Answer:
the line 1 has negative slope of -1/4 and line 2 has positive slope of 1/4.
Step-by-step explanation:
let the line 1 be y = -1/4x + 2 and line 2 be 2y = 1/2x - 4
these lines are in the form of y = mx + c
where m is the slope of the line and c is the intercept made with y axis.
dividing the line 2 by 2 we get [tex]y = \frac{1}{4}x -2[/tex]
line 1 meets x axis when y = 0 applying y = 0 in equation 1 we get x = 8
line 2 meets x axis when y=0 applying y = 0 in equation 2 we get x = 8
line 1 meets y axis when x = 0 applying x= 0in equation 1 we get y = 2
line 2 meets y axis when x = 0 applying x= 0in equation 2 we get y = -2
therefore line 1 passes through (8,0)and (0,2) with negative slope of -1/4
and line 2 passes through (8,0) and (0,-2) with positive slope of 1/4.
In the figure, AC and BD bisect each other. Complete the statements to prove that quadrilateral ABCD is a parallelogram.
-First options:
•Alternate Interior Angles Theorem
•Vertical Angles Theorem
•Alternate Exterior Angles Theorem
-Second options:
•Converse of Alternate Exterior Angles Theorem
•Converse of Alternate Interior Angles Theorem
•Converse of Corresponding Angles Theorem
•Converse of Exterior angle theorem
Answer:
1. Vertical Angles Theorem
2. Converse of Alternate Interior Angles Theorem
Step-by-step explanation:
First option:
Lines AC and BD intersect at point E. Angles AEB and CED are opposite angles formed when these two lines intersect and are called vertical angles. By vertical angles theorem, these angles are congruent. So,
Vertical Angles Theorem
Second option:
[tex]\triangle BEC\cong \triangle DEA[/tex] by SAS postulate, then
[tex]\angle CBE\cong \angle ADE[/tex] as corresponding sides of congruent triangles.
Converse of Alternate Interior Angles Theorem states that if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel.
So, [tex]\overline{BC}\cong \overline{AD}[/tex] by
Converse of Alternate Interior Angles Theorem
Answer:
1.B 2.B
Step-by-step explanation:
The volume of a large can of tuna fish can be calculated using the formula V= πr(r)h. Write an equation to find the radius, r, in the terms of V and h.
The equation [tex]r=\sqrt\frac{V}{3.14h}[/tex] can be used to find the radius.
Step-by-step explanation:
Given,
Volume of large can;
V=πr(r)h
V=πr²h
Dividing both sides by πh
[tex]\frac{V}{\pi h}=\frac{r^2\pi h}{\pi h}\\\\\frac{V}{\pi h}=r^2\\\\r^2=\frac{V}{\pi h}[/tex]
Taking square root on both sides
[tex]\sqrt{r^2}=\sqrt{\frac{V}{\pi h}}\\r=\sqrt\frac{V}{\pi h}[/tex]
Putting π=3.14
[tex]r=\sqrt\frac{V}{3.14h}[/tex]
The equation [tex]r=\sqrt\frac{V}{3.14h}[/tex] can be used to find the radius.
Keywords: volume, square root
Learn more about square root at:
brainly.com/question/10978510brainly.com/question/11007026#LearnwithBrainly
Which expression is equivalent to (4x^3y^5)(3x^5y)^2 ?
