Answer:
y=-ax(x-500)^2(x-1000)
Step-by-step explanation:
While flying at an altitude of 1.5 km, a plane measures angles or depression to opposite ends of a large crater, shown in the image below. Find the width of the crater
Check the picture below.
notice the alternate interior angles in the picture.
[tex]\bf tan(68^o)=\cfrac{\stackrel{opposite}{1.5}}{\stackrel{adjacent}{x}}\implies x=\cfrac{1.5}{tan(68^o)}\implies x\approx 0.61 \\\\[-0.35em] ~\dotfill\\\\ tan(56^o)=\cfrac{\stackrel{opposite}{1.5}}{\stackrel{adjacent}{w}}\implies w=\cfrac{1.5}{tan(56^o)}\implies w\approx 1.01 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{\textit{width of the crater}}{x+w\implies 1.62}~\hfill[/tex]
The width of the crater is 1.61 km.
Given that:Plane is flying at altitude of 1.5 km
The angle of depressions to point A = 68 degrees/
The angle of depression to point B = 56 degrees.
Calculations:In the given diagram below, we can see:
Angle XPD is right angle and thus we have:
[tex]\angle APD + \angle APX = 90\\\angle APD = 180 - \angle APX = 90 - 68 = 22^\circ[/tex]
Similarly, Angle YPD is right angle and thus:
[tex]\angle DPB + \angle BPY = 90\\\angle DPB = 90 - \angle BPY = 90 - 56 = 34^\circ[/tex]
Since the triangle ADP and triangle PDB are right angled triangles, thus we have by trigonometric ratios:
[tex]tan(22) = \dfrac{AD}{PD}\\\\0.404 \times 1.5 = AD\\\\AD = 0.606\: \rm km[/tex]
Similarly,
[tex]tan(34) = \dfrac{BD}{PD}\\\\0.674 \times 1.5 = BD\\\\BD = 1.01 \: \rm km[/tex]
The width of the crater = AD + DB = 1.01 km + 0.606 km = 1.61 km
Thus, width of the crater is 1.61 km.
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RACTICL
n set
1. How much interest is earned in 9 months on a deposit of
$7000 at 8 percent simple interest?
Answer:
$420
Step-by-step explanation:
Principal = $7000
Rate = 8%
Time = 9 months
9 months = 3/4 or 0.75 of a year
Simple Interest = Principal * Rate * Time ÷ 100
= $7000 * 8% * 0.75 ÷ 100
= $420
The sum of a number and two is equal to eight
Answer:
I'm pretty sure if you subtract 2 from eight you will find the answer of 6 i'm not sure if that question was implying this answer but I hope this helps
Step-by-step explanation:
What is the domain of the relation graphed below?
A. domain:{-5, -4,-3, -2,0, 1, 2, 3, 4, 5}
B. domain:{-3, -2,0, 1,4}
C. domain:{-5, -4,-3, 1, 2,5)
D. domain:{(-5, 0), (-4, 1), (-3, 4), (1, -2), (2, 4), (5, -3)}
Answer:
C. (-5,-4,-3,1,2,5) From the graph we can see the following points first come x-axis and Y-axis like (x, y). From graph we can see 6 points they are (-5,6),(-4,1),(-3,4),(2,4),(1,-2),(5,-3) Here the first no. is the domain like in (-5,6). -5 is domain and 6 is range so all the first no. of the points is in option C so it is the domain.
HI PLS HELP ITS DUE AT 12 AND ITS 11:45 WILL MARK BRAINLIEST
Answer:
Answer = 3.14 * 40 = 125.6m^2
Step-by-step explanation:
Let R be the greater radius and r be the smaller radius
A) Area of the sidewalk = \pi R^2 - \pi r^2 - This can be the expression
B) pi = 3.14
= pi (R^2-r^2)
= pi (11^2-9^2)
= pi (121-81)
= pi *40
That was the simplified expression
Answer = 3.14 * 40 = 125.6m^2
The equation 3x2 = 6x - 9 has two real solutions
True
False
Answer: FALSE
Step-by-step explanation:
The first step is to rewrite the equation in the form [tex]ax^2+bx+c=0[/tex], then:
[tex]3x^2 = 6x - 9\\3x^2-6x +9=0[/tex]
Now, we need to calculate the Discriminant with this formula:
[tex]D=b^2-4ac[/tex]
We can identify in the given equation that:
[tex]a=3\\b=-6\\c=9[/tex]
Then, we only need to substitute these values into the formula:
[tex]D=(-6)^2-4(3)(9)[/tex]
[tex]D=-72[/tex]
Since [tex]D<0[/tex] then the equation has no real solutions.
