What is the general formula for Logarithms?

the value of log2 log32 is 0.5899 and  the base of the logarithm is raised to the value that was equated earlier and this expression is equal to the logarithm.

logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = logb n. For example, 23 = 8; therefore, 3 is the logarithm of 8 to base 2, or 3 = log2 8.J

The logarithmic equation that has the same solution as x-4=2^3 is log2(x-4)=3.

Logarithm

The logarithm of a number can be calculated from the following relationship:

Thus, the base of the logarithm is raised to the value that was equated earlier and this expression is equal to the logarithm.

So, we have that the third expression

Therefore, this expression is the one corresponding to x-4=2^3.

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Answer: 1000

Step-by-step explanation:

i took this quiz before ! !

The given expression is equivalent to 22 for x = 17 and y = 12.

Given is the expression as follows -

2x - y

For x = 17 and y = 12, we can evaluate the expression as -

2 x 17 - 12

34 - 12

22

Therefore, the given expression is equivalent to 22 for x = 17 and y = 12.

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To find the sides of an isosceles triangle given the angles, use the Law of Cosines to calculate the length of each side.

An isosceles triangle has two angles and two sides that are both equal.. To find the sides, you will need to use the Sine Law. The Sine Law states that the ratio of the length of a side of a triangle to the sine of its opposite angle is equal for all sides and angles of the triangle.

For example, if you have the angles A and B, and you know that they are both equal (i.e. they are the angles of an isosceles triangle), then you can use the Sine Law to calculate the length of the sides:

Side AB = Side BC = (Side AC) x (Sin A / Sin B)

Where A and B are the angles of the triangle and Side AC is the known side length.

Once you have calculated the length of the two equal sides, you can then use the Pythagorean Theorem to calculate the length of the third side (the base).

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On solving the provided question, we can say that  - he need 56  answers he need to get correct if he want a grade of 80 percent on a test with 70 questions

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. It has no measuring systems. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) * 100%.

Assuming that all of the questions are equally weighted, 56 is equal to 80% of 70. (.80)(70)=56 Therefore, 56 out of 70 is the lowest number you may get correct, or 80%.

So, the maximum number of questions you may omit is 14. As an alternative, if you desire 80% accuracy, you can have no more than 20% errors.

20% of 70

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Answer:

Converting from degrees to radians is actually very simple, it is a one step unit conversion.All we need to know to solve this is that (π)radians=(180)degrees Therefore 135degrees⋅(π)radians180degrees=(135180)π radians =3π4 radians

Step-by-step explanation:

hope this helps

On solving the provided question, we can say that - the both triangle similar triangle ABC and triangle DEF

Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.

here,

AB = DE

BC = EF

AC = DF

so, by SSS both triangles are similar

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Answer:

see explanation

Step-by-step explanation:

if the denominator of a rational expression is zero then the expression will be undefined.

the numerator is the part of the rational expression that makes it zero.

solve the numerators in each to find values of x

1

[tex]\frac{x+6}{x-4}[/tex]

x + 6 = 0 ( subtract 6 from both sides )

x = - 6 ← value that makes expression equal to zero

2

[tex]\frac{(x+4)(x-2)}{x+6}[/tex]

(x + 4)(x - 2) = 0

equate each factor to zero and solve for x

x + 4 = 0 ⇒ x = - 4

x - 2 = 0 ⇒ x = 2

x = - 4 and x = 2 make the expression equal to zero

3

[tex]\frac{2x+10}{3x-12}[/tex]

2x + 10 = 0 ( subtract 10 from both sides )

2x = - 10 ( divide both sides by 2 )

x = - 5 ← value that makes expression equal to zero

Answer:

1)  x = -6

2)  x = -4  and  x = 2

3)  x = -5

Step-by-step explanation:

A rational expression is undefined when the denominator equals zero.

A rational expression equals zero when the numerator equals zero.

