the difference of 13 and m

after simplifying the logarithm expression log₆ 8 + 2log₆ 3 + log₆ 12 - log₆ 24, we get the result as log₆ 36.

We are given the logarithm expression as:

log₆ 8 + 2log₆ 3 + log₆ 12 - log₆ 24

Now, we can also write 2log₆ 3 as:

2log₆ 3 = log₆ 3²

So, the logarithm expression will become:

log₆ 8 + log₆ 3² + log₆ 12 - log₆ 24

Now, we will use the property that is:

logₐ x + logₐ y = logₐ (x × y)

So, we get the logarithm expression as:

log₆ ( 8 × 3² × 12   / 24)

=log₆ (8 × 9 × 12  / 24)

= log₆ (36)

= log₆ 36

Therefore, after simplifying the logarithm expression log₆ 8 + 2log₆ 3 + log₆ 12 - log₆ 24, we get the result as log₆ 36.

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Answer:

33 square meters per hour

Step-by-step explanation:

The approximate number of grains of salt it would take to reach the height of Mt. Everest is; 0.2963 * 10⁸

We are given;

Approximate length of a grain of salt = 9.8 * 10⁻⁴ ft

Approximate height of Mt. Everest = 2.9035 * 10⁴ ft

Now, we want to know the approximate number of grains of salt it would take to reach the height of Mt. Everest. To get this it means we have to divide the Approximate height of Mt. Everest by the Approximate length of a grain of salt.

According to Laws of exponents, we know that;

x³/x² = x^(3 - 2) = x¹

Thus;

Approximate number of grains of salt it would take to reach the height of Mt. Everest = (2.9035 * 10⁴)/(9.8 * 10⁻⁴) = (2.9035/9.8) * (10⁴⁻⁽⁻⁴⁾) = 0.2963 * 10⁸

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The number positioned at point A is -4.25.

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.

This ultimately implies that, a number line can be used to compare two numbers such as 4 and 1. Also, a number line typically increases in numerical value towards the right and decreases in numerical value towards the left.

In this scenario, the given number line uses a scale of 1:0.25. Therefore, the number (numerical value) that is placed at point A is given by:

Point A = -4.5 - 0.25

Point A = -4.25.

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The value of x that makes this equation (X-2)/2= (X+4)/4  to be true is 8.

An equation ca be described as the mathematical terms which can contains different digits as well we a as alphabet and it can simplified so that a particular expression or term can be found, in the given equation we were told to find the value of x by simplify the equation which is done below.

(X-2)/2= (X+4)/4

Then if we cross multiply we will have

(4x - 8) =(2x+8)

then we can simplify further and collect the like terms which is

2x=16

x=8

There, the correct option is B

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Answer:

The answer is 1

I hope this helps

The image is (−8,−1). See explanation.

Explanation:

To find an image of P(x,y) in translation Ta,b you add a and b to x and ycoordinates respectively, so the image is:

Ta,b(x,y)=(x+a,y+b)

Here we can write that:

T−3,−2(−5,1)=(−5−3,1−2)=(−8,−1)

The value of the first number is 9 , and

the value of the second number is 8 .

In the question ,

statements about two numbers is given ,

let the first number be x ,

let the second number be y .

According to the first statement " One number is one more than a second number "

translating it into the equation form , we get

x=y+1      ...(i)

According to the second statement which states " Five times the first is 3 less than 6 times the second "

translating it into the equation form , we get

5*x = 6*y - 3

5x = 6y - 3

Substituting the value of x from equation (i) , we get

5(y+1) = 6y - 3

5y + 5 = 6y - 3

6y-5y = 5+3

y = 8 ,

substituting  y=8 in the the equation (i) ,

x = 8 + 1

x = 9

hence the first number = 9  and the second number = 8 .

Therefore , the value of the first number is  9, and

the value of the second number is 8 .

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The distance between the starting point and the second obstacle is 13 meters.

And the total length of one lap is equal to the perimeter of the triangle, which measures 30 meters.

We can see that this distance is equal to the hypotenuse of the triangle on the image.

The two legs measure:

5 meters and 12 meters.

Then using the Pythagorean theorem we can write:

d^2 = 5^2 + 12^2

d = √(5^2 + 12^2) = 13

So the distance between the starting point and obstacle 2 is 13 meters.

b) This will be the perimeter of the triangle, it is:

P = 13 m + 12m + 5m = 30m

One full lap has a length of 30 meters.

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After approximately 1.4 seconds will the ball reach the ground.

The relation between height and the time in seconds is,

y = -4.9x² + 9.8

Here y represent height in meters and x is time in seconds.

Let us assume that the origin is on the ground,

Now we know,

If the ball is dropped from the top at t = 0.

It will reach down to the ground after x seconds.

When it will down to the ground, and the value of y will become zero,

We can write,

y = -4.9x² + 9.8

0 = -4.9x² + 9.8

4.9x² = 9.8

x² = 2

x = √2

x = 1.41 seconds.

The time taken by ball to reach down to the ground is 1.41 seconds.

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166.25E + 4500 cells will be present in the sample after 5 days.

