Teachers receive 30% educators discount at a museum. An adult ticket costs $24. How much would a teacher pay for admission into the museum?

Given:

[tex]3(4^x)=5^(x+1)[/tex]

To find:

The solution of the given equation.

Solution:

We have,

[tex]3(4^x)=5^(x+1)[/tex]

It can be written as

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

[tex]3((2^{2x})=5^(x+1)[/tex]      [tex][\because (a^m)^n=a^{mn}][/tex]

Taking log on both sides.

[tex]\log [3((2^{2x})]=\log 5^(x+1)[/tex]

[tex]\log 3+ \log ((2^{2x})=\log 5^(x+1)[/tex]        [tex][\because \log (ab)=\log a+\log b][/tex]

[tex]\log 3+ 2x\log 2=(x+1)\log 5[/tex]      [tex][\because \log x^n=n\log x][/tex]

Putting values of logarithms, we get

[tex]0.477+ 2x(0.301)=(x+1)0.699[/tex]      [tex][\because \log 2 =0.301, \log 3=0.477, \log 5=0.699][/tex]

[tex]0.477+ 0.602x=0.699x+0.699[/tex]

[tex]0.602x-0.699x=0.699-0.477[/tex]

[tex]-0.097x=0.222[/tex]

Divide both sides by -0.097.

[tex]x=\dfrac{0.222}{-0.097}[/tex]

[tex]x=-2.288656[/tex]

[tex]x\approx -2.289[/tex]

Therefore, the value of x is -2.289.

Answer:

49-9i²

Step-by-step explanation:

(7+3i)(7-3i)

expand the brackets

49-21i +21i -9i²

49-9i²

Answer:

There are 6 mini cars and 12 tricycles.

Step-by-step explanation:

In the playground, there is a driving learning area that has mini cars and tricycles. If there are 18 vehicles and 64 tires in all, how many miniature cars and how many tricycles are there?

Given that there are a total of 18 vehicles in the driving learning area.

Let there are x number of the mini car,

so, the number of tricycles = 18-x

As one car has 4 tires, so the total number of car tires = 4x

As one tricycle has 3 tires, so the total number of tricycle tires = 3(18-x)

Given that the total number of tires is 60, so

4x+3(18-x) =60

4x+54-3x=60A

x=60-54=6

So, the total number of mini cars= 6

and the total number of tricycles = 18-6=12

Hence, there are 6 mini cars and 12 tricycles.

Answer:

No :)

Step-by-step explanation:

the .2 is added to 16 so it's.2 bigger

Answer:

No.

Step-by-step explanation:

Because 16 is 16.00, while 16.2 is 16.02.

16.2 is .02 more than 16.

Answer:

800 birds

Step-by-step explanation:

1/4 of the birds = 200

200 x 4 = 800

Answer:

800

Step-by-step explanation:

1/4 of 800 is 200

you can solve this by multiplying 200 by 4. to under stand this concept just multiply the population by the reciprocal

Answer:

It is said that g is increasing when the slope is positive.

Answer:

It is a fifty v fifty chance so it can be either depends on the height you throw or which side you throw it at

Step-by-step explanation:

Answer:

1.875

Step-by-step explanation:

I used a calculator

Answer:

1.36

Step-by-step explanation:

Answer:

hope my answer is helpful to you

plz mark me as brainlist and also follow me

thank you

Answer: The answer is ASA

I hope this helps!

Answer:

The answer is 3500

Step-by-step explanation:

All you have to do is get 175% of 2000. This is 3,500.

Answer:

23.84 feet

Step-by-step explanation:

Solving this question above, we using Trigonometric function tangent = Opposite/Adjacent

Opposite side + h = Height of the tree

We are told that:

A student is standing 20 feet away from the base of a tree. He looks to the top of the tree at a 50 degree angle of elevation. His eyes are 5 feet above the ground.

20 feet = Adjacent side = Distance form the tree

tan 50 = (h+5)/20

Cross Multiply

h + 5 = 20 × tan50

h = 20tan50 - 5

h= 18.835071852

h =18.84

Therefore the height of the tree is calculated as:

18.84+5 feet

=23.84 feet

Answer:

24 feet

Step-by-step explanation:

EZ

Answer:

x = 10

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define Equation

72 = 5x + 22

Step 2: Solve for x

Step 3: Check

Plug in x into the original equation to verify it's a solution.

Here we see that 72 does indeed equal 72.

∴ x = 10 is the solution to the equation.

Answer:

The correct answer would be 4.11

Answer:

5/12

Step-by-step explanation:

The pitch of the roof is 5/12.

Option H is the correct answer.

Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can apply this theorem only in a right triangle.

Example:

The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.

Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

We have,

We know that the pitch of a roof is defined as the ratio of the vertical rise to the horizontal distance, and is typically expressed as a fraction.

In this case, we are given that the roof is 13 feet long, with 5 feet of vertical rise and x feet of horizontal distance.

Therefore,

The pitch of the roof.

