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Solve the system of linear equations BY ELIMINATION. Show a step-by-step process.
3x - 2y = -2
5x - 3y = -4

Answer:

x =5

Step-by-step explanation:

c = 5√2

a = x

b = x

Formula

x^2 + x^2 = c^2                    Combine the x^2

Solution

2x^2 = (5√2)^2                    Expand the right side

2x^2 = 2*25                         Divide both sides by 2

x^2 = 25                               Take the square root of both sides.

x = 5

The G(x) is the new function of the f(x) which is translated 4 units down is 4x²+2.

A function assigns the value of each element of one set to the other specific element of another set.

The given function can be transformed from the initial position of the new position by subtracting the 4 from the initial function.

We know that in the initial function y=4x²+6, y is the output, while x is the input for the function f(x).

As the G(x) is the new function of the f(x) which is translated 4 units down. therefore,

[tex]G(x) = f(x)-4\\\\G(x) = 4x^2+6-4\\\\G(x) =4x^2+2[/tex]

hence, the G(x) is the new function of the f(x) which is translated 4 units down is 4x²+2.

Learn more about Function:

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Answer:

3

Step-by-step explanation: 10*3 is equal to 30.

Answer:3

Step-by-step explanation:3 is 10 times as much as 30 which is 3x10=30

Answer:

y = 90

Step-by-step explanation:

Y is a right angle, and if we check, 90 + 90 = 180. The total angle sum of a straight line is 180 degrees.

Answer:

Step-by-step explanation:

Hey there!

• When you hear the word “mean” in mathematics it usually defined as “average”.

• To find it you have to ADD all of the numbers DIVIDE all of the numbers you have in the given data plot.

YOUR EQUATION:

10 + 8 + 5 + 12 + 20 / 5

= 18 + 5 + 12 + 20 / 5

= 23 + 12 + 20 / 5

= 35 + 20 / 5

= 55 / 5

= 11

Therefore, your answer is: 11

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

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Answer:

x=1/2,x=9

Step-by-step explanation:

[tex]2x^{2} -19+9=0\\\\2x^{2} -18x-x+9=0\\\\2x(x-9)-1(x-9)=0\\\\(2x-1)(x-9)=0[/tex]

2x-1=0......I

x-9=0.......II

Solving I

2x-1=0

2x=1

x=1/2

Solving II

x-9=0

x=9

Answer:

x=67 degrees

Step-by-step explanation:

2x + 46 = 180

2x = 134

x = 67

[tex]\\ \tt\longrightarrow 3=\dfrac{3}{10}=0.3[/tex]

[tex]\\ \tt\longrightarrow 8=\dfrac{8}{10}=0.8[/tex]

[tex]\\ \tt\longrightarrow 15=\dfrac{15}{100}=0.15[/tex]

[tex]\\ \tt\longrightarrow \dfrac{18}{10}=1.8[/tex]

[tex]\\ \tt\longrightarrow 33=\dfrac{33}{100}=0.33[/tex]

[tex]\\ \tt\longrightarrow 49=\dfrac{49}{100}=0.49[/tex]

[tex]\\ \tt\longrightarrow 64=\dfrac{64}{100}=0.64[/tex]

[tex]\\ \tt\longrightarrow 108=\dfrac{108}{100}=1.08=1.1[/tex]

[tex]\\ \tt\longrightarrow 251=\dfrac{251}{1000}=0.251[/tex]

Answer:

mean = 24

Step-by-step explanation:

From inspection, there are 7 values.

The values are 12, 13, 15, 28, 28, 30, 42

To find the mean, sum the numbers: 12 + 13 + 15 + 28 + 28 + 30 + 42 = 168

Divide by the number of values:  168 ÷ 7 = 24

Therefore, mean = 24

Answer:

40

Step-by-step explanation:

Sum of all angles of triangle = 180°

∠W + ∠X + ∠Y = 180

10x + 17 + 2x - 9 + 3x + 7 = 180

10x + 2x  +3x + 17 - 9 + 7 = 180

Combine like terms

15x + 15 = 180

       15x = 180- 15

         15x = 165

            x = 165/15

x = 11

∠Y =  3x +7  = 3*11 + 7 = 33 + 7 = 40

Answer:

X is 11 and after substitution y is 40

Answer:

[tex]A=x^2+23x+49[/tex]

Step-by-step explanation:

Hi there!

The area of the shaded region is equal to the area of the big rectangle minus the area of the square.

Area of the big rectangle:

[tex]A=lw\\A=(x+10)(2x+5)[/tex]

Area of the square:

[tex]A=a^2\\A=(x+1)^2[/tex]

Area of the shaded region:

[tex]A=(x+10)(2x+5)-(x+1)^2[/tex]

Expand:

[tex]A=(x+10)(2x+5)-(x+1)^2\\A=2x^2+5x+20x+50-(x+1)^2\\A=2x^2+5x+20x+50-(x^2+2x+1)\\A=2x^2+5x+20x+50-x^2-2x-1[/tex]

Combine like terms:

[tex]A=2x^2-x^2+5x+20x-2x+50-1\\A=x^2+23x+49[/tex]

I hope this helps!

Answer:

A. (-1, -1/2) is the correct answer.

Answer:

163°

Step-by-step explanation:

Since those 2 arrows are straight lines that go through each other, angles that are opposite are the same. So the opposite of y is 163°.

