The least common denominator of two fractions is 30. If you add the two denominators, their sum is 17. What are the denominators?

Answers

Answer 1

x+y=17
x*y=30
It should be 15 and 2

Related Questions

helpppppppppppppppppppppppp

Answers

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.

What is the area of a sector with a central angle of π3 radians and a radius of 12.4 m? Use 3.14 for π and round your final answer to the nearest hundredth. Enter your answer as a decimal in the box.

Answers

Answer: [tex]80.47\ m^2 [/tex]

Step-by-step explanation:

The area of a sector is given by :-

[tex]\text{Area of sector}=\frac{\theta}{2}\times( r^2), \text{where }\theta\text{ is measure of central angle in radians.}[/tex]

Given :Central angle = [tex]\theta=\frac{\pi}{3}[/tex]

radius = 12.4 m

Then,

[tex]\text{Area of sector}=\frac{\frac{\pi}{3}}{2}\times( (12.4)^2)\\\\\Rightarrow\ \text{Area of sector}=\frac{\pi}{6}\times153.76\\\\\Rightarrow\ \text{Area of sector}=\frac{3.14}{6}\times153.76\\\\\Rightarrow\ \text{Area of sector}=80.4677333333\approx80.47\ m^2 [/tex]

what is a possible value for the missing term of the geometric sequence ?
50, blank, 450, ..

a. 1,350
b. 150
c. 3
d. 53

Answers

50 * 3 = 150 and 150 * 3 = 450

So the answer is b 150

The prime factorization of a number is 2^3*3^2*5. Which is a true statement about the factors of the number?
1. Fifteen is a factor of the number because both 3 and 5 are prime factors.
2. Fifteen is not a factor of the number because 15 is odd and the number is even.
3. Sixteen is a factor for the number because 2^3=8 and 16 is divisible by 8.
4. Sixteen is not a factor of the number because the exponent of 2 is not even.

Answers

2^3 = 8
3^2 = 9

8 * 9 * 5 = 360
15 is a factor of 360, so the answer would be 1. Fifteen is a factor of the number because both 3 and 5 are prime factors

Fifteen is a factor of the number because both 3 and 5 are prime factors and this can be determined by using the arithmetic operations.

Given :

Number -- [tex]2^3\times 3^2\times 5[/tex]

The following steps can be used in order to determine the correct statement:

Step 1 - Write the given number.

[tex]2^3\times 3^2\times 5[/tex]

Step 2 - Simplify the above expression.

[tex]= 8\times 9 \times 5[/tex]

Step 3 - Multiply 8 by 9 in the above expression.

[tex]= 72\times 5[/tex]

Step 4 - Multiply 72 by 5 in the above expression.

= 360

Step 5 - 15 is a factor of 360.

Therefore, the correct option is 1).

For more information, refer to the link given below:

https://brainly.com/question/10454590

What is the sum of the “outer” and “inner” products as described in the FOIL method when multiplying (x + 5)(x - 6)?

A. -6x

B. -x

C. x

D. 5x

Answers

The "outer" terms are x and -6, so their product is -6x.
The "inner" terms are +5 and x, so their product is 5x.
The sum of "outer" and "inner" terms is -6x +5x = -x. (selection B)

A metal Fabricating Company produces 150,000 souvenir tokens each year. In a random sample of 400 tokens, 3 have stamping errors. Predict the total number of coins that will have stamping errors in a year.

Answers

1125
150000 divided by 400 equals 375, times 3 equals 1125.

A FIELD HOCKEY TEAM IS A RECTANGLE 60YARDS BY 100YARDS .WHAT IS THE LENGTH OF THE DIAGONAL FROM ONE CORNER TO THE FIELD TO THE OPPOSITE CORNER ROUND YOUR ANSWER TO THE NEAREST HUNDRETH

Answers

60^2 + 100^2 = X^2
3600 + 10000 = X^2
13600 = x^2
X = Sqrt(13600)
X = 116.619

Diagonal = 116.62 yards

60^2 + 100^2 = c^2
3600 + 10000 = c^2
13600 = c^2
c = 116.62 yd

The profits of mr cash’s company is represented by the equation p(t)=-3t^2+18t-4, where p(t) is the amount of profit in hundreds of thousands of dollars and t is the number of years of operation. he realizes his company is on the down turn and wishes to sell before he ends up in debt. in what year of operation does mr cash’s business show the maximum profit?

