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Law Incorporation [45]
3 years ago
5

7. Select all the properties that can be

Mathematics
1 answer:
mixer [17]3 years ago
8 0

Answer:

7y-15=-29

The steps to solve this is as follows:

Adding 15 to both sides;

7y-15+15=-29+15        (Addition Property of Equality)

=> 7y =-14

Diving by 7 on both sides we get;

\frac{7y}{7} =\frac{-14}{7}    (Inverse Property of  Multiplication)

Finally we get;

y= -2

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3 years ago
A rhombus ABCD has AB = 10 and m∠A = 60°. Find the lengths of the diagonals of ABCD.
melisa1 [442]
Three important properties of the diagonals of a rhombus that we need for this problem are:
1. the diagonals of a rhombus bisect each other
2. the diagonals form two perpendicular lines
3. the diagonals bisect the angles of the rhombus

First, we can let O be the point where the two diagonals intersect (as shown in the attached image). Using the properties listed above, we can conclude that ∠AOB is equal to 90° and ∠BAO = 60/2 = 30°. 

Since a triangle's interior angles have a sum of 180°, then we have ∠ABO = 180 - 90 - 30 = 60°. This shows that the ΔAOB is a 30-60-90 triangle.

For a 30-60-90 triangle, the ratio of the sides facing the corresponding anges is 1:√3:2. So, since we know that AB = 10, we can compute for the rest of the sides.

\overline{OB}:\overline{AB} = 1:2
\overline {OB}:10 = 1:2
\overline{OB} = \frac{1}{2}(10) = 5

Similarly, we have

\overline{AO}:\overline{AB} = \sqrt{3}:2
\overline {AO}:10 = \sqrt{3}:2
\overline{AO} = \frac{\sqrt{3}}{2}(10) = 5\sqrt{3}

Now, to find the lengths of the diagonals, 

\overline{AD} = 2(\overline{AO}) = 10\sqrt{3}
\overline{BC} = 2(\overline{OB}) = 10

So, the lengths of the diagonals are 10 and 10√3.

Answer: 10 and 10√3 units

8 0
3 years ago
I need to solve for 3x+7=-x-1
Andrew [12]

3x+7=-x-1

move -x to the other side

sign changes from -x to +x

3x+x+7=-x+x-1

3x+x+7=-1

4x+7=-1

move 7 to the other side

sign changes from +7 to -7

4x+7-7=-1-7

4x=-8

Divide by 4 for both sides

4x/4=-8/4

Answer: x=-2

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