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3 years ago

Are all equilateral triangles acute?

Mathematics

1 answer:

Anvisha [2.4K]3 years ago

8 0

Answer:

Yes, all equilateral triangles are acute.

Step-by-step explanation:

yea

hope this helps :)))

You might be interested in

H. Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 :

frutty [35]

Answer:

so here is the answer hope it helps

8 0

3 years ago

Classify each function as even, odd, or neither even nor odd.

drek231 [11]

The function

f(x) is even

g(x) is neither even nor odd

h(x) is odd

Steps:

for an even function it holds that f(-x) = f(x):

f(-x) = (-1)^6 x^6 - (-1)^4 x^ 4 = x^6 - x^4 = f(x) => f is even

for an odd h(x) it holds that h(-x) = -h(x):

$h(-x) = (-1)^5x^5-(-1)^3x^3 = -(x^5-x^3) = -h(x) \implies h(x)\,\, \mbox{even}$

It is easy to show that g(x) does not match any of the two possibilities above.

8 0

3 years ago

Read 2 more answers

What is the nth term rule of the quadratic sequence below?

Vladimir [108]

Answer:

3n² + 5n - 2

Step-by-step explanation:

Given sequence:

6, 20, 40, 66, 98, 136, ...

Calculate the first differences between the terms:

$6 \underset{+14}{\longrightarrow} 20 \underset{+20}{\longrightarrow} 40 \underset{+26}{\longrightarrow} 66 \underset{+32}{\longrightarrow} 98 \underset{+38}{\longrightarrow} 136$

As the first differences are not the same, calculate the second differences:

$14 \underset{+6}{\longrightarrow} 20 \underset{+6}{\longrightarrow} 26 \underset{+6}{\longrightarrow} 32 \underset{+6}{\longrightarrow} 38$

As the second differences are the same, the sequence is quadratic and will contain an n² term.

The coefficient of the n² term is half of the second difference.

Therefore, the n² term is: 3n²

Compare 3n² with the given sequence:

$\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2 & 3 & 12 & 27 & 48 \\\cline{1-5} \sf operation & +3&+8 & +13 & +18 \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}$

The second operations are different, therefore calculate the differences between the second operations:

$3 \underset{+5}{\longrightarrow} 8 \underset{+5}{\longrightarrow} 13\underset{+5}{\longrightarrow} 18$

As the differences are the same, we need to add 5n as the second operation:

$\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2 +5n & 8&22 & 42 & 68\\\cline{1-5}\sf operation & -2 &-2 &-2 & -2 \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}$

Finally, we can clearly see that the operation to get from 3n² + 5n to the given sequence is to subtract 2.

Therefore, the nth term of the quadratic sequence is:

3n² + 5n - 2

6 0

2 years ago

A rain barrel is full of water and used to water the garden. The rain barrel loses water at the rate 2.5 gallons of water per mi

soldier1979 [14.2K]

Answer: y - 37.5 = 2.5 ( x - 7)

Explanation:

1) The point-slope form is has this form:

y - y1 = m (x - x1)

Where m is the slope or rate of change and x1, y1 are the coordinates of the point.

2) you are told that the the rate of change of water (m) is 2.5

m = 2.5

3) The point is given by that after 7 min the rain barrel contains 37.5 gallons. This is:

x1 = 7
y1 = 37.5

4) Replace those value in the point-slope model:

y - 37.5 = 2.5 ( x - 7)

That is the point-slope model or equation.

4 0

3 years ago

What is the solution of the system ? 2x+3y=4 x-y=-3

fgiga [73]

Change the equation, x - y = -3, to isolate x or y and plug that new equation into the equation 2x + 3y = 4

I changed it to: x = y - 3
so
2(y - 3) + 3y = 4
2y - 6 + 3y = 4
5y - 6 = 4
5y = 4 + 6
5y = 10
y = 10/5
y = 2

then you plug that 2 into the equation x = y - 3 to get the value of x

x = (2) - 3
x = -1

you can check this by plugging the x and y values into the equation 2x + 3y = 4

2(-1) + 3(2) = 4
-2 + 6 = 4
4 = 4

hope this helps :)

6 0

3 years ago