Answers

Answer: 3rd year of operation

Explanation:

Note that p(t) is a quadratic function and so its graph is a parabola. Since the coefficient of t² in p(t) is negative, the maximum point in p(t) exist at its vertex. Moreover, the maximum value of p(t) is the y-coordinate of its vertex.

Note that p(t) can be expressed as:

[tex]p(t) = a(t-h)^2 + k [/tex] (1)

Where (h, k) are the coordinates of the vertex of p(t).

To manipulate p(t) in the form expressed in equation (1), we factor out the coefficient of t² in p(t) so that

[tex]p(t) = -3t^2+18t-4 \\ \boxed{p(t) = -3 \left( t^2 - 6t + \frac{4}{3} \right)}[/tex]

Then, we let

[tex]q(t) = t^2 - 6t + \frac{4}{3}[/tex]

So that

[tex]p(t) = -3q(t)[/tex] (2)

We need q(t) to be expressed as the sum of a perfect square trinomial and a constant. To form the perfect square trinomial in q(t), we can find a constant k such that [tex]t^2 - 6t + k [/tex] is a perfect square.

To find the value of k, we divide the coefficient of t by 2 and get the square of the result. Since the coefficient of t in q(t) is -6,

[tex]k = \left( \frac{-6}{2} \right)^2 = 9[/tex]

To avoid changing the value of q(t), if we add the constant k = 9, we need to subtract it by the same number. Since k = 9,

[tex]q(t) = t^2 - 6t + \frac{4}{3} + k - k \\ = t^2 - 6t + \frac{4}{3} + 9 - 9 \\ = (t^2 - 6t + 9) + \frac{4}{3} - 9 \\ \boxed{q(t) = (t - 3)^2 - \frac{23}{3}} [/tex]

From equation (2),

[tex]p(t) = -3q(t) \\ p(t) = -3\left( (t - 3)^2 - \frac{23}{3} \right) \\ \boxed{p(t) = -3 (t - 3)^2 + 23}[/tex]

Hence the vertex of p(t) is (3, 23) and maximum value is attained at t = 3. Therefore, the Mr. Cash's business has maximum profit at the 3rd year of operation.

How many pieces of pie will you have if 4 banana caramel cream pies are sliced into 1 8 servings? A) 12 B) 18 C) 24 D) 32

Answers

Final answer:

When 4 banana caramel cream pies are sliced into 1/8 servings, the number of pieces of pie obtained is 32.

Explanation:

To determine the number of pieces of pie obtained when 4 banana caramel cream pies are sliced into 1/8 servings, we need to find the total number of pie servings. Each pie is sliced into 1/8 servings, so if we have 4 pies, we can calculate the total number of servings by multiplying 4 by 1/8.

4 x 1/8 = 4/8 = 1/2

Therefore, we will have 1/2 pie when 4 banana caramel cream pies are sliced into 1/8 servings. Since 1/2 pie is equivalent to 4/8 pie, the answer is D) 32 pieces.

A field project superintendent earns an annual salary of $72,800, and she contributes $7900 per year to her 401(k) plan. If she has a required deduction for income taxes (federal, state, and local combined) of 28% of pretax income, how much does she have withheld in income taxes per year?

Answers

Contributions to one's 401K plan are taken out without paying tax on them (they are pre-tax contributions). In the end, when you retire you will pay taxes on the money but it is deferred for now.

What this means in terms of the question is that we should deduct the $7,900 first and then take 28% of what is left for taxes.

This person's salary is $72,800 a year and they set aside $7,900 for their retirement account (401K) so that leaves $72800-$7900 = $64,900

She now pays taxes of 28% on this amount ($64,900). Percent means "out of 100" so 28% means [tex] \frac{28}{100}=.28 [/tex] and to find 28% of 64900 we multiply (64900)(.28) = $18172.

