Plz helpp FASTTFind the area of triangle ABC with vertices A(2, 3), B(1, -3), and C(-3, 1).
a.
10 units2
c.
14 units2
b.
12 units2
d.
16 units2

Answers

Answer 1

Answer:

The area of the triangle will be 14 square units. Then the correct option is C.

What is the triangle?

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The triangle ABC with vertices A(2, 3), B(1, -3), and C(-3, 1).

Then the area of the triangle is given as,

A = 1/2 | {[2 x (-3) + 1 x 1 + (-3) x 3] - [3 x 1 + (-3) x (-3) + 2 x 1]} |

A = 1/2 | {[-6 + 1 - 9] - [3 + 9 + 2]} |

A = 1/2 | {-14 - 14} |

A = 1/2 x 28

A = 14 square units

The area of the triangle will be 14 square units. Then the correct option is C.

More about the triangle link is given below.

brainly.com/question/25813512

#SPJ2

Answer 2

Answer: Are you sure about your solves??

I think correct answer is 6,

I don't know but the standard way is in the photo:

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Can someone show me how to solve this? A boat took 5 hours to travel 60km up a river, against the current. The return trip took 3 hours. Find the speed of the boat in still water and the speed of the current.

Answers

Yes, I can.

And even though you haven't asked to be shown how to do it,
I'll go ahead and do that too:

Call the speed of the boat (through the water) 'B'.
Call the speed of the current (the water) 'C'.

When the boat is going 'up' the river, against the current,
his speed past the riverbank is (B - C).

When the boat is going 'down' the river, the same way as the current,
his speed past the riverbank is (B + C).

The problem says it took him 5 hours to travel 60 km against the current.
Distance = (speed) x (time)
60 km = (B - C) x (5 hours)

The problem also says it took him 3 hours to return.
The distance to return is the same 60 km.
The other direction is the same direction as the current,
so his speed on the return is (B + C).
Distance = (speed) x (time)
60 = (B + C) x (3)

Now we have two equations, so we can find 'B' and 'C'.

5B - 5C = 60
3B + 3C = 60

Multiply each side of the first equation by 3, and
multiply each side of the second equation by 5:

15B - 15C = 180
15B + 15C = 300

Add the second equation to the first one:

30B = 480
B = 480/30 = 16 km per hour.

Subtract the second equation from the first one:

-30C = -120
C = -120/-30 = 4 km per hour.

The speed of the boat through the water (B) is 16 km per hour.
The speed of the water past the riverbank is 4 km per hour.

Check:

-- When the boat is going along with the current, his speed past the riverbank
is (16 + 4) = 20 km per hour. In 3 hours, he covers (3 x 20) = 60.

-- When the boat is going against the current, his speed past the riverbank
is (16 - 4) = 12 km per hour. In 5 hours, he covers (5 x 12) = 60 km.

yay !

The box plots show the data distributions for the number of text messages Will and Jaime sent each day.What is the difference of the medians?

1
2
4
7

Answers

If I’m understanding this question right then the answer is 2 because the 2 numbers in the middle are 2 and 4 and 4-2 is 2.

Your difference will be 2

Erin and Aimee are each responsible for mowing half of their back yard. the yard is rectangular with dimensions 75 feet by 90 feet. Erin starts mowing the corner, gradually working her way towards the middle by mowing concentric bands around the outside edges. If the mower cuts a three foot wide path, at what point should Erin and Aimee stop mowing?

Answers

Answer:

Erin should stop at three and a half rounds.

Step-by-step explanation:

One complete round will mow 954 square feet, the total area that she has to mow 3375 square feet. If she goes around three and a half times, she should be finished and stop. This was quite hard to figure out, and may very well be incorrect in some way, but I hope this helps.

Kathy lives directly east of the park. The football field is directly south of the park. The library sits on the line formed between Kathy's home and the football field at the exact point where an altitude to the right triangle formed by her home, the park, and the football field could be drawn. The library is 9 miles from her home. The football field is 12 miles from the library.a. How far is the library from the park?
b. How far is the park from the football field?