Given rational expression:

[tex]\dfrac{x+6}{x-4}[/tex]

Set the numerator to zero and solve for x:

[tex]\implies x+6=0[/tex]

[tex]\implies x=-6[/tex]

Given rational expression:

[tex]\dfrac{(x+4)(x-2)}{x+6}[/tex]

Set the numerator to zero:

[tex]\implies (x+4)(x-2)=0[/tex]

Apply the zero-product property and solve for x:

[tex]\implies x+4=0 \implies x=-4[/tex]

[tex]\implies x-2=0 \implies x=2[/tex]

Given rational expression:

[tex]\dfrac{2x+10}{3x-12}[/tex]

Factor the numerator and denominator:

[tex]\dfrac{2(x+5)}{3(x-4)}[/tex]

Set the numerator to zero and solve for x:

[tex]\implies 2(x+5)=0[/tex]

[tex]\implies x+5=0[/tex]

[tex]\implies x=-5[/tex]

Answer: 348

Step-by-step explanation: 12*29 = 348, which is the largest multiple less than 350.

Answer:

C - 5

Step-by-step explanation:

We know

Emmet had c caramels

His sister took 5 caramels, that means subtract 5, so the equation is

c - 5

The margin of error for the true proportion of all individuals who are fans of the New York Yankees is 0.058.

The Correct option is (B).

The formula to calculate the margin of error  for the true proportion is;

M = √[p(1 - p)/n]

Given:

n= 40

p = 44/70

Now, The general formula for the margin of error would be:

z x √[p (1-p) ÷ n]

where:

z = values for selected confidence level

p = sample proportion

n = sample size

Since the confidence level is not given,

√[p (1-p) ÷ n]  

=√[44/70 (1 - (44/70) ÷ 70]

=√[0.6286 (0.3714)] ÷ 70

=√0.2335 ÷ 70

= √0.0033357

= 0.05775 or 0.058

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The greatest common factor of 20q¹⁰ - 10q⁹ + 30q⁸ + 20q⁷ is 10q⁷.

The GCF stands for greatest common factor. In this case, greatest can be changed to highest, and factor to divisor. The highest common factor is often referred to as the biggest common factor, highest common factor, or highest common divisor (GCD).

The largest number among all the common factors of the given numbers is known as the GCF (Greatest Common Factor) of two or more numbers. The greatest integer that may be used to divide two natural numbers x and y without producing any remainders is called their GCF. There are three main methods for calculating GCF: division, multiplication, and prime factorization.

the factor of 20q¹⁰ is 2*2*5*q*q*q*q*q*q*q*q*q*q

the factor of 10q⁹ is 2*5*q*q*q*q*q*q*q*q*q

the factor of 30q⁸ is 2*3*5*q*q*q*q*q*q*q*q

the factor of 20q⁷ is 2*2*5*q*q*q*q*q*q*q

So that the common factor of all the above terms is 2*5*q*q*q*q*q*q*q

the common factor of all the above terms= 10q⁷

So that the greatest common factor of 20q¹⁰ - 10q⁹ + 30q⁸ + 20q⁷ is 10q⁷.

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To simplify 3 ratios, divide each part of the ratio with the same amount and keep diving numbers in the ratio until they are as small as possible but they remain as whole numbers.

To simplify or reduce a fraction, first, we need to find a common factor between the ratio numbers. When we have multiple ratio numbers, we must find a common factor between all of them.

The greatest factor between all the ratio numbers (greatest common factor) will be utilised to divide or reduce the ratios down to their lowest form.

For example reduce the ratio 350: 250: 125

The first step is to determine a common factor between all of the ratio numbers. In this example, we can see that all of the numbers end in either 5 or 0. This means that each number should have 5 as a factor.

If numbers are large and we are not sure of the greatest common factor between them all, we can reduce by a common factor and then reduce again.

Now divide each number by 5 and see what we get.

