write an expression that can be used to find 4 times 275 using mental math and properties of numbers.

2 answers:

6 0

Rough estimate: 4 times 300 = 1200

Properties of numbers: 4 times (300-25) = 4 times 300 - 4 times 25
= 1200 - 100
= 1100 (exact answer)

sashaice [31]3 years ago

4 0

(200×4) + (70×4) + (5×4)

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7 0

3 years ago

What is the value of f(-12) if f(x) = 4x - 12

Cerrena [4.2K]

Answer:

-36

Step-by-step explanation:

Just plug in -12 for x

f(x) = 4 x (-12) -12

-48 - 12 = -36

8 0

3 years ago

Find the two small as possible solutions

solong [7]

Answer: $\bold{b)\quad \dfrac{5}{6},\ \dfrac{25}{6}}$

<u>Step-by-step explanation:</u>

$12cos\bigg(\dfrac{2\pi}{5}x\bigg)+10=16\\\\\\12cos\bigg(\dfrac{2\pi}{5}x\bigg)=6\\\\\\cos\bigg(\dfrac{2\pi}{5}x\bigg)=\dfrac{1}{2}\\\\\\cos^{-1}\bigg[cos\bigg(\dfrac{2\pi}{5}x\bigg)\bigg]=cos^{-1}\bigg(\dfrac{1}{2}\bigg)$

$\text{Use the Unit Circle to determine when}\ cos=\dfrac{1}{2}\quad \rightarrow \quad\text{at}\ \dfrac{\pi}{3}\ and \ \dfrac{5\pi}{3}\\\\\\\dfrac{2\pi}{5}x=\dfrac{\pi}{3}\qquad and\qquad \dfrac{2\pi}{5}x=\dfrac{5\pi}{3}\\\\\\\bigg(\dfrac{5}{2\pi}\bigg)\dfrac{2\pi}{5}x=\dfrac{\pi}{3}\bigg(\dfrac{5}{2\pi}\bigg)\quad and\quad \bigg(\dfrac{5}{2\pi}\bigg)\dfrac{2\pi}{5}x=\dfrac{5\pi}{3}\bigg(\dfrac{5}{2\pi}\bigg)\\\\\\.\qquad \qquad \large\boxed{x=\dfrac{5}{6}\qquad and \qquad x=\dfrac{25}{6}}$