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4 years ago

Please Help due today!!

Mathematics

1 answer:

Wewaii [24]4 years ago

6 0

<span>Angle 7 and 5 are vertical angles, so they're equal. Angles 7 and 8 are supplementary, so they have to add up to 180. 2x + 15 + 3x = 180 Solve for x, then plug it into the expression for angle 7 to get you answer</span>

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WITCHER [35]

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3 years ago

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Currently, I am $9$ times as old as my son. Next year, I will be $7$ times as old as my son. How old is my son now?

grandymaker [24]

Answer:

He is 3 years old.

Step-by-step explanation:

3 times 9 is 27. She is 9 times older than her 3 year old son.

Next year he will be 4 and she will be 28. 4 times 7 is 28. She will be 7 times older than her son.

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If the square is 3 by 4 and shaded area is 5/8 by 3/7 what is the area of shaded region

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4 years ago

In the trapezoid ABCD (AB∥CD) point M∈AD, so that AM:MD=3:5. Line L ∥AB and going through point M intersects diagonal AC and leg

siniylev [52]

Answer:

$\dfrac{AP}{PC}=\dfrac{3}{5}$

$\dfrac{BN}{CN}=\dfrac{3}{5}$

Step-by-step explanation:

Consider triangles AMP and ADC. In these triangles,

angle A is the common angle, so $\angle MAP\cong \angle DAC$ by reflexive property;
angles AMP and ADC are congruent as corresponding angles when two parallel lines MP and CD are cut by transversal AD.

Hence, triangles AMP and ADC are similar by AA similarity theorem.

Similar triangles have proportional corresponding sides, thus

$\dfrac{AM}{AD}=\dfrac{AP}{AC}\\ \\\dfrac{3x}{3x+5x}=\dfrac{AP}{AC}\\ \\\dfrac{AP}{AC}=\dfrac{3}{8}\Rightarrow AP=\dfrac{3}{8}AC\\ \\PC=AC-AP=AC-\dfrac{3}{8}AC=\dfrac{5}{8}AC,$

$\dfrac{AP}{PC}=\dfrac{\frac{3}{8}AC}{\frac{5}{8}AC}=\dfrac{3}{5}$

Consider triangles ACB and PCN. In these triangles,

angle C is the common angle, so $\angle ACB\cong \angle PCN$ by reflexive property;
angles ABC and PCN are congruent as corresponding angles when two parallel lines PN and AB are cut by transversal BC.

Hence, triangles ACB and PCN are similar by AA similarity theorem.

Similar triangles have proportional corresponding sides, thus

$\dfrac{CP}{AP}=\dfrac{CN}{CB}\\ \\\dfrac{5x}{3x+5x}=\dfrac{CN}{CB}\\ \\\dfrac{CN}{CB}=\dfrac{5}{8}\Rightarrow CN=\dfrac{5}{8}CB\\ \\BN=BC-CN=BC-\dfrac{5}{8}BC=\dfrac{3}{8}BC,$

$\dfrac{BN}{CN}=\dfrac{\frac{3}{8}BC}{\frac{5}{8}BC}=\dfrac{3}{5}$

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3 years ago

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Answer:

132 is the answer

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