Marcus said the product of 7/8 × 1 3/4 is 9/4.<br><br> How can you tell that his answer is wrong?

Simplify: -7/9-(-5/12)+1/3.

alexandr1967 [171]

Step-by-step explanation:

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7 0

2 years ago

Read 2 more answers

Show that the points (0.-1).(2, 1).(0.3) and (-2, 1) are the vertices of a square ABCD.

Inessa05 [86]

The diagram is below

A = (0,-1)
B = (2,1)
C = (0,3)
D = (-2,1)

Let's find the distance from A to B using the distance formula.

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(0-2)^2 + (-1-1)^2}\\\\d = \sqrt{(-2)^2 + (-2)^2}\\\\d = \sqrt{4 + 4}\\\\d = \sqrt{8}\\\\d \approx 2.828\\\\$

The distance from A to B is exactly $\sqrt{8}$ units or approximately 2.828 units. This is the length of side AB.

Through very similar steps, you should find that the other side lengths of BC, CD and AD are all the same.

Since AB = BC = CD = AD, this means we have a rhombus. Recall a rhombus is any quadrilateral with all four sides the same length.

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Let's find the slope of line AB

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{1 - (-1)}{2 - 0}\\\\m = \frac{1 + 1}{2 - 0}\\\\m = \frac{2}{2}\\\\m = 1\\\\$

Line AB has a slope of 1.

Through similar steps, you should find the slope of line BC is -1.

Rule: Whenever two slopes multiply to -1, then their corresponding lines are perpendicular.

Based on that rule, lines AB and BC are perpendicular. This means they meet up at a right angle (aka 90 degree angle).

You should find that line CD has a slope of 1, so BC and CD are perpendicular. Lastly, line AD has a slope of -1. So all the slopes mentioned are either +1 or -1. The slopes alternate as you move around the figure. This all shows that any two adjacent sides meet at a 90 degree angle.

Therefore, this figure is a rectangle. Any rectangle has all four angles of 90 degrees.

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The first section showed that we have a rhombus. The second section afterward showed that we also have a rectangle. The combination of a rhombus and a rectangle at the same time leads to a square.

Therefore, quadrilateral ABCD is a square.

5 0

3 years ago

A satellite is in orbit 600\ \mathrm{k}\mathrm{m}600 km above Earth's surface. Earth's radius is about 6370\ \mathrm{k}\mathrm{m

yKpoI14uk [10]

The distance from the satellite to the Earth's horizon is 6398 km

<h3>Pythagoras theorem</h3>

Pythagoras theorem is used to show the relationship between the sides of a right angled triangle. It is given by:

Hypotenuse side² = Adjacent side² + Opposite side²

Let x represent the distance from the satellite to the Earth's horizon

Hence:

x² = 6370² + 600²
x² = 40936900
x = 6398 km

The distance from the satellite to the Earth's horizon is 6398 km

Find out more on Pythagoras theorem at: brainly.com/question/343682

6 0

2 years ago

What is the slope-intercept form of the equation y+18 = 2(x - 1)?

kenny6666 [7]

Answer: y = 2x - 20

1. y + 18 = 2(x - 1)
2. y + 18 = 2x - 2
3. y + 20 = 2x
4. y = 2x - 20

4 0

3 years ago

Practice another write the function in terms of unit step functions. find the laplace transform of the given function. f(t) = t,

balu736 [363]

Using the Laplace transform to solve the given integral equation f(t) = t, 0 ≤ t < 4 0, t ≥ 4 is $\frac{4(1-2e^-5s)/}{s}$

explanation is given in the image below:

Laplace remodel is an crucial remodel approach that's particularly beneficial in fixing linear regular equations. It unearths very wide programs in var- areas of physics, electrical engineering, manipulate, optics, mathematics and sign processing.

The Laplace transform technique, the function inside the time domain is transformed to a Laplace feature within the frequency area. This Laplace function could be inside the shape of an algebraic equation and it may be solved without difficulty.

Learn more about Laplace transformation here:-brainly.com/question/14487437

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7 0

2 years ago

Marcus said the product of 7/8 × 1 3/4 is 9/4. How can you tell that his answer is wrong?