The equation of a linear graph with a y-intercept of 2/5 and a gradient -1/4 is:

a. Shaunnie's mistake was that she multiplied 10 times 5. When you multiply 10x5, it is the same as 10+10+10+10+10. However, the question asked about 10⁵. 10⁵ means 10 to the fifth power which is the same as 10x10x10x10x10. She needs to multiply 10 to itself, ten times. This equals 1,000,000.

b. Marlon made the mistake of not moving the decimal point. Marlon added the two zeros to the end when he multiplied 2.5 to 10² because 10² is the same as 100. However, when multiplying with a decimal, the decimal needs to move as well. He needs to move the decimal place to the right two places. His answer should be 250. The last zero is dropped because it is to the right of the decimal and not followed by another number.

<h3>Further Explanation</h3>

Numbers to the nth power.

When a number has a power as in 10², this means that you multiply that number by itself however many times the power indicates. A number to the 29th power would be multiplied by itself 29 times.

Multiplying Decimals

When multiplying decimals, it is important to remember to shift the decimal to the correct place. A number multiplied by ten moves the decimal one place to the right. A number multiplied by 100 moves the decimal two places to the right. A number multiplied by 1000 moves the decimal three places to the right. A trick for remembering is the number of zeros in 10, 100, or 1000. For each zero, move the decimal

<h3>Answer Details</h3>

Subject: Math

Level: Middle School

Topic: Powers

<h3>Keywords</h3>

powers, multiplication, multiplying with decimals

<h3>Learn More</h3>

Checking decimal multiplication: brainly.com/question/923608

Math Powers: brainly.com/question/100928

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3 years ago

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What is the area of a rectangle with vertices at (6,-3), (3,-6), (-1,-2), and (2,1). Enter your answer In the box

vladimir2022 [97]

Answer:

24 units

Step-by-step explanation:

Start by plotting on the rectangular coordinate system the four points given: (6,-3), (3,-6), (-1,-2) , and (2, 1)

Please see attached image for guidance with the answer.

These four points are represented with green dots in the image.

Notice that such rectangle can be viewed as inscribed in a larger square that is 7 units by 7 units, and on which these four points (the vertices of the rectangle) touch the square's perimeter.

So to make the calculation simple, we can find the area of the larger square (very simple to calculate since it is 7 times 7 = 49) and subtract from it the area of the four triangles that are depicted in yellow and in light green. Such result will give us the area of the rectangle (white background).

Out of the four triangles whose areas we need to extract, we notice that they are all right angle triangles with simple formulas to calculate their areas: base times height divided by 2.

The triangles in green have base 3 and height 3 so their areas are: (3 * 3) /2 = 4.5. since they are two of these the total area of the green triangles is 4.5*2 = 9

We do something similar with the yellow triangles, noticing that their base and heights are 4 and 4 respectively which gives an area of (4*4)/2 = 8

Again, since there are two of them, we multiply this by 2: 8 * 2 = 16

Now to calculate the area of the white rectangle we do:

Area of big square minus area of green triangles minus area of yellow triangles: 49 - 9 - 16 = 24

3 0

3 years ago