A wooden beam is (3y2 + 7y+1) meters long. If a piece of length (y2 - 10) meters is cut off, express the length of the
remaining piece of beam as a polynomial in y.

Answer:

Interval Notation: [-2, 10]

Set Notation: {x|-2≤x≤10}

Step-by-step explanation:

Answer: a = 2.5 (an-1)

Step-by-step explanation: trust me;)

The function which is used to represent the geometric progression 8, 20, 50, 125, 312.5, ... is [tex]a_{n} = 8(2.5)^{n-1}[/tex].

sequence where each succeeding term is produced by multiplying each preceding term by a fixed number, which is called a common ratio. This progression is as a geometric sequence of  numbers.

[tex]a_{n} =ar^{n-1}[/tex]

Where,

[tex]a_{n}[/tex] is the nth term of the sequence or geometric progression

n is the total number of terms

r is the common ratio

and a is the first term

According to the given question

We have

A geometric progression

8, 20, 50, 125, 312.5

Now the common ratio for the above progression is given by

[tex]r = \frac{20}{8} = 2.5[/tex]

And the first term is

a = 8

Therefore, the function which is used to represent the above sequence is given by

[tex]a_{n} = 8(2.5)^{n-1}[/tex]

Hence, the function which is used to represent the geometric progression 8, 20, 50, 125, 312.5, ... is [tex]a_{n} = 8(2.5)^{n-1}[/tex].

Learn more about geometric progression here:

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The fraction of the money belonging to Rachel is [tex]\frac{5}{16}[/tex]

Let [tex]R[/tex] be the amount of money Rachel has

Let [tex]N[/tex] be the amount of money Neil has

Let [tex]C[/tex] be the amount of money Caroline has

Let [tex]M[/tex] be the total amount of money shared between the three people

Then, from the problem we have the following relationships

[tex]R+N+C=M\\\\5N=R \implies N=\frac{R}{5}\\\\\frac{C}{2}=R\implies C=2R[/tex]

Substituting the formulae for [tex]N[/tex] and [tex]C[/tex] into the sum [tex]R+N+C=M[/tex], we get

[tex]R+\frac{R}{5}+2R=M\\\\\frac{5R+R+10R}{5}=M\\\\\frac{16R}{5}=M\\R=\frac{5M}{16}[/tex]

Or, we can say that, [tex]R=\frac{5}{16}\text{ of }M[/tex]

Therefore, the fraction of money Rachel gets is [tex]\frac{5}{16}[/tex] of the total amount.

For an additional example of how to solve word problems that involve sharing money among people, see this answered question: https://brainly.com/question/23286685

Constant rates are used to illustrate linear functions.

(a) The average rate of change

This is calculated using:

[tex]\mathbf{Rate = \frac{y_2 -y_1}{x_2 -x_1}}[/tex]

So, we have:

[tex]\mathbf{Rate = \frac{31.5-22.50}{3.5 - 2.5}}[/tex]

[tex]\mathbf{Rate = \frac{9}{1.0}}[/tex]

[tex]\mathbf{Rate = 9.0}[/tex]

Hence, the average rate of change is $9.0 per hour

(b) A function that models the table of values

Let x represent hours, and y represent the earnings.

So, we have:

[tex]\mathbf{y =m (x - x_1) + y_1}[/tex]

Where:

m =Rate = 9.0

So, we have:

[tex]\mathbf{y = 9(x - 2.5) + 22.5}[/tex]

Expand

[tex]\mathbf{y = 9x - 22.5 + 22.5}[/tex]

[tex]\mathbf{y = 9x }[/tex]

Represent as a function

[tex]\mathbf{f(x) = 9x }[/tex]

Hence, the function that models the table is: [tex]\mathbf{f(x) = 9x }[/tex]

(c) Amount earned for 7.5 hours

This means that x = 7.5

So, we have:

[tex]\mathbf{f(7.5) = 9 \times 7.5 }[/tex]

[tex]\mathbf{f(7.5) = 67.5}[/tex]

Hence, the amount earned in 7.5 hours is $67.5

Read more about constant rates at:

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Answer:

960

Step-by-step explanation:

We start with the variable "x". Let's call "x" Raina's penny bank.

After adding 360 pennies, at the end, she has 5/8x, or 5/8.

So we start with

(1/4)x + 360 = 5/8x

Let's subtract 1/4x from both sides

360 = 5/8x - 1/4x

Remember, we need to use common denominators to subtract, so 1/4 becomes 2/8

360 = 5/8x - 2/8x

Now we simplify to get

360=3/8x

Multiply the reciprocal of 3/8 to both sides which is 8/3

360 * 8/3 = x

Answer is 960 pennies.

Therefore Raina's bank hold 960 pennies.

Answer:

we need to get the same number below to make it easier. so 1/4 will be equal to 2/8.

then she adds 360 pennies so it's 5/8 full.

therefore, the 360 pennies = 3/8 full

because 5/8 - 2/8 = 3/8.

now, we need to divide 360/3 so we can get how much pennies when it's 1/8 full.

360 pennies/3 = 120 pennies = 1/8 full.

now to get a full bank we just need to multiply 120 x 8 because 1/8 x 8 = 1 which means a full fraction.

120 pennies x 8 = 960 pennies.

Raina's bank can hold up to 960 pennies.

Answer:

Option D is correct.

Step-by-step explanation:

2/5 + 4/10

=> 2/5 + 2/5

=> 4/5

4/5 = 8/10

Therefore, Option D is correct.