Answers

see the attached figure to better understand the problem

Let

z---------> distance from the library to the park in miles

x-------> distance from the park to the to the football field in miles

y-------> distance from the park to Kathy's home in miles

we know that

In the right triangle ABC

Applying the Pythagorean Theorem

$x^(2) +y^(2) =(12+9)^(2) \n x^(2) +y^(2)=441$ -----> equation $1$

In the right triangle ABD

Applying the Pythagorean Theorem

$12^(2) +z^(2) =x^(2) \n 144 +z^(2)=x^(2)$ -----> equation $2$

In the right triangle BCD

Applying the Pythagorean Theorem

$9^(2) +z^(2) =y^(2) \n 81 +z^(2)=y^(2)$ -----> equation $3$

Add equation $2$ and equation $3$

$144 +z^(2)=x^(2)$

$81 +z^(2)=y^(2)\n ------$

$144+81+2z^(2) =x^(2) +y^(2)$ -----> equation $4$

Substitute equation $1$ in equation $4$

$144+81+2z^(2)=441\n 2z^(2) =441-225\n 2z^(2)=216\n z^(2)=108\n z=√(108) miles\n z=10.39 miles$

Find the value of x

$144 +z^(2)=x^(2)\n 144 +√(108)^(2)=x^(2) \n x^(2) =144+108\n x^(2) =252\n x=√(252) miles\n x=15.87 miles$

therefore

the answer is

Part a) The distance from the library to the park is equal to $10.39 miles$

Part b) The distance from the park to the to the football field is equal to $15.87 miles$

Look at the picture in the attachment.

Using the Pythagorean theorem, set up a system of three equations:
$x^2+y^2=(12+9)^2 \n12^2+z^2=x^2 \n9^2+z^2=y^2 \n \nx^2+y^2=441 \n144+z^2=x^2 \n81+z^2=y^2$

$\hbox{substitute } 144+z^2 \hbox{ for } x^2 \hbox{ and } 81+z^2 \hbox{ for } y^2 \hbox{ in the first equation:} \n144+z^2+81+z^2=441 \n225+2z^2=441 \n2z^2=441-225 \n2z^2=216 \nz^2=(216)/(2) \nz^2=108 \nz=√(108) \nz=√(36 * 3) \nz=6√(3) \n z \approx 10.39$

$81+z^2=y^2 \n81+108=y^2 \n189=y^2 \n√(189)=y \n√(9 * 21)=y \ny=3√(21) \n y \approx 13.75$

a. The library is approximately 10.39 miles (exactly: 6√3 miles) from the park.
b. The park is approximately 13.75 miles (exactly: 3√21 miles) from the football field.

A rectangular bedroom floor has an area of 100 square feet and a length of 10 feet. What is the perimeter of the floor?

Answers

The area is calculated by multiplying the length by width, the perimeter is calculated by adding up every side of the rectangle

Considering that we already are given the length of the floor we must divide 100 (the area) by 10 (the length) to get the width

100/10= 10 (the width)

The perimeter is equal to each side of the rectangle added together, a rectangle has two lengths and two widths

Therefore: 10 (the length) + 10 (the length) + 10 (the width) + 10 (the width) = 40

The perimeter is 40 feet

A storage tank is being designed for iodine. The storage tank is to be spherical and will withstand a maximum hydrostatic pressure of 1 comma 375 millimeters of mercury [mm Hg]. What is the diameter of the tank in meters [m]? The density of iodine is 5 comma 010 kilograms per cubic meter left bracket kg divided by m cubed right bracket.

Answers

Answer:

3.73 m

Step-by-step explanation:

1375 mm Hg corresponds to a pressure of 18693.264 kgf/m^2.

Dividing that by the density will give the depth allowed, which is the diameter of the sphere:

(18693.264 kgf/m^2)/(5010 kgf/m^3) ≈ 3.73 m

The sphere can be up to 3.73 m in diameter.

_____

1 kgf is the force produced by a 1 kg mass in Earth's gravity field, about 9.8 N.

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Plz helpp FASTTFind the area of triangle ABC with vertices A(2, 3), B(1, -3), and C(-3, 1).a.10 units2c.14 units2b.12 units2d.16 units2

Answers

What is the triangle?

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Plz helpp FASTTFind the area of triangle ABC with vertices A(2, 3), B(1, -3), and C(-3, 1).
a.
10 units2
c.
14 units2
b.
12 units2
d.
16 units2