3

asambeis [7]

X=2
To check it you plug in 2 for x. Which then gives you:

3+(2-14)=-15+6 which then gives you:
3+-12=-15+6 which the gives you:
-9=-9

6 0

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

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

so

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

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

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

so

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

4 0

3 years ago

Part a which projectile spends more time in the air, the one fired from 30∘ or the one fired from 60∘? which projectile spends m

bearhunter [10]

The correct answer is the One fired from from 60° . This is because the projectile fired from 60° has a greater vertical velocity compared to the one fired from 30° and therefore spends more time on air. Vertical velocity is the velocity of a body as it moves upwards, it is normally affected by the gravitational acceleration, however it is not affected by the horizontal velocity.

5 0

3 years ago

Read 2 more answers

What is 6.051×105 written in standard form?

alex41 [277]

6.051 × $10^{5}$ = 605,100

So, your answer would have to be 605,100

Since the exponent of the scientific notation is a positive five ((5)), move the decimal point to the right

8 0

3 years ago

What is 4567-213+866= please dont answer except Johannes02

Alexandra [31]

5220 is your answer

please can i have a brainliest

6 0

3 years ago

Read 2 more answers