What is the solution to the inequality below?
x2 < 49
I am going to assume that you mean:
x² < 49
To solve this you must do the opposite of squaring, which would be taking the square root. What you do to one side you must do to the other.
√x² < √49
x < 7
Hope this helped!
~Just a girl in love with Shawn Mendes
Final answer:
To solve the inequality x^2 < 49, we take the square root of both sides resulting in the solution -7 < x < 7, which means x can be any real number between -7 and 7.
Explanation:
The student's question is about solving an inequality involving a square of a variable, specifically x^2 < 49. To solve this inequality, we will first take the square root of both sides, keeping in mind that when we take the square root of a square inequality, we must consider both the positive and negative roots. Therefore, we can express the inequality as -7 < x < 7, since both positive and negative square roots of 49 are 7 and -7, respectively. This represents the range of values for x where the original inequality holds true.
The solution implies that x can take on any real value that is less than 7 and greater than -7. There's no need for tools like completing the square or the quadratic formula here, as the inequality is already in a solvable form.
What is the volume of the composite figure?
Answer: 372in³
Step-by-step explanation:
All we have to do is find the volume of the two separate rectangular prisms and add them up.
First we will find the volume of the standing prism:
5in * 3in * 12in = 180in³
Now the other prism:
12in * 4in * 4in = 192in³
Now add them up:
180in³ + 192in³ = 372in³
Answer:
372 [tex]inches^{3}[/tex]
Step-by-step explanation:
Imagine the figures are each separate. The top figure's dimensions would be L=12 in, W=4 in, and H=4 in. The bottom figure's dimensions would be L=5 in, W=3 in, and H=12 in. So, do the volume formula for each: L x W x H and then add them together.
12 x 4 x 4 = 192 inches^3
5 x 3 x 12 = 180 inches^3
192 + 180 = 372 inches^3
What are the solutions of the quadratic equation
4x2 - 30x + 45 = 0
Answer:
Step-by-step explanation:
note :
the discriminat of each quadratic equation : ax²+bx+c=0 ....(a ≠ 0) is :
Δ = b² -4ac
1 ) Δ > 0 the equation has two reals solutions : x = (-b±√Δ)/2a
2 ) Δ = 0 : one solution : x = -b/2a
3 ) Δ < 0 : no reals solutions
in this exercice : 4x²-30x+45=0
a= 4 b= -30 c=45
Δ = (-30)² - 4(4)(45) = 900 - 720 = 180.......continu
what is the value of y
Answer:
B y=54 degrees
Step-by-step explanation:
Since a triangle's angles always add up to 180.
180-72=108
108/2=54
It must be divided by two because y is two angles not one.
Given the following functions f(x) and g(x), solve f over g (−5) and select the correct answer below:
f(x) = 2x − 20
g(x) = x − 1
−5
5
one sixth
30
=====================================================
Plug x = -5 into f(x)
f(x) = 2x-20
f(-5) = 2(-5) - 20
f(-5) = -10-20
f(-5) = -30
Then plug x = -5 into g(x)
g(x) = x-1
g(-5) = -5-1
g(-5) = -6
Divide the two results
(f/g)(-5) = f(-5)/g(-5)
(f/g)(-5) = (-30)/(-6)
(f/g)(-5) = -5
For this case we have the following functions:
[tex]f (x) = 2x-20\\g (x) = x-1[/tex]
We must find [tex]\frac {f (-5)} {g (-5)}[/tex], then:
We have in mind that:
[tex]+ * - = -[/tex]
Equal signs are added and the same sign is placed.
[tex]\frac {f (-5)} {g (-5)} = \frac {2 (-5) -20} {- 5-1} = \frac {-10-20} {- 6} = \frac {-30} {- 6} = 5[/tex]
Answer:
5
Liesl grew 7/12 of a foot in one year. Her little sister grew 1/3 of a foot during that same year. How much more did Liesl grow than her little sister did
Answer:
The answer to this is 0.25
Step-by-step explanation:
7/12= 0.58333 repeating, and 1/3 is 0.3333 repeating. When you subtract 7/12 from 1/3 you get 0.25
Hope it helps
Answer:
0.25
Step-by-step explanation:
How is the equation of this circle written in standard form?
x2 + y2 - 6x + 14y = 142
A)
(x - 3)2 + (y + 7)2 = 200
B)
(x+ 3)2 + (y - 7)2 = 200
(x - 6)2 + (y + 14)2 = 142
D)
(x+6)2 + (y- 14)2 = 142
Answer:
A
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius.
