Answer:
W'' = (2, -3)
Step-by-step explanation:
Reflection over the x-axis negates the y-coordinate and leaves the x-coordinate alone. The W becomes ...
... W' = (-2, -3)
Reflection over the y-axis negates the x-coordinate and leaves the y-coordinate alone. The W' becomes ...
... W'' = (2, -3)
Answer:
The coordinates of point W'' are (2,-3).
Step-by-step explanation:
The coordinates of given point are W(-2,3).
If point W is reflected over the x-axis, then
[tex](x,y)\rightarrow (x,-y)[/tex]
[tex]W(-2,3)\rightarrow W'(-2,-3)[/tex]
If point W' is reflected over the y-axis, then
[tex](x,y)\rightarrow (-x,y)[/tex]
[tex]W'(-2,-3)\rightarrow W''(2,-3)[/tex]
Therefore the coordinates of point W'' are (2,-3).
PLEASE HELP NEED ASAP!!!
(a) To make use of the forms of the equation for a line this problem requires, we must first calculate the slope (m) of the line between the two given points. That is computed by ...
... m = (change in y)/(change in x)
... m = (8 -3)/(2 -0) = 5/2
The second given point tells us the y-intercept (b) is 3, so the equation for the line is ...
... y = mx + b
... y = 5/2x + 3
(b) As in part (a), we must calculate the slope of the line. That is ...
... m = (change in y)/(change in x)
... m = (4 -3)/(1 -3) = 1/(-2) = -1/2
Using the first point (h, k) in the point-slope form of the equation of a line, we have ...
... y -k = m(x -h)
... y -4 = -1/2(x -1) . . . . . point-slope equation
Simplifying this, we get
... y = -1/2x +1/2 +4
... y = -1/2x +9/2 . . . . . slope-intercept equation
(c) The slopes of the two equations are different, so they must intersect at exactly one point. The equations are consistent.
(d) We can substitute the "y" from one equation into the other to give ...
... 5/2x +3 = -1/2x +9/2
... 3x = 3/2 . . . . . . . add 1/2x -6/2
... x = 1/2 . . . . . . . . divide by 3
Using the first equation to find y:
... y = (5/2)·(1/2) +3 = 5/4 +12/4
... y = 17/4
The point of intersection is (x, y) = (1/2, 17/4).
Standard FIF.2 DOK: 18. An outfielder throws a ball vertically upward with a velocity of 30 meters per second. Its distance from the ground after t seconds is approximately equal to 30t -5t2 meters. How many seconds will it take the ball to reach its maximum distance from the ground?
Answer:
t = 3
Step-by-step explanation:
y = - 5t^2 + 30t Take out - 5 as a common factory = -5(t^2 - 6t) Complete the squarey = -5(t^2 - 6t + (6/2)^2) Add (6/2)^2 outside the brackets. Why add?y = -5(t^2 - 6t + 9) + 9 Express the bracketed part as a perfect squarey = -5(t - 3)^2 + 9 The highest point reached will be nineThat occurs when -5(t -3)^2 = 0That happens when t = 3The ball thrown vertically upward reaches its maximum height after 3 seconds, as calculated by setting the derivative of the position function, which represents the velocity, to zero.
The question is about determining how many seconds it will take for a ball thrown vertically upward to reach its maximum height. The ball's position as a function of time is given by 30t - 5t2 meters. To find when the ball reaches its maximum height, we need to find the time at which the velocity is zero. The velocity function is the derivative of the position function, which is 30 - 10t. Setting the velocity equal to zero gives us the time when the ball reaches its maximum height:
0 = 30 - 10t
t = 3 seconds
The ball will reach its maximum distance from the ground after 3 seconds.
find the mean of the following numbers.
-2, 9, -10, 3, 5, 1
A. -6
B. -1
C. 1
D. 6
Answer:
C - 1
Step-by-step explanation:
The mean is the sum total of all the given value within the data set divided by the number of values in the data set. By counting, you can find that we have 6 values in our data set.
First thing you need to do is add all the numbers given together in order to get the sum of the values in the given data set. Follow these steps presented below:
-2 + 9 - 10 + 3 + 5 + 1
7 - 10 + 3 + 5 + 1
- 3 + 3 + 5 + 1
0 + 5 + 1
5 + 1
6
Now, in order to find the mean, take the sum (6) and divide by the amount of numbers there are; 6.
