MATHEMATICS MIDDLE SCHOOL

What is the solution to the system?-2x + y + 6z = 1
3x + 2y + 5z = 16
7x + 3y – 4z = 11

Answers

Answer 1
Answer:

Answer:

x = 4, y = -2, z = 3

Step-by-step explanation:

\left\{\begin{array}{ccc}-2x+y+6z=1&(1)\n3x+2y+5z=16&(2)\n7x+3y-4z=11&(3)\end{array}\right\n\n(1)\n-2x+y+6z=1\qquad\text{add}\ 2x\ \text{to both sides}\ny+6z=2x+1\qquad\text{subtract}\ 6z\ \text{from both sides}\ny=2x-6z+1\n\n\text{Substitute it to (2) and (3):}\n\n\left\{\begin{array}{ccc}3x+2(2x-6z+1)+5z=16\n7x+3(2x-6z+1)-4z=11\end{array}\right\qquad\text{use the distributive property}\n\n

\left\{\begin{array}{ccc}3x+4x-12z+2+5z=16&\text{subtract 2 from both sides}\n7x+6x-18z+3-4z=11&\text{subtract 3 from both sides}\end{array}\right\n\left\{\begin{array}{ccc}7x-7z=14&\text{divide both sides by 7}\n13x-22z=8\end{array}\right\n\left\{\begin{array}{ccc}x-z=2&\text{multiply both sides by (-13)}\n13x-22z=8\end{array}\right

\underline{+\left\{\begin{array}{ccc}-13x+13z=-26\n13x-22z=8\end{array}\right}\qquad\text{add both sides of the equations}\n.\qquad\qquad-9z=-18\qquad\text{divide both sides by (-2)}\n.\qquad\qquad \boxed{z=2}\n\n\text{Put it ot the equation}\ x-z=2:\nx-2=2\qquad\text{add 2 to both sides}\n\boxed{x=4}\n\n\text{Put the values of}\ x\ \text{and}\ z\ \text{to the equation}\ y=2x-6z+1:\n\ny=2(4)-6(2)+1\ny=8-12+1\n\boxed{y=-3}

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The bag was filled with red marbles and blue marbles in the ratio of 5:7. If there were 180 marbles in the bag,how many were red?

Answers

You just have to multiply each number by 180 and that's how many you have of each color respectively
R + B = 5/7 x 180
R + B = 900/7 = 128, 4/7
If R = B than R is 450/7 = 64, 2/7
R or B = 64, 2/7

The domain of f(x) is the set of all real values except 7, and the domain of g(x) is the set of all real values except -3. Which of thefollowing describes the domain of (gof)(x)?
all real values except X -3 and the x for which fex) 7
all real values except X -3 and the x for which f(x) -3
all real values except x 7 and the x for which f(x) 7
all real values except x * 7 and the x for which f(x) -3

Answers

Answer:

Third choice

Step-by-step explanation:

The domain of f(x) is the set of all real values except 7, i.e x\ne7

and the domain of g(x) is the set of all real values except -3, i.e x\ne -3

The domain of g\circ f is the set of all real numbers x in the domain of f  such that f(x) is in the domain of g(x).

However any numbers that are excluded from the domain of f must also be excluded from the domain of g\circ f.

Therefore the correct choice is all real values except x=7 and the x for which f(x) =7

A rhombus has a perimeter of 217 cm. what is the length of each side of the rhombus

Answers

A rhombus has 4 equal sides.
The perimeter is the side lengths added together.

P = s + s + s + s
P = 4s
217 = 4s

Divide by 4 to find the length of one side.

s = 54.25 cm

Maria works 24.5 hours each week at a bookstore . she earns 8.76 per hour . How much does she earn each week

Answers

Since Maria works 24.5 hours a week and 8.76 per hour, you find the total amount by multiplying 24.5 (hours) by 8.76 (amount per hour)

That gets you $214.62.
She earns 24.5 x 8.76 = 214.62

24 miles per hour is equal to how many feet per second

Answers

We already know that 1 mile = 5280 foot
Also we know that 1 hour = (60 * 60) seconds
                                          = 3600 seconds
Then
24 miles per hour = (24 * 5280)/3600
                             = 126720/3600
                             = 35.2 feet/sec
So 24 miles/hour is equal to 35.2 feet per second. The only important thing is to know the conversions correctly. Then the problem becomes easy to solve. I hope the conversions and the procedure for solving the question is clear to you and in future you will be able to do such problems on your own without requiring any help.
24 miles per hour is equal to 35.2 feet per second

Complete each statement from the information given and state the reasons and the triangle criterion you used.

Answers

Answer:

Triangle GAS = Triangle IOL by rule AAS

Step-by-step explanation:

The points must be ordered correctly so they correspond within the triangles. Point G = Point I, Point A = Point O, Point S = Point L.

A rule for determining Triangle Congruency is AAS. If two angles and a side of a triangle are equal to one of another triangle, the triangles are congruent.
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