The subject is operations on rational expressions.


The instructions are add or subtract the following expressions. Remember to find a common denominator when necessary. Reduce all answers to lowest terms.

Answer:

Here's what I get  

Step-by-step explanation:

Part A

The graph shows a polynomial of odd degree. It is probably a third-degree polynomial — a cubic equation.

Part B

The standard form of a cubic equation is

y = ax³ + bx² + cx + d

The factored form of a cubic equation is

y = a(x - b₁)(x² + b₂x + b₃)

If you can factor the quadratic, the factored form becomes

y = a(x - c₁)(x - c₂)(x - c₃)

Part C

The zeros of the function are at x = -25, x = - 15, and x = 15.

Part D

The linear factors of the function are x + 25, x + 15, and x - 15.

Part E

y = a(x + 25)(x + 15)(x - 15) = a(x + 25)(x² - 225)  

y = a(x³ + 25x² - 225x - 5625)

Part F

When x = 0, y = 1.

1 = a[0³ +25(0)² - 225(0) - 5625] = a(0 + 0 - 0 -5625) = -5625a

a = -1/5625

Part G

[tex]y = -\dfrac{1}{5625}( x^{3} + 25x^{2} - 225x - 5625)\\\\y = \mathbf{ -\dfrac{1}{5625} x^{3} - \dfrac{1}{225}x^{2} + \dfrac{1}{25} x + 1}[/tex]

Answer

Actually, the answer should be -0.0007(x+20)(x+5)(x-15)

Step-by-step explanation:

This is continuing off of the previous answer

PART C

The zeros should be (15,0), (-5,0), and (-20,0)

PART D

x - 15, x + 5, and x + 20

PART E

a(x - 15)(x + 5)(x + 20)

Standard: [tex]a(x^{3} + 10x^{2} -275x-1500)[/tex]

PART F

The y-intercept is at (0,1), so we replace the x's with 0:

1 =[tex][(0)x^{3} +10(0)x^{2} -275(0)-1500][/tex] and this gives us (0+0-0-1500) which also equals -1500

Then we do [tex]\frac{1}{-1500}[/tex] which gives us -0.0006 repeating which rounds to -0.0007

a= -0.0007

PART G

Just place the numbers where they should go and your answer is

y =-0.0007(x + 20)(x + 5)(x - 15)  

the placement for (x + 20) (x + 5) and (x - 15) doesn't matter as long as they are behind -0.0007

Answer:

B.

Step-by-step explanation:

All the possible outcomes are listed on choice B.

The event is a set of outcomes. if we flip three coins and obtain more tails than heads is E = {ttt, tth, tht, htt} option (B) is correct.

A set is a collection of clearly - defined unique items. The term "well-defined" applies to a property that makes it simple to establish whether an entity actually belongs to a set. The term 'unique' denotes that all the objects in a set must be different.

We have three coins.

As we know, in a coin there are two sides head and a tail.

If we flip three coins then the set of all the possible outcomes:

O = {HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}

The set of outcomes has more tails than heads.

E = {ttt, tth, tht, htt}

We can find the probability, the probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

Probability = 4/8 = 1/2

Thus, the event is a set of outcomes. if we flip three coins and obtain more tails than heads is E = {ttt, tth, tht, htt} option (B) is correct.

Learn more about the set here:

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[tex]\frac 1c=\frac1{c_1}+\frac1{c_2} [/tex]

$\frac1c=\frac{c_1+c_2}{c_1c_2}$

$\implies c=\frac{c_1c_2}{c_1+c_2}$

Answer:

see details below

Step-by-step explanation:

a) week 1 :  #10" / (#10"+#12") = 509 / 736 =  69% (to nearest percent)

b) week 2 :  #10" / (#10"+#12") = 766 / 1076 = 383/538 = 71% (to nearest percent)

A).69% for week 1

B)71% for week 2

Answer:

1 f(n) = 3(5)^x-1

2 f(n) = 40(3/2)^x-1

Step-by-step explanation:

The first number in the sequence, times the (multiplicative factor)^ x-1 is the rule for geometric sequences.