Given,

Cells 24% compounded continuously,

A sample of the virus has 125 cells.

To find:

No cells will be present in the sample after 5 days

Solution:

a = p ( 1 + r/n)nt

a = 125 ( 1 + 24/24)^24*5

a = 125(2)^120

a = 125 * 1.3292279957849E+36

a = 166.25E + 4500

166.25E + 4500 cells will be present in the sample after 5 days.

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The accuracy thresholds that apply when a number has been rounded or shortened are known as error intervals. In other words, they represent the range of values that a number may have taken had it not been rounded off or truncated.

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The inequality that show the amount of water that each member uses is 7x + 5785.23 ≤ 11375.50.

1) Place all terms of the inequality on the same side.

2) Replace the sign of inequality with the sign of equality.

3) Solve the equation, that is, find its root.

4) Study the sign of the equation, identifying the values ​​of x that represent the solution of the inequality.

Let x represent the amount of water each member uses monthly. The Wilson family is a family of 7 people. They have used 5,785.23 gallons of water and cannot exceed 11,375.50 gallons per month. Hence:

7x + 5785.23 ≤ 11375.50

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Answer:

Step-by-step explanation:

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Answer:

The area of Ava's closet is 2 square feet.

Step-by-step explanation:

The area of the bedroom is 36 and it is 6 times as many square feet as her closet. They are basically saying that the closet has 1/6th the area of the bedroom.

Now we can form an equation to find the area of her closet.

36 ÷ 6 = 6

So, therefore, the area of the closet is 6 square feet.

We know the width of the closet, which is 3 feet. Since the formula of area for her closet is Length × Width, we can form an equation for this.

X in this equation is what we are trying to solve for, which is the length of the closet.

X = 6 ÷ 3

X = 2

So, therefore, the area of Ava's closet would in the end be 2 square feet.

Let me know if you have any questions! :)

The equation of the linear function represented by the given table in slope intercept form is y = 2x - 2.

The equation of line can be determine using the slope-intercept formula;

y = mx + b

Where m is slope and b is the y-intercept.

From the given table, we use to points;

Point 1( -1, -4 )

Point 2( 1, 0 )

First, we find the slope of the line.

Slope m = (y₂ - y₁) / (x₂ - x₁ )

Slope m = ( 0 - (-4) ) / (1 - (-1) )

Slope m = ( 0 + 4) ) / (1 + 1) )

Slope m = 4 / 2

Slope m = 2

Next, we find the y-intercept b, using a slope m = 2 and a point ( -1, -4 ).

y = mx + b

-4 = 2(-1) + b

-4 = -2 + b

b = -4 + 2

y-intercept b = -2

Now that we have the slope m and y-intercept b, plug the values into to y = mx + b to determine the equation of line.

y = mx + b

y = 2x + (-2)

y = 2x - 2

Therefore, the equation of the linear function is y = 2x - 2.

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Prove that x = 50 in the following equation: 1/5x – 5 = 5

Write the equation:

1/5x – 5 = 5

Add 5 to both sides:

1/5x – 5 + 5 = 5 + 5

1/5x = 10

Multiply each side by 5:

5 × 1/5x = 10 × 5

–5 + 5 cancels out, leaving you with:

1x = 10 × 5

1x = 50

Divide both sides by 1 to get x:

1x/1 = 50/1

The 1 cancels out:

x = 50/1

Answer:

x = 50 ✔

Check your work by plugging in 50 as x:

1/5x – 5 = 5

1/5 × 50 – 5 = 5

Multiply:

1/5 × 50/1 – 5 = 5

50/5 – 5 = 5

Get rid of the fraction by dividing:

50 ÷ 5 = 10

10 – 5 = 5

Subtract:

10 – 5 = 5

5 = 5 ✔

I have just proven that x = 50 because the answer I got when I checked my work was balanced. Hope that helps! Have an amazing rest of your day! :)

The number of calories in 6 cups of cereal are 960 calories.

Given that:-

Number of calories in 3/4 cups of cereal = 120 calories

We have to find the number of calories in 6 cups of cereal.

We will use the unitary method in this question.

Number of calories in 1 cup of cereal = 120*(4/3) = 160 calories

Hence,

Number of calories in 6 cups of cereal = 160*6 = 960 calories

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Considering the numerical representation of integers with n bits, it is found that 8 bits would have to be set aside in order to store the number of high school students taking CS105 across the nation.

For this problem, we work with unsigned numbers, excluding negatives, as the number of students is a discrete amount that starts with 0 and increases by 1 for each new student.

For unsigned integers with n bits, we have that:

For this problem, we want to represent an amount of 220, hence the number of bits needed is found as follows:

2^n - 1 ≥ 220

2^n ≥ 221

log2(2^n) ≥ log(2)(221)

n ≥ 7.8.

The number of bits cannot be a decimal amount, hence n is rounded up, and thus, 8 bits are needed to represent the amount.

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Inversely proportion - The work out value of R and A is 3.6 and 2 respectively.

What is inversely proportion?

