What is the measure of

[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:

[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:

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?

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:

Theoretical probability: 50/100 or 50%

Experimental probability: 12/20 or 60%

Step-by-step explanation:

Let's find out both probabilities asked.

Theoretical probability:

In the whole bank, here are 100 coins (20 nickels + 30 quarters + 50 one-dollars), among which there are 50 one-dollar coins. So the probability to pick up a one-dollar coin is 50 out 100, so...

TP = 50/100 or 50%

Experimental probability:

For the experimental probability, we know Jonathan picked out 20 coins, out of which 12 were one-dollar coins, so the probability is 12 out of 20...

EP = 12 / 20 = 60%

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:

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: 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

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.

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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:

The solution set is ∅

Step-by-step explanation:

The expression

y = ax^2 + bx + c

is a quadratic equation.

The vertex is located at (-2, 5) and the graph opens up, this means that it never intercepts the x-axis.

The solution set is ∅

Please see attached image

Answer:

[tex]y=\frac{-5}{4}x^{2} -5b[/tex]

Step-by-step explanation:

Assume c = 0

Using the formula for the x-coordinate of the vertex, b can be calculated in terms of a:

[tex]x=\frac{-b}{2a} \\-2=\frac{-b}{2a} \\b=4a[/tex]

B can then be substituted into the quadratic equation, along with the coordinates of the vertex, to solve a:

[tex]y=ax^{2}+bx\\y=ax^{2}+4ax\\5=a(-2)^{2}+4(-2)a\\5=4a-8a\\5=-4a\\a=\frac{5}{-4}[/tex]

AND

[tex]b=4a\\b=\frac{-5}{4} *4\\b=-5[/tex]

Substituting into the quadratic equation:

[tex]y=\frac{-5}{4}x^{2} -5b[/tex]

Because a is negative, the parabola opens up.

Answer:

31

Step-by-step explanation:

I beleve

Answer:

It is actually C) 30 gallons

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:

Making it the answer A

Step-by-step explanation:

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:

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

Answer:

x=2

Step-by-step explanation:

First of all cross-multiply.

1/2x=1/4

(1) x (4) =1 x 2x

4=2x

After flip the equation.

2x=4

Then divide both sides by 2.

2x/2=4/2

x=2

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:

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:

Step-by-step explanation:

64

There are 8 numbers on the spinner.

The first spinner could be 1 of 8 and the second spin could also be 1 of 8.

To find the total outcomes, multiply the number of outcomes of each spin by each other.

Spin 1 : 8 out comes

Spin 2: 8 outcomes

Total outcomes = 8 x 8 = 64

The answer is D. 64

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:

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.

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:

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:

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.

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

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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:

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:

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