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3 years ago

Triangle ABC has vertices A (1,1) B (7,1) C (4,9) (A)Find the perimeter of triangle ABC. (B) Find the area of triangle ABC

Mathematics

1 answer:

BartSMP [9]3 years ago

3 0

9514 1404 393

Answer:

perimeter = 6+2√73 ≈ 23.09 units
area = 24 units²

Step-by-step explanation:

It can help to draw a figure.

The altitude of this isosceles triangle is 8 units, and it splits the base into equal lengths of 3 units. Using the Pythagorean theorem, we find the length of a side to be ...

BC = AC = √(3² +8²) = √73

The perimeter is the sum of the lengths of those two sides and the base:

P = 2(√73) +6 ≈ 23.088 . . . units

The area is given by the formula ...

A = 1/2bh

A = (1/2)(6 units)(8 untis) = 24 units²

The perimeter is 6+2√73 ≈ 23.09 units.

The area is 24 units².

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Resolve 3x-1÷(x+1)^2 into partial fraction<br>

garri49 [273]

9514 1404 393

Answer:

3/(x +1) -4/(x +1)^2

Step-by-step explanation:

The partial fraction expansion will be of the form ...

A/(x+1)^2 +B/(x+1)

We can find the values of A and B by writing the sum of these terms:

= (A +B(x +1))/(x +1)^2

Then we require ...

B = 3

A +B = -1 ⇒ A = -4

So, the desired expansion is ...

3/(x +1) -4/(x +1)^2

4 0

3 years ago

AXYZ has vertices X(-4,2), Y(4.2), and Z(0, - 1). Is AXYZ scalene, isosceles, or equilateral?

ivolga24 [154]

Answer:

Isosceles triangle.

Step-by-step explanation:

In order to determine the nature of the triangle, we will need to get the sides XY, XZ and YZ using the distance formula;

For XY;

X(-4,2), Y(4.2)

XY = √(2-2)²(4-(-4)²)

XY = √(4+4)²

XY = √8²

XY = 8

For XZ;

X(-4,2), Z(0, - 1)

XZ = √(-1-2)²(0-(-4))²

XZ = √(-3)²+4²

XZ = √9+16

XZ = √25

XZ = 5

For XZ;

Y(4.2), Z(0, - 1)

YZ = √(-1-2)²(0-(4))²

YZ = √(-3)²+(-4)²

YZ = √9+16

YZ = √25

YZ = 5

Since XZ = YZ = 5, this shows that two sides are equal. Hence the triangle is an isosceles triangle.

NB: Isosceles triangle only have two of its sides and angles equal

5 0

3 years ago

Choose the graph that matches the following system of equations: x − 3y = −12 2x − y = 1 a line includes points 0 comma 1 and ne

bezimeni [28]

To choose the graph, we must make sure that it satisfies both equations of the system simultaneously.
We have then:
a line includes points 0 comma 4 and 3 comma 5
Verifying:
(0, 4)
(0) - 3 (4) = -12
0-12 = -12
-12 = -12
(3, 5)
2x - y = 1
2 (3) - (5) = 1
6-5 = 1
1 = 1
answer
The graph that matches the system of equations is
a line includes points 0 comma 4 and 3 comma 5

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3 years ago

Find the percent of change for the following:

Inessa05 [86]

Answer:

Step-by-step explanation:

3% increase

6% decrease

18% increase

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3 years ago

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Solve the equation 4/15=2/y+8

suter [353]

Answer:

-0.258620689

Step-by-step explanation:

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3 years ago

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Triangle ABC has vertices A (1,1) B (7,1) C (4,9) (A)Find the perimeter of triangle ABC. (B) Find the area of triangle ABC​

Triangle ABC has vertices A (1,1) B (7,1) C (4,9) (A)Find the perimeter of triangle ABC. (B) Find the area of triangle ABC