Solve the logarithmic equation algebraically ?

Kellie's original number given the analogy and corresponding equation is 13

let

(x × 2) × 3 = x + 65

2x × 3 = 65 + x

6x = 65 + x

6x - x = 65

5x = 65

x = 65/5

x = 13

check:

6x = 65 + x

6(13) = 65 + 13

78 = 78

Therefore, the unknown number, x is 13

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Step-by-step explanation:

the perimeter is

2×length + 2×width = 86

length = 3×width

now we use the second equation as variable identity in the first equation :

2×3×width + 2×width = 86

6×width + 2×width = 86

8×width = 86

width = 86/8 = 43/4 = 10.75 cm

length = 3×width = 3×10.75 = 32.25 cm

Check the picture below.

Answer:

Step-by-step explanation:

Explanation

On a 6 sided die, there are three even numbers (2,4,6)

That's 1/2 the number on the die.

So getting 6 even numbers is

P(6) = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 0.00781

Where did that extra 1/2 come from? Well one of the numbers thrown was an odd number, and it has to be counted.

P(7) = the same answer.                            0.00781

Total                                                           0.0156

Answer:

Ernest is wrong, because the sandwich can be made in 6 different ways (lunch > sandwich: white bread > cheese, pickles, mayonnaise ; wheat bread > cheese, pickles, mayonnaise) and the lunch can be made in 8 different ways.

Answer:

7

Step-by-step explanation:

[tex]\dfrac 13(15+6)\\\\\\=\dfrac{21}3\\\\\\=7[/tex]

Work Shown:

5x-6 = 44

5x-6+6 = 44+6 ... see note 1

5x = 50

5x/5 = 50/5 ... see note 2

x = 10

Using proportions, it is found that it's value before the 2-day drop was of 264 points.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, the value dropped by 25%, that is, it was 75% of the original amount, and the dropped value was of 198 points, hence the original amount was:

0.75x = 198

x = 198/0.75

x = 264

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Answer:

No solution

Step-by-step explanation:

[tex]3(5x - 4) < 15x \\ 15x - 12 < 15x \\ 15x - 15x < 12 \\ 0 < 12[/tex]

Answer:

x = z - m + y

Step-by-step explanation:

Given:

[tex]\displaystyle \large{z = m+x-y}[/tex]

To solve for x-term, we have to isolate it. We can do by subtracting m-term both sides and add y-term both sides.

[tex]\displaystyle \large{z-m+y=m+x-y-m+y}\\\\\displaystyle \large{z-m+y=x}\\\\\displaystyle \large{x=z-m+y}[/tex]

Therefore, the answer to this question is x = z - m + y

Please let me know if you have any questions regarding my answer or explanation!

Vowels = {a, e, i, o, u}

There are 5 vowels out of 26 letters in the English alphabet. This leaves 26-5 = 21 consonants.

The theoretical probability of getting a consonant is 21/26 = 0.8077 = 80.77% approximately

Wayne found the empirical probability of a consonant as 60% which is quite a distance away from the 80.77% mentioned. The discrepancy is likely because vowels are tended to be used quite often in many words.

Words that are composed of consonants only are quite rare, but they do happen. Example: "fly" is a word with only consonants. I'm considering y to be a consonant.

Answer:

Pretty sure it would be sin(0) cos (0) - sin^2(0)

The values that represent those having type O blood are the values from 000 to 449.

RNG refers to a random number generator, this means that from 000 to 999 (a total of 1000 numbers) each has the same probability of being randomly selected by the program.

Then, if we want to represent a probability of the 45%, then 0.45 of the number of elements must be assigned to what we want to represent (having type O blood).

0.45*1000 = 450

Then we can assign the first 450 numbers to have type O blood, the first 450 numbers are: {000, 001, ..., 449}

So the values that represent those having type O blood are the values from 000 to 449.

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Answer:

  $3.65

Step-by-step explanation:

The two purchases describe relations between quantity and price that can be used to write a system of equations for the prices of the hockey pucks and hockey sticks. These equations can be solved to find the price of a hockey puck.

__

Let x and y represent the prices of a hockey puck and a hockey stick, respectively. The two purchase values are ...

  5x +3y = 23.50

  5x +y = 20.00

Rearranging the second equation, we have an expression for y:

  y = 20.00 -5x . . . . . . subtract 5x from both sides

Substituting this into the first equation gives ...

  5x +3(20.00 -5x) = 23.50 . . . . . substitute for y

  -10x +60.00 = 23.50 . . . . . . simplify

  x -6.00 = -2.35 . . . . . . . . divide by -10

  x = 3.65 . . . . . . . . . . . add 6

One hockey puck costs $3.65.

