Mathematics Middle School

Solve the following system of equations algebraically for all values of x,y and z
x+3y+5z=45
6x-3y+2z=-10
-2x+3y+8z=72

Answers

Answer 1
x + 3y + 5z = 45
6x - 3y + 2z = - 10
------------------------add
7x + 7z = 35

6x - 3y + 2z = -10
-2x + 3y + 8z = 72
----------------------add
4x + 10z = 62

7x + 7z = 35....multiply by 4
4x + 10z = 62...multiply by -7
---------------------
28x + 28z = 140 (result of multiplying by 4)
-28x - 70z = - 434 (result of multiplying by -7)
--------------------add
- 42z = - 294
z = -294/-42
z = 7

4x + 10z = 62
4x + 10(7) = 62
4x + 70 = 62
4x = 62 - 70
4x = - 8
x = -8/4
x = -2

x + 3y + 5z = 45
-2 + 3y + 5(7) = 45
-2 + 3y + 35 = 45
3y + 33 = 45
3y = 45 - 33
3y = 12
y = 12/3
y = 4

solution is (-2,4,7) <==
Answer 2
Final answer:

The system of equations x+3y+5z=45, 6x-3y+2z=-10, -2x+3y+8z=72 can be solved algebraically to get the values x=6, y=12, z=-1.

Explanation:

First, we can combine the first and the second equations and the first and third equations to cancel out y.

Doing so, we get: x+3y+5z+6x-3y+2z=45-10 and x+3y+5z-2x+3y+8z=45+72

The new equations simplify to 7x+7z=35 and -x+13z=117

Next, we can divide the first new equation by 7 to get x+z=5. Subtract x from both sides to get z=5-x.

Substitute z=5-x into the second equation to find the value of x.

Performing these substitutions gives x=6. Substituting x=6 back into the equation z=5-x gives z=-1.

Finally, we substitute x=6 and z=-1 back into the original equations to solve for y: y=(45-6-5(-1))/3 = 12

So, x=6, y=12, z=-1 are the solutions to the system of equations.

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Related Questions

How many times smaller is 3 × 10-7 than 6 × 10-6?

Answers

3*10-7=23
6*10-6=54
it is 2.35 times smaller. 

Need help asap! Need to find the value of x

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X-45+x+x-45+x-45+x=540, x=135
uvghvghb mb bm nk bjnjbkjbkbk khbh khbhk h b jbn  h jhb

A school collected x food items and divided them equally among 6 charities. Each charity received 250 items. How many items did the school collect?

Answers

The school collected 1500 cans

1,500 you just have to multiply 250 times 6. since each charity received 250 items and there are 6 charities. Don't know if i explained it right but the answer is 1,500
 

PLEASE HELP ...... Geometry Homework, I'll give brainliest

Answers

There are a few facts we'll need to hold onto for this problem:

- Supplementary angles (two angles that form a straight angle when added) add to 180°
- The interior angles of a triangle add to 180°
- Sides opposite congruent angles in a triangle are also congruent
- Alternate interior angles are congruent when formed by a transversal through two parallel lines

With that in mind, let's get to the problem. First, what data have we been given?

Let's drop another point on the ground to the left of point T called S, so we can get all of this data together. We know that:

 [tex]AB = 2.4\ mi\\\overrightarrow{ST}||\overrightarrow{AC}\\\angle{ATS}=40\textdegree\\\angle{BTS}=80\textdegree[/tex]

We don't know the measure of ∠ATB, but we do know that it shares the larger angle ∠BTS (which is 80°) with ∠ATS (which is 40°). Since ∠ATB + ∠ATS = ∠BTS, we can clearly see that ∠ATB must also be 40°, so now we have the new data that ∠ATB = 40° to work with.

Next, notice that ∠BTS and ∠CBT are alternate interior angles, and the lines they rest on, [tex]\overrightarrow{ST}[/tex] and [tex]\overrightarrow{AC}[/tex], are parallel. This implies that ∠BTS and ∠CBT are congruent, which makes ∠CBT = 80°. 

∠CBT and its neighboring angle ∠ABT, when combined, form a straight angle, making them supplementary to one another. This means that ∠CBT + ∠ABT = 180°, or 80° + ∠ABT = 180°. Subtracting 80° from both sides, we see that ∠ABT = 100°.

