Mathematics College

Which of the following is equal to the rational expression when x ≠ 5 or -1?
 [tex] \frac{(x-7)(x+1)}{(x+1)(x-5)} [/tex]

a. [tex] \frac{x+1}{x-7} [/tex]
b. [tex] \frac{x+1}{x-5} [/tex]
c. [tex] \frac{x-7}{x+1} [/tex]
d. [tex] \frac{x-7}{x-5} [/tex]

Answers

Answer 1
When x ≠ 5 and x ≠ -1, the expression can be simplified by cancelling the common factor in the numerator and denominator, namely (x+1) to leave us with (x-7) / (x-5), for which there is only one valid choice out of the four.
Answer 2

Answer:

[tex]\frac{(x-7)}{(x-5)}[/tex]

option D is correct

Step-by-step explanation:

[tex]\frac{(x-7)(x+1)}{(x+1)(x-5)}[/tex]

In an rational expression , if we have same factors at the top and bottom  then we cancel it out

In our given rational expression we have x+1  at the top and  bottom

so we cancel out x+1

After cancelling out x+1, we are left with

[tex]\frac{(x-7)}{(x-5)}[/tex]

option D is correct



Related Questions

Choose the correct conic section to fit the equation. x^2/36-y^2=1 Circle Ellipse Parabola Hyperbola

Answers

Think its hyperbola. Dont quote me.

Choose the correct conic section to fit the equation. x^2/36-y^2=1 Circle Ellipse Parabola Hyperbola

Solution:

The general equation of circle is:-

(x-h)²+(y-k)=r²

The general equation of ellipse is:-

[tex] \frac{(x-h)^{2}}{a^{2}}+\frac{(y-k)^{2}}{{b^{2}}}=1 [/tex]

The general equation of parabola is:-

y = a(x-h)²+k

The general equation of hyperbola is:-

[tex]\frac{(x-h)^{2}}{a^{2}}-\frac{(y-k)^{2}}{{b^{2}}}=1[/tex]

The equation of conic section is: x^2/36-y^2=1

[tex]\frac{(x-0)^{2}}{36}-\frac{(y-0)^{2}}{1}}=1[/tex]

[tex]\frac{(x-0)^{2}}{6^{2}}-\frac{(y-0)^{2}}{{1^{2}}}=1[/tex]

Hence, this is hyperbola.

Answer: Hyperbola Option (D)

10) Given that two tangent lines are constructed from the shared point A outside a circle with the center O and points of tangency B and C, what is the relationship between ∠OAB and ∠OAC?

Answers

Those two angles are congruent.

_____
The angles are corresponding parts of congruent triangles (CPCT). Triangles OBA and OCA are right triangles congruent by the HL postulate. The "H" is segment OA. The "L" is the radius, OB or OC. Of course the angles at B and C are 90° as with any radius and tangent line.

Jim picked a card from a standard deck. What is the probability that Jim picked a heart or an ace?

Answers

Answer:

The answer is actually 16/52.

Step-by-step explanation:

There are 13 hearts and 4 aces. However, one of the 4 aces is a heart, so there would only be 3 other aces.

13 hearts + 3 other aces = 16

There are 52 cards in a deck, so the probability would be 16/52.

Solve for x. Use the completing the squares method. Round decimals to the nearest tenth. 2x2+16x=−18 (

Answers

To solve by completing square method we proceed as follows:
2x^2+16x=-18
dividing through by 2 we get:
x^2+8x=-9
but
c=(-b/2a)^2
c=(-8/2)=16
hence
x^2+8x+16=-9+16
x^2+8x+16=7
(x+4)(x+4)=7
(x+4)^2=7
thus getting the square root of both sides
x+4=+/-√7
x=-4+/-√7
x=

Answer:

[tex]x = -4 \frac{+}{-} 2\sqrt{5\\}[/tex]

Step-by-step explanation:

A company has a minimum required rate of return of 9% and is considering investing in a project that costs $350,000 and is expected to generate cash inflows of $140,000 at the end of each year for three years. the net present value of this project is

Answers

The net present value of the  project can be calculated as follows:

NPV = - Cost + present value of all cash flows

Cost = $350,000
Present value of all cash flows = C*{[1-(1+r)^-n]/r}
Where C = Yearly cash flows = $140,000, r = discount rate = 9%, n = time of generating cash flows = 3 years.