To obtain this form use the method of completing the square.
Given
x² + y² - 6x + 14y = 142
Collect the x and y terms together
x² - 6x + y² + 14y = 142
add (half the coefficient of both x and y terms )² to both sides
x² + 2(- 3)x + 9 + y² + 2(7)y + 49 = 142 + 9 + 49
(x - 3)² + (y + 7)² = 200 → A
Which statement is false ?
Answer:
B
Step-by-step explanation:
Create a dot plot for the data in the table. Hover over each number on the number line. Then click
and drag up to create the dots.
To create a dot plot, you draw a number line from the smallest to the largest value in your dataset. Then, for each number in the dataset, mark a dot above the corresponding number on the line. If a number occurs more than once, stack the dots.
Explanation:Creating a dot plot for a set of data on a number line involves the following steps:
identify the lowest and the highest values in your dataset. These values will define the extents of your number line.Create the number line starting from the smallest value to the largest value.For each number in the dataset, place a dot above the corresponding number on the number line. If a number occurs more than once, you stack the dots vertically.Unfortunately, as this is a text-based platform, it's impossible to hover over the numbers and drag to create a dot plot interactively. This instruction seems to be meant for a specific interactive software or online tool.
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tell whether the graph of the equation is a horizontal or a vertical line. Explain your choice.
y=-1
Answer:
horizontal line
Step-by-step explanation:
The equation of a horizontal line parallel to the x- axis is
y = c
where c is the value of the y- coordinates the line passes through.
The equation of a vertical line parallel to the y- axis is
x = c
where c is the value of the x- coordinates the line passes through.
Hence
y = - 1 is a horizontal line passing through all points with a y- coordinate - 1
Find the product.
(n 3)2 · (n 5)4
For this case we must find the product of the following expression:
[tex](n ^ 3) ^ 2 * (n ^ 5) ^ 4[/tex]
By definition of power properties we have to:
[tex](a ^ n) ^ m = a ^ {n * m}[/tex]
Rewriting the expression we have:
[tex]n ^ 6 * n ^ {20} =[/tex]
By definition of multiplication of powers of the same base, we put the same base and add the exponents:
[tex]n^{6 + 20} =\\n^{26}[/tex]
Answer:
[tex]n^{26}[/tex]
Answer:
n^26
Step-by-step explanation:
2(n-1)+4n=2(3n-1)
n=0
no solution
infinitely many solutions
n= - 4
HELP PLEASE!!!!!!!
Answer:
Infinitely many solutions.
Step-by-step explanation:
2 (n - 1) + 4n = 2 (3n - 1) Let's simplify this to solve it.
2n - 2 + 4n = 6n - 2 Distribute 2(n-1) and 2(3n-1)
2n + 4n - 2 = 6n - 2 Rearrange the left side of the equation.
6n - 2 = 6n - 2 Add 2n + 4n.
-6n -6n Subtract 6n from both sides.
-2 = -2? Yes, -2 equals -2.
Therefore, the answer is infinitely many solutions, meaning that n can be any real number.
An equation can have no solution, one solution or infinitely many solutions.
The equation [tex]2(n -1) + 4n = 2(3n - 1)[/tex] has infinitely many solutions
Given that:
[tex]2(n -1) + 4n = 2(3n - 1)[/tex]
Open brackets
[tex]2n -2 + 4n = 6n - 2[/tex]
Collect like terms
[tex]2n + 4n - 6n= - 2+2[/tex]
[tex]0 = 0[/tex]
When the solution to an equation is 0 on both sides, the equation has infinitely many solutions
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the number line below represents the solution to which inequality?
<--|--|--|--|--|--O--|--|--|--|--|--|--|--|--|-->
__ -6__-4__-2 __0 __2 __4 __6
(Filled circle)
(Arrow pointing left from -2)
F. -2x + 7 > 8
_
G. 7x + 11 < 4
_
H. 6x - 9 < -21
_
J. -3x -15 < -27
_
The number line represents the solution to the inequality -2x + 7 > 8, and the solution is x < -0.5.
Explanation:The filled circle and the arrow pointing left on the number line indicate that the solution to the inequality is to the left of -2.
The inequality that represents this solution is -2x + 7 > 8.