That is she has $18,172 withheld in taxes each year.

Could someone explain this to me?

Answers

This is a simple differentiation problem. Let's start by taking the derivative of both sides (with respect to x):
[tex]5y^4\frac{dy}{dx}+6y^2x+6x^2y\frac{dy}{dx}+20x^3 = 0[/tex]

Simplify:
[tex] \frac{dy}{dx} (5y^4+6x^2y) + 6y^2x+20x^3 = 0[/tex]

Solve for dy/dx:
[tex] \frac{dy}{dx} = \frac{-6y^2x-20x^3}{5y^4+6x^2y} [/tex]

Now, plug in the given points:
[tex]\frac{dy}{dx} = \frac{-6(2)^2(-1)-20(-1)^3}{5(2)^4+6(-1)^2(2)} = \frac{24+20}{80+12}[/tex]

Further simplification gives:
[tex]\frac{dy}{dx}|_{(2,-1)} =\frac{44}{92} = \frac{11}{23} [/tex]

So, your answer is 11/23 or B.

Does the equation x2 - 4x + y2 = -3 intersect the x-axis?

Answers

To find out whether or not the equation x^2 - 4x + y^2 = -3 intersects the x-axis, we must set y = 0 in the equation (because at every point on the x-axis, y = 0).

x^2 - 4x + 0 = -3

We then want to solve for x. We can do this by factoring.

x^2 - 4x + 3 = 0

By factoring...

(x - 3)(x - 1)

We can set each of these equations = 0 to solve where the function crosses the x-axis.

x - 3 = 0
x = 3

x - 1 = 0
x = 1

So we know at x = 1 and x = 3, the function x^2 - 4x + y^2 = -3 intersects the x-axis.

Answer:

Yes, because the center is on the x-axis.

Step-by-step explanation:

First, write the equation in standard form by completing the square.

x2 - 4x + y2 = -3

x2 - 4x + 4 + y2 = -3 + 4

(x - 2)2 + y2 = 1

The circle is centered at (2, 0) with a radius of 1. Since the circle is centered on the x-axis, it intersects the x-axis two times, at (3, 0) and (1, 0).

An investment of $750 will be worth $1500 after 12 years of continuous compounding at a fixed interest rate. What percent is the interest rate?

Answers

Final answer:

The interest rate is 100%, or 1 as a decimal, for continuously compounded interest.

Explanation:

To find the interest rate, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the final amount ($1500)P is the principal amount ($750)r is the interest rate (unknown)n is the number of times interest is compounded per year (continuously compounded)t is the time in years (12)

Using the given information, we can plug in the values and solve for r:

$1500 = $750(1 + r/1)^(1*12)$2 = 1 + rr = $2 - 1 = $1

The interest rate is 100%, or 1 as a decimal, for continuously compounded interest.

The interest rate, for continuous compounding, is approximately 5.775%.

To find the interest rate for continuous compounding, we can use the formula for compound interest:

[tex]\[ A = P \times e^{rt} \][/tex]

Where:

- [tex]$ A $[/tex] is the final amount of money,

- [tex]$ P $[/tex] is the principal amount (initial investment),

- [tex]$ r $[/tex] is the interest rate (annual rate in decimal),

- [tex]$ t $[/tex] is the time the money is invested for (in years),

- [tex]$ e $[/tex] is the base of the natural logarithm, approximately equal to 2.71828.

Given:

- [tex]$ P = $750 $[/tex],

- [tex]$ A = $1500 $[/tex],

- [tex]$ t = 12 $[/tex] years.

We need to solve for [tex]$ r $[/tex], the interest rate.

