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3 years ago

Lines AB, CD, and EF intersect at point G. How many PAIRS of vertical angles are there in this diagram

Mathematics

1 answer:

trasher [3.6K]3 years ago

6 0

There are 3 pairs of vertical angles

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Please help me with this #5

shepuryov [24]

$\text{Given that,}\\\\a_1 = 10~ \text{ and}~ a_n = a_{n-1} -4~\text{for}~ n\geq 2\\\\a_2 = a_{2-1} -4 = a_1 -4 = 10 -4 = 6\\\\a_3 = a_{3-1} - 4=a_2 -4 = 6 -4 =2\\\\a_4 = a_{4-1} -4 = a_3 -4 = 2 -4 = -2\\\\\text{The first four terms are:}~ 10,~ 6,~ 2~, -2$

8 0

2 years ago

If a/b < c/d with b > 0, d > 0, prove that a+c / b+d lies between the two fractions a/b and c/d .

Tems11 [23]

Divide through everything by b :

$\dfrac{a+c}{b+d} = \dfrac{\dfrac ab + \dfrac cb}{1 + \dfrac db}$

Since a/b < c/d, it follows that

$\dfrac{a+c}{b+d} < \dfrac{\dfrac cd+\dfrac cb}{1 + \dfrac db}$

Multiply through everything on the right side by b/d to get

$\dfrac{a+c}{b+d} < \dfrac{\dfrac{bc}{d^2}+\dfrac cd}{\dfrac bd+1} = \dfrac{\dfrac cd\left(\dfrac bd+1\right)}{\dfrac bd+1} = \dfrac cd$

and so (a + c)/(b + d) < c/d.

For the other side, you can do something similar and divide through everything by d :

$\dfrac{a+c}{b+d} = \dfrac{\dfrac ad + \dfrac cd}{\dfrac bd + 1}$

and a/b < c/d tells us that

$\dfrac{a+c}{b+d} > \dfrac{\dfrac ad + \dfrac ab}{\dfrac bd + 1}$

Then

$\dfrac{a+c}{b+d} > \dfrac{\dfrac ab + \dfrac{ad}{b^2}}{1 + \dfrac db} = \dfrac{\dfrac ab\left(1+\dfrac db\right)}{1 + \dfrac db} = \dfrac ab$

and so (a + c)/(b + d) > a/b.

Then together we get the desired inequality.

5 0

3 years ago

A store I selling all toaster ovens at 15% off. Write an equation in the form y=kx

slavikrds [6]

The answer is y equals 0.85 x. Hope this help you

5 0

3 years ago

Write and evaluate the expression. Then, complete the statements. Ten less than the quotient of thirty and a number Evaluate whe

Artyom0805 [142]

Answer:

expression: (30/t) - 10

evaluation: 30/2 - 10 = 5

Step-by-step explanation:

8 0

3 years ago

How do I find the domain and range of a graph?

tia_tia [17]

The domain is the x-axis and the range is the y-axis.

To find the domain, you measure or count the widest part of this oval horizontally. So that is 3 units to the right of 0 and 3 units to the left of 0. I counted it exactly on the axis because that is the widest part of the oval.

To find the range, you again count or measure the widest part of the oval vertically. So that is 4 units above 0 and 4 units below 0.

Final Answer

D: -3 ≤ x ≤ 3

R: -4 ≤ x ≤4

7 0

4 years ago