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3 years ago

If 5 times a number is subtracted from 3 times itssquare, the result is 2. Find the number.

Mathematics

1 answer:

grandymaker [24]3 years ago

5 0

Answer:

x = 2 or x = - 1/3

Step-by-step explanation:

3x² - 5x = 2

3x² - 5x - 2 = 0

(x - 2) (3x + 1) = 0

x = 2 or x = - 1/3

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Elena L [17]

Answer: a = 4, b = 163,422

Step-by-step explanation:

$P = P_{0} e^{kt}$ P is the new population, P₀ is the initial population, k is the growth rate, t is the time elapsed.

Part a) What do we know?

P = 7003

P₀ = unknown

k = .21 (converted 21% into a decimal)

t = 36 yrs (2006 - 1970)

$P = P_{0} e^{kt}$ need to solve for P₀

$7003 = P_{0} e^{(.21)(36)}$

$7003 = P_{0} e^{7.56}$

7003 = P₀ (1920)

$\frac{7003}{1920} = P_{0}$

3.6 = P₀

rounded to the nearest whole number = 4

Part b) What do we know?

P = unknown

P₀ = 7003

k = .21 (converted 21% into a decimal)

t = 15 yrs (2021 - 2006)

$P = P_{0} e^{kt}$ need to solve for P₀

$P = 7003 e^{(.21)(15)}$

$P = 7003 e^{3.15}$

P = 7003(23.33)

P = 163,422.46

rounded to the nearest whole number = 163,422

*************************************************************

Answer: 2, -1

Step-by-step explanation:

eˣ² = eˣ * e²

eˣ² = eˣ⁺²

x² = x + 2

x² - x - 2 = 0

(x - 2)(x + 1) = 0

x - 2 = 0 or x + 1 = 0

x = 2 or x = -1

Check both answer for validity:

eˣ² = eˣ⁺²

e⁴ = e⁴ or e¹ = e¹

TRUE TRUE

*****************************************

Answer: 0 = ln 1

Step-by-step explanation:

$e^{-10} = \frac{1}{e^{10}}$

$ln(e^{-10}) = ln(\frac{1}{e^{10}})$

-10 = ln 1 - 10 log rules say division is subtraction

0 = ln 1

5 0

2 years ago

Find the slope of a line that passes through the

Doss [256]

Given that,

Point 1 = (-6,9)

Point 2 = (2,9)

To find,

The slope of a line that passes through the given pair.

Solution,

We have,

x₁ = -6, x₂ = 2, y₁ = 9, y₂ = 9.

The formula for the slope of a line is given by :

$m=\dfrac{y_2-y_1}{x_2-x_1}\\\\=\dfrac{9-9}{2-(-6)}\\\\=0$

Hence, the slope of the line that passes through the given pair is 0.

4 0

2 years ago

If possible please answer

mrs_skeptik [129]

Answer:

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2 years ago

What is a real life word problem for the equation y=2x

lara [203]

Answer:

You want to buy some golden apples. Each golden apple cost $2. How much much does golden apples pass cost?

y = total cost

x = amount of apple

7 0

2 years ago

A 10 metre length of Wood is marked out into 10 equal lengths. How many metres from one end is the third mark?

Eduardwww [97]

3 metres from one end to the third mark

Solution:

Total length of wood = 10 metre

Wood is marked into 10 equal length.

$$\text{Length of each marking}=\frac{\text{Total length}}{\text{Number of marking}}$

$$=\frac{10}{10}$

= 1 metre

Length of each marking = 1 metre

Number of metres from one end to third mark = 1 + 1 + 1 = 3 metre

The image of the marking is attached below.

Hence 3 metres from one end to the third mark.

7 0

3 years ago

If 5 times a number is subtracted from 3 times itssquare, the result is 2. Find the number.​

If 5 times a number is subtracted from 3 times itssquare, the result is 2. Find the number.