(3x^5y)^2=
3^2=9
(x^5)^2=x^10
y^2=y^2
(3x^5y)^2=9x^10y^2
9x^10y^2(4x^3y^5)=
9*4=36
x^10*x^3=x^13
y^2*y^5=y^7
9x^19y^2(4x^3y^5)= 36x^13y^7
Final answer: 36x^13y^7
Answer:
BBBBB!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
Find the median of 46 43 39 48 52 40 42 98 20 38. If the observation 42 is replaced by 92. Find the nest median
The median of given data is 42.5
And
The median after replacing 42 with 92 is 44.5
Step-by-step explanation:
A median is the middle value of the data that divided the data in two equal parts
Given data is:
46 43 39 48 52 40 42 98 20 38
First of all, the data has to arranged in ascending order
20, 38, 39, 40, 42, 43, 46, 48, 52, 98
As the number of values is even, n=10, the median will be the average of middle two numbers
20, 38, 39, 40, 42, 43, 46, 48, 52, 98
[tex]Median = \frac{42+43}{2}\\=\frac{85}{2}\\=42.5[/tex]
The median is 42.5
Now,
Replacing 42 with 92
20, 38, 39, 40, 92, 43, 46, 48, 52, 98
The data has to be re-arranged
So,
20, 38, 39, 40, 43, 46, 48, 52, 92, 98
As the number of values is same,
[tex]New\ median = \frac{43+46}{2}\\=\frac{89}{2}\\= 44.5[/tex]
Hence,
The median of given data is 42.5
And
The median after replacing 42 with 92 is 44.5
Keywords: Median, mode
Learn more about median at:
brainly.com/question/788903brainly.com/question/774670#LearnwithBrainly
which of the following is an even function
f(x) = 7 is a even function
Solution:
Given that we have to find the even function
A function is even if and only if f(–x) = f(x)
Steps to follow:
Replace x with -x and compare the result to f(x). If f(-x) = f(x), the function is even.
If f(-x) = - f(x), the function is odd.
If f(-x) ≠ f(x) and f(-x) ≠ -f(x), the function is neither even nor odd.
Option 1[tex]f(x) = (x - 1)^2[/tex]
Substitute x = -x in above function
[tex]f(-x) = (-x - 1)^2[/tex]
Thus [tex]f(-x) \neq f(x)[/tex]
So this is not a even function
Option 2f(x) = 8x
Substitute x = -x in above function
f(-x) = 8(-x) = -8x
Thus [tex]f(-x) \neq f(x)[/tex]
So this is not a even function
Option 3[tex]f(x) = x^2 - x[/tex]
Substitute x = -x in above function
[tex]f(-x) = (-x)^2 - (-x) = x^2 + x[/tex]
Thus [tex]f(-x) \neq f(x)[/tex]
So this is not a even function
Option 4f(x) = 7
f(-x) = 7
Thus f(-x) = f(x)
Thus it is a even function
Answer:
A
Step-by-step explanation:
edg verified
-Which equation is the inverse of y=2x2 + 25 ?
Answer:
y=sqrt(1/2x-25/2), -sqrt(1/2x-25/2).
Step-by-step explanation:
y=2x^2+25
x=2y^2+25
2y^2=x-25
y^2=1/2x-25/2
y=sqrt(1/2x-25/2), -sqrt(1/2x-25/2)
-18u+16u-7=9 solve for u
-18u+16u-7=9
-2u - 7 = 9 (combine like terms)
-2u = 16 (add 7 on both sides)
u = -8
Answer:
The correct answer to this problem is u = -8.
Step-by-step explanation:
To solve this problem, we first must combine like terms on the left side of the equation. This means adding together the two terms that have a "u" multiplied by a number. To combine them, we simply add the coefficients together, as we would with constant values. This is modeled below:
-18u+16u-7=9
-2u - 7 = 9
Next, we want to add 7 to both sides of the equation. This will cancel out the -7 on the left side of the equation, isolating the term with the variable u (what we are trying to solve for).
-2u - 7 + 7 = 9 + 7
-2u = 16
Finally, we want to divide both sides by -2 in order to isolate the variable u. This will get rid of the coefficient of negative 2 and give us our answer.
u = 16/-2 = -8
Therefore, the answer to this question is u = -8.
Hope this helps!
