45 POINTS & BRAINLIST -- PLEASE HELP
Convert the following functions.
A) Convert the exponential function, 12^3=x^4 y^3 z^6, to its corresponding logarithmic function.
B) Write the log form from Part A into the expanded log form. **expression must be fully expanded for full credit**

[tex]7x + 8 = ( - 5x) + 32 \\ 7x + 5x = 32 - 8 \\ 12x = 24 \\ x = \frac{ \cancel{24} {}^{ \: \: \: 2} }{ \cancel{12}}\\x=2 [/tex]

[tex] \Large{\boxed{\sf x = 2}} [/tex]

[tex] \\ [/tex]

Given equation:

[tex] \sf 7x + 8 = -5x + 32 [/tex]

[tex] \\ [/tex]

Substract 8 from each side :

[tex] \sf 7x + 8 - 8 = -5x + 32 - 8 \\ \\ \sf 7x = -5x + 24 [/tex]

[tex] \\ [/tex]

Add 5x to both sides :

[tex] \sf 7x + 5x = -5x + 24 + 5x \\ \\ \sf 12x = 24 [/tex]

[tex] \\ [/tex]

Divide both sides by 12 :

[tex] \sf \dfrac{12x}{12} = \dfrac{24}{12} \\ \\ \\ \boxed{\boxed{\sf x = 2}} [/tex]

[tex] \\ \\ [/tex]

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Answer:

$43.30

Step-by-step explanation:

What we know,

3 hamburgers = $12.99

Coleman wants to know how much would he have to pay for 10 hamburgers,

In order to find out how much 10 hamburgers cost, you need to find out how much 1 hamburger costs,

To find how much 1 hamburger costs divide 12.99 by 3,

12.99/3

= 4.33

Now we know that 1 hamburger cost $4.33,

Now time to find out how much 10 hamburgers cost,

Multiply 4.33 by 10,

4.33 × 10

= 43.30

Therefore it cost $43.30 for 10 hamburgers.

Answer:5.4

Step-by-step explanation:

so first you cross multiply and then you solve for x from there. You shold get 5.385164807. But you need to round that so I rounded to the nearest tenth, which would be 5.4

[tex]~~~~~~4(2x-3)(5x+2) = 0\\\\\implies (2x -3)(5x+2) = 0\\\\\implies 2x -3=0 ~~~~~~\text{or}~~~~~~ 5x +2 = 0\\\\\implies 2x =3 ~~~~~~~~~~~\text{or}~~~~~~ 5x = -2\\\\\implies x = \dfrac 32 ~~~~~~~~~~~~ \text{or}~~~~~~ x = -\dfrac 25\\\\\text{Hence,}~ x = \dfrac 32, ~ x = -\dfrac 25[/tex]

Answer:

36 pizzas

no sauce left over

Step-by-step explanation:

Take the total amount and divide by 4

144/4 =36

The cook can make 36 pizzas

Ther is no sauce left over

Answer:

B

Step-by-step explanation:

It goes up by one, to the right by 2. Or flip that, Im dyslexic

Answer:

B!!

Step-by-step explanation:

Hope nthis helps!!!!!

Step-by-step explanation:

out of the 21 students, 8 do not play neither basketball nor baseball.

so, 13 students play at least one of these games.

10 play basketball, and 9 play baseball. that would be 19 together. but we have only 13 players.

that means 6 students (19 - 13) must play both games.

remember, a probability is always

desired cases / possible cases

so, when we are looking for the students, who play both games, we have 6 desired cases out of a total of 21.

and the probability to pick one of them is therefore

6/21 = 2/7 = 0.285714286...

Answer:

one can would be about $0.41

Step-by-step explanation:

Take $2.46 and divide it by 6 because that is the number of cans in the pack, the answer is $0.41 per can.

Answer:

x=7.16 or0.84

Step-by-step explanation:

The solution is in the image

The game is an illustration of probability, and the probability that each player wins is 1/12

From the question, we have the following parameters:

Number of a pair of numbers = 3

A die has 6 possible outcomes.

So, the probability of getting the first pair is:

P1 = 1/6

The probability of getting the second pair is:

P2 = 1/6

The probability of getting the first and the second pairs is

P = 1/6 * 1/6

Evaluate

P = 1/36

There are three pairs of numbers in total.

So, the probability of winning is:

P(Win) = 3 * 1/36

Evaluate

P(Win) = 1/12

Hence, the probability that each player wins is 1/12

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Answer:

1/12.

Step-by-step explanation:

The probability that each player has of winning is 1/12.

The location with the greatest amount of rainfall is Beaumont, while the location with the least amount is El Paso.

The first step is to make sure to use the same units. Due to this, let's convert everything to meters.

Based on this, Beaumont has the greatest amount of rainfall and El Paso has the lowest amount of rainfall.

The ratio for these places are 1.5 to 0.2 or 1.5/ 2 = 0.7. This ratio implies that there is a difference of 0.7 meters in the amount of rainfall in these places.

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The other person is right, I used this and it worked.

