1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Debora [2.8K]
1 year ago
5

Need help with pre-cal

Mathematics
1 answer:
timurjin [86]1 year ago
3 0

A plot of the points A(-2, 11), B(5, 7), C(1, 0) is given by the option;

  • D

  • The triangle is a right triangle given that (AC)² = (AB)² + (BC)²

  • The area of the ∆ABC is 32.5 square units.

  • Sum of the squares of the lengths of the legs of the triangle = <u>130</u>

  • Square of the length of the hypotenuse of the triangle = <u>130</u>

<h3>How can ∆ABC be proven to be a right triangle from its dimensions?</h3>

The coordinates of the vertices of the triangle are;

A = (-2, 11), B = (5, 7), C = (1, 0)

Therefore, on the coordinate plane, we have;

The highest and leftmost point of the triangle is the vertex, <em>A</em>

The second highest and rightmost point of the triangle is the vertex, <em>B</em>

The<em> </em>vertex of the triangle that is midway between <em>A </em>and <em>B </em>and the lowest vertex of the triangle is the vertex <em>C</em>

  • The<em> </em>correct<em> </em>option that shows the points ABC and triangle ABC is the option <em>D</em>.

The lengths of the sides of the triangle are;

AB = √((-2 - 5)² + (11 - 7)²) = √(65)

BC = √((5 - 1)² + (7 - 0)²) = √(65)

AC = √((-2 - 1)² + (11 - 0)²) = √(130)

Therefore;

(AC)² = 130 = (AB)² + (BC)² = 65 + 65

Which gives;

  • (AC)² = (AB)² + (BC)²

Therefore;

  • ∆ABC is a right triangle, from the definition of a right triangle.

The legs of ∆ABC are AB and BC

AC is the hypotenuse of ∆ABC

The area of ∆ABC is therefore;

Area = (1/2) × AB × BC

Which gives;

Area of ∆ABC = (1/2) × √(65) × √(65)

√(65) × √(65) = 65

  • Area of ∆ABC = (1/2) × 65 = 32.5

(AB)² + (BC)² = 65 + 65 = 130

Therefore;

  • Sum of the squares of the lengths of the legs of the triangle = 130

(AC)² = 130

  • Square of the length of the hypotenuse of the triangle = 130

Learn more about right triangles here:

brainly.com/question/2284306

#SPJ1

You might be interested in
Dawn bought 12 grams of chocolate. she ate half of the chocolate. How many grams of chocolate did she eat?
andre [41]
Half of twelve is six.

She ate 6 grams.
7 0
3 years ago
Read 2 more answers
What is the value of these coins?
Alborosie

Answer:

$2.39

Step-by-step explanation:

4 pennies=4

2 nickels=10

10 dimes=100

5 quarters=125

$2.39

3 0
3 years ago
Read 2 more answers
Find w(4) for the function w(x) = 3x + 7.
monitta
W(4) = 3(4) + 7
w(4) = 12 + 7
w(4) = 19
7 0
3 years ago
Read 2 more answers
Six runners are entered in a race. Assume there are no ties. In how many ways can first and second places be awarded?
Stells [14]

Answer:

the karla question. the answer is unfair

Step-by-step explanation:

because the multiple of 3 is 6

but there is no multiple of 4

so therefore it is not fair

7 0
3 years ago
I have no idea how to do these geometry problems! if someone could explain to me how to do them that'd be awesome!
Murljashka [212]

"BISECT" an angle means split it into two equal angles.

In this diagram, you can see the long line  GH,  and they're telling us that  GH  "<u>bisects</u>" the big angle.  That means that the angles on both sides of line GH are equal ... their measures are the same number of degrees.  

Now, in the diagram, those angles on each side of  GH  are labeled.  On one side, the angle is labeled  3x-3  and on the other side the angle is labeled  4x-14 .  We don't know the measure of these angles because we don't know what ' x ' is.  BUT ... we know that the two angles are EQUAL, because GH is a '<u>bisect</u>or'.  Maybe we can use this clue to find ' x '.

We know their measures are equal, so we can write ...

3x - 3  =  4x - 14

Subtract  3x  from each side:  -3  =  x - 14

Add  14  to each side:    11  =  x

Look at that !  Is that cool or what ! ?  ' x ' is 11 .

So the angle above GH is  3x-3 . . . that's 30°

and the angle below GH is  4x-14 . . . that's also 30° .

Yay !  They really ARE equal.

Now let's look back at the question:

a).  'x' is 11° .  Angle FGH is the angle above GH, that's 30° .

b).  Angle HGI is the angle below GH, that's also 30° .

c).  Angle FGI is the whole big angle.  That's 30° + 30° = 60° .

5 0
3 years ago
Other questions:
  • How to solve intergers with 3 numbers
    6·1 answer
  • Tom went on a bike ride to the store 3 miles away if it took Time 1/2 hour to get there in 2/3 of an hour to get back what was h
    5·1 answer
  • Solve the differential equation y prime equals the product of 2 times x and the square root of the quantity 1 minus y squared .
    7·1 answer
  • How do you make −6x+5y=9 into slope intercept form?
    10·1 answer
  • What is the ratio of 4 cm x 72 cm what is the ratio of 6 cm x 48 cm what is the ratio of 8 cm x 36 cm and what is the ratio of 2
    9·1 answer
  • 9
    8·1 answer
  • Calculate p² +3q when p=2 and q=2​
    5·2 answers
  • Philip has a box of crayons. 45 are yellow, 12 are green, 25 are blue, and 8
    14·1 answer
  • On a coordinate plane, 2 right triangles are shown. The first triangle has points A (negative 1, 3), B (negative 1, 1), C (3, 1)
    7·1 answer
  • Rachel has a bag of fruit that has a mass of 50 hectograms. Rachel converts this mass to centigrams. Her work is shown below.
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!