Therefore,

NPV = -350,000 + 140,000*{[1-(1+0.09)^-3]/0.09} = $4,381.25

If we reject the null hypothesis, h0: ρ = 0 , what can we conclude about the population correlation coefficient?

Answers

If the null hypothesis, [tex]H_0:\:\rho =0[/tex] is rejected, then we can conclude that the correlation coefficient is significant. This means that there is enough evidence to conclude that a relationship exists between the two (or more) variables involved in the regression. 

what kinds of symmetry does the capital letter E have

Answers

It has reflectional symmetry where the line of reflection (mirror line) is horizontal and it cuts through the middle of the letter
Answer[:]
The capital letter E has three kinds of symmetry(s):

1) Horizontal Line of Symmetry
2) One line of symmetry (NOT meaning they only have one type of symmetry, they have one LINE of symmetry)
3) Reflectional Symmetry (If you were to flip it on it's side, and cut it in half, then both sides would be the same)


[:] DustinBR [:]

A camera manufacturer spends $2,100 each day for overhead expenses plus $9 per camera for labor and materials. The cameras sell for $14 each. a. How many cameras must the company sell in one day to equal its daily costs? b. If the manufacturer can increase production by 50 cameras per day, what would their daily profit be?

Answers

$400 have a nice one!  :) 

Here, first we need to find the number of cameras that can be sold, so that total costs are equal to total revenues.

Let the number of cameras that can be sold be "x".

Total revenue = $ 14x

Total costs will be = $ 2100 + $9x

So, the equation that will be formed ⇒

14 x = 2100 + 9x

5x = 2100

x = 420

Thus, in order to make total costs equal to total revenues, 420 cameras are required to be sold.

If instead of 420, 470 cameras are sold, the daily profit will be calculated as under -

Total revenue = $ 14 × 470 cameras = $ 6,580

Total costs = $ 2100 + ( $ 9 × 470 cameras) = $ 6,330

Daily profit = Total revenue - Total costs = $ 6,580 - $ 6,330 = $ 250


The function P(x) = 3,113(1.2795)^x models the population, in millions, of California since 1990. Use the function to complete the following.

The number 3.113 represents
(a) The current population, in millions, of California.
(b) The population, in millions, of California in 1990
(c) The amount, in millions, that the population increases each year

The number 1.2795 represents
(a) The population, in millions, of California in 1990.
(b) The amount, in millions, that the population increases each year.
(c) The rate the population of California is increasing each year.

Answers

For this case we have a function of the form:
 y = A (b) ^ x
 Where,
 A: initial amount
 b: growth rate
 x: time
 We then have the following function:
 P (x) = 3,113 (1.2795) ^ x
 Where,
 The number 3.113 represents:
 (b) The population, in millions, of California in 1990
 The number 1.2795 represents:
 (c) The rate of the population of California is increasing each year.

Which value of r indicates a stronger​ correlation: requals0.811 or requalsnegative 0.861​? explain your reasoning?

Answers

The closer the magnitude of r is to 1, the stronger the correlation.

r=-0.861 indicates stronger correlation than r=0.811 because |-0.861| > |0.811|.

a tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an intial speed of 130 feet per second. What is the maximum height, in feet, the ball will attain? round to the nearest hundredth

Answers

For this case, the first thing to do is write the equation of moving the ball.
 We have then:
 h (t) = - 16t ^ 2 + 130t + 2
 Deriving we have:
 h '(t) = - 32t + 130
 We match zero:
 -32t + 130 = 0
 We cleared t:
 t = 130/32
 t = 4.0625 s
 We evaluate the value of t = 4.0625 s in the equation of motion:
 h (4.0625) = - 16 * (4.0625) ^ 2 + 130 * (4.0625) + 2
 h (4.0625) = 266.0625 feet
 Answer:
 The maximum height, in feet, the ball will attain is:
 h (4.0625) = 266.0625 feet

Final answer:

Using the kinematic equation for vertical motion, the maximum height a tennis ball will reach when fired at an initial speed of 130 ft/s from a height of 2 feet is approximately 264.91 feet.

