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marysya [2.9K]
3 years ago
14

Andrew needs a ladder to hang holiday lights. His house is 24 feet tall and he has a flower bed that extends 4 feet out from the

side of the house. How long of a ladder will he need to reach the top and be out of the flower bed?
Mathematics
1 answer:
blsea [12.9K]3 years ago
5 0

Answer:

24.33 feet

Step-by-step explanation:

The flower bed, the ladder and the house form a right angled triangle where the length of the ladder is the hypotenuse side.

Let L = length of ladder, H = height of house = 24 feet and l = length of flower bed = 4 feet.

Using Pythagoras' theorem,

L² = H² + l²

So, L = √(H² + l²)

substituting the values of the variables, we have

L = √[(24 ft)² + (4 ft)²]

L = √[576 ft² + 16 ft²]

L = √[592 ft²]

L = 24.33 ft

The ladder must be at least 24.33 feet long to reach the top and be out of the flower bed

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-2(x+1)+6x&lt;-14<br>I need help​
jeka57 [31]

Answer:

x<-3

Step-by-step explanation:

-2(x+1)+6x<-14

Distribute

-2x-2 + 6x < -14

Combine like terms

4x -2 < -14

Add 2 to each side

4x-2+2 < -14+2

4x < -12

Divide by 4

4x/4 < -12/4

x<-3

3 0
3 years ago
Fiona bought some socks that cost $4.95 for each pair and some belts that cost $6.55 each. Fiona spent $27.95 in all. Let a repr
Romashka [77]
The question lacks the total number of socks and belts altogether. Thsi value is necessary so that we can create another equation to solve the unknowns.

if assumed that a = b, the answer, a = b = 2.43 will not make sense since you cannot buy 43% of a pair of socks. Completely define the conditions so that the answer can be obtained. 

by trial and error, 3 pair of socks and 2 belts would be a sensible answer
6 0
3 years ago
Read 2 more answers
The length of a rectangle is (x-8) units, and its width is(x+11) units. What is an expression for this.
Ipatiy [6.2K]

Answer:

(x²+3x-88) square units

Step-by-step explanation:

Area of a rectangle = Length × Width

Given

length of a rectangle is (x-8)units

Its width is (x+11) units.

Required

Expression for the area of the rectangle

Substituting the given function into the formula.

Area of the rectangle = (x-8)(x+11)

Area of the rectangle = x(x)+11x-8x-88

Area of the rectangle = x²+3x-88

Hence the expression that represents the area of the rectangle is x²+3x-88 units²

8 0
3 years ago
Please look at the picture.
Vladimir79 [104]

Answer:

J.

Step-by-step explanation:

There is no solution because these are parallel lines.

Parallel lines never intersect and so they have no solution.

8 0
2 years ago
Using Multiple regression, the relationship of Y to four other variables was established as: Y = 12 + 3X₁ – 5X₂ + 7X₃ + 2X₄ When
alexdok [17]

Answer:

The estimate of Y changes by -2 or decreases by 2.

Step-by-step explanation:

We are given the following information:

Using Multiple regression, the relationship of Y to four other variables was established as:

Y = 12 + 3X_1- 5X_2 + 7X_3 + 2X_4

X_1 increases 2 units and X_2 increases 1 unit, while X_3 and X_4 remain unchanged.

Predicted Y =

Y_p = 12 + 3(X_1+2) - 5(X_2+1) + 7X_3 + 2X_4

Change in Y =

Y_p - Y \\= 12 + 3(X_1+2) - 5(X_2+1) + 7X_3 + 2X_4-(12 + 3X_1 - 5X_2 + 7X_3 + 2X_4)\\= 12-12+3(X_2+1-X_2)-5(X_2+1-X_2) + 7X_3 - 7X_3 + 2X_4 - 2X_4\\=3 - 5\\= -2

The estimate of Y changes by -2 or decreases by 2.

3 0
3 years ago
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