Letters w, x, y, and z are angle measures. Which should equal 92° to prove that r ∥ s? w x y z
Answer:
its the letter w
Step-by-step explanation:
i got an 100 on the test
1. In which quadrant or on which axis do each of the points (-2,4) , (3,-1) ,(-1,0), (1,2) and (-3,-5) lie? Verify your answer by locating them on the cartesian plane
Point (-2 , 4) lies in the 2nd quadrant
Point (3 , -1) lies in the 4th quadrant
Point (-1 , 0) lies on the negative part of the x-axis
Point (1 , 2) lies in the 1st quadrant
Point (-3 , -5) lies in the 3rd quadrant
Step-by-step explanation:
Let us revise the signs of the coordinates in each quadrant
x and y coordinates are positive in the 1st quadrantx-coordinate is negative and y-coordinate is positive in the 2nd quadrantx and y coordinates are negative in the 3rd quadrantx-coordinate is positive and y-coordinate is negative in the 4th quadrantThe general point on the positive part of x-axis is (x , 0), and on the negative part of x-axis is (-x , 0)The general point on the positive part of y-axis is (0 , y), and on the negative part of y-axis is (0 , -y)Now let us check the points
Point (-2 , 4) ⇒ red point
∵ x = -2 and y = 4
∵ x-coordinate is negative and y-coordinate is positive
∴ Point (-2 , 4) lies in the 2nd quadrant
Point (3 , -1) ⇒ blue point
∵ x = 3 and y = -1
∵ x-coordinate is positive and y-coordinate is negative
∴ Point (3 , -1) lies in the 4th quadrant
Point (-1 , 0) ⇒ green point
∵ x = -1 and y = 0
∵ x-coordinate is negative and y-coordinate is zero
∴ Point (-1 , 0) lies on the negative part of the x-axis
Point (1 , 2) ⇒ purple point
∵ x = 1 and y =2
∵ x and y coordinates are positive
∴ Point (1 , 2) lies in the 1st quadrant
Point (-3 , -5) ⇒ black point
∵ x = -3 and y = -5
∵ x and y coordinates are negative
∴ Point (-3 , -5) lies in the 3rd quadrant
Look to the attached graph for more understand
Learn more:
You can learn more about the four quadrant in brainly.com/question/9381523
#LearnwithBrainly
Here are the vertices of rectangle FROG: (-2,5),(-2,1),(6,5),(6,1). Find the perimeter of this rectangle. If you get stuck, try plotting the points on a coordinate plane. For the rectangle FROG, the perimeter is . Find the area of the rectangle FROG. For the rectangle FROG, the area is
Answer:
Part 1) The perimeter of rectangle is equal to 24 units
Part 2) The area of rectangle is equal to 32 square units
Step-by-step explanation:
Part 1) Find the perimeter of rectangle
we know that
The perimeter of rectangle is equal to
[tex]P=2(L+W)[/tex]
where
L is the length of rectangle
W is the width of rectangle
we have
[tex]F(-2,5),R(-2,1),O(6,1),G(6,5)[/tex]
Plot the figure to better understand the problem
using a graphing tool
see the attached figure
Remember that in a rectangle opposite sides are congruent and the measure of each interior angle is equal to 90 degrees
so
[tex]FG=RO=L\\RF=OG=W[/tex]
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
step 1
Find the distance FG
[tex]F(-2,5),G(6,5)[/tex]
substitute the values
[tex]d=\sqrt{(5-5)^{2}+(6+2)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(8)^{2}}[/tex]
[tex]FG=8\ units[/tex]
step 2
Find the distance RF
[tex]R(-2,1),F(-2,5)[/tex]
substitute the values
[tex]d=\sqrt{(5-1)^{2}+(-2+2)^{2}}[/tex]
[tex]d=\sqrt{(4)^{2}+(0)^{2}}[/tex]
[tex]RF=4\ units[/tex]
step 3
Find the perimeter
[tex]P=2(L+W)[/tex]
we have
[tex]FG=RO=L=8\ units\\RF=OG=W=4\ units[/tex]
substitute
[tex]P=2(8+4)=24\ units[/tex]
Part 2) Find the area of rectangle FROG
we know that
The area of rectangle is equal to
[tex]A=LW[/tex]
we have
[tex]FG=RO=L=8\ units\\RF=OG=W=4\ units[/tex]
substitute
[tex]A=(8)(4)=32\ units^2[/tex]
The area and the perimeter of the rectangle FROG is evaluated as:
Area(FROG) = [tex]32 \: \rm unit^2[/tex]Perimeter(FROG) = [tex]64\: \rm units[/tex]How to find the area and the perimeter of a rectangle?For a rectangle with length and width L and W units, we get:
Area of the rectangle = [tex]L \times W \: \rm unit^2[/tex]Perimeter of the rectangle = [tex]2(L + W) \: \rm unit^2[/tex]What is the distance between two points ( p,q) and (x,y)?The shortest distance(straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:
[tex]D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.[/tex]
The coordinates of the points of the rectangle FROG are given as:
F(-2,5), R(-2,1), G(6,5), and O(6,1) (from its plot, as given below)
FR and RO are length and width pair(we can call any one of them as length and other as width) of the considered rectangle as they are adjacent to each other.
