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kykrilka [37]
1 year ago
6

Sammy has a 10-foot ladder, which he needs to climb to reach the roof of his house. the roof is 12 feet above the ground. the ba

se of the ladder must be at least 1.5 feet from the base of the house. how far is it from the top of the ladder to the edge of the roof? draw a sketch.
Mathematics
1 answer:
timama [110]1 year ago
6 0
<span>Using the Pythagorean theorum we can solve this v a^2+b^2= c^2. A is the distance from base of house to ladder A= 1.5, c ifls length of ladder, c= 10. (1.5)^2 + ;b^2 = (10)^2. Solve for b. B= 9.88. 12 foot height of house - 9.88 feet to top of angled ladder = 2.11 from top of ladder to edge of roof</span>
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Ella completed the following work to test the equivalence of two expressions.
MrRa [10]
Answer:

The expressions are not equivalent because Ella did not know that you can’t use substitution to test for equivalence.

Step-by-step explanation:

Equivalent algebraic expressions are those expressions which on simplification give the same resulting expression.

Two algebraic expressions are said to be equivalent if their values obtained by substituting any values of the variables are same.

Two expressions 3f+2.6 and 2f+2.6 are not equivalent, because when f=1,

3f + 2.6 = 3.1 + 2.6 = 3 + 2.6 = 5.6

2f + 2.6 = 2.1 + 2.6 = 2 + 2.6 = 4.6

5.6 = 4.6

Method of substitution can only help her to decide the expresssions are not equivalent, but if she wants to prove the expressions are equivalent, she must prove it for all values of f.

3f + 2.6 = 2f + 2.6

3f = 2f

3f - 2f = 0

f = 0

This is true only when f=0.

Hence,

The expressions are not equivalent because Ella did not know that you can’t use substitution to test for equivalence.
6 0
1 year ago
Read 2 more answers
How many distinct pairs of disjoint non-empty subsets of A are there, the union of which is all of A?
Mrac [35]
A = {1, 2, 5, 6, 8}
{1} U {2, 5, 6, 8} 
{2} U {1, 5, 6, 8} 
{5} U {1, 2, 6, 8} 
{6} U {1, 2, 5, 8} 
{8} U {1, 2, 5, 6} 
{1, 2} U {5, 6, 8} 
{1, 5} U {2, 6, 8} 
{1, 6} U {2, 5, 8}
{1, 8} U {2, 5, 6} 
{1, 2, 5} U {6, 8} 
{1, 2, 6} U {5, 8}
{1, 2, 8} U {5, 6}
{1, 5, 6} U {2, 8}
{1, 5, 8} U {2, 6}
{1, 6, 8} U {2, 5} 
The answer is 15 distinct pairs of disjoint non-empty subsets.
5 0
1 year ago
Torrey starts a new job with an annual salary of $60,000. For each year she continues to work for the same company, she will rec
GarryVolchara [31]
The third choice will work
6 0
1 year ago
Read 2 more answers
Mya is doing a 45-minute cardio workout. She has completed 4 5 of the workout. In how many minutes will her workout be done?
Alika [10]

Answer:

9 minutes

Step-by-step explanation:

45/5 equals 9

6 0
2 years ago
calculeaza lungimea segmentului ab in fiecare dintre cazuri:A(1,5);B(4,5);A(2,-5),B(2,7);A(3,1)B(-1,4);A(-2,-5)B(3,7);A(5,4);B(-
Tatiana [17]

Answer:

1. 3; 2. 12; 3. 5; 4. 13; 5. 10; 6. 10

Step-by-step explanation:

We can use the distance formula to calculate the lengths of the line segments.

d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}

1. A (1,5), B (4,5) (red)

d = \sqrt{(x_{2} - x_{1}^{2}) + (y_{2} - y_{1})^{2}} = \sqrt{(4 - 1)^{2} + (5 - 5)^{2}}\\= \sqrt{3^{2} + 0^{2}} = \sqrt{9 + 0} = \sqrt{9} = \mathbf{3}

2. A (2,-5), B (2,7) (blue)

d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}} = \sqrt{(2 - 2)^{2} + (7 - (-5))^{2}}\\= \sqrt{0^{2} + 12^{2}} = \sqrt{0 + 144} = \sqrt{144} = \mathbf{12}

3. A (3,1), B (-1,4 ) (green)

d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}} = \sqrt{(-1 - 3)^{2} + (4 - 1)^{2}}\\= \sqrt{(-4)^{2} + 3^{2}} = \sqrt{16 + 9} = \sqrt{25} = \mathbf{5}

4. A (-2,-5), B (3,7) (orange)

d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}} = \sqrt{(3 - (-2))^{2} + (7 - (-5))^{2}}\\= \sqrt{5^{2} + 12^{2}} = \sqrt{25 + 144} = \sqrt{169} = \mathbf{13}

5. A (5,4), B (-3,-2) (purple)

d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}} = \sqrt{(-3 - 5)^{2} + (-2 - 4)^{2}}\\= \sqrt{(-8)^{2} + (-6)^{2}} = \sqrt{64 + 36} = \sqrt{100} = \mathbf{10}

6. A (1,-8), B (-5,0) (black)

d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}} = \sqrt{(-5 - 1)^{2} + (0 - (-8))^{2}}\\-= \sqrt{(-6)^{2} + (-8)^{2}} = \sqrt{36 + 64} = \sqrt{100} = \mathbf{10}

6 0
1 year ago
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