Answer: The perimeter of the largest triangle = 117 units.
Step-by-step explanation:
Sides of smaller triangle = 10,20 and 15 units
Longest side = 20 units
Longest side of larger triangle = 52 units
Sides of two similar triangles are proportional.
Let k be proportionality constant.


Length of other two sides,

So sides of larger triangle = 52 units, 26 units , 39 units
Perimeter of largest triangle = 52 +26+39 = 117 units
Hence, the perimeter of the largest triangle = 117 units.
Answer:
144 units²
Step-by-step explanation:
The net of the right triangular prism consists of 3 rectangles and 2 equal triangles
Let's solve for the area of each:
✔️Area of rectangle 1 = L*W
L = 11
W = 3
Area of rectangle 1 = 11*3 = 33 units²
✔️Area of rectangle 2 = L*W
L = 11
W = 4
Area of rectangle 2 = 11*4 = 44 units²
✔️Area of rectangle 3 = L*W
L = 11
W = 5
Area of rectangle 3 = 11*5 = 55 units²
✔️Area of the two triangles = 2(½*base*height)
base = 4
height = 3
Area of the two traingles = 2(½*4*3)
= 12 units²
✔️Surface area of the right triangle = area of rectangle 1 + area of rectangle 2 + area of rectangle 3 + area of the two triangles
= 33 + 44 + 55 + 12
= 144 units²
Answer:
-3, 1, 4 are the x-intercepts
Step-by-step explanation:
The remainder theorem tells you that dividing a polynomial f(x) by (x-a) will result in a remainder that is the value of f(a). That remainder will be zero when (x-a) is a factor of f(x).
In terms of finding x-intercepts, this means we can reduce the degree of the polynomial by factoring out the factor (x-a) we found when we find a value of "a" that makes f(a) = 0.
__
For the given polynomial, we notice that the sum of the coefficients is zero:
1 -2 -11 +12 = 0
This means that x=1 is a zero of the polynomial, and we have found the first x-intercept point we can plot on the given number line.
Using synthetic division to find the quotient (and remainder) from division by (x-1), we see that ...
f(x) = (x -1)(x² -x -12)
We know a couple of factors of 12 that differ by 1 are 3 and 4, so we suspect the quadratic factor above can be factored to give ...
f(x) = (x -1)(x -4)(x +3)
Synthetic division confirms that the remainder from division by (x -4) is zero, so x=4 is another x-intercept. The result of the synthetic division confirms that x=-3 is the remaining x-intercept.
The x-intercepts of f(x) are -3, 1, 4. These are the points you want to plot on your number line.
Answer:
Habrá 100 chocolates en total en 5 cajas de chocolates.
Step-by-step explanation:
Esta pregunta es resolvida usando proporciones, con lo uso de regla de tres
.
11 cajas, 220 chocolates:
Entonces:

20 chocolates por caja.
Calcula cuántos chocolates habrá en total en 5 cajas de chocolates.
20 chocolates por caja, entonces:
5*20 = 100
Habrá 100 chocolates en total en 5 cajas de chocolates.