We denote length of a line segment AB by |AB|
Thus, we get:
Length of the rectangle = |FR| = [tex]\sqrt{(-2-(-2))^2 + (1 - 5)^2 } = 4[/tex] unitsWidth of the rectangle = |RO| = [tex]\sqrt{(6-(-2))^2 + (1 - 1)^2 } = \sqrt{64} = 8 \: \rm units[/tex]Now with the help of length and width, we can evaluate its perimeter and area, as shown below:
Area(FROG) = [tex]L\times W = 4 \times 8= 32 \: \rm unit^2[/tex]Perimeter(FROG) = [tex]2(L + W) = 2(4 + 8) = 64\: \rm units[/tex]Learn more about distance between two points here:
https://brainly.com/question/16410393
Order each group from least to greatest.
Answer:
(1) 5 , PI + 2, 17/3
(2) 3/2, sqrt (5), 2.5
(3) Sqrt(5)/2, PI – 2, 5/4
Step-by-step explanation:
For each number, begin by comparing the whole numbers. The one with the least whole number is the smallest while the one with the largest is the biggest number.
If the numbers being compared have the same whole numbers, check the decimal places. Begin with tenths. The one with the lowest number is the smallest number. If they are the same compare the hundredths, if they are the same compare thousandths...until you find a decimal that is different and can differentiate the numbers.
Learn More:
https://brainly.com/question/11506796
https://brainly.com/question/11410123
#LearnWithBrainly
Please help me with these five problems dont understand them
Answer:
22. 150 minutes
23. ½ day
24. 0,045 minutes
25. 1,5 weeks
26. 1 year
Use the quadratic formula to find the solutions to the equation.
7- 3x+1=0
Answer:
B
Step-by-step explanation:
quadratic formula:
x = [-b ± sqrt(b^2 - 4ac)] / 2a
1. find a, b, and c
a = 1
b = -3
c = 1
2. plug values into formula
x = [3 ± sqrt(9-4•1•1)] / 2
3. simplify
x = [3 ± sqrt(5)] / 2
This is B.
Answer:
Option b) is correct
ie., [tex]x=\frac{3\pm \sqrt{5}}{2}[/tex]
Step-by-step explanation:
Given quadratic equation is [tex]x^{2}-3x+1=0[/tex]
To find the solutions of given equation:
Solution of quadratic equation [tex]ax^{2}+bx+c=0[/tex]
[tex]x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}[/tex] where a,b, are coefficients of [tex]x^{2}[/tex] and x respectively and c is constant.
From the given quadratic equation a=1, b=-3 and c=1
[tex]x=\frac{-(-3)\pm \sqrt{(-3)^{2}-4(1)(1)}}{2(1)}[/tex]
[tex]x=\frac{3\pm \sqrt{9-4}}{2}[/tex]
[tex]x=\frac{3\pm \sqrt{5}}{2}[/tex]
Therefore Option b) is correct
ie., [tex]x=\frac{3\pm \sqrt{5}}{2}[/tex]
5% tax on $1.50 What us total cost
Answer:
Step-by-step explanation:
In order to obtain the total amount that Monica was charged you should follow some steps.
