw the required figure.
Observe that from the figure that, the shape consists of a square ABCG and rectangle FCDE.
Find the area of the given shape.
area of the given shape = ar(ABCG) + ar (FCDE)
= 3 × x × 6
= 18x
Therefore, the expression for the area of the given figure is 18x.
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Explain how you know that <4 and <6 are the same side interior angles
Angles ∠4 and ∠6 are the same side interior angles.
Interior angles are defined as the inner of two angles formed when two sides of a polygon intersect. Any of the four angles are formed when a third line intersects a pair of parallel lines.
If two angles are on opposite sides of a transversal, they are alternate. A transversal is a line that runs parallel to two horizontal lines. The alternate angles are alternate interior angles if they are located between the two parallel lines. The alternate angles are alternate exterior angles if they are located outside of the two parallel lines.
Angles ∠4 and ∠6 are known as alternate interior angles based on the information provided. As a result, you have the following options:
They are located on opposing sides of the transversal.
They are located between the two lines crossed by the transversal.
Therefore Angles ∠4 and ∠6 are the same side interior angles.
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What is the equation of the line that passes through the points (5,3) and
(5,-2)?
Answer:
x = 5
Step-by-step explanation:
I'm going to assume that this is asking you to graph in Slope-Intercept form, but if I am mistaken, comment on my answer and I will happily change it.
Slope-Intercept form:
y = mx + b
You leave y and x as variables, while m and b are to be substituted for slope and y-intercept. y-intercept is when x=0, where a point on a line is on the y axis.
To help you learn, for example, we have an equation is slope-intercept form:
y = 8x + 3
In this case, the slope is 8 and the y intercept is 3 as m is the slope and b is the y-intercept.
The slope is the steepness of the graph. The value of the slope is how much the y-value increases if the x-value increases by 1.
We can find the slope from 2 points using this formula:
[tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
So, we plug in our points into the formula.
[tex]\frac{-2-3}{5-5}[/tex]
Simplify.
[tex]\frac{-5}{0}[/tex]
Anything divided by 0 is undefined. This means the line we are graphing is completely vertical, known as undefined. We can only get this if the x value stays the same no matter what. In this case, the x value stays the same when the y value changes, meaning a undefined slope.
We have a special case here. If the slope is undefined, we do not use y = mx+b. Instead, we use:
x = what the x values of the 2 points are
x values of both points: 5
x = 5
a 2 qaurt bucket of paint costs $20.32. What is the price per cup?
Answer:
$2.54
Step-by-step explanation:
2 qaurt = 8 cups
20.32/8=$2.54 percup
which expression is equivalent to xy ^ 2/9
The expression that is equivalent to xy^2/9 is [tex]x\sqrt[9]{y^{2} }[/tex] , the correct option is (d) .
an Algebraic Expression is defined as an expression that is written using the combination of variables and numbers joined by mathematical operators .
For Example : 2x+ 3y , 3y , 2xy are all algebraic expressions .
In the question ,
it is given that ,
the algebraic expression is xy^2/9 ,
we need to find an equivalent expression to the given expression .
we know that the x^(1/n) is written as [tex]\sqrt[n]{x}[/tex] .
So , xy^2/9 = [tex]x.(y^{2})^{\frac{1}{9} }[/tex] = [tex]x\sqrt[9]{y^{2} }[/tex]
Therefore , The expression that is equivalent to xy^2/9 is [tex]x\sqrt[9]{y^{2} }[/tex] , the correct option is (d) .
The given question is incomplete , the complete question is
Which expression is equivalent to xy^2/9 ?
(a) √(xy⁹)
(b) [tex]\sqrt[9]{xy^{2} }[/tex]
(c) x(√y⁹)
(d) [tex]x\sqrt[9]{y^{2} }[/tex]
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Write an equation in slope-intercept form for the line that passes through (9, 12) and is parallel to y=4
Answer:
y= 12
Step-by-step explanation:
Just change the y-value (b in y=mx+b)
teen obesity: the 2013 national youth risk behavior survey (yrbs) reported that 13.7% of u.s. students in grades 9 through 12 who attend public and private school were obese. after seeing extensive efforts to educate parents and teens on healthy lifestyles, we want to know if the proportion has decreased this year. we select a random sample of 200 u.s. students and find that 11% are obese.after performing the hypothesis test for p
There is a 13.3% chance that a sample of 200 U.S students in grades 9 through 12 who attend public and private school will have 11% or fewer obese students if 13.7% of the population is obese this year.(Option D)
Given:
The 2013 national youth risk behavior survey (yrbs) reported that 13.7% of u.s. students in grades 9 through 12 who attend public and private school were obese.
consider the random sample:
200 US students
11% are obese.
