Answer:
[tex]g(x) = \frac{-2}{x-1}+5\\\\[/tex]
The graph is shown below.
=========================================================
Explanation:
Notice that if we multiplied the denominator (x-1) by 5, then we get 5(x-1) = 5x-5.
This is close to 5x-7, except we're off by 2 units.
In other words,
5x-7 = (5x-5)-2
since -7 = -5-2
Based on that, we can then say,
[tex]g(x) = \frac{5x-7}{x-1}\\\\g(x) = \frac{5x-5-2}{x-1}\\\\g(x) = \frac{(5x-5)-2}{x-1}\\\\g(x) = \frac{5(x-1)-2}{x-1}\\\\g(x) = \frac{5(x-1)}{x-1}+\frac{-2}{x-1}\\\\g(x) = 5+\frac{-2}{x-1}\\\\g(x) = \frac{-2}{x-1}+5[/tex]
This answer can be reached through alternative methods of polynomial long division or synthetic division (two related yet slightly different methods).
-------------------------
Compare the equation [tex]g(x) = \frac{-2}{x-1}+5\\\\[/tex] to the form [tex]g(x) = \frac{a}{x-h}+k\\\\[/tex]
We can see that
a = -2h = 1k = 5The vertical asymptote is x = 1, which is directly from the h = 1 value. If we tried plugging x = 1 into g(x), then we'll get a division by zero error. So this is why the vertical asymptote is located here.
The horizontal asymptote is y = 5, which is directly tied to the k = 5 value. As x gets infinitely large, then y = g(x) slowly approaches y = 5. We never actually arrive to this exact y value. Try plugging in g(x) = 5 and solving for x. You'll find that no solution for x exists.
The point (h,k) is the intersection of the horizontal and vertical asymptote. It's effectively the "center" of the hyperbola, so to speak.
The graph is shown below. Some points of interest on the hyperbola are
(-1,6)(0,7) .... y intercept(1.4, 0) .... x intercept(2, 3)(3, 4)Another thing to notice is that this function is always increasing. This means as we move from left to right, the function curve goes uphill.
Help me with this question. Question linked
Answer:
The value of B is 5.
As you can see, the graph f(x) is shifted down 4 units.
And, the graph g(x) is shifted up 5 units.
the "b" value represents the number of unit a graph/function is shifted up or down.
Let me know if this helps!
2. In a 100m race, Luke was 2m ahead of Azam. Chandra was 3m behind Luke, Maggie was 7m ahead of Chandra. Luke was 5m behind Darren. Who was in the first place?
Answer:
luke won
Step-by-step explanation:
he is 2 meters ahead of azam witch is in 2dn place
You have 576 feet of fencing to enclose a rectangular plot of land. Find the dimensions of the rectangular plot that would maximize the area. List the smaller number first.
Answer:
The dimension that maximizes area is 144ft by 144ft
Step-by-step explanation:
Given
[tex]P = 576[/tex] -- perimeter
Required
The dimension that gives maximum area
Perimeter is calculated as:
[tex]P= 2 * (L + W)[/tex]
So, we have:
[tex]2 * (L + W) = 576[/tex]
Divide through by 2
[tex]L + W = 288[/tex]
Make L the subject
[tex]L = 288 -W[/tex]
Area is calculated as:
[tex]A = L * W[/tex]
Substitute [tex]L = 288 -W[/tex]
[tex]A = (288 - W) * W[/tex]
Open bracket
[tex]A = 288W - W^2[/tex]
Differentiate A with respect to W
[tex]A' = 288 - 2W[/tex]
Set to 0 to calculate W
[tex]288 - 2W = 0[/tex]
Collect like terms
[tex]2W = 288[/tex]
Divide by 2
[tex]W = 144[/tex]
Recall that:
[tex]L = 288 -W[/tex]
[tex]L = 288 - 144[/tex]
[tex]L = 144[/tex]
b) Use Greens theorem to find∫x^2 ydx-xy^2 dy where ‘C’ is the circle x2 + y2 = 4 going counter clock wise.
