100 points!!! Show your work on paper

Answer:

17

Step-by-step explanation:

fhxc. t thug g h y yxhxg yxtzt

The correct equation of exponential function is  [tex]f(x) = 6 * (\frac{1}{3} )^x[/tex]

What is an exponential function?

An exponential function is one that has the formula f (x) = [tex]a^{x}[/tex], where x is a variable and a constant that serves as the function's base and must be greater than 0.

Given,

         starting value = 6

          constant ratio = 1/3

The general form of an exponential function

                [tex]f(x) = ab^{x}[/tex]

      where a = starting value i.e when x = 0

                  b = rate of change in exponential equation

  So substituting our given values in the above equation, the exponential function is

           [tex]f(x) = 6 * (\frac{1}{3} )^x[/tex]

Now the value 6 can be divided by 3 only if the value of x = 1

          [tex]f(1) =\frac{6}{3} = 2[/tex]

If x = 5, then equation becomes,

          [tex]f(5) = 6 * (\frac{1}{3} )^5 = \frac{2}{81}[/tex]

So we cannot simply divide 6 by 3 without considering the value of x.

Therefore the correct equation of exponential function is

           [tex]f(x) = 6 * (\frac{1}{3} )^x[/tex]

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Subtract the sum that appears on the same side of the equation as the "x" to isolate the "x" on one side of the algebraic equation. For instance, rewrite the equation "x + 5 = 12" as "x = 12 - 5" and then find "x" in the new equation. The answer is "x = 7"

Linear equations in two variables, for example, are used when a linear equation contains two variables. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, and 3x - y + z = 3.

A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the numbers m and b provide the line's slope (m) and the value of y. (b). Because (0,y) is the location where the line crosses the y-axis, the value of y when x is 0 is referred to as the y-intercept.

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We can conclude that the supplement angle of 89° will be 91°.

Angles that add up to 180 degrees are referred to as supplementary angles.

For instance, angle 130° and angle 50° are complementary angles since the sum of these two angles is 180°.

The sum of complementary angles is 90 degrees.

Two angles are complementary if their sum equals 90 degrees, and supplementary if their sum equals 180 degrees.

So, we have an angle of 89°.

We know that the supplement angle is an angle of measure 180°.

Now, the supplement angle of 89° will be as follows:

180 - 89

91°

Therefore, we can conclude that the supplement angle of 89° will be 91°.

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1. The radius is 7feet and the height is 40 feet

2. The amount of gas filled in tank is 6,154.4 feet³.

Given that the diameter of the cylindrical tank = 14 feet

Length of cylindrical tank = 40 feet

Diameter of cylindrical tank = 14 feet

Radius of cylindrical tank = 14 / 2 = 7 feet

Amount of gas filled in tank = Volume of tank

Amount of gas filled in tank = πr²h

Amount of gas filled in tank = (3.14)(7)²(40)

Amount of gas filled in tank = (3.14)(49)(40)

Amount of gas filled in tank = 6,154.4 feet³

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Answer:

0.39 is the answer to this question

Examining the number line, the value of y is calculated to be 5

The value of RS and ST are 33 and 28 respectively

A number line is a horizontal representation of number parts with equal intervals

The numbers in a number line is arranged to be increasing from left to right , hence drawing a number line will have the smaller values to the left of the bigger values

In the problem, the given data include:

RS = 6y + 3​,

ST = 4y + 8​,

RT = 61.

From the number line we can say that

RT = RS + ST

61 = 6y + 3 + 4y + 8

collecting like terms

61 - 8 - 3 = 6y + 4y

10y = 50

divide through by 10

y = 5

RS = 6y + 3​,

RS = 6 * 5 + 3​ = 30 + 3 = 33

RS = 33

ST = 4y + 8​,

ST = 4 * 5 + 8 = 20 + 8 = 28

ST = 28

​

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The equation that represent y, the total number of letters Natasha put in an envelope in x hours is y = 42x.

Natasha has a job putting letters to the envelope to be mailed. In one hour she put 42 letters in the envelope.