They are said to be inversely proportional when one quantity's value rises relative to another's decline or vice versa. It implies that the two quantities behave inherently differently. For instance, time and speed have an inverse relationship. The time decreases as you increase the speed. Inverse proportion, varying inversely, inverse variation, and reciprocal proportion are additional terms used here to describe this kind of proportion.

Given, R [tex]\alpha[/tex] 1/A

R = k/A

When R = 12 and A = 1.5

12= k× 1.5

k= 18

Now, when A=5, R= 18/5 = 3.6

And when R= 9, A = 18/9=2

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Answer: 4.20

Step-by-step explanation:

6.30 / 3 = 2.10

2.10 x 2 = 4.20

The percent error for the batteries is 20%

Estimated defective batteries as per Saif = 12 batteries

Actual defective batteries = 10

Percent error is given by the formula:

Percent error = (E-T/E)*100

where E is the experimental value and T is the theoretical value

Substituting the values in the formula we get:

= (12-10/12)*100

= 20%

The difference between an approximate or measured value and an exact or known value is expressed as a percentage error, also known as a % error. In science, it is used to document the discrepancy between a real or accurate value and a measured or experimental value.

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The ordered pairs (x, y) which are the solutions to the equation 4x - 5y = 24 are option A (6, 0), option C (1, -4) and option D (-9, -12)

Given,

The equation: 4x - 5y = 24

We have to find the ordered pairs in the form (x, y) which are the solutions to the equation:

Lets check:

Option A: (6, 0)

Substitute this in the equation:

We get

4 × 6 - 5 × 0 = 24

24 - 0 = 24

24 = 24

(6, 0) satisfies the equation.

Option B: (4, 8)

Substitute this in the equation:

We get

4 × 4 - 5 × 8 = 24

16 - 40 = 24

-24 ≠ 24

(4, 8) does not satisfies the equation.

Option C: (1, -4)

Substitute this in the equation:

We get

4 × 1 - 5 × -4 = 24

4 - (-20) = 24

4 + 20 = 24

24 = 24

(1, -4) satisfies the equation

Option D: (-9, -12)

Substitute this in the equation:

We get

4 × -9 - 5 × -12 = 24

-36 + 60 = 24

24 = 24

(-9, -12) satisfies the equation

Therefore, the solutions for the equation 4x - 5y = 24 are option A (6, 0), option C (1, -4) and option D (-9, -12)

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Answer:

see explanation

Step-by-step explanation:

since QR ≅ RS , the triangle is isosceles with base angles congruent, so

∠ Q = ∠ S , that is

8x - 17 = 5x + 1 ( subtract 5x from both sides )

3x - 17 = 1 ( add 17 to both sides )

3x = 18 ( divide both sides by 3 )

x = 6

Then

∠ Q = 8x - 17 = 8(6) - 17 = 48 - 17 = 31°

∠ R = 19x + 4 = 19(6) + 4 = 114 + 4 = 118°

∠ S = 5x + 1 = 5(6) + 1 = 30 + 1 = 31°

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: f = 2[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

Let's consider two points (1 , 3) and (7 , f), now we can write the slope (m) of line in form of these points as :

[tex] \qquad \tt \rightarrow \: m = \cfrac{y2 - y1}{x2 - x1} [/tex]

[tex]\qquad \tt \rightarrow \: - \dfrac{1}{6} = \dfrac{f - 3}{7 - 1} [/tex]

[tex]\qquad \tt \rightarrow \: - (7 - 1) = 6(f - 3)[/tex]

[tex]\qquad \tt \rightarrow \: - 6 = 6(f - 3)[/tex]

[tex]\qquad \tt \rightarrow \: f - 3 = - \dfrac{6}{6} [/tex]

[tex]\qquad \tt \rightarrow \: f - 3 = - 1[/tex]

[tex]\qquad \tt \rightarrow \: f = - 1 + 3[/tex]

[tex]\qquad \tt \rightarrow \: f = 2[/tex]

Value of f is 2, so the point is : (7 , 2)

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

No

Step-by-step explanation:

In order to have the same ratio, it would have to be 2:3 and 4:6 because you divide it by 2

Cosine is a trigonometric ratio that means

[tex] = \frac{adjacent}{hypotenuse} [/tex]

THE ADJACENT SIDE IS THE ONE WITH MAGNITUDE 17CM AND THE HYPOTENUSE IS THE LONGEST SIDE WITH 37CM

COS(63°) AS A FRACTION IS

[tex] \frac{17}{37} [/tex]

From the given graph, the numeric values of the expressions are given as follows:

To find the numeric value of a function, we replace each instance of the variable in the function by the desired value.

On the graph of the function, the equivalent to this is that we have to find where the x-axis has the value, and find the value of y for which the function passes through the y-axis.

From the graph, when x = -1, f(x) passes the point at y = 12, hence f(-1) = 12.

For the second item, applying the same logic, we have that:

Hence:

f(1) - g(1) = 10 - 2 = 8.

For the third item, we have to look at the graph of g(x), and find the value of x when y = 4, hence g(x) = 4 when x = 2.

For the fourth item, the functions intersect at point (3,8), hence f(x) = g(x) when x = 3.

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