Answer:

graph A on edge 2020

Step-by-step explanation:

I took the test

Answer:

[tex]\sqrt{52}[/tex]

Step-by-step explanation:

[tex]a^{2} + b^{2} =c^{2}[/tex]

Here, a = 4, and b = 6.  So if you square a, you get 16.  If you square b, you get 36.

16+36 = 52 = [tex]c^{2}[/tex]

Take the square root of 52 and [tex]c^{2}[/tex] and you get that c = [tex]\sqrt{52}[/tex]

This can be simplified further.  c = [tex]\sqrt{52} = \sqrt{13*4} = 2\sqrt{13}[/tex]

Answer:C. 100, 96, 94, 90.

Step-by-step explanation:

If shireen starts at 100, and if the number is 4 more than the number after it. You must subtract 4 to the previous number to get the next number.

So= 100-4= 96

= 96-4= 94

=94-4 = 90

ANSWER IS= 100, 96, 94, 90, etc....

I hope this helps!

Answer:

Measure of arc CD = 112°

Step-by-step explanation:

Since quadrilateral ABCD is a cyclic quadrilateral,

m∠A + m∠C = 180°

129° + m∠C = 180°

m∠C = 180° - 129°

m∠C = 51°

Since, m(arc BD) = 2(m∠C) [Since measure of the arc is double of its inscribed angle]

                           = 2(51°)

                           = 102°

Since, m(arc BD) + m(arc CD) + m(arc BC) = 360°

102° + m(arc CD) + 146° = 360°

m(arc CD) = 360° - (102° + 146°)

                = 112°

Therefore, measure of arc CD is 112°.

Answer:

Hey there!

2/3 of 90 cm would be 60 cm.

Hope this helps :)

Answer

[tex] \boxed{60}[/tex]

Step by step explanation

To multiply one fraction by another, multiply the numerators for the numerator and multiply the denominators for its denominator and reduce the fraction obtained after multiplication into lowest term :

[tex] \mathsf{ \frac{2}{3} \times 90}[/tex]

⇒[tex] \mathsf{ \frac{2 \times 90}{3 \times 1} }[/tex]

⇒[tex] \mathsf{ \frac{180}{3} }[/tex]

⇒[tex]60[/tex]

Hope I helped!

Best regards!!

Answer:

[tex]\huge\boxed{BD = 12\ units}[/tex]

Step-by-step explanation:

If AB = 5 , then AE = 5 [Radii of the same circle]

So,

AC = AE + EC

AC = 8+5

AC = 13 units

Now, Using Pythagorean theorem to find the missing side i.e. BD because tangent strikes the circle at 90 degrees making the triangle a right angled triangle

[tex]c^2=a^2+b^2[/tex]

Where c = AC , a = BD and b = AB

[tex]13^2 = BD^2+5^2[/tex]

169 = BD² + 25

Subtracting 25 to both sides

169 - 25 = BD²

BD² = 144

Taking square root on both sides

BD = 12 units

Answer:

A. No solution

Step-by-step explanation:

Choose 1 answer:

A. No solutions

B. Exactly one solution

C. Infinitely many solutions

Solution

Given:

4(y-30)=4y+12

Open parenthesis

4y-120=4y+12

Collect like terms

4y-4y=12+120

0=142

There is no solution to the equation, therefore, the answer is A

Step-by-step explanation:

Hey, there!!!

Let me simply explain you about it.

We generally use the distance formula to get the points.

let the point R be (x,y)

As it an equilateral triangle it must have equal distance.

now,

let's find the distance of PQ,

we have, distance formulae is;

[tex]pq = \sqrt{( {x2 - x1)}^{2} + ( {y2 - y1)}^{2} } [/tex]

[tex]or \: \sqrt{( {5 + 3)}^{2} + ( {2 - 2)}^{2} } [/tex]

By simplifying it we get,

[tex] 8[/tex]

Now,

again finding the distance between PR,

[tex] pr = \sqrt{( {x2 - x1}^{2} + ( {y2 - y1)}^{2} } [/tex]

or,

[tex] \sqrt{( {x + 3)}^{2} + ( {y - 2)}^{2} } [/tex]