Answer:

A

Step-by-step explanation:

Slope = +1

Y-int = 2

Answer:

b

Step-by-step explanation:

64 = 2x^2

32 = x^2

x = 4√2

ans is b

Answer:

B. supplementary angles

Step-by-step explanation:

what is the result of the addition of 20 and 6

[tex]\boxed{\sf twenty~plus~six }\boxed[/tex]

Answer:

31.9 grams

Step-by-step explanation:

35 - 3.1 = 31.9 grams

Hope this helped you!

The coordinates of solution of the system of equation which is obtained by plotting the equation on the graph is (-2,2).

A system of equation is the set of equation in which the finite set of equation is present for which the common solution is sought.

The first equation given in the problem is,

[tex]x+y=0[/tex]

Rearrange it,

[tex]y=-x[/tex]                    .....1

The second equation given as,

[tex]-3x+4y=14[/tex]

Rearrange it,

[tex]-3x+4y=14\\4y=14+3x\\y=\dfrac{14+3x}{4}[/tex]                    .....2

Plot the graph of both the line as shown below in the attached image. In this equation the solution is the point of intersection which is (-2,2).

Thus, the coordinates of solution of the system of equation which is obtained by plotting the equation on the graph is (-2,2).

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Answer:

59304

Step-by-step explanation:

4.11x 10⁴=41100, 9.6 =( 1+9.6/100)=1.096

x(n)−population after n years

x(n)=x(0)×1.096^n=41100x1.096^n

x(4)=41100×1.096⁴=59304.007

= 59304

An equation represents the town's population after 4 years is [tex]x(4)=4.11\times10^4(1+\frac{9.6}{100})^4[/tex].

Given that, a town has a population of [tex]4.11\times10^4[/tex] and shrinks at a rate of 9.6% every year.

If a constant rate of growth be R% per annum, then population after n years = [tex]P(1+\frac{R}{100} )^n[/tex]

Now,

[tex]x(4)=4.11\times10^4(1+\frac{9.6}{100})^4[/tex]

⇒ [tex]x(4)=4.11\times10^4(1+0.096)^4[/tex]

⇒ [tex]x(4)=41100\times(1.096)^4[/tex]

⇒ x(n)=41100×1.443

⇒ x(n)=59307.3

Therefore, an equation represents the town's population after 4 years is [tex]x(4)=4.11\times10^4(1+\frac{9.6}{100})^4[/tex].

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Answer: 15 dimes 12 nickels 12 pennies 7 quarters?

Step-by-step explanation:

Answer:

823

Method 1

Break the three numbers into hundreds, tens and units, then add these separately (starting with the units)

197 = 1 hundred, 9 tens, 7 units

203 = 2 hundreds, 0 tens, 3 units

423 = 4 hundreds, 2 tens, 3 units

Units: 7 + 3 + 3 = 13

Tens: 9 + 2 = 11 tens = 110

Hundreds: 1 + 2 + 4 = 7 hundreds = 700

Add these together: 700 + 110 + 13 = 823

Method 2

First add 203 to 197:

Borrow the 3 from 203 and add it to 197:  197 + 3 = 200

Add the remaining 200:  200 + 200 = 400

Now add 423 to 400:  400 + 423 = 823

⇒ 203 + 197 + 423 = (203 + 197) + 423

                                = 400 + 423

                                = 823

Answer:

First you have to multiply negative four in parentheses, then add minus two

-4×(-8+3x)=32-12x

2+32-12x=34-12x

34-12x=82

-12x=48

x=-4

Answer:

70 kilometers

Step-by-step explanation:

if 1 cm is equal to 20 kilometers, then 3 cm would be 60 kilometers, and 0.5 cm would be 10 kilometers. making 3.5 cm 70 kilometers.

The length which result in a ratio closest to the golden ratio is equal to  7.5 inches and 4.5 inches. Option C is correct.

The line segment is made with two end points. Length of a line segment is the distance of both the ends of it.

A 12 inch line segment is divided into two parts. Suppose the line segment is AC which is divided into AB and BC parts. Thus,

AB+BC=AC

AB+BC=12                   ....1

The value of golden ratio is equal to 1.618. It can also be given as (1+√5)/2. The ratio of both segment is equal to golden ratio. Thus

[tex]\dfrac{AB}{BC}=\dfrac{AC}{AB}=\dfrac{1+\sqrt{5}}{2}\\\dfrac{12}{AB}=1.618\\AB=7.4166 \rm\; in[/tex]

Put this value in equation one as,

AB+7.4166=12    

AB=4.5834

The length which result in a ratio closest to the golden ratio is equal to  7.5 inches and 4.5 inches. Option C is correct.

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Answer:

5x² + 9x - 10

Step-by-step explanation:

To completely simplify this equation, add all like terms.

3x² - 5 + 1 + 2x² + 9x - 6

= 5x² + 9x - 10

hope this helps :)

Any smooth curve connecting two points is called an arc. The correct option is c.

