Wendy drew a scale drawing of the auditorium. She used the scale 3 inches : 2 feet. The stage is 18 feet wide in real life. How wide is the stage in the drawing?

Answer:

√245 or 15.65247...

Step-by-step explanation:

a² + b² = c²

14² + 7² = c²

196 + 49 = c²

245 = c²

√245 ≈ c

When you have a right triangle, you can use the Pythagorean Theorem to find the missing side length. (but it only works for RIGHT triangles)

Pythagorean Theorem:

a² + b² = c²         Since you know a=14 and b=7, plug it into the equation

(14)² + (7)² = c²

196 + 49 = c²

245 = c²

√245 = c    or 15.6524758425 = c

Answer:

B. 90 + 90 √2

Step-by-step explanation:

From first base to the second base, it will travel 90 feet.

From the second base to the home plate, it will travel a longer distance.  How much?  Well, if you look at the layout of the field, you'll see that if you draw a line from second base to the home plate, you'll form two rectangular triangles, one with the 1st base, another one with the 3rd base.

The line from the 2nd base to home plate is the hypotenuse, which we can easily find by:

h²=90² + 90²

h = √(2 * 90²)

h = 90 √2

So, from second base to home plate, the ball has traveled 90 √2

Overall: 90 + 90 √2

Simplify the radical 75 first:

[tex]\sqrt{75}[/tex]

5[tex]\sqrt{3}[/tex]

Next simplify the radical 12:

[tex]\sqrt{12}[/tex]

2[tex]\sqrt{3}[/tex]

Now that both radicals have the same number under the radical you can subtract the number in front normally

[tex]5\sqrt{3} -2\sqrt{3}[/tex]

[tex]3\sqrt{3}[/tex]

Hope this helped!

:

Pls mark brainliest I need help

Answer:

∠G = 50°

Step-by-step explanation:

The measure of the angle between the 2 tangents is

[tex]\frac{1}{2}[/tex] ( major arc - minor arc )

minor arc HF = 130° and major arc HF = 360° - 130° = 230°

Hence

∠G = 0.5(230° - 130°) = 0.5 × 100° = 50°

Answer:

x=9

Step-by-step explanation:

We have been given the following proportion;

x/6 = 6/4

In order to solve for x, we simply make x the subject on the left hand side;

To do this we multiply both sides by 6,

(x/6)*6 = (6/4)*6

x = 36/4

x = 9

The value of x is thus 9

if you simplify the answer you get its x=9

Answer:

[tex]\dfrac{1}{1296}[/tex]

Step-by-step explanation:

When a fair die is tossed once, there are 6 possible outcomes: 1, 2, 3, 4, 5, 6.

The probability of rolling 5 is [tex]\dfrac{1}{6}.[/tex]

When a fair die is tossed four times, the probability of rolling 5 all four times is

[tex]\dfrac{1}{6}\cdot \dfrac{1}{6}\cdot \dfrac{1}{6}\cdot \dfrac{1}{6}=\dfrac{1}{6^4}= \dfrac{1}{1296}[/tex]

Simplif 1/2t to t/2

t/2 + 8 = 5/2t - 10

Simplify 5/2t to 5t/2

t/2 + 8 = 5t/2 - 10

Multiply both sides by 2

t + 16 = 5t - 20

Subtract t from both sides

16 = 5t - 20 - t

Simplify 5t - 20 - t to 4t - 20

16 = 4t - 20

Add 20 to both sides

16 + 20 = 4t

Simplify 16 + 20 to 36

36 = 4t

Divide both sides by 4

36/4 = t

Simplify 36/4 to 9

9 = t

Switch sides

t = 9

Answer:

t = 9.

Step-by-step explanation:

1/2 t + 8 = 5/2 t - 10

         - 8      -5/2 t

1/2 t - 5/2 t   =   -10 - 8

-2t = -18

t = 9.

B is the correct answer

Answer:

B

Step-by-step explanation:

The slope would be 1/6

Answer:

3/x + 2/(x+1) = 3/5x

[3 · 5(x + 1) + 2 · 5x] / 5x(x + 1) = 3(x + 1) / 5x(x + 1)

3 · 5(x + 1) + 2 · 5x = 3(x + 1)

15x + 15 + 10x = 3x + 3

15x + 10x - 3x = -15 + 3

22x = -12

x     = -12/22 = -6/11

I think that 2/4 would be bigger because 2/4 is the same as 1/2 and 1/2 is bigger than 1/8. Imagine a pizza, if i have 1/2 of a whole pizza i would have more pizza than a friend who had 1/8 of the whole pizza.

I hope this helps :)

If you simplify 2/4, you will get 1/2. 1/2 is bigger than 1/8.

