MATHEMATICS MIDDLE SCHOOL

Complete the equation of the line through (-9,-7) and (-6,-3)

Answers

Answer 1

Answer:

The equation of the line through (-9, -7) and (-6, -3) is $y+3=(4)/(3)(x+6)$

Solution:

Given, two points are (-9, -7) and (-6, -3)

We have to find that a line that passes through the given two points.

First let us find the slope of the line that passes through given two points.

The slope of the line "m" is given as:

$\mathrm{m}=(y_(2)-y_(1))/(x_(2)-x_(1))$

$\text { where, }\left(x_(1), y_(1)\right) \text { and }\left(x_(2), y_(2)\right) \text { are two points on line. }$

So slope of our line $=(-3-(-7))/(-6-(-9))=(-3+7)/(-6+9)=(4)/(3)$

Now, let us find the line equation using point slope form:

$\mathrm{y}-\mathrm{y}_(1)=\mathrm{m}\left(\mathrm{x}-\mathrm{x}_(1)\right) \text { where } \mathrm{m} \text { is slope and }\left(\mathrm{x}_(1), \mathrm{y}_(1)\right) \text { is point on the line. }$

By substituting the values we get,

$\text { Then, line equation } \rightarrow y-(-3)=(4)/(3)(x-(-6))$

$y+3=(4)/(3)(x+6)$

Hence, the line equation is $y+3=(4)/(3)(x+6)$

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Complete the expanded form for the number 81.402

Answers

80 000
1 000
    400
      00
      2

Write the steps for how to use a number line to multiply a 2-digit number by 20. give an example

Answers

To obtain the multiplication of $2$ digits number by $20$ first jump two times the $2$ digit number then jump $10$ times by the result we get in step 1.

Further explanation:

A straight line that has all real numbers is known as number line.

The steps involve in multiplying 2-digit number by $20$ are as follows.

1. First multiply the two digit number by 2 and the get the result.

2. Multiply the result by $10$ to obtain the final result.

For example we have to multiply $15$ by $20$ on the number line.

Following are the steps involve in multiply $15$ by $20$ on the number line.

Step 1

Multiply 15 by 2 as,

$\begin{gathered}A = 15 \cdot 2 \n= 30 \n \end{gathered}$

Make 2 jumps of 15 to get 30.

Step 2

Multiply $30$ to $10$ to obtain the final result.

$\begin{gathered}B = 30 \cdot 10 \n = 300 \n \end{gathered}$

Now make 10 jumps of 30 to get $300$ .

To obtain the multiplication of 2 digits number by $20$ first jump two times the 2 digit number then jump $10$ times by the result we get in step 1.

Kindly refer to the image attached to the question.

Learn more:

1. Problem on multiplication brainly.com/question/573729

2. Problem on division brainly.com/question/545132

3. Problem on lines brainly.com/question/8554769

Answer details:

Grade: Junior school

Subject: Mathematics

Chapter: Number line

Keywords: two digit number, number line, twenty, multiply, add, jump, examples, multiplication.

Final answer:

To multiply a 2-digit number by 20 using a number line, draw a number line, plot your 2-digit number, make jumps of 20 units equal to your 2-digit number. The end point is the product.

Explanation:

To use a number line to multiply a 2-digit number by 20, follow these steps:

First, draw a number line. You can start at 0 and end at a number that is more than the product of your multiplication.
Plot your 2-digit number on the number line.
Start from your plotted point, and make jumps of 20 units each. The number of jumps should be equal to the quantity of your 2-digit number.
The point where you land, after making the necessary jumps, is the product of your multiplication.

For example, if you want to multiply 3 by 20: plot 3 on your number line, jump 3 points of 20 units each from point 3. You will land at 60, which is the product of 3 and 20.

Learn more about Number line multiplication here:

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Artificial turf in on athletic fields was first introduced in the 1960s. Its safety has been controversial since then. One issue that has been investigated is whether injuries of football players tend to be more serious on artificial turf than grass. A study followed 24 NCAA division 1A college football teams over three seasonsIn total there were 1050 injuries that occurred on field turf. Of the field turf injuries, 83.3333% were minor and 10.857% were substantial.

77.972% of grass injuries were minor.

4.26% of injuries occurred on grass were severe.

(There is a total of minor injuries on grass and on field turf is equal to 1813.

How many injuries were severe and occurred on field turf? Write your answer as an integer.

How many injuries were severe? Write your answer as an integer.

Answers

1. Out of 1050 injuries that occurred on field turf:
$(1050)(0.8333) = 875$ were minor and $(1050)(0.10857) = 114$ were substantial. This leaves 1050 - 875 - 114 = 61 severe injuries.

2. If there were 1813 total minor injuries, and 875 were on field turf, then 1813 - 875 = 938 were on grass. This is 77.972% of all grass injuries, so $0.77972x = 938$ gives $x = 1203$ total grass injuries.

Since 4.26% of grass injuries were severe, this is (1203)(0.0426) = 51 severe grass injuries. Adding this to the 61 severe turf injuries gives a total of 112 severe injuries.

Describe how you can find the prime factorization of a number

Answers

I think it would be easier to understand when u see a problem worked out, prime factorization of 18:
18
/\
6X3
/\
3X2
so the prime factorization is 2X3X3
hope that was helpful! :D

Round 16,311 to the nearest thousand

Answers

The round off value of 16311 is

what is rounding off?

Rounding off means a number is made simpler by keeping its value intact but closer to the next number. It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.

Given:

16311.

Now,

To round off nearest thousand focus on the place value of hundred place value.

Now, focus the value on hundred place value is less than 5 or greater than 5.

As, the number is less than 5 it will go towards previous number.

The round will lie between 16000 and 17000.

hence, the round off will be 16000.

Learn more about round off here:

brainly.com/question/13391706

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16000.
You just need to take the numbers in the thousands place and left, and if the numbers on the right are greater than 500, you round up. In this case, 311 is less than 500 so you round down and get 16000.

Ms. Lewis purchased a new computer for $1,150 at the Apple Store. If sales tax is 7.5%, what was the total cost of her purchase?

Answers

Answer:

$1236.25

Step-by-step explanation:

1150 x 0.075 = 86.25

86.35 + 1150 = 1236.25

Answer:

The total cost was 1,236.25

Step-by-step explanation:

7.5% of 1,150 is 86.25

1,150+86.25=1,236.25

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