6/6 = 1
Therefore, the mean is 1.
Hope this helps!
1.) Of the 140 pages in a book, 25% of them have illustrations. How many pages have illustrations?
To determine how many pages have illustrations, 25% of the total 140 pages are calculated, resulting in 35 pages with illustrations.
Explanation:The student's question pertains to calculating the number of pages with illustrations based on a given percentage of the total pages in a book.
To find the answer, we need to calculate 25% of 140 pages. To do this, we multiply the total number of pages by the percentage of pages that have illustrations, remembering that 25% is the same as 0.25 in decimal form.
Therefore:
Number of pages with illustrations = 140 pages × 0.25 = 35 pages
So, there are 35 pages with illustrations in the book.
HURRRYYYY
A. It is stretched horizontally by a factor of 2 and translated up 3.
B. It is compressed horizontally by a factor of 2 and translated up 3.
C. It is stretched vertically by a factor of 2 and translated up 3.
D. It is compressed vertically by a factor of 2 and translated up 3.
The first graph, X is multiplied by 2 (2x) which compresses the graph horizontally by the factor of 2.
Then 3 is added , which shifts the graph up 3 units.
The answer would be: B. It is compressed horizontally by a factor of 2 and translated up 3.
Jana paid a $75 initial fee to join a sports club and a monthly fee of $14 per month. Write an expression that shows how much Jana spends after x months of membership at the sports club.
Answer:
y=14x+75 where y is equal to 14x+75. Hope this helps.
Step-by-step explanation:
Answer:
y=14x+75
Step-by-step explanation:
y=mx+b is the slope intercept form which you will use for equations like these.
the M represents what it recurring, and in this case it is 14 dollars per month
The b represents your initial value and in this case it is 75 dollars
The 14x represents that it is 14 per, and the 75 represents the initial cost.
whats the most easiest way to find the mean...of a dot plot
"Easiest" depends on several factors, including your understanding of what you're trying to do and of how the mean is calculated.
The most straight-forward way is to
multiply the value of a column by the number of dots in that columnadd the productsdivide by the total number of dotsOne of my favorite ways is this.
Choose a value near the middle of the plot and call it the (provisional) mean. Often, I will choose a value that has the most dots, or that has dots fairly symmetrically distributed around it.Match dots that are symmetrically located around that mean and cross them off. That is, for every dot that is 1 unit above the (provisional) mean, cross off it and a dot that is 1 unit below the (provisional) mean. (With some experience, you can recognize non-symmetrical dots that can cancel. For example, one that is +2 and one that is +3 together will cancel one that is -5.)For the dots left over, multiply the number of dots by their distance from the (provisional) mean, and add the products. Most likely, some will be positive, some will be negative.Divide the total from the previous step by the total number of dots. Add that (signed) result to the provisional mean. This gives the true mean.If the distribution is reasonably symmetrical, this second method gives you fewer (and smaller) products to compute, and you can probably do them in your head.
If the perimeter of the rectangle is 30 cm and value of j is 8.
a) Create an equation that you can use to find the value of h
b) Solve the equation. What is the value of h?
PART A
Equation:__________________________
PART B
Solve the equation. Show your work
Answer: h =______________________
A square is cut in half on the diagonal creating two equal triangles each triangle has an area of 0.72 square units what is the side length in units of the original square?
The side length of the original square is calculated by associating the area of the triangle with the square's side length. It is determined to be 1.2 units.
Explanation:To find the side length of the original square, we need to first understand how the area of a triangle is related to the square. When a square is cut on the diagonal, it forms two triangles. The area of a triangle is given by the formula 1/2 * base * height. In the case of these triangles, the base and height are the same, and equal to the side length of the square, which we'll call 'a'.
The area of one triangle is given as 0.72 square units. So, 0.72 = 1/2 * a * a. Simplifying this, we get a² = 2*0.72 = 1.44. Taking the square root of both sides, we find that a = √1.44 or a = 1.2 units.