We're almost done; we now bring our attention now to the triangle formed by the points ABT. What do we know about this triangle? We're given that one of its sides, AB, is equal to 2.4 mi; most recently, we determined that one of its angles, ∠ABT, was equal to 100°; and even earlier, we found that the second one of its angles, ∠ATB, was equal to 40°. We have two angles and a side, which, as I'm about to demonstrate, is more than enough for our purposes. If we've found the measures of two angles of triangle ABT, we can use the fact that a triangle's interior angles add to 180° to find the third angle, ∠BAT. We have:

∠ABT + ∠BTA + ∠BAT = 180°

Substituting ∠ABT and ∠BTA for the values we found for them:

100° + 40° + ∠BAT = 180°
140° + ∠BAT = 180°
∠BAT = 40°

We now know that ∠BAT and ∠BTA are congruent, which means that the triangle BTA is isoceles. This means that the sides opposite those angles will also be congruent. The side opposite ∠BTA is the line segment AB, which we know to be 2.4 mi, which means the side opposite ∠BAT, BT - the side we've been looking for - must also be 2.4 mi.

What is 6.5 c =____ fl oz

Answers

 here you go :
6.5 c = 52 fl oz

hope i helped :-)

1 cup = 8 fluid ounces

6.5 cups x 8 = 52 fluid ounces

Solve the equation. What is the value of x? x-6.8=356.3

Answers

the answer is 363.1 i used a calculater to find the answer. so 356.3+ 6.8 = 363.1 so x=363.1

To solve the equation x - 6.8 = 356.3, add 6.8 to both sides to isolate x, resulting in x = 363.1.

To solve the equation x - 6.8 = 356.3, we need to isolate the variable x. To do this, we can add 6.8 to both sides of the equation, effectively moving the 6.8 from the left side to the right.

Step-by-step:

Add 6.8 to both sides: x - 6.8 + 6.8 = 356.3 + 6.8Simplify both sides: x = 363.1

The value of x is 363.1.

If the sun approximately 1.5 * 10/11 meters from Earth how long does it take for light to reach earth

Answers

The sun is 1.5*10^11 METERS from the Earth. In that case it takes approximately 8.3 minutes for sunlight to reach Earth. 
t=(1.5*10^11/3.0*10^8)/60=8.33 minutes 
If you did want a hypothetical that puts the Earth at 1.5*10^11 kilometers from the sun, then it would take 8333.3 minutes for the sunlight to reach the "Earth's" surface. 
t=(1.5*10^14/3.0*10^8)/60=8333.3 minute

Answer:

500

Step-by-step explanation:

Acellus

a road sign casts a shadow 14 meters long while a nearby tree casts a shadow 27.8 meters long. if the road sign in 3.5 meters high how tall is the tree

Answers

The tree is about 6.95 meters tall.

The height of the tree is 6.95 m

What are similar triangles?

Two triangles are said to be similar triangles if their corresponding sides are in equal ratio and corresponding angles are congruent.

Given that, a road sign casts a shadow 14 meters long while a nearby tree casts a shadow 27.8 meters long and the road sign in 3.5 meters

Since, both the figures will be the similar triangles,

Then, by definition of similar triangles,

Therefore,

Let the height of the tree be x,

3.5 / 14 = x / 27.8

x = 6.95

Hence, the height of the tree is 6.95 m

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True or False: The sum of all the angles around a point is 180°.

Answers

this statement is false
Hope this helps






that statement will be false 

What is the value of x in the equation 2x+3y=36 when y = 6

Answers

The value of x is 9.
2x+3(6)=36
2x+18=36
     -18 -18
2x=18

2x/2=x
18/2=9
x=9

Vertex F of ΔDEF has coordinates (−3, 7). If ΔDEF is reflected over the y-axis, what are the coordinates of vertex Fʹ?

Will give brainliest

Answers

The reflection will be on the other side of the y-axis.
Its coordinates will be (3, 7).

For every 240 days of milking, cow's milk production decreases by 2.

Which shows the average change in cow's production?

A. -120 gallons per day
B. - (1/120) gallons per day
C. 1/20 gallons per day.
D. 120 gallons per day.

Answers

It's B. 1/120 gallons per day

The solution is Option B.

