Identify a pattern and find the next three numbers in the pattern.
1,3,9,27,81, . . .

Answer:

x=4

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

2x-2=6

Okay, first we need to create the inverse of this equation.

The inverse of subtraction is addition.
2(x)-2=6


2x = 6+2

Now, we solve the right-hand side.

2x = 8

Then, divide both sides by the greatest common factor.

We get x by itself.

2x = 8
/2     /2
x = 4

The restriction will be f-¹(x) range: y ≥ 0

Domain of a function:

The domain of a function refers to the set of all possible inputs for the function. For example, we get that the domain of f(x) = x² is all real numbers, and the domain of g (x) = 1 / x is all real numbers except for x = 0( as it will make the function indefinite.) Some special functions can also be defined whose domain are limited.

Range of a function:

The range of a function refers to the complete set of all possible resulting values of the dependent variable, after we have substituted the domain.

So, the restriction will be f-¹(x) range: y ≥ 0 as x² will always be positive.

Therefore, the restriction will be f-¹(x) range: y ≥ 0.

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The coordinates of the midpoint of a segment with the given endpoints will be (1, 9.5).

Let AB be the line segment and C be the mid-point of line segment AB. Let the coordinate of point A (x₁, y₁), the coordinate of point B (x₂, y₂), and the coordinate of the mid-point (x, y).

Then the coordinate of the mid-point of the line segment is given as,

(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]

The endpoints are A(2, 14) and C(0, 5).

Then the coordinates of the midpoint of a segment with the given endpoints will be

(x, y) = [(2 + 0) / 2, (14 + 5) / 2]

(x, y) = (2/2, 19/2)

(x, y) = (1, 9.5)

The coordinates of the midpoint of a segment with the given endpoints will be (1, 9.5).

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The next 2 terms if it is a geometric sequence is 360 and 480.

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant. where r is the common ratio between successive terms.

Given:

The sequence in the form

[tex]f_{1} =120,[/tex]

[tex]f_{n} =f_{n-1}[/tex]         for n>2

According to given question we have

[tex]f_{1} =120,[/tex]

The formula would be:

[tex]f_{n} =f_{n-1}+f_{1}[/tex]         for n>2

[tex]f_{2} =f_{2-1}+f_{1} =f_{1}+f_{1} =240\\\\f_{3} =f_{3-1}+f_{1} =f_{2}+f_{1} =240+120=360\\\\f_{4} =f_{4-1}+f_{1} =f_{3}+f_{1} =360+120=480\\[/tex]

Therefore, the next 2 terms if it is a geometric sequence is 360 and 480.

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Ben will receive £390

Alex and Ben share £520

They share this money in the ratio 1:3

The fraction of this amount that Ben will receive can be calculated as follows

1 + 3

= 4x

4x= 520

x= 520/4

x= 130

Ben Fraction= 130 × 3

= 390

Hence Ben's fraction of the money is £390

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The value of h(g(t))(-6) is 24.

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Functions are ubiquitous in mathematics and are essential for formulating physical relationships in the sciences.

An example of this would be y=x².

If you put in anything for x, you get one output for y. We would say that y is a function of x since x is the input value.

Given:

g(t) = t² + 4t

h(t) = 2t

h(g(t))

=h( t² + 4t)

=2( t² + 4t)

And, h(g(t)) (-6)

=2( (-6)² + 4(-6))

=2(36-24)

=2*12

=24

Hence, the value of the function is 24.

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x=2

10-2(2x+1)=4(x-2)

10-4x-2=4x-8

10-2=8x-8

8=8x-8

16=8x

2=x

Answer:

X = 2

Step-by-step explanation:

[tex] \sf \: First, solve \: the \: brackets. [/tex]

[tex] \sf \: 10 - 2(2x + 1) = 4(x - 2) \\ \sf10 - 4x - 2 = 4x - 8 \: \: \: \: \: \: \: [/tex]

[tex] \sf \: Combine \: like \: terms .[/tex]

[tex] \sf8 - 4x = 4x - 8[/tex]

[tex] \sf \: Subtract \: 4x \: from \: both \: sides \: to \: remove \: 4x.[/tex]

[tex] \sf \: 8 - 4x - 4x = 4x - 8 - 4x \\ \sf8 - 8x = - 8[/tex]

[tex] \sf \: Subtract \: 8 \: from \: both \: sides \: to \: remove \: 8.[/tex]

[tex] \sf8 - 8 - 8x = - 8 - 8 \\ \sf - 8x = - 16[/tex]

[tex] \sf \: Divide \: both \: sides \: by \: -8.[/tex]

[tex] \sf \: x = 2[/tex]

Bruce's principle is $140.

