What is the standard form equation of the line shown below?
Graph of a line going through negative 1, 1 and 1, 4
−3x + 2y = 5
3x − 2y = −5
y − 4 = three halves(x − 1)
y = three halvesx + five halves
Answers
Final answer:
The standard form equation of the line through the points (-1, 1) and (1, 4) is 3x - 2y = -5.
Explanation:
The standard form equation of a line can be represented as Ax + By = C, where A, B, and C are constants. To find the equation of the line through the points (-1, 1) and (1, 4), we can use the point-slope form.
First, find the slope using the formula m = (y2 - y1)/(x2 - x1). In this case, m = (4 - 1)/(1 - (-1)) = 3/2.
Next, choose one of the given points, let's say (-1, 1), and substitute the values into the point-slope formula. y - y1 = m(x - x1). We have y - 1 = (3/2)(x - (-1)).
Simplify the equation by distributing the slope and rearranging the terms. y - 1 = (3/2)x + 3/2.
Finally, convert the equation to standard form by moving all terms to one side and multiplying by a common denominator. 3x - 2y = -5.
Related Questions
Find a possible formula for a fourth degree polynomial g g that has a double zero at 1 1 g(−4)=0 , g(5)=0 , and g(0)=−6
Answers
g(-4) = 0 so x+4 = 0 meaning that (x+4) is a factor
g(5) = 0 so x-5 = 0 meaning that (x-5) is a factor
all together, we have
(x-5)*(x+4)*(x-11)^2
let's expand this out
(x-5)*(x+4)*(x-11)^2
(x^2-x-20)*(x^2-22x+121)
x^2(x^2-22x+121) - x(x^2-22x+121) - 20(x^2-22x+121)
x^4-22x^3+121x^2-x^3+22x^2-121x-20x^2+440x-2420
x^4-23x^3+123x^2+319x-2420
This is multiplied by some constant k such that
k*(x^4-23x^3+123x^2+319x-2420) = -6
where plugging in x = 0 leads to -6
Let's plug in x = 0 and find out what happens with k
k*(x^4-23x^3+123x^2+319x-2420)
k*(0^4-23*0^3+123*0^2+319*0-2420)
k*(-2420)
-2420k
So -2420k = -6 leads to k = 3/1210
Therefore, the equation is [tex]y = \frac{3}{1210}(x^4-23x^3+123x^2+319x-2420)[/tex]
The fourth degree polynomial g(x) with a double zero at x=1, zeros at x=-4 and x=5, and satisfying g(0)=-6 is g(x) = 3/10(x-1)²(x+4)(x-5).
A possible formula for a fourth degree polynomial g(x) with specific characteristics. The polynomial must have a double zero at x=1, zeros at x=-4 and x=5, and must satisfy g(0)=-6.
Since the polynomial has a double zero at x=1, we can represent that part of the polynomial as (x-1)². The other two zeros at x=-4 and x=5 give us factors of (x+4) and (x-5) respectively. Multiplying these factors gives us a polynomial that satisfies the zero requirements: (x-1)²(x+4)(x-5).
Now, we need to find the constant k that will make the polynomial satisfy g(0) = -6. We set up the equation using the known factors:
k(x-1)²(x+4)(x-5) and substitute x with 0 to solve for k. This gives us k(0-1)²(0+4)(0-5) = -6. Solving for k, we find k = 3/10.
Therefore, the formula for the polynomial g(x) is g(x) = 3/10(x-1)²(x+4)(x-5).
Y is the midpoint of segment XZ. The coordinates of X are (2, 4) and of Y are (-1, 1). Find the coordinates of Z. ...?
Answers
z(x2,y2)=(x2,y2)
midpoint (x,y)=(-1,1)
2+x2/2=-1;4+y2/2=1
2+x2=-2;4+y2=2
x2=-4;y2=-2
z(x2,y2)=(-4,-2)
X(2,4); Y(-1,1). Z(a,b). Y is the midpoint of XZ
(2+a)/2=-1
2+a=-2
a=-4
(4+b)/2=1
4+b=2
b=-2
Then Z is (-4,-2)
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Anna wants to take fitness classes. She compares two gyms to determine which would be the best deal for her. Fit Fast charges a set fee per class. Stepping Up charges a monthly fee, plus an additional fee per class. What is the system of equations representing these costs?
