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4 years ago

M–[(m–n)÷(−2)](−5), if m=−4, n=−6

Mathematics

1 answer:

jeka944 years ago

5 0

Answer:

-9

Step-by-step explanation:

We are given the expression m–[(m–n)÷(−2)](−5). Substituting -4 for m and -6 for n, we get:

-4–[(-4 + 6)÷(−2)](−5)

We must do the work that appears inside parentheses first:

-4–[( 2 )÷(−2)](−5)

Next we must do the work that appears inside square brackets:

-4–[ -1 ](−5)

Multiplication comes next. The above expression becomes:

-4 - [ 5 ]

which in turn comes out to -9

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What are expressions for MN and LN? Hint Construct the altitude from M to LN.

Nikitich [7]

The question is missing the figure. So, it is in the atachment.

Answer: MN = x $\sqrt{2}$ LN = $\frac{x}{2}.(\sqrt{2} + \sqrt{6} )$

Step-by-step explanation: The first figure in the attachment is the figure of the question. The second figure is a way to respond this question by tracing the altitude from M to LN as suggested. When an altitude is drawn, it forms a 90° angle with the base, as shown in the drawing. To determine the other angle, you have to remember that all internal angles of a triangle sums up to 180°.

For the triangle <u>on the left</u> of the altitude:

45+90+angle=180

angle = 45

For the triangle <u>on the right</u>:

30+90+angle=180

angle = 60

With the angles, use the Law of Sines, which is relates sides and angles, as follows:

$\frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC}$

For MN:

$\frac{x}{sin(30)} = \frac{MN}{sin(45)}$

MN = $\frac{x.sen(45)}{sen(30)}$

MN = x $\sqrt{2}$

For LN:

$\frac{LN}{sen(105)} =\frac{x}{sin(30)}$

LN = $\frac{x.sin(105)}{sin(30)}$

We can determine sin (105) as:

sin(105) = sin(45+60)

sin(105) = sin(45)cos(60) + cos(45)sin(60)

sin(105) = $\frac{\sqrt{2} }{2}.\frac{1}{2} + \frac{\sqrt{2} }{2}.\frac{\sqrt{3} }{2}$

sin(105) = $\frac{\sqrt{2} }{4} + \frac{\sqrt{6} }{4}$

LN = $\frac{x.sin(105)}{sin(30)}$

LN = $x.(\frac{\sqrt{2} }{4} + \frac{\sqrt{6} }{4} ) .2$

LN = $\frac{x}{2}.(\sqrt{2} + \sqrt{6} )$

The expressions for:

MN = x $\sqrt{2}$

LN = $\frac{x}{2}.(\sqrt{2} + \sqrt{6} )$

6 0

3 years ago

SOMEONE HELP WHAT IS THE ANSWER TO THESE QUESTIONS PLEASE HELP

romanna [79]

10.
Answer: 42° and 138°
Steps: First find value of x by adding both equations and setting them equal to 180°:
3x + 12x - 30 = 180
15x - 30 = 180
15x = 210
x = 14

Next, put value of x into equations to find the angle:
3x
3(14)
42°

12x - 30
12(14) - 30
168 - 30
138°

11. Answer: 28°
Steps: Complementary angles add up to 90°, so subtract 62° from 90° to find its complementary angle.
90 - 62 = 28

12. Answer: Corresponding angles are congruent.

7 0

3 years ago

What is the geometric mean of the pair of numbers? 245 and 5

VLD [36.1K]

Answer:

Step-by-step explanation:

The geometric mean of n numbers is the n-th root of their product.

The geometric mean of these two numbers is ...

√(245·5) = √1225 = 35

7 0

3 years ago

(9x+72) (12x+66) find the values of x and y