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3 years ago

If line MO bisects angle PMN, angle PMN =74 and angle OMN =(2x+7)

Mathematics

1 answer:

Valentin [98]3 years ago

6 0

Answer:

Step-by-step explanation:

We can find the value of x from the question

If If line MO bisects angle PMN at M, then <PMO = < OMN and

<PMO + < OMN = <PMN

The equation then becomes;

<OMN + < OMN = <PMN

2<OMN = <PMN

Given

angle PMN =74 and

angle OMN =(2x+7)

Substituting the values into the formula to get x

2(2x+7) = 74

open the bracket

4x+14 = 74

Subtract 14 from both sides

4x+14-14 = 74-14

4x = 60

x = 60/4

x = 15

Hence the value of x is 15°

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10. A In the adjoining Figure, ab is perpendicular to bc and ed is to cd while bc=cd . prove i) triangle abc is corresponding to

xxTIMURxx [149]

Part (i)

1) AB is perpendicular to BC, ED is perpendicular to CD, BC = CD (given)

2) Angles ABC and CDE are right angles (perpendicular lines form right angles)

3) Angles ABC and CDE are equal (all right angles are equal)

4) Angles ACB and DCE are equal (vertical angles are equal)

5) Triangles ABC and EDC are congruent (ASA)

Part (ii)

6) AB = DE (corresponding parts of congruent triangles are equal)

4 0

2 years ago

34 in.

Troyanec [42]

Answer:

Step-by-step explanation:

Lateral surface area of the triangular prism = Perimeter of the triangular base × Height

By applying Pythagoras theorem in ΔABC,

AC² = AB² + BC²

(34)² = (16)² + BC²

BC = $\sqrt{1156-256}$

= $\sqrt{900}$

= 30 in.

Perimeter of the triangular base = AB + BC + AC

= 16 + 30 + 34

= 80 in

Lateral surface area = 80 × 22

= 1760 in²

Total Surface area = Lateral surface area + 2(Surface area of the triangular base)

Surface area of the triangular base = $\frac{1}{2}(\text{Base})(\text{Height})$

= $\frac{1}{2}(30)(16)$

= 240 in²

Total surface area = 1760 + 2(240)

= 1760 + 480

= 2240 in²

Volume = Area of the triangular base × Height

= 240 × 20

= 4800 in³

6 0

2 years ago

Which of the following is equivalent to the quadratic equation below after

Temka [501]

Answer:

Step-by-step explanation:

x^2 + 10x + 5 - 30 = 0

x^2 + 10x - 25 = 0

x^2 + 10x = 25

x^2 + 10x + 25 = 25 + 25

(x + 5)^2 = 50 <====

3 0

3 years ago

Pleaseee help...will mark BRAINLIEST!

olga2289 [7]

Answer:

Step-by-step explanation5:

3 0

3 years ago

Please help me solve for x =

Sladkaya [172]

Answer:

x = 13

Step-by-step explanation:

Given that Δ NML and Δ PST are similar right triangles, we can set up the following proportional statement to establish their relationship:

$\frac{ML}{NM} = \frac{ST}{PS}$

$\frac{8}{10} = \frac{x - 1}{x + 2}$

Cross multiply:

8(x + 2) = 10 (x - 1)

8x + 16 = 10x - 10

Subtract 8x from both sides:

8x - 8x + 16 = 10x - 8x - 10

16 = 2x - 10

Add 10 to both sides:

16 + 10 = 2x - 10 + 10

26 = 2x

Divide both sides by 2:

$\frac{26}{2} = \frac{2x}{2}$

13 = x

Verify whether x = 13 is the correct value:

$\frac{ML}{NM} = \frac{ST}{PS}$

$\frac{8}{10} = \frac{x - 1}{x + 2}$

$\frac{8/2}{10/2} = \frac{4}{5}$

$\frac{x -1}{x+2} = \frac{13 - 1}{13 + 2} = \frac{12}{15} = \frac{12 / 3}{15 /3} = \frac{4}{5}$

This shows the proportional relationship between $\frac{ML}{NM} = \frac{ST}{PS}$ , and that ΔNML and ΔPST are indeed similar right triangles.

Therefore, the correct answer is x = 13.

4 0

3 years ago