To solve this inequality, we can subtract 7 from both sides to isolate the x variable.
This gives us -2x > 1. Finally, we divide both sides of the inequality by -2, remembering that when we divide by a negative number, the inequality sign flips.
So, the solution to the inequality is x < -0.5.
Thus, Correct option for the given number line is F. -2x + 7 > 8.
Final answer:
The number line indicates the solution to the inequality H. 6x - 9 < -21, where x < -2, including -2 (since the circle is filled). The solution matches the given number line plot.
Explanation:
The number line given indicates the solution to an inequality that includes all numbers to the left of – the filled circle on –2, which means –2 is included in the solution set. This represents an inequality that is of the form x ≤ a where a is –2 in this case. Now let's analyze each of the provided inequalities.
F. -2x + 7 > 8: Solving this we get –x > 1 or x < –1, which does not match the plot.
G. 7x + 11 < 4: Solving this inequality we get x < –1, which also is not a match.
H. 6x - 9 < -21: Resolving this inequality leads to x < –2, which matches the number line.
J. -3x - 15 < -27: Solving this we get x > 4, which is incorrect as per the number line plot.
Therefore, the correct inequality is H. 6x - 9 < -21.
blank CDs come in spindles of 25 or 60. Rachel needs 230 blank CDs for her eighth grade science class. how many spindles of each amount should she buy?
The answer is:
She needs to buy 3 spindles of 60 CDS and 2 spindles of 25 CDs.
Why?We know that the possibilities will depend always on how many CDs contain each type of spindles.
There is only one possible combination of spindles that can give the exact amount of CDs needed.
Let's try to find the combinations:
- First combination: With 1 spindle of 60 CDs:
[tex]Spindles_{25}=\frac{TotalCDs-NoOfSpindles_{60}}{25} \\\\Spindles_{25}=\frac{230-60}{25}=\frac{170}{25}=6.8Spindles[/tex]
Since the result is not a whole number, we know that the first combination does not work.
- Second combination: With 2 spindles of 60 CDs:
[tex]Spindles_{25}=\frac{TotalCDs-NoOfSpindles_{60}}{25} \\\\Spindles_{25}=\frac{230-(2)*60}{25}=\frac{110}{25}=4.4Spindles[/tex]
Since the result is not a whole number, we know that the second combination does not work.
- Third combination: With 3 spindles of 60 CDs:
[tex]Spindles_{25}=\frac{TotalCDs-NoOfSpindles_{60}}{25} \\\\Spindles_{25}=\frac{230-(3)*60}{25}=\frac{230-180}=\frac{50}{25}=2Spindles[/tex]
Since the result is a whole number, we know that the third combination works.
Hence, the combination will be:
[tex]TotalCDs=3Spindles_{60}+2Spindles_{25}=3*60+2*25=180+50=230[/tex]
She needs to buy 3 spindles of 60 CDs and 2 spindles of 25 CDs.
Have a nice day!
Answer:2 of 25 cds 3 of 60 cds
Step-by-step explanation:
1. 3x60=180
2.2×25=50
3. So for science class she needs quality 2 of 25
4. Quality of 3 of 60
So there u go
more questions for 10 points
To find the midpoint, add the two X values together and divide that by 2 and then add the two Y values together and divide by 2.
X = 8 +3 = 11 /2 = 5.5
Y = 5 +7 = 12 /2 = 6
Depending on how you need to answer the midpoint for X could stay the fraction 11/2, or you can divide it and get 5.5
The midpoint is (11/2,6) or (5.5,6)
Answer:
nope
Step-by-step explanation:
Reginald is distributing n boxes of paper to the copy rooms in an office building. If he places 6 boxes of paper in each copy room, there are 7 boxes left over. In order to place 7 boxes of paper in each room, he will need 2 more boxes. How many copy rooms are in the office building?
Answer:
The total number of copy rooms in the building is 9.
Step-by-step explanation:
With the given information we can compute the total number of copy rooms (let's call them r) and the boxes of paper Reginald has to distribute among them (already named n).
From the first arrangement we can see that if reginald gives 6 boxes of paper to each room, he will still have 7 boxes. We can write this as:
[tex]n = 6 \cdot r + 7[/tex]
From the second arrangement we can see that if reginald gives 7 boxes of paper to each room, he would still need 2 boxes. We can write this as:
[tex]n = 7 \cdot r - 2[/tex]
From the above, we have a 2x2 system of equations, which can be solved by any method. In this case, we can use equalization to easily find the number of rooms. From the 2 relations we can write:
[tex]6 \cdot r + 7 = 7 \cdot r - 2[/tex]
Puting known and unknowns on opposite sides, we get:
[tex]7+2 = (7-6) \cdot r [/tex]
Solving we get:
[tex]9 = r[/tex]
Therefor the total number of rooms is 9.