How much was the net price? You can obtain this value either by clearing the x:
X * 5% = $1.50
X = $1.50 / 5%
Or by using simple rule of three:
If 5% is $1.50
Then 100% is X
So you obtain = $30
Now you just need to sum The net prices and the taxes
Net + tax = Total Charge
$30 + $1.5 = $31.5
Answer:
.08 cents rounded
Step-by-step explanation:
1.50x.05%=.075
Solve the following absolute value inequality graphically: |x|-3>1.
Answer:
x < -4 ∪ x > 4
Step-by-step explanation:
The absolute value function is shifted down 3 units. The solution space is values of x where y = |x|-3 is greater than 1. The solution is shown in red in the attachments, and the left and right (dashed) sides of the inequality are shown in blue.
__
I personally prefer to rewrite the inequality so the comparison is to zero. That is done in the second attachment, which rewrites it to ...
|x| -4 > 0
by subtracting 1 from both sides. It is often easier to read the values of x-intercepts than it is to read the coordinate values where lines cross each other.
Find the slope of the line that passes through (2, 1) and (7, 10).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer: Slope = [tex]\frac{9}{5}[/tex]
Step-by-step explanation:
Slope = [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
[tex]x_{1}[/tex] = 2
[tex]x_{2}[/tex] = 7
[tex]y_{1}[/tex] = 1
[tex]y_{2}[/tex] = 10
Substituting into the formula , we have :
Slope = [tex]\frac{10 - 1}{7 - 2}[/tex]
Slope = [tex]\frac{9}{5}[/tex]
-15w -6w +7w=14 solve for w
Answer:
w=-1
Step-by-step explanation:
-15w-6w+7w=14
-21w+7w=14
-14w=14
w=14/-14
w=-1
Answer:
-15w -6w +7w=14
- 21w+7w =14
-14w =14
divide both sides by 14
-w = -1
w = 1
Step-by-step explanation:
PLZ HELP HURRY!!! HAVE A DEADLINE!!!
Plot the line for the equation on the graph.
y−2=−2(x+4)
I kinda tried it dont know if i did it right heres the graph.... and what i did... need help!
Answer:
y = -2x - 6
The y-intercept will be (0,-6)
One point will be at (1,-8)
The line will go downward since it is a negative slope
Step-by-step explanation:
y−2=−2(x+4)
Distribute
y - 2 = -2x - 8
Move the constant to the other side
y - 2 = -2x - 8
+2 = +2
y = -2x - 6
Madelinie can decorate 100 cookies in 2 hours. How many cookies can she decorate in 5 hours
Answer:
250 Cookies
Step-by-step explanation:
First calculate the cookies decorated per hour
100 ÷ 2 = 50 cookies per hour
Number of cookies in 5 hours = 50 × 5
= 250 Cookies
Answer:
250
Step-by-step explanation:
Divide 100 by 2 to get the hourly rate which would be 50. Then take the hourly rate and multiply it by the number of hours given, 5. 5 multiplied by 50 equals 250 cookies
Will mark brainlest please help
Which of the following systems of inequalities has point C as a solution?
f(x) ≤ 3x + 4
g of x is less than or equal to negative one half times x minus 5
f(x) ≥ 3x + 4
g of x is less than or equal to negative one half times x minus 5
f(x) ≤ 3x + 4
g of x is greater than or equal to negative one half times x minus 5
f(x) ≥ 3x + 4
g of x is greater than or equal to negative one half times x minus 5
Answer:
B) f(x) ≥ 3x + 4
g of x is less than or equal to negative one half times x minus 5
Step-by-step explanation:
hope it helps
Answer:
The Answer is B.
f(x) ≥ 3x + 4
g(x) ≤ -1/2x - 5
Hope This Helps!
