You have $50 in your bank account. Each week you plan to deposit $6 from your allowance and $20 from your paycheck. The equation b = 60 + (20+6)w gives the amount b in your account after w weeks. How many weeks from now will you have $215 in your bank account?

Answer:

-7

Step-by-step explanation:

2x + 3 = x - 4

      -3 =     -3

     2x = x - 7

     -x    -x

      x = -7

Answer:

[tex](f + g)(x) = 7 - 6x[/tex] --- (1)

[tex](f - g)(x) = 6x - 1[/tex] -- (2)

[tex](f . g)(x) =4(5^x)[/tex] ---- (3)

[tex](f / g)(x) = \frac{4}{5^x}[/tex] ----- (4)

[tex](f + g)(x) = -7x-7[/tex] --- (5)

[tex](f - g)(x) = 9x+ 9[/tex] --- (6)

[tex](f . g)(x) = (-8)(x+1)^2[/tex] --- (7)

[tex](f / g)(x) = -\frac{1}{8}[/tex] ----- (8)

[tex]F(t) = \frac{9}{5}t^2 + 32[/tex] ---- (9)

[tex]T(t) = (t - 2)^2 - 4[/tex] --- (10)

Step-by-step explanation:

Given

[tex]f(x) = 3[/tex]

[tex]g(x) = 4 - 6x[/tex]

Solving (1): (f + g)(x)

[tex](f + g)(x) = f(x) + g(x)[/tex]

So, we have:

[tex](f + g)(x) = 3 + 4 - 6x[/tex]

[tex](f + g)(x) = 7 - 6x[/tex]

Solving (2): (f - g)(x)

[tex](f - g)(x) =f(x) - g(x)[/tex]

So, we have:

[tex](f - g)(x) =3 - (4 - 6x)[/tex]

[tex](f - g)(x) =3 - 4 + 6x[/tex]

[tex](f - g)(x) =-1 + 6x[/tex]

[tex](f - g)(x) = 6x - 1[/tex]

Given

[tex]f(x) = 4[/tex]

[tex]g(x) = 5^x[/tex]

Solving (3): (f . g)(x)

[tex](f . g)(x) =f(x) * g(x)[/tex]

So, we have:

[tex](f . g)(x) =4 * 5^x[/tex]

[tex](f . g)(x) =4(5^x)[/tex]

Solving (4): (f / g)(x)

[tex](f / g)(x) = \frac{f(x)}{g(x)}[/tex]

So, we have:

[tex](f / g)(x) = \frac{4}{5^x}[/tex]

Given

f(x) = x + 1

g(x) = -8 - 8x

Solving (5): (f + g)(x)

[tex](f + g)(x) = f(x) + g(x)[/tex]

So, we have:

[tex](f + g)(x) = x + 1 -8-8x[/tex]

Collect Like Terms

[tex](f + g)(x) = x -8x+ 1 -8[/tex]

[tex](f + g)(x) = -7x-7[/tex]

Solving (6): (f - g)(x)

[tex](f - g)(x) = f(x) - g(x)[/tex]

So, we have:

[tex](f - g)(x) = x + 1 -( -8-8x)[/tex]

[tex](f - g)(x) = x + 1 +8+8x[/tex]

Collect Like Terms

[tex](f - g)(x) = x +8x+ 1 +8[/tex]

[tex](f - g)(x) = 9x+ 9[/tex]

Solving (7): (f . g)(x)

[tex](f . g)(x) = f(x) . g(x)[/tex]

So, we have:

[tex](f . g)(x) = (x+1) . (-8 - 8x)[/tex]

Factorize

[tex](f . g)(x) = (x+1) .(-8) (1 + x)[/tex]

Rewrite as:

[tex](f . g)(x) = (x+1) .(-8) (x+1)[/tex]

[tex](f . g)(x) = (-8)(x+1) (x+1)[/tex]

[tex](f . g)(x) = (-8)(x+1)^2[/tex]

Solving (8): (f / g)(x)

[tex](f / g)(x) = \frac{f(x)}{g(x)}[/tex]

So, we have:

[tex](f / g)(x) = \frac{(x+1)}{(-8-8x)}[/tex]