350/5: 225/5: 125/5

70: 45: 25

When we divide each one by 5 again, we can see that each number again ends in 5 or 0 which means that 5 is still a factor of each number.

Now divide each number by 5 again and get a final ratio of 14: 9: 5.

70/5: 45/5: 25/5

14: 9: 5

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Answer:

13.

Step-by-step explanation:

Let X be the number.

Given information from the question, we can formulate an equation:

Six times a number less 20 = 4 times the same number increased by 6

6X - 20 = 4X + 6

From the equation, we can solve for X.

6X - 4X = 6 + 20

2X = 26

X = 26 ÷ 2

X = 13

Therefore the number is 13.

The value of the unknown number is = 13.

Let the unknown number be expressed by the variable = x.

According to the question, the mathematical linear equation in one variable that is 'x' can be expressed as:

=> 6x - 20 = 4x + 6

=> 6x - 4x = 6 + 20

=> 2x = 26

=> x = 26/2

=> x = 13

Therefore, the value of 'x' which is the unknown number is 13.

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Answer: -1/4

Step-by-step explanation:

Rate of change is just another term for slope. To calculate slope, we just need any 2 points on the graph and apply the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].

[tex]m=\frac{1-2}{4-0} =\frac{-1}{4} =-\frac{1}{4}[/tex]

This means -1/4 is the rate of change.

The formula for K in terms of F is [tex]K = \frac{5}{9} (F-32) + 273[/tex]

The given expression:

[tex]F = \frac{9}{5} (K-273) + 32[/tex]

To find the formula for K

The formula for K is obtained by making K the subject of the formula as shown below:

[tex]F = \frac{9}{5} (K-273) + 32[/tex]

subtract 32 from LHS.

[tex]F-32 = \frac{9}{5} (K-273)[/tex]

multiply 5 with LHS

[tex]5(F-32) = 9(K-273)[/tex]

Take numerator 9 to LHS

[tex]\frac{5}{9}(F-32) = K-273[/tex]

take -273 from RHS to LHS

[tex]\frac{5}{9}(F-32) + 273 = K[/tex]

Thus the formula for K in terms of F is [tex]K = \frac{5}{9} (F-32) + 273[/tex]

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Across the y-axis, translated 2 units to the right and four units to the left, the new function is now h(x) = -(x + 2)3 - 4

Step (i): The type of transformation change of the function

a) The translated left "c" units are x - c;

b) The translated right "c" units are x + c

Step (ii) The given function is translated "2" units right side, then the new function is

followed by the translated "4" units left sides and reflected across the y-axis.

Now the new function is h(x).

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Answer:

  A. 78

Step-by-step explanation:

You want the measure of one base angle of an isosceles triangle when it is given as (6x+6)° while angle K is given as 2x°.

You don't need to solve any equations to determine the correct answer choice. You just need to understand the relationship between angles in an isosceles triangle.

The two base angles in an isosceles triangle are congruent, so neither can be more than 90°. (Eliminates choice C.)

The base angle at (6x+6) is more than 3 times angle K at (2x), so the base angle cannot be as little as 12.75. (Eliminates choices B and D.)

The only viable answer choice is A. 78°.

The sum of angles in any triangle is 180°. The two base angles in an isosceles triangle are the same measure, so we have ...

  (6x +6)° +(6x +6)° +2x° = 180°

  14x +12 = 180 . . . . . . . . . . . divide by °, collect terms

  14x = 168 . . . . . . . . . . subtract 12

  x = 12 . . . . . . . . . . divide by 14

  ∠D = (6x +6)° = (6·12 +6)° = 78°

__

Additional comments

We are referring to the angle marked 2x° as "angle K" because Brainly doesn't like the word a.pex to show up in an answer.

We know triangle DKT is isosceles because the sides are marked with a single hash mark. The congruent base angles are opposite the congruent sides.

