What is the simplified expression for 4 power 4 multiplied by 4 power 3 over 4 power 5

MissTica

1. -10/9
2. 2/5
3. -2/5
4. 3/5
5. 1/10
6. -10/3

3 0

3 years ago

A triangle has a perimeter of 72 units, and two of its sides measure x units and 3x units, respectively. Which inequality repres

blagie [28]

Answer:

$x$

Step-by-step explanation:

Given: Perimeter of triangle= 72 units

Measure of one of the side= x units

Measure of second side = 3x units

We know the perimeter of triangle is equal to sum of all sides.

Now, finding the possible value of x

forming an inequality to determine the value of x

Remember triangle has three sides, however, measure of only two sides are given.

⇒ $x+3x < 72\ units$

⇒ $4x$

Dividing both side by 4

⇒ $x < 18$

∴ The inequality to represents all possible values of x is $x < 18$

4 0

3 years ago

LORAN is a long range hyperbolic navigation system. Suppose two LORAN transmitters are located at the coordinates (−60,0) and (6

USPshnik [31]

LORAN follows an hyperbolic path.

The equation of the hyperbola is: $\mathbf{\frac{x^2}{2500} + \frac{y^2}{1100} = 1}$

The coordinates are given as:

$\mathbf{(x,y) = (-60,0)\ (60,0)}$

The center of the hyperbola is

$\mathbf{(h,k) = (0,0)}$

The distance from the center to the focal points is given as:

$\mathbf{c = 60}$

Square both sides

$\mathbf{c^2 = 3600}$

The distance from the receiver to the transmitters is given as:

$\mathbf{2a = 100}$

Divide both sides by 2

$\mathbf{a = 50}$

Square both sides

$\mathbf{a^2 = 2500}$

We have:

$\mathbf{b^2 = c^2 - a^2}$

This gives

$\mathbf{b^2 = 3600 - 2500}$

$\mathbf{b^2 = 1100}$

The equation of an hyperbola is:

$\mathbf{\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1}$

So, we have:

$\mathbf{\frac{(x - 0)^2}{2500} + \frac{(y - 0)^2}{1100} = 1}$

$\mathbf{\frac{x^2}{2500} + \frac{y^2}{1100} = 1}$

Hence, the equation of the hyperbola is: $\mathbf{\frac{x^2}{2500} + \frac{y^2}{1100} = 1}$

Read more about hyperbolas at:

brainly.com/question/15697124

7 0

3 years ago

Read 2 more answers

Monitors manufactured by TSI Electronics have life spans that have a normal distribution with a standard deviation of 1300 hours

matrenka [14]

Answer:

0.03593

Step-by-step explanation:

We solve using z score formula

z = (x-μ)/σ, where

x is the raw score = 17,340

μ is the population mean = 15,000

σ is the population standard deviation = 1300

z score:

z = 17340 - 15000/1300

z =1.8

Probability value from Z-Table:

P(x<17340) = 0.96407

P(x >17340) = 1 - P(x<17340)

= 1 - 0.96407

= 0.03593

The probability that the life span of the monitor will be more than 17,340 hours is 0.03593

5 0

3 years ago

Which sequence of transformations produces a congruent figure? (−x, y)(x−4, y+2) (x+2, 2y)(x+1, y−4) (x+2, y)(−x, −2.5y) (−x, 3y

True [87]

Answer:

(−x, y)(x−4, y+2)

Step-by-step explanation:

If the figure is to be congruent, there must be no dilation. Any transformation having a multiplier on x or y cannot be a solution.

The only remaining choice is the one shown above, which involves a reflection across the y-axis and a translation.

4 0

4 years ago