Factorize

[tex](f / g)(x) = \frac{(x+1)}{-8(1+x)}[/tex]

[tex](f / g)(x) = \frac{1}{-8}[/tex]

[tex](f / g)(x) = -\frac{1}{8}[/tex]

Solving (9):

From the question, we have that:

[tex]F(c) = \frac{9}{5}c + 32[/tex]

[tex]C(t) = t^2[/tex]

Required

Determine function F in terms of c

The implication of this question is to solve for [tex]F(c(t))[/tex]

If [tex]F(c) = \frac{9}{5}c + 32[/tex] and [tex]C(t) = t^2[/tex],

Then

[tex]F(c(t)) = \frac{9}{5}*t^2 + 32[/tex]

[tex]F(c(t)) = \frac{9}{5}t^2 + 32[/tex]

This can be rewritten as:

[tex]F(t) = \frac{9}{5}t^2 + 32[/tex]

Solving (10):

[tex]T(h) = h^2 - 4[/tex]

[tex]h(t) = t - 2[/tex]

Required

Find [tex]T(h(t))[/tex]

If [tex]T(h) = h^2 - 4[/tex]  and   [tex]h(t) = t - 2[/tex], then

[tex]T(h(t)) = (t - 2)^2 - 4[/tex]

This is gotten by substituting t -2 for h

The solution can be rewritten as:

[tex]T(t) = (t - 2)^2 - 4[/tex]

Answer:

d

Step-by-step explanation:

the graph increases then goes horizontal

Answer:

D

Step-by-step explanation:

D is the choice you have to make. The culprit is the word quickly. You can't tell if the speed is increasing quickly or not.

The correct part of d is that the bicycle stays at a constant rate until  the end of the timing of the graph.

Answer:

$2271.54

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Compounded Interest Formula: [tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

Step-by-step explanation:

Step 1: Define

P = 800.00

r = 0.11

n = 1

t = 10

Step 2: Find A

The midpoint of the line segment CD whose coordinates (-2,-4) and D (6,2) will be (2, -1).

Let AB be the line segment and C be the mid-point of line segment AB. Let the coordinate of point A (x₁, y₁), the coordinate of point B (x₂, y₂), and the coordinate of the mid-point (x, y).

Then the coordinate of the mid-point of the line segment is given as,

(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]

The endpoint of the segment CD is given as C(-2, -4) and D(6, 2). Then the mid-point of the line segment CD will be

(x, y) = [(-2 + 6) / 2, (-4 + 2) / 2]

(x, y) = (4/2, -2/2)

(x, y) = (2, -1)

The midpoint of the line segment CD whose coordinates (-2,-4) and D (6,2) will be (2, -1).

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Answer:

There are 108° in each interior angle of a regular pentagon. This process can be generalized into a formula for finding each interior angle of a REGULAR polygon Each interior angle of a “regular” polygon is given by where n = the number of sides in the polygon.

Step-by-step explanation:

Answer:

In a nutshell, [tex]\frac{3}{5}[/tex] is not equivalent to [tex]\frac{18}{32}[/tex].

Step-by-step explanation:

Now we proceed to demonstrate that Edgar's statement is false:

1) [tex]\frac{3}{5}[/tex] Given

2) [tex]\frac{3}{5} \times \frac{2}{2}[/tex] Modulative property/Existence of multiplicative inverse

3) [tex]\frac{6}{10}[/tex] [tex]\frac{a}{b}\times \frac{c}{d} = \frac{a\cdot b}{c\cdot d}[/tex]

4) [tex]\frac{6}{10}\times \frac{3}{3}[/tex] Modulative property/Existence of multiplicative inverse

5) [tex]\frac{18}{30}[/tex] [tex]\frac{a}{b}\times \frac{c}{d} = \frac{a\cdot b}{c\cdot d}[/tex]/Result

In a nutshell, [tex]\frac{3}{5}[/tex] is not equivalent to [tex]\frac{18}{32}[/tex].