The slope / average change in cow's production is m = - 1/120 gallons per day

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of the equation A is

For every 240 days of milking, cow's milk production decreases by 2

So , the value of y = 2 gallons

The value of x = 240 days

Now , the slope of the equation is given as

Slope m = y/x

And , The slope of a line is a measure of its steepness, slope is calculated as "rise over run" or change in y divided by change in x

Substituting the values in the equation , we get

Slope m = 2/240

Slope m = 1/120

Since the cow's milk production decreases by 2 , the slope will be negative

So , slope m = -1/120 gallons / day

Hence , the average change in cow's production is -1/120 gallons / day

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If y= 3x - 5 find the value of y when x = -1

Answers

3 times -1 is -3. -3 - 5 is -8 so -8 is the answer.
y= 3(-1) -5
y= -3 -5
 the answer is y= -8

Alex has 175 baseball cards.Rodney has 3 times as many baseball cards as Alex.How many fewer cards does Alex have than Rodney?

Answers

Alex = 175 baseball cards 

Rodney = 175 * 3

Rodney = 525 

Rodney - Alex = 525 - 175 = 350

Alex has 350 less cards than Rodney 

The difference between Rodney's and Alex's baseball cards is 350.

Alex has 350 fewer baseball cards than Rodney.

What is subtraction?

Subtracting means to take away from a group or a number of things.

When we subtract, the number of things in the group reduces or becomes less.

We have,

The number of baseball cards Alex has:

= 175

The number of baseball cards Rodney has:

= 3 x 175

= 525

We need to find out how much Alex's cards are fewer than Rodney's cards so we find the difference between the number of cards between them.

The difference between Rodney's and Alex's baseball cards:

=  525 - 175

= 350

Thus Alex has 350 fewer baseball cards than Rodney.

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Identify the coefficient of the term -2mnp.

A. 2

B. -2

C. m

D. mnp

I think it is -2 but need a second opinion

Answers

Answer:

b -2

Step-by-step explanation:

The coefficient of the given term -2mnp is -2. Therefore, option B is the correct answer.

The given term is -2mnp.

What is the coefficient of the term?

A coefficient is an integer that is written along with a variable or it is multiplied by the variable. In other words, a coefficient is the numerical factor of a term containing constant and variables.

A coefficient is the numerical factor.

Now, the coefficient of the term -2mnp is -2.

The coefficient of the given term -2mnp is -2. Therefore, option B is the correct answer.

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The sum of five consecutive numbers is -20. Which is the least of these five numbers?

Answers

Since the numbers are consecutive, they can be represented by:
x, x+1, x+2, x+3, x+4

Their sum is -20 = x+x+1+x+2+x+3+x+4.  Result:  -20=5x+10, or 5x=-30, or x = -6.

Then the numbers are -6, -5, -4, -3 and -2.  These do add up to -20, as required.

The smallest of these is -6.
Consecutive numbers means 1,2,3 or 102,103,104 etc.

2,3,4,5,6 add to 20
So -2, -3, -4, -5, -6 add to -20

-6 is the least of the 5 consecutive numbers which sum to-20

which coin has a diameter with a 5 in the hundredths place?


U.S Coins
________________________________
Penny | 0.750 |
________________________________|
Nickle | 0.835 |
________________________________|
Dime | |
________________________________|
Quater | 0.955 |
________________________________|
Half Dollar | 1.205 |
________________________________|

Answers

It would be both the penny and the quarter.

The hundredth place would be the third one from the left.

_._ _ _

So therefore the quarter and penny both have a five in that spot.

74=53-7x I have to solve for x and havent quite grasped the concept of algebra

Answers

If 74 = 53-7 • x you have to figure out the rest of the problem by working backward.
53 - 7 = 46
So you have to divide 74 and 46 to get x.
74/46 = 1.6086
You then multiply 1.6086 and 46 which is 73.995 which rounds to 74.
53-7 = 46; 74/46 = 1.6086; 1.6086 • 46 = 74

Hope this helped, if you need it explained more just ask!! :)

If seven pencils cost $.84 find the cost of 10 pencils

Answers

Salutations!

If seven pencils cost $.84 find the cost of 10 pencils?

Lets solve this!

To solve this question, you need to first divide .84 ÷ 7 which gives you the answer 0.12. Then multiply 0.12 with 10 which gives you the cost of 10 pencils. 0.12 is the cost of only one pencil.

Lets forms this into statements ---

Cost of 7 pencils = $ .84

Cost of 1 pencil = $ 0.12

Cost of 10 pencil equals = .84 ÷ 7 = 0.12

                                      = 0.12 × 10 = 1.2

Cost of 10 pencils is $1.2

Hope I helped (:

Have a great day!

