Answer:
In 6 different ways can the three students form a set of class officers.
Step-by-step explanation:
There are 3 people Leila, Larry, and Cindy and 3 positions president, vice-president, and secretary.
We need to find In how many different ways can the three students form a set of class officers.
This problem can be solved using Permutation.
nPr = n!/(n-r)! is the formula.
Here n = 3 and r =3
So, 3P3 = 3!/(3-3)!
3P3 = 3!/1
3P3 = 3*2*1/1
3P3 = 6
So, in 6 different ways can the three students form a set of class officers.
Segment XY is dilated through point M with a scale factor of 2. Which segment shows the correct result of the dilation?
1. AE
2. BF
3. CG
4. DH
Answer:
4.DH
Step-by-step explanation:
let's assume the point P to be the point that X will be after it is dilated.
we know that after dilation the length of PM should be two two times the length of XY
PM = 2.XY ===>[tex]\frac{PM}{XY}[/tex] = 2
and from proportionality theorem we now that:
[tex]\frac{PM}{XY}[/tex] = [tex]\frac{MX}{MP}[/tex] = 2
So we know XY should be half the size of MP and we can see the only line matching is DH thus the answer is DH
using the discriminant, how many solutions and what type of solution(s) does k^2-10k+25=0 have?
a. 2; irrational
b. 2; rational
c. 1; rational
d. no real solutions
Answer:
c. 1; rational
Step-by-step explanation:
k² − 10k + 25 = 0
The discriminant of ax² + bx + c is b² − 4ac.
If the discriminant is negative, there are no real roots.
If the discriminant is zero, there is 1 real root.
If the discriminant is positive, there are 2 real roots.
If the discriminant is a perfect square, the root(s) are rational.
If the discriminant isn't a perfect square, the root(s) are irrational.
Finding the discriminant:
a = 1, b = -10, c = 25
(-10)² − 4(1)(25) = 0
The discriminant is zero, so there is 1 rational root.
Which of the following is rational?
3•π
2/3 +9.26
45 + 36
14.3+5.78765239
Let's consider each of the options and evaluate whether the given number is rational or not. Remember, a rational number is any number that can be expressed as the quotient or fraction of two integers (where the denominator is not zero).
1. **3•π**: This number is not rational because π (pi) is an irrational number. An irrational number is a number that cannot be expressed as a simple fraction - its decimal goes on forever without repeating. When you multiply an irrational number by an integer (in this case 3), the result is still irrational.
2. **2/3 + 9.26**: To determine if this sum is rational, we can evaluate each addend. The fraction 2/3 is clearly rational, as it is already expressed as a quotient of two integers. The decimal 9.26 can be expressed as a fraction because it is a terminating decimal; in fraction form, it is \( \frac{926}{100} \) which simplifies to \( \frac{463}{50} \) when reduced to lowest terms. The sum of two rational numbers is also rational (since both can be written as fractions, and the sum of two fractions is a fraction), so this number is indeed rational.
3. **45 + 36**: Both 45 and 36 are integers and the sum of two integers is also an integer. Integers are a subset of rational numbers, because they can be expressed as a fraction with a denominator of 1 (e.g., \( \frac{45}{1} + \frac{36}{1} \)). Thus, this number is rational.
4. **14.3 + 5.78765239**: The number 14.3 is a terminating decimal and can be represented as a fraction (\( \frac{143}{10} \)). However, 5.78765239 is given without any indication that it is a repeating or terminating decimal. If it is a non-repeating and non-terminating decimal, then it cannot be expressed as a fraction and would be considered irrational. Without further information, we cannot determine if this number is rational or not. Therefore, we can neither confirm nor deny that the sum is rational.
Given these considerations, the rational option from the given choices is **45 + 36**.
A certain ferry moves up and down a river between Town A and B. It takes the ferry two hours to travel to Town A and only an hour and thirty minutes to return to Town B. If the current is 5mph how far apart are the two cities?
Answer:
the Answer is 60 miles.
Step-by-step explanation:
The current of the river is towards city B; hence, the reason the ferry moves faster from town A to B than when coming back from town B to A. The distance between both towns is 60m.
