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3 years ago

What is the product in lowest terms?

Mathematics

2 answers:

BaLLatris [955]3 years ago

8 0

I don't know what lowest terms means but the answer is -416216.

Gala2k [10]3 years ago

7 0

-539 is the lowest term out of your answers

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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

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

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

4 0

3 years ago

Sasha wants to make 8 batches of soup. She has six pounds of potatoes. If 1 batch requires 3/4 pounds of potatoes. Does she have

Finger [1]

Yes she does, because 6lbs/.75lbs = 8

7 0

3 years ago

Read 2 more answers

Solve the equation. 11 6 = n + 7 9 6 11 =n+ 9 7 start fraction, 11, divided by, 6, end fraction, equals, n, plus, start frac

belka [17]

Answer:

n = 19/18

Step-by-step explanation:

Given:

11/6 = n + 7/9

Find n

11/6 = n + 7/9

Subtract 7/9 from both sides of the equation

11/6 - 7/9 = n + 7/9 - 7/9

11/6 - 7/9 = n

(99-42) / 54 = n

n = 57/54

n = 19/18

4 0

3 years ago

The population of a city is about 200,000 and is growing at a rate of 0.6% per year.

IgorC [24]

A)

$\bf \qquad \textit{Amount for Exponential Growth}\\\\
A=P(1 + r)^t\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{initial amount}\to &200000\\
r=rate\to 0.6\%\to \frac{0.6}{100}\to &0.006\\
t=\textit{elapsed time}\to &t\\
\end{cases}
\\\\\\
A=200000(1+0.006)^t\implies A=200000(1.006)^t$

B) $\bf A=200000(1.006)^4$

5 0

3 years ago

Plspls pls pls pls plssssssssss

Schach [20]

Answer:

Answe below

Step-by-step explanation:

its actually 18/7

3 0

3 years ago

Read 2 more answers