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3 years ago

Rewrite the following using the GCF and the distributive property :32 + 54

Mathematics

1 answer:

oksian1 [2.3K]3 years ago

3 0

Answer:

GCF: 2

Step-by-step explanation:

GCF: 2

(2*16) + (2*27)

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What whole number is equivalent to 8/2

svetoff [14.1K]

4 is the whole number equivalent. When dealing with an improper fraction or one that is "top heavy" you take the denominater (the bottom number) unto the numerator.
Two(2)goes into 8, 4 times, making it whole!

7 0

3 years ago

Read 2 more answers

100 points!!! Pre calculus. I need helpppppppppp

Fantom [35]

Answer:

We have function,

$y = 3 - 6 \sin {}^{} (2x + \frac{\pi}{2} )$

Standard Form of Sinusoid is

$y = - 6 \sin(2x + \frac{\pi}{2} ) + 3$

Which corresponds to

$y = a \sin(b(x + c)) + d$

where a is the amplitude

2pi/b is the period

c is phase shift

d is vertical shift or midline.

In the equation equation, we must factor out 2 so we get

$y = - 6(2(x + \frac{\pi}{4} )) + 3$

Also remeber a and b is always positive

So now let answer the questions.

a. The period is

$\frac{2\pi}{ |b| }$

$\frac{2\pi}{ |2| } = \pi$

So the period is pi radians.

b. Amplitude is

$| - 6| = 6$

Amplitude is 6.

c. Domain of a sinusoid is all reals. Here that stays the same. Range of a sinusoid is [-a+c, a-c]. Put the least number first, and the greatest next.

So using that<em> rule, our range is [6+3, -6+3]= [9,-3] So our range</em> is [-3,9].

D. Plug in 0 for x.

$3 - 6 \sin((2(0) + \frac{\pi}{2} )$

$3 - 6 \sin( \frac{\pi}{2} )$

$3 - 6(1)$

$3 - 6$

$= - 3$

So the y intercept is (0,-3)

E. To find phase shift, set x-c=0 to solve for phase shift.

$x + \frac{\pi}{4} = 0$

$x = - \frac{\pi}{4}$

Negative means to the left, so the phase shift is pi/4 units to the left.

f. Period is PI, so use interval [0,2pi].

Look at the graph above,

6 0

3 years ago

As the number of baseball cards increases, what happens to the money spent in dollars?

Nat2105 [25]

Answer:

decreases

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

<img src="https://tex.z-dn.net/?f=%5Csf%20-4%28-4x-5%29" id="TexFormula1" title="\sf -4(-4x-5)" alt="\sf -4(-4x-5)" align="absmi

insens350 [35]

Answer:

$- 4( - 4x - 5) = - 4 \times - 4x - ( - 4) \times ( - 5) \\ = 16x - 20$

3 0

2 years ago

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The diameter of the average cell in the human body is 1 x 10-5 meters. The diameter of a grain of sand is about 2 x 10-4 meters.

MariettaO [177]

PART A:

Scientific notation is given by A×10ⁿ where A is any number in a unit and 'n' is an integer.

0.000025 = 2.5×10⁻⁵

PART B:

Diameter of grain of sand ÷ Diameter of human body average cell
(2×10⁻⁴) ÷ (1×10⁻⁵)
(2÷1) × (10⁻⁴÷10⁻⁵)
2 × (10⁻⁴ ⁻ ⁻⁵) = 2 × 10⁽⁻⁴⁺⁵⁾ = 2 × 10¹ = 20 times bigger

PART C:

The diameter of human body's average cell in nanometer
1 × 10⁻⁵ metre = 1 × 10⁻⁵ × 10⁹ = 1 × 10⁽⁻⁵⁺⁹⁾ = 1 × 10⁴ nanometer

PART D:

Smallest bacteria = 300 nanometer
300 nm = 300 ÷ 10⁹ = (3 × 10²) ÷ 10⁹ = 3 × (10²⁻⁹) = 3 × 10⁻⁷ meter

PART E:

Laws of exponents that are applied in scientific notation is

xᵇ × xᵃ = x⁽ᵇ⁺ᵃ⁾
xᵇ ÷ xᵃ = x⁽ᵇ⁻ᵃ⁾

7 0

3 years ago