A system of equations is shown below:

3x − y = 2
x + y = 6

The x−coordinate of the solution to this system of equations is

Answer:

[tex]\frac{1}{2}[/tex] , or the first option

Step-by-step explanation:

The formula to find the slope of a line is [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]. It doesn't matter which set of coordinates is (x₁,y₁), as long as you make sure you put them in the right places.

(x₁,y₁) = (1,2)

(x₂,y₂) = (5,4)

[tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]   Plug in your numbers

[tex]\frac{4 - 2}{5 - 1}[/tex]   Simplify

[tex]\frac{2}{4}[/tex]   Simplify

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

Answer:

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

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (1, 2) and (x₂, y₂ ) = (5, 4)

m = [tex]\frac{4-2}{5-1}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]

[tex](x+3)(x+5) =x^2+5x+3x+15=x^2+8x+15[/tex]

[tex]x^2+8x+15[/tex]

Use the FOIL method of multiplying binomials.

First term in each binomial: [tex]x*x=x^2[/tex]

Outside terms: [tex]x*5=5x[/tex]

Inside terms: [tex]3*x=3x[/tex]

Last term in each binomial: [tex]3*5=15[/tex]

Add them all together. [tex]x^2+5x+3x+15[/tex]

Simplify. [tex]x^2+8x+15[/tex]

Answer:  A) 7 o---------------→

Step-by-step explanation:

[tex]\dfrac{2}{9}x+3>4\dfrac{5}{9}\\\\\\\text{Subtract 3 from both sides:}\\\\\dfrac{2}{9}x>1\dfrac{5}{9}\\\\\\\text{Convert the mixed number into an improper fraction:}\\\\\dfrac{2}{9}x>\dfrac{14}{9}\\\\\\\text{Multiply both sides by }\dfrac{9}{2}\text{ to isolate x:}\\\\x>\dfrac{14}{9}\times \dfrac{9}{2}\\\\\\\text{Simplify (cancel out the 9's and factor out a 2:}\\\\x>7[/tex]

The graph will have an open dot at 7 and the arrow will point to the right.

7 o--------->

Answer:

A

Step-by-step explanation:

EDGE 23

For this case we have the expression:

"the square root of 4" is represented algebraically as:

[tex]\sqrt {4}[/tex]

Then, we can express the given statement as:

[tex]3 \sqrt {4} -2 \sqrt {4} =[/tex]

They are similar terms, we can subtract:

[tex]3 \sqrt {4} -2 \sqrt {4} = \sqrt {4} = \sqrt {2 ^ 2}[/tex]

By definition of power properties we have that:

[tex]\sqrt [n] {a ^ n} = a ^ {\frac {n} {n}} = a[/tex]

Then the expression is reduced to:

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

Answer:

[tex]3 \sqrt {4} -2 \sqrt {4} = 2[/tex]

Answer:

Hundreds

Step-by-step explanation:

The value of 5 is given based on the place value in which it is located.

The 5 is located in the "hundreds" place value, and so Hundreds is your answer.

Place value:

3: Thousands

5: Hundreds

9: Tens

0: Ones

Answer:

Making it the answer A

Step-by-step explanation:

Answer:

2p

Step-by-step explanation:

Take a trip back to simple division. What's 12/6? If you put 12 p's evenly into 6 piles, how many p's are in each pile?

2

Therefore, the answer is 2p.

Answer:

4x(2x+3)

Step-by-step explanation:

Since the common factor of 8x^2 and 12x is 4x, put that out and separate the distributed remaining factors.

Answer: 4 seconds

Step-by-step explanation:

We have the equation that models the height of the golf ball in feet after being hit.

When the ball reaches the ground its height is equal to zero.

Then to solve this problem you must equal h to zero and solve the equation for the variable t

[tex]h = -16t^2 + 64t=0[/tex]

[tex]-16t^2 + 64t=0[/tex]

Take 16t as a common factor

[tex]-16t(t - 4)=0[/tex]

The equation is equal to zero when t = 0 and when t = 4

t = 0 is at the instant in which the ball has just been hit and t = 4 seconds is the instant in which the ball touches the ground.