Hoped this helped.

Answer:

C. (I think)

Step-by-step explanation:

So, it is definitely not a right triangle so A and D can step out. And it is not equilateral because all sides are not the same length, that means B is out. It might be C.

Answer:

0

Step-by-step explanation:

20+(-6x)+6x+(-20)=20-6x+6x-20

                            =0

Answer:

(y+3)=−6(x+9) ( y + 3 ) = − 6 ( x + 9 )

Step-by-step explanation:

Answer: number 4 is +(positive) because the exponent is even.

Number 5 is -(negative) because the exponent is odd.

Step-by-step explanation:

7) Solution:

→ (2)³

→ 2 × 2 × 2 {Expanded form}

→ +8

Ans: Positive

4) Solution:

→ (-6)⁴

→ -6 × -6 × -6 × -6

→ +1296

Ans: Positive

5) Solution:

→ (-3)⁷

→ -3 × -3 × -3 × -3 × -3 × -3 × -3

→ -2187

Ans: Negative

Answer:

We write it as $1841.67 (Rounded)

Step-by-step explanation:

The 7 will round up to the hundredths (0.01) place.

Hoped this helped.

Answer:

[tex]\frac{a}{3} =b[/tex]

Step-by-step explanation:

a = 2a - 3b

→ Minus 2a from both sides

-a = -3b

→ Multiply everything by -1

a = 3b

→ Divide both sides by 3

[tex]\frac{a}{3} =b[/tex]

Answer:

b = 2/3a -1/3A

Step-by-step explanation:

A=2a-3b

Subtract 2a from each side

A-2a=2a-2a-3b

A -2a = -3b

Divide each side by -3

A/-3  -2a/-3 = -3b/-3

-A/3 + 2/3a = b

b = 2/3a -1/3A

Answer:

i think its the 3rd option

Step-by-step explanation:

i'd'k what it is but you can read it over and over again

(p.s Brainleist?)

Answer:

x=22/3

Step-by-step explanation:

amys share would be 45:30 so amys is 45 and marys 30

Answer:

Parallel

Step-by-step explanation:

So if they have the same slope but different y-intercepts, it would be parallel because the slope stays the same so the line doesnt change, just the starting point

For example use the following equations

y = x + 2  

y = x + 3  

In the graph, these equations are parallel

Using continuous compounding and compound interest, it is found that Matthew would have $17 more than Elizabeth in his account.

Compound interest:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

Continuous compounding:

[tex]A(t) = Pe^{rt}[/tex]

The parameters are:

For both of them:

Elizabeth:

Then:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]A(8) = 970\left(1 + \frac{0.06625}{365}\right)^{365(8)}[/tex]

[tex]A(8) = 1648[/tex]

Matthew:

Then:

[tex]A(t) = Pe^{rt}[/tex]

[tex]A(8) = 970e^{0.0675(8)}[/tex]

[tex]A(8) = 1665[/tex]

The difference is:

1665 - 1648 = 17

Hence, Matthew would have $17 more than Elizabeth in his account.

A similar problem is given at https://brainly.com/question/24507395

Answer:

the answer is B. x=75 y=68

Answer:

B. x = 75, y = 68

Step-by-step explanation:

The river will not reach a level of 7 ft. after 5 hours.

A linear equation is in the form:

y = mx + b

where y, x are variables, m is the rate of change and b is the initial value of y.

Let y represent the height of the water level after x hours.

Since the  river is 1 ft below its average water level and  begins to rise by a constant rate of 1.5 ft per hour. Hence:

b = -1, m = 1.5. The equation becomes:

y = 1.5x - 1

To reach a level of 7 ft. That is y = 7:

7 = 1.5x - 1

1.5x = 8

x = 5.3 hours

The river will not reach a level of 7 ft. after 5 hours.

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Answer:

6.5, will not

Step-by-step explanation:

The water level is 6.5 ft above normal after 5​ hours, so it

will not reach a level of 7 ft above normal after 5 hours.

Answer:

-4

Step-by-step explanation:

3 - 5 = -2

2 x -2 = -4

Remember BIDMAS (adding this because of character limit)

Answer:

Step-by-step explanation:

y - x means the the difference in the number of women compared with men.

So if there are 20 women and 14 men, y - x = 20 -1 4 = 6 ,  that is 6 more women than men.

If there are more men than women then y - x will have a negative value,  and there will be, if we flip the above numbers. 6 more men than women.

Answer:

x=5

y=3

then ,

x+2y= 5+2 *3

= 5+6

= 10

Answer:

35.113 km per hour is the correct answer

Answer:

135 divided by 4

Step-by-step explanation:

Answer:

(–4)(9)

(6)(–6)

(6)(6)(–2)

Step-by-step explanation:

(–4)(–9)(2)

=36(2)

=72, No

(–4)(9)

=-36, Yes

(6)(6)(–2)

=36(-2)

=-72, Yes

(–6)(–6)

=36, No

(6)(–6)

=-36, Yes

Answer:

1 12 ounce can would last 18 days, I don't know how long he is planning on leaving his dogs

Answer:

Step-by-step explanation:

Facts to know :

-diagonals of rhombus are angle bisector so angle A is double 28

∡A = 28*2 = 56°

-opposite angles in a rhombus are congruent so angle A and angle C have the same measure

∡C = 56°

-the sum of angles in a rhombus is 360°

360 - 2*56 = 360-112 = 248

248 /2 = 124

∡B = ∡D = 124°