Learn more about Square and Triangle Area here:
https://brainly.com/question/33583698
#SPJ3
what are the real and complex solutions of the polynomial equation? x^4-41x^2=-400
show your work please
The real solutions are -5, -4, 4, 5. There are no complex solutions.
Step-by-step explanation:The equation ...
... x^4 -41x^2 +400 = 0
can be factored as ...
... (x^2 -16)(x^2 -25) = 0
... (x -4)(x +4)(x -5)(x +5) = 0
So, all roots are real and are ...
... x ∈ {-5, -4, 4, 5}
_____
These are the values of x that make the factors zero.
Final answer:
The real solutions of the polynomial equation x^4 - 41x^2 = -400 are x = 4, -4, 5, and -5. There are no complex solutions since the equation can be factored into real numbers without the need for complex terms.
Explanation:
To find the real and complex solutions of the polynomial equation x^4 - 41x^2 = -400, we can begin by rewriting the equation in a more familiar quadratic form. Adding 400 to both sides gives us:
x^4 - 41x^2 + 400 = 0
We can set y = x^2, which turns our equation into:
y^2 - 41y + 400 = 0
Factoring this quadratic equation, we get:
(y - 16)(y - 25) = 0
So, y = 16 or y = 25. Since y = x^2, we solve for x:
x^2 = 16 → x = ±4
x^2 = 25 → x = ±5
Therefore, the real solutions are x = 4, -4, 5, -5. There are no complex solutions in this case because all values of x are real numbers.
Please help if you can
Answer:
rational: √81, √121
irrational: √89, √131
Step-by-step explanation:
You know your squares, so you know that 81 = 9² is a perfect square. Its square root is 9, a rational number.
And you know that 121 = 11², another perfect square. Its square root is 11, a rational number.
The remaining numbers are not the roots of squares of integers, so will be irrational.
What is the sale tax for a purchase of $2,500 and what is the cost of an item with a sales tax of $108?
Answer:
4.32%
Step-by-step explanation:
Step 1:
To solve this, we must know how to find sales tax first. Let's use this equation:
t = p × r
Let t stand for the total amount of sales tax
Let c stand for the purchase
Let r stand for the sales tax rate.
Step 2:
Now, let us plug in what is given. We know that the purchase made cost $2,500:
t = $2,500 x r
Annddd, we also know that the sales tax is $108:
$108 = $2,500 x r
Therefore, our equation is:
$108 = $2,500 x r
Step 3:
We can simplify this to:
$108 = $2,500r
Step 4:
All we need to do is divide each side by 2500 because the goal is get r all by itself
[tex]\frac{108}{2500} =\frac{2500r}{2500}[/tex]
Step 5:
This gives us:
r = 0.0432
Step 6:
We're not done! Since we are dealing with a percentage, we would multiply .0432 by 100% and that gives us our final answer of
4.32% is our sales tax
15. convert the following values into scientific notation, a) 42,670,000 B) 0.0000008
Answer:
8x10^-7
Step-by-step explanation:
First one you have correct however the second one you were close lets figure it out:
0.0000008
In order to move the decimal in front of the eight we have to "jump" 7 times to the right. Furthermore since we have to move the decimal to the right our exponent will be negative. That means that we have:
[tex]0.0000008=8 \times 10^{-7}[/tex]
~~~Brainliest Appreciated~~~
To express in scientific notation, move the decimal so it is after the first non-zero digit, and count the number of steps as the power of 10. 42,670,000 becomes 4.267 * 10^7 and 0.0000008 becomes 8 * 10^-7.
Explanation:To convert a value to scientific notation, you need to express it as a product of a number between 1 and 10 and a power of 10.
For the value 42,670,000 we rewrite it as 4.267 * 10^7 which means first you move the decimal to the left until it is after the first digit and then count how many places you moved it to determine the power of 10. For the value 0.0000008, it's a similar process, but slightly different because it is less than one. We get 8 * 10^-7, the power of 10 is negative to reflect that we moved the decimal to the right.Learn more about Scientific Notation here:
https://brainly.com/question/16936662
#SPJ2
i will give the brainlesit
Answer:
option 4
Step-by-step explanation:
tan30° = 17/x
=>1/√3 = 17/x
=>x = 17√3
for y,
sin30° = 17/y
=>1/2 = 17/y
=>y = 34
For this case we must find the value of y (Hypotenuse) and the value of x (leg adjacent to the 30 degree angle) of the triangle shown.