Answer:

x = 17

<2 = 121

Step-by-step explanation:

We know that angle 1 and angle 3 form a linear pair, which means they add to 180

7x+2 + 3x+8 = 180

Combine like terms

10x+ 10 = 180

Subtract 10 from each side

10x+10-10 = 180-10

10x = 170

Divide by 10

10x/10 =170/10

x = 17

Angle 1 and angle 2 are vertical angles and vertical angles are equal

<1 = <2 = 7x+2 = 7(17) +2 =119+2=121

The total number of handshakes was 234.

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the answer to your question is:

D (2, -6)

i hope this was helpful ;)

The sales price on an item that is $50 with a 54% markdown is $23

The given parameters are

Item price = $50

Markdown = 54%

The sales price on an item that is $50 with a 54% markdown is calculated as

Sales price = Item price * (1 - Markdown)

So, we have

Sales price = 50 * (1 - 54%)

Evaluate

Sales price = 23

Hence, the sales price on an item that is $50 with a 54% markdown is $23

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Answer:

88

Step-by-step explanation:

6+5=11

8/2=4

11x(4)2

The value of the expression 6 + 5 . (8 ÷ 2) 2 is 46.

BODMAS rule is a rule of calculating expressions which include more than one different mathematical operations.

BODMAS is an abbreviation for Brackets, Orders, Division, Multiplication, Addition and Subtraction.

So while calculating expressions including different operations, we should follow this order.

Here, the given expression is  6 + 5 . (8 ÷ 2) 2.

By BODMAS rule, we should calculate the expression in the bracket first.

8 ÷ 2 = 4

So, the expression becomes  6 + 5 × 4 × 2.

There are two operations, multiplication and addition here.

We should go for multiplication first.

5 × 4 × 2 = 40

The expression becomes 6 + 40 = 46.

Hence we got the value of the expression 6 + 5 . (8 ÷ 2) 2 as 46.

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Answer:

b

Step-by-step explanation:

Answer:

After 20 years 18.75 gm of sample will remain.

Step-by-step explanation:

The half-life is the time it takes for any amount of Cobalt-60 to decay to half the starting amount.

20 years is 4 times the half-life of 5 years. So there would be

(300 g) / 2⁴ = 18.75 g

remaining after 20 years.

In other words, after 5 years, 300 g decays to 150 g.

After another 5 years (total 10 years), 150 g decays to 75 g.

After another 5 years (total 15 years), 75 g decays to 37.5 g.

After another 5 years (total 20 years), 37.5 g decays to 18.75 g.

Answer:

a. Correct

b. Incorrect

c. Correct

d. Incorrect

e. Incorrect

Step-by-step explanation:

b. Incorrect because negative hours do not make sense

d. 80 is achieved only with more than 3.89 hours of study, so 3.5 is not enough

e. No, the score is the dependent, it comes out of the formula.

Answer:

0.525%

Step-by-step explanation:

Since we are trying to find the probability of a sequence of events we simply need to multiply the probability of each of these events happening separately from one another. We are told that the probability that the light will be red is 65% that means that the probability that it will be green and that the driver will not need to stop is 35%. This probability remains the same every day of the week. Therefore we need to multiply this probability 5 times, one time for each weekday Monday through Friday, but first we need to turn this percentage into a decimal form by dividing it by 100...

35% / 100 = 0.35

0.35 * 0.35 * 0.35 * 0.35 * 0.35 = 0.00525 ...multiply by 100 to get percentage

0.00525 * 100 = 0.525%

Finally, we can see that the probability that she will not have to stop at the light all next week is 0.525%

Answer:

c

Step-by-step explanation:

It might be wrong but I think its right

Answer:

36

2^2 = 4

9^0 = 1

Answer:

The number of scooters that need to be produced so that the average cost per scooter is $180 is 430 scooters.

Step-by-step explanation:

Note: This question is not properly structured/written. The question is therefore rewritten properly before answering the question as follows:

To manufacture scooters, the manufacturer has a fixed cost of $34,400 plus a variable cost of $100 per scooter. Find n, the number of scooters, that need to be produced so that the average cost per scooter is $180.

The explanation of the answer is now provided as follows:

The number of scooters can be calculated as follows:

Variable cost per scooter = $100

n = number of scooter = ?