Step 1 :

**Substitute the Given Values into the Formulaa :

[tex]\[ 1500 = 750 \times e^{12r} \][/tex]

Step 2 :

**Divide Both Sides by 750**:

[tex]\[ \frac{1500}{750} = e^{12r} \][/tex]

[tex]\[ 2 = e^{12r} \][/tex]

Step 3 :

**Take the Natural Logarithm of Both Sides**:

[tex]\[ \ln(2) = \ln(e^{12r}) \][/tex]

[tex]\[ \ln(2) = 12r \ln(e) \][/tex]

[tex]\[ \ln(2) = 12r \][/tex]

Step 4 :

**Solve for [tex]$ r $[/tex]**:

[tex]\[ r = \frac{\ln(2)}{12} \][/tex]

[tex]\[ r = \frac{0.693}{12} \][/tex]

[tex]\[ r = 0.05775 \][/tex]

Step 5 :

**Convert the Interest Rate to a Percentage**:

[tex]\[ r_{\text{percentage}} = 0.05775 \times 100\% \][/tex]

[tex]\[ r_{\text{percentage}} = 5.775\% \][/tex]

So, the interest rate is approximately 5.775%.

Answers anybody???????

Answers

The area of the 150° sector is
.. As = (1/2)*r^2*(5π/6)

The area of the white triangle in that sector is
.. At = (1/2)*r^2*sin(5π/6)

The orange shaded area is the difference between these.
.. A = As -At = (1/2)*r^2*(5π/6 -sin(5π/6))
.. = (1/2)*(27.8 in)^2*(5π/6 -1/2)

.. A ≈ 818.4 in^2

what is the slope of the line through (2,-2) and (9,3)

Answers

[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 2 &,& -2~) % (c,d) &&(~ 9 &,& 3~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{3-(-2)}{9-2}\implies \cfrac{3+2}{9-2}\implies \cfrac{5}{7}[/tex]

The perimeter of a rectangle is 42 inches. If the length of the rectangle is 14 inches, which equation could be used to find the width, x? A. 2(x + 14) = 42 B. x + 2(14) = 42 C. 14(x + 2) = 42 D. x + 14 = 42

Answers

A. 2(x+14) = 42

(2x = 14
x = 7

2(7) + 2(14) = 14 + 28 = 42)

Answer:

Option A is correct

equation [tex]2(x+14)=42[/tex] could be used.

Step-by-step explanation:

Given: The length of a rectangle [tex](l)[/tex] is 14 inches and perimeter of rectangle is 42 inches.

Perimeter(P)of a rectangle in inches is given by:

[tex]P= (2l+w)[/tex] ; where [tex]l[/tex] is the length of the rectangle and w is the width of the rectangle.

Substitute the value of P=42 inches , w =x inches and [tex]l = 14[/tex] inches in the above formula we get;

[tex]42 = 2 \cdot (14+x)[/tex]

Divide by 2 on both sides we get;

[tex]21 = 14+x[/tex]

On simplify, we get;

x = 21-14 = 7 inches

therefore, the width of the rectangle is, x = 7 inches

Check :

Substitute the value of x =7 in option A.

[tex]2(x+14) =42[/tex]

[tex]2(7+14)=42[/tex]

[tex]2\cdot 21 =42[/tex]

42 = 42

Hence, the only equation that could be used to find the width, x is, [tex]2(x + 14) = 42[/tex]

Find the value of the missing side of a triangle practice

Answers

There are many formulas to finding a side of a triangle.

Be sure to understand the differences between a right-angled triangle and an irregular-shaped triangle.

Right-angled triangle
Two sides must be known.
[tex] {a}^{2} = {b}^{2} + {c}^{2} [/tex]
where 'a' squared is the hypotenuse of the triangle.

To find the non-hypotenuse side, the formula can be rearranged to
[tex] {b}^{2} = {a}^{2} - {c}^{2} [/tex]
'b' can be any non-hypotenuse side.

Non-right angled triangle.
Cosine rule
Two sides and an angle must be know.
[tex]a = {b}^{2} + {c }^{2} - 2ab \cos(angle \: facing \: a) [/tex]
That is just a few of the formulas I have listed.

the width of an architects desk is represented by four times x squared and the length is represented by the expression 2x cubed. what represents the area of the tabletop

Answers

You will use the formula A=lw to find the area. Substitute 2x^3 in for the length and 4x^2 for the width. You would multiply both of these. 2×4 = 8, and x cubed times x squared equals X to the fifth power. You will add the exponents together because the exponent tells you how many times to multiply that value. If there are three x multiplied together (in x cubes) and two x multiplied together(in x squared) that makes five x multiplied together. The answer is represented as A=8x^5. ^ means to the power of.

