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3 years ago

The coordinates for the vertices of a right triangle are (1, 4), (6, 4), and (6,1). What is the length of the longer leg?

Mathematics

1 answer:

Nataly_w [17]3 years ago

6 0

Check the picture below.

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}
\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ 1 &,& 4~) 
% (c,d)
&&(~ 6 &,& 1~)
\end{array}~~~ 
% distance value
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
d=\sqrt{(6-1)^2+(1-4)^2}\implies d=\sqrt{5^2+(-3)^2}
\\\\\\
d=\sqrt{25+9}\implies d=\sqrt{34}$

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3 years ago

Read 2 more answers

A linear function has an x-intercept of 12 and a slope of 3/8. How does this

Alekssandra [29.7K]

Answer:

O It has the same slope and a different y-intercept.

Step-by-step explanation:

y = mx + b

m = 3/8

b = 12

y = (3/8)x + 12

---

Data in the table: slope is the rise (y) over the run (x) between two points (assuming the data represent a linear line).

Change in x and y between two points. I'll choose (-2/3,-3/4) and (1/3,-3/8).

Change in y: (-3/8 - (-3/4)) = (-3/8 - (-6/8)) = 3/8

Change in x: (1/3 - (-2/3)) = (1/3+2/3) = 3/3 = 1

Slope = (Change in y)/(Change in x) = (3/8)/1 = 3/8

The slope of the equation is the same as the data in the table.

Now let's determine if the y-intercept is also the same (12). The equation for the data table is y = (2/3)x + b, and we want to find b. Enter any of the data points for x and y and then solve for b. I'll use (-2/3, -3/4)

y = (3/8)x + b

Use (-2/3, -3/4)

-3/4 =- (3/8)(-2/3) + b

-3/4 = (-6/24) + b

b = -(3/4) + (6/24)

b = -(9/12) + (3/12)

b = -(6/12)

b = -(1/2)

The equation of the line formed by the data table is y = (3/8)x -(1/2)

Therefore, It has the same slope and a different y-intercept.

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2 years ago

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lbvjy [14]

Answer:

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Step-by-step explanation:

Lets solve the expressions one by one

1. 7-5

we can see that it is simple subtraction. A smaller number is being subtracted from a large number.

So the answer is 2

2. -7+5

There are two numbers with different signs. When there is a number with plus and a number with minus both quantities are subtracted but the larger quantity determines the sign of the answer.

In this case, 7 is larger and has negative sign, the answer will be -2

3. -7-5

When there are two numbers with minus sign they are added but the answer has the minus sign with it.

So the answer will be: -12

4. 7-(-5)

When minus is multiplied with minus it converts to positive

$= 7-(-5) = 7+5 = 12$

Hence,

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-7+5 => -2
-7-5 => -12
7-(-5) => 12

3 0

2 years ago