By definition:
[tex]Tangent (30) = \frac {17} {x}\\x = \frac {17} {Tangent (30)}\\x = \frac {17} {\frac {\sqrt {3}} {3}}\\x = \frac {17 * 3} {\sqrt {3}}\\x = \frac {51 \sqrt {3}} {3}\\x = 17 \sqrt {3}[/tex]
Now, we look for the value of y:
[tex]Sine (30) = \frac {17} {y}\\y = \frac {17} {sine (30)}\\y = \frac {17} {\frac {1} {2}}\\y = 34[/tex]
Answer:
[tex]x = 17 \sqrt {3}\\y = 34[/tex]
Option D
the amount y (in bales) of hay remaining after feeding cows for x days is y=-3.5x+ 105
The given linear equation describes how the amount of hay decreases by 3.5 bales for each day cows are being fed. The initial amount of hay is given as 105 bales.
Explanation:The equation provided, y=-3.5x + 105, is a linear equation wherein y represents the amount of hay remaining (in bales) and x represents the days of feeding cows. This equation tells us that for every day that passes (an increase in x by 1), the amount of hay decreases by 3.5 bales. When x = 0, which represents the beginning before any hay has been eaten, there are 105 bales of hay available.
To further illustrate, after one day (x = 1), the amount of hay left would be calculated as y=-3.5(1) + 105 = 101.5 bales. After two days (x = 2), y=-3.5(2) + 105 = 98 bales, and so on.
Learn more about Linear Equation here:https://brainly.com/question/32634451
#SPJ2
A cylindrical coffee can has a height of 14 centimeters. The radius of the base is 5 centimeters. What is the area of its label?
The area of the label for a cylindrical coffee can with a height of 14 cm and a radius of 5 cm is approximately 440 square centimeters.
Explanation:The subject in this case is Mathematics, and the question pertains to the use of geometry to determine the area of a label on a cylindrical coffee can. Specifically, the question asks to calculate the area of the cylindrical surface (lateral surface), which will be used as the label area. To calculate this, one needs to use the formula for the lateral surface area of a cylinder, which is 2πrh, where r is the radius and h is the height of the cylinder.
Given a cylinder with a height of 14 centimeters and a radius of 5 centimeters, the area of the label can be calculated as follows:
Area = 2π(5 cm)(14 cm) = 2π×5 cm×14 cm = 2×3.1416×5 cm×14 cm ≈ 440 cm².
Solve the equation. PPLLLLLLLLZZZZZZZZ HELP!!!!!!!!!!!!!!!!!!!!!
-7/3n = - 42
A. n = 92
B. n = 294
C. n = -21 4/7
D. n = 18
Answer:
The correct answer is 1 / 18.
Step-by-step explanation:
We are given the following equation for which we need to solve for the variable n:
[tex]-\frac{7}{3n} =-42[/tex]
So for solving this, we will rearrange the equation in a manner that isolates the variable n, making it the subject of the equation.
[tex]-\frac{7}{3n} =-42[/tex]
[tex]-\frac{7}{42} =3n[/tex]
[tex]\frac{1}{6} =3n[/tex]
[tex]n=\frac{1}{6*3} \\\\n=\frac{1}{18}[/tex]
Therefore, the value of n is equal to 1 / 18.
What is the exact value of x?
5*21^5x = 16
[tex]\bf \textit{Logarithm of exponentials} \\\\ log_a\left( x^b \right)\implies b\cdot log_a(x) \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf 5\cdot 21^{5x}=16\implies 21^{5x}=\cfrac{16}{5}\implies \stackrel{\textit{taking \underline{log } to both sides}}{\log\left( 21^{5x} \right)=\log\left( \cfrac{16}{5} \right)} \\\\\\ 5x\log(21)=\log\left( \cfrac{16}{5} \right)\implies 5x=\cfrac{~~\log\left( \frac{16}{5}\right)~~}{\log(21)}\implies x=\cfrac{~~\log\left( \frac{16}{5}\right)~~}{5\log(21)} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill x\approx 0.0764094095937~\hfill[/tex]
Answer:
X=log 3.2/5 log 21
Step-by-step explanation:
X=0.0764094
Question is in the picture, I dont get it.