Can someone help me please I would appreciate it.
I well mark brainliest if u explain
Please.

Answers

The answer is c to my calculations.

What is the approximate area of the circle shown below 60cm

Answers

It is A 2827cm
This is the answer your welcome

Answer:

[tex]\text{Hence, the approx. area of circle }2827 cm^2[/tex]

Step-by-step explanation:

Given the diameter of circle 60 cm

we have to find the area of circle

Diameter=60 cm

Radius=30 cm

[tex]\text{Area of circle=}\pi r^2[/tex]

[tex]=\frac{22}{7}\times (30)^2=2828.57143\sim 2827(approx)[/tex]

[tex]\text{Hence, the approx. area of circle }2827 cm^2[/tex]

Option A is correct

Ryanne is 14. her brother's age is three more than half her age. how old is her brother?

Answers

Ryanne = 14
half her age : 14 ÷ 2 = 7
three more : 7 + 3 = 10
Her brother is 10 years old.

Answer:

10 years old

Step-by-step explanation:

I will use the letter r to denote Ryanne's age:

r = 14

And according to the problem, her brother's age is THREE MORE THAN HALF HER AGE

so, we start by finding how much is half of Ryanne's age:

r/2 = 14/2 = 7

and next, we find that three more than half her age is:

7 + 3 = 10

Her brother is 10 years old

Twenty-seven minus of a number (x) is not more than 36. What is the number? x > 42 x ≥ -6 x < 3 x ≤ -6

Answers

27 - 1.5x ≤ 36
54 - 3x ≤ 72
-3x ≤ 72 - 54
-3x ≤ 18
x ≥ 18/(-3)
x ≥ -6
..........................................................

Write an equation of the line pictured in the graph.

Answers

The equation is y= -2x + 1

The answer is y = -2x + 1

If c is a constant such that 9x^2+10x+c is equal to the square of a binomial, then what is c?

I NEED HELP SO BAD PLEASE PLEASE PLEASE

Answers

(9x^2+10x+c) = (3x+b)^2
= 9x^2 + 6b x+ b^2

1) 6b= 10
b+ 5/3

2) c=b^2
c= (5/3) ^2
c= 25/9

(9x^2+10x+25/9)=(3x+5/3)^2

I hope this helps:)

table Mary used Delicious (d) and Golden Delicious (g) apples to make homemade applesauce. Delicious apples are $0.75 each and Golden Delicious apples are $1.25 each. Mary spent $21.00 on 22 apples. How many Golden Delicious apples did Mary buy?

Answers

1. To solve this problem, you must make a System of equations.

2. The equations are:

d+g=22 (i)
0.75d+1.25g=21 (ii)

3. If you clear "d" from the equation (i), you have:

d+g=22
d=22-g

4. Now, you must substitute d=22-g into the equation (ii):

0.75d+1.25g=21
0.75(22-g)+1.25g=21

5. When you clear "g", you obtain its value:

16.5-0.75+1.25g=21
16.5+0.5g=21
0.5g=21-16.5
g=4.5/0.5
g=9 Golden Delicious apples

6. If you also want to know the value of "d", you can substitute g=9 into the equation (i) and clear "d":

d+g=22
d+9=22
d=22-9
d=13 Delicious apples

How many Golden Delicious apples did Mary buy?

The answer is: Mary bought 9 Golden Delicious apples.

Tldr: The answer is 9

WILL GIVE A BRAINLEST!!!!!!

Solve and check : c-4/c-2=c-2/c+2 - 1/2-c

The solution is c =

How many extraneous solutions are there?