Let
[tex]s \to[/tex] speed in still water
[tex]d \to[/tex] distance between both cities
The given parameters are:
[tex]t_{AB} =2[/tex] -- from A to B
[tex]t_{BA} =1.5[/tex] -- from B to A
[tex]s_c = 5mph[/tex] -- speed of the current
Speed is calculated as:
[tex]Speed = \frac{Distance}{Time}[/tex]
The speed (s) from town A to town B is:
[tex]s = s_c + \frac{d}{t_{AB}}[/tex] --- i.e. speed of the current + speed in still water from A to B
[tex]s = 5 + \frac{d}{2}[/tex]
Multiply through by 2
[tex]2s = 10 + d[/tex]
Make d the subject
[tex]d = 2s - 10[/tex]
The speed (s) from town B to town Ais:
[tex]s = -s_c + \frac{d}{t_{BA}}[/tex] --- i.e speed in still water from B to A - . speed of the current
[tex]s = -5 + \frac{d}{1.5}[/tex]
Multiply through by 1.5
[tex]1.5s = -7.5 + d[/tex]
Make d the subject
[tex]d = 1.5s + 7.5[/tex]
So, we have:
[tex]d = 1.5s + 7.5[/tex] and [tex]d = 2s - 10[/tex]
Equate both values of d
[tex]2s - 10 = 1.5s + 7.5[/tex]
Collect like terms
[tex]2s - 1.5s= 10 + 7.5[/tex]
[tex]0.5s= 17.5[/tex]
Divide both sides by 0.5
[tex]s = 35[/tex]
Substitute [tex]s = 35[/tex] in [tex]d = 1.5s + 7.5[/tex] to calculate distance (d)
[tex]d =1.5 *35 + 7.5[/tex]
[tex]d =52.5 + 7.5[/tex]
[tex]d =60[/tex]
The distance between town A and B is 60m.
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which of these quadrilateral types must have congruent diagonals. a. rectangle, square, rhombus b.square, rhombus c.rectangle, square d.parallelogram, rectangle, square, rhombus
Rectangles and squares always have congruent diagonals due to their geometrical properties, making option c (rectangle, square) the correct answer.
The question asks which of the given sets of quadrilaterals must have congruent diagonals. The key to answering this question is understanding the properties of each kind of quadrilateral mentioned. Rectangles and squares always have congruent diagonals because their diagonals bisect each other and are of equal length due to the right angles at the corners of the shapes.
A rhombus, while having diagonals that bisect each other at right angles, does not necessarily have congruent diagonals because the angles between adjacent sides do not guarantee equal lengths of diagonals. As such, the correct answer is c.rectangle, square, where both of these shapes must have diagonals of equal length due to their geometrical properties.
*****WILL GIVE BRAINLEST IF CORRECT******
Conner's work is correct. To combine and make it simple, you Multiply:
(3^5+9)+(6^8+10) which will equal 3^14 6^18.
But Jane's work, instead of adding, Jane multiplies. So, Conner is correct.
Hope that helped!
How would you explain this ?
Answer:
Step-by-step explanation:
The first thing you have to do is look at the mother curve. That curve is y = 1/x
It becomes undefined at x = 0 (I will show both curves below).
That is not what has been given. The graph you have been given becomes undefined at x = - 1 , so the equation of the curve (so far) y = 1/(x + 1)
Now we have to worry about the y intercept. When x = 0, y = 4. That can be accomplished in two ways
A. y = 4/(x + 1) or
B. y = 2/(x + 1) + 2 or
C. y = 1/(x + 1) + 3
All three of these will give a value of y = 4 when x = 0. But you have 1 problem left. What happens as x goes to say 5.
The value of A will give y = 4/(5 + 1)=4/6 = 2/3. Which does not work.
The value of C will give y = 1/(5 + 1) + 3 which gives 3 1/5 which also does not work.
Only B works. y = 2/(5+1) + 2 = 2/6 + 2 = 2 1/3 which is a little above the horizontal asymptote.
Red: y = 1/x
Blue: y = 2/(x + 1) + 2
The value at the end is never going to change. y will always be just a bit
If the length width and height of a cube all quadruple what happened to the volume of the cube
Answer:
if the length, width and height of a cube quadruple, then the volume of the cube will be multiplied by 64.
Step-by-step explanation:
Given a cube of width W, height H and length L, the volume of the cube will be: Volume = W*H*L
If all the three parameters quadruple, then:
New Width = 4W
New Height = 4H
New Length = 4L
New Volume = 4W*4H*4L = 64WHL
Therefore, if the length, width and height of a cube quadruple, then the volume of the cube will be multiplied by 64.
Answer:
Volume will be multiplied by 64.
Step-by-step explanation:
We are to find the effect of quadrupling the length, width and height of a cube on its volume.