Explanation:

Calculating the Maximum Height of a Tennis Ball

The maximum height that a tennis ball will attain when fired vertically can be calculated using the kinematic equations that describe projectile motion. Given that the initial speed of the ball is 130 feet per second and it is launched from a height of 2 feet, we can use the equation for vertical motion:

v^2 = u^2 + 2gh

where v is the final velocity (0 ft/s at the highest point), u is the initial velocity (130 ft/s), g is the acceleration due to gravity (-32.2 ft/s^2, negative because it is directed downwards), and h is the height gained. Rearranging the formula to solve for h we get:

h = (v^2 - u^2) / (2g) = (0 - 130^2) / (2 * -32.2)

After calculating h, we add the initial launch height of 2 feet to find the maximum height above ground:

Maximum Height = h + 2 feet

By plugging in the values, we can find the maximum height to be:

Maximum Height = (0 - 16900) / (-64.4) + 2 ≈ 264.91 feet (rounded to the nearest hundredth).

Therefore, the maximum height attained by the tennis ball is approximately 264.91 feet.

How do you solve this

Answers

Try this solution (the required value is marked with red).

Q # 17 please solve the figures

Answers

Answer: First option:
Angle C is congruent with angle X, angle D is congruent with angle Y, angle A is congruent with angle Z

Write the related series for the finite sequence –7, –10, –13, . . ., –22. then find the sum.–7 + (–10) + (–13) + (–16) + (–19) + (–22) = –87
 –7 + (–10) + (–13) + (–15) + (–18) + (–22) = –85
 –7 + (–10) + (–13) + (–14) + (–18) + (–22) = –84
–7 + (–10) + (–13) + (–17) + (–20) + (–22) = –89

Answers

I would say the last one, -7+(-10)+(-13)+(-17)+(-20)+(-22)=-89 , it seems the most reasonable since you go up by -3, hope this is correct and helps if not i apologize 

Answer: [tex]-7+(-10)+(-13)+(-16)+(-19)+(-22)=-87[/tex]

Step-by-step explanation:

Given finite sequence : -7, -10, -13, . . ., -22.

Difference between first and second term=[tex]-10-(-7)=-10+7=-3[/tex]

Difference between second and third term =[tex]-13-(-10)=-13+10=-3[/tex]

Hence, the common difference = -3

The next term after -13 =[tex]-13+(-3)=-13-3=-16[/tex]

The next term after -16 =[tex]-16+(-3)=-16-3=-19[/tex]

The next term after -19 =[tex]-19+(-3)=-19-3=-22[/tex].........which is the last term of the sequence.

Now, the sum of the given sequence =[tex]-7+(-10)+ (-13) + (-16) + (-19) + (-22) [/tex]

[tex]=-7-10-13-16-19-22= -87[/tex]

Volume and Surface Area

Math help 100 points

Answers

Part 1) we have that
volume smaller solid=512 cm³
volume larger solid=2197 cm³

we know that
volume larger solid=[scale factor]³*volume smaller solid
scale factor=∛[volume larger solid/volume smaller solid]
scale factor=∛[2197/512]-----> scale factor=1.625


Part 2) 
the ratio of the surface areas is equal to [scale factor]²
1.625²-------> 2.64

Part 3)
surface area smaller solid=960 cm²
then
surface area larger solid=scale factor²*surface area smaller solid
surface area larger solid=[1.625]²*960-----> 2535 cm²
 surface area larger solid is  2535 cm²


Answer:

1 - V = Smaller solid=512 cm³

    V = Larger solid=2197 cm³

2-  1.625² = 2.64

3 - SA of big solid is found 2535 cm²

hey can you please help me posted picture of question

Answers

We have the following function:
 C (t) = 6t - 180
 Clearing t we have:
 6t = c + 180
 t = c / 6 + 180/6
 Rewriting:
 t (c) = (c + 180) / 6
 Answer:
 The inverse function for this case is given by:
 t (c) = (c + 180) / 6
 option A

The first term in a sequence is -2 and the common ratio is 3. What is the sixth term of the sequence?

Answers

It's the Geometric Sequence.