An altitude from K to segment DT would divide the triangle into two congruent right triangles, each with its half of angle K being x°. Then angles K/2 and T are complementary to that, so you could write ...

  6x +6 +x = 90   ⇒   7x = 84   ⇒   x = 12   ⇒   ∠D = 90° -12° = 78°

Once again, recognition that 6x+6 is somewhat greater than x means that angle D must be somewhat more than 45°. (The larger of two things is always greater than half their sum.)

The options (a),(b) and (d) are true regarding the apothem of equilateral triangle.

What is an apothem of a polygon?

A line segment from a regular polygon's centre to one of its sides is known as the apothem.

The given options are the following:

a)The apothem can be found using the Pythagorean theorem.

b)The apothem can be found using the tangent ratio.

c)The perimeter of the equilateral triangle is 15 cm.

d)The length of the apothem is approximately 2. 5 cm.

e)The area of the equilateral triangle is approximately 65 cm².

Now we will see if each option is true or not

a) From below figure,

      b = 8.7 / 2 = 4.35 cm

      From right angled triangle ΔABD,

    Using Pythagorus Theorem,

       a² + b² = 5²

       a² + 4.35² = 5²

       a = [tex]\sqrt{5^{2} - 4.35^{2} }[/tex] = 2.5 cm

Apothem can be found using Pythagorus Theorem.

b) From the figure, the radius divide the angle 60° of equilateral triangle to two 30° angles.

So from ΔABD,

tan 30° = a / 4.35

0.577 = a / 4.35

a = 2.5 cm

The apothem can be found using tangent ratio.

c) Perimeter of given equilateral triangle = 3 × side length

                                                                    = 3 × 8.7 = 26.1 cm

   This option is false.

d) From options (a) and (b) we found that length of apothem a = 2.5 cm

Therefore this option is true.

e) The area of given equilateral triangle = [tex]\frac{\sqrt{3} }{4} } * side^{2}[/tex] = [tex]\frac{\sqrt{3} }{4} * 8.7^{2}[/tex]

                                                                       = 32.8 cm²

Therefore this option is false.

Therefore options (a),(b) and (d) are true regarding the apothem of equilateral triangle.

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Answer: (2x+6y)^2 = (2x+6y)(2x+6y) = 4x^2 +12xy + 12yx + 36y^2 = 4x^2 + 24xy + 36y^2

So the result of (2x+6y)^2 is 4x^2 + 24xy + 36y^2

Sequencing, selection, and iteration are the three fundamental building blocks that make up an algorithm.

An algorithm in mathematics is a process, a description of a series of steps that can be used to solve a mathematical computation, but they are now much more prevalent than that. The long division algorithm is perhaps the most well-known application of algorithms in science (and in daily life, for that matter).

Algorithms are all about figuring out the most effective ways to perform the math, despite the fact that the above explanation might sound a little fussy and detailed. Mathematicians are known for being lazy, so they frequently seek out shortcuts, as the anonymous mathematician puts it. For locating these short cuts, algorithms are used.

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Answer:

Step-by-step explanation:

perp. -2

y - 2 = -2(x + 5)

y - 2 = -2x - 10

y = -2x - 8

answer:

5x-5

step-by-step explanation:

from the question, it can be determined that karen makes 4x-5 (x representing the amount of free throws made by kimi). since the question is asking you to find the total or sum of their free throws, you add 4x-5 and x to get the answer above. hope that helps!

Answer:

  135.5 m

Step-by-step explanation:

Given a triangle with angles A=46°, B=103°, and side c=97 m, you want to find the length of side 'a'.

Given one side and two angles we can solve the triangle using the Law of Sines:

  a/sin(A) = b/sin(B) = c/sin(C)

In order to do that, we need to have a (side, angle) pair, so we need to find the measure of angle C.