Therefore, the equation that best represent y, the total number of letters Natasha put in an envelope in x hours if she continue at the same rate can be calculated as follows;

1 hours = 42 envelopes

x hours = ?

cross multiply

Therefore,

y = 42x

where

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Answer:

6

Step-by-step explanation:

For dividing fractions it's also useful to know that the first fraction (3/4) is called the dividend and the second fraction (1/8) is called the divisor.

Here is a really quick way to divide fractions. In the divisor (the second fraction) we flip the numerator and the denominator. This is known as the reciprocal and basically it means the reverse of the fraction. When we find the reciprocal, we also have to change the division sign to a multiplication sign:

3/4 times 8/1

Once you've flipped the second fraction and changed the symbol from divide to multiply, we can multiply the numerators together and the denominators together and we have our solution:

So we multiply the numerators: 3x8=24

Then multiply the denominators: 4x1=4

Then we have the inproper fraction 24/4

So we divide 24 by 4 to make the answer a proper fraction

Finally you get your answer 6!

The correct answer is B.

The height of the triangle is 19.36cm.

What is an isosceles triangle?

An isosceles triangle in geometry is a triangle with two equal-length sides. It can be stated as having precisely two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.

Here, we have

Given:  An isosceles triangle has congruent sides of 20 cm. The base is 12 cm.

An isosceles triangle has two congruent sides. The height of an isosceles triangle is also the median and the perpendicular bisector of the triangle dividing the base in half and forming two congruent right triangles.

we use the Pythagorean theorem to solve for the triangle's height.

a² + b² = c²

5² + h² = 20²

h² = 400 - 25

h² = 375

h  = 19.36cm

Hence, the height of the triangle is 19.36cm.

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The size of the animal population in year 2004 (t=0) is 200 thousands individuals.

Population is a term used to describe the total number of people that live in a specific geographic area. This can be a country, a state, a city, or any other area of the world. Population size and density are important factors in understanding the landscape of an area and its resources.

The size of the animal population in year 2004 (t=0) can be calculated by substituting t=0 into the given equation:

P(t)=210t+400/(t+2)

P(0)=210 × 0 + 400/(0+2)

P(0)=400/2

P(0)=200
Therefore, the size of the animal population in year 2004 (t=0) is 200 thousands individuals.

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Answer:

30miles

Step-by-step explanation:

As you can see in the graph, the distance between tim and jan is creating 2 right triangles

You can solve this using pythagoras theorem,

Triangle (1) :

[tex] x^{2} = {5}^{2} + {12}^{2} \\ {x} = \sqrt{{5}^{2} + {12}^{2} } \\ = \sqrt{169 } \\ = 13[/tex]

X (1) = 13 miles

Triangle (2):

[tex] {x}^{2} = {15}^{2} + {8}^{2} \\ x = \sqrt{ {8}^{2} + {15}^{2} } \\ = \sqrt{289} \\ = 17 [/tex]

X(2) = 17 miles

Now, the distance = x(1) + x(2)

= 13 + 17

=30 miles

Therefore, Tim and Jan are 30 miles apart

The equation of the line that passes through the points (17,10) and (8,10) is y = 10.

Slope is a measure of the steepness of a line or a linear function. It is often represented by the letter "m" and is calculated as the ratio of the change in the y-coordinates of two points divided by the change in the x-coordinates of those same two points. In other words, it is the ratio of the "rise" to the "run" of the line. The slope of a line can be positive, negative, zero, or undefined.

The slope-intercept form of a linear equation is a way to represent the equation of a line in the form of y = mx + b, where m is the slope and b is the y-intercept of the line. The y-intercept is the point where the line crosses the y-axis, and it is represented by the value of b. This form of the equation is useful because it allows us to easily identify the slope and y-intercept of a line, as well as to graph the line using these values.

Calculate the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

In this case, the slope is:

m = (10 - 10) / (8 - 17) = 0

Use the point-slope form of the equation, y - y1 = m(x - x1)

In this case, the point slope form is:

y - 10 = 0(x - 17)

Simplify the above equation, we get:

y = 10

The equation of the line in slope-intercept form is:

y = 10

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Answer:

hasn't done nothing but I think it is matrix

The value of x is 7.

Two or more angles are said to be vertical angles if only they are formed by same two lines intersecting at a point. Thus the two angles have equal measure of value.