By simplifying it we get,

[tex] = \sqrt{ {x}^{2} + {y}^{2} + 6x - 4y + 13 } [/tex]

now, finding the distance of QR,

[tex]qr = \sqrt{( {x - 5)}^{2} + ( {y - 2)}^{2} } [/tex]

or, by simplification we get,

[tex] \sqrt{ {x}^{2} + {y}^{2} - 10x - 4y + 29 } [/tex]

now, equating PR and QR,

[tex] \sqrt{ {x}^{2} + {y}^{2} + 6x - 4y + 13} = \sqrt{ {x}^{2} + {y}^{2} - 10x - 4y + 29 } [/tex]

we cancelled the root ,

[tex] {x}^{2} + {y}^{2} + 6x - 4y + 13 = {x}^{2} + {y}^{2} -10x - 4y + 29[/tex]

or, cancelling all like terms, we get,

6x+13= -10x+29

16x=16

x=16/16

Therefore, x= 1.

now,

equating, PR and PQ,

[tex] \sqrt{ {x}^{2} + {y}^{2} + 6x - 4y + 13 } = 8} [/tex]

cancel the roots,

[tex] {x}^{2} + {y}^{2} + 6x - 4y + 13 = 8[/tex]

now,

(1)^2+ y^2+6×1-4y+13=8

or, 1+y^2+6-4y+13=8

y^2-4y+13+6+1=8

or, y(y-4)+20=8

or, y(y-4)= -12

either, or,

y= -12 y=8

Therefore, y= (8,-12)

by rounding off both values, we get,

x= 1

y=(8,-12)

So, i think it's (1,8) is your answer..

Hope it helps...

Answer:

1,8.9

Step-by-step explanation:

Answer:

(if you just add them together), it is 16 hours and 12 minutes

Step-by-step explanation:

8 hours plus 7 hours is 15 hours. 54 minutes plus 6 minutes is another hour. We then have 12 minutes left over. This could also be 16 1/5 hrs.

[tex]|\Omega|=2^5=32\\|A|=10\\\\P(A)=\dfrac{10}{32}=\dfrac{5}{16}[/tex]

Answer:

answer is 5/16

Step-by-step explanation: i did plato

Answer:

Step-by-step explanation:

0.6821 multiplied by 0.0261 is .01754181

putting that into standard from would be 1.754181 x 10^-2

Answer:

Divide by -8.

Step-by-step explanation:

48 is a multiple of 8, an we are trying to isolate p, so you should divide both sides by +/- 8.

Answer:

Step-by-step explanation:

You would do 48 divided by -8, and your answer would be -6

And just to clarify, -8 times -6 = 48. (You can use a calculator if still unsure)

Answer:

653.12 ft²

Step-by-step explanation:

2πrh + 2πr²

2(3.14)(8)(5) + 2(3.14)(8)²

251.2 + ²401.92 = 653.12

Step-by-step explanation:

Here,

radius of a cylinder (r)= 8 ft.

height (h)= 5 ft.

now,

area of a cylinder (a)= 2.pi.r(r+h)

now, putting the values we get,

a = 2×3.14×8(8+5)

after simplification we get,

Area of cylinder is 653.12 sq.ft.

Hope it helps....

Answer:

The perimeter of the rectangle is represented by [tex]p = 32\cdot d + 9[/tex], measured in centimeters.

Step-by-step explanation:

The perimeter ([tex]p[/tex]) of a rectangle, measured in centimeters, is represented by this formula:

[tex]p = 2\cdot (w+l)[/tex]

Where [tex]w[/tex] and [tex]l[/tex] are width and length, measured in centimeters.

If [tex]w = 6.8\cdot d-4.2[/tex] and [tex]l = 9.2\cdot d+8.7[/tex], the expression that represents the perimeter is:

[tex]p = 2\cdot (16\cdot d +4.5)[/tex]

[tex]p = 32\cdot d + 9[/tex]

The perimeter of the rectangle is represented by [tex]p = 32\cdot d + 9[/tex], measured in centimeters.