Answer:
a = 0, b = 1/2
Step-by-step explanation:
Multiplication and division of complex numbers in polar form is pretty simple.
... a·Cis(α) × b·Cis(β) = ab·Cis(α+β) . . . . . multiply magnitudes; add angles
... a·Cis(α) / (b·Cis(β)) = (a/b)·Cis(α-β) . . . divide magnitudes, subtract angles
In your case, you have ...
... 2·Cis(120°) / (4·Cis(30°)) = (2/4)·Cis(120° -30°) = (1/2)·Cis(90°)
Of course, Cis(90°) = cos(90°) +i·sin(90°) = 0 +i.
... (1/2)·Cis(90°) = 1/2·(0 +i) = 0 + 0.5i
_____
Comment on the use of a calculator
It helps to be aware of how your calculator handles complex numbers. This one can express complex numbers in exponential format, equivalent to a polar form, but requiring specific notation. In this case, the variable D has been assigned the value π/180 so multiplying by it converts degrees to radians. The result of the division is (1/2)i, not 1/(2i).
What is the value of x in the solution to the following system of equations? x − 2y = 2 3x + y = 6 Answer for Blank 1:
Answer:
x=2, y=0
Step-by-step explanation:
x − 2y = 2
3x + y = 6
I am going to use elimination to solve this system.
Multiply the second equation by 2
2(3x+ y) =2* 6
6x +2y =12
Now add the first equation. This will eliminate y
6x +2y =12
x − 2y = 2
-----------------------
7x = 14
Divide by 7
7x/7 =14/7
x=2
We still need to find y
3x + y = 6
3x+y=6
We know x so substitute it in
3(2) +y =6
6+y=6
Subtract 6 from each side
6+y-6 = 6-6
y=0
How many solutions does the system have?
y=−2x−4
y=3x+3
A. One solution
B.No solutions
C. Indefinitely about of solutions
Answer: one solution
Step-by-step explanation:
The two lines have different slopes, so they can't be the same line (infinitely many solutions) or parallel (no solutions). The lines intersect at
3x+3 = -2x - 4
5x = -7
x = -7/5
3(-7/5) + 3 = -2(-7/5) - 4
-21 + 15 = 14 - 20
-6 = -6
Answer:
The answer is one solution
Step-by-step explanation:
I tried it on khan and it was correct.
find the missing lenghts of the sides
Answer:
x = 8 ; y = 8√2
Step-by-step explanation:
In the given figure, two base angles are equal.
In an isosceles triangle, the sides opposite to the equal angles are equal.
∴ x= 8
The triangle is also right angled.
Using Pythagoras theorem,
hypotenuse² = base² + perpendicular²
y² = 8² + x² = 8² + 8² = 128
y = √128 = 8√2
∴ x = 8 ; y = 8√2
Answer:
option 2
Step-by-step explanation:
tan45° = x/8
=>1 = x/8
=>x =8
for y,
cos45° = 8/y
=>1/√2 = 8/y
=>y = 8√2
The glee club has $90 to spend on pens and pencils. Each pen costs $0.75 and each pencil costs $0.15. Let x represent the number of pens, and let y represent the number of pencils.
Part A
Select the equation that describes the number of club pens and pencils that the glee club can buy.
A. 0.15x + 0.75y = 90
B. 0.75x + 0.15y = 90
C. 0.90(x + y) = 90
Part B
What is the greatest number of each type of writing tool that the club can buy?
greatest number of pens = ?
greatest number of pencils = ?