The n-th term of a geometric sequence with initial value a and common ratio r is given by:

[tex]a_n=a_1\cdot r^{n-1}\ for\ n\in\mathbb{N^+}[/tex]

We have:

[tex]a_1=-2;\ r=3;\ n=6[/tex]

Substitute:

[tex]a_6=-2\cdot3^{6-1}=-2\cdot3^5=-2\cdot243=-486[/tex]

Answer: The sixth term is equal -486.

The balance on a car loan after 4 years is $8,996.32. The interest rate is 5.6% compounding annually. What was the initial value of the loan?

Answers

To evaluate the initial value we use the formula:
A=P(1+r)^n
where
A=future value
P=principle amount
r=rate
n=time
thus plugging in our values we get:
8996.32=P(1+5.6/100)^4
solving for p we shall have:
8996.32=1.2435P
hence:
P=$7234.5
Thus the initial amount was $7234.5

hey can you please help me posted picture of question

Answers

The correct answer is the las option (Option D), which is:

 D. f(x)=(x+4)^4

 The explanation is shown below:

 1. The initial function was G(x)=x^4, whose graph shows that the shape has its vertex at 0,0.
 
 2. If the it was shift 4 units to the left, you only has to add a 4 to the function.

 3. Therefore, you obtain the the equation of the final shape is:

 f(x)=(x+4)^4

 As you can see, the answer is the option D.

what is the difference between the greatest amount and least amount of gasoline used to mow lawns?

1/8 2/8 3/8/4/8 5/8

Answers

Answer:
The difference is 4/8 which is equivalent to 1/2

Explanation:
The given values of gasoline amounts are as follows:
1/8 , 2/8 , 3/8 , 4/8 , 5/8

Since all the values have the same denominator, therefore, we can base our comparison on the numerator. The larger the numerator, the larger the value of the fraction.

Based on this, we can note that:
the least amount of gasoline is 1/8
the greatest amount of gasoline is 5/8

The difference between the two can be computed as follows:
difference = greatest amount - least amount
difference = 5/8 - 1/8
difference = 4/8 which can be simplified to give 1/2

Hope this helps :)

a marble is selected at random from a jar containing 6 red marbles 3 yellow Marbles and 2 green marbles what are the odds in favor of selecting a red marble

Answers

Total Marbles = 6 + 3 + 2 = 11
Total Red marbles = 6

P(red) = 6/11

1. You can afford a monthly mortgage payment of $1,650 and can get a 15-year 5.625% loan. What is the maximum loan you can get so your payment does not exceed $1,650?

2. You apply for a home equity loan. The lender gets an appraisal on your home, showing a value of $183,500. You have a first mortgage with a current balance of $87,435. Based on a 75% LTV ratio, what is the maximum line of credit you can get?

Answers

1. A suitable financial calculator will tell you the present value of 180 monthly payments of $1650 at an interest rate of 5.625% is ...
  $200,307.94

2. .75*$183,500 -87,435 = 50,190
The maximum line of credit you can get is $50,190.

Determine the values of the constants b and c so that the function given below is differentiable. f(x)={2xbx2+cxx≤1x>1

Answers

Assuming the function is

[tex]f(x)=\begin{cases}2x&\text{for }x\le1\\bx^2+cx&\text{for }x>1\end{cases}[/tex]

For [tex]f(x)[/tex] to be differentiable, it necessarily has to be continuous. For this condition to be met, we need

[tex]\displaystyle\lim_{x\to1^-}f(x)=\lim_{x\to1^+}f(x)=f(1)[/tex]
[tex]\iff\displaystyle\lim_{x\to1}2x=\lim_{x\to1}(bx^2+cx)[/tex]
[tex]\iff2=b+c[/tex]

For the derivative to exist, the one-sided limits of the derivative must also exist and be equal. We have

[tex]f'(x)=\begin{cases}2&\text{for }x<1\\2bx+c&\text{for }x>1\end{cases}[/tex]

[tex]\displaystyle\lim_{x\to1^-}2=\lim_{x\to1^+}(2bx+c)[/tex]
[tex]\iff2=2b+c[/tex]

Now we solve for [tex]b[/tex] and [tex]c[/tex]:

[tex]\begin{cases}b+c=2\\2b+c=2\end{cases}\implies b=0,c=2[/tex]
Final answer:

To make the function differentiable, we need to make it continuous at x = 1 by ensuring that both sides of the function have the same value. The values of the constants b and c are b = 1 - c, where c is any real number.

