4y - x = 5 + 2y ..... (1)
3x + 7y = 24 ..... (2)
by grouping like terms in (1)
4y - x = 5 + 2y
4y - 2y - x = 5
<span>-x + 2y = 5 </span> ..... (1a)
by multiplying (1a) through by -3
(-3)(-x) + 2(-3)y = 5(-3)
3x - 6y = -15 ..... (1b)
by subtracting 1a from 2
3x -3x + 7y - (-6y) = 24 - (-15)
13y = 39
⇒ y = 3
by substituting y=3 into (2)
3x + 7(3) = 24
3x = 24 - 21
3x = 3
⇒ x = 1
∴ solution to the system is x=1 when y = 3
Answer:
Option D is correct.
Length of PQ is 36 unit.
Explanation:
If the measures of two sides in one triangle are proportional to the corresponding sides in the another triangle and their including angles are congruent, then the triangles are similar.
Given: Right angle triangle ABC at B , Length of AB = 12 unit and length of BC = 11.5 unit and in right angle triangle PQR at Q , length of QR = 34.5 unit.
Also it is given that Angle A is congruent to angle P and angle C is congruent to angle R.
To find the length of QR:
It is given that ΔABC and ΔPQR are Similar triangle
then, by the definition of similar triangle:

Substitute the value of AB, QR and BC to solve for PQ;
or

On simplify:

Therefore, the length of side PQ is 36 units.
The first two are true and the last one is false
Answer:
#5: Equivalent
#6: Not Equivalent
1. 3x+6
2. 4y-4
3. x²+6x
4. xy+4x
5. 3x²+3xy-3x
Step-by-step explanation:
for #6 the equivalent: 2x(x+3)= 2x²+6x
The line needs to be 8.06 m long
Explanation
Given that the ladder is 7 feet tall and the bottom of the slide should be 4 m away from the ladder.
The ladder,slide and the ground connecting them makes the sides of a right angled triangle with ladder as the height and ground as the base.
base=4m
height=7m
hypotenuse can be determined using pythagoras law