Proof:

Draw 2 mental circles in your head. then draw lines that will make the circles out of 2 and out of 8. Now color in 1/2 of the first circle and 1/8 of the second circle. You can see that the 1/2 is bigger than the 1/8.

Hope I helped, sorry if I'm wrong ouo.

~Potato.

Copyright Potato 2019.

Answer:

The correct answer option is 20.3.

Step-by-step explanation:

We are given a right angled triangle with one known angle and one known side length and we are to find the value of x.

To find the value of x, we will use the appropriate trigonometric ratio.

[tex] sin 5 2 = \frac { x } { 2 5 . 8 } [/tex]

[tex] x = sin 52 \times 2 5 . 8 [/tex]

x = 20.3

Answer:

Step-by-step explanation:

Use the sine:

[tex]sine=\dfrac{opposite}{hypotenuse}[/tex]

We have

[tex]opposite=x,\ hypotenuse=25.8,\ \sin52^o\approx0.788[/tex]

Substitute:

[tex]\dfrac{x}{25.8}=0.788[/tex]              multiply both sides by 25.8

[tex]x\approx20.3[/tex]

Step-by-step Answer:

f and f^(-1) are inverses of each other within a specified domain, with the property that

y=f(x)  <=> (is equivalent to)  f^(-1)(y)=x

since

2=f(4), by the definition of inverse functions, f^(-1)(2) = 4

-4, -2, -2 hope that will help you

Step-by-step explanation:

Step-by-step explanation:

Odd numbers are any numbers that end with 1, 3, 5, 7, 9.

Out of the numbers inbetween 75 & 100, the odd numbers are:

75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99,

which makes 13.

Set the amount of numbers you got over the total amount.

13/27

You have a 13/27, or 48.15% chance of picking an odd number.

~

Answer:

25 inches

Step-by-step explanation:

i first started with 18×8=144 then i did 144-119 and got 25.

Find the mean for both:

Sierra: 2 + 11 + 12 + 13 + 15 =  53

53/5 =10.6

Median is the middle value = 12

Alek: 9 + 11 + 11 + 12 + 13 = 56

56/5 = 11.2

Median = 11

A: The medians do not equal the mean.

B: Sierra's are more spread out, ( no identical ages and a greater range ).

C: Sierra's mean is less than Alek.

D. Sierra has an outlier (2).

The answer would be B

Answer:

n = 28

Step-by-step explanation:

3/4n - 18 = 1/4n - 4 (eliminate fractions by multiplying each value by 4)

(3/4n * 4) - (18 * 4) = (1/4n * 4) - (4 * 4)

3n - 72 = 1n - 16 (move values with variable to same side)

3n - 1n - 72 = 1n - 1n -16

2n - 72 = -16 (move numeric values to same side)

2n - 72 + 72 = -16 + 72

2n = 56  (isolate n by dividing out the 2)

2n/2 = 56/2

n = 28

Independent is x. Dependent is y

Answer:

Independent : x

Dependent: y

Step-by-step explanation:

y= 5x

The independent variable is the variable we change

Independent : x

The dependent variable depends on the value of the other variable

Dependent: y

Answer:

0.3

Step-by-step explanation:

In the bag are 12 red, 10 blue, 15 white, and 13 black marbles.

So total = 12 + 10 + 15 + 13 =  50 marbles

The probability he pulls a white marble = 15/50 = 0.3

Answer:

option 1 is correct:

y = -5cos(2x - π)

Final answer:

The maximum value of the quadratic function y = -2x^2 - 16x - 29 is 3, occurring at x = -4, found by determining the vertex of the parabola, which opens downwards due to the negative coefficient of the x^2 term.

Explanation:

To find the maximum or minimum value of the quadratic function y = -2x² - 16x - 29, we can utilize the properties of parabolas. Since the coefficient of the x² term is negative, the parabola opens downwards, meaning the vertex will give us the maximum value. The vertex of a parabola given by y = ax² + bx + c is found at the x-coordinate x = -b/(2a). Substituting the values from the given equation:

x = -(-16)/(2*(-2)) = -16/(-4) = -4

Now, we substitute this value back into the original equation to find the y-coordinate of the vertex:

y = -2(-4)² - 16(-4) - 29

y = -2(16) - 64 - 29

y = -32 + 64 - 29

y =3

Therefore, the maximum value of the function is 3, and it occurs at x = -4.