Null hypothesis:
Null hypothesis = 13.7%
= 13.7/100
= 0.137
Alternative hypothesis = p < 0.137.
Therefore the null hypothesis = 0.137.
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If you are given a continuous function that has a domain of [-3, 4] which of the following values are included in the given domain?
A continuous function that has a domain of [-3, 4] will include all the values as -3,-2,-1,-0,-1,-2,3,4
What do you mean by continuous function?
In mathematics, a continuous function is one where a continuous variation of the argument results in a continuous variation of the function's value (i.e., a change without a leap). This indicates that there aren't any discontinuities, or sudden changes in value. More specifically, a function is continuous if it is possible to guarantee that its value will not vary significantly even with arbitrarily tiny changes to its parameter. Any function that is not continuous is said to be discontinuous.
It is given that a continuous function has a domain of [-3,4]
According to the definition of closed interval,
[-3,4] will contain all the elements between them and including them.
Therefore, [-3,4] will contain elements as -3,-2,-1,-0,-1,-2,3,4
Hence, a continuous function that has a domain of [-3, 4] will include all the values as -3,-2,-1,-0,-1,-2,3,4
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Chee buys a two-pint bottle of juice for $3.52. What is the unit rate of the cost of the juice per fluid ounce?
The unit rate of the cost of the fluid per ounce is $0.11
How to calculate the cost of the fluid per ounce ?
Chee buys two pint bottle of juice
The two pints costs $3.52
The unit rate of the cost of the juice per fluid ounce can be calculated as follows
1 pint is equals to 16 fluid ounce
2 pints= 2 × 16
= 32
The cost per fluid ounce is
= 3.52/32
= 0.11
Hence the unit rate of the cost of the juice per fluid ounce is $0.11
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Write a linear equation in slope-intercept form to model the situation.
An Uber driver charges a $10 pick-up fee plus $0.20 per mile.
O C=10+.2m
Om = 2+10C
O C = 2+10m
O C = .25m + 10
Slope intercept form become C = 10 + 0.20m
What do you mean by linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
Both linear equations with one variable and those with two variables exist.
The standard form or the general form of linear equations in one variable is written as, Ax + B = 0; where A and B are real numbers, and x is the single variable.
Slope intercept form is y = mx + c where m is the slope and c is the y-intercept.
It is given that an Uber driver charges a $10 pick-up fee plus $0.20 per mile.
Let m be the total miles.
According to question, the equation become
Total charges, C = 10 + 0.20m
Therefore, slope intercept form become C = 10 + 0.20m
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BRAINLY USERS I NEED HELP
So a freshman in algebra 1 and im on unit 4 i been stuck on this question trying to find out how to solve it for almost over 15 minutes can you please help
Answer:
Step-by-step explanation:
There are 14 red jellybeans and 17 blue jellybeans in a bag. If you randomly select three jellybeans in a
row, without replacement, what is the probability that you get at least one red jellybean?
Out of 32 cards, Mookie guessed the color correctly 18 times. What would this be as a decimal? ((Type in 4 digits after the decimal))
Answer:
0.5625
Step-by-step explanation:
18/32=0.5625
The price received for a bicycle is given by the equation b = 100 – 10x2, where x is the number of bicycles produced, in millions.
It costs the company $60 to make each bicycle.
What is the profit function for the company?
P = –10x2 – 60x + 100
P = –10x3 + 40x
P = – 10x2 + 40
Answer:
B
Step-by-step explanation:
one of your cars is blue. it can travel 31 1/2 miles on 1 1/4 gallons of gas how many miles can it travel on one mile of gas
Answer:
25.2 miles per gallon
Step-by-step explanation:
[tex]\frac{31.5}{1.25}[/tex]
i need this, right now, please, is math
Answer:
The answer is eleven. 11
Identify whether each system of equations has infinitely many solutions or no solution.
The first system of equations has no solution and the second set of equations has a unique solution.
If we are having two equations as
[tex]a_{1} x^{2} +b_{1} x+ c_{1} =0[/tex]
and [tex]a_{2} x^{2} +b_{2} x+ c_{2} =0[/tex]
The condition at which these equations will have infinitely many solutions is
[tex]\frac{a_{1} }{a_{2} } =\frac{b_{1} }{b_{2} } =\frac{c_{1} }{c_{2} }[/tex]
The condition at which these equations will have infinitely many solutions is
[tex]\frac{a_{1} }{a_{2} } =\frac{b_{1} }{b_{2} } \neq \frac{c_{1} }{c_{2} }[/tex]
For, the 26th question, we have
4x +8y = -8
4x +8y +8 = 0
x +2y +2 =0 equation(1)
x =-2y +1
x +2y -1 = 0 equation(2)
On comparing these equations with the general form, we have
[tex]a_{1} = 1, a_{2} =1\\b_{1} = 2, b_{2} = 2\\c_{1} = 2, c_{2} = -1[/tex]
So, [tex]\frac{a_{1} }{a_{2} } =\frac{b_{1} }{b_{2} } \neq \frac{c_{1} }{c_{2} }[/tex]
Thus, this system of equations has no solution.
