Simplify 12 − 32 + (5 − 1)2. <br> A) 12 <br> B) 18 <br> C) 19 <br> D) 97

What is 44 feet per second as a unit rate.

MariettaO [177]

Answer:

44fps, or 44:1

Step-by-step explanation:

it is already a unit rate

3 0

3 years ago

Read 2 more answers

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

Mr. Taylor raised all his students’ scores on a recent test by five

Darina [25.2K]

2. The mean is the average so it phase shifted up five points where as the range is the difference between the highest and lowest # which wouldn't change if all the numbers were adjusted.

3 0

4 years ago

I'll mark brainlest just help

Zinaida [17]

The correct answer is option c bro.

4 0

3 years ago

Michael is 3 years older that Jafi. Li-Li is half Jafi's age and 2 years older than Clara. If Clara is 5 years old, how old is J

Ahat [919]

Clara is 5yo
Li-Li is 2 years older then Clara, so
Li-Li is 7yo
Li-Li is half Jafi's age. so Jafi's age is twice Li-Li's
Answer: Jafi is 14yo.

5 0

3 years ago

Simplify 12 − 32 + (5 − 1)2. A) 12 B) 18 C) 19 D) 97