Answer:

Completing the experiment a few more times and combining the results to the trails already done.

Answer:

Completing the experiment a few more times and combining the results to the trails already done.

Step-by-step explanation:

Answer:

An obtuse angle is an angle that is bigger than 90° degrees, but doesn’t reach a straight line at 180°.

Step-by-step explanation:

i didnt see a figure above but this is the answer to "what is the measure if obtuse angle in degrees?"

Answer:

809mi

Step-by-step explanation:

There are two ways to travel form Tamaulipas to Sorona. The first if the direct route from Sorona to Tamaulipas which is 809mi. The another route is to travel to Colima from Sorona and then travel to Tamaulipas from Colima. This is the long distance routes in which there are two destination points. The direct route is shorter in length therefore preferable.

Answer:

1.5

Step-by-step explanation:

1.54324

The 5 is in the tenths place

We look at the next digit to determine if we need to round up or we leave it alone

The next digit is a 4.  It is under 5 so we leave the 5 alone

1.5

The tenths place is one place to the right of the decimal point.

This means the digit in the rounding place is 5

Since the digit to the right of the rounding

place, 4, is less than 5, round down.

This means that the digit in the rounding place, 5, stays the same and

we change all digits to the right of the rounding place to 0.

So our answer is 1.50000 or 1.5.

Answer:

a) 3 x 20 = 60

b) -2x20 = -40

question c and d are unclear as we do not know how many questions were wrong and how many were not answered.

Sorry but I hope that helped

Answer:

a)  60 points

b)  0 point

c)  22 points

d)  -11 points

Step-by-step explanation:

a)  20 * 3 = 60 points (all answered correct)

b)   0 point (Minimum score if you don't answer any of the questions)

c)  10 * 3 = 30 points

    (14 - 10)  * -2 = -8 points

    right minus wrong =  30 - 8 = 22 points  

d)  5 * 3 = 15 points

    (18 - 5) * -2 = -26 points

    right minus wrong = 15 - 26 = -11 points

Answer:

Choice A

Step-by-step explanation:

Answer:

The probability is 0.97682

Step-by-step explanation:

We start by finding the z-values of the runner times given.

Mathematically;

z-score = (x-mean)/SD

From the question, mean = 13 seconds and SD = 0.3 seconds

So for 12.4 seconds, we have;

z = (12.4-13)/0.3 = -0.6/0.3 = -2

For 14 seconds, we have;

z = (14-13)/0.3= 1/0.3 = 3.33

So the probability we want to calculate is;

P(-2<z<3.33)

We can find this using the standard normal distribution table

Mathematically;

P(-2<z<3.33) = P(z<3.33) - P(z < -2)

Using the standard normal distribution table, the value of this is;

P(-2<z<3.33) = 0.97682

Answer:

Step-by-step explanation:

Area of the rectangle length x width

7.5x5.3 =39.75 sq.m

so, B is the correct answer.

Answer:

1 hour

Step-by-step explanation:

No. of pages print in 1.5 hours = 900

dividing LHS and RHS by 1.5 so that we get 1 hour in LHS

no. of page print in 1.5/1.5 (1) hours = 900/1.5 = 600.

Thus, it takes 1 hour to print 600 pages.

Given that we have to find  how

long will it take her to print a book of 600 pages.

Answer is 1 hour.

The other answer is correct, its both !<3

Answer:

Both

Step-by-step explanation:

Both Tori and Gavin are correct, the two methods work. Completed this in Khan Academy, it's correct.

Answer:

Step-by-step explanation:

the answer is option D

WHEN YOU SUBSTITUTE THE VALUES YOU WILL GET IT............

Answer:

The last one.

Step-by-step explanation:

For x>3, the graph should start at x=3 and y = 2*3-3 = 3 with an open circle, since x must not be equal to 3.

The last graph is the only one that has that.

Furthermore, the middle part is a straight line from -2 ≤ x ≤ 3. The 'or equals' part in there reveals that the straight line segment should have closed circles, all solutions that don't have that can be discarded. So that hint alone points you to the last solution.