Now, For the 27th question, we have
2x - 3y = 6
2x -3y -6 = 0 equation(3)
[tex]y = \frac{2}{3}x -2 \\\\3y = 2x -6\\\\3y -2x +6 = 0[/tex] equation (4)
On comparing these equations with the general form, we have
[tex]a_{1} = 2, a_{2} =3\\b_{1} = -3, b_{2} = 2\\c_{1} = -6, c_{2} = 6[/tex]
So, [tex]\frac{a_{1} }{a_{2} } \neq \frac{b_{1} }{b_{2} }[/tex]
Thus, this system of equations has a unique solution.
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Change 08:00 to 12 hour clock time using a.m. and p.m
Answer:
8.00am
Step-by-step explanation:
from 12 at night to 12 noon the time notation for 24 hrs and 12 hrs stay the same
Help me find the I-intercept for the linear function
Answer: (0,9)
Step-by-step explanation:
4-2=2
2-2=0
3+3=6
6+3=9
or just put this into the calculator on the table button
Convert 47 grams to ounces. (1 gram = 0.0352 ounce)
A: 0.0007 ounce
B: 1.6544 ounces
C: 16.544 ounces
D: 1,335.23 ounces
Answer:
1.6544 ounces
Step-by-step explanation:
47x0.0352
1.6544 ounces
Hopes this helps please mark brainliest
solving with master product 3x^2-17x+10=0
explain what the symbols and sd represent.
The symbols d and sd represent:
The differences in the mean of the paired data entries in the dependent samples.
What is the standard deviation?
A measure of a set of values' variance or dispersion is called the standard deviation.
Here,
d: the difference between paired data in the dependent samples.
sd: standard deviation.
The dependent samples' dependent samples' standard deviation for the variance between the means of the paired data items.
Hence, the differences in the mean of the paired data entries in the dependent samples.
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Please help don’t answer if you don’t know:/ PLEASE HELP
Answer:
A See work below
B 7.07
C [tex]\sqrt{50}[/tex]
Step-by-step explanation:
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
[tex]5^{2}[/tex] + [tex]5^{2}[/tex] = [tex]c^{2}[/tex]
25 + 25 = [tex]c^{2}[/tex]
50 = [tex]c^{2}[/tex]
[tex]\sqrt{50}[/tex] = [tex]\sqrt{c^{2} }[/tex]
[tex]\sqrt{50}[/tex] = c This is the exact answer. [tex]\sqrt{50}[/tex] is an irrational number. This means that it never terminates or repeats in the decimal form.
[tex]\sqrt{50}[/tex] ≈ 7.07 Rounded
Answer(s):
[tex]5\sqrt{2}[/tex] and [tex]7.07[/tex]
Step-by-step explanation:
substitute a=5 and b= 5 into Pythagorean Theorem:
[tex]a^2+b^2=c^2\\(5)^{2}+ (5)^{2} = c^2[/tex]
Simplify:
[tex]25+25=c^{2}[/tex]
[tex]50=c^{2}[/tex]
square root of c^2 and 50
[tex]\sqrt{50} =\sqrt{c^2} \\\\\sqrt{50} =c[/tex]
Use prime factorization to reduce [tex]\sqrt{50}[/tex] to [tex]5\sqrt{2}[/tex]
So here are the answers:
Radical form [tex]5\sqrt{2}[/tex]
Rounded to nearest hundredth: [tex]7.07[/tex]
Hope this answer helps :)
Triangle abc ha a perimeter of 22cm
Ab =8cm
Bc=5
I triangle abc a right angle triangle
ΔABC is not a right angled triangle.
What is right angled triangle?
A right-angle triangle is one that has angles between its two sides that equal 90 degrees.
Main Body:
First let's find the length of the last side. We can do this by adding AB and BC together, then subtracting this amount from the perimeter of Triangle ABC, 22 cm.
ABC - (AB + BC) ⇒ 22 - (8 + 5)
=22 - 13 = 9 cm
The hypotenuse is always the longest side of a triangle, so we know that the side we figured out is the hypotenuse. Now we can use the Pythagorean Theorem to see whether the triangle is a right triangle.
Pythagorean Theorem: a² + b² = c², where a and b are legs and c is the hypotenuse.
If a² + b² do equal c², then the triangle is a right triangle.
⇒8² + 5² = 9²
⇒64 + 25 = 81
⇒89 > 81
Therefore triangle is not a right triangle, but we know that it is obtuse since a and b together are longer than c.
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