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Vinil7 [7]
3 years ago
13

Carolyn was asked to solve the following system of equations. Her work is shown. What is the solution to the system of linear eq

uations?

Mathematics
1 answer:
Natalka [10]3 years ago
8 0

Answer:

(11, 13)

Step-by-step explanation:

Carolyn's work is incorrect. Below is the correct solution:

Given:

3x - 2y = 7 ----› Equation 1

y = x + 2 -----› Equation 2

Substitute y = (x + 2) in equation 1

3x - 2y = 7 ----› Equation 1

3x - 2(x + 2) = 7 (substitution)

3x - 2(x) -2(+2) = 7 (distributive property)

[Note: this is where Carolyn made a mistake]

3x - 2x - 4 = 7

Collect like terms

x - 4 = 7

x = 7 + 4 (addition property of equality).

x = 11

Substitute x = 11 in equation 2

y = x + 2 -----› Equation 2

y = 11 + 2 (substitution)

y = 13

✅The solution to the system of equations would be:

(11, 13)

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(1 point) If p(x) and (x) are arbitrary polynomials of degree at most 2, then the mapping =p(-1)q(-1) + p(070) +p(3)q(3) defines
Ainat [17]

If p(x) and q(x) are arbitrary polynomials of degree at most 2 then

||p||||q|| = 26(\sqrt{640}) and angle between p(x) and q(x) is 0.233.

Given that

<p,q> = p(-1)q(-1) + p(0) q(0) + p(3)q(3)

and p(x) = 2x²+ 6 , q(x)= 4x²-4x

then the values of p and q at x = -1,0,3 are given as;

x = -1,

p(-1) = 2(-1)² + 6 = 8   ,    q(-1) = 4(-1)² - 4(-1) = 8

x = 0,

p(0) = 2(0)² + 6 = 6   ,    q(0) = 4(0)² - 4(0) = 0

x = 3,

p(3) = 2(3)² + 6 = 24  ,  q(3) = 4(3)²- 4(3) = 24.

<p,q> = p(-1)q(-1) + p(0)q(0) + p(3)q(3)

         = (8)(8) + (6)(0) + 24(24)

         = 64 + 0 + 576

<p,q> = 640

Now we have to find ||p|| ||q||, for this we'll find ||p|| and ||q||

||p|| = \sqrt{ < p,p > }

     = \sqrt{8(8) + 6(6) + 24(24)}

     = \sqrt{676}

||p|| = 26

and

||q|| = \sqrt{ < q,q > }

      =\sqrt{8(8) + 0(0) + 24(24)}

||q||  =\sqrt{640}

∴||p||||q|| = 26(\sqrt{640\\)

Now we have to find angle between p(x) and q(x),

∴ α = cos⁻¹\frac{ < p,q > }{||p||||q||}

      = cos ⁻¹ \frac{640}{26(\sqrt{640}) }

      = cos ⁻¹ \frac{4\sqrt{10} }{13}

  α  = 13.34°

In radian

α = 0.233.

To know more about Inner product here

brainly.com/question/14185022

#SPJ4

5 0
1 year ago
HELP PLEASE 80 POINTS
alexgriva [62]

Answer:

  • x = 15/p
  • x = -3

Step-by-step explanation:

<h3>Given</h3>
  • 4(px + 1)=64
<h3>Find</h3>
  • Solve for x
  • Find x when p = -5
<h3>Solution</h3>
  • 4(px + 1) = 64
  • 4(px + 1)/4 = 64/4
  • px + 1 = 16
  • px = 15
  • x = 15/p

<u>When p = -5, substitute p:</u>

  • x = 15/p
  • x = 15/(-5) = -3
4 0
3 years ago
Read 2 more answers
I need help here’s a picture can somone explain what I need to do??
galina1969 [7]

Answer:

176 square feet

Step-by-step explanation:

add the areas of the rectangle and triangle

rectangle area is

16 times 8 which is

128

rectangle area is

1/2 times 12 times 8 which is

48

then add them

128 plus 48 is

176 square feet

5 0
2 years ago
What is the volume of a sphere with the diameter of 16 inches using 3.14 for pi
VMariaS [17]

Answer:

V≈2144.66in³

Step-by-step explanation:

5 0
3 years ago
Please please help im confused again
timama [110]

Answer:

A_s=179  \ yd

Step-by-step explanation:

Area of Circle can be calculated using following formula

A=\pi r^{2}

Where r is radius of circle

<u>Area of outer circle (r=11 yd)</u>

A_1=\pi (11)^{2}\\A_1=379.94 \ yd

<u>Area of inner circle (r=8 yd)</u>

A_2=\pi (8)^{2}\\A_2=200.96 \ yd

Area of shaded region

A_s=A_1-A_2

A_s=379.94-200.96\\A_s=179  \ yd

3 0
2 years ago
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