Answer:
x= 2 and y = -4
Step-by-step explanation:
8x + 3y = 4 ---------------------------------(1)
-7x + 5y = -34 -----------------------------(2)
Multiply through equation (1) by 5 and multiply through equation(2) by 3
40x + 15y = 20 ----------------------------(3)
-21x + 15y =-102----------------------------(4)
Subtract equation (4) from equation (3)
61x = 122
Divide both-side of the equation by 61
61x/61 = 122/61
(At the left-hand side of the equation 61 will cancel-out 61 leaving us with just x, while at the left-hand side of the equation 122 will be divided by 61)
x = 122/61
x=2
Substitute x= 2 into equation (1)
8x + 3y = 4
8(2) + 3y = 4
16 + 3y = 4
Subtract 16 from both-side of the equation
16-16 + 3y = 4-16
3y = -12
Divide both-side of the equation by 3
3y/3 = -12/3
y = -4
x= 2 and y = -4
You can solve by using Pythagoras theorem.
Let the longest side be c.
a^2 + b^2 = c^2
If this holds, it is a right angle.
But, 3.5^2 + 4.5^2 is not equal to 5.5^2.
Answer:
18 yards of material needed to make 24 shirts
Step-by-step explanation:
The unit rate is
1 shirt
------------------------------ = 1 1/3 shirts per yard of material = 4/3 shirt/yard
0.75 yards material
This rate could also be written as 3/4 yard per shirt
Multiply this latter rate by 24 shirts:
3 yard
-------------- * 24 shirts = 18 yards of material needed to make 24 shirts
4 shirt
Question 4
The magnitude;
Using Pythagoras theorem,
(-200)² + (-530)² = 320900
Length = √320900
= 566.5 mi
To get the angle
Tan θ = opposite/adjacent
= 200/530
= 0.3774
θ = tan^-1 (0.3774)
= 20.67
≈ 21°
The direction from the Cartesian plane is south of west.
Therefore, the magnitude and the direction will be;
About 566.5 mi, 21° south of west
Question 5.
To get the resultant of two vectors we just add the two vectors given.
This involves adding the corresponding values.
Thus, for <-6,5> and <6,-5>
Resultant vector = <(-6+6),(5+-5>
= <0,0>
(-19,7) (4, 15) hshw wjwhw