Then the answer is t=4 seconds

Answer:

area = 50.27 sq inches

circumference = 25.14 in

Step-by-step explanation:

given radius r = 4 in

area = πr² = 3.142 x 4² = 50.27 square inches

circumference = 2πr = 2 x 3.142 x 4 = 25.14 inches

Answer:

[tex]\frac{29u}{5x}[/tex]

Step-by-step explanation:

If 'x' does not equal 0 then:

[tex]\frac{u}{x}+\frac{5u}{x}-\frac{u}{5x}[/tex] ⇒ [tex]\frac{6u}{x}-\frac{u}{5x}[/tex]

⇒ [tex]\frac{29u}{5x}[/tex]

Then, the solution is: [tex]\frac{29u}{5x}[/tex]

Answer:

28.2 US tablespoons

Step-by-step explanation:

If 8 tablespoons of extract are mixed with distilled water to total 300 mL,  the final concentration is 28.2 US tablespoons.

8 tablespoons + 300 mL = 28.2 US tablespoons

Answer:

418.294 milliliters or 28.28 tablespoons.

Step-by-step explanation:

As we know 1 tablespoon = 14.7868 ml.

                  8 tablespoons = 14.7868 × 8

                                           = 118.294 ml.

Final concentration  = 300 ml + 118.294 ml

                                 = 418.294 ml.

If you want to convert the final concentration to tablespoon

418.294 ÷ 14.7868 = 28.28 tablespoons.

The final concentration would be 418.294 milliliters or 28.28 tablespoons.

Hey there! :)

-4c + 3d = 8e ; solve for d.

In order to solve for d, you must isolate it (get it onto its own side). So, let's start off by adding 4c to both sides.

-4c + (-4c) + 3d = 8e + (-4c)

Simplify.

3d = 8e - 4c

Then, divide both sides by 3.

3d ÷ 3 = (8e - 4c) ÷ 3

Simplify.

d = 8/3e - 4/3c

Therefore, [tex]d = \frac{8}{3} e  -\frac{4}{3} c[/tex]

Answer: 2x^2-y^2+5xy-2y

a. There is four terms in the simplified expression.

b. Two terms in the simplified expression are negative.

Step-by-step explanation:

Write the expression like an addition/ subtraction problem.

-3x²+2y²+5xy-2y

+5x²-3y²

_________

This makes it easier to identify what to combine for like terms.

Final answer:

The simplified expression is 2x² - y² + 5xy - 2y. There are two negative terms in the simplified expression: -y² and -2y.

Explanation:

To simplify the expression -3x² + 2y² + 5xy - 2y + 5x² - 3y², we need to combine like terms. The like terms are the ones that contain the same variables to the same power. Here’s a step-by-step explanation:

The simplified expression is 2x² - y² + 5xy - 2y.

Now, to answer the question about the number of negative terms: in the simplified expression, there are two negative terms, which are -y² and -2y. A term is considered negative if it has a minus sign in front of it, indicating that it is less than zero when all other variables are considered to be positive.

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange the given equation into this form

10x + 20y + 40 = 0 ( divide all terms by 10 to simplify )

x + 2y + 4 = 0 ( subtract x + 4 from both sides )

2y = - x - 4 ( divide all terms by 2 )

y = - [tex]\frac{1}{2}[/tex] x - 2 ← in slope- intercept form

with slope m = - [tex]\frac{1}{2}[/tex] and y- intercept c = - 2

Answer:

31

Step-by-step explanation:

I beleve

Answer:

It is actually C) 30 gallons

Step-by-step explanation:

2x-1 <7

2x <7+1

2x/2 <8/2

x <4

5x+3 <3

5x <3-3

5x <0

x <0

The solution of the given inequalities is x < 0.

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.

We have,

2x - 1 < 7

And

5x + 3 < 3.

Now,

Take 2x - 1 < 7 ,

Now,

Rearrange variable terms to the left side of the equation,

i.e.

2x < 7 + 1

2x < 8

We get,

x < 4

Now,

Take 5x + 3 < 3,

Now,

Rearrange variable terms to the left side of the equation,

i.e.

