Answer:
Solution: x = -2; y = 3 or (-2, 3)
Step-by-step explanation:
<u>Equation 1:</u> y = -5x - 7
<u>Equation 2:</u> -4x - 3y = -1
Substitute the value of y in Equation 1 into the Equation 2:
-4x - 3(-5x - 7) = -1
-4x +15x + 21 = -1
Combine like terms:
11x + 21 = - 1
Subtract 21 from both sides:
11x + 21 - 21 = - 1 - 21
11x = -22
Divide both sides by 11 to solve for x:
11x/11 = -22/11
x = -2
Now that we have the value for x, substitute x = 2 into Equation 2 to solve for y:
-4x - 3y = -1
-4(-2) - 3y = -1
8 - 3y = -1
Subtract 8 from both sides:
8 - 8 - 3y = -1 - 8
-3y = -9
Divide both sides by -3 to solve for y:
-3y/-3 = -9/-3
y = 3
Therefore, the solution to the given systems of linear equations is:
x = -2; y = 3 or (-2, 3)
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Tanya run 50 yards across the diagonal of the rectangular field.
<u>Step-by-step explanation</u>:
Step 1 :
- Length of the rectangular field = 40 yards
- width of the rectangular field = 30 yards
Step 2 :
Measure of the diagonal = √(length^2 + width^2 )
Step 3 :
Diagonal = √(40^2 + 30^2 )
= √(1600 + 900)
= √2500
= ±50
Step 4 :
Since distance cannot be negative, The measure of diagonal = 50 yards.
∴ Tanya runs diagonally across a rectangular field is 50 yards.
Answer:
$95.89875
Step-by-step explanation:
The original price of the necklace is 119.5. And we are subtracting 25% from this. 119.5 - 25% = 119.5 - 1/4 since 25% is 25/100 which is also 1/4.
So without tax, the price of the necklace is 119.5 - 29.875 which is 89.625.
The tax is 7%. So we should add 89.625 to 7%. This is complicated, but it should result in 95.89875.
If we round this to the nearest cent, it should be <em>$95.9</em>.
Answer: See Below
<u>Step-by-step explanation:</u>
NOTE: You need the Unit Circle to answer these (attached)
5) cos (t) = 1
Where on the Unit Circle does cos = 1?
Answer: at 0π (0°) and all rotations of 2π (360°)
In radians: t = 0π + 2πn
In degrees: t = 0° + 360n
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Where on the Unit Circle does 
<em>Hint: sin is only positive in Quadrants I and II</em>
In degrees: t = 30° + 360n and 150° + 360n
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Where on the Unit Circle does 
<em>Hint: sin and cos are only opposite signs in Quadrants II and IV</em>
In degrees: t = 120° + 360n and 300° + 360n
