Answer:
D. All three chose a valid first step toward solving the equation.
Step-by-step explanation:
Aaron, Blaine, and Cruz are solving the equation 4/7 (7 − n) = −1. Aaron started his solution by multiplying both sides of the equation by 7/4 . Blaine started by using the distributive property to multiply 4/7 by both 7 and −n. Cruz started by dividing both sides of the equation by 4/7 .
Which of the following is true?
A. Blaine and Cruz made an error in picking their first steps.
B. Cruz made an error in picking his first step.
C. All three made an error because the right side equals -1.
D. All three chose a valid first step toward solving the equation.
Given:
4/7(7 - n) = -1
Aaron:
4/7(7 - n) = -1
Multiple both sides by 7/4
4/7(7 - n) * 7/4 = -1 * 7/4
7 - n = -7/4
- n = -7/4 - 7
- n = (-7-28)/4
- n = -35/4
n = 35/4
Blaine:
4/7(7 - n) = -1
4/7(7 - n) × 7 = -1 × 7
4(7 - n) = -7
28 - 4n = -7
-4n = -7 - 28
- 4n = - 35
n = -35/-4
n = 35/4
Cruz:
4/7(7 - n) = -1
Divide both sides by 4/7
4/7(7 - n) ÷ 4/7 = -1 ÷ 4/7
4/7(7 - n) × 7/4 = -1 × 7/4
7 - n = -7/4
- n = (-7-28)/4
- n = -35/4
n = 35/4
D. All three chose a valid first step toward solving the equation.
Answer:
The complement of the given set in interval notation is![(-\infty,-5]\cup(6,\infty)](https://tex.z-dn.net/?f=%28-%5Cinfty%2C-5%5D%5Ccup%286%2C%5Cinfty%29)
. It can we written as (-inf,5]U(6,inf).
Step-by-step explanation:
The given set in interval notation is
(−5,6]
It means the set is defined as
If B is a set and U is a universal set, then complement of set B contains the elements of universal set but not the elements of set B.
Here, universal set is R, the set set of all real numbers.
The complement of the given set is
Complement of the given set in interval notation is
![A^c=(-\infty,-5]\cup(6,\infty)](https://tex.z-dn.net/?f=A%5Ec%3D%28-%5Cinfty%2C-5%5D%5Ccup%286%2C%5Cinfty%29)
Therefore the complement of the given set in interval notation is. It can we written as (-inf,5]U(6,inf).
<h3>
Answer: </h3><h3>
speed of train A = 44 mph</h3>
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Work Shown:
x = speed of train A
y = speed of train B
"train A travels 4/5 the speed of train B" (I'm assuming "train one" is supposed to read "train B"). So this means x = (4/5)y
distance = rate*time
d = x*7
d = (4/5)y*7 = (28/5)y represents the distance train A travels
d = y*7 = 7y represents the distance train B travels
summing those distances will give us 693
(28/5)y + 7y = 693
5*( (28/5)y + 7y ) = 5*693
28y + 35y = 3465
63y = 3465
y = 3465/63
y = 55
Train B's speed is 55 mph
4/5 of that is (4/5)y = (4/5)*55 = 4*11 = 44 mph
Train A's speed is 44 mph
Answer:
Julio's number is 31
Step-by-step explanation:
Let's assume Julio's number is x
If we subtract 14 from x, we'd have
x - 14
We multiply the difference by -7, we'll have
-7(x - 14) = -7x + 98
Note that multiply 2 negative signs gives a positive sign, that is,
- x - = +
-7 x -14 = 98
When we multiply the difference by -7, the result is -119
-7x + 98 = -119
To collect like terms, we subtract 98 from both sides of the equation
-7x + 98 - 98 = -119 - 98
-7x = -217
We then divide both sides by -7, that is the coefficient of x
-7x/-7 = -217/-7
x = 31.
Therefore, Julio's number is 31