5x < 3 - 3

5x < 0

We get,

x < 0

So,

The intersection of the two solution will give us the solution to the system of inequalities, i.e.

x < 0 is the solution to the inequalities.

Hence, we can say that the solution of the given inequalities is x < 0.

To know more about inequality click here

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Answer:

The formula is a^2+2a+ sqrt a^2+h^2

Step-by-step explanation:

a=base edge

h=height

Answer:

The formula is A=a²+2a(√a^2 )/4+h²

Step-by-step explanation:

Answer:

72

Step-by-step explanation:

Answer:

72

Step-by-step explanation:

Absolute value is the distance a number is from 0.

For example, look at the following number line.

<-|-------|--------|---------|---------|----------|---------|->

 -6      -5       -4       -3        -2         -1         0

The absolute value of -6 is 6 since the number -6 is 6 digits away from 0.

So likewise if:

|-6| = 6

[keep in mind that this symbol ---> |  | is the absolute value symbol]

then:

|-72| = 72

Since -72 is 72 digits away from 0.

I hope this helps! :)

Answer:

a = 2, b = 6

Step-by-step explanation:

To obtain g(f(x)) substitute x = f(x) into g(x), that is

g(x + 3) = a + b(x + 3)²

            = a + b(x² + 6x + 9) = a + bx² + 6bx + 9b

For a + bx² + 6bx + 9b = 6x² + 36x + 56

Then coefficients of like terms must be equal

Comparing like terms

x² term ⇒ b = 6

constant term ⇒ a + 9b = 56 ⇒ a + 54 = 56 ⇒ a = 56 - 54 = 2

[tex]g(f(x))=a+b\cdot(x+3)^2=a+b(x^2+6x+9)=a+bx^2+6bx+9b=\\=bx^2+6bx+9b+a\\\\6x^2+36x+56=bx^2+6bx+9b+a\\b=6\\9b+a=56\\9\cdot6+a=56\\a=2\\\\\\\boxed{a=2,b=6}[/tex]

Answer:

x = -2 and y = 3

Step-by-step explanation:

It is given that,

4x + 5y = 7    ----(1)

3x – 2y = –12   ---(2)

To find the solution of given equations

eq(1) * 3 ⇒

12x + 15y = 21   ----(3)

eq(2) * 4 ⇒

12x - 8y = -48  ---(4)

eq(3) - eq(4) ⇒

12x + 15y = 21   ----(3)

12x - 8y = -48 ---(4)

 0 + 23y = 69

y = 69/23 = 3

Substitute the value of y in eq(1)

4x + 5y = 7    ----(1)

4x + 5*3 = 7

4x = 7 - 15 = -8

x = -8/4 = -2

Therefore x = -2 and y = 3

Answer:

tan²x

Step-by-step explanation:

Using the Pythagorean identity

sin²x + cos²x = 1

Divide all terms by cos²x

[tex]\frac{sin^2x}{cos^2x}[/tex] + [tex]\frac{cos^2x}{cos^2x}[/tex] = [tex]\frac{1}{cos^2x}[/tex], that is

tan²x + 1 = sec²x ( subtract 1 from both sides )

tan²x = sec²x - 1

Answer:

Because the negative in the front cancels out the other neg.

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

If you expand the brackets in -(3 - 2x) by multiplying all numbers by -1 (the negative symbol in front of the brackets represents negative 1 just without the 1)

Thus you get -3 + 2x.

Then rearranging the equation by swapping the 2x with the -3 you get 2x - 3.

The equation that shows the water remaining in the barrel is given by y = -(1/10)x + 60

A linear equation is in the form:

y = mx + b

Where y,x are variables, m is the rate of change and b is the initial value of y.

Let y represent the amount of water remaining after x minutes.

Jim's yard contains 60 gallons of water. Hence b = 60.

