27^x = 9^(x − 4) x = 8 x = 4 x = −4 x = −8

Give an equation of a line that is parallel to −3x + 7y =4. Explain why your line is parallel to the given line and how you arri

koban [17]

Answer:

3x -7y = 0

Step-by-step explanation:

Parallel lines have the same slope.

Changing the constant in a linear equation like this only changes the y-intercept. It has no effect on the slope of the line. So, we can change the constant from 4 to 0 and we will have a line with the same slope, parallel to the original, but with a different y-intercept.

The "standard form" of the equation of a line has the leading coefficient positive. We can make that be the case by using the multiplication property of equality, multiplying both sides of the equation by -1.

Parallel line:

-3x +7y = 0

In standard form:

3x -7y = 0

3 0

2 years ago

Convert 0.34285714285 into an improper fraction

Stolb23 [73]

Answer:

34285714285/100000000000

Step-by-step explanation:

To write 0.34285714285 as a fraction you have to write 0.34285714285 as the numerator and put 1 as the denominator. Now you multiply the numerator and denominator by a number that makes the numerator to a whole number.

And finally, we have:

0.34285714285 as a fraction equals 34285714285/100000000000

5 0

3 years ago

Find the value of annuity if the periodic deposit is $250 at 5% compounded quarterly for 10 years

mylen [45]

Answer:

The value of annuity is $P_v = \$ 7929.9$

Step-by-step explanation:

From the question we are told that

The periodic payment is $P = \$ 250$

The interest rate is $r = 5\% = 0.05$

Frequency at which it occurs in a year is n = 4 (quarterly )

The number of years is $t = 10 \ years$

The value of the annuity is mathematically represented as

$P_v = P * [1 - (1 + \frac{r}{n} )^{-t * n} ] * [\frac{(1 + \frac{r}{n} )}{ \frac{r}{n} } ]$ (reference EDUCBA website)

substituting values

$P_v = 250 * [1 - (1 + \frac{0.05}{4} )^{-10 * 4} ] * [\frac{(1 + \frac{0.05}{4} )}{ \frac{0.08}{4} } ]$

$P_v = 250 * [1 - (1.0125 )^{-40} ] * [\frac{(1.0125 )}{0.0125} ]$

$P_v = 250 * [0.3916 ] * [\frac{(1.0125)}{0.0125} ]$

$P_v = \$ 7929.9$

8 0

3 years ago

A stone is launched into the air from a height of 240 feet. The height, h, of the stone, in feet, t seconds after launch is give

rosijanka [135]

A projectile is an object launched into space, and moving under the influence of gravity and momentum. The stone here is an example. Thus, the time taken for the stone to reach the ground is 10 seconds.

On launching of the stone into space, it behaves as a projectile. Thus moving under the influence of gravity and its momentum. Its momentum is the product of its mass and velocity.

The height h, is given as:

h = 16 $t^{2}$ + 32t + 240

Differentiating the expression with respect to t, we have;

32t + 32 = 0

t = -1 seconds

Substitute the value of time, t, in the equation for the height;

h = 16 - 32 + 240

= 224

h = 224 m

Total height, S = 240 + 224

= 464

S = 464 m

The total height covered by the stone is 464 m.

From the second equation of free fall,

S = Ut + $\frac{1}{2}$ g $t^{2}$

S = $\frac{1}{2}$ g $t^{2}$

464 = $\frac{1}{2}$ *9.8* $t^{2}$

$t^{2}$ = $\frac{928}{9.8}$

= 94.694

t = $\sqrt{94.694}$

= 9.7311

t ≅ 10 seconds

The time taken for the stone to hit the ground is 10 seconds.

Thus option A is the required answer.

Visit: brainly.com/question/13834669

7 0

2 years ago

Consider the number line with the plotted square roots.

ZanzabumX [31]

Answer: 19 Startroot and 24 endroot

Step-by-step explanation:

8 0

3 years ago