Answer:
<h3>perpendicular line:
y = -¹/₆
x + 4¹/₃
</h3><h3> parallel line:
y = 6x - 45
</h3>
Step-by-step explanation:
y=m₁x+b₁ ⊥ y=m₂x+b₂ ⇔ m₁×m₂ = -1
{Two lines are perpendicular if the product of theirs slopes is equal -1}
y = 6x - 7 ⇒ m₁=6
6×m₂ = -1 ⇒ m₂ = -¹/₆
The line y=-¹/₆
x+b passes through point (8, 3) so the equation:
3 = -¹/₆
×8 + b must be true
3 = -⁴/₃ + b
b = 4¹/₃
Therefore equation in slope-intercept form:
y = -¹/₆
x + 4¹/₃
y=m₁x+b₁ ║ y=m₂x+b₂ ⇔ m₁ = m₂
{Two lines are parallel if their slopes are equal}
y = 6x - 7 ⇒ m₁=6 ⇒ m₂=6
The line y=6x+b passes through point (8, 3) so the equation:
3 = 6×8 + b must be true
3 = 48 + b
b = -45
Therefore equation in slope-intercept form:
y = 6x - 45
Answer:
Since each cracker in the 190 gram box costs $ 0.0078 while the 850 gram box costs $ 0.0082 each, the 190 gram box is a better deal.
Step-by-step explanation:
Knowing that a 190-gram box of crackers costs $ 1.49 and an 850-gram box costs $ 6.99, to determine which of them is a better deal, the following calculation must be performed:
1.49 / 190 = 0.0078
6.99 / 850 = 0.0082
Therefore, since each cracker in the 190 gram box costs $ 0.0078 while the 850 gram box costs $ 0.0082 each, the 190 gram box is a better deal.
Answer:
Yes
Step-by-step explanation:
There are 10 mm in 1 cm.
We have 300 mm, so let's convert this to cm by using a proportion:
, where x is the number of cm in 300 mm.
Cross-multiplying, we get: 10x = 300, so x = 30 cm.
Clearly, 30 cm > 3 cm, so yes, 300 mm is greater than 3 cm.
Hope this helps!
Answer:
First brand of antifreeze: 21 gallons
Second brand of antifreeze: 9 gallons
Step-by-step explanation:
Let's call A the amount of first brand of antifreeze. 20% pure antifreeze
Let's call B the amount of second brand of antifreeze. 70% pure antifreeze
The resulting mixture should have 35% pure antifreeze, and 30 gallons.
Then we know that the total amount of mixture will be:
Then the total amount of pure antifreeze in the mixture will be:
Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -0.7 and add it to the second equation:
+
--------------------------------------
We substitute the value of A into one of the two equations and solve for B.
Answer:
23
Step-by-step explanation:
x+x+1=x+2=72
3x+3=72
3x=69
x=23
23+24+25=72
