Geometry work number 6

x = ㏑₂8 in the logarithmic function.

A logarithmic function is the inverse of an exponential function.

Given  function if f(x) = [tex]2^{x}[/tex],

When strength is equal to 8 pascals, f(x) = 8

Therefore, 8 = [tex]2^{x}[/tex]

Taking log on both sides:

                 ln8 = ln[tex]2^{x}[/tex]

                 ln8 = xln2

       or         x  = ln8/ln2

                    x = ㏑₂8

Hence, the required function is x = ㏑₂8.

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Answer:

C

Step-by-step explanation:

x² + 6x - 7 = 0 ( add 7 to both sides )

x² + 6x = 7

to complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(3)x + 9 = 7 + 9

(x + 3)² = 16

Answer: 3/7

Step-by-step explanation:

1. We know that 2/4 + 2/4 is 1.
2. 1 can also be expressed as 7/7, because its easier to subtract 7/7 and 4/7 because they have the same denominator

3. 7/7-4/7=3/7

Answer:

3/7

Step-by-step explanation:

Answer: The answer is 121

Answer:

(1/2x+3)(1/2x+3)

         OR

[tex](1/2x+3)^{2}[/tex]

When solving a system of linear equations by substitution, normally, we want to try to solve for the easiest one to get to or we choose a variable with unit coefficient.

A variable is a quantity that could change depending on the circumstances of an experiment or mathematical problem. Typically, a variable is denoted by a single letter. The general symbols for variables most frequently used are the letters x, y, and z.

A constant component of a word as opposed to a variable. a measurement of some property or characteristic using a number (as of a substance, device, or process)

There are many factors, it is all a matter of preference, normally, we want to try to solve for the easiest one to get to

example;

if we have

(x-3)^2+y=9

we would solve for y because it is less tricky or we choose a variable with unit coefficient.

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The five requirements that a person should know about their pet before owning one are shown below.

An animal that you keep as a pet in your home is for your entertainment and company.

There are 5 requirements that a person should know about their pet before owning one.

Freedom from thirst and hunger All canines and felines have to have quick access to food and clean water.

Liberation from discomfort.

Freedom from discomfort, harm, or illness.

Having the ability to act normally.

Freedom from anxiety and pain.

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Number is the equivalent of the one written in scientific notation is

3. 21 × 104 kg = kg 2. 0 × 10-5 l = l

Numbers that are either too large or too little to be conveniently stated in decimal form can be expressed using scientific notation. It can also be referred to as standard form in the UK, standard index form, or scientific form.

Using scientific notation, one can express extremely big or extremely small values. When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation. For instance, 650,000,000 can be represented as 6.5 108 in scientific notation.

we have the number,

[tex]$0.000013$we know that$0.000013=\frac{13}{1000,000}=\frac{13}{10^6}=13 * 10^{-6}=1.3 * 10^{-5}$[/tex]

[tex]thereforethe answer is$1.3 * 10^{-5}$[/tex]

Numbers that are either too large or too little to be conveniently stated in decimal form can be expressed using scientific notation. It can also be referred to as standard form in the UK, standard index form, or scientific form.

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Answer:

25

64

Step-by-step explanation:

x^2

5^2

25

(X+3)^2

(5+3)^2

8^2

64

Hopes this helps please mark brainliest

Answer:

a) x = 25

b) 16

Step-by-step explanation:

a) x^2 = 5^2 = 25

b) (x + 3)2 = (5 + 3)2= (8)2 = 16

The percent increase in the total number of students on the honor roll is   9.4% .

In the question,

it is given that ,

last year , the number of boys in the honor roll is = 60 boys ,

the number of girls in the honor roll is = 100 girls ,

total number of students last year = 160

percent increase in the number of boys in the honor roll is = 20% ,

so , number of boys become = 60 + (0.20*60) = 72 boys ,

percent increase in the number of girls in the honor roll is = 3% ,

so , number of girls become = 100 + (0.03*100) = 103 girls ,

total number of students this year = 103 + 72 = 175 .

increase in number of students = 175 - 160 = 15

So , percent increase is = (15/160) × 100

= 0.09375 × 100

= 9.375 %

≈ 9.4%

Therefore , the percent increase is 9.4% .

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Answer: 40 in2

Step-by-step explanation:

Area of a triangle = 1/2 (base)(height)

Side AB is common to both triangles

BC = 5(BD)

Area ABD = 8, therefore Area ABC = 5(8) = 40

Answer:

1. This study uses blocking to reduce variability from known factors.

2. This study uses random sampling.

Step-by-step explanation:

Hope it helps!

Answer:

d=24

Step-by-step explanation:

In linear equation, The number of miles that he walked when he was covered and 2/3 of the distance to the gym will be 7/30 miles.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                     Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Patrick walks 9/10 miles to the gym.

Then the number of miles that he walked when he was covered 2/3 of the distance to the gym will be

⇒ 9 / 10 - 2 / 3

⇒ (27 - 20) / 30

⇒ 7 / 30

The number of miles that he walked when he was covered and 2/3 of the distance to the gym will be 7/30 miles.

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The function representing the graph is f(x) = (x + 5)²(x - 3)². The correct option is (a).

A function y = f(x) is a one to one relationship between two sets X and Y where the set X is called the domain and Y the range of function f(x) ans x ∈ X and y ∈ Y.

The given graph of the function cuts x axis at (-5,0) and (3,0) and y axis at (0,225) respectively.

Since the zeros of a function is the point at which it cuts the x-axis, the zeros at of the given functions are -5 and 3.