Since the length, width and height of a cube are all of the same dimension, let us represent it was a variable [tex] S [/tex].
[tex] V o l u m e = S ^ 3 [/tex]
[tex]New Volume = (4S)^3 =64S^3[/tex]
Therefore, if the length width and height of a cube all are quadrupled, the volume will be 64 times.
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In this unit you have learned about several different ways to solve quadratic equations. How do you determine which method to use when you’re trying to solve a quadratic equation?
Answer:
You will use this formula x= -b +
[tex] x = - b + \sqrt{ { \: - 4ac}^{?} } [/tex]
Step-by-step explanation:
4n
[tex] {?}^{?} [/tex]
so you want to do n to the second power minus and minus 39 equals 0 so you using the quadratic formula
Which of the following disjunctions is false?
2 · 3 = 6 or 4 + 5 = 10
5 - 3 = 2 or 3 · 4 = 12
3 + 4 = 9 or 5 · 2 = 11
6 · 2 = 11 or 3 + 5 = 8
Answer:
Option C 3 + 4 = 9 or 5 · 2 = 11 is correct answer
Step-by-step explanation:
Disjunction states that if we have p or q then the disjunction is true if either p is true or q is true or p and q are true.
The disjunction is false when both p and q both are false.
1. 2 · 3 = 6 or 4 + 5 = 10
Disjunction is true because 2.3 =6 is true while 4+5=10 is false
2. 5 - 3 = 2 or 3 · 4 = 12
Disjunction is true because 5-3 =2 is true and 3.4=12 is also true.
3. 3 + 4 = 9 or 5 · 2 = 11
Disjunction is false because 3+4 =7 and not 9 and 5.2 =10 and not 11. Since both are false so, this disjunction is false.
4. 6 · 2 = 11 or 3 + 5 = 8
Disjunction is true because 6.2=12 and not 11 is false but 3+5 = 8 is true.
So, Option C 3 + 4 = 9 or 5 · 2 = 11 is correct answer.
f(x)=3.7-2x
g(x) = 0.25x-5
What is f(x) + g(x)
A) h(x)=3.95x-7
B) h(x)=8.7-2.25x
C) h(x)=-1.3-1.75x
D) h(x)=3.95-7x
Answer:
C) h(x)=-1.3-1.75x
Step-by-step explanation:
f(x)=3.7-2x
g(x) = 0.25x-5
f(x) + g(x) =3.7-2x + 0.25x-5
Combine like terms
= -1.75x - 1.3
Answer:
The answer is C.) h(x)=-1.3-1.75x
Step-by-step explanation:
two less than a number divided by four
Answer:
=x/4 - 2 (the third choice.
Step-by-step explanation:
Letting the number be x, the phrase two less than a number divided by four is expressed using the following steps:
We first take the the number x then divide by four then subtract 2.
The expression becomes:
(x/4) - 2
To solve an algebraic expression such as the one you described – "two less than a number divided by four" – you can follow these steps:
1. Start by identifying the variable, which is typically represented by "x." In this case, "a number" will be our variable "x."
2. The phrase "two less than" indicates a subtraction of two from a certain value. In algebraic terms, "two less than x" would be written as "x - 2."
3. Finally, the phrase "divided by four" tells us to take our result from step 2 and divide it by 4. So, we place the expression "(x - 2)" over 4, indicating division.
Putting it all together, the algebraic expression that represents the phrase "two less than a number divided by four" is:
(x - 2) / 4
To evaluate this expression for a particular value of x, you would substitute the value of x into the expression and then perform the calculation.
For example, if x is 10, you would evaluate the expression as:
(10 - 2) / 4
= 8 / 4
= 2
So, when x is 10, the value of the expression "two less than a number divided by four" is 2.
Cathy uses 3/4 teaspoon of vanilla in a batch of cookies. How many teaspoons are needed for 8 batches of cookies
please help meeeeeeeee!
The velocity v at time t of an object travelling in a straight line is given by v = t - 3. Determine the distance it travels from t = 0 and t = 4.
