helpppppppppppppppppppppppp

Answers

Answer 1

The first thing to is factor the denominator of the rational function:
[tex] x^{2} -2x-3[/tex] to do this we'll need to find two number whose product is -3 and its sum is -2; those numbers are 1 and -3, so:
[tex] x^{2} -2x-3=(x+1)(x-3)[/tex]
Now we can rewrite our rational function as follows:
[tex]f(x)= \frac{x-3}{(x+1)(x-3)} [/tex]
Notice that we have a common factor (x-3) in both numerator and denominator; therefore we can cancel them:
[tex]f(x)= \frac{1}{x+1} [/tex]

Taking all the above into consideration we realize that x=3 is a removable discontinuity; the correct answer is the first one: there is a hole in x=3 and asymptote at x=-1.

Related Questions

The two figures are similar. What is the value of the marked angle?

A. 108
B. 72
C. 90
D. 162

Answers

B. 72

When two figures are similar, they always have the same angles.

I think its b

Hope this helps

Find the value of x and the value

A: x=20,y=45
B:x=45,y=20
C:x=60,y=120
D:x=90,y=60

Answers

we have that

[3y°+6y°+2x°+90°]=360°
9y°+2x°=270°

but we know that
2x°=90°------------------ > x=45°
therefore
9y°+2x°=270°--------> 9y°+2(45°)=270°
9y°=270°-90°------------------> y=20°

the answer is
x=45°
y=20°
the option B:x=45°,y=20°

Sara left home and drove East 12 miles to Bakersville for her friends birthday cake then she drove 10 miles south to a friends house how far apart is Sarah's friends house and Sarah's house

Answers

From home to Bakersville Sarah covered 12 miles East, the 10 miles south to her friends.
Therefore, using Pythagoras's theorem The distance from Sarah's home to her friend's house will be;
=√ 12²+10²
= √244
= 15.62 miles

picking a multiple of 5 from the integers between 1 and 40

Answers

Multiples of 5 end in 5 or 0 this would mean
5,10,15,20,25,30,35,40 are all multiples of 5

find the measures of two angles one positive and negative that are coterminal with pi/2

Answers

Answer: The required measures of two angles one positive and negative that are co-terminal with [tex]\dfrac{\pi}{2}[/tex] are [tex]-\dfrac{3\pi}{2}[/tex] and [tex]\dfrac{5\pi}{2}.[/tex]

Step-by-step explanation: We are given to find measures of two angles one positive and negative that are co-terminal with [tex]\dfrac{\pi}{2}.[/tex]

Let x and y represents the positive and negative co-terminal angles respectively.

We know that

the measures of any two co-terminal angles differ from each other by a multiple of [tex]2\pi.[/tex]

So, the values of x and y can be found as follows :

[tex]x=\dfrac{\pi}{2}-2\pi=-\dfrac{3\pi}{4},\\\\\\y=\dfrac{\pi}{2}+2\pi=\dfrac{5\pi}{2}.[/tex]

Thus, the required measures of two angles one positive and negative that are co-terminal with [tex]\dfrac{\pi}{2}[/tex] are [tex]-\dfrac{3\pi}{2}[/tex] and [tex]\dfrac{5\pi}{2}.[/tex]

Final answer:

The positive coterminal angle with π/2 is 5π/2, and the negative coterminal angle is -3π/2; both angles are found by adding and subtracting 2π radians from the original angle.

Explanation:

To find the measures of two angles, one positive and one negative, that are coterminal with π/2, we need to add and subtract 2π (360 degrees) to the original angle since the angles are coterminal when they share the same initial and terminal sides and differ by a full circle (360 degrees) or a multiple thereof. The angle π/2 radians is equivalent to 90 degrees, so adding 2π radians (360 degrees) gives us a positive coterminal angle, and subtracting 2π radians (360 degrees) gives us a negative coterminal angle.

Positive coterminal angle: π/2 + 2π = 5π/2.

Negative coterminal angle: π/2 - 2π = -3π/2.

Tara and julia run a race. Julia takes 42 seconds to run the race. She is 7 seconds faster than Tara. How many seconds does Tara take?

Answers

Yard takes 35 seconds to run the race.