Given that A and B are vertical angles, then this implies that there is a relationship between them i.e they are opposite and equal.

Such that;

m<A = m<B

(x + 27) = (2x + 20)

x + 27 = 2x + 20

collect like terms,

-20 + 27 = 2x - x

7 = x

x = 7

Therefore, the value of x is 7.

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Answer: Each chicken wing costs $2.30 ✅

Step-by-step explanation:

To find out how much each wing cost, we need to divide the total cost of the wings by the number of wings.

We can use the formula:

Cost per item = Total cost / Number of items

In this case:

Cost per wing = $16.10 / 7 wings

To find the cost of each wing we divide 16.10 by 7.

$16.10/7 = $2.30

Each chicken wing costs $2.30

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Answer:

[tex]\huge\boxed{\sf \$ 2.3}[/tex]

Step-by-step explanation:

Given that,

7 chicken wings = $16.10

Divide both sides by 7

1 chicken wing = $16.10/7

[tex]\rule[225]{225}{2}[/tex]

In order to find the magnitude of a vector, we use the Pythagorean theorem. The magnitude, also known as the length or the norm, of a vector, is the square root of the sum of the squares of its components.

In this case, we are given two vectors A and B, which are defined as

A = 5i + 7j

B = 2i + 3j.

The i and j components represent the x and y values of the vector respectively.

To find the magnitude of vector A-B, we need to first find the difference between the two vectors. This can be done by subtracting the components of vector B from the corresponding components of vector A. So,

A-B = (5i + 7j) - (2i + 3j) = 3i + 4j.

Now we can use the Pythagorean theorem to find the magnitude of this vector. The square root of the sum of the squares of the x and y components of the vector is the magnitude of the vector. So, the magnitude of

A-B = √(3^2 + 4^2)

A-B = √(9 + 16)

A-B= √25

A-B = 5. Therefore, the answer is (b) 5.

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The way to determine x, which is the price per pound of the grapes is B. Subtract 5.28 from 7.32 and then divide the difference by 2.4.

To find the price per pound of the grapes, you first needed to find the price of the grapes alone, without the cost of the watermelons.

This price of the grapes can be found by the formula :

= Total cost of fruit - Cost of watermelon

= 7. 32 - 5. 28

= $ 2. 04

Then, you can find the cost of each pound of grapes by the formula :

= Cost of grapes / Pounds of grapes purchased

= 2. 04 / 2 . 40

= $ 0. 85

In summary, you can find the price per pound of the grapes when you Subtract 5.28 from 7.32 and then divide the difference by 2.4.

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The full question is:

Zara bought 2.4 pounds of grapes and a watermelon that cost $5.28. The total cost of the fruit was $7.32. Which describes a way to determine x, the price per pound for the grapes?

The physical diameter of the sun will be 1309000km and the percentage of difference between the diameters will be 5.8%.

From the information, the sun has an angular diameter of about 0.5° and an average distance from the Earth of about 150 million km. The angular diameter in radians will be:

= 0.5π / 180

= 0.008727 radians

Distance from the sun = 150 × 10^6

The physical diameter of the sun will be:

= 150 × 10^6 × 0.008727

= 1309000km

The difference between the diameters will be:

= 1390000 - 1309000

= 8.1 × 10^4.

The percentage of difference will be:

= (8.1 * 10^4) / 1390000 × 100

= 5.8%

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Integration by parts can only be used to integrate functions that include either polynomials or exponential functions is False.

What is integration ?

Integration is a process of finding an antiderivative of a function, it is the reverse process of differentiation. It can be thought of as the area under the curve of the function or the accumulation of the function over a certain interval.

Integration by parts is a technique that can be used to integrate a wide variety of functions, not only functions that include polynomials or exponential functions. In fact, integration by parts can be used to integrate any function that can be expressed as the product of two functions, where one of the functions is the derivative of the other function. In other words, integration by parts allows us to evaluate an integral of the form ∫u(x)dv(x)dx by expressing it in terms of an integral of the form ∫v(x)du(x)dx.

It's just that those types of functions are more commonly used when applying this technique.