Answer:
Step-by-step explanation:
Given that total amount available is 90$
x represent the number of pens, and y represent the number of pencils.
cost of each pen is 0.75 and cost of each pencil is 0.15
Then we have total cost = cost of pens + cost of pencils
= [tex]0.75x+0.15y[/tex]=90
Hence option B is right
For finding out the greatest number of each type of writing tool, we can make the other 0 and find out
Hence maximum x = [tex]\frac{90}{0.75} =120[/tex]
maximum y =[tex]\frac{90}{0.15} \\=600[/tex]
Part A
The equation that describes the number of club pens and pencils that the glee club can buy is 0.75x + 0.15y = 90
Part B
Greatest number of pens that the club can buy = 120
Greatest number of pencils that the club can buy = 600
Cost of each pen = $0.75
Number of pens = x
Cost of each pencil = $0.15
Number of pencils = y
Total cost on pens and pencils = $90
(Cost of each pen) x (Number of pens) + (Cost of each pencil)x(Number of pencils) = Total cost
The equation that describes the number of club pens and pencils is:
0.75x + 0.15y = 90
The club buys the greatest number of pens when:
0.75x = 90
x = 90/0.75
x = 120
Greatest number of pens that the club can buy = 120
The club buys the greatest number of pens when:
0.15x = 90
x = 90/0.15
x = 600
Greatest number of pencils that the club can buy = 600
Learn more here: https://brainly.com/question/17784388
Receive 99 points if answered correctly with steps!
Point E is the midpoint of side BC of parallelogram ABCD (labeled counterclockwise) and AE ∩ BD =F. Find the area of ABCD if the area of △BEF is 3 cm2.
Answer:
36 cm²
Step-by-step explanation:
1. ΔBEF & ΔADF are similar; 2. the height of ΔABE is 3height of ΔBEF; 3. area of ΔABE is 3 area of ΔBEF; 4. area of ΔABE= area of ΔACE; 5. area of ΔABC = 2 area of ΔACE; 6. Area of ABCD = 2 area of ΔABC = 12 area of BEF.
36 cm²
Step-by-step explanation:
1. ΔBEF & ΔADF are similar; 2. the height of ΔABE is 3height of ΔBEF; 3. area of ΔABE is 3 area of ΔBEF; 4. area of ΔABE= area of ΔACE; 5. area of ΔABC = 2 area of ΔACE; 6. Area of ABCD = 2 area of ΔABC = 12 area of BEF.
find all the zeros in the equation x^4-6x^2-7x-6=0
show your work
To find the zeros of the polynomial equation, the equation has to be transformed into a quadratic equation. Using the quadratic formula, the roots of the quadratic can be found. Finally, substituting these roots again into the original given equation will give the solutions of the polynomial.
Explanation:To find the zeros of the equation x^4-6x^2-7x-6=0, we must use factoring or the quadratic formula. The quadratic formula is -b ± √b² - 4ac 2a, where a, b, and c are coefficients of the equation. However, since this equation is a quartic and not a quadratic, we first need to simplify it into a quadratic form, which can be more easily solved.
Let's write the equation as (x^2)^2 - 6*(x^2) - 7x - 6 = 0 and let y = x^2. So the equation becomes y^2 - 6y - 7x - 6 = 0. Solve this equation as a quadratic. After finding the values of y, substitute y = x^2 back into them to solve for x.
Without the original quadratic equation or an exact simplified equation, we are not able to provide concrete solutions. Applying the mentioned steps will help you find the precise solutions.
Learn more about Solving Polynomial Equations here:https://brainly.com/question/14837418
#SPJ3
NEED HELP PLEASE!
Consider the function represented by the equation 16b = 4r - 12. write the equation in function notation, where b is the independent variable. Must show work for full credit
Answer:
r(b) = 4b +3
Step-by-step explanation:
There are only two variables and the one that is not b is r. So, this amounts to solving for r. Divide the given equation by the coefficient of r:
... 4b = r -3
Add the constant:
... 4b +3 = r
Express in function notation.
... r(b) = 4b +3
This is converting to polar form, I need help and the answer too.
Answer:
2 cis (7/6 pi)
Step-by-step explanation:
r = sqrt( a^2 + b^2)
r = sqrt (-sqrt(3) )^2 + (-1)^2)
= sqrt(3 +1)
= sqrt(4)
= 2
theta = arctan (b/a)
theta = arctan (-1/-sqrt(3))
theta = 30
but this is in the third quardrant -a and -b
so add 180
theta = 210 degrees
convert this to radians
210 * pi/180 = 210/180 * pi = 21/18 * pi = 7/6 * pi
r cis (theta)
2 cis (7/6 pi)
Which graph can be used to find the solution for the equation 4x + 2 = x + 3?