42 - 7 is 35, so 35 seconds is the answer

can anyone give an explanation and answer to this question,my sister needed help on this also :) Thank you again for taking your time to answer and read this <3

what is the circumference of a circular pond with a radius of 14 meters?

Answers

You are given the radius which is the distance from a side of the circle to its center. This length is 14.
The circumference of a circle is calculated by 2πr
2π14 2*14=28
So it can be either 28π or you can take the first digits of π which are 3.1415 and multiply that by 28
28*3.1415= 87.96
Therefore you end up with 2 different answers...
87.96 or 28π

Can you solve the measure of an angle is twenty-nine times the measure of a supplementary angle. what is the measure of each angle

Answers

Hello,

Let's assume A the measure of the angle,
180-A the supplementary angle

A=29*(180-A)

A=29*180 -29A

30A=29*180

A=29*180/30
A=29*6
A=174

Proof: 174=29*(180-174)

how many triangles have the following measurements? A=38, a=432, b=382

Answers

There is only one such triangle.

_____
You know this because the given angle is opposite the longest given side. You only have ambiguous cases if the given angle is opposite the shorter of two given sides.

Using the Law of Sines, we determined that it is possible to form one triangle with the given measurements A=38°, a=432, and b=382. The calculation includes finding angle B and angle C, ensuring all triangle conditions are met.

To determine how many triangles can have the given measurements (A=38°, a=432, b=382), we need to check if these values satisfy the triangle inequalities and if they can form a possible triangle using the Law of Sines.

First, let's use the Law of Sines which states that:

sin(A)/a = sin(B)/b = sin(C)/c

Given:

A = 38° (angle)a = 432 (side opposite to angle A)b = 382 (side opposite to angle B)

We can calculate angle B using:

sin(B) = (b × sin(A)) / a

sin(B) = (382 × sin(38°)) / 432 ≈ 0.556

Finding the arc sine of 0.556, we get:

B ≈ 33.8°

Now, we find angle C:

C = 180° - A - B ≈ 180° - 38° - 33.8° = 108.2°

Using the Law of Sines again to find side c:

c = (a × sin(C)) / sin(A)

c = (432 × sin(108.2°)) / sin(38°) ≈ 676.85

Thus, it's possible to form one such triangle with the given conditions.

10 POINTS AND BRAINLIEST FOR CORRECT ANSWER!

A rectangle is inscribed in a square so that each vertex of the rectangle is located on one side of the square, and the sides of the rectangle are parallel to the diagonals of the square. Suppose that one side of the rectangle is twice the length of the other and that the diagonal of the square is 12 meters long. Find the sides of the rectangle.

Answers

9514 1404 393

Answer:

The sides of the rectangle are 4 and 8 meters long.

Explanation:

Please consider the attached figure. Both the rectangle and the square are symmetrical about the x- and y-axes, so we only need to consider the corner of the rectangle in one quadrant.

If the rectangle is twice as long as wide, then the distance of the corner to one axis (we chose y) will be twice the distance to the other axis. The locus of points for which that is true is the line with slope 1/2. The corner of the rectangle will be on that line.

If the corner of the rectangle is also on the square, then it will be located at the point of intersection of the line with slope 1/2 and the line representing the edge of the square. That point of intersection is the point (4, 2) on this graph. That is, half the length of the rectangle is 4 m, and half the width is 2 m. This indicates the sides of the rectangle are 8 m and 4 m in length.

The diagonals of the square are 12 m long, so orienting the square the way we have makes the x- and y-intercepts 6 units from the origin in each quadrant.

Answer:

Step-by-step explanation:

four and eight, use soh cah toa

If the radius of a circle is 18 yd, then the diameter of the circle is 9 yd
TRUE OR FALSE

Answers

FALSE because i pretty sure its 3

Answer:

Step-by-step explanation: False.

Please help! The question is attached. And also I know the numbers on the triangle are blurry. The number on the long bottom of the triangle is 24, the one in the corner of the bottom of the triangle is 90 degrees, the side length is 18, and the diagonal angle is 26.

Answers

If the legs of the triangle are what you say, there is no correct answer. The sin(θ) function is the ratio of the opposite side to the hypotenuse. In this case that's 18/26. Are you sure the opposite side length is not 10? It kinda looks like a 10 and that would make choice B correct.