Choose the place where the digit 1 sits in this number 3,215,544,957
｡☆✼★ ━━━━━━━━━━━━━━ ☾
10,000,000
It is is the tens millions place.
Have A Nice Day ❤
Stay Brainly! ヅ
- Ally ✧
｡☆✼★ ━━━━━━━━━━━━━━ ☾
Answer:
The eight place from the right.
Step-by-step explanation:
1, 10, 100, 1.000, 10.000, 100.000, 1.000.000, 10.000.000
Solve each compound inequality and graph its solution.
Good evening ,
Answer:
Look at the photo below for the answer.
:)
f(x) = 4x - 1
g(x) = x2 - 2
(f + g)(9) = ?
A. 118
B. 112
C. 119
D. 114
E. 116
F. 111
G. 110
H. 115
I. 113
J. 117
Answer:
D
Step-by-step explanation:
Find (f + g)(x) then evaluate (f + g)(9)
(f + g)(x) = f(x) + g(x)
= 4x - 1 + x² - 2 = x² + 4x - 3
Now substitute x = 9 into the expression
(f + g)(9) = 9² + 4(9) - 3 = 81 + 36 - 3 = 114 → D
Answer:
J.117
Step-by-step explanation:
f(x) =4x-1
if f(2)= 4(2)-1
f(2)= 8-1 = 7
f(2) = 7 equation 1
g(x) =x2-2
if g(4)= (4)2-2
g(4) = 8-2 = 6 equation 2
Now,
(f+g)(9) =?
subtitute equation 1 and 2
(7+6)(9)=?
(13)(9)=?
13×9= 117
Hence, the answer is 117
i have three fractions (9/10, 2/3, 2/4), i know that the order from largest to smallest is 9/10, 2/3, 2/4, but how do i actually go about figuring out WHY its in that order without just looking at it or using graphs?
Step-by-step explanation:
To compare fractions, they need to have the same denominator. So you need to find the least common multiple (LCM) of 10, 3, and 4.
To find the LCM, first write the prime factorizations.
3 = 3
4 = 2²
10 = 2×5
The LCM is the product of each factor raised to its highest exponent.
LCM = 2²×3×5
LCM = 60
Now we rewrite each fraction with this new denominator.
9/10 = 54/60
2/3 = 40/60
2/4 = 30/60
Answer:
You need to convert the numbers into the same format.
Step-by-step explanation:
If you want to keep them in fraction form, you need to find the least common multiple. This means the smallest number that can be divided by all of the denominators. For this example, the number would be 60, because 60/10 is 6, 60/3 is 2, and 60/4 is 15. Now that we know this, you need to make every denominator 60. You do this by multiplying the numerator by whatever you needed to multiply the denominator by to get 60. For example, you need to multiply 10 by 6 to get sixty, so you would multiply 9 by 6 as well. You would repeat this pattern with all of the numbers, getting 54/60 (9/10), 40/60 (2/3), and 30/60 (2/4). This makes it very easy to tell which is the larger number.
If you don't want to do all of that, you can use decimal form. To find what each number would be in decimal form, divide the numerator by the denominator. For example, 9 divided by ten is .9, 2 divided by 3 is .66..., and 2/4 is .5.
Find the slope and y intercept, convert to slope intercept form
3x + 12y = 12
Answer:
16=53
Step-by-step explanation:
12.9 x 14 .9 + 6= 12
Find the vertical asymptote(s) of f of x equals quantity 5 x squared plus 3x plus 6 end quantity over quantity x squared minus 100.
x = −5, 10
x = −10, 10
x = 5, −10
x = −5, 5
Answer:
x = 10 and x = -10
Step-by-step explanation:
Given the function
[tex]f(x)=\dfrac{5x^2+3x+6}{x^2-100}[/tex]
This function is undefied when the denominator equals to 0. Find these values for x:
[tex]x^2-100=0\\ \\(x-10)(x+10)=0\\ \\x-10=0\ \ \text{or}\ \ x+10=0\\ \\x=10\ \ \text{or}\ \ x=-10[/tex]
This means that vertical lines x = 10 and x = -10 are vertical asymptotes (the graph of the function f(x) cannot meet these lines because this function is undefined at x = 10 and x = -10)
Consider the line y=-3/2x - 3
Find the equation of the line that is perpendicular to this line and passes through the point (3, 6).
