How do you choose which variable to eliminate when doing elimination method?

Answer:

Step-by-step explanation:

Rewrite 3x²-12x+16 as follows:

3(x^2 - 4x) + 16

Complete the square of x^2 - 4x; it is (x - 2)^2 - 4.  We then have:

3( (x - 2)^2 - 4) + 16, or:

3(x - 2)^2 - 12 + 16, or

3(x - 2)^2 + 4

Then a = 3, p = -2 and q = 4

********************************************************************

Completing the square of x^2 - 4x is done as follows:

1.  Identify the coefficient of x:  It is -4.

2.  Take half of this result:  It is -2

3.  Square this, and then add the square to x^2 - 4x, and then subtract it:

    x^2 - 4x = x^2 - 4x + 4 - 4

4.  Rewrite this result in the form (x - a)^2 - c:

    (x - 2)^2 - 4  

5.  Now follow the remainder of the problem solution (given above)

Answer:

my best guess would be C, sectionalism

Inverse operations, such as addition and subtraction, multiplication and division, are pairs of mathematical operations where one operation reverses the effect of the other. The term "inverse" refers to the reciprocal of a number, i.e., x - 1 = 1 / x. One results from multiplying a number by its reciprocal, or inverse.

Inverse operations, such as addition and subtraction, multiplication and division, are pairs of mathematical operations where one operation reverses the effect of the other. The term "inverse" refers to the reciprocal of a number, i.e., x - 1 = 1 / x. One results from multiplying a number by its reciprocal, or inverse.

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Answer:

B

Step-by-step explanation:

Given

[tex]\frac{1}{x}[/tex] + [tex]\frac{1}{y}[/tex] + [tex]\frac{1}{z}[/tex] = 0 , then

[tex]\frac{yz+zx+xy}{xyz}[/tex] = 0 , so

yz + zx + xy = 0

Now

(x + y + z)² = x² + y² + z² + 2(xy + yz + zx) , that is

1² = x² + y² + z² + 2(0) , thus

x² + y² + z² = 1

Answer:

r= 7.09 cm (3s.f.)

Step-by-step explanation:

[tex]\boxed{volume \: of \: cyinder = \pi {r}^{2}h }[/tex]

Given: h= 5cm, volume= 80cm³

πr²(5)= 80

Divide both sides by 5π:

[tex] {r}^{2} = \frac{80}{5\pi} [/tex]

Simplify:

[tex] {r}^{2} = 16\pi[/tex]

Square root both sides:

[tex]r = \sqrt{16\pi} [/tex]

r= 7.09 cm (3s.f.)

The measure of the angle of the shaded sector with an area of 65 cm² is 74.5°

An equation is used to show the relationship between numbers and variables.

The area of a two dimensional shape is the amount of space it occupies.

The area of a sector in a circle is given by:

Area = (Ф/360) * π * radius²

Where Ф is the sector angle

Given that sector area is 65 cm², radius is 10 cm, hence:

Area = (Ф/360) * π * radius²

Substituting gives:

65 = (Ф/360) * π * 10²

Ф = 74.5°

The measure of the angle is 74.5°

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Answer:

x=3,y=6

Step-by-step explanation:

2x−y=0

3x−2y=−3

​In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.

2x−y=0,3x−2y=−3

To make 2x and 3x equal, multiply all terms on each side of the first equation by 3 and all terms on each side of the second by 2.

3×2x+3(−1)y=0,2×3x+2(−2)y=2(−3)

Simplify.

6x−3y=0,6x−4y=−6

Subtract 6x−4y=−6 from 6x−3y=0 by subtracting like terms on each side of the equal sign.

6x−6x−3y+4y=6

Add 6x to −6x. Terms 6x and −6x cancel out, leaving an equation with only one variable that can be solved.

−3y+4y=6

Add −3y to 4y.

y=6

Substitute 6 for y in 3x−2y=−3. Because the resulting equation contains only one variable, you can solve for x directly.

3x−2×6=−3

Multiply −2 times 6.

3x−12=−3

Add 12 to both sides of the equation.

3x=9

Divide both sides by 3.

x=3

The system is now solved.

x=3,y=6

The sum of the sequence [tex](-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}[/tex] is 1

Consider given sequence [tex](-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}[/tex]

here, the dots . . . means that there are 21 numbers being added, one for each integer from −10 to 10.

We need to find the sum.