It looks like the integral you want to find is
[tex]\displaystyle \int_C x^2y\,\mathrm dx - xy^2\,\mathrm dy[/tex]
where C is the circle x ² + y ² = 4. By Green's theorem, the line integral is equivalent to a double integral over the disk x ² + y ² ≤ 4, namely
[tex]\displaystyle \iint\limits_{x^2+y^2\le4}\frac{\partial(-xy^2)}{\partial x}-\frac{\partial(x^2y)}{\partial y}\,\mathrm dx\,\mathrm dy = -\iint\limits_{x^2+y^2\le4}(x^2+y^2)\,\mathrm dx\,\mathrm dy[/tex]
To compute the remaining integral, convert to polar coordinates. We take
x = r cos(t )
y = r sin(t )
x ² + y ² = r ²
dx dy = r dr dt
Then
[tex]\displaystyle \int_C x^2y\,\mathrm dx - xy^2\,\mathrm dy = -\int_0^{2\pi}\int_0^2 r^3\,\mathrm dr\,\mathrm dt \\\\ = -2\pi\int_0^2 r^3\,\mathrm dr \\\\ = -\frac\pi2 r^4\bigg|_{r=0}^{r=2} \\\\ = \boxed{-8\pi}[/tex]
Use the substitution methed to solve the system of equations. Choose the correct ordered pair.
2y+5x=13
2y+3x=5
Solve both equations for 2y :
2y + 5x = 13 ==> 2y = 13 - 5x
2y + 3x = 5 ==> 2y = 5 - 3x
Solve for x :
13 - 5x = 5 - 3x
8 = 2x
x = 4
Solve for y :
2y = 13 - 5×4
2y = -7
y = -7/2
As an ordered pair, the solution is then the point (x, y) = (4, -7/2).
50T Q12 A man wants to buy bags of gravel to cover his driveway. He decides to work out the area of his driveway. 1 bag of gravel covers 14m2 3m Sketch of driveway Not to scale 3m 8m 6m What is the area of his driveway? How many bags of gravel must he buy?
Answer:
hi amki nai patajjdkfkejd
solve the equation
0.09w+1.8
Step-by-step explanation:
0.09w + 1.8 = 0
0.09w = 0 - 1.8
0.09w = - 1.8
0.09w ÷ 0.09 = - 1.8/ 0.09
w = - 20
please Help with my area math question. I don't remember how to do it. multiply or add? and what is the answer to this?
Answer:
100 inches^3
Step-by-step explanation:
The volume of the back rectangle is
V = l*w*h
V = 8*5*1 = 40 inches ^3
The volume of the front rectangle is
V = 6*2*5 = 60 inches^3
Add the volumes
40+60 = 100 inches^3
Find the equation of a line that is perpendicular to x+y=8 and passes through the point (8, 10).
Answer:
Y = -x + 2
Step-by-step explanation:
y = -x + 8
y = 1x + b
10 = 8 + b
b = 2
Answer:
y-y1=m(x-x1)
y-10=8(x-8)
y-10=8x-64
y-10+64-8x
y+54-8x
y-8x+54
At a Noodles & Company restaurant, the probability that a customer will order a nonalcoholic beverage is .50. Find the probability that in a sample of 14 customers, at least 7 will order a nonalcoholic beverage
For each customer, there are only two possible outcomes. Either they will order an alcoholic beverage, or they will not. The probability of a customer ordering an alcoholic beverage is independent of any other customer, which means that the binomial probability distribution is used to solve this question..