Answers
fit fast = fee per class
stepping up = fee per class + monthly fee
now you just change all of that into variables, essentially:
F = cx
S = cx + m
so, fit fast is the cost of classes (c) times the number of classes taken (x). stepping up is the cost of classes times x, PLUS that additional monthly fee (m).
Answer:
its C on ed
Step-by-step explanation:
What is the square root of 69?
Answers
What is "Centroid of a triangle" and why is it important?
Answers
The girls group rented 2 canoes and 3 inner tubes for a total cost of $80. The boys group rented 1 canoe and 7 inner tubes for a total cost of $95. What is the cost to rent 1 canoe?
A. $18
B. $15
C. $25
D. $10
<33 please help
...?
Answers
For the girls,
2c + 3t = 80
For the boys,
c + 7t = 95
Solving the system of equations, multiply the second equation by 2 and subtract them.
2c + 3t = 80
2c + 14t = 190
---------------
11t = 110
t = 10
Substitute t to either equations,
c = 95 - 7t
c = 95 - 7(10)
c = 25
Therefore, one canoe costs $25 (C.)
The cost to rent 1 canoe from the rent made by the group of the girls and boys is $25.
What are word problems?Word problems are a mathematical interpretation by using variables, numbers, and arithmetic operations to solve real-life problems.
From the given information:
The group of girls: 2c + 3t = 80 --- (1)The group of boys: 1c + 7t = 95 ---- (2)Now, we can have a system of equations, and we can solve for the number of canoes and the inner tubes rented.
Using Elimination method:
2c + 3t = 80 --- × (1)
c + 7t = 95 --- × (2)
2c + 3t = 80
-2c + 14t = 190
0 + -11t = -110
-11t = -110
t = -110/-11
t = 10
From equation (1)
2c + 3t = 80
2c + 3(10) = 80
2c + 30 = 80
2c = 80 - 30
2c = 50
c = 50/2
c = 25
Therefore, we can conclude that the cost of the rent of 1 canoe is $25.
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If the discriminant of a quadratic equation is 4, which statement describes the roots?
-2 complex roots
-2 real roots
-1 real root
-1 complex root
PLEASE HELP
Answers
An equation can have 2 real roots if the discriminant is 4.
I hope my answer has come to your help. Have a nice day ahead and may God bless you always!
Answer:
Statement which describes the roots is:
2 real roots
Step-by-step explanation:
If the discriminant D of a quadratic equation follows:
D=0 then there are 2 equal real roots or 1 real root
D>0 then there are 2 unequal real roots
and if D<0 then there are 2 complex roots
Here, we are given the discriminant of a quadratic equation is 4
i.e. D=4 >0
So, it means quadratic equation has 2 real roots
Hence, statement which describes the roots is:
2 real roots
Hence, statement which describes the roots is:
2 real roots
Use the Law of Detachment to draw a logical conclusion from the two given statements. If not possible, choose not possible. If you drive safely, then you can avoid accidents. Teddy drives safely.
Teddy avoids accidents. If Teddy avoids accidents, he must drive safely. (my ans)
If Teddy does not drive safely, he does not avoid accidents.
not possible
Answers
Premise 2: Teddy drives safely
Conclusion: Teddy avoids accidents
Answer:
Teddy avoids accidents.
Step-by-step explanation:
You roll a red die and a green die. What is the size of the sample space of all possible outcomes of rolling these two dice, given that the red die shows an even number?
...?
Answers
Size of sample space = 18.
What does -2 (3-y) equal to?!!
Answers
(10^25)-7 is divisible by
a) 2 b)3 c)9 d) both 2 & 3
Answers
If the last digit of a number is divisible by 2, than the number is divisible by 2 (for example, in 828, the last digit is 8 which is divisible by 2 (8/2 = 4), so 828 is also divisible by 2).
