Simplify the expression. 7(3x + 5y) + 4y

Answers

Answer 1

Answer: =21x + 35y + 4y
= 21x + 39y

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Suppose that the functions f and g are defined for all real numbers x as follows.f(x) = 3x+3
g(x) = 5x
Write the expressions for (f times g)(x) and (f+g)(x) and evaluate (f-g)(2)

Answers

Answer:

Step-by-step explanation:

a) fg(x)

--> f(5x)

--> 3(5x)+3

--> 15x+3

b) f+g(x)

--> 3x+3+ 5x

c) (f-g)(2)

3x+3- 5x

--> 3(2)+3-5(2)

--> -1

Answer:

solution given:

f(x) = 3x+3

g(x) = 5x

now

(f times g)(x)=?

(f+g)=?

(f-g)=?

we have

(f times g)(x)=f(g(x))

substituting value of g(x)

f(g(x))=f(5x)

now replacing value of x in f(x)

f(5x)=3(5x)+3

solving it

f(5x)=15x+3

so (f times g)(x) =15x+3

Step-by-step explanation:

again,

(f+g)(x)=f(x)+g(x)=3x+3+5x=8x+3

(f+g)(x) =8x+3

again

we need to find (f-g)(x) first so

(f-g)(x)=f(x)-g(x)=3x+3-5x=-2x+3

now

(f-g)(2)=-2*2+3=-1

(f-g)(2)=-1

What is the distance between (-5,4) and (8,-2)

Answers

The distance between -5 and 8 is 13.

The distance between -2 and 4 is 6.

These two distances, including the hypotenuse which is the distance you want to discover - form a right angled triangle. The adjacent side of this right angled triangle has a length of 13, whilst its opposite side has a length of 6.

If you want to find the distance between (-5, 4) and (8, -2), you simply measure the hypotenuse of this invisible right angled triangle which has been formed. Let's call the length of this hypotenuse "d".

We shall use Pythagoras's theorem to produce our result:

${ d }^( 2 )={ 13 }^( 2 )+{ 6 }^( 2 )\n \n d=\sqrt { { 13 }^( 2 )+{ 6 }^( 2 ) } \n \n \therefore \quad d=\sqrt { 205 }$

[*Complete answer derived on a calculator]

This means that the distance between (-5, 4) and (8, -2) is $√(205)$ . $√(205)$ is approximately equal to 14.3.

BRAINLIST ANSWER!!!!!!!!!!!!!!!!!!!!!!!!!!!!1. A wooden plank is leaning against an outside wall of a building. The bottom of the plank is 3 ft from the wall. Find each of the following values, and show all your work.
(a) Find the approximate length of the plank. Round to the nearest tenth of a foot.
(b) Find the height above the ground where the plank touches the wall. Round to the nearest tenth of a foot.

2. A support wire is strung from a tree. The bottom of the wire is 24 ft from the tree. The length of the wire is 30 ft. Find each of the following values, and show all your work.
(a) Find the value of x. Round to the nearest tenth of a degree.
(b) Find the approximate height where the wire touches the tree. Round to the nearest foot.

Answers

Question 1:
(a) Using sine rule
ground/Sin 49 = plank/Sin 90

But sine 90 = 1, ground = 3 ft
Then,
3/Sin 49 = plank
Length of the plank = 3/Sin 49 ≈ 4.0 ft (rounded to nearest tenth)

(b) Height where the plank touches the wall

wall = Sqrt (plank^2 - ground^2) = Sqrt (4.0^2 - 3.0^2) ≈ 2.6 ft (Rounded to nearest tenth)

Question 2:
(a) Angle x
ground = 24 ft
support wire = 30 ft

Applying sine rule
support wire/Sin 90 = ground/Sin (90-x) ----- but Sin 90 = 1
Then,
Support wire = ground/Sin (90-x)
Sin (90-x) = ground/support wire = 24/30 = 0.8
90-x = Sin^-1(0.8) = 53.13 => x = 90-53.13 = 36.9°

(b) Height where the wire touches the tree (tree)
tree = Sqrt (support wire^2 - ground^2) = Sqrt (30^2 - 24^2) = 18 ft

I ONLY NEED HELP WITH PART BAn equation is shown below:

5x + 3(x – 5) = 6x + 2x – 15

Part A: Solve the equation and write the number of solutions. Show all the steps. (6 points)

Part B: Name one property you used to solve this equation. (4 points)

Answers

Hi there

5x+3(x-5)=6x+2x-15

Simplify both sides of the equation

5x+3(x-5)=6x+2x-15

Distribute

5x+3x-15=6x+2x-15

Combine like terms

(5x+3x)-15= (6x+2x)-15

8x-15=8x-15

Subtract 8x from both sides

8x-15-8x=8x-15-8x

-15=-15

Add 15 to both sides

-15+15=-15+15

0=0

All real numbers are solutions

To solve this equation I used " The distributive property"

I hope that's help !

Good night !

A line with a slope of 0 contains the point (3,4) . The point -2,? is also on the line. What is the missing y-coordinate?The solution is ___________

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