Answer:

[tex]y\leq -1/3[/tex]

The graph in the attached figure

Step-by-step explanation:

we have

[tex]-3(5y-4)\geq 17[/tex]

Applying the distributive property on the left side

[tex]-15y+12\geq 17[/tex]

Subtract 12 both sides

[tex]-15y\geq 17-12[/tex]

[tex]-15y\geq 5[/tex]

Multiply by -1 both sides

[tex]15y\leq -5[/tex]

Divide by 15 both sides

[tex]y\leq -5/15[/tex]

Simplify

[tex]y\leq -1/3[/tex]

The solution is the interval -------> (-∞, -1/3]

All real number less than -1/3

In a number line the solution is the shaded area down of y=-1/3 (close circle)

The graph is the attached figure

Answer:

D (136 -2a) + (3a+39)  = 180

Step-by-step explanation:

Since XQR = 180

<XQM + < MQR = XQR

136 -2a + (3a+39)  = 180

The correct answers are: C. Angle 4 F. Angle 6 In mathematics, exterior angles are formed outside between any side of a shape and a line extended from the next side.

The correct answer is option C and F.

In a triangle, the sum of the measures of the interior angles is always 180 degrees. Since angles 5, 3, and 1 are interior angles, their sum is 180 degrees.

The sum of the measures of the exterior angles of a triangle is always 360 degrees. Therefore, the sum of exterior angles 4, 6, and 2 is also 360 degrees.

Now, to determine the individual measures of the exterior angles, we know that the sum of the measures of the linear pairs (an exterior angle and its adjacent interior angle) is 180 degrees.

Therefore, angle 4 is an exterior angle since it forms a linear pair with angle 1.

Similarly, angle 6 is an exterior angle since it forms a linear pair with angle 3.

Angle 2 is not an exterior angle since it does not form a linear pair with any other angle in the given triangle.

So, the correct answers are:

C. Angle 4

F. Angle 6

Learn more about Exterior angles here:

https://brainly.com/question/2406986

#SPJ3

Answer:

14%

Step-by-step explanation:

Answer:

The answer is 14%

Step-by-step explanation:

Answer:

Equation that can find the value of the car on December 31, 2017 is:

A= 25000*(1-0.15)^7 and the value of car after 7 years is $8014.427.

Step-by-step explanation:

Price of car = $ 25,000

Rate of depreciation = 15 %

Formula used:

A= P(1-r)^n

where p= price of car

A= new price of car after depreciation

r = rate of depreciation i.e. 15/100 = 0.15

n= time in years 2017 - 2010 = 7 years

Putting values in formula:

A= 25000*(1-0.15)^7

A= 25000*(0.85)^7

A= $8014.427

So, Equation that can find the value of the car on December 31, 2017 is:

A= 25000*(1-0.15)^7 and the value of car after 7 years is $8014.427.

Answer:

The pattern is pretty clear. After $n$ years, in $200n$ the price will be:

$a_n= a_0(0.85)^{n-1}$

Step-by-step explanation:

Answer:

30%

Step-by-step explanation:

Answer:

Part 1) The area is [tex]A=4,069.44\ in^{2}[/tex]

Part 2) The circumference is [tex]C=226.08\ in[/tex]

Step-by-step explanation:

step 1

Find the area

we know that

The area of a circle (circular tablecloth) is equal to

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

we have

[tex]r=72/2=36\ in[/tex] ------> the radius is half the diameter

[tex]\pi =3.14[/tex]

substitute

[tex]A=(3.14)(36)^{2}[/tex]

[tex]A=4,069.44\ in^{2}[/tex]

step 2

Find the circumference

we know that

The circumference of a circle (circular tablecloth) is equal to

[tex]C=\pi D[/tex]

we have

[tex]D=72\ in[/tex]

[tex]\pi =3.14[/tex]

substitute

[tex]C=(3.14)(72)[/tex]

[tex]C=226.08\ in[/tex]

The numbers you are looking for are 23, 25, and 27. Let's start by defining a variable.  Let x be the first of the three odd numbers.  Since odd numbers are 2 apart, that means that the other two numbers are x + 2 and x + 4.

Now, their sum is x + (x + 2) + (x + 4) which equals 3x + 6.

Decrease that by the second number, x + 2.  That means:  3x + 6 - (x + 2), which is equal to 2x + 4.

So now we know that 2x + 4 = 50, and we can solve that easily:

2x + 4 = 50

2x = 46

x = 23

Therefore, the three odd numbers are 23, 25, and 27. Hope this helps! Please mark Brainliest. Thank you v much! :)

The answer to the problem is the three consecutive odd integers 23, 25, and 27.

Let's solve the problem step by step. We are looking for three consecutive odd integers. A useful way to express consecutive odd integers algebraically is as x, x+2, and x+4, where x is any odd integer.

The problem states that the sum of these integers minus the second one equals 50. This provides the equation: x + (x+2) + (x+4) - (x+2) = 50. Simplifying this equation, we get 2x + 4 = 50. We can further simplify to find that x = 23.

So, the three consecutive odd integers are 23, 25, and 27.

https://brainly.com/question/32448319

#SPJ11