Answer:
The larger number is -6, the smaller number is -15
Step-by-step explanation:
We have two numbers, a and b.
We know that one number is larger than another by 9.
Then we can write:
a = b + 9
then a is larger than b by 9 units.
If the greater number is increased by 10 (a + 10) and the lesser number is tripled (3*b), the sum of the two would be -41:
(a + 10) + 3*b = -41
So we got two equations:
a = b + 9
(a + 10) + 3*b = -41
This is a system of equations.
One way to solve this is first isolate one variable in one of the two equations:
But we can see that the variable "a" is already isolated in the first equation, so we have:
a = b + 9
now we can replace that in the other equation:
(a + 10) + 3*b = -41
(b + 9) + 10 + 3*b = -41
now we can solve this for b.
9 + b + 10 + 3b = -41
(9 + 10) + (3b + b) = -41
19 + 4b = -41
4b = -41 -19 = -60
b = -60/4 = -15
b = -15
then:
a = b + 9
a = -15 + 9 = -6
a = -6
There are two triangles in the figure(triangular prism) option third is correct.
<h3>What is a triangular prism?</h3>
When a triangle is, stretch it out to produce a stack of triangles, one on top of the other. A triangular prism is a name given to this novel 3D object.
The complete question is:
How many triangles are needed to draw the net of this object?
For the figure please refer to the attached picture.
As we can see in the figure we have given a triangular prism:
The triangular prism has two triangles.
A triangle for the base of the prism and a triangle for the top of the prism.
The lateral faces of the prism are rectangular.
Thus, there are two triangles in the figure(triangular prism) option third is correct.
Learn more about triangular prisms here:
brainly.com/question/16909441
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13 By the factor theorem, if the function is divisible by x - 3 then f(3) = 0. So we have:-
2(3)^3 + k(3)^2 + 7(3) - 3 = 0
9k = 3 - 21 - 54 = -72
k = -72/9 = -8 answer
14. Similarly , f(-4) = 0 , so we have:-
(-4)^3 + 9(-4)^2 + k(-4) - 12 = 0
-64 + 144 - 4k - 12 = 0
4k = -64 + 144 - 12 = 68
k = 68/4
k = 17 answer
Answer - Yes, corresponding angles converse