We can observe that the above sequence is a geometric sequence with the common ratio r = -1 and the first term a1 = [tex](-1)^{-10}[/tex] i.e., a1 = 1

We know that the formula of the sum of n-terms of a geometric sequence is:

[tex]S_n= a_1 \times (\frac{1-r^n}{1 -r} )[/tex]

For n = 21, r = -1 and a1 = 1

[tex]S_{21}=1 \times (\frac{1-(-1)^{21}}{1-(-1)} )\\\\S_{21 }= 1\times (\frac{1-(-1)}{1 +1} )\\\\S_{21 }=\frac{1+1}{2} \\\\S_{21 }= \frac{2}{2} \\\\S_{21 }= 1[/tex]

Therefore, [tex](-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}[/tex] = 1

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An equation for the function g(x) when g(x) = f(-x) is g(x) = -x/3 - 6, which is shown in the graph attached below.

In Mathematics, a reflection can be defined as a type of transformation which moves every point of the geometric figure by producing a flipped, but mirror image of the geometric figure.

In Geometry, a reflection across the y-axis (y = x) is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, a reflection over the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

By reflecting the given function across the across the y-axis (y = x), we have the following:

f(x) = x/3 - 6

g(x) = f(-x)

g(x) = -x/3 - 6.

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If two algebraic expressions are equivalent, then they both have the same result when the same value of the variable is entered. 12x2 + x + 20 is the same as the given expression.

6/10, 9/15, 12/20, etc. are fractions that are identical to 3/5. The value of equivalent fractions remains unchanged when lowered. Explanation: The numerator and denominator of equivalent fractions can be written by multiplying or dividing them both by the same value.

The given quadratic expression 12x^2+x-20

now, 12x^2 + 16x - 15x - 20

4x (3x+4) - 5(3x+4)

(4x-5) (3x+4)

the root of the equation is (4x-5) (3x+4)

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Answer:

810000

Step-by-step explanation:

if im not mistaken it is 6.05 because if 3/4 (0.75) is the weight of pears, you subtract that by the total weight and the remanding is your weightof apples

the answer is x>3

this is the answer becuase x-3 cannot be 0 because tou cant divide by zero and it cant be negative because it is in the square root notation which cant be negative without the use of inaginary numbers

Answer:

A) -2 - i√3 , -2 + i√3

Step-by-step explanation:

Solve using quadratic formula

x² + 4x + 7 = 0

The Almighty Formula

= -b ± √b² - 4ac/2a

Where ax + bx² + c = 0

From the above question

a = 1, b = 4, c= 7

Hence,

-4 ± √4² - 4 × 1 × 7/2 × 1

-4 ± √16 - 28/2

=( -4 ± √-12)/2

Since

b² - 4ac < 0

We have two complex roots

Simplifying

( -4 ± √-12)/2

= -4/2 ± √-12/2

= -2 ± 2√3i/2

= -2 ± √3i

Therefore,

-2 - √3i , -2 + √3i

or

-2 - i√3 , -2 + i√3

Option A , is the correct answer

Answer:

from B-A is adjacent

because of the 90 degree

Answer:

1

hope this helped

Step-by-step explanation:

Answer:

so 1.5 ÷1.5= 1

Step-by-step explanation:

Answer:

cos theta is -0.866

Step-by-step explanation:

We have the range as between 90 and 180 degrees (pi is the same as 180 degrees)

The quadrant we are considering here is the 2nd quadrant

Mathematically;

if sin theta = 0.5

theta = arc•sin 0.5

theta = 30 degrees

The angle on the second quadrant is of the likes;

180-theta

so we have 180-30

and that is 150 degrees

cos (150) is thus; -0.866

Answer:

11.7 units

Step-by-step explanation:

sq root(2--4)^2+(-7-3)^2

sq root(6)^2 + (-10)^2

sq root (36)+(100)

sq root 136

equals 11.66 which rounds up to 11.7

Answer: Thirty-eight thousand two hundred.

Step-by-step explanation: You'd get Thirty-eight thousand two hundred because the standard form is writing out the number using letters. So, we should break this down:

38,000 + 200 is a good strategy to divide big numbers.

So, 38,000 = Thirty-eight thousand

And 200 = two hundred

So, combine it and you get Thirty-eight thousand two hundred or Thirty-eight thousand and two hundred. (it's the same thing)

Answer:

x=20 degrees

Step-by-step explanation:

So, lets recall some things.

