Given that f(x)=2x-1, find f(3)

Answer:

              a₁ = -5, d = 7,  a₂ = 2, a₃ = 9, a₄ = 16

equation of sequence:    [tex]\boxed{\bold{a_n=7n-12}}[/tex]

Step-by-step explanation:

a₁ + a₂ + a₃ = 6    

a₁ + a₁ + d + a₁ + 2d = 6

3a₁ + 3d = 6

a₁ + d= 2     ⇒ a₁ = 2 - d

a₄ = 16

a₁ + 3d = 16

2 - r + 3d = 16

2d = 14

d = 7

a₁ = 2-7 = -5

a₁ = -5, d = 7   ⇒  a₂ = -5+7 = 2, a₃ = 2+7 = 9, a₄ = 9+7 = 16

equation of arithmetic sequence:

[tex]a_n=a_1+d(n-1)\\\\a_n=-5+7(n-1)\\\\\underline{a_n=7n-12}[/tex]

Answer:

30 units

Step-by-step explanation:

PT=TQ

3x+9=5x-5

3x-5x=-5-9

-2x=-14

x=7

Putting value of x in PT above

PT=3x+9=3x7+9

PT=30 units

Answer:

4/11

Step-by-step explanation:

Answer:

To find the answers, all I have to do is apply the operations (plus, minus, times, and divide) that they tell me to, in the order that they tell me to.

(f + g)(x) = f (x) + g(x)

= [3x + 2] + [4 – 5x]

= 3x + 2 + 4 – 5x

= 3x – 5x + 2 + 4

= –2x + 6

(f – g)(x) = f (x) – g(x)

= [3x + 2] – [4 – 5x]

= 3x + 2 – 4 + 5x

= 3x + 5x + 2 – 4

= 8x – 2

(f  × g)(x) = [f (x)][g(x)]

= (3x + 2)(4 – 5x)

= 12x + 8 – 15x2 – 10x

= –15x2 + 2x + 8

\left(\small{\dfrac{f}{g}}\right)(x) = \small{\dfrac{f(x)}{g(x)}}(  

g

f

​  

)(x)=  

g(x)

f(x)

​  

= \small{\dfrac{3x+2}{4-5x}}=  

4−5x

3x+2

​  

My answer is the neat listing of each of my results, clearly labelled as to which is which.

( f + g ) (x) = –2x + 6

( f – g ) (x) = 8x – 2

( f  × g ) (x) = –15x2 + 2x + 8

\mathbf{\color{purple}{ \left(\small{\dfrac{\mathit{f}}{\mathit{g}}}\right)(\mathit{x}) = \small{\dfrac{3\mathit{x} + 2}{4 - 5\mathit{x}}} }}(  

g

f

​  

)(x)=  

4−5x

3x+2

​

Step-by-step explanation:

Answer:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

x/4-(28/1)=0

Step by step solution :

STEP

1

:

28

Simplify ——

1

Equation at the end of step

1

:

x

— - 28 = 0

4

STEP

2

:

x

Simplify —

4

Equation at the end of step

2

:

x

— - 28 = 0

4

STEP

3

:

Rewriting the whole as an Equivalent Fraction

3.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using 4 as the denominator :

28 28 • 4

28 = —— = ——————

1 4

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

3.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x - (28 • 4) x - 112

———————————— = ———————

4 4

Equation at the end of step

3

:

x - 112

——————— = 0

4

STEP

4

:

When a fraction equals zero

4.1 When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

x-112

————— • 4 = 0 • 4

4

Now, on the left hand side, the 4 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

x-112 = 0

Solving a Single Variable Equation:

4.2 Solve : x-112 = 0

Add 112 to both sides of the equation :

x = 112

One solution was found :

x = 112

Step-by-step explanation:

make me as brain liest

Answer:

I believe it's 2(x-5)=3

Answer:

S = { }

Step-by-step explanation:

The set S has no members

Answer:

–4(x + 3) = 4(–x – 1) and 6x + 1 = 3(2x – 4)

Step-by-step explanation:

Answer:

1 ans 5

Step-by-step explanation:

no solution              –––

6x + 1 = 3(2x - 4)

6x + 1 = 6x - 4

6x - 6x + 1 = 6x - 6x - 4

1 ≠ -4

one solution

2 - 5x = 7x - 12

2 -5x + 5x = 7x + 5x - 12

2 = 12x - 12

2 + 12 = 12x - 12 + 12

14 = 12x

x = 14/12

infinite solutions

4(3 - x) = 2(6 - 2x)

12 - 4x = 12 - 4x

12 - 12 - 4x + 4x = 12 - 12 - 4x + 4x

0 + 0 = 0 + 0

0 = 0

one solution

5(x + 2) = 2(x - 4)

5x + 10 = 2x - 8

5x - 5x + 10 + 8 = 2x - 5x - 8 + 8

18 = -3x

x = -6

no solution                            –––

-4(x + 3) = 4(-x - 1)

-4x + 4x - 12 = -4x + 4x - 4

-12 ≠ -4

Answer: v=559

Step-by-step explanation:Solve for V

by simplifying both sides of the equation, then isolating the variable.

Exact Form:

V=−509

Decimal Form:

V=−5.¯5

Mixed Number Form:

V=−559

Hope this helps!!!!!!

Answer: It may be 25 or 101

Step-by-step explanation:

Answer:

Paul had 24

Step-by-step explanation:

He has 22 now. Subtract the 10 he just bought for 12, which was half of his original collection.

22-10=12

12×2=24

Answer:

see below

Step-by-step explanation:

Pair 1 is a rotation since we turn figure A into figure B

Pair 2 is a reflection since we flip figure A into figure B over a horizontal line

Pair 3 is a translation since we slide figure A into figure B by moving it down

Answer:

You can't it is a false statement.

