Find the sum of the infinite series, if possible.

The equivalent expression to the given expression [tex]2^{3x}[/tex] - 4  is equal to 8ˣ - 4.

The expression is equal to,

[tex]2^{3x}[/tex] - 4

Simplify the expression using the law of exponent we get,

yᵃᵇ = (yᵃ)ᵇ

Here  in the expression the value of y = 2,

Value of a = 3

and the value of b = x

Substitute the value in the formula we get,

= ( 2³ )ˣ - 4

value of the exponent 2³ = 2 × 2 × 2

                                          = 8

This implies the equivalent expression is,

= 8ˣ - 4

Therefore, the value of the given expression is equivalent to 8ˣ - 4.

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The length of the hypotenuse of the given right angled triangle is √113.

Three given side lengths of a triangle a, b and c are said to be the sides of the right angled triangle if -

a² = b² + c²

The above theorem is known as the Pythagoras theorem.

Now, we can write that -

(hypotenuse)² = (base)² + (perpendicular)²

(hypotenuse)² = (7 x 7) + (8 x 8)

(hypotenuse)² = 49 + 64

(hypotenuse)² = 113

(hypotenuse) = √113

So, the length of the hypotenuse of the given right angled triangle is √113.

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Answer:

In 8th grade math, it's essential to know the following words: variable, coefficient, expression, equation, absolute value, function, slope, y-intercept, x-intercept, exponent, rational number, irrational number, proportion, ratio, and statistic. It's also crucial to have a solid understanding of basic arithmetic operations, including addition, subtraction, multiplication, and division, as well as properties of fractions, decimals, and percentages. Understanding geometric principles such as area, perimeter, and volume is also vital. Mastery of these terms and concepts will help your nephew excel in 8th grade math.

Answer: variable, coefficient, expression, equation, absolute value, function, slope, y-intercept, x-intercept, exponent, rational number, irrational number, proportion, ratio, and statistic. It's also crucial to have a solid understanding of basic arithmetic operations, including addition, subtraction, multiplication, and division, as well as properties of fractions, decimals, and percentages

Im Proud of you Bryson :)

75% of students of a class answered Question No. 1 correct and 55% answered Question No. 1 correct and 20% answered neither question correctly . 50 is the percentage of students who only answered one question

A percentage is a quantity or ratio that is expressed as a fraction of 100. It is symbolised by the '%' percentage sign. 'pct' or 'pc' are the acronyms used to indicate the percentage. In sense, the percentage is measured in terms of 100 and is defined as the amount of one quantity that is made up of another.

Students answer Q.1 or Q.2 or both correctly = ( 100 - 20) = 80%

x% students answered both correctly

( 75 - x) + ( 55 - x) + x = 80

130 - x = 80

x = 50

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Your question is incomplete but most probably your full question was,

75% of students of a class answered Question No. 1 correct and 55% answered Question No. 1 correct and 20% answered neither question correctly . What percent of students answered both question correctly ?

Answer:

The size depends on their dimensions

Answer:

C. Their size depends on their dimensions

Locations in space or on a 2D flat surface are called points. Consider a house's address or even longitude and latitude coordinates. These places have no width, length, or height. A point has no dimensions. There are infinitely few points. They only seem to have a size because without it, the locations of the points wouldn't be visible.

This is why choices A B and D can be ruled out. Only choice C is true.

The box and whisker plot that has the greatest interquartile range is option 3..

The interquartile range of a data set can be found by finding the difference of the data at the beginning and end of the edges of the rectangular box in a box and whisker plot.

It is also the difference between the third and first quartile.

The box and whisker plot in option 3 has the greatest interquartile range because the difference of the Q3 and Q1 is close to 9, which is the highest compared to the other data.

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Answer:

The measure of an inscribed angle in a circle equals half the measure of its intercepted arc.

3) 56 + 2x = (1/2)(112 + x)

x = 0, so the measure of arc BCD is

360° - 112° = 248°.

5) 3 + 20x = (1/2)(43x - 3)

6 + 40x = 43x - 3

3x = 9, so x = 3

The measure of arc MLK is

360° - (43(3) - 3)° = 360° - 126° = 234°.

Answer:

$3.66.

Step-by-step explanation:

1 yard is equal to 3 feet. So, a 2-yard piece of brass wire is equivalent to 6 feet of brass wire. To find the price per foot, we need to divide the total cost by the total length. So, the price per foot is

The value of the identities are;

sin X= 3/√34

tan Y = 3/5

Option A

To determine the value, we need to take note of the different trigonometric identities. These identities are;

From the information given, we have that;

the hypotenuse side = √34

The opposite of X is 3

the opposite of Y is 5

Using the sine identity;

Substitute the opposite and the hypotenuse in the fraction order

sin X = 3/√34

Using the tangent identity, we have;

tan Y = 3/5

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5√2 is the value of x in the given triangle. Therefore, the correct option is option A among all the given options.

