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3 years ago

2x-7/3-5x+4/5=-x-4/30

Mathematics

1 answer:

Strike441 [17]3 years ago

5 0

Answer:

Exact form: -7/10

Decimal form: -0.7

Step-by-step explanation:

Isolate the variable by dividing each side by by factors that don't contain the variable.

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The population of a town is 13,000. It decreases at a rate of 5% per year. In about how many years will the population be less t

just olya [345]

This is an exponential decay problem.

Using the equation Y = a *(1-rate)^time

where Y is the future value given as 12,000 and a is the starting value given as 13,000.

The rate is also given as 5%.

The equation becomes:

12,000 = 13,000(1-0.05)^x

12,000 = 13,000(0.95)^x

Divide each side by 13000:

12000/13000 = 0.95^x/13000

12/13 = 0.95^x

Use the natural log function:

x = ln(12/13) / ln(0.95)

x = 1.56 years. ( this will equal 12,000

Round to 2 years it will be less than 12000.

3 0

4 years ago

Factoring Quadratic Expressions: 5p^2 - p - 18

Dennis_Churaev [7]

$5 p^{2} -p-18$

$5 p^{2}-10p+9p-18$

$5p(p-2)+9(p-2)$

$(p-2)(5p+9)$

3 0

3 years ago

if the formula for the perimeter of a rectangle is p=2l+2w, what is the formula for w in terms of p and l

aleksklad [387]

Answer:

(p-2l)/2 = w

Step-by-step explanation:

p=2l+2w

We want to solve for w.

The first step is to subtract 2l from each side

p-2l=2l-2l+2w

p-2l=2w

Then we will divide each side by 2 to isolate w

(p-2l)/2 = 2w/2

(p-2l)/2 = w

3 0

4 years ago

Find cos(2*ABC) 100POINTS

juin [17]

Answer:

$-\dfrac{7}{25}$

Step-by-step explanation:

Trigonometric Identities

$\cos(A \pm B)=\cos A \cos B \mp \sin A \sin B$

Trigonometric ratios

$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$

where:

$\theta$ is the angle
O is the side opposite the angle
A is the side adjacent the angle
H is the hypotenuse (the side opposite the right angle)

Using the trig ratio formulas for cosine and sine:

$\cos(\angle ABC)=\dfrac{3}{5}$

$\sin(\angle ABC)=\dfrac{4}{5}$

Therefore, using the trig identities and ratios:

$\begin{aligned}\implies \cos(2 \cdot \angle ABC) & = \cos(\angle ABC + \angle ABC)\\\\& = \cos (\angle ABC) \cos (\angle ABC) - \sin(\angle ABC) \sin (\angle ABC)\\\\& = \cos^2(\angle ABC)-\sin^2(\angle ABC)\\\\& = \left(\dfrac{3}{5}\right)^2-\left(\dfrac{4}{5}\right)^2\\\\& = \dfrac{3^2}{5^2}-\dfrac{4^2}{5^2}\\\\& = \dfrac{9}{25}-\dfrac{16}{25}\\\\& = \dfrac{9-16}{25}\\\\& = -\dfrac{7}{25} \end{aligned}$