[tex]~~~~~~~~\dfrac{1}{R} = \dfrac{1}{R_1} + \dfrac 1{R_2}\\\\\\\implies \dfrac 1{R_2} = \dfrac{1}{R } - \dfrac 1{R_1}\\\\\\\implies \dfrac 1{R_2} = \dfrac{R_1 -R}{RR_1}\\\\\\\implies R_2 = \dfrac{RR_1}{R_1-R}\\\\\\\text{When}~ R= 24~ \Omega ~ \text{and}~ R_1 = 30~ \Omega,\\\\R_2 = \dfrac{24 \times 30}{30-24}~\Omega\\\\\\~~~~~=\dfrac{720}{6}~ \Omega\\\\\\~~~~= 120~ \Omega[/tex]

Answer:

Step-by-step explanation:

By reading the box plot :

The median is the number that corresponds to the line in the center of the box which is 15 in our case.

Answer:

(- 5, 4 )

Step-by-step explanation:

under a reflection in the line y = x

a point (x, y ) → (y, x ) , then

G (4, - 5 ) → G' (- 5, 4 )

The coordinates of the image of vertex G are (-5, 4)

When reflecting a figure in a line or in a point, the image is congruent to the pre image. A reflection maps every point of a figure to an image across a fixed line. The fixed line is called the line of reflection.

here, we have,

Let us revise some cases of reflection

If the point (x, y) reflected across the x-axis , then its image is (x, -y)

If the point (x, y) reflected across the y-axis , then its image is (-x, y)

If the point (x, y) reflected across the line y = x , then its image is (y, x)

If the point (x, y) reflected across the line y = -x , then its image is (-y, -x)

From the given figure

∵ The line of the reflection is y = x

→ That means we will switch the coordinates of the point to find its image

∵ The coordinates of vertex G are (4, -5)

∴ The x-coordinate = 4 and the y-coordinate = -5

→ Switch the two coordinates

∴ The coordinates of its image G' are (-5, 4)

∴ The coordinates of the image of vertex G are (-5, 4)

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19x+12y=17

step 1: move the thing that you're looking for to the left side and all the rest to the right side:

(19x +12y)-19x = 17 -19x

12y = 17 -19x

step 2: to find y, you need to get rid of 12. to do so you need to devide everything by that number:

(12y)/12 = 17/12 -19/12 x

y= 17/12 -19/12 x

step 3: simplify of possible. ( in this exercise it isnt)

step 4: rearange the equation if necessary

y= 17/12 + -19/12x

y= -19/12x + 17/12

Answer:

A.

Step-by-step explanation:

Wren is at the grocery store buying fruit. She buys x pounds of apples for $1.68 per pound. She buys 2 fewer pounds of grapes for $2.48 per pound. The cost of the fruit, before tax, is $13.76. How many pounds of each fruit is she buying?

A.

2.8 pounds of apples and 4.8 pounds of grapes

B.

3.3 pounds of apples and 1.3 pounds of grapes

C.

3.8 pounds of apples and 1.8 pounds of grapes

D.

4.5 pounds of apples and 2.5 pounds of grapes

Answer:

$ 20384.32  

Step-by-step explanation:

Decreasing by 4 % each year means it retains 96 %

  25 000 ( .96)^5 = 20384.32

Step-by-step explanation:

please mark me as brainlest

An absolute value inequality to find the range of SAT mathematics test scores within one standard deviation of the mean is; |x – 515| ≤ 114

A) We are told that;

Mean score = 515

Standard deviation = 114

We are now given that people within one deviation of the mean have SAT math scores that are no more than 114 points higher or 114 points lower than the mean. Thus, the absolute value inequality is;

|x – 515| ≤ 114

B) The range of scores to within ±2 standard deviations of the mean is;

Range = 515 ± 2(114)

Range = 287 to 743

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Answer:

827/200

Step-by-step explanation:

Can't explain, it is I think.

Answer:

its A im really smart and because im smart

The vertex form of all expressions is given below.

We have given that the expressions

We have to write the function in vertex form.

The vertex form of a quadratic function is given by f (x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

Therefore the first equation

[tex]f(x)=(x-1)^2-7[/tex]

it can be written as

[tex]f(x)=1(x-1)^2+(-7)[/tex]

The second equation can be written as

[tex]f(x) = (x+1)^2 -7[/tex]

vertex for is,

[tex]f(x)=1(x-(-1))^2+(-7)[/tex]

The third equation is,

[tex]f(x) = (x -1)^2 - 5[/tex]

Vertex form is,

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

Forth equation is,

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

Vertex form is,

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

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Answer:

4(9^0+48(2)^-3) I think it's like this

Answer:

Answer: A. The contrapositive of the statement will be :

Step-by-step explanation:

The contrapositive of an if-then statement "p then q' is given by :

"If not q then not p".

The given statement is

Then the contrapositive of the statement will be :

Hence, A is the right option.

Answer:

50

Step-by-step explanation:

90+40= 130

There are 180 degrees in a triangle.

180- 130 = 50

Answer:

irrational

Step-by-step explanation:

It cant be square rooted perfectly.