What's the difference between residential heating and cooling systems and commercial/industrial heating, cooling, or refrigerating facilities? A. The amount of energy the building or facility uses B. The location of the system—in a home or a business C. The number of people that occupy the building or facility D. The size of the building or facility

Answers

c i believe is the answer

How can one 1/4x − 3 = 1/2x + 8 be set up as a system of equations?

a. 4y + 4x = −12
2y + 2x = 16

b.4y − x = −12
2y − x = 16

c.4y + x = −12
2y + x = 16

d.4y − 4x = −12
2y − 2x = 16

Answers

You can set y = to each side of the equation, then multiply by the denominator and put into standard form.

Left side:
.. y = 1/4x -3
.. 4y = x -12 . . . . multiply by 4
.. 4y -x = -12 . . . subtract x

Right side:
.. y = 1/2x +8
.. 2y = x +16 . . . multiply by 2
.. 2y -x = 16 . . . subtract x

These equations correspond to selection B.

Are the two expressions equivalent when x = 20?

8(12x + 4)

96x + 32

Answers

The solution of the two expressions for x = 20 will be equivalent.

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the two expressions are 8(12x + 4) and 96x + 32. The expressions will be solved as,

8(12x + 4) = 8[12(20) + 4 ] = 1952

96x + 32 = 96 (20) + 32 = 1952

To know more about an expression follow

https://brainly.com/question/25968875

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According to the Fundamental Theorem of Algebra, which polynomial function has exactly 11 roots?

A ) f(x) = (x - 1)(x + 1)^11

B ) f(x) = (x + 2)^3(x^2 -7x +3)^4

C ) f(x) = (x^5 + 7x + 14)^6

D ) f(x) = 11x^5 + 5x + 25

I originally chose A, but that was incorrect on my quiz.

Answers

B would be the right one

F(x) = (x+2)^3 = the highest power for this type turn out will be x^3
the other part is (x^2 - 7x + 3)^4, the highest power for this part will be x^8
since (x+2)^3(x^2-7x +3)^4 = the highest power of first part x^3 second part x^8
x^3 * x^8 = x^11 that result in 11 roots
This type of math, you don't need to configure the whole problem, you just need to know the basic rules of power of a number. For example, (x^2)^3, then 2*3 = 6 make x^6.
or x^2 * x^3 = x^2 + 3 = x^5.

Answer:

The correct answer is B

Step-by-step explanation:

Rylie's gross paycheck amount is $1305.60. She has 4% deducted from her paychecks for her 401(k). Her employer matches her deduction, up to 4%.

How mach is deducted from her paycheck for retirement plan?

A) $26.11
B) $52.22
C) $104.44
D) $522.24

Answers

The employer contribution does not get deducted from her paycheck. To find the amount deducted from her check we take 4% of 1305.60 = 0.04(1305.60) = $52.22.

The deduction from her paycheck is 52 dollars and 22 cents. Then the correct option is B.

What is the percentage?

The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.

Rylie's gross paycheck amount is $1305.60. She has 4% deducted from her paychecks for her 401(k). Her employer matches her deduction, up to 4%.

So the deduction will be given as

[tex]\rm Deduction = \dfrac{4}{100} *1305.6\\\\Deduction = 0.04 * 1305.6\\\\Deduction = 52.224 \approx 52.22[/tex]

The deduction from her paycheck is 52 dollars and 22 cents. Then the correct option is B.

More about the percentage link is given below.

https://brainly.com/question/8011401

highest value on the domain of the function is called what.

Answers

its called the maximum

What is the area of a sector with a central angle of 4pi/3 radians and a radius of 11cm
Use 3.14 for pi and round to the nearest hundredth

Answers

[tex]\bf \textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2}\quad \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\ ------\\ r=11\\ \theta =\frac{4\pi }{3} \end{cases}\implies A=\cfrac{\frac{4\pi }{3}(11)^2}{2}\implies A=\cfrac{\frac{484\pi }{3}}{2} \\\\\\ A=\cfrac{484\pi }{3}\cdot \cfrac{1}{2}\implies A=\cfrac{242\pi }{3}[/tex]

What is the measure of AC ? Enter your answer in the box. ° Circle with inscribed angle A B C. Angle A B C is 3 x minus 1.5 degrees. The intercepted arc A C is 3 x plus 9 degrees.