A polygon having three edges & three vertices is called a triangle. It can be considered one of the fundamental geometric shapes. A unique triangle and plane (i.e., the two-dimensional Euclidean space) are determined by any three non-collinear points in Euclidean geometry. In other words, every triangle has a location in a plane, and there is just one level that contains that triangle.

√2×√50 = √100 = 10.

1×√50 = √50 = 5√2

5√2 since √50 = √25×√2 = 5√2

Therefore, the correct option is option A among all the given options.

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Your question is incomplete but most probably your full question was,

The value of the product is  -6i² + 37ij - 6j²

Algebraic expressions are simply described as expressions that are composed of coefficients, their variables, constants, terms, and factors.

Also note that algebraic expressions are expressions that consists of mathematical or arithmetic operations.

These operations are listed thus;

From the information given, we have;

Then, the product is;

vw = (6i - j)(-i + 6j)

expand the bracket

= -6i² + 36ij + ij - 6j²

add the like terms

= -6i² + 37ij - 6j²

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Answer:

the answer is true

Expressing as single logarithm 3/2㏑4x⁶ - 2/5㏑2y²⁵ = ㏑(2x⁹/y¹⁰)

Since we have the logarithm expression

3/2㏑4x⁶ - 2/5㏑2y²⁵

To simplify, we proceed as follows

First, we use the power law of logarithm which states that

n㏑x = ㏑xⁿ

So, using this, we have that

3/2㏑4x⁶ - 2/5㏑2y²⁵ = ㏑4x⁶ - 2/5㏑2y²⁵

[tex]= ln4x^{6\times\frac{3}{2} } - ln2y^{25\times\frac{2}{5} } = ln4x^{3\times3} } - ln2y^{5\times2 }[/tex]

= ㏑4x⁹ - ln2y¹⁰

Using the subtraction law of logarithm, which states that

㏑a - ㏑b = ㏑(a/b), we have that

㏑4x⁹ - ln2y¹⁰ =  ㏑(4x⁹/2y¹⁰)

= ㏑(2x⁹/y¹⁰)

So, 3/2㏑4x⁶ - 2/5㏑2y²⁵ = ㏑(2x⁹/y¹⁰)

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Answer:

Step-byHow do I calculate the mean?

The mean can be calculated only for numeric variables, no matter if they are discrete or continuous. It's obtained by simply dividing the sum of all values in a data set by the number of value

-step explanation:

46+57+66+63+49+52+61+68= 462/8 the total number of observation

the answer 57

If 30% children travelling by bus is represented by 360 children, then total number of students who attended the school are 1200.

The "Percent" is a way of expressing a fraction or proportion as a number out of 100. It is a unit of measurement used to represent the relative size or amount of something compared to the whole.

If 30% of the children at a particular school travel by bus and this represents 360 children, we use this data to find total number of children who attend the school.

Let "X" be = total number of children at the school.

We know that 30% of X represents 360 children, so we can write an equation:

⇒ 30% of X = 360,

⇒ 30% × X = 360,

⇒ 0.3 × X = 360,            ...because 30% = 0.3,

⇒ X = 360/0.3 = 1200,

Therefore, there are 1200 students who attend the school.

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Answer:

Step-by-step explanation:

23/40 = 0.575

you just need to replace

Answer: x=14 y=10

Step-by-step explanation:

The combinations of side lengths that would not form a triangle with vertices X, Y, and Z is A. XY = 15 mm, YZ = 10 mm, and XZ = 28 mm.

We shall us the triangle inequality theory for this problem.

According to this theory, the addition of the lengths of any two sides of a triangle must be greater than the length of the third side.

Therefore, for the sides XY, YZ, and XZ to form a triangle, we must have:

XY + YZ > XZ

YZ + XZ > XY

XZ + XY > YZ

We can check each option to see if it satisfies these conditions:

A. XY = 15 mm, YZ = 10 mm, XZ = 28 mm

15 + 10 > 28 (not satisfied)

10 + 28 > 15 (satisfied)

28 + 15 > 10 (satisfied)

Option A does not satisfy the condition XY + YZ > XZ, so it would not form a triangle.

B. XY = 18 mm, YZ = 10 mm, XZ = 25 mm

18 + 10 > 25 (satisfied)

10 + 25 > 18 (satisfied)

25 + 18 > 10 (satisfied)

Option B satisfies all the conditions, so it would form a triangle.

C. XY = 18 mm, YZ = 13 mm, XZ = 22 mm

18 + 13 > 22 (satisfied)

13 + 22 > 18 (satisfied)

22 + 18 > 13 (satisfied)

Option C satisfies all the conditions, so it would form a triangle.