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
At a Noodles & Company restaurant, the probability that a customer will order a nonalcoholic beverage is .50
This means that [tex]p = 0.5[/tex]
Sample of 14 customers
This means that [tex]n = 14[/tex]
Probability that at least 7 will order a nonalcoholic beverage
This is:
[tex]P(X \geq 7) = 1 - P(X < 7)[/tex]
In which
[tex]P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)[/tex]
Then
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{14,0}.(0.5)^{0}.(0.5)^{14} = 0.0001[/tex]
[tex]P(X = 1) = C_{14,1}.(0.5)^{1}.(0.5)^{13} = 0.0009[/tex]
[tex]P(X = 2) = C_{14,2}.(0.5)^{2}.(0.5)^{12} = 0.0056[/tex]
[tex]P(X = 3) = C_{14,3}.(0.5)^{3}.(0.5)^{11} = 0.0222[/tex]
[tex]P(X = 4) = C_{14,4}.(0.5)^{4}.(0.5)^{10} = 0.0611[/tex]
[tex]P(X = 5) = C_{14,5}.(0.5)^{5}.(0.5)^{9} = 0.1222[/tex]
[tex]P(X = 6) = C_{14,6}.(0.5)^{6}.(0.5)^{8} = 0.1833[/tex]
So
[tex]P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) = 0.0001 + 0.0009 + 0.0056 + 0.0222 + 0.0611 + 0.1222 + 0.1833 = 0.3954[/tex]
[tex]P(X \geq 7) = 1 - P(X < 7) = 1 - 0.3954 = 0.6046[/tex]
0.6046 = 60.46% probability that at least 7 will order a nonalcoholic beverage.
For more on the binomial distribution, you can check https://brainly.com/question/15557838
Fill in the blank by performing the indicated elementary row operation(s).
6
1
5
-6R2+R
1
-5
0
Answer 7 Points
Keybo
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Prev
In this question, we are given a matrix, and we have to perform the given operation.
The matrix is:
[tex]\left[\begin{array}{ccc}6&-1&|5\\1&-5&|0\end{array}\right][/tex]
The following operation is given:
[tex]R_1 \rightarrow -6R_2 + R_1[/tex]
In which [tex]R_1[/tex] is the element at the first line and [tex]R_2[/tex] is the element at the second line.
Updating the first line:
[tex]R_{1,1} = -6*1 + 6 = 0[/tex]
[tex]R_{1,2} = -6*-5 - 1 = 30 - 1 = 29[/tex]
[tex]R_{1,3} = -6*0 + 5 = 5[/tex]
Thus, the filled matrix will be given by:
[tex]\left[\begin{array}{ccc}0&29&|5\\1&-5&|0\end{array}\right][/tex]
For another example where row operations are applied on a matrix, you can check https://brainly.com/question/18546657
Which equation can be used to find the length of Line segment A C?
Answer:
I don't see the problem.
Step-by-step explanation:
In the figure alongside, show that angle(a+b+c+d) = 4 right angles
Answer:
Proved
Step-by-step explanation:
a=180-x
c=a= 180-x
d=180-a = 180-(180-x) =x
b=d=x
adding every angle;
a+b+c+d= 180-x + x + 180-x + x
a+b+c+d = 180+180 = 360
a+b+c+d = 4 *90
The sum of the interior of the quadilateral is equal to 4 right angles.
The point where two lines meet is known as an angle
The given figure is a quadrilateral.
For the quadrilateral
The sum of opposite angles is 180degreesThe sum of all the interior angles is 360degreesAccording to the theorem;
a + c = 180 ...... 1
b + d = 180 ...... 2
Add both equations
a + b + c + d = 180 + 180
a + b + c + d = 360
Note that 1 right angle = 90degrees
4 right angles = 4(90) = 360 degrees
Therefore a + b + c + d = 4 right angles (Proved)
Learn more here: https://brainly.com/question/19546787
Below is a geometric sequence. 3, 9, 27, 51, ... (b) what is the common raters if the geometric sequence?
Find the measures of angles S and T in the triangle below.
which of these figures has rotational symmetry
9514 1404 393
Answer:
A
Step-by-step explanation:
The parallelogram has rotational symmetry of degree 2. It looks the same after rotation by 180°.