Answers

Inscribed angles are 1/2 of the measure of the intercepted arc. That means from this we have the equation
[tex](3x-1.5)=\frac{1}{2}(3x+9)[/tex]. Distribute the 1/2:
[tex]3x-1.5=\frac{1}{2}*3x+\frac{1}{2}*9 \\3x-1.5=\frac{1}{2}*\frac{3x}{1} + \frac{1}{2}*\frac{9}{1} \\3x-1.5=\frac{3x}{2}+\frac{9}{2} \\3x-1.5=1.5x+4.5[/tex]
We cannot have a variable on both sides of the equation, so cancel the 1.5x to avoid negatives:
[tex]3x-1.5-1.5x=1.5x+4.5-1.5x[/tex]
Combine like terms:
[tex]1.5x-1.5=4.5[/tex]
Cancel the -1.5 by adding:
[tex]1.5x-1.5+1.5=4.5+1.5 \\1.5x=6[/tex]
Divide both sides by 1.5:
[tex]\frac{1.5x}{1.5}=\frac{6}{1.5} \\x=4[/tex]
Since AC is 3x+9, we substitute 4 in for x:
3*4+9=12+9=21°

Use the Inscribed Angle theorem to get the measure of AC. The intercepted arc AC is [tex]21^{\circ}[/tex].

Given,

The inscribed angle [tex]\angle ABC[/tex] is [tex]3x-1.5[/tex].

And the Intercepted arc AC is [tex]3x+9[/tex].

What is the Inscribed Angle theorem?

We know that, Inscribed Angle Theorem stated that the measure of an inscribed angle is half the measure of the intercepted arc.

So,

[tex]3x-1.5=\frac{1}{2} (3x+9)[/tex]

[tex]2 (3x-1.5)=3x+9[/tex]

[tex]6x-3.0=3x+9[/tex]

[tex]6x-3x=9+3[/tex]

[tex]3x=12\\x=4[/tex]

Since the intercepted arc AC is [tex]3x+9[/tex], putting the value of [tex]x=4[/tex] we get,

intercepted arc AC is [tex]21^{\circ}[/tex].

Hence the intercepted arc AC is [tex]21^{\circ}[/tex].

For more details on the Inscribed Angle theorem follow the link:

https://brainly.com/question/5436956

Which of the following is not a classification of the number given below? -3

Answers

Hello!

I know for a fact that -3 classifies as an integer and a rational number for sure. So, that leaves us two options, real number, and whole number.

Given this information I think the correct answer is whole number, but it might also be real number. So sorry if I am wrong! : )

I hope this helps!
Please Rate & Thank!
Please mark as Brainliest!

Have a wonderful day! : )

Hannah has $1000 in her savings account. During 1 month , she withdraws $25. Each successive month, she withdraws $10 more than the previous month . How much remains in her savings account after 10 months ?

Answers

First month she withdrew $25, second month 35, third month 45, fourth month 55, fifth month 65, sixth month 75, seventh month 85, eight month 95, ninth month 105, tenth month 115
The total she withdrawn after ten months was $700.00. So $1000 - $700 = $300. That is how much that is left after ten months

Answer: A-$300 is correct

What is the value of x in the quadrilateral shown below?

A. 80°
B. 70°
C. 60°

Answers

A quadrilateral has 4 angles that add up to 360 degrees. So, to solve for x:

85+150+55=290
360-290= 70
X= 70 degrees

(HURRY!!! GET 24 PTS) The residential colony has a population of 5400 requires 60 liters of water is per person per day. For the effective utilization of rain water, a group of people decided for WATER HARVESTING. They constructed a water reservoir measuring 49mx27mx25m to collect the rain water. It this water reservoirs is full of water then for how many days it will last for the colony?

