write the equation of a line parallel to the line with the equation
a. 3x- 6y=12 b. 5x-y=10

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:

It depends on the numbers

Step-by-step explanation:

Give some examples

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

Step-by-step explanation:

15:30

Divide by 5

3:6

1:2

Answer:

3:4

Step-by-step explanation:

speed of cycle=15 km pers

speed of scooter=30 km per s

Now,

Ratio of speed= distance travelled ÷time taken

= (15+30)÷60 (1 hour=60 min)

= 45÷60

= 3÷4

= 3:4

:: The answer is 3:4.

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:

$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

Two triangles are congruent if two pairs of corresponding angles and included sides are congruent.

Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.

In order to prove △ABC ≅ △DBC by SAS. Then the additional information must be given will be

SAS: Two triangles are congruent if two pairs of corresponding sides and included angles are congruent.

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The total number of handshakes was 234.

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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]

Step-by-step explanation:

answer A should be correct

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:

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 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:

Step-by-step explanation:

Answer:

it's 8x

hope i could help :)

Answer:

x = 280/17 = 16.471

Step-by-step explanation:

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:

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:

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:

c

Step-by-step explanation:

It might be wrong but I think its right

Answer:

36

2^2 = 4

9^0 = 1

Answer:

8.5

Step-by-step explanation:

X^2 = 9^2 - 3^2

x^2 = 81 - 9

x^2 = 72

x = √72

x = 8.485

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:

b

Step-by-step explanation:

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:

264 square meters

Step-by-step explanation:

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:93

Step-by-step explanation: