Não, não podemos fazer um triângulo com os comprimentos dos lados de 2 cm, 3 cm e 10 cm. Isso ocorre porque a soma de 2+3 < 10. (in english: No, we cannot make a triangle with the side lengths of measurement 2 cm, 3 cm, and 10 cm. This is because sum of 2+3 < 10).
<h3>What is triangle inequality theorem?</h3>
Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side.
Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,
Now, for this case, the sides given are:
- a =2 cm,
- b = 3 cm,
- and c = 10 cm
But we see that:
a+ b = 5 cm which is < c which is of 10 cm.
Thus, these lengths don't satisfy the triangle inequality theorem, and therefore, cannot be sides of any triangle.
Learn more about triangle inequality theorem here:
brainly.com/question/342881
#SPJ1
The expression is:
(z^2 - 4)
_______
z - 3
_______________
z + 2
___________
z^2 + z - 12
You can factor the numerator z^2 - 4 = (z + 2) (z - 2)
And the denominatior z^2 + z + 12 = (z + 4)(z - 3)
That permits to write the quotient as:
(z + 2)(z - 2)
___________
z - 3
_______________
z + 2
___________
(z + 4)(z - 3)
Now you can multiplicate the numerator of the numerator times the denominator of the denominator, and multtiplicate the denominator of the numerator times the numerator of the denominator to obtain:
(z + 2)(z - 2)(z + 4)(z - 3)
____________________
(z - 3)((z + 2)
Cancel the factors (z - 3) and (z + 2) because they are in both the numerator and the denominator =>
(z - 2)(z + 4) = z^2 + 2z - 8
The restrictions are that none of the cancelled factors can be 0, so z ≠ 3 and z ≠- 4.
Answer:
Decrease
Step-by-step explanation:
So, I encourage you to grab a calculator and see for yourself
Put in the function: 4/5 into a standard calculator. You will see that it will come out to .8
Put in the function: 3/5 into a standard calculator. You will see that it will come out to .6
.6 is less than .8, just as 3/5 is less than 4/5.
Another analogy that can be used is seeing the fraction as a real-life object.
Let's say that you make two pies. You cut the pie evenly into five slices. You set them on the table and leave them for whoever wants to eat them. You see that Pie 1 has two slices missing (3/5) and that Pie 2 has one slice missing. (4/5)
3 out of 5 slices are left of Pie 1.
4 out of 5 slices are left of Pie 2.
Pie 1 has less than Pie 2 does.
Hope this has helped!
Answer:
5 felt pads.
7 cards.
Step-by-step explanation:
Remark
- The total number of items is 12
- So let the felt sheets be x
- Let the cards = y
Equations and Solution
x + y = 12
Now the price is 7.75 that she has to pay for the 12 items. She wants to come back with 0 dollars.
0.5x + 0.75y = 7.75 Multiply this equation by 2
x + 1.5y = 15.50 write the first equation underneath and subtract.
<u>x + y = 12</u>
.5y = 3 Divide by 0.5
y = 3/0.5
y = 7
So she can get 7 cards.
x + y = 12
x + 7 = 12
x = 12 - 7
x = 5
So she can buy 5 felt pads.