Answer:
LCM= 56
Step-by-step explanation:
Multiplies of 8- 8, 16, 24, 32, 40, 48, 56, 64, 72
Multiplies of 28- 28, 56, 84, 112
Then, you look at the numbers that are the same in both. In some cases, there will be more than one that shows up (but not in this case) and all you have to do is find the least common multiple or LCM.
Problem 1: Consider the (nonlinear) differential equation
[tex]y' = \frac{ - y(y + 1)}{x} [/tex]
Without solving the equation, check which of the following are solutions:
[tex]y(x) = {x}^{2} - 1[/tex]
[tex]y(x) = \frac{2}{x - 2} [/tex]
That is: do not use the method of integrating factors to solve. Just check by plugging in.
If y = x² - 1, then y + 1 = x² and y' = 2x. Then in the DE, we would have
2x = - (x² - 1) x² / x ⇒ 2 = - x² + 1
but this only true for some values of x. So the first choice is not correct.
If y = 2/(x - 2), then y + 1 = x/(x - 2) and y' = -2/(x - 2)². In the DE,
-2/(x - 2)² = - (2/(x - 2)) (x/(x - 2)) / x ⇒ -2/(x - 2)² = -2/(x - 2)²
so the second choice is the correct answer.
Answer the questions about the following function.
x + 6
f(x) =
x-12
(a) Is the point (5,-2) on the graph of f?
(b) If x= 3, what is f(x)? What point is on the graph of f?
(c) If f(x) = 2, what is x? What point(s) is (are) on the graph of f?
(d) What is the domain of f?
(e) List the x-intercepts, if any, of the graph of f.
(f) List the y-intercept, if there is one, of the graph of f.
(g) What are the zeros of f?
The given rational function has a vertical asymptote at x = 12, and the
graph has x and y-intercept at the negative x and y-axis.
Response:
(a) The point (5, -2) is not on the graph
(b) f(x) = -1
The point on the graph of f is (-1, 3)(c) If f(x) = 2, x = 30
The point on the graph of f is (30, 2)(d) Domain = (-∞, 12) ∪ (12, ∞)
(e) x-intercept is at x = -6, which is the point (-6, 0)
(f) The y-intercept is at y = -0.5, which is the point (0, -0.5)
(g) A zeros of f, is x = -6
Which method is used to evaluate the rational function?The possible given function is presented as follows;
[tex]f(x) =\mathbf{\dfrac{x + 6}{x - 12}}[/tex]
(a) When x = -2, we have;
[tex]f(-2) = \dfrac{(-2) + 6}{(-2) - 12} = \dfrac{4}{-14} = \mathbf{-\dfrac{2}{7}}[/tex]
Therefore;
The point ([tex]-\frac{2}{7}[/tex], -2) is on the graph, which gives;
The point (5, -2) is not on the graph(b) If x = 3, we have;
[tex]f(3) =\mathbf{ \dfrac{3 + 6}{3 - 12}} = \dfrac{9}{-9} =-1[/tex]
f(3) = -1The point on the graph of f is (-1, 3)(c) If f(x) = 2, we have;
[tex]f(x) =2 = \mathbf{ \dfrac{x + 6}{x - 12}}[/tex]
2·(x - 12) = x + 6
2·x - x = 6 + 2 × 12 = 30
x = 30
If f(x) = 2, x = 30The point on the graph of f is (30, 2)(d) The domain which is the list of possible x-values, which is expressed as follows;
Domain; -∞ < x < 12, and 12 < x < ∞
Which gives;
Domain = (-∞, 12) ∪ (12, ∞)(e) The x-intercepts are;
[tex]0 = \mathbf{ \dfrac{x + 6}{x - 12}}[/tex]
x-intercept is at x = -6, which is (-6, 0)(f) The y-intercept
[tex]At \ the \ y-intercept, \ f(x) = \dfrac{0 + 6}{0 - 12} = -\dfrac{1}{2} = \mathbf{ -0.5}[/tex]
The y-intercept is at y = -0.5, which is (0, -0.5)(g) The zeros of the graph, f, are the points at which the graph crosses the x-axis which at the point x = -6
A zeros of the graph is x = -6Learn more about the graph of functions here:
https://brainly.com/question/6676855
What is the area of this circle?
When calculating, use 3.14 as the estimation of n.
Round to one decimal place.
T
2 units
units2
Answer:
What does the circle look like?
Step-by-step explanation:
To find the area use 3.14 times the radius squared.
Give me the picture of the circle so I can solve it.
A charm bracelet costs $65, plus $25 for each charm. The equation -25x+y=65 represents the cost y (in dollars) of the bracelet, where x is the number of charms.
a. Graph the equation.
b. How much does a bracelet with three charms cost?
*This answer may be wrong (part a), so make sure to double check with someone trustworthy. Feel free to tell me if I had made any mistakes, and I will fix them. Congrats if you read through my whole answer! Good luck!