Pluging this solution into any of the 2 equations, we can obtain that the number of boxes of paper is 61.
As a reference, the following link is useful:
https://en.wikipedia.org/wiki/System_of_linear_equations
The number of boxes of paper exists at 61.
How to find the copy rooms in the office building?The whole number of copy rooms as r and the boxes of paper Reginald has to distribute among them (already named [tex]$\mathbf{n}$[/tex] ).
Reginald gives 6 boxes of paper to each room, he will always have 7 boxes. We can write this as:
[tex]$n=6 \cdot r+7$$[/tex]
Reginald shows 7 boxes of paper to each room, he would always require 2 boxes. We can write this as:
[tex]$n=7 \cdot r-2$$[/tex]
From the above equation, we have a [tex]$2 \times 2$[/tex] system of equations, which can be solved in any form. In this issue, we can utilize equalization to easily find the number of rooms.
From the 2 relations we can write:
[tex]$6 \cdot r+7=7 \cdot r-2$[/tex]
Putting known and unknowns on opposite sides, we get:
[tex]$7+2=(7-6) \cdot r$$[/tex]
Solving we get:
[tex]$9=r$$[/tex]
Thus the total number of rooms exists at 9.
Plugging this solution into any of the 2 equations, then we get
The number of boxes of paper exists at 61.
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what is the multiplicative rate of change for the exponential function graphed to the left
Looking at the given points on the right side from (0,2) to (1,6) for 1 increase in X ( 1-0=1) the Y value increases by 3 ( 6/2 = 3)
This same increase happens for th other two points: 18/6 = 3
54 / 18 = 3
The rate of increase is 3.
Which translation transformed the parent function, f(x), to g(x)?
a translation right 2 units
a translation left 2 units
a translation up 2 units
a translation down 2 unit
Answer:
A. A translation right 2 units:
We know that given f(x), the function g(x) = f(x+m), is the same function f(x) but shifted m units to the left. In that sense, a translation right 2 units would be:
g(x) = f(x-2).
B. A translation left 2 units:
We know that given f(x), the function g(x) = f(x+m), is the same function f(x) but shifted m units to the left. In that sense, a translation left 2 units would be:
g(x) = f(x+2).
C. A translation up 2 units:
We know that given f(x), the function g(x) = f(x) + m, is the same function f(x) but shifted m units up. In that sense, a translation up 2 units would be:
g(x) = f(x) + 2
D. A translation down 2 units:
We know that given f(x), the function g(x) = f(x) + m, is the same function f(x) but shifted m units up. In that sense, a translation down 2 units would be:
g(x) = f(x) - 2
Final answer:
The function f(x) translated to g(x) via a translation right 2 units, which shifts the graph of the function 2 units to the right on the x-axis.
Explanation:
The transformation that transformed the parent function, f(x), to g(x) is a translation right 2 units. This is because when the argument of the function f(x) becomes f(x-2), the graph of f(x) is shifted to the right by 2 units along the x-axis. To understand this, let us consider the original function y = f(x).
The graph of the new function y = f(x-2) is the same as the original, but every point on the graph has been moved 2 units to the right. This can also be viewed as if the x-axis (and origin) has shifted 2 units to the left while the graph remains stationary.
Which shows the correct substitution of the values a, b, and c from the equation 0 = 4x2 + 2x – 1 into the quadratic formula below?
Quadratic formula: x =
For this case we have a quadratic equation given by:
[tex]4x ^ 2 + 2x-1 = 0[/tex]
The roots are found by means of the quadratic formula below:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]
Where:
[tex]a = 4\\b = 2\\c = -1[/tex]
So, we have:
[tex]x = \frac {-2 \pm \sqrt {2 ^ 2-4 (4) (- 1)}} {2 (4)}[/tex]
Or in an equivalent way we have:
[tex]x = \frac {-2 \pm \sqrt {2 ^ 2 + 4 (4) (1)}} {2 (4)}[/tex]
Answer:
The correct option will be:
[tex]x = \frac {-2 \pm \sqrt {2 ^ 2-4 (4) (- 1)}} {2 (4)}[/tex]
Answer:
a = 4, b = 2 and c= -1
Step-by-step explanation:
Quadratic formula: x =√[-b ± v(b² - 4ac)]/2a
Here quadratic equation is 4x2 + 2x – 1
a = 4, b = 2 and c= -1
x =[-b ± √(b² - 4ac)]/2a
= [-2 ± √(2² - 4*4*-1)]/2*4
= [-2 ± √(4 + 16)]/8
= [-2 ± √20)]/8
= [-2 ± 2√5)]/8
= [-1 ± √5)]/4
x = [-1 ± √5)]/4
What is the slope-intercept equation of the line below?
