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monitta
3 years ago
9

Solve the system by the substitution method. 2x-y= -24 x+7y= 3

Mathematics
1 answer:
meriva3 years ago
6 0
2x - y = -24
x + 7y = 3

Solve one equation for a variable and plug the resulting value into the second equation.

x + 7y = 3           Subtract 7y from both sides
       x = -7y + 3

Now, plug that x-value into the x of the first equation.

            2x - y = -24   Plug in the x-value
2(-7y + 3) - y = 24     Use the Distributive Property
  -14y + 6 - y = -24     Combine like terms (-14y and -y)
       -15y + 6 = -24     Subtract 6 from both sides
             -15y = -30     Divide both sides by 15
                  y = 2

Next, plug the y-value back into the second equation.

  x + 7y = 3      Plug in the y-value
x + 7(2) = 3     Multiply
   x + 14 = 3     Subtract 14 from both sides
          x = -11

y = 2 and x = -11
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A baseball diamond is a square with side 90 feet. A batter hits the ball and runs toward first base with a speed of 24 ft/sec. A
sweet [91]

9514 1404 393

Answer:

  10.73 ft/s

Step-by-step explanation:

When the runner is halfway to first base, the triangle formed by his position and the first and second bases is a right triangle with legs of 45 ft and 90 ft. The angle between the runner's direction and the line from his position to 2nd base is ...

  angle = arctan(90/45) ≈ 63.43°

The "speed made good" in the direction of 2nd base is the product of the cosine of this angle and the runner's speed toward first.

  speed toward 2nd = cos(63.43°)×(24 ft/s) ≈ 10.73 ft/s

The rate the runner's distance to 2nd base is decreasing is 10.73 ft/sec.

6 0
3 years ago
What is the measure of arc QR?
riadik2000 [5.3K]

Answer:

answer is the third choice : 104

Step-by-step explanation:

Inscribed Angle Theorem

If an angle is inscribed in a circle, then the measure of the angle equals one half the measure of its intercepted arc.

so the intercepted arc is TWICE the measure of an angle inscribed in a circle

1. A central angle is an angle with endpoints located on a circle's circumference and vertex located at the circle's center. A central angle in a circle determines an arc.

2. An inscribed angle is an angle formed by three points on the circle's circumference.

Angle at the Center Theorem: An inscribed angle is half of the central angle (if they determine the same arc).

In your case angles:

1. ∠QSR is insribed (determines the arc QR);

2. ∠QTR is central (determines the arc QR).

Then by Angle at the Center Theorem, m∠QTR=2m∠QSR=2·52°=104°. Arc QR has the same measure as central angle QSR.

gathmath

brainly.com/question/12799434

brainly.com/question/3432326

http://cms5.revize.com/revize/williamsvilleschools/southhigh/mr_quill/geometry_r/docs/Unit%2013/Unit%2013%20Class%20Notes%20KEY.pdf

3 0
2 years ago
This is one question. Algebra 2 transformations
Talja [164]

Answer:

End result is ln(-x) + 1

Step-by-step explanation:

1,  ln x + 2

2. ln(x + 2) + 2

3. ln(x + 2 - 2) + 2 = ln x + 2

4. ln x + 1

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8 0
3 years ago
Read 2 more answers
PLS HELP ME
eimsori [14]

Answer:

5.5

Step-by-step explanation:

2,3,3,4,5,7,8,8,8,10,10,12

The mean of this data is 7.5.  So what you are trying to figure out is the mean between 2 and 7.  Since that is 3 and 4 it would be 3.5.  So 3.5 is the Q1.  Now you have to figure out the mean between 8 and 12.  That is 9.  This is Q3.  You have to subtract 9-3.5 and that is the interquartile range. So 5.5 is the answer.  I hope that made sense.

6 0
2 years ago
Solve.
Serggg [28]

Answer:

The solution is (4, 0)

Step-by-step explanation:

Using Linear combination method to solve:

2d + e = 8\\d - e = 4\\

Since "e" have the same coefficient in both equation with opposite operator; we will add.

(2d + d) + (e - e) = (8 + 4)\\3d = 12\\

Divide both side by coefficient of d which is 3

\frac{3d}{3}  = \frac{12}{3} \\d = 4\\

Since d = 4; put 'd' into any of the equation to get 'e'

2d + e = 8\\2(4) + e = 8\\8 + e = 8\\e = 8 - 8\\e = 0\\

Therefore, the solution is (4, 0)

5 0
4 years ago
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