Hence , Integration by parts can only be used to integrate functions that include either polynomials or exponential functions is False.

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The equation can be written as a linear combination of the vectors in S:

z = 5*(1, 2, −2) -1*(2, −1, 1)

v = -2*(1, 2, −2) + 7*(2, −1, 1)

w = -12*(1, 2, −2) + 11*(2, −1, 1)

What is the linear combination?

Linear combination is the process of adding two algebraic equations so that one of the variables is eliminated. Addition or subtraction can be used to perform a linear combination.

(a) z = (−3, −1, 1)

We can write z as a linear combination of the vectors in S by using the following equation:

z = as1 + bs2

Here, we can find the values of a and b by solving the following system of equations:

-3 = a1 + b2

-1 = a2 + b(-1)

1 = a*(-2) + b*1

Solving this system of equations, we get:

a = 5

b = -1

Therefore, z can be written as a linear combination of the vectors in S as:

z = 5*(1, 2, −2) -1*(2, −1, 1)

(b) v = (−2, −5, 5)

we can write v as a linear combination of the vectors in S by using the following equation:

v = as1 + bs2

Here, we can find the values of a and b by solving the following system of equations:

-2 = a1 + b2

-5 = a2 + b(-1)

5 = a*(-2) + b*1

Solving this system of equations, we get:

a = -2

b = 7

Therefore, v can be written as a linear combination of the vectors in S as:

v = -2*(1, 2, −2) + 7*(2, −1, 1)

(c) w = (1, −23, 23)

we can write w as a linear combination of the vectors in S by using the following equation:

w = as1 + bs2

Here, we can find the values of a and b by solving the following system of equations:

1 = a1 + b2

-23 = a2 + b(-1)

23 = a*(-2) + b*1

Solving this system of equations, we get:

a = -12

b = 11

Therefore, w can be written as a linear combination of the vectors in S as:

w = -12*(1, 2, −2) + 11*(2, −1, 1)

Therefore, The equation can be written as a linear combination of the vectors in S:

z = 5*(1, 2, −2) -1*(2, −1, 1)

v = -2*(1, 2, −2) + 7*(2, −1, 1)

w = -12*(1, 2, −2) + 11*(2, −1, 1)

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hello my friend if i am being helpful please please please rate my work and give me a like

The cubic function of the given expression would be = (2x + 4). That is option A.

Cubic function is defined as the multiplication of variables by itself into three different times.

The factors of the given cubic function f(x) = 8x³ +64 can be calculated using the following steps:

(2x + 4)³ = X

(2x)³ = 8x³

(4)³ = 64

Therefore the cubic function of the given equation is (2x + 4).

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The probability of randomly drawing three consecutive red marbles is  [tex]\frac{27}{512}[/tex]  

What is probability?

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

Here Total number of marbles = 3+3+2 = 8.

Now probability of randomly drawing three consecutive red (R) marbles is

=> P(3 consecutive red) = P(red)×P(red)×P(red)

=> P(3 consecutive red) = [tex]\frac{3}{8}\times \frac{3}{8}\times \frac{3}{8}[/tex] = [tex]\frac{27}{512}[/tex]

Hence the probability of randomly drawing three consecutive red marbles is  [tex]\frac{27}{512}[/tex]  .

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x = 2

All the sides are 2 so if the length on the bottom is 2, then it would be the same for the top :)

Answer:

x=2

Step-by-step explanation:

This shape is a regular polygon so all the sides are the same length

Therefore , the solution of the given problem of expression comes out to be for addition +2 and subtraction -2.

Multiplying, dividing, adding, and subtracting are necessary math operations. When combined, the following expression would appear: A mathematical operator, some data, and an equation Values, variables, and functions make up a statement of fact's constituent parts, such as additions, deductions, multiplications, divisions, etc. It is possible to contrast and compare words and phrases.

Here,

Given :

So, for addition expression:

=> -5 + 2 = -3

So , for the subtraction expression:

=> -5 -(-2) = -3

Therefore , the solution of the given problem of expression comes out to be for addition +2 and subtraction -2.

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Answer:

3x-6 is more than -3

Step-by-step explanation:

3x-6=0

  +6 +6

3x=6

3/   3/

x=3