_____
Additional comment
When a figure only looks like itself after a full rotation of 360°, it is said to have rotational symmetry of degree 1. All of the figures here will return to their original appearance after one 360° rotation. So, we assume the intent of the question is to identify figures with a rotational symmetry of degree greater than 1.
Assume that the matrices below are partitioned conformably for block multiplication. Compute the product.
[I 0] [W X]
[K I] [Y Z]
Multiplying block matrices works just like multiplication between regular matrices, provided that component matrices have the right sizes.
[tex]\begin{bmatrix}\mathbf I&\mathbf 0\\\mathbf K&\mathbf I\end{bmatrix}\begin{bmatrix}\mathbf W&\mathbf X\\\mathbf Y&\mathbf Z\end{bmatrix} = \begin{bmatrix}\mathbf{IW}+\mathbf{0Y}&\mathbf{IX}+\mathbf{0Z}\\\mathbf{KW}+\mathbf{IY}&\mathbf{KX}+\mathbf{IZ}\end{bmatrix}[/tex]
[tex]\begin{bmatrix}\mathbf I&\mathbf 0\\\mathbf K&\mathbf I\end{bmatrix}\begin{bmatrix}\mathbf W&\mathbf X\\\mathbf Y&\mathbf Z\end{bmatrix} = \begin{bmatrix}\mathbf W+\mathbf 0&\mathbf X+\mathbf 0\\\mathbf{KW}+\mathbf Y&\mathbf{KX}+\mathbf Z\end{bmatrix}[/tex]
[tex]\begin{bmatrix}\mathbf I&\mathbf 0\\\mathbf K&\mathbf I\end{bmatrix}\begin{bmatrix}\mathbf W&\mathbf X\\\mathbf Y&\mathbf Z\end{bmatrix} = \begin{bmatrix}\mathbf W&\mathbf X\\\mathbf{KW}+\mathbf Y&\mathbf{KX}+\mathbf Z\end{bmatrix}[/tex]
(I assume I is the identity matrix and 0 is the zero matrix.)
Álgebra 2 need help
Answer:
first term = -1/5
I cant see part b (sorry its too blurry)
thirteenth term = -0.2
part d: -19a/95a -0.2a
Step-by-step explanation:
socratic
Draw a frequency polygon for the following data:
Marks
0 - 10
10 - 20 20 - 30 30 - 40 40 - 5050 - 60
错误。
No. of Students
7
15
22
30
16
10
Answer:
See attachment
Step-by-step explanation:
Given
[tex]\begin{array}{ccccccc}{Marks} & {0-10} & {10-20} & {20-30} & {30-40} & {40-50} & {50-60}\ \\ {Students} & {7} & {15} & {22} & {30} & {16} & {10} \ \end{array}[/tex]
Required
The frequency polygon
We have:
[tex]\begin{array}{ccccccc}{Marks} & {0-10} & {10-20} & {20-30} & {30-40} & {40-50} & {50-60}\ \\ {Students} & {7} & {15} & {22} & {30} & {16} & {10} \ \end{array}[/tex]
First, we calculate the midpoint of each class
[tex]\begin{array}{ccccccc}{Midpoint} & {(0+10)/2} & {(10+20)/2} & {(20+30)/2} & {(30+40)/2} & {(40+50)/2} & {(50+60)/2}\ \\ {Students} & {7} & {15} & {22} & {30} & {16} & {10} \ \end{array}[/tex]
[tex]\begin{array}{ccccccc}{Midpoint} & {5} & {15} & {25} & {35} & {45} & {55}\ \\ {Students} & {7} & {15} & {22} & {30} & {16} & {10} \ \end{array}[/tex]
Lastly, we plot the midpoint against the frequency of students (see attachment)
I need help ASAP please
Answer:
5:10
6 (-2,0)
7 (-5,6)
8 (5,3)
9 No, ab=8 CD=6
Step-by-step explanation:
What is the sum of the interior angles of a regular polygon with 5 sides?
