"Systems of Linear Magic"
DIRECTIONS
You are given the following system of equations. Answer the questions
below using this system.
1st Equation: 4x + y = 7
2nd Equation: 2x + y = 11
1.) Solve the system of equations by using the elimination method.
2.) Following the steps described in the "How to Create a Magic Potion"
section on page 1, let's brew a magic potion! Answer the following
questions about your "magic potion"equation.
A.) What is the factor that you have multiplied the 2nd equation by?
C.) What is the magic potion equation you have created?
3.) Using your newly created "magic potion" equation along with the original
2nd equation, solve this new system of equations by using the elimination
method.
4.) Why do you think this "magic potion" method works mathematically to
give us the exact same solution? Use at least 2 complete sentences.

Answer:

x = 3.16

Step-by-step explanation:

x * x = 10

[tex]x^2 = 10[/tex]

square root both sides

[tex]\sqrt{x^2} = \sqrt{10}[/tex]

[tex]x = \sqrt{10}[/tex]

x is appr. 3.16

Answer:

x=  √-10, √ 10

Step-by-step explanation:

The scale factor of the enlargement will be 3. Then the center of enlargement is marked in the diagram.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

Shape A is enlarged to give shape B.

Then the scale factor of the enlargement will be

⇒ 3 / 1

Then the center of enlargement is marked in the diagram.

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Answer:

-8 or -1

Step-by-step explanation:

x*2+9x+8=0

(x+8)(x+1)=0

x+8=0 or x+1=0

x= -8 or x= -1

Answer:

3497.47 feet

I think it's the answer because when you look where I've drawn...that's where the angle of depression is and 6600 is the hypotenuse, so you use the sine method where you have opposite over hypotenuse

[tex] \sin(32 = opposite \6600) [/tex]

and you'll get your answer as 3497.47

2.5 miles/hour

Simply 15/6

Answer:

Colin walks an average speed of 2.5 miles per hour.

Step-by-step explanation:

15/6= 5 miles/2 hours

2.5

Answer:

I think

each division is subtracted like

8 - 4 = 4

so that why it's written as

1/4 ...........

1/8 1/8 ..........

Step-by-step explanation:

if understand I need brainlist

if not then also

thanks

Answer:

6x - 5 = (-9x) - 9

6x + 9x = (-9) + 5

15x = (-4)

x = (-4/15)

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:x = -\cfrac{4}{15} [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: 6x - 5 = - 9x - 9[/tex]

[ add 9x and 5 on both sides ]

[tex]\qquad \tt \rightarrow \: 6x - 5 + 9x + 5 = - 9x - 9 + 9x + 5[/tex]

[tex]\qquad \tt \rightarrow \: 6x + 9x = - 9 + 5[/tex]

[tex]\qquad \tt \rightarrow \: 15x = - 4[/tex]

[tex]\qquad \tt \rightarrow \: x = - \cfrac{4}{15} [/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The selling price of the article including VAT will be 1000.

The cost at which an article is sold is known as the selling price.

Let the market price will be x

Given data;

Discount=20 %

The amount of the discount is;

[tex]\rm Discount = x- x \times \frac{20}{100} =\frac{80x}{100}[/tex]

Applied tax is;

[tex]\rm \frac{80x}{100} +\frac{80x}{100} \times \frac{15}{100} =904 \\\\ \frac{8000x+1040 x}{10000} =904 \\\\ 9040 x = 904 \times 10000 \\\\\ x=\frac{904 \times 10000}{9040} \\\\ x=1000[/tex]

Hence, the selling price of the article including VAT will be 1000.

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Answer:

x-2y/x

Step-by-step explanation:

x²-4xy+4y²/x²+xy-6y²÷x²+3xy/x²+6xy+9y² = x-2y/x

The graph that represents the system of inequalities will be y ≤ −2x + 3; y ≤ x + 3

The equation of the line will be:

y = mx + b

In this case, we can observe that both lines have the same y intercept and that the lines are solid.

Hence, graph that represents the system of inequalities will be y ≤ −2x + 3; y ≤ x + 3. The graph is attached.

When the coordinate grid shows points A through, the point that is a solution to the system of inequalities is negative 6 point G at negative 3, negative 10 point H at negative 4.

Finally, the graph that represents the following system of inequalities: y ≤ −3x + 1 y ≤ 1 over 2x + 3 is the graph of two intersecting lines where both lines are solid.

One line of x passes through points negative 2, 2 and 0, 3 and is shaded above the line. The other line g of x passes through points 0, 1 and 1, negative 2 and is shaded above the line.

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Answer:

-7,-6,-5 are the values when x=0,1,2

Step-by-step explanation:

please mark me as brainlest

Answer:

Step-by-step explanation:

y =x - 7

Substitute x = 0 and find the y-value

       y = 0 - 7

      y = -7

(0,-7)

Substitute x = 1,

    y = 1 - 7

    y = - 6

(1,-6)

Substitute x = 2,

        y = 2 - 7

       y = -5

(2,-5)

Answer:

The equation of the blue graph is g(x)=(x-3)^{2} +1g(x)=(x−3)

2

+1 . Below is the explanation

Step-by-step explanation:

Given:

The graph of f(x)=x^{2}x

2

To find:

The equation of the transformed graph g(x).

