Solve the equation below for x.
log2x + log(2x - 1) = log3x

Answer:

9 1/3, 12 1/2, 14 3/4

Step-by-step explanation:

I assume the formula you’re working with is A=b*h since nothing says otherwise...

((Patio 1))

So you have your area (147) and your base (15 3/4), now you need to plug them in, which should look like this:

147= 15 3/4*h

You need to isolate your h in order to get the missing number, so you should divide both sides by 15 3/4 OR 63/4 ((15*3—>60+3=63))

Dividing by a fraction is the equivalent of multiplying by its reciprocal... so

147 * 4/63 = 588/63 which can be simplified to 84/9 once both the numerator and denominator are divided by 7

In mixed number for it is 9 3/9 which simplified becomes 9 1/3

You solve the other similarly

Diaz family spend $ 20 if they bought 3 adults tickets and 1 children's ticket

Solution:

Let "a" be the cost of each adult ticket

Let "c" be the cost of each student ticket

The Spencer family bought 3 adult tickets and 2 children's tickets for $23.50

Therefore, we frame a equation as:

[tex]3 \times a + 2 \times c = 23.50[/tex]

3a + 2c = 23.50 --------- eqn 1

The Yang family bought 2 adult tickets and 4 children's tickets for $25

Therefore, we frame a equation as:

[tex]2 \times a + 4 \times c = 25[/tex]

2a + 4c = 25 ----------- eqn 2

Let us solve eqn 1 and eqn 2

Multiply eqn 1 by 2

6a + 4c = 47 ---------- eqn 3

Subtract eqn 2 from eqn 3

6a + 4c = 47

2a + 4c = 25

( - ) --------------

4a = 47 - 25

4a = 22

Divide both sides of equation by 4

a = 5.5

Substitute a = 5.5 in eqn 1

3(5.5) + 2c = 23.50

16.5 + 2c = 23.50

2c = 23.50 - 16.5

2c = 7

Divide both sides of equation by 2

c = 3.5

Thus, cost of each adult ticket = $ 5.5

Cost of each student ticket = $ 3.5

How much would the Diaz family spend if they bought 3 adults tickets and 1 children's ticket?

Total cost = 3a + 1c

Total cost = 3(5.5) + 1(3.5) = 16.5 + 3.5

Total cost = 20

Thus Diaz family spend $ 20

Final answer:

The Diaz family would spend $20 for 3 adult tickets and 1 children's ticket at the zoo after solving the system of linear equations given by the Spencer and Yang families' purchases.

Explanation:

Let A be the price of an adult ticket and C be the price of a children's ticket. We are given:

3A + 2C = $23.50 (Spencer family)

2A + 4C = $25 (Yang family)

To solve this system, we can multiply the first equation by 2 and the second equation by 3:

6A + 4C = $47 (Spencer family doubled)

6A + 12C = $75 (Yang family tripled)

Subtracting the first equation from the second gives us:

8C = $28

Dividing both sides by 8 yields:

C = $3.50

Now that we know the price of a children's ticket, we can substitute this value back into one of the original equations to find the price of an adult ticket.

3A + 2(3.50) = $23.50

3A + $7 = $23.50

3A = $16.50

A = $5.50

With the price of both ticket types known, we can now calculate the cost for the Diaz family:

3A + 1C = 3($5.50) + 1($3.50)

3A + 1C = $16.50 + $3.50

3A + 1C = $20

Therefore, the Diaz family would spend $20 if they bought 3 adult tickets and 1 children's ticket.

Answer:

lets consider an example like

20 divided by 2/4 so we can rewrite as

2/4*  x      =20

so , 2*   x     =20*4

2*     x      =80

x=80/2

x=40

similarly,we can write the fraction as (20*4/2)-we can see that reciprocal of the fraction 2/4 is 4/2

x=20*4/2=80/2=40

so, we can say that dividing by a fraction results in the same answer as multiplying by its reciprocal.