Which implies that the factors are (x + 5) and (x - 3) respectively.

The given factors are valid for options (a) and (d).

Now, at x = 0 f(x) should be 225.

It can be checked for both the options as follows,

(a) f(x) = (x + 5)²(x - 3)²

=> f(0) = (0 + 5)²(0 - 3)²

           = 5² × -3²

           = 225

Hence, the function that represents the given graph is f(x) = (x + 5)²(x - 3)².

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Answer: Number of small boxes = 7, Number of large boxes =3

Step-by-step explanation:

Let x= Number of small boxes , y = Number of large boxes.

As per given , 30x+55y=375  (i)

x+y=10   (ii)

Multiply (ii) by 30, we get

30x+30y=300    (iii)

Eliminate (iii) from (i), we get

25y=75

⇒ y= 3   [Divide both sides by 25]

Put y=3 in (ii), we get

x+3=10 ⇒ x=7

Hence,  Number of small boxes = 7, Number of large boxes =3

Hope this helps!!! :)

Answer:

107 degrees

Step-by-step explanation:

The four angles of a parallelogram add up to 360 degrees. Any two adjacent angles of a parallelogram add up to 180 degrees. So y is equal to 180 degrees minus 73 degrees, which is equal to 107 degrees.

Answer: 15

Step-by-step explanation:

15+3=18

Part a

This represents a translation of 2 units to the right. So, the points are [tex](6, -3), (0,0), (8, -15)[/tex].

Part b

This represents a translation of 9 units up. So, the points are [tex](4,6), (-2,9), (-10,-6)[/tex].

Part c

This represents a translation of 3 units left and 1 unit down. So, the points are [tex](1, -4), (-5, -1), (-13, -16)[/tex].

The output will be if Input (x) = a number is y = 3x - 8, so option D is correct.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given:

Input (x) = a number,

Output (y) = 8 less than 3 times x.

Assume a number x which is an input,

3 times of x  = 3x,

8 less than 3 times of x = 3x - 8

Therefore, the output will be if Input (x) = a number is y = 3x - 8.

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Answer:

Hope this help :)

Step-by-step explanation:

Answer:

-62272

Step-by-step explanation:

Multiplication on a piece of paper also a positive multiplied by a negative is negative so -556 * 112 = -66272.

The value of the given expression is 15% of $28 = (15×28)/100 = $4.2, 20% of $74 = (20×74)/100 = $14.8, 18% of $128 = (18×128)/100 = $23.04

What is an expression?

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.

Here, we have

Given the following expression and we have to find the values of given expressions.

15% of $28 = (15×28)/100 = $4.2

20% of $74 = (20×74)/100 = $14.8

18% of $128 = (18×128)/100 = $23.04

Hence, the value of the given expression is 15% of $28 = (15×28)/100 = $4.2, 20% of $74 = (20×74)/100 = $14.8, 18% of $128 = (18×128)/100 = $23.04

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The roster form of the set P is; {-2, -1, 0, 1}

The builder notation of the set P is; {x : x ∈ I, −2 < x ≤ 1}

We are told that P is the set of integers that are greater than -3 and less than or equal to 1.

Roster form of sets is done by listing the elements of the set, separated by commas, inside a set of curly brackets.

Since P is the set of integers that are greater than -3 and less than or equal to 1, then the possible numbers are; (-2, -1, 0, 1)

The roster form is; {-2, -1, 0, 1}

The builder notation of this set is;

{x : x ∈ I, −2 < x ≤ 1}

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Answer: Sam

Step-by-step explanation: I am pretty sure. Hope you find it helpful!

The Assessment Triangle and the Domains and Dimensions of the Assessment Framework.

Perimeter of A/perimeter of B = a/b

Given that triangles ABC and DEF are similar triangles, we have the following:

Perimeter of triangle ABC = x

One side length of triangle ABC = 4 cm

Perimeter of triangle DEF = 12 + 6 + 9 = 27 cm

One side length of triangle DEF = 6 cm

Therefore:

x/27 = 4/6

Cross multiply

6x = (27)(4)

6x = 108

6x/6 = 108/6

x = 18

Thus, the perimeter of tr8angle DEF that is similar to triangle ABC is: 18 cm.

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A number plus1/5 of the number can be expressed as n + 1/5n .

A number is defined as it is an arithmetic value which is used to represent the given quantity or in making calculations. Hence, a number is a mathematical concept which is used to count, measure, and label it . Thus, we can say that numbers form the basis of mathematics.

n = number

A number in which we plus 1/5 of the number then it can be expressed as;

1 + 1/5 n

6/5 + n

n + 1/5 n

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By solving the linear matrices we got the values X = 1000000  , Y = 800000 ,  Z = 200000

According to algebra, an equation is a statement that shows the equality of two mathematical expressions. For instance, the equation 4x + 5 = 15 consists of the two equations 4x + 5 and 15, which are separated by the 'equal' sign.

According to the given information

X + Y + Z  =  2000000

0.07X + 0.085Y + 0.095Z = 157000

Y = 4Z

Y = 4Z is substituted into the first and second equations as follows:

X + 5Z = 2000000

0.07X + 0.085 (4Z) + 0.095Z = 157000

X = 2000000 - 5Z

0.07X + 0.435Z = 157000

0.07 (2000000 - 5Z) + 0.435Z = 157000

140000 - 0.35Z + 0.435Z = 157000

0.085Z + 140000 = 157000

0.085Z = 17000

Z = 200000

Y = 800000

X = 1000000

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