Answer:
5
Step-by-step explanation:
To solve with calculus, distance is the integral of speed:
d = ∫ |v| dt
d = ∫₀⁴ |t − 3| dt
d = -∫₀³ (t − 3) dt + ∫₃⁴ (t − 3) dt
d = ∫₀³ (3 − t) dt + ∫₃⁴ (t − 3) dt
d = (3t − ½ t²) |₀³ + (½ t² − 3t) |₃⁴
d = [ (9 − 9/2 ) − (0 − 0) ] + [ (8 − 12) − (9/2 − 9) ]
d = 9/2 + 1/2
d = 5
You can also find this geometrically. Graph y = |x − 3|, then find the area under the curve. You will find it's the area of two triangles.
d = ½ (3)(3) + ½ (1)(1)
d = 5
It's important to note that distance is not the same thing as displacement. Displacement is the difference between where you start and where you stop. Distance is length of the path you take.
Evaluate 2g – 4, if the value of g = 5.
Answer:
6
Step-by-step explanation:
imputing 5 into g which makes the equation: 2(5) - 4
2(5) - 4
10 - 4
6
Answer:
6
Step-by-step explanation:
2(5)-4
2*5 is 10
10 subtracted by 4 is 6
Hope this helps ^-^
Complete the solution of the equation. Find
the value of y when x equals -2.
-9x - 3y = 6
Answer:
y=4
Step-by-step explanation:
-9x - 3y = 6
Let x =-2
-9(-2) -3y =6
18 -3y =6
Subtract 18 from each side
18-18-3y = 6-18
-3y = -12
Divide each side by -3
-3y/-3 =-12/-3
y=4
simplify the following fraction (5/9x3/5)+6/7
Answer:
1 4/21
Step-by-step explanation:
(5/9*3/5)+6/7
The 5's cancel
(3/9)+6/7
Cancel a 3 in the numerator and a 3 in the denominator
1/3 + 6/7
We need to get a common denominator of 21
1/3 *7/7 + 6/7 *3/3
7/21 + 18/21
25/21
This is an improper fraction
21 goes into 25 1 time with 4 left over
1 4/21
Answer: [tex]\frac{25}{21}[/tex]
Step-by-step explanation:
The first step is to make the multiplication of the fractions inside the parentheses. To do this, you must multiply the numerator of the first fraction by de numerator of the second fraction and the denominator of the first fraction by the denominator of the second fraction:
[tex](\frac{5}{9}*\frac{3}{5})+\frac{6}{7}=\frac{15}{45}+\frac{6}{7}[/tex]
Now you can reduce the fraction [tex]\frac{15}{45}[/tex]:
[tex]=\frac{1}{3}+\frac{6}{7}[/tex]
And make the corresponding addition: in this case the Least Common Denominator (LCD) will be the multiplication of the denominators. Divide each denominator by the LCD and multiply this quotient by the corresponding numerator and then add the products. Therefore you get:
[tex]=\frac{7+18}{21}=\frac{25}{21}[/tex]
I need help on number 2 please, would really appreciate the help!
Answer:
1st piece = 15 inch
2nd piece = 15 inch
3rd piece = 30 inch
Step-by-step explanation:
2.
Let length of first piece be x
since 2nd piece is same, so 2nd piece's length is also x
third piece is TWICE, so its length is 2x
Total length of all the 3 pieces is 60, so we setup an equation and solve for x:
x + x + 2x = 60
4x = 60
x = 60/4 = 15
Hence, first piece is 15, second piece is 15, third piece is 2(15) = 30
Which sequence is modeled by the graph below?