Answer:

32.5

Step-by-step explanation:

Take 30% of $25, and get 7.5, then add $7.50 to $25. Now she's making $32.50 an hour.

Answer:

16/x - 4 = 40

16/x = 44

16 = 44x

16/44 = 44x

Hope this helps! pls rate me!

Step-by-step explanation:

Step-by-step explanation:

In order to rationalise the denominator, numerator and denominator must be multiplied by [tex] \sqrt[3]{9x^{10}}[/tex]

Answer:

[tex]Area\ of\ a\ trinagle = \frac{5}{12}x^2[/tex] [tex]or\ 0.42x^2[/tex]

Step-by-step explanation:

Given:

Height of the triangle [tex]h = x[/tex]

Base of the triangle [tex]b=\frac{5}{6}x[/tex]

We need to find the area of the triangle.

Solution:

Using given Formula:

[tex]Area\ of\ a\ trinagle = \frac{1}{2}bh[/tex]

Where:

b = Base of the triangle.

h = Height of the triangle.

Substitute [tex]h = x[/tex] and [tex]b=\frac{5}{6}x[/tex] in equation in given formula.

[tex]Area\ of\ a\ trinagle = \frac{1}{2}(\frac{5}{6})x\times x[/tex]

[tex]Area\ of\ a\ trinagle = \frac{5}{12}x^2[/tex]

[tex]Area\ of\ a\ trinagle =0.42x^2[/tex]

Therefore, Area of the triangle is [tex]\frac{5}{12}x^2[/tex] or [tex]0.42x^2[/tex].

Answer:

-9/4

Step-by-step explanation:

-4/3x-3=1/3x+3/4

-4/3x-1/3x-3=3/4

-5/3x=3/4+3

-5/3x=3/4+12/4

-5/3x=15/4

x=(15/4)/(-5/3)

x=(15/4)(-3/5)

x=-45/20

simplify

x=-9/4

Answer:

Each apples cost about $0.14

Step-by-step explanation:

cost / amount = price per piece

67 / 470 = 0.14

So every apple costs about $0.14

Answer:

t = -8

Step-by-step explanation:

combine like terms, so -3t + 7t = 4t and 34 - 2 = 32

so 4t - 8 = 32 + 9t

then subtract 4t from both sides and subtract 32 from both sides. You will get: -40 = 5t.

Then divide both sides by 5 so you will get -8 = t

Answer: t= -8

Step-by-step explanation:

Answer:

The aquarium needs 56 more gallons to be completely filled.

Step-by-step explanation:

To get the amount remaining you have to first divide 1120 by 100

1120/100=11.2

Then multiply it by 95

11.2*95=1064

You take the maximum amount (1120) and subtract the amount in the tank (1064) to get the amount left.

1120-1064= 56

With 56 gallons as your final answer.

Answer:

Please read the answers below.

Step-by-step explanation:

a. If he rides at a rate of 3 miles per hour, how long will it take?

Time = Distance/Rate

Time = 24/3 = 8 hours

At 4 miles per hour?

Time = 24/4 = 6 hours

At 6 miles per hour?

Time = 24/6 = 4 hours

b. Write an equation that Han can use to find t, the time it will take to ride 24 miles, if his rate in miles  per hour is represented by r.

The equation is the same we used in the part a of the problem:

t = 24/r

c. On graph paper, draw a graph that shows t in terms of r for a 24-mile ride.

The graph is attached.

Answer:

d

Step-by-step explanation:

Answer:

4s+9c

Step-by-step explanation:

6s+9c-2s

-2s. -2s

4s+9

Answer:

Approx. 5.3 miles

Step-by-step explanation:

Answer:

1 necklace is $19!

Step-by-step explanation:

4•$8=$32

$70-$32=$38

$38/2=$19

Answer:

{(-34/7, -16/7)}

Step-by-step explanation:

Rearrange values, multiply to solve for x.