A. 1260
B. 180
C. 360
D. 540
Answer:
540 is the ans
Step-by-step explanation:
this is the correct answer
180
Step-by-step explanation:
the measure of interior angles of polygon =180×(n-2)
identify the roots of the equation and the multiplicities of the roots 8(x - 2)³ = 0
Answer:
The root of the equation is 2 with multiplicity 3
Step-by-step explanation:
8(x-2)^3=0
(x-2)^3=0
The root of the equation is 2 with multiplicity 3
What is the volume of the following rectangular prism?
Answer:
44/3
Step-by-step explanation:
V=L*W*H
WH=22/3
V=2*(22/3)
Find the first five terms of the sequence..
Answer:
The Next fiver tems are - 2, -2,-8,-12,-16
Step-by-step explanation:
Answer:
2,-6,2,-6,2
Step-by-step explanation:
a1 = 2
an = -an-1 -4
Let n =2
a2 = -a1 -4 = -2-4 = -6
Let n=3
a3 = -a2 -4 = - (-6) -4 = +6 -4 = 2
Let n = 4
a4 = -a3 -4 = -2 -4 = -6
Let n=5
a5 = -a4 -4 = -(-6) -4 = +6-4 = 2
I purchased a new Apple iPad on Amazon for $249.00. The tax rate is 8.625%. What is the total purchase price of the iPad?
Answer:
270.47625
Step-by-step explanation:
249 is the original price
(249/100) · 8.625 = 21.47625 the tax total
249 + 21.47625 = 270.47625
This graph represents which expression?
Answer:
x >7
Step-by-step explanation:
There is an open circle at 7, which means it cannot equal 7. The line goes to the right
x >7
Please help do in an hour
Answer:
-4
Step-by-step explanation:
a1 = -8
an = an-1 +2
a2 = a1+2 = -8+2 = -6
a3 = a2+2 = -6+2 = -4
find the measure of a
Answer:
Hello,
answer D 48°
Step-by-step explanation:
In the right triangle down, a+42°=90° ==> a=90°-42°=48°
PLEASE HELP
Solve the equation for y. Identify the slope and y-intercept then graph the equation.
2y-3x=10
Y=
M=
B=
Please Include a picture of the graph and show your work if you can
Hey there! I'm happy to help!
Here is our equation.
[tex]2y-3x=10[/tex]
Let's add 3x to both sides.
[tex]2y=3x+10[/tex]
Divide both sides by 2.
[tex]y=\frac{3}{2}x+5[/tex]
Here is slope intercept form.
[tex]y=mx+b\\m=slope\\b=y-intercept[/tex]
So, we can just find those two things in the equation, and here are our answers.
[tex]y=\frac{3}{2}x+5\\m=\frac{3}{2}\\b=5[/tex]
The graph is down below. If our y-intercept is 5, then one of our points is (0,5). You can then plug a random x-value into the formula to find another point and then draw the line going through the two points.
[tex]y=\frac{3}{2}(2)+5\\y=3+5\\y=8\\(2,8)[/tex]
Have a wonderful day and keep on learning! :D
please help me with geometry
Answer:
A. If the side lengths are the same, then a triangle is not scalene.
Step-by-step explanation:
A triangle can be defined as a two-dimensional shape that comprises three (3) sides, three (3) vertices and three (3) angles.
Simply stated, any polygon with three (3) lengths of sides is a triangle.
In Geometry, a triangle is considered to be the most important shape.
Generally, there are three (3) main types of triangle based on the length of their sides and these include;
I. Equilateral triangle: it has all of its three (3) sides and interior angles equal.
II. Isosceles triangle: it has two (2) of its sides equal in length and two (2) equal angles.
III. Scalene triangle: it has all of its three (3) sides and interior angles different in length and size respectively.