coordinate plane showing the points 1, 6; 2, 0.6; and 3, 0.06
Answer:
[tex]\large\boxed{a_n=6\left(\dfrac{1}{10}\right)^{n-1}}[/tex]
Step-by-step explanation:
Check:
[tex]n=1\\\\a_1=6\left(\dfrac{1}{10}\right)^{1-1}=6\left(\dfrac{1}{10}\right)^0=6(1)=6\qquad\bold{CORRECT}\ (1,\ 6)\\\\n=2\\\\a_2=6\left(\dfrac{1}{10}\right)^{2-1}=6\left(\dfrac{1}{10}\right)^1=6\left(\dfrac{1}{10}\right)=\dfrac{6}{10}=0.6\qquad\bold{CORRECT}\ (2,\ 0.6)\\\\n=3\\\\a_3=6\left(\dfrac{1}{10}\right)^{3-1}=6\left(\dfrac{1}{10}\right)^2=6\left(\dfrac{1}{100}\right)=\dfrac{6}{100}=0.06\qquad\bold{CORRECT}\ (3,\ 0.06)[/tex]
Answer:
[tex]a_n=6\left(\frac{1}{10}\right)^{n-1}[/tex]
Option 3 is correct
Step-by-step explanation:
The coordinates are (1,6) (2,0.6) and (3,0.06)
If we make table of given coordinate:
x : 1 2 3
y : 6 0.6 0.06
[tex]a_1=6,a_2=0.6,a_3=0.06[/tex]
Ratio of the sequence:
[tex]r=\dfrac{a_2}{a_1}=\dfrac{0.6}{6}=0.1[/tex]
Formula of geometric sequence:
[tex]a_n=ar^{n-1}[/tex]
[tex]a_n=6\cdot 0.1^{n-1}[/tex]
[tex]a_n=6\left(\frac{1}{10}\right)^{n-1}[/tex]
Hence, The sequence model by [tex]a_n=6\left(\frac{1}{10}\right)^{n-1}[/tex]
what is the value of y
Answer:
A
Step-by-step explanation:
since you know the measure of the angle that isn't a is 50, because 180 - 130 = 50, and since the sum of all the angles in the triangle has to be 180, y = 130/2 which equals 65
Given the following coordinates complete the reflection transformation. A(1,−5) B(2,−2) C(5,−2) Transformation: Complete the double reflection over the lines y=−1 followed by y=1. A"( , ) B"( , ) C"( , )
Answer:
A''(1,-1) B''(2,2) C''(5,2)
Step-by-step explanation:
Points A(1,−5) B(2,−2) C(5,−2)
reflection over y=-1
Perpendicular distance between points y-coordinates of points (A, B and C) and y=-1 are 4,1 and 1
after reflections, the perpendicular distance will be 8,2,2 and the points will be at
A'(1,3) B'(2,0) C'(5,0)
again reflection over y=1
Perpendicular distance between points y-coordinates of points (A', B' and C') and y=1 are 2,1 and 1
after reflections, the perpendicular distance will be 4,2,2 and the points will be at
A''(1,-1) B''(2,2) C''(5,2)!
Diem is using a cylinder shape container to hold 42 in³ of liquid. The height of the container is 3 inches tall.
What is the best approximation for the radius of the container?
1.1 in.
2.1 in.
3.5 in.
4.5 in.
Answer:
The correct answer option is B. 2.1 inches.
Step-by-step explanation:
We are given that the cylinder is to hold 42 in³ of liquid while the height of this container is 3 inches tall.
We are to find the best approximation for the radius of this container.
We know that the formula for the volume of a cylinder is given by:
Volume of cylinder = [tex]\pi r^2h[/tex]
Substituting the given values in the above formula to get:
[tex]42=\pi \times r^2 \times 3[/tex]
[tex]r^2 = \frac{42}{\pi \times 3 }[/tex]
[tex]\sqrt{r^2} = \sqrt{4.46}[/tex]
r = 2.1 inches
106 + (147x + 92)= what
Given
106 + (147x + 92)
Combine like terms
106 + 92 = 198
Simplify
147x + 198
Answer
147x + 198
106 + (147x + 92) = what
To solve this expression, you need to apply the distributive property, which states that a(b + c) = ab + ac.
Therefore, 106 + (147x + 92) = 106 + 147x + 92, which simplifies to 239 + 147x.
How many months are in ¾ of a year
Answer:
9
Step-by-step explanation:
Answer:
9 months
Step-by-step explanation:
There are 12 months in a year
Multiply 12 months by 3/4
12 *3/4
36/4
9
There are 9 months in 3/4 of a year
What is the value of x?
A. 155°
B. 60°
C. 35
D. 25°
Answer: C
Step-by-step explanation:
First, you should see that the bottom right corner is an angle on the other side. So subtract 180 from 95 to get 85. Since all angles in a triangle add up to 180, You do 85 + 60 + x = 180. You simplify further to get 145 + x = 180.
Subtracting 145 from both sides leaves you with x = 35, which gives you C.
So C is the correct answer.
Find the least positive angle measurement that is coterminal with –100°.
Answer:
260 degrees is coterminal with -100 degrees.
Step-by-step explanation:
So a full rotation about a circle is 360 degrees.
So if we do 360+(-100) we get 260.
They will share the same terminal ray because if we go 100 clockwise from the initial ray that will be an angle coming counterclockwise 260 from the initial ray.
100+260=360.
Answer:
260°
Step-by-step explanation:
Co terminal angles are angle ± 360°n where n = 0, 1, 2, 3, ....