(5) 2y = 3x + 10

(-2) 5y = 4x + 8

Solve for x.

10y = 15x + 50 ↓

-10y = -8x -16

Combine and evaluate.

0 = 7x + 34

Subtract 34 from both sides.

7x = -34

Divide both sides by 7.

x = [tex]\frac{-34}{7}[/tex]

Plugin x value into either equation to solve for y.

2y = (3 × [tex]\frac{-34}{7}[/tex]) + 10

2y = [tex]\frac{-102}{7}[/tex] + 10

2y = [tex]\frac{-32}{7}[/tex]

y = [tex]\frac{-16}{7}[/tex]

Answer:

The number of faculty member is 45.

Step-by-step explanation:

Ratio of faculty members to students = 1 : 15

Number of students = 675

Total = Number students + faculty members

Let the total be t

Let the faculty member be f

Representing the ratio, we have:

[tex]\frac{15}{16} * t = 675\\\frac{15t}{16} = 675\\15t = 16 * 675\\15t = 10800\\\frac{15t}{15} =\frac{10800}{15} \\t = 720[/tex]

Therefore, the total number of both the students and faculty member is 720. To get the number of faculty member:

Total = Number students + faculty members

[tex]720 = 675 + f\\f = 720 - 675\\f = 45[/tex]

The number of faculty member is 45.

Answer: Pedro= 1205. Ricky= 1488

Step-by-step explanation:

It is found that Ricky hits 1202 base and Pedro hits = 1485 base

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

Given that

Pedro + Ricky = 2693 hits

Let Ricky hits = x

So, the Pedro hits will be = x + 283

( x + 283 ) + x = 2693

2 x + 283 = 2693

2 x = 2693 - 283

2 x = 2404

x = 1202

So, the Ricky hits 1202 base

Thus Pedro hits (1202 + 283) = 1485 base

Learn more about equations here;

https://brainly.com/question/25180086

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Answer:

do u mean 5/12

Step-by-step explanation:

Answer:

645.56

Step-by-step explanation:

50000/1000 13.37=673.50

673.50

-27.94

Answer: the answer is 5 feet per second

Step-by-step explanation:

Answer:

The middle point is 3

Step-by-step explanation:

Yo sup??

The mid point can be found out by taking the sum of the two values and dividing it by 2

mid point=(12+(-7))/2

=5/2=2.5

Hope this helps

Answer:

9ft wide

Step-by-step explanation:

First we convert it to ratios

[tex]\frac{6}{x} \frac{2}{3}[/tex]

Then we cross-multiply

6*3=2x

Multiply 6 and 3

18=2x

Solve for x

x=18/2

x=9

Answer:

14

Step-by-step explanation:

4+3=7

4/2=2

7•2=14

Answer:22

Step-by-step explanation:

66/3=22 so each part is 22 1 part for adults is 22

I multiply 1200 times 5 and yet 6000 because it says what is the height

Answer:

Option C

Step-by-step explanation:

We are given that

[tex]f(x)=-x[/tex]

The line passing through the points (0,0),(-6,6) and (6,-6).

[tex]g(x)=2x[/tex]

The line passing through the points (-3,-6),(0,0) and (3,6).

We have to find the graph of (g-f)(x).

[tex](g-f)(x)=g(x)-f(x)=2x-(-x)=2x+x[/tex]

[tex](g-f)(x)=3x[/tex]

Substitute x=0

[tex](g-f)(0)=3(0)=0[/tex]

[tex](g-f)(2)=3(2)=6[/tex]

[tex](g-f)(-2)=3(-2)=-6[/tex]

[tex](g-f)(-6)=3(-6)=-18[/tex]

Option C is true.

Answer: It's about 10.34%

Step-by-step explanation:

Answer:

40.54

Step-by-step explanation:

32.43×3%=2.27

32.43×18%=8.107.

2.27+5.84=8.11.

32.43+8.11=40.54 total paid.