If the sum of all the digits of a number is divisible by 3, then the number is divisible by 3 (for example, in 396, the sum of the digits is 18 (3+9+6=18), so 396 is also divisible by 3).
Similarly, if the sum of all the digits of a number is divisible by 9, then the number is divisible by 9.
Now, let's check it out for 10²⁵ - 7. Let's first take simple examples:
10² - 7 = 100 - 7 = 93 (The last digit is not divisible by 2. Also, the sum of the digits is 9+3=12 and it is divisible only by 3, but not by 9).
10³ - 7 = 1000 - 7 = 993 (The last digit is not divisible by 2. Also, the sum of the digits is 9+9+3=21 and it is divisible only by 3, but not by 9).
10⁴ - 7 = 10000- 7 = 993 (The last digit is not divisible by 2. Also, the sum of the digits is 9+9+9+3=30 and it is divisible only by 3, but not by 9).
....
10²⁵-7 =..... There are many zeros, but based on the previous examples, we can make a conclusion that the last digit is not divisible by 2. Also, the sum of the digitsit is divisible only by 3, but not by 9.
△ABC△ABC is similar to △XYZ△XYZ. Also, side ABside AB measures 6 cm, side BCside BC measures 18 cm, and side XYside XY measures 12 cm.
What is the measure of side YZside YZ ?
Answers
Answer:
36
Step-by-step explanation:
Convert the slope of -0.6 to a fraction in simplest form
Answers
Simple question! Thank you for the help so far! :D
Answers
Answer:
○ [tex]\displaystyle y ≤ -7[/tex]
Step-by-step explanation:
Whenever you divide\multiply by a negative, you reverse the inequality symbol.
I am joyous to assist you anytime.
Electronics Warehouse is having a blowout sale. A television that normally sells for $275 is on sale for 30% off. How much is the discount?
Answers
Step-by-step explanation:
Triangle XYZ is isosceles. The measure of the vertex angle, Y, is twice the measure of a base angle. What is true about triangle XYZ? Check all that apply?
Answers
Answer:
The answers are,
The measure of angle Z is 45°.
The perpendicular bisector of Line segment X Z creates two smaller isosceles triangles.
Angle Y is a right angle.
Step-by-step explanation:
I got it right on geometry test.
Santa has lots of mixed up socks in his sack! If he has 6 green socks, 4 gold socks, 8 black socks and 2 red socks, what is the minimum he needs to pull out of his sack to get a matching pair?
Answers
Jeffrey is planning to tile his bathroom. He is taking measurements before he goes to the hardware store to buy the tile. What is the best unit of measure for Jeffrey to use?
A.cubic feet
B.yards
C.square feet
D.square yards
Answers
Answer:
(C) Square feet
Step-by-step explanation:
In order to take the measurements, he should use the square feet unit of measure.
As, the cubic feet also known as unit of volume can be defined as the volume of the cube with sides of one foot in length. Since, the bathroom is two dimensional therefore, cubic feet can't be used.
Yards are basically a unit of length use to measure length and perimeter and square yards are used in measuring the long space and the bathroom is bit too small for it.
Therefore, square feet should be used to measure.
how does sin(-13pi/4) = -5pi/4
we were asked to find the exact value of sin(-13pi/4)
how does sin(-13pi/4) = -5pi/4
we were asked to find the exact value of sin(-13pi/4)
Answers
13π / 4 needs to be 'reduced' so that we find out where on the Unit Circle you are.
To do this, subtract out 8π / 4 (2π, or a whole Unit Circle) until you can't do it anymore without getting a negative number.
Subtracting out 8π/4 gives you 5π/4.
Sin 5π/4 = -√2 / 2
The reason I chose 8π/4 was because your fraction had 4 in the denominator. If it had, say, 12 in the denominator, the subtraction would have been 24π/12 (still giving 2π, or a whole Unit Circle). Make sense?
The equation sin(-13π/4) = -5π/4 is incorrect.
The correct value for sin(-13π/4) is actually 1/√2 or √2/2, not -5π/4.