Answers

we have that
(c-4)/(c-2)=(c-2)/(c+2) - 1/(2-c)
- 1/(2-c)=-1/-(c-2)=1/(c-2)

(c-4)/(c-2)=(c-2)/(c+2)+ 1/(c-2)------- > (c-4)/(c-2)-1/(c-2)=(c-2)/(c+2)
(c-4-1)/(c-2)=(c-2)/(c+2)---------------- > (c-5)/(c-2)=(c-2)/(c+2)

(c-5)/(c-2)=(c-2)/(c+2)------------- > remember (before simplifying) for the solution that c can not be 2 or -2
(c-5)*(c+2)=(c-2)*(c-2)------------------ > c²+2c-5c-10=c²-4c+4
-3c-10=-4c+4----------------------------- > -3c+4c=4+10----------- > c=14

the solution is c=14

the domain of the function is (-∞,-2) U (-2,2) U (2,∞) or
all real numbers except c=-2 and c=2

The solution is c = 14

How many extraneous solutions are there? zero

30 POINTS + BRAINLIEST!

Answers

We have to find the value of 'x' in [tex] \sin (x+22)^{\circ}=\cos (2x-7)^{\circ} [/tex]

By using the complementary angle formula which states:

[tex] \cos (90-\Theta )=\sin \Theta [/tex]

Now,

[tex] \cos (90^{\circ}-(x+22)^{\circ})=\cos (2x-7)^{\circ} [/tex]

Therefore, we get

[tex] 90-(x+22)= (2x-7) [/tex]

[tex] 90-x-22= (2x-7) [/tex]

[tex] 68=3x -7 [/tex]

[tex] 75=3x [/tex]

[tex] x=25^{\circ} [/tex]

Answer:

Lets go by a step-by-step process.

Step-by-step explanation:

\cos (90-\Theta )=\sin \Theta

Now,

\cos (90^{\circ}-(x+22)^{\circ})=\cos (2x-7)^{\circ}

Now we have...

90-(x+22)= (2x-7)

90-x-22= (2x-7)

68=3x -7

75=3x

x=25^{\circ}

PLEASE HELP
7.03

1. Write the sum using summation notation, assuming the suggested pattern continues.
1 - 3 + 9 - 27 + ...

A) summation of one times three to the power of n from n equals zero to infinity
B) summation of one times three to the power of the quantity n plus one from n equals zero to infinity
C) summation of one times negative three to the power of n from n equals zero to infinity
D) summation of one times negative three to the power of the quantity n plus one from n equals zero to infinity

2. Write the sum using summation notation, assuming the suggested pattern continues.
-4 + 5 + 14 + 23 + ... + 131

A) summation of the quantity negative four plus nine n from n equals zero to fifteen
B) summation of negative thirty six times n from n equals zero to fifteen
C) summation of the quantity negative four plus nine n from n equals zero to infinity
D) summation of negative thirty six times n from n equals zero to infinity

3. Write the sum using summation notation, assuming the suggested pattern continues.
25 + 36 + 49 + 64 + ... + n2 + ...

A) summation of n squared from n equals five to infinity
B) summation of n minus one squared from n equals five to infinity
C) summation of n squared from n equals six to infinity
D) summation of n plus one squared from n equals five to infinity

4. Find the sum of the arithmetic sequence.
-1, 2, 5, 8, 11, 14, 17

A) 56
B) 63
C) -7
D) 20

5. Find the sum of the geometric sequence.
1, one divided by four, one divided by sixteen, one divided by sixty four, one divided by two hundred and fifty six

A) 341
B) one divided by one hundred and ninety two
C) one divided by seven hundred and sixty eight
D) three hundred and fourty one divided by two hundred and fifty six

6. Find the sum of the first 8 terms of the sequence. Show all work for full credit.
1, -3, -7, -11, ...

Answers

6.
1, -3, -7, -11, -15, -19, -23, -27...

sum:
8/2 (1 + -27)
8/2 (-26)
-104

This are 6 question and 6 answers

Problem 1. Write the sum using summation notation, assuming the suggested pattern continues.
1 - 3 + 9 - 27 + ...

Answer: option C) summation of one times negative three to the power of n from n equals zero to infinity

Explanation:

1) Sequence: 1 - 3 + 9 - 27: given

2) ratio of two consecutive terms:

- 3 / 1 = - 3

9 / (-3) = - 3

-27 / (9) = - 3

=> ratio = - 3 means that every term is the previous one multiplied by - 3

3) terms

First term: 1 * (-3)^0 = 1

Second term: 1* (-3)^1 = - 3

Third term: 1 * (-3)^2 = 9

Fourth term: 1 * (-3)^3 = - 27

So, the summation is:

∞
∑ 1 * (-3)^n ,
n=0

which is read summation of one times negative three to the power of n from n equals zero to infinity => option C.

