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Bas_tet [7]
3 years ago
14

The top of a ladder rests at a height of 15 feet against the side of a house. If the base of the ladder is 6 feet from the house

, what is the length of the ladder? Round to the nearest foot.
Mathematics
1 answer:
Advocard [28]3 years ago
4 0

Answer:

The length of the ladder is 16\ ft

Step-by-step explanation:

Let

L ----> the length of the ladder

we know that

Applying the Pythagoras theorem

L^{2}=15^{2} +6^{2}

L^{2}=261

L=\sqrt{261}\ ft

L=16\ ft

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Round off 7284 to 1sf​
AVprozaik [17]

Answer:

7000

Step-by-step explanation:

This is because when you round to the significant figure, you basically look at any digits at the start of the number, which isn't zero. In this case, it would be in the thousands place 7284. So you round 7284 to the nearest thousands, which, would be 7000

6 0
3 years ago
Read 2 more answers
Solve for W <br> V = L + W
Elena L [17]

Answer:

W = -L + V

Step-by-step explanation:

V = L + W

~Subtract L to both sides

V - L = W

Best of Luck!

5 0
3 years ago
The axis of symmetry for the function f(x) = –2x2 + 4x + 1 is the line x = 1. Where is the vertex of the function located?
egoroff_w [7]

Answer:

(1, 3)

Step-by-step explanation:

You are given the h coordinate of the vertex as 1, but in order to find the k coordinate, you have to complete the square on the parabola.  The first few steps are as follows.  Set the parabola equal to 0 so you can solve for the vertex.  Separate the x terms from the constant by moving the constant to the other side of the equals sign.  The coefficient HAS to be a +1 (ours is a -2 so we have to factor it out).  Let's start there.  The first 2 steps result in this polynomial:

-2x^2+4x=-1.  Now we factor out the -2:

-2(x^2-2x)=-1.  Now we complete the square.  This process is to take half the linear term, square it, and add it to both sides.  Our linear term is 2x.  Half of 2 is 1, and 1 squared is 1.  We add 1 into the set of parenthesis.  But we actually added into the parenthesis is +1(-2).  The -2 out front is a multiplier and we cannot ignore it.  Adding in to both sides looks like this:

-2(x^2-2x+1)=-1-2.  Simplifying gives us this:

-2(x^2-2x+1)=-3

On the left we have created a perfect square binomial which reflects the h coordinate of the vertex.  Stating this binomial and moving the -3 over by addition and setting the polynomial equal to y:

-2(x-1)^2+3=y

From this form,

y=-a(x-h)^2+k

you can determine the coordinates of the vertex to be (1, 3)

5 0
3 years ago
Read 2 more answers
Nick was surveying his field and saw some cows and ducks. Nick counted a total of 80 heads and
Natali [406]

Answers:

  • Total equation:  x+y = 80
  • Legs equation:  2x+4y = 248
  • How many ducks? 36
  • How many cows? 44

====================================================

Further explanation:

  • x = number of ducks
  • y = number of cows

x+y = 80 is the total equation (ie the head count equation) since we assume each animal has 1 head, and there are 80 heads total.

That equation can be solved to y = 80-x after subtracting x from both sides.

The legs equation is 2x+4y = 248 because...

  • 2x = number of legs from all the ducks only
  • 4y = number of legs from all the cows only
  • 2x+4y = total number of legs from both types of animals combined

We're told there are 248 legs overall, so that's how we ended up with 2x+4y = 248

------------

Let's plug y = 80-x into the second equation and solve for x.

2x+4y = 248

2x+4( y ) = 248

2x+4( 80-x ) = 248

2x+320-4x = 248

-2x+320 = 248

-2x = 248-320

-2x = -72

x = -72/(-2)

x = 36

There are 36 ducks

Now use this x value to find y

y = 80-x

y = 80-36

y = 44

There are 44 cows.

------------

Check:

36 ducks + 44 cows = 80 animals total

36*2 + 44*4 = 72 + 176 = 248 legs total

The answers are confirmed.

5 0
2 years ago
Trevor was reading a book for a book report. Last week, he read 35 pages of the book. This week, he read 4.5 times as many pages
navik [9.2K]

9514 1404 393

Answer:

  see below

Step-by-step explanation:

Multiply the numbers as though they were integers, then mark off a number of decimal places in the product equal to the total number of decimal places in the numbers being multiplied (1).

6 0
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