Answer (a):
Coordinate: (0, 65)
Slope: -25
Step-by-step explanation:
Hint: In the graph, make one space represent 5 units to make the graph simpler (be careful on step #4 when plotting)
1.) Find the y - intercept to find a coordinate the line goes through.
2.) Rewrite the equation -25x + y = 65 in slope - intercept form.
y = 25x + 65
65 is the y - intercept at (0, 65)
3.) The slope is -25, so the slope is negative. To have a slope of 25, we can use the rise/run formula for the slope.
4.) Go 25 units to the left (to get to -25) and one unit down. Plot this point in the graph.
5.) After you have plotted these two points down (y - intercept and slope), draw a line through it.
Answer (b):
$140
Step-by-step explanation:
1.) We plug in 3 in x because it has three charms.
2.) New equation: -25(3) + y = 65
-75 + y = 65
3.) We add 75 to both sides to isolate y.
-75 + y = 65
+75 + y = 65 + 75
y = 140
Triangles ABC and YZX are similar. Use the measurements given in the image below to find the side length of ZX. In your answer, give the side length of ZX and explain how you calculated it. X А 25 Y 40 50 20 Z UD 60 C (100 points if it's correct)
Answer:
ZX = 30 unitsStep-by-step explanation:
Since the triangles are similar, the ratio of corresponding sides are same.
ZX is the largest side and corresponding side is BC = 60, the shortest sides are BC = 40 and YZ = 20:
ZX / 60 = 20/40ZX / 60 = 1/2ZX = 60/2ZX = 30Which of the following number line graphs shows the solution set of 3|x| + 1 > 7?
Answer:
D
Step-by-step explanation:
When doing this problem remember that absolute value is a number's distance from zero, and distance is always positive. So, absolute value makes any number positive. This means that |±x| = x. To find the correct number graph, first solve the inequality.
3|x| + 1 > 7Subtract 1 from both sides
3|x| > 6Divide both sides by 3
|x| > 2Then, we need to use absolute value. Any number with a distance from 0 greater than 2 fulfills this inequality. So, the number graph should represent -2 > x and x > 2. Additionally, because the inequality is looking for greater than but not equal to, the circles should be open.
$10,574.40 rounded 2 decimal places
Answer:
$10,574.40
Step-by-step explanation:
$10,574.40 is already rounded to two decimal places. Rounding to two decimal places means rounding to the hundredths place.
I am a solid.
I have 6 vertices.
I have 5 faces.
3 of my faces are rectangles, the other 2 are triangles.
What am I?
Answer:
a triangular prism
Step-by-step explanation:
The 6 vertices are the vertices of the two triangular faces. The 3 rectangles join those to make a triangular prism.
When going to a field trip, how can you apply your understanding on percent?
Answer:
if you go to a gift shop,percents off prices of items? if you buy lunch there, and your school gives you how much of percent of your payment will go towards lunch? if your school gives you percent of what will go to each such as 5 percent will go to the bus 50 percent will go to your ticket?
You pick a card at random. Without putting the first card back, you pick a second card at random.
4
5
6
7
What is the probability of picking a 6 and then picking a 7?
What function is x=2 mapped to 32?
Please just state if they are agasent, supplementary, or neither!!! I need nothing else!!!
Step-by-step explanation:
1) supplementary
2) complementary
3) neither
4) neither
5) supplementary
6) complementary
7) supplementary
8) neither
9) complementary
how to solve for x in an equation like 12sin(30)=x
or am i doing that wrong too
Answer:
what type of triangle is this ?
Step-by-step explanation:
if p= (-2 4) then find Ry=1 (p)
Please Help
The reflection mapping of the equation p(-2, 4) is [tex]\mathbf{R_{y =1}(P)=(-2,-2)}[/tex]
To solve this question, we must understand what is reflection mapping is all about.
What is reflection mapping?In mathematical concepts, a reflection is indeed a mapping via a Euclidean plane to itself. The isometry of this usually has a hyperplane with designated fixed points that are commonly referred to as axis.
From the given information, we have:
The given points P = (-2, 4)
Required to find:
[tex]\mathbf{R_{y =1}(P)}[/tex]
Hence, the image of P under the axis(point of reflection line) is y = 1
The mapping of this reflection in line is y = kThus,
[tex]\mathbf{(x,y) = (x,2k-y)}[/tex]
[tex]\mathbf{(x,y) = (-2,2(1)-4)}[/tex]
[tex]\mathbf{(-2,4) = (-2,-2)}[/tex]
Therefore, we can conclude that the [tex]\mathbf{R_{y =1}(P)=(-2,-2)}[/tex]
Learn more about reflection mapping here:
https://brainly.com/question/25998325
2) Given that XY || AC, what is YC if BX = 10, BA = 15, and BY = 8?
