Match the vocabulary word with the correct definition.

1. trapezoid
A trapezoid with legs of the same length.
2. bases of a trapezoid
A quadrilateral with at least one pair of parallel sides.
3. legs of a trapezoid
The parallel sides.
4. median of a trapezoid
The segment connecting the midpoints of the legs.
5. isosceles trapezoid
The nonparallel sides

[tex]\bf \textit{surface area of a cone}\\\\ SA=\pi r\sqrt{r^2+h^2}+\pi r^2~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} \stackrel{\textit{half of diameter}}{r=6~\hfill }\\ h=7 \end{cases}\implies SA=\pi (6)\sqrt{6^2+7^2}+\pi 6^2 \\\\\\ SA=6\pi \sqrt{85}+36\pi \implies SA=6\pi (\sqrt{85}+6)\implies SA\approx 286.88[/tex]

The volume of a cone increases by a factor of 27 when its height is multiplied by 3, as the volume of a cone scales with the cube of its linear dimensions.

The question asks how many times larger the volume of a cone becomes if its height is multiplied by 3. The volume of a cone is given by the formula V = ([tex]\frac{1}{3}[/tex]1/3)πr²h, where r is the radius and h is the height. If you multiply the height by 3, the volume will increase by a factor of 3 since volume scales with the third power of the linear dimensions. Therefore, the new volume would be 3³, or 27 times the original volume. This result can also be demonstrated by the mathematical expression Vnew = ([tex]\frac{1}{3}[/tex])πr²(3h) = 27Voriginal.

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 height of the tower is 150 ft

Step-by-step explanation:

Let the height of the tower be H feet.

The corresponding sides will then be in the same proportion.

The ratio of the shadows will be in the same proportion as the ratio of the heights.

[tex]\frac{H}{10}=\frac{120}{8}[/tex]

We multiply both sides by 10 to get:

[tex]\frac{H}{10}\times 10=\frac{120}{8}\times 10[/tex]

[tex]H=150[/tex]

Therefore, the height of the tower is 150 ft

Answer:

Height of the tower = 150 foot

Step-by-step explanation:

We need to find height of the tower with 120-foot shadow.

We have a 10-foot  street sign casts a shadow of 8 feet.

[tex]\texttt{Ratio of height to shadow height =}\frac{10}{8}=\frac{5}{4}[/tex]

We have

       [tex]\frac{\texttt{Height of tower}}{\texttt{Shadow height of tower}}=\frac{5}{4}\\\\\frac{\texttt{Height of tower}}{120}=\frac{5}{4}\\\\\texttt{Height of tower}=\frac{5}{4}\times 120=150feet[/tex]

Height of the tower = 150 foot

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:

first off, welcome to brainly, second, your answer is 14.4

Step-by-step explanation:

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

https://brainly.com/question/20383699

#SPJ2

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:

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:

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:

[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.

Answer:

81

Step-by-step explanation:

Given

x² - 18x = 29

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 9)x + (- 9)² = 29 + (- 9)²

x² + 2(- 9)x + 81 = 29 + 81

(x - 9)² = 110

Answer:

81

Step-by-step explanation:

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:

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:

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:

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:

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:

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:

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!

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:

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:

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:

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]

[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:

-56

Step-by-step explanation:

Simplify the following:

-4 (9 + 5)

9 + 5 = 14:

-414

-4×14 = -56:

Answer:  -56

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