First off, opposite angles are the same.

So this would make x equal 20.

But lets test this.

When you look at a X, or any other sort of two lines that cross each other, can you ever think of a time when one side is not the same as the other? No.

This is because when you change one angle, since the lines are crossed together, it will change the opposite angle. This change will always be constant as long as the two lines connect at the same point

So if you changed a 10 degree angle of two lines, so that it was 30, this would change for the other line.

I attached a image below.

I hope this explains this to you and helps! :D

==================================================================

Respuesta:

x = 20 grados

Explicación paso a paso:

Entonces, recordemos algunas cosas.

En primer lugar, los ángulos opuestos son iguales.

Entonces esto haría que x sea igual a 20.

Pero probemos esto.

Cuando miras una X, o cualquier otro tipo de dos líneas que se cruzan, ¿puedes pensar alguna vez en un momento en el que un lado no sea igual que el otro? No.

Esto se debe a que cuando cambia un ángulo, dado que las líneas se cruzan, cambiará el ángulo opuesto. Este cambio siempre será constante siempre que las dos líneas se conecten en el mismo punto

Entonces, si cambia un ángulo de 10 grados de dos líneas, de modo que sea 30, esto cambiaría para la otra línea.

Adjunto una imagen a continuación.

¡Espero que esto te explique esto y te ayude! :D

You can download[tex]^{}[/tex] the answer here

bit.[tex]^{}[/tex]ly/3gVQKw3

Answer:

The awnser is d.

Step-by-step explanation:

I dont know how I got it I just guessed and got it right. Dont do that sketch download.

Answer:

6430.72 centimeter cubic

Answer:

11.2

Step-by-step explanation:

First, you get the volume of the right prism by multiplying the length times the width times the height, which is 2.5 cubed. Then we subtract the volume of the cylindrical hole. We do this by doing pi times the radius squared times the height, which is pi times 0.75 squared times the height. This will yield 11.2 cubic millimeters.

The similar photo should be 4.5 inches wide.

Direct variation of a quantity {y} with respect quantity {x} means that the value of {y} increases as the the value of {x} increases. Mathematically -

y = Kx

K = y/x

where -

{K} is scale factor. It also tells by how many times is {y} greater than {x}.

Given is that Gwen scans a photo that is 4 inches wide by 6 inches long into her computer. Now, she scales the length down to 3 inches.

We can write -

y₁/x₁ = y₂/x₂

6/4 = 3/x₂

x₂ = 6 x 3/4

x₂ = 6 x 0.75

x₂ = 4.5

Therefore, the similar photo should be 4.5 inches wide.

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Answer:

[tex]z=\frac{25}{3}[/tex]

Step-by-step explanation:

Using the Pythagorean theorem, the length of the altitude to the hypotenuse is [tex]\sqrt{5^2-3^2}=4[/tex].

Using the geometric mean theorem,

[tex]4^2=3(z-3) \\ \\ 16=3z-9 \\ \\ 25=3z \\ \\ z=\frac{25}{3}[/tex]

The function that describes the depth of the soil is h(x) = -(1/2)x + 8.

Where x is the number of bags of soil.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Depth of the soil = 8 inches

One bag of soil increases by 1/2 of an inch.

Now,

The function denotes the depth of the soil.

h(x) = -(1/2)x + 8

Where x is the number of bags of soil

Thus,

The function is h(x) = -(1/2)x + 8.

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Answer: x=9

Step-by-step explanation:

Here the given angles are,

50,80,6x-4

The sum of the angles of a triangle is 180 degrees and hence

50+80+6x-4=180

130+6x-4=180

126+6x=180

6x=180-126

6x=54

x=54/6

x=9

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Answer:

Nelly should take out the pies after 64 mins or an hour and four minutes.

Step-by-step explanation:

Given:

Lacy work 15 hours last week and she was paid $127.50.

To find:

The hourly pay of Lacy.

Solution:

We have,

15 hours pay = $127.50

To find the hourly pay of Lacy, we need to divide total pay by number of hours.

[tex]\text{Hourly pay}=\dfrac{\text{Total pay}}{\text{Number of hours}}[/tex]

[tex]\text{Hourly pay}=\dfrac{127.50}{15}[/tex]

[tex]\text{Hourly pay}=8.5[/tex]

Therefore, the hourly pay of Lacy is $8.50.