Explanation:

The function given is:

f(x)={2xbx2+cxx ≤ 1  x > 1

To determine the values of the constants b and c such that the function is differentiable, we need to make sure that the function is continuous at x = 1 and both sides of the function have the same derivative at x = 1.

To do this, we need to find the limits of the function as x approaches 1 from both the left and the right sides.

From the given function, we can see that when x ≤ 1, the function is a polynomial and is differentiable for any value of b and c.

However, when x > 1, the function is not differentiable unless we choose the values of b and c such that the function becomes continuous at x = 1.

To make the function continuous, we need to make sure that both sides of the function have the same value at x = 1.

Substituting x = 1 into the given function, we have 2b(1)(1) + c(1) = b + c = 1 (since the function should be continuous at x = 1).

Therefore, the values of the constants b and c that make the function differentiable are b = 1 - c, where c is any real number.

Learn more about Differentiability of a Function here:

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Unit rate of 3 1/2 and 1/4

Answers

Hello.

 3 1/2 ÷ 1 1/47/2 ÷ 5/47/2 · 4/528/102.8 2.8 is the unit rate 

Have a nice day

please help!! I don't understand

Answers

Answer:

(4, 5)

Step-by-step explanation:

All the medians intersect at the same point. RU and PS are medians so they intersect at the same point that medians QT and PS intersect.

a customer buys three bottles of water at ninety nine cents each. there is seven percent tax on each bottle. what is the total bill?

Answers

If the tax was 7 cents then each bottle would cost 1.06 each, because tax doesn't mean it's three dollars plus tax which comes to 3.07, it's that if you have a water bottle coming out to 99 cents each and the tax was 7 cents, you add 7 to 99. Which in money, comes out to 1.06 each bottle. So the total bill is 3.18. 
I hope this helped! I don't wanna get your answer wrong! >o<
The total bill of each bottle plus tax would be $5.04


At the sandwich shop, there are four different types of meat and three different types of cheese. If you select a sandwich without looking, what is the probability that it has your favorite type of meat on it?

give answer as a fraction

Answers

If you only have one favorite type of meat the probability 1/4
I don't know why you gave extra information about the cheese because the question didn't ask anything about the cheese

The solution is : 1/4  is the probability that it has your favorite type of meat on it.

What is probability?

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

Here, we have,

given that,

At the sandwich shop, there are four different types of meat and three different types of cheese.

If you select a sandwich without looking,

then we need to find the probability.

Solution

There are four different types of meat and three different types of cheese

Probability = number of required outcome / number of possible outcome

Total amount of meat = number of possible meat = 4

If you only have one favorite type of meat the probability 1/4

Hence, the correct answer is Option B.

The solution is : 1/4  is the probability that it has your favorite type of meat on it.

To learn more on probability click:

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which statement describes the ratio of weight to mass and the value of x in the table?

Answers

To find the ratio, pick any pair of corresponding table values.
  weight/mass = (196 N)/(20 kg) = 98/10 N/kg

You can find x from ...
  (98/10)x = 1078
  x = 1078*10/98 = 110

The appropriate choice is ...
  B   The ratio is 98/10; x = 110

Christina goes to the market with $50. She buys one papaya for $20 and spends the rest of the money on bananas. Each banana cost $6. Write an inequality for the number of bananas purchased

Answers

50 is greater than or equal to 20 + 6x
50 is greater or equal to 20. How you do that is you write a greater than sighn and put a line under it.

Using the law of cosines, a=_ rounded to the nearest tenth.

Answers

a^2 = 4.0^2 + 3.7^3 - 2*4*3.7 cos 334

= 4.865

a =  2.2  to nearest tenth.

Answer: a = 2.2

Given that: b = 4.0, c = 3.7, A=33.

The law of cosine is:

[tex]a^2=b^2+c^2-2bccosA\\a^2=4.0^2+3.7^2-2(4.0)(3.7)cos(33)\\a^2=4.86535118882\\a=\sqrt{4.86535118882}\\a=2.20575410888\\a=2.2[/tex]

So a = 2.2

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