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2 years ago

Solve for b in the equation: 2b + 3c = 14

1 answer:

8 0

Remember you can do anything to an equation as long as you do it to both sides

2b+3c=14
minus 3c both sides
2b=14-3c
divide both sides by 2
$b= \frac{14-3c}{2}$

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Given limit of f (x) = 4 as x approaches 0. what is limit of one-fourth left-bracket f (x) right-bracket superscript 4 baseline

Otrada [13]

The limit of the given function if $\lim_{x \to 0} f(x)=4$ is 64

<h3>Limit of a function</h3>

Given the following limit of a function expressed as;

$\lim_{x \to 0} f(x)=4$

We are to determine the value of the function

$\frac{1}{4} \lim_{x \to 0} [f(x)]^4$

This can also be expressed as

$\frac{1}{4} \lim_{x \to 0} [f(x)]^4\\ = \frac{1}{4}(4)^4 \\=1/4\times 256\\=64$

Hence the limit of the given function if $\lim_{x \to 0} f(x)=4$ is 64

Learn more on limit of a function here: brainly.com/question/23935467

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4 0

1 year ago

Write and equati9n of a l8ne that passes through (1,-2) and is perpendicular to -4x+7y=21

yarga [219]

Given:

A line passes through (1,-2) and is perpendicular to $-4x+7y=21$ .

To find:

The equation of that line.

Solution:

We have, equation of perpendicular line.

$-4x+7y=21$

Slope of this line is

$m_1=-\dfrac{\text{Coefficient of x}}{\text{Coefficient of y}}$

$m_1=-\dfrac{-4}{7}$

$m_1=\dfrac{4}{7}$

Product of slope of two perpendicular lines is -1.

$m_1\times m_2=-1$

$\dfrac{4}{7}\times m_2=-1$

$m_2=-\dfrac{7}{4}$

Now, slope of required line is $-\dfrac{7}{4}$ and it passes through (1,-2). So, the equation of line is

$y-y_1=m(x-x_1)$

where, m is slope.

$y-(-2)=-\dfrac{7}{4}(x-1)$

$4(y+2)=-7(x-1)$

$4y+8=-7x+7$

$4y+7x=7-8$

$7x+4y=-1$

Therefore, the equation of required line is $7x+4y=-1$ .

7 0

2 years ago

The price of a company's share dropped by 3.50% by the end of the first year, down to $44.25. During the second year the price o

omeli [17]

Answer:

a. $45.86

b. $43.87

c. Percentage change = -4.40%)

Step-by-step explanation:

a. Let the price of share at the beginning of first year be represented with X

Now, Price of company's share dropped by 3.50% at the end of first year.

So, Price of share at the end of first year = x - 3.5% of x

= x - 0.035x

= 1x - 0.035x

= 0.965x

But it is equal to $44.25

=> 0.965x = 44.25

x = 44.25 / 0.965

x = 45.8549223

x = $45.86

b. During second year price of share decreased by $1.99. Therefore, Price of share at the end of second year = $45.86 - $1.99 = $43.87

c. Percentage change in the price of shares over two years = {(45.86 - 43.87)/45.86} *100

= (1.99/45.86)*100

= 0.04339294 * 100

= 4.40%

Now, as price of shares has dropped, the percentage change will be negative. (Δ% = -4.40%)

5 0

2 years ago

What is the equation of the line with the same slope as the equation x-4y=3 and the y-intercept(0,-8)?

katen-ka-za [31]

Answer:

y = 1/4x -8

Step-by-step explanation:

First find the slope of the line

x-4y =3

Subtract x from each side

x-4y -x = -x+3

-4y = -x+3

Divide each side by -4

-4y/-4 = -x/-4 +3/-4

y = 1/4 x -3/4

This is in the form y= mx+b where the slope is m and the y intercept is b

The slope is 1/4

We want the same slope

y = 1/4x +b

we know the y intercept is -8

y = 1/4x -8

8 0

3 years ago

Read 2 more answers

Create your own real-world example of a relation that is a function. Domain: The set of Range: The set of

ivanzaharov [21]

Answer:

C(t)=5000 -10t

Step-by-step explanation:

There are many examples in the real world of relationships that are functions.

For example, imagine a tank full of water with a capacity of 5000 liters, this tank has a small hole, by which 10 liters of water are lost every hour.

If we call C the amount of water in the tank as a function of time, then we can write the following equation for C:

$C(t)=C_{0}-at\\$

Where:

C (t): Amount of water in the tank as a function of time

$C_{0}$ : Initial amount of water in the tank at time t = 0

a: amount of water lost per hour

t: time in hours

Then the equation is:

$C(t)=5000 -10t$

The graph of C (t) is a line of negative slope. This relation is a function since for each value of t there is a single value of C.

Its domain is the set of all positive real numbers t between [0,500]

Because the time count starts at t = 0 when the tank is full and ends at t = 500 when empty

Its Range is the set of all positive real numbers C between [0,5000] Because the amount of water in the tank can never be less than zero or greater than 5000Litres

7 0

3 years ago

Read 2 more answers