Pitch = vertical rise / horizontal distance

Pitch = 5 / x

We don't know the value of x, but we can use the fact that the roof is 13 feet long to solve it.

Since the horizontal distance and vertical rise form the legs of a right triangle, we can use the Pythagorean theorem to find the value of x.

x² + 5² = 13²

x² + 25 = 169

x² = 144

x = 12

Now,

Pitch = 5 / x

         = 5 / 12

Therefore,

The pitch of the roof is 5/12.

Learn more about the Pythagorean theorem here:

https://brainly.com/question/14930619

#SPJ2

Answer: 2w + 4 = 35

Step-by-step explanation:

Carl's two checked bags and his one backpack together weigh 35kg.

Carl's two checked bags have equal weight so both their weight can be denoted as 2w.

Equation is;

2w + 4 = 35

If you were to solve;

2w + 4 = 35

2w = 35 - 4

w = 31/2

w = 15.5kg

Answer: y = 5/2 x + 8

Step-by-step explanation:

Find m using two points (-2,3) and (0,8) = 8-(3) / 0- (-2) = 5/2

y = 5/2 x + b

8 = 5/2 (0) + b

8 = b

y = 5/2 x + 8

Answer: C

Step-by-step explanation:

Answer:

Option C is the correct answer.

Step-by-step explanation:

Let's take 1 point from each graph and make sure that they have the same "x" coordinate. We are going to notice that it does not matter what 2 points with he same "x" coordinate we are going to choose the "y" value of the the point located on the red graph will always be greater by 1. That means that if black graph has the equation (y = f(x)), the red graph is going to have and equation that looks like (y = f(x) + 1). Now we get the following......

y = f(x) + 1

y - 1 = f(x) + 1 - 1

y - 1 = f(x)

So the answer is the option c.

Answer:

−1.9d + 4.6h − 18

Explanation:

8h − 6.9d − 18 + 5d − 3.4h

= 8h + −6.9d + −18 + 5d + −3.4h

[ Combine Like Terms ]

= 8h + −6.9d + −18 + 5d + −3.4h

= (−6.9d + 5d) + (8h + −3.4h) + (−18)

= −1.9d + 4.6h + −18

- PNW

Answer:

105 kg per bag

Step-by-step explanation:

...... ....................

Answer:

Answer is 12 isnt it

Step-by-step explanation:

12×4=48

48+9=57

Answer:

-1

Step-by-step explanation:

Answer:

Slope = difference in y / difference in x

slope = 0 - 2 / 2 -0

slope = -2 / 2

slope -1

Step-by-step explanation:

Answer:

(x,y)=(-8,-1)

Step-by-step explanation:

(2) rearrange

x=-2+6y

-4(-2+6y)+5y=27

8-24y+5y=27

8-19y=27

-19y=19

y=-1

x=-2+6(-1)

x=-2-6

x=-8

Hope this helps :)

Answer: 5¹⁵/₁₆

Step-by-step explanation:

The Wildflower Trail is currently 2³/₈ miles long.

If the city will extend it by 2¹/₂ in 5 years, the length in five years will be;

= 2³/₈ * 2¹/₂

= 19/8 * 5/2

= 95/16

= 5¹⁵/₁₆

Answer:

4.5 units

Step-by-step explanation:

To get the distance we need the coordinates of the points

A is ( 3,1)

B is (-1,-1)

Let A be (x1,y1) and B be (x2,y2)

So applying the formula, we have the distance as;

D = √(-1-3)^2 + (-1-1)^2

D = √(16 + 4)

D = √20

D = 4.5 units

Answer:

Third choice, 3/20

Step-by-step explanation:

Add all the numbers on the right side of the chart together:

16 + 12 + 22 + 15 + 26 + 9 = 100

So they're rolled the dice 100 times, and of that, they got a 4 fifteen times. So it's 15/100, simplify that equation and it's 3/20

Simplifying an equation means making an equation have smaller numbers if possible. For this question 15 and 100 can both be divided by 5, it is also the biggest number they can both be divided by, so u divide both by 5 and it's 3 and 20, making it 3/20

Answer:

[tex]y = x + 2[/tex]

Step-by-step explanation:

Given

The attached graph

Required

Determine the equation

First, pick any 2 corresponding coordinates

[tex](x_1,y_1) = (0,2)[/tex]

[tex](x_2,y_2) = (6,8)[/tex]

Next, calculate the slope (m)

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \frac{8-2}{6-0}[/tex]

[tex]m = \frac{6}{6}[/tex]

[tex]m =1[/tex]

The equation is calculated as:

[tex]y - y_1 = m(x - x_1)[/tex]

Where:

[tex](x_1,y_1) = (0,2)[/tex] and [tex]m =1[/tex]

[tex]y - 2 = 1(x - 0)[/tex]

[tex]y - 2 = (x - 0)[/tex]

[tex]y - 2 = x[/tex]

Make y the subject

[tex]y = x + 2[/tex]