A) 4
XB) 6
0)
8
D) 12
The parallel lines XY and AC is an illustration of similar triangles
The value of YC is 12 units
How to determine the length of YCFrom the question, we have:
Parallel lines XY || AC
This means that:
BA : BX = YC : BY
Substitute known values in the above ratio
15 : 10 = YC : 8
Express the ratio as fractions
[tex]\frac{15}{10} = \frac{YC}{8}[/tex]
This gives
[tex]1.5 = \frac{YC}{8}[/tex]
Multiply both sides by 8
[tex]YC = 12[/tex]
Hence, the value of YC is 12 units
Read more about similar triangles at:
https://brainly.com/question/14285697
rotation transformation of rotates the shape 125 clockwise.?
Answer:
90 degree rotation counterclockwise.
I think its right, BE SAFE! Hope it helps :3
(01.06 LC)
Which of the following statements best describes adjacent angles?
O Adjacent angles are vertical.
O Adjacent angles are supplementary.
O Adjacent angles share interior points.
O Adjacent angles share a side.
Answer:
(d) Adjacent angles share a side
Step-by-step explanation:
Adjacent angles share a side and a vertex. They have no interior points in common.
__
In the attachment, 'a' and 'b' are adjacent angles.
Line AC and line DB intersect at point P. Solve for angle BPQ.
To earn full credit for presenting and defending your mathematical solution, you must share the equation, show the steps to solving for the variable x, show the steps to solving for angle BPQ.
Answer:
Angle BPQ = 64°
Step-by-step explanation:
4x + 12 +2x = 90
6x + 12 = 90
- 12 -12
6x = 78
x = 13°
BPQ = ((4(13) + 12)°
(52 + 12)°
64°
what is the volume of the figure below
18x12x13x5 divided by 1/2
Answer: is 28080
Step-by-step explanation:
6. - - What is the sum of the measures of the interior angles of a convex polygon with n sides? A (n-2)90 C. (n-2)180 B. (n-2)120 D. (n-2)360 It is the sum of the measures of the interior angles of a heptagon. A 720° C. 1,080° B. 900° D. 1,260° 7
Answer:
a 720
Step-by-step explanation:
because u use pemdas
please answer with explanation
Answer:
Step-by-step explanation:
area formula
Using diagonals: A = (d1 × d2) : 2
we use the inverse formula
A * 2 : d1
225 * 2 : 15 =
30cm
--------------------
check
15 * 30 : 2 = 225
the answer is good
I need help with some questions ASAP in the law category. It's actually personal finance but it doesn't give you that option. answer whatever and you still get the points. (:
which statement correctly explains the association of the scatterplot
Answer:
B. Since the y - values decrease as the x - values increase the scatter plots show a negative association.
Step-by-step explanation:
A positive association would be the y - values and the x - values both increases.
I hope this helps!
Please help, find the area of only the shaded area.
Answer:
Area shaded ≈ 30.92
Area shaded in terms of π = 144 - 36π
Step-by-step explanation:
Square:
The length of this square is 4 * 3m, which is 12mThe area of the square : 12² = 144Circle:
The area of one circle is 3²π = 9πThe area of 4 circles is 9π * 4 ≈113.08Subtract:
144 - 113.0830.92-Chetan K
Find the product. Simplify your answer.
(q–4)(3q–1)
Multiplying Binomials
Answer:
3q^2-13q+4
Step-by-step explanation:
Answer:
3q^2-13q+4
Step-by-step explanation:
q (3q-1)-4 (3q-1)
3q^2-q-12q+4
3q^2-13q+4
The graph of a quadratic function with vertex (-3,3) is shown in the figure below.
Find the domain and the range.
Answer:
Domain:(∞,-∞)
Step-by-step explanation:
Well, I think this is correct because (-3,3) defines the limit. The parabola shows that there are infinite ranges of values within it. It is pretty much straightforward. All values must fit in from (-3,∞) to (-∞,3)
let me know if im wrong im just refreshing my thinking process at this moment.
can someone problem solve a side of a square?
Answer:
yeah
Step-by-step explanation:
give me the pic and ill solve
the area of the square is 144 square meters. the length is 12 m
How do you solve this? I know the formula is y=mx+b
Answer:
put it in the formula
Step-by-step explanation:
What is the ratio of cats to pumpkins? What is the ratio of pumpkins to cats? Write
your answer in three different ways in the simplest form.
Please Help me I don't understand :)
Answer:
There is 1 cat to 3 pumpkins
1 : 3
1 to 3
[tex]\( \displaystyle \frac{1}{3} \)[/tex]
Step-by-step explanation:
A ratio says how much of one thing there is compared to another thing.
There are 2 cats and 6 pumpkins, so we say:
"There are 2 cats to 6 pumpkins"
Ratios can be shown in different ways:
Use the ":" to separate the values: 2 : 6
Use the word "to": 2 to 6
[tex]\textsf{write it like a fraction}:\ \( \displaystyle \frac{2}{6} \)[/tex]
This ratio can be reduced to its simplest form by divide both numbers by 2. So the ratio in its simplest form is:
There is 1 cat to 3 pumpkins
1 : 3
1 to 3
[tex]\( \displaystyle \frac{1}{3} \)[/tex]
A football player runs 80 yards in 25 seconds. If he maintains the same rate of speed, how far could he run in 60 seconds?
Answer:
192 would be your answer.