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Nata [24]
3 years ago
15

If y is 9 and x is 12, what additional information is necessary to show that triangle DUM is congruent to triangle MAP using the

SAS postulate?

Mathematics
1 answer:
Law Incorporation [45]3 years ago
6 0
                         Δ DUM         Δ MAP

hypotenuse:      15                2y-3
short leg:             12                0.5x + 6

y = 9 ⇒ 2(9) - 3 = 18 - 3 = 15 Congruent with the hypotenuse of Δ DUM
x = 12 ⇒ 0.5(12) + 6 = 6 + 6 = 12 Congruent with the short leg of Δ DUM

SAS postulate states that two triangles are congruent if 2 of its sides and 1 angle have equal measure. Both the hypotenuse and short leg are equal in measure. Thus, both triangles are congruent with each other.
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What is the equation of the line that is parallel to the line x = –2 and passes through the point (–5, 4)?x = –5x = 4y = –5y = 4
Rainbow [258]

x = -5 is the equation of the line that is parallel to the line x = –2 and passes through the point (–5, 4)

<em><u>Solution:</u></em>

Given that, we have to write the equation of line that is parallel to line x = -2 and passes through point (-5, 4)

From given,

The equation of the line in standard form is x = -2

<em><u>This is a vertical line, so the parallel line will also be a vertical line of the form:</u></em>

x = a

Since we are given that the line should pass through the point (-5, 4)  then the equation of the line is:

x = -5

Thus the equation of line is found

3 0
3 years ago
Read 2 more answers
Which is the simplified form of (9c^-9)^-3<br> b 1/729 c^27
rosijanka [135]

<u>ANSWER</u>

(9 {c}^{ - 9} )^{ - 3}=\frac{{c}^{ 27} }{729}

<u>EXPLANATION</u>

The given expression is

(9 {c}^{ - 9} )^{ - 3}

Recall that:

({a}^{m} )^{n}  =  {a}^{mn}

We use the law of exponents to get

(9 {c}^{ - 9} )^{ - 3}  = 9^{ - 3}  {c}^{ - 9 \times  - 3}

Let us multiply in the exponents to get:

(9 {c}^{ - 9} )^{ - 3}  = 9^{ - 3}  {c}^{ 27}

Recall again that:

{a}^{ - m}  =  \frac{1}{ {a}^{m} }

This implies that:

(9 {c}^{ - 9} )^{ - 3}  =  \frac{1}{ {9}^{ 3} }  \times {c}^{ 27}

We expand the power to get:

(9 {c}^{ - 9} )^{ - 3}  =  \frac{1}{9 \times 9 \times 9} \times {c}^{ 27}

(9 {c}^{ - 9} )^{ - 3}=\frac{1}{729}  \times {c}^{ 27}

We multiply out to get:

(9 {c}^{ - 9} )^{ - 3}=\frac{{c}^{ 27} }{729}

7 0
3 years ago
Write an equation parallel to the line
Schach [20]
The easiest way to find a parallel equation is to write your equation in slope-intercept form. The general equation for slope-intercept form is y = mx + b, where m = the slope of the equation, b = the y intercept, and x and y are your variables.

You're given 5x + 10y = -4. 
1) Move 5x to the right side by subtracting 5x from both sides:
5x + 10y = -4
10y = -5x - 4

2) Divide both sides by 10 to get y by itself on the left. Simplify:
10y = -5x - 4\\&#10;y = - \frac{5}{10} x -  \frac{4}{10} \\&#10;y = - \frac{1}{2}  x -  \frac{2}{5}



<span>Remember that for parallel lines, the slope, m, is the same for both equations. You can make the y-intercept, b, whatever number you want.

When the equation is in slope-intercept form, </span>y = - \frac{1}{2} x - \frac{2}{5}, you can see that m =  - \frac{1}{2}. 

A parallel equation is in the form: 
y = - \frac{1}{2} x + b

Plug in anything you want for b. One example is: y = - \frac{1}{2} x + 3

-------

Answer: y = - \frac{1}{2} x + 3 (just one example)



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3 years ago
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