Here, we have,
To understand why, let's break down the calculation step by step:
The sine function represents the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle.
In this case, we have an angle of -13π/4.
To find the reference angle,
we can add 2π to -13π/4 to bring it into the standard range of angles:
-13π/4 + 2π = -5π/4
Now, we can find the reference angle of -5π/4 in the unit circle or trigonometric table.
The reference angle of -5π/4 is π/4.
Since sine is positive in the second quadrant,
the value of sin(-5π/4) is the same as sin(π/4), which is 1/√2 or √2/2.
Therefore, the correct exact value of sin(-13π/4) is 1/√2 or √2/2, and not -5π/4.
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The area of a rectangle is 70 square inches and the length of the rectangle is 3 inches longer than the width.
The area of a rectangle is found by multiplying the length times the width.
Which equation models this situation?
3w = 70
w(w+3)=70w(w+3)=70
w + 3 = 70
w + 3w = 70
Answers
If ∠BAC = 17° and ∠CED = 17° are the two triangles, ΔBAC and ΔCED similar? If so, by what criterion?
A) yes, by AA similarity criterion
B) yes, by SAS similarity criterion
C) yes, by SSA similarity criterion
D) no, not possible to tell.
Answers
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Answer:
Option A is correct.
Yes, by AA similarity criterion
Step-by-step explanation:
AA(Angle-Angle) Similarity Criterion states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
In ΔBAC and ΔCED
[tex]\angle BAC = \angle CED = 17^{\circ}[/tex] [Angle] [Given]
[tex]\angle C = \angle C[/tex] [Angle] [Common angle]
Therefore, by AA similarity criterion;
[tex]\triangle BAC \sim \triangle CED[/tex]
Therefore, ΔBAC and ΔCED are similar by AA similarity criterion.
8 is 40% of what number
Answers
divide 8 by .40
n = 20
or x = 8/40%
x = 20
Find the polar coordinates of the point that has rectangular coordinates (-3,3*sqrt of 3) write your answer using degrees. THANK YOU:)
Answers
y = 3*sqrt(3)
r = sqrt(x^2 + y^2)
r = sqrt((-3)^2 + (3*sqrt(3))^2)
r = sqrt(9+27)
r = sqrt(36)
r = 6
theta = arctan(y/x)
theta = arctan(3sqrt(3)/(-3))
theta = arctan(-sqrt(3))
theta = -60 degrees which is coterminal to 300 degrees
So the polar form is (r,theta) = (6, 300)
The math test has 10 multiple choice questions, each with 4 answers. If Betty guesses correctly on the first 2 questions, what is the probability that she will guess correctly on the third question?
Answers
Answer: The probability that she will guess correctly on the third question [tex]=\frac{1}{4}[/tex]
Step-by-step explanation:
Given: The math test has 10 multiple choice questions, each with 4 answers.
To find probability that she will guess correctly on the third question, we need to just look at only one question which has 4 options and one of them is the right answer, thus probability of choosing the right answer from 4 option is the fraction of 1 over 4.
The probability that she will guess correctly on the third question
[tex]=\frac{\text{answer of a question}}{\text{total options of a question}}[/tex]
[tex]=\frac{1}{4}[/tex]
Is 53 prime or composite
Answers
Answer:
it is prime
Step-by-step explanation:
Remember:
Prime numbers have 2 factors:
1
Itself
to which subset of the real numbers does the number 1.68 belong?
a. rational numbers
b. natural numbers, whole numbers, integers, rational numbers
c. rational numbers, irrational numbers
d. none of the above ...?
Answers
The number "1.68" is: natural numbers, whole numbers, integers, rational numbers.
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
Answer:
a.rational number
Step-by-step explanation:
We are given that a real number 1.68
We have to find that given number belongs to which set
We know that
N={1,2,3...}
Whole numbers set ={0,1,2...}
Integers=Z={...-3,-2,-1,0,1,2,,,}
Rational number :That number which can be written in the form of [tex]\frac{p}{q}[/tex] where q is not equal to zero ,p and q are belongs to integers.
Irrational number: That number which is not rational is called irrational number.
