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stepladder [879]
3 years ago
9

State whether the following coordinates on a Cartesian plane form an acute, obtuse or right triangle: a) (-1, 1), (7,-2) and (1,

-5) --_______ b) (0,6), (1, 2) and (5,3) ___
Mathematics
1 answer:
LiRa [457]3 years ago
3 0

Answer:

a) Acute triangle

b) Right triangle

Step-by-step explanation:

∵ A triangle having sides a, b and c is called,

Acute : If a² + b² > c² or a² + c² > b² or b² + c² > a²,

Obtuse : if a² + b² < c² or a² + c² < b² or b² + c² < a²

Right : a² + b² = c² or a² + c² = b² or b² + c² = a²,

a) Let A≡(-1, 1), B≡(7,-2) and C≡(1,-5),

By the distance formula,

AB=\sqrt{(7-(-1))^2+(-2-1)^2}=\sqrt{(7+1)^2+(-3)^2}=\sqrt{8^2+3^2}=\sqrt{64+9}=\sqrt{73}\text{ unit}

Similarly,

BC=\sqrt{45}\text{ unit}

CA=\sqrt{40}\text{ unit}

∵ The sum of any two sides is greater than third side,

So, ABC is a triangle,

Now,

AB^2 + BC^2 > CA^2

⇒ ABC is an acute triangle.

b) Let P≡(0,6), Q≡(1,2) and R≡(5,3),

By the distance formula,

PQ = √17 unit,

QR = √17 unit,

RP = √34 unit,

∵ The sum of any two sides of PQR is greater than third side,

⇒ PQR is a triangle ,

Also,

RP^2=PQ^2+QR^2

Hence, PQR is a right triangle.

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Witch is bigger 8 meters or 80 centimeters
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8 meters

Step-by-step explanation:

80 centimeters is like a one hundredth of 8 meters

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Find the perimeter of the figure.
Ksenya-84 [330]

Answer:

Well I’m not sure what you want but I’ll give you both,

The perimeter is 25 units

The area is 28.5 units ^2

Step-by-step explanation:

Well to find perimeter just count every unit which is what I did and got 25 units.

To find the area jsut split them into two shapes and find the area for both.

Triangle formula: bh/2

Rectangle: Lw

Well we have 3 for base and 3 for height.

3*3=9

9/2=4.5

4.5 is the triangle

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3*8=24

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8 0
3 years ago
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Calculate the value for each determinant:
Dafna1 [17]

Answer:

See explanations below

Step-by-step explanation:

Example of how to find the determinant of a 2×2 matrices is as shown;

\left[\begin{array}{ccc}a&b\\c&d&\end{array}\right]

= (a*d)-(b*c)

= ad - bc

Applying this to solve the given questions

1) (3*4) - (-3*-1)

= 12 - (3)

= 9

2) (-12*5)-(-1*12)

= -60 - (-12)

= -60+12

= -48

3) (0*4)-(-1*17)

= 0-(-17)

= 0+17

= 17

4) (8*-1)-(-4*-1)

= -8-(4)

= -8-4

= -12

5) (2*-1)-(2*-1)

= -2-(-2)

= -2+2

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6) 1(1) - 0(0)

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4 0
3 years ago
Farmer Samantha has a cylindrical grain silo with a diameter of 12 feet and a height of 40 feet. The silo is filled with grain t
sammy [17]

Answer:

161,234 pounds of grain will remain in the silo

Step-by-step explanation:

In this question, we are to calculate the amount of grains that will be left in a silo if 20 cows feed on the content for 100 days.

Firstly, we need to calculate the amount of grains present in the silo.

This we can do by first calculating the volume of the silo. Since it is cylindrical in shape, we apply the formula for the volume of a cylinder.

Mathematically, the volume of a cylinder is

V = pi * r^2 * h

Here we have the r = D/2 = 12/2 = 6 feet and h = 40 feet. Plugging this , we have;

V = pi * 6^2 * 40 = 1440pi cubic feet

Now, per cubic feet, we have a weight of 48 pounds. The weight of grains thus present in the silo is thus;

1440pi * 28 = 1440 * pi * 48= 69,120pi pounds of grain

Let’s calculate what the cows would feast on. That would be 20 * 28 * 100 = 56,000 pounds of grains

Now we need to know what will remain. We just need to subtract what is consumed by the cows from we have inside the silo

What is inside the silo would be 69,120 * 22/7 = apprx 217,234 pounds

What will remain is thus 217,234 - 56,000 = 161,234 pounds of grain

3 0
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Evaluate 0.1m+8-12n0.1m+8−12n0, point, 1, m, plus, 8, minus, 12, n when m=30m=30m, equals, 30 and n=\dfrac14n= 4 1 ​ n, equals,
Rom4ik [11]

Answer:

8

Step-by-step explanation:

We are required to evaluate:

0.1m+8-12n

When m=30, n=\frac{1}{4}

Substituting these values into the expression, we have:

0.1m+8-12n=0.1(30)+8-12(\frac{1}{4})\\=3+8-\frac{12}{4}\\=3+8-3\\=8

8 0
2 years ago
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