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Bogdan [553]
3 years ago
8

Using the quadratic formula to solve x2 + 20 = 2x, what are the values of x?

Mathematics
1 answer:
zheka24 [161]3 years ago
6 0

\bf{Hey\ there!}

\bf{Quadratic\ formula\ is:}\bf{x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}} \ or \ you\ could\ say\ ax^2+bx+c=0

\bf{\bullet\ First: subtract\ by\ 2x\ on\ your\ sides\ that\ you're\ working\ with}

\bf{Like:x^2+20-2x=2x-2x}

\bf{We\ get:x^2-2x+20=0}

\bf{\bullet \ a=1}\\ \bf{\bullet \ b=-2}\\ \bf{\bullet \ c=20}

\bf{x=\frac{-(-2)\pm\sqrt{(-2)^2-4(1)(20})}{2(1)}

\bf{(-2)^2-4(1)(20)=-76} \\ \\ \bf{2(1)=2}

\bold{-(-2)=-1(-2))=+2}

\bf{x=\frac{2\pm\sqrt{-76}}{2}}

\bf{Thus\ there\ is\ NO\ REAL\ SOLUTIONS}

\text{Good\ luck\ on\ your\ assignment\ and\ enjoy\ your\ day!}

\frak{LoveYourselfFirst:)}

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The table includes points on a quadratic function used to model the shape of a hole for one support beam at a new building site.
erastovalidia [21]

The hole is 8 feet deep at ground level ⇒ 3rd answer

Step-by-step explanation:

The form of the quadratic function is y = ax² + bx + c, where

  • a is the coefficient of x²
  • b is the coefficient of x
  • c is the y-intercept (at x = 0)

The vertex point of the quadratic is (h , k), where h=\frac{-b}{2a}

and k is the value of y when x = h

The table:

→  x  :  -2   ,  0  ,  2

→  y  :  -6   , -8  ,  -6

∵ x represents distance from hole's center in feet

∵ y represents the depth from level ground

∴ The quadratic function is y = ax² + bx + c

∵ c is the value of y at x = 0 ⇒ y-intercept

- From the table at x = 0 ⇒ y = -8

∴ c = -8

- Substitute its value in the function model

∴ y = ax² + bx - 8

- To find the values of a and b substitute x and y in the model by

   the coordinates of the point in the table

∵ x = -2 and y = -6

∴ -6 = a(-2)² + b(-2) - 8

∴ -6 = 4a - 2b - 8

- Add 8 to both sides

∴ 2 = 4a - 2b

- Switch the two sides

∴ 4a - 2b = 2 ⇒ (1)

∵ x = 2 and y = -6

∴ -6 = a(2)² + b(2) - 8

∴ -6 = 4a + 2b - 8

- Add 8 to both sides

∴ 2 = 4a + 2b

- Switch the two sides

∴ 4a + 2b = 2 ⇒ (2)

Now we have a system of equation to solve it

Add equations(1) and (2) to eliminate b

∵ 8a = 4

- Divide both sides by 8

∴ a = 0.5

- Substitute value of a in equation (1) or to to find b

∵ 4(0.5) + 2b = 2

∴ 2 + 2b = 2

- Subtract 2 from both sides

∴ 2b = 0

- Divide both sides by 2

∴ b = 0

Substitute the values of a and b in the function model

∴ y = 0.5x² + (0)x - 8

∴ y = 0.5x² - 8

∵ y represents the depth from level ground

∵ The vertex of the function model is (h , k)

∴ The deep of the hole at ground level is the value of k

∵ h=\frac{-b}{2a}

∴ h=\frac{-(0)}{2(0.5)}

∴ h = 0

∵ k is the value of y when x = h

- From the table at x = 0 ⇒ y = -8

∴ k = -8

- Ignore the sign (-) because the k represents the depth of the

  hole in feet

∴ The deep of the hole at ground level is 8 feet

The hole is 8 feet deep at ground level

Learn more:

You can learn more about the quadratic function in brainly.com/question/1332667

#LearnwithBrainly

4 0
3 years ago
I don't understand how to do this problem.
Delicious77 [7]
Answers: 

x = 4
EF = 14
CF = 7
EC = 7

-------------------------------------------------------------
-------------------------------------------------------------

Work Shown:

C is the midpoint of segment EF. This means that EC = CF. In other words, the two pieces are congruent. 

Use substitution and solve for x
EC = CF
5x-13 = 3x-5
5x-13+13 = 3x-5+13
5x = 3x+8
5x-3x = 3x+8-3x
2x = 8
2x/2 = 8/2
x = 4

Now that we know that x = 4, we can use this to find EC and CF

Let's compute EC
EC = 5x - 13
EC = 5*x - 13
EC = 5*4 - 13 ... replace x with 4
EC = 20 - 13
EC = 7

Let's compute CF
CF = 3x - 5
CF = 3*x - 5
CF = 3*4 - 5 ... replace x with 4
CF = 12 - 5
CF = 7

As expected, EC = CF (both are 7 units long).

By the segment addition postulate, we can say EC+CF = EF

EC+CF = EF
EF = EC+CF
EF = 7+7
EF = 14
8 0
3 years ago
Point A of rectangle ABCD is located at coordinates (3,7). If rectangle ABCD is translated down 7 and left 5, what are the new c
uranmaximum [27]

Answer:

The new co-ordinates are A¹ ( -2 , 0)

Step-by-step explanation:

<u><em>Step(i):</em></u>-

Point A of rectangle ABCD is located at coordinates (3,7).

<u><em>Type of transformation </em></u><em>                               </em><u><em> change of co-ordinate point</em></u>

<em>Vertical translation up 'd' units                   (x, y)→ (x, y +d)</em>

<em>Vertical translation down 'd' units              (x, y)→ (x, y -d)</em>

<em>Horizontal translation left 'C' units              (x, y)→ (x - c , y) </em>

<em>Horizontal translation right 'C' units             (x, y)→ (x + c , y) </em>

<u><em>Step(ii</em></u><em>):-</em>

<em>Given rectangle ABCD is translated down 7 and left 5</em>

<em>Given Point A(3 ,7) </em>

Vertical translation down '7' units  t

The new co-ordinate A¹ ( 3 , 7-7)→ A¹( 3, 0) and Horizontal translation left ''5' units

Now the new co-ordinates are A¹ ( 3-5 , 7-7)

<u><em>Final answer:-</em></u>

The new co-ordinates are A¹ ( -2 , 0)

7 0
3 years ago
Ben made a model that was 5 3/4 inches tall. Laquisha made a model that was 70 11/12 inches long. How many times as tall was Laq
RSB [31]
Laquishas model is 12 1/3 times taller than bens.
3 0
3 years ago
Can you pls answer and explain?
vesna_86 [32]
18 ft bexause the shadow would be 4 feet taller than the actual person
6 0
3 years ago
Read 2 more answers
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