Find the equation of the line that is parallel to this line and passes through the point (3, 6).
Answer:
Part 1) Equation of a perpendicular line is [tex]y=\frac{2}{3}x+4[/tex]
Part 2) Equation of a parallel line is [tex]y=-\frac{3}{2}x+\frac{21}{2}[/tex]
Step-by-step explanation:
Part 1) Find the equation of the line that is perpendicular to the given line and passes through the point (3, 6).
we have
[tex]y=-\frac{3}{2}x-3[/tex]
The slope of the given line is [tex]m=-\frac{3}{2}[/tex]
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of the slopes is equal to -1)
so
The slope of the perpendicular line to the given line is equal to
[tex]m=\frac{2}{3}[/tex]
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{2}{3}[/tex]
[tex]point\ (3,6)[/tex]
substitute
[tex]y-6=\frac{2}{3}(x-3)[/tex]
Convert to slope intercept form
[tex]y=mx+b[/tex]
Isolate the variable y
[tex]y-6=\frac{2}{3}x-2[/tex]
[tex]y=\frac{2}{3}x-2+6[/tex]
[tex]y=\frac{2}{3}x+4[/tex]
Part 2) Find the equation of the line that is parallel to the given line and passes through the point (3, 6).
we have
[tex]y=-\frac{3}{2}x-3[/tex]
The slope of the given line is [tex]m=-\frac{3}{2}[/tex]
Remember that
If two lines are parallel, then their slopes are the same
so
The slope of the parallel line to the given line is equal to
[tex]m=-\frac{3}{2}[/tex]
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-\frac{3}{2}[/tex]
[tex]point\ (3,6)[/tex]
substitute
[tex]y-6=-\frac{3}{2}(x-3)[/tex]
Convert to slope intercept form
[tex]y=mx+b[/tex]
Isolate the variable y
[tex]y-6=-\frac{3}{2}x+\frac{9}{2}[/tex]
[tex]y=-\frac{3}{2}x+\frac{9}{2}+6[/tex]
[tex]y=-\frac{3}{2}x+\frac{21}{2}[/tex]
Help with the step by step
Step-by-step explanation:
First, distribute the -4 to the parenthesis:
24a-22=-4+24a
Add 22 to both sides:
24a-22+22=-4+22+24a
Simplify:
24a=18+24a
Subtract 24a from both sides:
24a-24a=18+24a-24a
Simplify:
0=18
hope this helps :)
If age is an explanatory variable and height is the corresponding response variable, which of these would be represented by the y - axis on a scatterplot?
Answer:
The height variable should be represented by the y-axis on a scatterplot.
Step-by-step explanation:
The explanatory variable and independent variable are similar terms. When a variable is not at all dependent on any factor then it is called an explanatory variable. So, it must be plotted along the independent axis i.e. x-axis.
On the other hand, a response variable is an alternate term of the dependent variable and in our case height is a corresponding dependent variable of explanatory variable age.
Therefore, the height variable should be represented by the y-axis on a scatterplot. (Answer)
Answer:Height
Step-by-step explanation:
-x^4y^2+7x^3y^3-3xy^5+2x^2y^4 in descending powers of x
Answer:
-x^4y^2 +7x^3y^3 +2x^2y^4 -3xy^5
Step-by-step explanation:
The powers of x in the terms of the given expression are ...
4, 3, 1, 2
so, we want to swap the last two terms to put them in the desired order:
-x^4y^2 +7x^3y^3 +2x^2y^4 -3xy^5