Answer:

670/1000 un simplified, 67/100 simplified

Answer:

Factors of 120:

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120

Prime Factors:

2, 3,and 5

Step-by-step explanation:

Factors are: numbers that can be multiplied together to get a certain number

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Answer: 3

Step-by-step explanation: 6 is 3 and 3 so b is 3 and x is 3

Answer:

No

Step-by-step explanation:

2(0)+7

=0+7

=7

therefore,(0,7) is not a solution to the equation 2x+y=6

0=×

7=y

Answer: no it isn’t

Step-by-step explanation: this is super simple so do solve this you have know your x and y values on coordinate points in this case (0,7) our x here is 0 and our y is 7 (the x will always be the first number and the y will be the last)

Here we are given a equation all we have to do is plug 0 for x and 7 for y.
2(0)+7=6

2 x 0= 0

So: 0+7=7

7 does NOT equal to 6 therefor (0,7) is NOT a solution

Answer:

48

Step-by-step explanation:

42 + 6 = 48 total words

Answer:

74

Step-by-step explanation:

42+6+(50-42)+(60-42)

Answer:

[tex]y = \frac{4}{3}x + 2[/tex]

Step-by-step explanation:

Find the equation for the line in slope-intercept form: [tex]y = mx + b[/tex]

where m is the slope (gradient) and b is the y-intercept.

To find the slope (m)

Choose 2 points on the line:  (0, 2) and (6, 10)

Let (0, 2) = [tex](x_1,y_1)[/tex]

Let (6, 10) = [tex](x_2,y_2)[/tex]

Use the slope formula:  [tex]m=\frac{y_2-y_1}{x_2-x_1} =\frac{10-2}{6-0} =\frac{4}{3}[/tex]

Therefore, [tex]y = \frac{4}{3}x + b[/tex]

To find the y-intercept

The y-intercept is when x = 0 (where the line intersects the x-axis).

By inspection, the line intersects the y-axis at y = 2.  

Therefore, y-intercept = 2

So, [tex]y = \frac{4}{3}x + 2[/tex]

Answer:

c = 14.9

Step-by-step explanation:

use the pythagorean thereom:

a² + b² = c²

a² = 11 × 11 = 121

b² = 10 × 10 = 100

c² = 121 + 100 = 221

now find the square root of 221:

√221 = 14.866...

round to the nearest tenth:

the 6 next to the 8 means round up.

so the hypotenuse is 14.9

Answer:

Step-by-step explanation:

Number series : 9, 14, 19, 24

First term = a1 = 9

common difference = a2 - a1 = 14 - 9=5

Find the nth term:

an = a1 + + (n - 1)d

an = 9+ (n - 1)(5)

an = 9+5n - 5

an = 4 + 5n

Find the 10th term:

an = 4 + 5n

a10 = 4 + 5(10)

a10 = 4 + 50

a10 = 54

Find the 50th term:

an = 4 + 5n

a50 = 4 + 5(50)

a50 = 254

Find the difference between the 10th and

50th term:

Difference = 254 - 54 = 200

Answer: The difference is 200

Given the data from the question, the difference between the 10th term and the 50th term is 200

This is a type of sequence which have common difference between each term. It is represent mathematically as:

Tₙ = a + (n – 1)d

Where

Tₙ = a + (n – 1)d

T₁₀ = 9 + (10 – 1)5

T₁₀ = 9 + (9)5

T₁₀ = 9 + 45

T₁₀ = 54

Tₙ = a + (n – 1)d

T₅₀ = 9 + (50 – 1)5

T₅₀ = 9 + (49)5

T₅₀ = 9 + 245

T₅₀ = 254

Difference = T₅₀ – T₁₀

Difference = 254 – 54

Difference = 200

Learn more about arithmetic sequence:

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Answer:

1234567890987654321123456789 is the answer

Step-by-step explanation:

and also hey

Step-by-step explanation:

you know how to multiply two expressions ?

every term of every expression is multiplied with every term of the other expression and the results are added (while considering any specific signs, if course).

(2x² + 3)(2x² - 3) = 2x²×2x² + -3×2x² + 3×2x² + 3×-3 =

4x² - 6x² + 6x² - 9 = 4x² - 9

and that is exactly the right side of the original equation.

so, it is correct.

Answer:

You will need “paper sticks” that are 3cm, 4cm and 5cm long. Each measurement should have its own colour (e.g., 3cm red, 4cm green, 5cm blue). You will need to make approximately 12 of each “stick”.

Step-by-step explanation:

Answer:

value/total value • 100 = percentage

Step-by-step explanation:

if 5 out 100 kids have red backpacks then 5% of kids have red backpacks

5/100 • 100 = percentage

0.05 • 100 = percentage

5% = percentage

if 13 cars out of 41 have flat tires, then 32% of the cars have flat tires

13/41 • 100 = percentage

0.31707317073... • 100 = 31.707317073... %

depending on your precision, you may include as many decimal places as you like, unless the question specifies it.  For our example, we will round to 2 decimal places.

31.707317073... % = 31.71%

if you're looking to find percentages for probability, you will use the same equation.

the odds of flipping a coin and it landing on heads are 50%

possibilities:

Heads, Tails

there is one outcome where our result occurs out of the two possible outcomes

1/2 • 100 = percentage

0.5 • 100 = percentage

50% = percentage

Hope this helps and wasn't confusing

Answer:

$300.15

Step-by-step explanation:

The price of the golf club is 100% of its price.

The shipping and handling add 15% of the price.

That means he will pay a total of 115% of the price of the golf club.

115 of $261 = 1.15 × $261 = $300.15

Answer: $300.15

Answer:

16, 10

Step-by-step explanation:

There are 4 quarts in a gallon, so 4 gallons has 16 qt.

There are 2 pints in a quart, so 5 quarts has 10 pt.