The interest that Bruce earned is $9.80

The interest rate that Bruce savings account is 7%.

Simple interest is the interest that that is earned a certain amount over a period of time given a principal and the number of years.

Simple interest = amount deposited x time x interest rate.

A graph can be described as a pictorial representation of data. A graph has a y-axis and the x-axis. The y-intercept is a point where the graph touches the y-axis. The y-intercept represents the initial amount that is deposited. The principle is $140.

The slope of the graph represents the rate at which the amount invested increases in value.

Interest Bruce earned after 1 year : change in the slope

149.80 - 140 = $9.80

Interest rate = Interest / (principle x time)

9.80 / (140 x 1) = 0.07 = 7%

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Answer:

y=-2x+6

Step-by-step explanation:

Please see attachment.

Hope this helps!

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The standard form of the given equation is; x + (-y) = -5

We are given the equations;

x + 6 = 0  -----(1)

y - 3 = 4   -----(2)

Add 4 to both sides of equation 2 to get;

y - 3 + 4 = 0

y + 1 = 0    -----(3)

Put y + 1 for 0 in eq 1 to get;

x + 6 = y + 1

The standard form of an equation is expressed in the form;

Ax + By = C

Thus;

x + 6 = y + 1 can be rewritten as;

x + (-y) = 1 - 6

x + (-y) = -5

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The distance from the line x=4 to the given point (-2,5) is 6 units .

Distance formula from line to point :

The distance from the line ax+by+c=0 to the point (u,v) is given by the formula

[tex]distance=\frac{|au+bv+c|}{\sqrt{a^{2} +b^{2} } }[/tex]

In the given question

the equation of the line is [tex]x=4[/tex]

taking all the terms to Left side we get

[tex]x-4=0[/tex]

[tex]1.x+0.y-4=0[/tex]

given the points (-2,5)

From above values we the values as a=1 , b=0 , c=-4 , u=-2 , v=5 .

Substituting the values in the distance formula we get

[tex]d=\frac{|1*(-2)+0*(5)-4|}{\sqrt{1^{2} +0^{2} } }[/tex]

[tex]=\frac{|-2+0-4|}{1} \\ \\ =|-6|\\ \\ =6[/tex]

Therefore , the distance from the line x=4 to the given point (-2,5) is 6 units.

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Answer:

x = 5

Step-by-step explanation:

[tex]12x = 70 - 2x[/tex]

[tex]14x = 70[/tex]

[tex]x = 5[/tex]

Answer:

Here :))

Step-by-step explanation:

The formula for an arithmetic series  -5,-3.5,-2,-0.5,1, is An = A1 + (n-1)d

See the pattern

-5-(-3.5)= -1.5

-3.5-(-2)= -1.5

The formula for an arithmetic series  -5,-3.5,-2,-0.5,1, is  An = A1 + (n-1)d

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.

Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.

An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.

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I) There are 8.76* 10³ hours in 1 year.

II) The exact number of hours in one year is 8.76582*10³ hours.

Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.

Given:

1 hour=3600 seconds

1 year = 31556952 seconds.

Now,

I)  Use scientific notation to estimate the number of hours in one year.

1 day = 24 hours

1 year = 365 days

So, number of hours in one year is given by,

=24*365

=8760

=8.76* 10³

So, there are 8.76* 10³ hours in 1 year.

II) 1 year = 31556952 seconds.

1 hour = 3600 seconds

In one year the number of hour is given by,

=31556952/3600

=8765.82

=8.76582*10³

So, the exact number of hours in one year is 8.76582*10³ hours.

III)

The exact numbers of hours using 365 days is 8760 which is written as  in scientific notation but using the given data we get  hours.

Comparing these answers the first one has only 3 significant figures and the second answer has six significant figures.

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Exercise 1

5 3/4 + (-1/4)

Multiply 5 and 4 to get 20.

20 + 3/4 - 1/4

Add 20 and 3 to get 23.

23/4 - 1/4

Since the fractions 23/4 and 1/4 have the same denominator, subtract their numerators to subtract them.

23 - 1/4

Subtract 1 from 23 to get 22.

22/4

Reduce the fraction 22/4 to its lowest expression by extracting and canceling 3.

11/4

Exercise 2

-2/3 + 1/6

Convert -2/3 and 1/6 to fractions with like denominators.

- 2×2/3 × 2 + 1/6

Simplify

-4/6 + 1/6

Since -4/6 and 1/6 have the same denominator, add their numerators to add them together.

-4 + 1/6

Add −4 and 1 to get −3.