The least positive = - 100° + 360° = 260°
For triangle ABC, which one is equivalent to sin(A)?
cos(B)
sin(B)
cos(C)
tan(C)
Answer: cos(C)
Step-by-step explanation: Use SohCahToa. Sin(A) is opposite over hypotenuse. The opposite is line BC. Use angle C. To get line BC, you will need the adjacent, and also the hypotenuse. Cos will get you this. Therefore, your answer is Cos(C).
The one which is equivalent to [tex]sin(A)[/tex] will be [tex]Cos(C)[/tex] .
What are trigonometric ratios ?Trigonometric ratios are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
There are six trigonometric ratios [tex]Sin\theta,Cos\theta,Tan\theta,Cot\theta,Sec\theta,Cosec\theta[/tex] .
We have,
[tex]\triangle ABC[/tex] Right angled at [tex]B[/tex] .
So,
[tex]sin(A)=\frac{Perpendicular}{Height}[/tex]
So, in [tex]\triangle ABC[/tex] ,
[tex]sin(A)=\frac{BC}{AC}[/tex]
Now,
To find its equivalent we will look from angle [tex]C[/tex] ,
So, in options we two trigonometric ratios from angle [tex]C[/tex],
So, take [tex]Cos(C)[/tex] ,
[tex]Cos(C)=\frac{Base}{Hypotenuse}[/tex]
[tex]Cos(C)=\frac{BC}{AC}[/tex]
i.e. Equivalent to [tex]sin(A)[/tex] is [tex]Cos(C)[/tex]
Hence, we can say that the one which is equivalent to [tex]sin(A)[/tex] will be [tex]Cos(C)[/tex] which is in option [tex](c)[/tex] .
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A patient received 84 mL per hour of normal saline solution. How many liters did the patient receive in 24-hour period?
Answer:
2.106 liters
Step-by-step explanation:
24 * 84 mL = 2016 mL = 2.106 L
Answer: 84*24=2016
You multiply 84 by 24 to get 2016.
Two taps A and B can fill a cistern in 20 and 30 minif both are opend simultaneously how long will it take to fill the cistern
Answer:
it would take roughly 6 and a half minutes i think
Which can be the first step in finding the equation of the line that passes through the points 5,-4 and -1,8 in slope-intercept form?
The first step in finding the equation of the line would be to find the slope of the points.
The slope-intercept form of a line is given by:
[tex]\[ y = mx + b \][/tex]
where:
- [tex]\( m \)[/tex] is the slope of the line, and
- [tex]\( b \)[/tex] is the y-intercept.
To find the equation of the line that passes through the points (5, -4) and (-1, 8) in slope-intercept form, you need to follow these steps:
1. Find the slope [tex](\( m \))[/tex]:
The slope [tex](\( m \))[/tex] is given by the formula:
[tex]\[ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} \][/tex]
Pick two points, let's say (x1, y1) = (5, -4) and (x2, y2) = (-1, 8), and substitute them into the formula to find [tex]\( m \)[/tex].
[tex]\[ m = \frac{{8 - (-4)}}{{-1 - 5}} \][/tex]
Simplify the expression to find [tex]\( m \)[/tex].
2. Use the slope and one of the points to find the y-intercept [tex](\( b \))[/tex]:
Substitute the slope [tex](\( m \))[/tex] and one of the points (let's use (5, -4)) into the slope-intercept form equation and solve for [tex]\( b \)[/tex].
[tex]\[ -4 = m \cdot 5 + b \][/tex]
Substitute the value of [tex]\( m \)[/tex] that you found in step 1 and solve for [tex]\( b \)[/tex].
3. Write the equation in slope-intercept form:
Once you have the values of [tex]\( m \) and \( b \)[/tex], substitute them into the slope-intercept form equation.
[tex]\[ y = mx + b \][/tex]
Write the final equation.
By following these steps, you can find the equation of the line passing through the given points in slope-intercept form.
To find the equation of the line passing through (5,-4) and (-1,8), calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1), which results in a slope of -2.
Explanation:The first step in finding the equation of the line that passes through the points (5,-4) and (-1,8) in slope-intercept form is to calculate the slope (m) of the line. The slope of a line is determined by the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. In this case, we would use the following calculation:
Let Point 1 be (5, -4) and Point 2 be (-1, 8).The slope m = (8 - (-4)) / (-1 - 5)m = (8 + 4) / (-1 - 5)m = 12 / -6m = -2
With the slope, you can then use the point-slope form or directly the slope-intercept form (y = mx + b) to find the equation, using either of the two points to solve for b, the y-intercept.