Final answer:

To calculate the cost of 10 pencils when seven pencils cost $0.84, you find the price per pencil by dividing $0.84 by 7, which equals $0.12 per pencil. Then, multiply $0.12 by 10 to get the total cost of 10 pencils, which is $1.20.

Explanation:

To answer the question, we first need to find the cost of one pencil. Since seven pencils cost $0.84, we can divide that amount by seven to get the cost of one pencil.

Here is the calculation:

Cost of seven pencils = $0.84

Cost of one pencil = $0.84 ÷ 7

Cost of one pencil = $0.12

Now that we know the cost of one pencil, we can find the cost of 10 pencils by multiplying this amount by 10.

Here is the calculation:

Cost of 10 pencils = $0.12 × 10

Cost of 10 pencils = $1.20Therefore, the cost of 10 pencils is $1.20.

The winner in a vote for class president received 3/4 of the 240 votes. How many votes did the winner receive?

Answers

The answer to3/4 of 240 is 180
Now, to solve this, you would need to cross multiply. The equation would look like this...
[tex] \frac{3}{4} [/tex] = [tex] \frac{x}{240} [/tex]

After cross multiplying, you would be left with the following. 
4x = 720

All you would have to do now is solve for x. 
[tex] \frac{4x}{4} [/tex] = [tex] \frac{720}{4} [/tex] = 180

The answer would be, the winner for class president received 180 votes. 

I hope this helps!

Please help, need asap

Answers

For the first option, since when x is going down (to the left) the function is going up, it's not approaching 0. For the second option, since when x is going up (to the right) it's going up, it's not approaching negative infinity (negative infinity is all the way down). For the third one, since when x is going down the y values are climbing, we can assume that the function's values go to positive infinity. For the last one, since when x=0 y=0, when x=0 the function does not go to infinity

got it wrong plss help and explain

Answers

Because it says "not black" we would do white marbles
There are 15 white marbles and a total of 20
So the fraction of white marbles to total would be 15/20

Because the answer is wanted as a decimal divide 15 by 20
15/20=.75

There is a .75 chance that she will not draw a black marble

What’s 28.2 rounded to the nearest tenth

Answers

It's already rounded to the nearest tenth
28.2 to the nearest tenth is 28.2

If Amanda walks at an average speed of 2.72 miles per hour, how long will it take her to walk 6.8 miles?

Answers

it is 2.5
hope this helped

Ms. Zab gave a group of five students a total of 18.75 liters of water for a science experiment. If each student in the group used the same amount of water for their experiment, how much water did each student use?

Answers

D. 3,750 mL
Because you have to convert liters to milliliters

There are 35 more musicians in the String section of a city Symphony Orchestra than in its Brass section. There are 29 musicians in the Brass section. 1. How many musicians in all are in the String and Brass sections of the Symphony Orchestra?

Answers

35 - 29 = 6. 6+29+35 = 70
70 in the string and brass sections of the Symphony Orchestra.

Equation of the tangent line

Answers

Find the eqn. of the tangent line to the curve of f(x) = x^2 + 5x -5 at (0,-5).

Differentiate f(x) to obtain an expression for the derivative (slope of the tangent line):

             f '(x) = 2x + 5

Subst. 0 for x here:  f '(0) = 2(0) + 5 = 5     (at the point (0, -5))

Use the point-slope equation of a str. line to find the eqn of the tan. line:

y-k = m(x-h), where (h,k) is a point on the line and m is the slope:

y - [-5] = 5(x-0), or y+5 = 5x.  Then y = 5x - 5 is the eqn. of the TL to the given curve at (0,-5).

You are going on a road trip over a distance of 3000 kilometers with three friends. The car consumes 6 liters of gas per 100 kilometers and gas costs $1.20,per liter.

Answers

180 liters and  $216.00 for gas.

What is the resluf of convertig 14 inches into centimeters? Remember that 1 inch =2.54 centimeters.

Answers

multiply 14 x 2.54

14 x 2.54 = 35.56 centimeters

Simplify .4 ^ square root of 6
-----------------------------
5 ^ square root of 6

Answers

Simplified the answer is in decimal form 0.00000026.
4^√6 / 5^√6

0.5789

hope that helps, God bless!
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