Problem 2. Write the sum using summation notation, assuming the suggested pattern continues.

- 4 + 5 + 14 + 23 + ... + 131

Answer: option A) summation of the quantity negative four plus nine n from n equals zero to fifteen

Probe the statement A):

15
∑ (- 4 + 9n)
n=0

Now develop that summation: - 4 +9(0) - 4+ 9(1) - 4 + 9(2) - 4 + 9(3) +....+ - 4 + 9(15) = - 4 + 5 + 14 + 23 + 131

Which is the very same sequence given.Therefore, the first statement if right.

Problem 3. Write the sum using summation notation, assuming the suggested pattern continues.
25 + 36 + 49 + 64 + ... + n^2 + ...

Answer: option A) summation of n squared from n equals five to infinity

Explanation

First term: 25 = 5^2
Second term: 36 = 6^2
Third term: 49 = 7^2
Fourth term: 64 = 8^2

nth term n^2

last term: the sequence is infinite

So, you can see that the sequence is the sum of the square of the integers from n = 5 to infinity =
∞
∑ (n^2)
n = 5

which is what summation of n squared from n equals five to infinity means.

Problem 4. Find the sum of the arithmetic sequence.
-1, 2, 5, 8, 11, 14, 17

Answer: option A) 56

Explanation:

You just have to sum all the terms (since they are few numbers that is the best way): - 1 + 2 + 5 + 8 + 11 + 14 + 17 = 56

Answer: 56

Problem 5. Find the sum of the geometric sequence.
1, one divided by four, one divided by sixteen, one divided by sixty four, one divided by two hundred and fifty six

Answer: option D) 341 / 256

Explanation:
Write in form of fractions: 1 + 1/4 + 1/16 + 1/64 + 1/256

You'd better use the formula for the summation of a geometric sequence

k
∑ A * (r^n) = A * (1 - r^k) / (1 - r)
n=1

In this case: r = 1/4 (the ratio)
k = 5 (the number of terms)
A = 1 (the first term)

=> The sum = 1 * [1 - (1/4)^5 ] / [ 1 - 1/4], which when you simplify turns into 341 / 256 which is the option D.

Problem 6. Find the sum of the first 8 terms of the sequence. Show all work for full credit.
1, -3, -7, -11, ...

Answer: - 104

Explanation:

You can either sum the 8 terms or use the formula for the sum of an aritmetic sequence.

I will sum the 8 terms.

Note the the constant distance to sum is - 4, so the sum of the first eight terms is:

1 - 3 - 7 - 11 - 15 - 19 - 23 - 27 = - 104

Match each whole number with a rational exponential expression. HELPP ME PLEEASE FASTTT

Answers

1. 343^(2/3)
3rdrt[(343(343)]
49

2. [2,197^(1/3)]^2
[3rdrt(2,197)]^2
169

3. 729^(2/3)
3rdrt[729(729)]
81

4. (1,000^2)^(1/3)
3rdrt(1,000^2)
100

5. [3rdrt(9261)]^2
441

6. [3rdrt(216^2)]
36

Hope this helps!

Answer:

1. 49

2. 169

3. 81

4. 100

5. 441

6. 36

Step-by-step explanation:

1. [tex](343)^{\frac{2}{3}}=\sqrt[3]{(343)^{2} }[/tex]

= [tex]\sqrt[3]{(343)(343)}=\sqrt[3]{(7^{3})(7)^{3}}[/tex]

= 7×7 = 49

2. [tex](2197^{\frac{1}{3}})^{2}=(\sqrt[3]{2197})^{2}[/tex]

= [tex](\sqrt[3]{13^{3}})^{2}=13^{2}[/tex]

= 169

3. [tex]729^{\frac{2}{3} }=(\sqrt[3]{729})^{2}[/tex]