Any smooth curve connecting two points is called an arc. The arc length is the measurement of how long an arc is. The length of an arc is given by the formula,

[tex]\rm{ Length\ of\ an\ Arc = 2\times \pi \times(radius)\times\dfrac{\theta}{360} = 2\pi r \times \dfrac{\theta}{2\pi}[/tex]

where

θ is the angle, that arc creates at the centre of the circle in degree.

If the central angle has a measure of π/2(90°), then the length of the arc will be one-fourth of the total, while if the measure of the angle is π(180°), then the length of the arc will be half of the total.

Similarly, if the measure of the angle is 3π/4, then the length of the arc will be three-fourth of the total, while if the measure of the angle is 2π(360°), then the length of the arc will be 2πr.

Hence, the correct option is c.

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The area of the considered trapezoid  PQRS in simplest radical form is given by: Option c: 256 + 128√3 (in sq. units)

The area of a trapezoid is the half of the product of sum of its parallel sides to the height of that trapezoid (the distance between those parallel sides).

Thus, if we have:

Length of its parallel sides = 'a' and 'b' units respectively

Perpendicular distance between its parallel sides = 'h' units,

Then, we get:

[tex]A = \dfrac{1}{2}\times(a+b) \times h \: \rm unit^2[/tex]

Consider the figure attached below, which is a bit more labeled figure of the given trapezoid.

We constructed PA perpendicular to the level of SR, and therefore, as SR is parallel to PQ, we have PA perpendicular to PQ too.

Similarly, QB is constructed perpendicular to both PQ and SR.

Thus, for PQBA, all pair of adjacent sides are perpendicular to each other, therefore its a rectangle.

Sum of parallel sides = Length of PQ + Length of SR

= 24 + |SR| = 24 + |SB| + |BR| = 24 + |AS| - |AS| + |SB| |+ |BR|

= 24 + |AS| + |SB| + |BR| - |AS| = 24 + |AB| + |BR| - |AS|

Due to PABQ being a rectangle (its four sides are such that adjacent sides are perpendicular to each other), we have |PQ| = |AB| = 24 units.

Thus, we get:

Sum of parallel sides = 24 + |AB| + |BR| - |AS| = 48 + |BR| - |AS|

Perpendicular distance between its parallel sides = |PA| = |QB|

Thus, we need to find the values of 3 line segments, which are:

|BR|, |AS|, and |PA| (instead of |PA|, we can find |QB| too, since both are of same length).

From the perpective of angle R(interior) in right triangle RBQ, we know the side RQ's length (32 units), and want length of BR.

Thus, its hypotenuse and base from the perspective of angle R (interior).

Thus, we can use cosine ratio or secant ratio. Let we use cosine ratio.

Then, we get:
[tex]\cos(30^\circ) = \dfrac{|BR|}{|RQ|} \\\\|BR| = 32 \times \cos(30^\circ) = 32 \times \dfrac{\sqrt{3}}{2} = 16\sqrt{3}\: \rm units[/tex]

For the same triangle as in case 1 (ie RBQ), but now taking the sine ratio, we get:

[tex]\sin(30^\circ) = \dfrac{|BQ|}{|RQ|} \\\\|BQ| = 32 \times \sin(30^\circ) = 16 \: \rm units[/tex]

This is same as |PA| because of PQBA being a rectangle.

The angle PSA is supplement of angle PSR as both joined make a straight line ASR. Thus, we get:
[tex]m\angle PSA + m\angle PSR = 180^\circ\\m\angle PSA = 180^\circ-135^\circ = 45^\circ[/tex]

Thus, for the triangle PSA, similar to the first case or second case, but now using tangent ratio as we've got |PA| = |QB| = 16 units, we get:

[tex]\tan(m\angle PSA) = \dfrac{|PA|}{|AS|}\\\tan(45^\circ) = \dfrac{|PA|}{|AS|} \\\\|AS| = 1 \times 16 = 16 \: \rm units[/tex]

Thus, we get:

Sum of parallel sides = 48 + |BR| - |AS| = 48 + 16√3 - 16 = 32 + 16√3 units

Perpendicular distance between its parallel sides = |PA| = |QB| = 16 units.

Thus, Area of the trapezoid PQRS is evaluated as:

[tex]A = \dfrac{1}{2} \times \text{Sum of parallel sides} \times \text{Distance between those sides}\\A =\dfrac{1}{2} \times (32 + 16\sqrt{3}) \times 16 \\\\A = 256 + 128\sqrt{3} \: \rm unit^2[/tex]

Thus, the area of the considered trapezoid  PQRS in simplest radical form is given by: Option c: 256 + 128√3 (in sq. units)

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Answer:

no

Step-by-step explanation:

(- 3)² = - 3 × - 3 = 9 ≠ -9

Answer:

no , see below

Step-by-step explanation:

when you raise a number to a power, you multiply the number by itself the amount of times the power is. so if (-3) has a power of 2 , we multiply -3 by itself twice.

so we get -3 × -3

a negative times a negative is a positive

so -3 × -3 = 9 , not -9