Total variable cost = Variable cost per scooter * n = $100 * n = $100n

Total cost = Fixed cost + Total variable cost = $34,400 + $100n

Average cost per scooter = Total cost / n = $180 ................ (1)

Substituting the value for Total cost into equation (1) and solve for n, we have:

($34,400 + $100n) / n = $180

$34,400 + $100n = $180n

$34,400 = $180n - $100n

$34,400 = $80n

n = $34,400 / $80

n = 430

Therefore, the number of scooters that need to be produced so that the average cost per scooter is $180 is 430 scooters.

Answer: 30-4=x  4+x=30 x=26

Step-by-step explanation: So he has 30 tickets and he gives 2 to each of his friends which means that lee has 26 friends with 4 tickets left over.

Answer:

14 cars, 42 vans

Step-by-step explanation:

can divide the total by 4, since the number of cars is just 3x the number of vans

x+3x=56

4x=56

56/4

14 cars times 3 plus the original 14

There are 14 cars times 3 plus the original 14.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given Between 7 and 8 o'clock, there were 56 vehicles in the zoo parking lot. There were 3 times as many vans as cars.

Then it can divide the total by 4, since the number of cars is just 3x the number of vans.

x+3x=56

4x=56

56/4

Therefore, there are 14 cars times 3 plus the original 14.

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Answer:

it's 8x

hope i could help :)

Answer:

[tex] \frac{ - 2}{3} [/tex]

Step-by-step explanation:

if it is right mark me brainliest

Answer: [tex]\dfrac{b}{5}[/tex]

Step-by-step explanation:

Given: Let b = Total number of books.

Total shelves = 5

Number of books on each shelf = (Total number of books) ÷ (Total shelves)

= b  ÷ 5

[tex]=\dfrac{b}{5}[/tex]

The required expression for the number of books on each shelf = [tex]\dfrac{b}{5}[/tex]

Answer:

It depends on the numbers

Step-by-step explanation:

Give some examples

Answer:

264 square meters

Step-by-step explanation:

Answer: The final answer is 3390.

Step-by-step explanation:

Before answering the question, you have to understand that a linear growth pattern is a straight-line pattern (not exponential growth).

-From 1994 to 1996 are 2 [years]

-In 2 [years], there is a growth of 2734-2570 = 164 [students]

-With a linear growth, we can take the above [number of students] (164) divided by 2 [years] to get a [growth rate] of 82 [students per year]
⇒ [tex]\frac{164}{2} =82[/tex] [[tex]\frac{number of students}{years}[/tex] or number of students per year or growth rate]

-From 1996 to 2004, there are 8 [years]

-Therefore:

8 [years] × 82 [students per years] = 656 [students] => increased in students

-We add 656 [students] increased to 2734 [students] in 1996 = 3390 [students] in 2004

The final answer is 3390.

Hope this help. :D

Answer:

3 34/45

Step-by-step explanation:

The common denominator of these is 45.

13/15 = 39/45

8/3 = 120/45

2/9 = 10/45

Add that up and that is 169/45

Simplify as a mixed number, and it would be 3 34/45

Answer:

169/45

Step-by-step explanation:

First lets do 13/15 + 8/3.

We can multiply 8/3 by 5 to both num and denom for a ration, with the denominator being 15: 40/15.

Then add 13/15 to 40/15 to get 53/15

Now multiply that by 3 to both num and denom to get 159/45. This is to get the least common factor with 9.

2/9 can be multiplied by 5 to both num and denom to get the least common factor with 15: 10/45

Now add 159/45 with 10/45 = 169/45

169/45 is the least it can be simplified so that is the answer.

Answer:

There are 8 inventors.

Step-by-step explanation:

Given that there are 3 more than twice as many salespeople as inventors.

Also given that the whole company has 27 employees.

i.e.

s + i = 27

substituting s = 3+2i

3 + 2i + i= 27

3 + 3i = 27

3i = 27 - 3

3i = 24

divide both sides by 3

i = 8

VERIFICATION

As the total number of employees is 27.

so the salespeople will be:

s = 3+2i

  = 3 + 2(8)

  = 3 + 16

  = 19

Thus, the total employees are verified as:

s + i = 27

19 + 8 = 27

27 = 27