Hence, given number 1.68 belongs to rational numbers set.
Answer : a.rational number
can someone plz help me ?
Answers
BU ARADA GERÇEK HESP
HAZYAR2992
Which expression completes the equation? 24 divided by 6 + 20=
Answers
The expression that completes the equation is 3(7+1).
To complete the equation "24 divided by 6 + 20,"
we need to perform the division first, and then add 20 to the result.
6 | 24 | 4
24
_____
0
Here, Divisor= 6, Remainder= 0 and Quotient= 4
So, 4 + 20 = 24
Then, the equivalent value is
3 (7+1)
= 3 x 8
= 24
Therefore, the expression that completes the equation is 3(7+1).
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The question attached here is incomplete, the complete Question is
Choose the expression that completes the equation.
24 ÷ 6 + 20 =______
2(7 + 10)
4(4 + 3)
3(7 + 1)
3(7 + 7)
As Claudia walks away from a 264-cm lamppost, the tip of her shadow moves twice as fast as she does. What is Claudia’s height?
Answers
As Claudia walks away from a 264-cm lamppost, the tip of her shadow moves twice as fast as she does, so the Claudia’s height is 132 cm.
To solve this problem, we can use the concept of similar triangles.
Let's assume Claudia's height is h cm.
Since Claudia's shadow tip moves twice as fast as she does, her shadow's length must be twice her height, or 2h cm.
According to the question, as Claudia walks away from the lamppost, her shadow moves twice as fast as she does.
This means the ratio of the length of the shadow to the distance Claudia walks is the same as the ratio of the distance the shadow moves to the distance Claudia walks.
We can set up the following proportion:
(2h) / 264 = h / x
where x is the distance Claudia walks from the lamppost.
Solve for h by cross multiplying:
2h * x = 264 * h
2hx = 264h
Divide both sides by h:
2x = 264
Divide both sides by 2:
x = 132 cm
Therefore, Claudia's height is h = 132 cm.
By using the principles of similar triangles and the given information that Claudia's shadow moves at double her pace, we establish a proportion between the heights and shadow lengths, solve the equation, and find that Claudia's height is 176 cm.
Explanation:To solve the problem of finding Claudia's height based on the information given about her shadow, we need to apply the principles of similar triangles. The situation describes a real-world application of similar triangles, where Claudia and her shadow form one triangle, and the lamppost and its shadow form another. These triangles are similar because the angles are the same: the angle of elevation to the sun is the same for both Claudia and the lamppost, and the ground provides the same angle for both bases.
Let's denote Claudia's height as h, the distance Claudia walks away from the lamppost as x, and therefore the length of her shadow will be 2x (since it moves twice as fast). The similar triangles give us the following proportion:
Height of Lamppost / Height of Claudia = Length of Lamppost's Shadow / Length of Claudia's Shadow
264 cm / h = (x + 2x) / 2x
This simplifies to:
264 / h = 3 / 2
Solving for h, we get:
2 * 264 = 3h
h = 2 * 264 / 3
h = 528 / 3
h = 176 cm
Therefore, Claudia's height is 176 cm.
A car travels 180 miles north in 3 hours. What is the average velocity? Show your work and include units. Average velocity = distance/time. Know this equation for the test and how to calculate average velocity.
Answers
I hope I helped! :D
The change in position or displacement of an object in the time interval is known as average velocity of the object. The value of the average velocity is 60 miles per hour.
Given-
A car travels 180 miles north in 3 hours.
Average velocity- The change in position or displacement of an object in the time interval is known as average velocity of the object. It can be positive or negative depending upon the sign of the displacement.
[tex]\overline v=\dfrac{\Delta v}{\Delta t}[/tex]
Here [tex]\Delta v[/tex] is the change in displacement and [tex]\Delta t[/tex] is the change in time.
Use this formula to find the average velocity in the given formula we have to put the values velocity and time given in the question. Therefore,
[tex]\overline v=\dfrac{180}{3}[/tex]
[tex]\overline v=60[/tex]
Hence, the value of the average velocity is 60 miles per hour.
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