Answer:
option C
Step-by-step explanation:
to find the solution for the equation 4x + 2 = x + 3, graph the equations
y= 4x+2 and y=x+3
Lets make a table for each equation
x y= 4x+2
-1 4(-1) + 2= -4+2 = -2
0 4(0) + 2= 2
1 4(1) + 2= 6
plot all the points on graph
Lets make table for second equation
x y= x+3
-1 -1+3 = 2
0 0+3 = 3
1 1+3 = 4
Plot the point on the graph and make a line
option C is correct
Answer:
The required graph of the equation is shown below:
Step-by-step explanation:
Consider the provided equation.
[tex]4x + 2 = x + 3[/tex]
Solve the equation for x.
[tex]4x-x=3-2[/tex]
[tex]3x=1[/tex]
[tex]x=\frac{1}{3}[/tex]
Now substitute x=1/3 in [tex]y=4x + 2[/tex]
[tex]y=\frac{4}{3} + 2=\frac{10}{3}[/tex]
So, the graph will be the lines which intersect at (1/3,10/3)
The correct graph is 3rd one.
Alternate method:
The equation [tex]4x + 2 = x + 3[/tex] can be written as:
[tex]y= 4x + 2 \\y= x + 3[/tex]
Draw the graph for both equation.
For [tex]y= 4x + 2[/tex]
Substitute x=0 in above equation,
[tex]y= 4(0) + 2[/tex]
[tex]y=2[/tex]
Substitute y=0 in above equation,
[tex]0= 4x + 2[/tex]
[tex]-2=4x[/tex]
[tex]x=\frac{-1}{2}[/tex]
Now use the coordinate (0,2) and (-1/2,0) to draw the graph of straight line.
For [tex]y=x + 3[/tex]
Substitute x=0 in above equation,
[tex]y=3[/tex]
Substitute y=0 in above equation,
[tex]0=x + 3[/tex]
[tex]x=-3[/tex]
Now use the coordinate (0,3) and (-3,0) to draw the graph of straight line.
Hence, the required graph of the equation is shown below:
What is m<PTX
someone please help me
Answer:
60°
Step-by-step explanation:
The triangle PTX is equilateral, so all of its angles are 60°.
___
Adding up the lengths that make PX, you find they're the same as the lengths that make PT. The sides of ΔPQU are all the same length, so all the triangles are similar and equilateral.
Choose the equation below that represents the line passing through the point (2, -4) with a slope of one half.
y = one halfx + 5
y = one halfx − 3
y = one halfx − 5
y = one halfx + 3
y = (1/2)x - 5
Step-by-step explanation:Try the answers:
... -4 ≠ (1/2)·2 + 5
... -4 ≠ (1/2)·2 - 3
... -4 = (1/2)·2 - 5 . . . . . the third choice works
... -4 ≠ (1/2)·2 + 3
___
You can write the point-slope form equation and simplify.
... y -k = m(x -h) . . . . . . equation for line of slope m through point (h, k)
... y -(-4) = (1/2)(x -2) . . . filled in with your values, m=1/2, (h, k) = (2, -4)
... y = (1/2)x -1 -4 . . . . subtract 4, eliminate parentheses
... y = (1/2)x - 5 . . . . . simplified. (Matches the 3rd selection.)
Answer: y = one half x − 5
Step-by-step explanation:
We know that , the equation of line that passes through point (a,b) and has slope m is given by :-
[tex](y-b)=m(x-a)[/tex]
Given : Point = (a,b)=(2, -4)
Slope = [tex]\dfrac{1}{2}[/tex]
Then, the equation of the line will be (substitute all the values in the above formula) :-
[tex](y-(-4))=\dfrac{1}{2}(x-2)[/tex]
[tex]\Rightarrow\ y+4=\dfrac{1}{2}(x-2)[/tex]
[tex]\Rightarrow\ y+4=\dfrac{1}{2}x-1[/tex]
Subtract 4 from both sides , we get
[tex]y=\dfrac{1}{2}x-1-4[/tex]
[tex]y=\dfrac{1}{2}x-5[/tex]
Hence, the correct answer is y = one half x − 5