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2 years ago

the line containing the altitude to the hypotenuse of a right triangle whose vertices are p(-1, 1), q(3, 5), and r(5, -5).

Mathematics

1 answer:

finlep [7]2 years ago

8 0

The equation of the straight line is given by 5y-x=6

An equation can be used to describe a straight line drawn on the Cartesian Plane. These equations have a generic structure and can change based on the slope and where the line intersects the axes.

We will greatly simplify this issue by utilizing the fact that this triangle is specified as a right triangle. We would have had to establish the presence of a right angle if it had been presented as a general triangle.

The segment QR is the hypotenuse of the triangle.

Any side's altitude is located along a line that is perpendicular to that side. We are aware that the slopes of perpendicular lines are negative reciprocals, or:

Slope of line joining Q(3, 5) and R(5, -5)

m= $\frac{y_2-y_1}{x_2-x_1}$

Hence slope is= -10/2= -5

Now we know that for two perpendicular line the slope of one line is the negative reciprocal of the other.

Slope of line perpendicular to QR=1/5

This line passes through P(-1,1)

Equation of the straight line that passes through (1,-1) and with a slope of 1/5 is given by:

$(y-y_1)=m(x-x_1)\\$

Substituting the values we get:

y-1=1/5(x+1)

or,5y-5=x+1

or,5y-x=6

Hence the equation of the required line is : 5y-x=6

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Katen [24]

Answer:

$17.35/h

Step-by-step explanation:

In order to get the amount per hour he made, you first need to calculate the global amount of money he made.

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Then he worked a total of 98 hours for that money.

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3 years ago

What is -0.75p-2=0.25p

ki77a [65]

you move first the number without the variable to the other side with the opposite sign

-0.75p=0.25+2

-0.75p=2.25

then as -0.75 is multiplying you pass it to the other side dividing

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3 years ago

Read 2 more answers

Question 10 (1 point) Solve for x. 1/2+x/6=4/3

jek_recluse [69]

Answer:

The value of x for the given expression is 5 .

Step-by-step explanation:

Given expression as

$\dfrac{1}{2}$ + $\dfrac{x}{6}$ = $\dfrac{4}{3}$

Now, arrange the equation

So, $\dfrac{x}{6}$ = $\dfrac{4}{3}$ - $\dfrac{1}{2}$

<u>Taking L.C.M on right hand side </u>

Or, $\dfrac{x}{6}$ = $\dfrac{8 -3}{6}$

Or, $\dfrac{x}{6}$ = $\dfrac{5}{6}$

Or, x = $\frac{5\times 6}{6}$

∴ x = 5

So, The value of x = 5

Hence,The value of x for the given expression is 5 . Answer

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2 years ago

5x^{4}-7x^{3}-5x^{2}+5x+1-0

den301095 [7]

Answer:

5x^4 -7x^3-5x^2+5x+1

Step-by-step explanation:

Hey!

You would just add all the numbers up, and by making sure that you combine all like terms. In this case it is just 1-0 = 1 and so the solution would be the same as your question but with a 1 and you would get rid of the -0.

Hope this helps!

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2 years ago

Select the point that is a solution to the system of inequalities.<br> y≤2x-2<br> y≤ x²-3x

miss Akunina [59]

Both statements are true. Therefore (4,2) is a solution and option D is correct.

The given inequalities are $y\leq 2x-2$ and $y\leq x^{2} -3x$ .

We need to select the point that is a solution to the system of inequalities (-2,-1), (1,3), (2,1) and (4,2).

<h3>What is an example of a system of inequalities in real life?</h3>

Inequalities can be seen in the speed limits on roads, the minimum age for seeing certain movies, and the distance you have to walk to go to the park. Inequalities represent a limit of what is permitted or achievable rather than a precise quantity.

Any point is a solution to this system of inequality if it satisfies both inequalities.

Check the inequalities by each option.

For (-2, -1), $-1\leq 2(-2)-2 \implies -1\leq -6$ .

This statement is false because -1 is greater than -6. Therefore (-2,-1) is not a solution and option A is incorrect.

For (1, 3), $3\leq 2(1)-2 \implies 3\leq 0$

This statement is false because 3 is greater than 0. Therefore (1,3) is not a solution and option B is incorrect.

For (2,1), $1\leq 2(2)-2 \implies 1\leq 2$ .

$1\leq 2^{2} -3(2) \implies 1\leq -2$

This statement is false because 1 is greater than -2. Therefore (2,1) is not a solution and option C is incorrect.

For (4,2), $2\leq 2(4)-2 \implies 2\leq 6$

$2\leq 4^{2} -3(4) \implies 2\leq 4$

Both statements are true. Therefore (4,2) is a solution and option D is correct.

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2 years ago