The water leaks out of the barrel at a rate of 1 gallon every 10 minutes. Hence m = -1/10. The equation is:

y = -(1/10)x + 60

The equation that shows the water remaining in the barrel is given by y = -(1/10)x + 60

Find out more on linear equation at: https://brainly.com/question/14323743

Answer:

Step-by-step explanation:

x= 6± √(6)^2-4(1)(6)   /2(1)

=6± √12   /2

=6± 2√3   /2

=3± √3

Answer:  The required solution of the given quadratic equation is

x = 3 + √3  and  x = 3 - √3.

Step-by-step explanation:  We are given to solve the following quadratic equation using quadratic formula :

[tex]x^2-6x+6=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

Quadratic formula :  The solution of a quadratic equation of the form [tex]ax^2+bx+c=0,~a\neq 0[/tex] is given by

[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

For the given quadratic equation (i), we have

a = 1,  b = -6   and   c = 6.

Therefore, the solution of equation (i) is given by

[tex]x\\\\\\=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\\=\dfrac{-(-6)\pm\sqrt{(-6)^2-4\times 1\times6}}{2\times1}\\\\\\=\dfrac{6\pm\sqrt{36-24}}{2}\\\\\\=\dfrac{6\pm\sqrt{12}}{2}\\\\\\=\dfrac{6\pm2\sqrt{3}}{2}\\\\=3\pm\sqrt3.[/tex].

Thus, the required solution of the given quadratic equation is

x = 3 + √3  and  x = 3 - √3.

Answer:

Volume = 784*pi

Step-by-step explanation:

We are given the height and radius of cylinder

So,

Radius = r = 7

Height = h = 16

The formula for finding volume of cylinder is:

[tex]Volume=\pi r^{2} h\\Putting\ in\ the\ values\ of\ r\ and\ h\\Volume=\pi *(7)^{2}*16\\V=\pi *49*16\\V=784\pi [/tex]

Answer:

Volume of cylinder = 784 cubic units

Step-by-step explanation:

Points to remember

Volume of cylinder =  πr²h

Where r - Radius of cylinder and

h - Height of cylinder

To find the volume of cylinder

It is given that,

radius r = 7 units and height h = 16 units

Volume of cylinder =  πr²h

 = π * 7² * 16

 = 784 cubic units

Therefore Volume of cylinder = 784 cubic units

Answer:

x + y - 2 = 0

Step-by-step explanation:

First, set the equation equal to 2 by moving 2 to the other side of the equation to get x + y = 2, then move -x over to the other side to end up with y = -x + 2. The reason being is because the rate of change [slope] is -1. Simply do rise\run until you hit another endpoint, starting from your y-intercept. As you can see, you go two blocks south, then go two blocks over east. Now, if when you look carefully, you will see that -2\2 = -1. This is the simplification of the slope. Do you understand?

Answer:

x = -4

Step-by-step explanation:

Using the slope formula,

we would get (3+2)/(0),

which isn't possible. Then, we realize why. A line will not have an equation when going straight up and down. And that's what this line is doing. Both of the x values are the same, so it's only going up. So therefore, the equation is x = a constant.

This constant is -4

Hope this helps!

ANSWER

[tex]x = - 3[/tex]

EXPLANATION

When a quadratic equation is in the vertex form,

[tex]f(x) = a {(x - h)}^{2} + k[/tex]

the equation of axis of symmetry is simply

[tex]x = h[/tex]

The given quadratic equation is

[tex]f(x) = {(x + 3)}^{2} - 8[/tex]

We can rewrite this as

[tex]f(x) = {(x - - 3)}^{2} - 8[/tex]

We now compare to

[tex]f(x) = a {(x - h)}^{2} + k[/tex]

We have

[tex]h = - 3 \: \: \: and \: \: k = - 8[/tex]

Therefore equation of axis of symmetry is:

[tex]x = - 3[/tex]

Answer:

y = -2x+1

Step-by-step explanation:

The slope is found by

m = (y2-y1)/(x2-x1)

   = (-1-5)/(1--2)

    = -6/(1+2)

    = -6/3

    = -2

Then we can use point slope form to make an equation

y-y1 = m(x-x1)

y-5 = -2(x--2)

y-5 = -2(x+2)

Distribute

y-5 = -2x -4

Add 5 to each side

y-5+5 = -2x-4+5

y = -2x+1

This is in point slope form