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Mathematics

1 answer:

tankabanditka [31]3 years ago

7 0

Answer:

Step-by-step explanation:

3C + 8T = 58 ----- (eq1)

5C + 2T = 23 ------(eq2)

Multiply equation (1) by 5 and equation (2) by 3

15C + 40T = 290 -----(eq3)

15C + 6T = 69 ----------(eq4)

Subtract equation (4) from (3)

34T = 221

T = 221/34

T = $6.5

Therefore 1 Table will cost $6 and 5 cents

Solve for (C) in equation (1)

3C + 8T = 58

3C + 8(6.5) = 58

3C + 52 = 58

3C = 58-52

3C = 6

C = 6/3

C = $2

1 Chair will cost $2

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The height of a triangle is 3cm less than twice the base. The area is 10cm2

Kamila [148]

Answer:

The base is 4cm and the height is 5cm.

Step-by-step explanation:

This is a solve the system question. Call H the height of the triangle and B the base. The question tells us:

$H=2B-3$

and

$\frac{B \times H}{2}=10$

Sub the first equation into the second (as H is already isolated). You will end up with a quadratic equation - solve that any way you wish (e.g. quadratic formula). I've provided the factored form below which shows you the roots:

$\frac{B(2B-3)}{2}=10\\\frac{2B^2-3B}{2}=10\\2B^2-3B=20\\2B^2-3B-20=0\\(2B+5)(B-4)=0\\B= - \frac{5}{2},4$

In this question, we take B=4. You can't have a negative side length so the other answer is eliminated. Now sub the value for B into either of the original equations. I'll use the first, again because H is already isolated:

$H=2(4)-3\\H=8-3\\H=5$