= [tex](\sqrt[3]{9^{3}})^{2} = 9^{2}[/tex]

= 81

4. [tex](1000^{2})^{\frac{1}{3}}=(\sqrt[3]{1000})^{2}[/tex]

= 10²

= 100

5. [tex](\sqrt[3]{9261})^{2}=(\sqrt[3]{(21)^{3} })^{2}[/tex]

= 21²

= 441

6. [tex](\sqrt[3]{216})^{2}=(\sqrt[3]{6^{3} })^{2}[/tex]

= 6²

= 36

Which polynomial is a quintic trinomial?

x³ + 2x² -8x + 16
x² + 4
3x⁵ + 7x² -9x⁴
-x⁴ -5x² +1

Answers

Answer:

3x⁵ + 7x² -9x⁴

Step-by-step explanation:

In the order given, the polynomials have degrees 3, 2, 5, 4. The one of degree 5 is "quintic." That one also happens to be a trinomial. It is ...

3x⁵ + 7x² -9x⁴

Other Questions

NEED A ANSWER ASAPRead the sentence.The advertisement is good because it shows a picture of a car accident to warn against the dangers of speeding.Which is the most accurate and precise replacement for the underlined word?refreshingentertainingacceptablecompelling What was the significance of the 36 30' line?It divided the territories between the U.S. and Britain.It set aside the Native American territories.It was the northern border of Missouri.It was the dividing line for slavery and free in future states. An american executive of a multinational home-furnishings chain finds that one of the company's production units in philippines employs children to work in its factories. however, most of the children employed at the factory are orphans who will be sold as forced labor or pushed into prostitution, if they lose their jobs. the executive finds that all the available alternatives seem ethically unacceptable. in this example, the american executive faces the free-rider problem. an ethical dilemma. a veil of ignorance. the tragedy of the commons. before the wiesel family members are taken, maria. their former maid, offers to hide them in a safe shelter. What does mr wiesel say about this offer? what does the famit decide? Samantha???s job involves studying ecosystems and their components. Specifically, she deals with the population and growth of the organisms in the ecosystem. What???s Samantha???s profession? 1. conservationist 2. entomologist 3. population ecologist 5. veterinarian 22 gallons of gas cost $65.56 what is the unit rate for one gallon of gas Elige la respuesta correcta del futuro (irregular).--Mi hermana _______ diversin en el parque. Question 1 options:tendrtengatener tiena How do you make your presence known in Paraguay?whistlingknocking at the doorwalking in the houseclapping at the gate A chlorine ion (Cl-) would most likely bond with _____. Cl- Mg K+ O Wut is 65% as a fraction? Explique (en anglais s'il faut) l'erreur dans cette phrase.Nous n'avons dit rien. when preparing an emergency supply kit for a family, which is the minimun number of days the supplies shoulds last23730 Which of the following statements is true?A.There is not enough food produced in the world to feed everyone.B.The biggest cause of hunger and malnutrition is the cost of getting food to people who need it most.C.Most countries have enough arable land and resources to feed their own population and export a surplus.D.Malnourishment is only seen in a few countries with very limited food supplies. Explain how attitudes influence behavior in HEALTH ORGANIZATIONS ? Which of the following is an example of how President Lincoln expanded presidential power? A.He asked Congress to call for 75,000 volunteers to enlist in the army. B.He disbanded the creation of military tribunals that were attempting to try those considered disloyal to the Union. C.He encouraged Congress to declare war on the CSS by ordering a blockade of the South. D.He suspended the writ of habeas corpus, imprisoning thousands of suspected Confederate sympathizers. Gas costs $1.64 a gallon. Elaine spent $23.78 at the gas station.How many gallons of gas did she but? Supporters of the constitution were known as ______ and opponents to the constitution were called ______. Which plot element is the turning point in the conflict where the main character must make a decision or take action that determines the direction of the story?A. Falling ActionB. ResolutionC. ClimaxD. Exposition Help brainlest answer will get 20 points . Solve For X .It has to have an explanation and work ! A patient who works in a coal mine is referred to an occupational health center. which services are provided to ensure the safety of the patient