Answer: x > 6
Step-by-step explanation: -4(2x+2) < -40
-8x - 8 < -40
+8 +8
-8x < 48
/-8x /-8x
x > 6 *The less than sign got flipped to a greater than sign because we divided by a negative.
Answer:
c=10mm
Step-by-step explanation:
Using pythagoras theorem,
hypotenuse²=base²+altitude²
=√19²+9²
=19+81
=100
Hypotenuse²=100
Hypotenuse=√100
=10
Answer: 49
Step-by-step explanation:
a=1 ,b=14, c=?
b^2-4ac =0
(14)^2-4(1)(c)=0
196-4c=0
196=4c
c=49
Check:
(x)^2+2(x)(7)+(7)^2
x^2+14x+49
(x+7)^2
Answer:
5/9
Step-by-step explanation:
Let's begin by determining the factors of the problem. We know that Robert ran a race that is 2/3 of a mile long. Therefore, we know that 2/3 is a factor in the equation. We also know that, of the 2/3 mile, he ran 5/6 of it. Now the tricky part is deciding how the two fractions are related.
To make this easier, let's substitute a different number for 5/6. We'll say 2.
If he has completed TWICE the length of the race, how would you determine how far he ran?
You would multiply 2/3 by 2! This same principle can be applied to the problem.
To determine the total distance run in miles, we can write it as 2/3 * 5/6
(NOTE that * is known as "times" or "multiplied by")
With this, you multiply the numerators (2 * 5 = 10) and the denominators (3 * 6 = 18) and then make your fraction... 10/18!
But you're not done yet. Always remember to simplify when possible. Both terms are divisible by 2. Therefore, it can be written as 5/9.
Hope this helped!
Answer:
C. y = -2/3x +22/3
Step-by-step explanation:
You can choose the correct answer by realizing that the line must have a y-intercept greater than 6. The given point is (2, 6) and the line goes up and to the left from there. The y-intercept is obviously more than 6.
The only reasonable answer choice is ...
y = -2/3x +22/3 . . . . . a y-intercept of 7 1/3
_____
There are a lot of ways to work problems like these. One is to write the equation of the line, then match that to the answer choices.
Another is to eliminate all the "impossible" answer choices, then choose the appropriate one from what's left. (The given line has a negative slope, eliminating choices A and B.)
I like to use the simplest method that will determine the correct answer. Here, that involves reading and understanding the question to obtain some idea of where the desired line must appear on the graph.
Of course, it helps to know that "slope-intercept form" is ...
y = mx +b . . . . . . m represents the slope; b is the y-intercept