-3/6

Reduce the fraction -3/6 to its lowest expression by extracting and canceling 3.

-1/2

Exercise 3

-8/5 + (-3/4)

Convert -8/5 and 3/4 to fractions with like denominators.

-32/20 - 15/20

Since -32/20 and 15/20 have the same denominator, subtract their numerators to subtract them.

-32 - 15/20

Subtract 15 from −32 to get −47.

-47/20

The division will give a value of 0.15 × 10^10.

The information is to divide the quantity 1.365 times ten raised to the eighteenth power end quantity divided by the quantity 9.1 times ten raised to the eighth power end quantity.

This will be:

(1.365 × 10^18) / (9.1 × 10^8)

= 1.365/9.1 × 10^10

= 0.15 × 10^10

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Answer:

First option A

Step-by-step explanation:

Solved this by looking at the points of the graph from left to right. (-3,-2) is the first being the furthest left then so on.

The given lograthimic expression 7log p + 2logq can be written as log(p^7q^2).

According to the given question.

We have a lograthimic expression.

7log p + 2logq

As we know that, a logarithmic expression is an expression that involves the logarithm of an expression containing a variable.

Also according to the product  and power rule we know that

log(mn) = logm + logn

log(x^y) = ylogx

Therefore, the given lograthimic expression 7log p + 2logq can be written as

7log p + 2logq

= log p^7 + log q^2

= log(p^7q^2)

Hence, the given lograthimic expression 7log p + 2logq can be written as log(p^7q^2) as log(p^7q^2).

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Answer: 154º

Step-by-step explanation: vertically opposite angles => xº = 154º

Answer:

Step-by-step explanation:

First Number : x - 5

Second Number : x

x + ( x - 5) = 31

     2x - 5 = 31

            2x = 31 + 5

           2x/2 = 36/2

               x = 18

Then plugin x= 18 into First numer X - 5

   x - 5

  18 - 5 = 13

18 + 13 = 31

so .....

First Number is 13

Second number is 18

Answer:

The last option:  x = 0

Step-by-step explanation:

The line of symmetry for a figure is a straight line that divides the figure into two congruent figures

The vertical line passing along the y axis is the line of symmetry and since it passes through all y values where x = 0, the equation is x = 0

Answer:

9/8 = 1  1/8

Step-by-step explanation:

Answer: 52

Step-by-step explanation: it might not be it. GOD BLESS.

Inductive reasoning is a bottom-up technique, whereas deductive reasoning is a top-down approach. The given conclusion is deductive reasoning.

Inductive reasoning is a bottom-up technique, whereas deductive reasoning is a top-down approach. Inductive thinking proceeds from the particular to the universal, whereas deductive reasoning proceeds from general premises to specific conclusions.

Given the statements,

From the given sentences, the first sentence is a general statement, the second statement is a specific statement. And, at the last, the third statement is a conclusion statement.

Hence, the given conclusion is deductive reasoning.

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=========================================================

Explanation:

Vertical angles are always congruent.

Set the two expressions equal to one another and solve for x.

6x - 6 = 3(x+6)

6x - 6 = 3x + 18

6x - 3x = 18 + 6

3x = 24

x = 24/3

x = 8

Then use this x value to find each angle

Both angles are 42 degrees each to confirm the answer.

The proof is completed and showed that < 2 ≅ < 3 as required.

Given data

<1 and <2 are linear pair

<1 + <3 = 180 degrees

required to proof <2 ≅ <3

linear pair implies mathematically that the sum of the two angles are 180 degrees, hence we have:

< 1 + < 2 = 180 degrees    equation 1

also given that,

< 1 + < 3 = 180 degrees    equation 1

equating equation 1 and equation 2 gives

< 1 + < 2 = < 1 + < 3

< 2 = < 3

Hence the required proof

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The ratio of the volume of the hemispherical tank to its surface area is, V/A = 2r/9.

A three-dimensional object's total surface area exists the whole area of all of its external surfaces.

Let r be the radius of the circle and h be the height

To find volume of the hemispherical tank and its surface area.

Here,

TSA = Total Surface Area

CSA = Curved Surface Area

Volume of a hemisphere (V) = (2/3) πr³

TSA of the hemispherical tank(A) = CSA of the tank + CSA of the base.

TSA(A)  = 2πr² + πr² = 3πr²

The ratio of the volume of the hemispherical tank to its surface area is,

V/A = (2/3)πr³ / 3πr²

V/A = 2r/9

Therefore, the ratio of the volume of the hemispherical tank to its surface area is, V/A = 2r/9.

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