Answers

First compute the amount of water needed per day:
[tex]60\times5400=324000L[/tex]
Transform the above amount to m^3:
[tex]324000\times0.001=324\,m^3[/tex]
Compute the volume of the reservoir:
[tex]49\times27\times25=33075\,m^3[/tex]
Now compute the number of days covered by the amount of water like this:
[tex] \frac{33075}{324}=102\,\,\,\text{days.} [/tex]

what he said hope it helped

Step-by-step explanation:

675,360.41 in expanded notation

Answers

{600,000,00} {70,000,00} {300,00} {6000} {40} {1}

The expanded notation of 675,360.41 is 6 * 100000 + 7* 10000 + 5 * 1000 + 3 * 100 + 6 * 10 + 0 * 1 + 4 * 0.1 + 1 * 0.01

How to rewrite the number?

The number is given as:

Number = 675,360.41

Express the numbers using their place values

Number = 6 * 100000 + 7* 10000 + 5 * 1000 + 3 * 100 + 6 * 10 + 0 * 1 + 4 * 0.1 + 1 * 0.01

The above expression represents the expanded notation

Hence, the expanded notation of 675,360.41 is 6 * 100000 + 7* 10000 + 5 * 1000 + 3 * 100 + 6 * 10 + 0 * 1 + 4 * 0.1 + 1 * 0.01

Read more about expanded notation at:

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What is a simpler form of the radical expression square root of 36g^6?

Answers

√(36g^6) = 6g^3 . . . . a simpler form

glacier is moving at a rate of 0.3 inches every hour. The table below represents this relationship.Glacial Movement
Distance Moved (inches)
Time
(hours)
0.3
1
0.6
2
0.9
3
x
4

What value of x completes the table?
1.2
1.5
3.6
13.3

Answers

1.2 Inches, It moves 0.3 inches in 1 hour so if in 1 hour it moves 0.3 and in 2 0.6 and in 3 0.9 so in 4 hours it will move 1.2 inches

Answer:

The correct option is 1.

Step-by-step explanation:

It is given that the glacier is moving at a rate of 0.3 inches every hour. It means the average rate of change is 0.3.

Let d is the total moved distance of glacier and t is number of hours. Then the total moved distance of glacier after t hours is defined as

[tex]d=0.3t[/tex]

At t=1,

[tex]d=0.3(1)=0.3[/tex]

At t=2,

[tex]d=0.3(2)=0.6[/tex]

At t=3,

[tex]d=0.3(3)=0.9[/tex]

At t=4,

[tex]d=0.3(4)=1.2[/tex]

Total moved distance of glacier after 4 hours is 1.2 inches.

The value of x is 1.2. Therefore the correct option is 1.

a taxi company charges passengers $2.00 for a ride, no matter how long the ride is, and an additional $0.20 for each mile traveled. the rule c=0.20m + 2.00 describe the relationship between the number of miles m and the total cost of the ride c.

Answers

The cost of the ride varies by however many miles is driven, however the charging rate stays the same no matter how long the ride is. In the expression 0.20m + 2.00 , 2.00 is the constant as it stays the same, and 0.20 is the coefficient as is varies with however many miles are driven.

What is the x-coordinate for the minimum point in the function f(x) = 4 cos(2x − π) from x = 0 to x = 2π?

Answers

For us to get the minimum point of the function, we have to know that the range of the cosine function is from -1 to 1. Therefore, we will have the minimum value of f(x) when cos(2x-π) is equal to -1.

[tex]cos(2x- \pi )=-1[/tex]
[tex]2x- \pi=\pi[/tex]
[tex]2x=2\pi[/tex]
[tex]x=\pi[/tex]

The x-coordinate for the minimum point of the function f(x) must be π.

we have
f(x) = 4 cos(2x − π)

using a graph tool
see the attached graph

the x-coordinate for the minimum point from x = 0 to x = 2π
if the interval is [0,2π]
there are 3 minimal points
(0,-4) (π,-4) (2π, -4)

if the interval is (0,2π)
there is 1 minimal point
(π,-4)

What is the solution of the system?

{ 2x+y=15

{x−y=3

Enter your answer in the boxes.
(__ ,__ )

Answers

2x+y=15
+ x -y= 3
-------------
3x = 18
x= 6

2(6)+y=15
12+y=15
y=15-12
y= 3

(6,3)

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