The red graph f(x) is moved right 3 units and up 1 unit to get g(x).

When graph is moved right 3 units , 3 should be subtracted with x.

When graph is moved up 1 unit, 1 is added at the end.

So, our g(x)=(x-3)^{2} +1(x−3)

2

+1

The equation of the blue graph is g(x)=(x-3)^{2} +1g(x)=(x−3)

2

+1

The inverse function of g(x) will be g⁻¹(x) = (4x + 3) / 2. Then the value of the inverse function, at x = -3, will be 4.5.

Let the function will be

f: X → Y

Then the inverse function will be

f⁻¹: Y → X

The function is given below.

g(x) = (2x – 3) / 4

Then the inverse function of g(x) will be

g⁻¹(x) = (4x + 3) / 2

Then the value of the inverse function, at x = -3, will be

g⁻¹(-3) = [4(-3) + 3] / 2

g⁻¹(-3) = -4.5

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Answer:

x = [tex]\frac{1}{2}[/tex] , x = - [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

(2x - 1)(3x + 4) = 0

equate each factor to zero and solve for x

2x - 1 = 0 ( add 1 to both sides )

2x = 1 ( divide both sides by 2 )

x = [tex]\frac{1}{2}[/tex]

and

3x + 4 = 0 ( subtract 4 from both sides )

3x = - 4 ( divide both sides by 3 )

x = - [tex]\frac{4}{3}[/tex]

So

And

Answer: x+y=23, 3x+2y = 55 x + y = 55, 3x + 2y = 55 x+y=23, 2x+3y= 55 x+y=55, 2x+3y =23

Step-by-step explanation: The question said the sum is x+y so if the sum is 55, x+y=55

Answer:

X=20; the labeled angles are 80 and 100

Step-by-step explanation:

These angles are "consecutive interior angles" so they will add up to be 180.

180 = 5x + 4x

180 = 9x

180/9 = 9/x

20=x

Answer:

[tex]\huge\boxed{E.\ 5^{4+x}}[/tex]

Step-by-step explanation:

Use:

[tex]a^n\cdot a^m=a^{n+m}[/tex]

[tex]5^4\cdot5^x=5^{4+x}[/tex]

Answer:

Good idea for thanks......

Answer:

387

Step-by-step explanation:

6(4)³ + 3(1)²

6(64) + 3(1)

384 + 3

= 387

Answer:

87 = <1

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

124 = 37 + <1

Subtract 37 from each side

124 -37 = <1

87 = <1

Answer:

C. Ф = 4 radians

Step-by-step explanation:

Given,

Radius of the Circle (r) = 3cm

Length of the Arc (S) = 12cm

In any circle of radius r, the arc length S to the circumference equals the ratio of the angle θ subtended by the arc at the centre and the angle in one revolution. Thus, measuring the angles in radians, S=rθ.

Therefore, S = r*Ф

12 = 3*Ф

Hence, Ф = 4 radians

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Answer:

x=9

if

a^b = a^c

then b=c

so in this case x=9

Answer:

128

Step-by-step explanation:

0.6 (the percentage) x 80.00= 48.00

48.00 + 80.00 = 128.00

Answer:

128

Step-by-step explanation:

60% + 100% (new price) = 160% = 1.6

80 x 1.6 = 128

The Standard form of the equation of circle is (x+21)² + (y+19)² = 849

To transform general form to a standard form, you can use completing the square method or you can convert this equation

x² + y² + Dx + Ey + F = 0 to x² + y² + (-2h)x + (-2k)y + (h²+k²-r²) = 0

Here, Given: x² + y² + 42x + 38y − 47 = 0

Required: Find the values of h, k, and r using this formula

x² + y² + (-2h)x + (-2k)y + (h²+k²-r²) = 0

On comparing we get,

-2h = 42

  h = 21

-2k = 38

 k = 19

-47 = h² + k² - r²

-47 = 21² + 19² - r²

   r² = 849

  r = √849

Thus, the Standard form of the equation of circle is (x+21)² + (y+19)² = 849

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A quadrilateral in which opposite sides are parallel is called a parallelogram. The measure of the ∠GFH is 16°.

A quadrilateral in which opposite sides are parallel is called a parallelogram. Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

For a parallelogram and a rhombus opposite sides are parallel, therefore, the sides that are parallel are,

AB║DC║ED║FG

Since the sides are parallel,

∠ABC = ∠FGH = 126°

Also, ∠AHC and ∠GHF lie on the same line, therefore,

∠AHC + ∠GHF = 180°

∠GHF = 180° - 142° = 38°

Now, in ΔGHF

∠GHF + ∠HFG + ∠GFH = 180°

∠GFH = 180° - 126° - 38°

∠GFH = 16°

Hence, the measure of the ∠GFH is 16°.

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Using translation concepts, it is found that the graph of function g if g(x) = f(x) − 11 is a shift down of 11 units of function f(x).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, we have that g(x) = f(x) − 11 represents a shift down of 11 units of function f(x).

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