Step-by-step explanation:

You probably made an error.

3 + 5 is 8 unless you wanted this 3 + 2 = 5

A standard form equation is when it is set up

Ax + By = C.

6x + 2y = 4

A slope-intercept form equation is when it is set up y=mx+b.

Y = - 3x + 2

In order to go from one form to another, all you have to do is change the order of the given numbers.  First you want to move the Ax to the opposite side of the equation, by either adding or subtracting it.  At this point your equation will be set up By = -Ax + C.  Then you want to divide the B from the By and the rest of the equation.  Therefore you will have y = - Ax/B + C/B.  This is the same thing as the slope-intercept form, just a few of the letters are different.

Example 1:        

Change from standard to slope form

8x + 4y = 16

8x + 4y = 16  first subtract  8x

4y = -8x + 16   then divide all by 4

y = -2x + 4   slope form

Example 2:

 6x + 3y = 21

6x + 3y = 21  subtract  6x

3y = -6x + 21  then divide all by 3

y = -2x + 7   slope form

pls mark brainest

Given:

The garden is a right triangle with base 10m and height 15m.

To draw:

The garden such that 1 unit on the grid below represents 2 m.

Solution:

We have,

1 unit = 2 m

So,

1 m = 0.5 units

Using this conversion, we get

10 m = 5 units

15 m = 7.5 units

Therefore, the base garden on the grid is 5 units and height is 7.5 units as shown below.

My     will     to     live.                                  

..................................................

Answer:

1731996

Step-by-step explanation:

i think thats the answer if not sorry hopefully i helped <3

Answer:

I can help you!

Step-by-step explanation:

3x7 you should add #7 3 times. That would be 21

9x8 you should add #8 9 times. That would be 72

12x9 you should add #9 12 times. That would be 108

Hope it helped

Answer:

[tex]y=2x-5[/tex]

Step-by-step explanation:

Let's start by finding the slope using the two points given. Use the formula for slope below:

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

Identify your values:

[tex]x_1=0\\x_2=4\\y_1=-5\\y_2=3[/tex]

Substitute:

[tex]m=\frac{3-(-5)}{4-0}[/tex]

Combine terms:

[tex]m=\frac{8}{4}[/tex]

Simplify:

[tex]m=2[/tex]

_

Let's graph these two points. As seen on the graph attached, we can see that [tex]-5[/tex] is the y-intercept. With our slope and y-intercept, we have the information needed to formulate an equation in slope-intercept form:

[tex]y=mx+b[/tex]

Identify your values:

[tex]m=2[/tex]

[tex]b=-5[/tex]

Substitute:

[tex]y=2x-5[/tex]

Answer:

The answer is 4

Step-by-step explanation: I did the work and it works out like that I hope this helps

Answer:

A & C & D

Step-by-step explanation:

A & C & D both show the commutative property of multiplication and therefore is the correct answer because 3/5(6) = 18/5 and 3(6/5) is also 18/5.

3 x (6÷5) is also 18/5

(3×6)÷5 is also 18/5

Answer:

x = 7

Step-by-step explanation:

................Hi.....................

Answer:

The shorter side is 8 feet

the longer side is 16 feet

Step-by-step explanation:

lets call the shorter side x.

let's call the longer side 2x (because it's twice as long as the shorter side)

you know that the perimeter is 48 feet.

the perimeter would be 2(short side) + 2(long side)

using this, you can make the following equation:

2(x) + 2(2x) = 48

open the parenthesis.

2x + 4x = 48

6x = 48

x = 8

2x = 16

Answer:

3 19/24

Step-by-step explanation:

Answer:

y=- 2/5x+7

Step-by-step explanation:

Answer:

Step-by-step explanation:

Cost of the car = $21000

Mark up = 1/3*21000 = $7000

Sale price = 21000 + 7000 = $28000

Answer:

A)

10 miles.

B)

0 hours, 40 minutes, and 0 seconds.  

Step-by-step explanation:

Remember that distance is given by the formula:

[tex]d=st[/tex]

Where d is the distance, s is the speed, and t is the time.

We know that the bird leaves its nest and travels 15 miles per hour for x hours. So, let's substitute 15 for s and x for t:

[tex]d=15x[/tex]

On the return trip, the bird travels 3 miles per hour slower and has 2 miles left after x hours.

Since this is the return trip, the distance d remains the same. We know that the bird travels 3 miles per hour slower, so it's speed is 15-3 or 12 miles per hour.

However, after x hours, it still has 2 miles left until reaching the destination. So, we will subtract 2 from d. This gives us the equation:

[tex]d-2=12x[/tex]

We can solve this using substitution. Since we already know that d is 15x. Substitute:

[tex]15x-2=12x[/tex]

Solve for x. Subtract 12x from both sides:

[tex]3x-2=0[/tex]

Add 2 to both sides:

[tex]3x=2[/tex]

Divide both sides by 3:

[tex]x=2/3[/tex]

Therefore, the bird traveled for a total of 2/3 hours or 40 minutes.

And the distance the bird traveled is:

[tex]d=15x[/tex]

Substitute 2/3 for x to get:

[tex]d=15(2/3)=30/3=10\text{ miles}[/tex]

And we're done!

Answer:

They are both 45 degrees

Step-by-step explanation:

The square in the middle means a right angle (90) and 5 and 6 are equal too so they both equal 45

Answer:

23760 pounds

Step-by-step explanation:

396 passengers

60 pounds for each passenger

total pounds plane can carry=passengers × pounds

= 396×60

= 23760 pounds

....