D. XY = 15 mm, YZ = 10 mm, XZ = 22 mm

15 + 10 > 22 (satisfied)

10 + 22 > 15 (satisfied)

22 + 15 > 10 (satisfied)

Option D satisfies all the conditions, so it can form a triangle.

Therefore, the combinations that would not form a triangle is A, where XY = 15 mm, YZ = 10 mm, and XZ = 28 mm.

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The solution of the differential equation is y + e²ˣ = Ceˣ, if Ceˣ > 0

or -y - e²ˣ = Ceˣ, if Ceˣ < 0.

The solution of the differential equation is calculated as follows;

dy/dx = e²ˣ + y

Apply the method of separating viables;

dy/dx = e²ˣ + y

dy/(y + e²ˣ) = dx

Integrate both sides;

∫ dy/(y + e²ˣ) = ∫ dx

ln|y + e²ˣ| = x + C

To solve for y, we need to exponentiate both sides;

|y + e²ˣ| = e^(x+C) = Ceˣ

The final solution becomes;

y + e²ˣ = Ceˣ, if Ceˣ > 0

or

-y - e²ˣ = Ceˣ, if Ceˣ < 0

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The values of a, h and k for the function include the following:

a = 2

h = 3

k = -2

In Mathematics and Geometry, the general form of a logarithm function is represented by the following mathematical equation:

f(x) = alog(±x + h) + k

Where:

Based on the given logarithm function f(x) = 2log₄(x + 3) - 2, we can reasonably infer and logically deduce that the scale factor (a) used is equal to 2.

This ultimately implies that, the values of a, h and k for the function are 2, 3, and -2 respectively.

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To calculate the number of different meals available when selecting an appetizer, an entrée, and a dessert, we need to multiply the number of choices for each course.

Using the multiplication principle of counting, we can find the total number of meal options as follows:

Total number of meal options = number of appetizer choices x number of entrée choices x number of dessert choices

Total number of meal options = 5 x 13 x 4

Total number of meal options = 260

Therefore, there are 260 different meals available when you select an appetizer, an entrée, and a dessert from the given choices.

The length of the side of the square is given as follows:

20 cm.

In the figure, there are two expressions used to give the side length to each square, as follows:

In a square, all the four side lengths have the same length, hence the value of x is obtained as follows:

6x - 1 = 4x + 6

2x = 7

x = 3.5 cm.

Then the side length of the square is obtained as follows:

6(3.5) - 1 = 20 cm.

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Answer:

25%

Step-by-step explanation: Because a 25 % increase is calculated by multiplying by 1.25.

The initial sum of the number of students in College P and College Q is 5040.

We have,

Let's assume that the number of students in college Q is represented by Q, and the number of students in college P is represented by P:

P = Q - 0.32Q = 0.68Q

We also know that if 960 more students enroll in college P, the two colleges will have the same number of students.

So, we can set up another equation:

P + 960 = Q

We can substitute the first equation into the second equation to eliminate P:

0.68Q + 960 = Q

Solving for Q, we get:

0.32Q = 960

Q = 3000

The initial number of students in college Q was 3000.

We can use this value to find the initial number of students in college P:

P = 0.68Q = 0.68(3000) = 2040

So, the initial sum of the number of students in College P and College Q is:

P + Q = 2040 + 3000 = 5040

Therefore,

The initial sum of the number of students in College P and College Q is 5040.

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The complete question.

College P has 32% less students then college Q if 960 more students college P , the two college will have the same number of student what is the sum of the number of student in college p and college Q initially?

1) 5880

2)5040

3)8400

4)6720​

Answer:

-12

Step-by-step explanation:

(-3)4

-3*4

-12

Elaborate ur question about - 34

Answer:

y = 1/2x + 5

Step-by-step explanation:

hope this helps :)

Answer:

y= 1/2x +5

Step-by-step explanation:

3x-6y=-30

-3x -3x

-6y = -3x -30

/-6 /-6 /-6

y = 1/2 +5

The equivalent logarithmic value of the given expression log 3  + log 6 is equal to logarithm of 18.

The expression is equal to,

log 3  + log 6

By using the law of multiplication we have,

Log A + Log B = Log ( A × B )

Using the properties of logarithms, we can simplify the expression and get the equivalent logarithm number ,

Substitute the value of A = 3 and value of B = 6 in the formula we have,

log 3 + log 6

= log (3 × 6)

= log 18

Therefore, the expression log 3 + log 6 is equivalent to the logarithm of 18.

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The domain of the graph is -∝ < x < ∝ and the range of the graph is y > 0

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we can see that

The function is an exponential function

This means that the domain is the set of all real numbers

For the range

We can see that the y values are greater than 0

This means that the range is y > 0

Hence, the domain of the graph is -∝ < x < ∝ and the range is y > 0

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Answer (Respuesta):

-4

Step-by-step explanation:

-2t + 5 = 13

-2t = 8

t = -4

f(-4) = 13

Respuesta: -4