T
Answer:
y = mx + b
Step-by-step explanation:
Since there is no illustration, that is all I can give you. I apologize.
Answer:
y=mx +b is the formula
Step-by-step explanation:
I think you are missing a part of the question.
Please help me out brainiest and 30 points
Match each of the four lines with a line that is perpendicular to it.
Choices to pair with the equations are
y=74x+2
y=−65x+1
y=−74x+9
y=−56x−5
y=65x−5
y=−47x+2
y=47x+9
y=56x+1
Answer:
y = (5/6)x - 7
is with
y = - (6/5)x + 1
y = - (5/6)x - 8
is with
y = (6/5)x - 5
y = - (7/4)x - 1
is with
y = (4/7)x + 9
y = (7/4)x - 2
is with
y = - (4/7)x + 2
Step-by-step explanation:
You can double check by dividing -1 by the number before x. The answer from that calculation will be the number before the x of the perpendicular line's equation
pair with their perpendicular equations are
y = (5/6)x - 7y = - (6/5)x + 1
y = - (5/6)x - 8y = (6/5)x - 5
y = - (7/4)x - 1y = (4/7)x + 9
y = (7/4)x - 2y = - (4/7)x + 2
What is condition of perpendicular line?The given line is perpendicular to the required line under the condition of perpendicular lines m1×m2=–1.
As, m1*m2=-1
m1= -1/m2
For first equation
y = (5/6)x - 7
m1= 5/6
So, m2= -1/m2= -6/5
Hence, the equation of perpendicular line is y = - (6/5)x + 1.
Similarly,
y = (5/6)x - 7
m1= 5/6
So, m2= -1/m2= -6/5
Hence, the equation of perpendicular line is y = (6/5)x - 5.
again,
y = - (7/4)x - 1
m1=-7/4
So, m2= -1/m2= 7/4
Hence, the equation of perpendicular line is y = (4/7)x + 9
again,
y = (7/4)x - 2
m1= 7/4
So, m2= -1/m2= -4/7
Hence, the equation of perpendicular line is y = - (4/7)x + 2.
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What are the vertical asymptotes of the function f(x) =5x+5/x2 + x-2
let's recall that the vertical asymptotes for a rational expression occur when the denominator is at 0, so let's zero out this one and check.
[tex]\bf \cfrac{5x+5}{x^2+x-2}\qquad \stackrel{\textit{zeroing out the denominator}~\hfill }{x^2+x-2=0\implies (x+2)(x-1)=0}\implies \stackrel{\textit{vertical asymptotes}}{ \begin{cases} x=-2\\ x=1 \end{cases}}[/tex]
Final answer:
The vertical asymptotes of the function f(x) = (5x+5)/(x² + x - 2) occur where the denominator equals zero. Factoring the denominator, we find the vertical asymptotes to be at x = -2 and x = 1.
Explanation:
The student is asking about the vertical asymptotes of the function f(x) = (5x+5)/(x² + x - 2). To find the vertical asymptotes of a function, we look for values of x where the denominator is equal to zero, because these are the points where the function is undefined and the graph of the function will approach infinity.
To find the vertical asymptotes, set the denominator equal to zero and solve for x:
x² + x - 2 = 0
Factoring the quadratic equation, we get:
(x+2)(x-1) = 0
Therefore, the vertical asymptotes are at x = -2 and x = 1, since these are the values of x for which the denominator becomes zero.
cube root of b to the 27 power
[tex]\sqrt[3]{b^{27}}=\sqrt[3]{(b^9)^3}=b^9[/tex]
vertical angles must check all that apply
Answer:
Vertical angles must have the same vertex and be congruent as well.
Step-by-step explanation:
Answer:
Correct answer is B and C.
Step-by-step explanation:
Vertical angles are those angles opposite each other when two lines intersect. So, they have the same vertex.
When two lines intercept form 4 angles. Those that are opposite to each other are vertical angles, these angles are always congruent.