  A + B + C = 180°

  46° +103° +C = 180° . . . use the given measures

  C = 31° . . . . . . . . . . . . . subtract 149°

Now, we can find 'a' from ...

  a/sin(A) = c/sin(C)

  a = c·sin(A)/sin(C) = (97 m)·sin(46°)/sin(31°) ≈ 135.477286 m

The distance from B to the tree at C is about 135.5 meters.

Answer:

[tex]x=\sqrt{153}[/tex]

Step-by-step explanation:

[tex](\overline{BC})^2 = (\overline{AB})^2 + (\overline{AC})^2\\\\(13)^2=(x)^2+(4)^2\\\\169 = x^2+16\\\\169-16=x^2\\\\153=x^2\\\\\sqrt{x^2} = \sqrt{153}\\\\x=\sqrt{153}[/tex]

The values that can be eliminated from the solution set of the inequality are given as follows:

Values of x ≤ 0.

The perimeter of a rectangle of length l and height h is given by the formula presented as follows:

P = 2(l + h).

The dimensions for this problem are given as follows:

The perimeter must be less than 120, hence the inequality is given as follows:

2(x + 4 + x) < 120

4x + 8 < 120

4x < 112

x < 28.

However, a side length must assume positive values, meaning that values of x ≤ 0, that is, zero and negative values, are eliminated from the solution.

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To write an expression in factored form, its products needs to be deduced.

What is an expression?

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.

Factoring is the process of representing a given number or algebraic statement as the product of its components.

For example - Consider the binomial 3x^2-9x.

On simplifying it -

3x^2-9x = 3x(x-3)

So, here 3x^2-9x is the expanded form and 3·x·(x-3) is the factored form.

Another example is - Consider y^2-100.

The terms used here can all be expressed as squares.

y^2 − 100 = y^2 − 10^2

(y + 10)(y − 10)

The factors in this case are (y + 10) and (y - 10).

Therefore, the products are the factors of an expression.

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The expression equivalent to -3 - 3x -1x is 4 - 2x.

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.

To get to this you can combine like terms:

-3 - 3x - 1x = -3 - (3x + 1x)

= -3 - (4x)

= -3 - 4x

= -4x - 3

= 4 - 2x

Hence  4 - 2x is equivalent to -3 - 3x -1x

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For mileages of 40 or less, Company A will charge less than Company B. For mileages above 40, Company B will charge less than Company A.

To compare the prices of the two companies, we need to determine the total cost for each company at different mileage.

For Company A, the total cost is the initial fee of $50. This is a fixed price, regardless of the mileage driven.

For Company B, the total cost is the initial fee of $30 plus the additional cost per mile driven. To calculate this, we can use the formula:

Total cost = initial fee + (mileage * additional cost per mile)

For Company B, this would be:

Total cost = $30 + (mileage * $0.50)

To find out when Company A charges less than Company B, we need to compare the total costs of the two companies at different mileage. We can set up the following inequality:

$50 <= $30 + (mileage * $0.50)

To solve for mileage, we need to isolate it on one side of the inequality. To do this, we can subtract $30 from both sides:

$20 <= (mileage * $0.50)

Then, we can divide both sides by $0.50:

40 <= mileage

So for mileages of 40 or less, Company A will charge less than Company B. For mileages above 40, Company B will charge less than Company A.

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The amount of a program that can be parallelized limits the amount of time it takes to run. For example, if 90% of the program can be parallelized, the theoretical maximum speedup utilizing parallel computing would be 10 times regardless of the number of processors employed.

The amount of a program that can be parallelized limits the amount of time it takes to run. For example, if 90% of the program can be parallelized, the theoretical maximum speedup utilizing parallel computing would be 10 times regardless of the number of processors employed. Parallel computing is a sort of computation in which several computations or processes are performed at the same time. Large issues are frequently broken into smaller ones, which may then be tackled concurrently.

Here,

Parallelization can only speed up a program so much. For example, if 90% of the program can be parallelized, the theoretical maximum speedup utilizing parallel computing would be ten times regardless of the number of processors employed.

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