simplify the expressions

Answer:

a. 1500 = 1000 × 1.05^x

b. 1500 = 1000 × 1.05^x

Divide both sides by 1000

1500/1000 = 1.05^x

Take the natural log of both sides

ln(1500/1000) = ln(1.05^x)

ln(1.5) = x ln(1.05)

x = ln(1.5) / ln(1.05)

x = 5.12 years

The equation should be rearranged such that "y" is on the left and everything else is on the right.

Plot the "y=" line, using a solid line for y or y and a dashed line for y or y>. For "more than" or "less than" indications, shade above the line (y> or y), or below the line variable (y or y).

The symbols for less than and less than or equal to are "" and "," respectively. In contrast to less than or equal to, which requires that the variable or quantity be either equal to or less than the specified limit, less than means that the variable or quantity must have a value lower than the specified limit. There must be a difference between a and b's values.

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The complete question is " How do you graph the inequality y≥−5?"

When the scale factor is between 0 and 1, a dilation is considered a reduction.

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The 10 types of equation used in the mathematics are explained.

The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions.

Thus, the 10 types of equation are mentioned.

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The required component form of the vector V is given as  v=<51.3,-73.3>. Option D is correct.

Vector is defined as property of object that describes both magnitude and direction of object when in motion is called vector.

here,
|V| = 89.5
and Ф = 305
now,
x component = |V| cos305°
                    = 89.5×cos305° = 51.3

y component =  |V| sin305°

                    = 89.5×sin305° = -73.3

Thus, the required component form of the vector is given as  v=<51.3,-73.3>. Option D is correct.

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The exponential function cannot be found.

To find an exponential function, f(x)=[tex]a^{x}[/tex], containing the point, set f(x) in the function to the y value 3 of the point, and set x to the x value 0 of the point. 3 = [tex]a^{0}[/tex]

Solve the equation for a.

Let's rewrite the equation,

[tex]a^{0}[/tex] = 3

Anything with 0 in power is 1

1 = 3

As, 1 ≠ 3

There are no solution.

Since there is no real solution, the exponential function cannot be found.

Hence, the exponential function cannot be found.

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No. of pages read on day of planning are represented by vertical intercept.

The difference between vertical intercept of original plan and line drawn by Lin is 10 unit.

The slope intercept form equation for a straight line with a slope, 'm', and 'c' as the y-intercept can be given as:

y = mx + c.

Given,

No. of pages Lin read on day of planning = 30

No. of pages she plans to read everyday = 40

If total pages are y for x days then,

y = 40x + 30

which is the original plan of Lin.

comparing it with slope-intercept form of line

y = mx + c

slope m = 40

vertical intercept of original plan c = 30 unit

slope m represents the no. of pages read everyday.

vertical intercept represents the no. of pages read on day of planning.

vertical intercept c' of line drawn by Lin = 40 unit

Comparing intercept of original plan to line drawn by Lin

= |c - c'|

= |30 - 40|

= 10 unit

Hence, the vertical intercept represents the no. of pages read on day of planning.

There is 10 unit difference between vertical intercept of original plan and line drawn by Lin.

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This problem can be represented with color counters/tiles. In this case, the red counters represent positive numbers and the black ones represent negative numbers.

One technique to introduce the idea of adding and subtracting numbers is through the use of integer tiles. When working on the kind of issue that many students find more challenging—problems like -4 + -5—this paradigm might be helpful.

One positive counter and one negative counter/tile equal zero because 1+(−1)=0. Draw a line through the counters that equals zero.

The remaining counters represent the answer. Therefore, 4+(−2)=2. The answer is the difference between 4 and 2. The answer takes on the sign of the larger number. In this case, the four has a positive value and it is greater than 2.

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Cosθ and secθ are positive when θ is in the third quadrant while other trigonometric ratios are negative.

The values of all trigonometric functions depending on the side ratio of a right-angled triangle are known as trigonometric ratios. The ratios of a right-angled triangle's sides to any acute angle are the angle's trigonometric ratios. Trigonometric ratios can be used to calculate the lengths of one (or both) of the acute angles in a right triangle if you know the lengths of two of its sides.

given

sinθ = - 4 / 5

cosθ = 3/5

tanθ = -4/3

secθ = 5/3

cotθ = -3/4

cosecθ  = - 5/4

as Cosθ and secθ are positive when θ is in the third quadrant while other trigonometric ratios are negative.

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The buses will pass each other at 12:37:30 PM

To find the time when the two buses will meet, you need to find the time that Bus 2 will take to travel to the point where the buses will meet, and the time that Bus 1 will take to travel the same distance.

You can find the time that Bus 2 will take to travel to the point where the buses will meet by dividing the distance (550 miles) by the speed of Bus 2 (50 mph), which is 11 hours.

Then you can find the time that Bus 1 will take to travel the same distance by dividing the distance (550 miles) by the speed of Bus 1 (80 mph), which is 6.875 hours (or 6 hours and 52.5 minutes).

Now, you can subtract the time that Bus 2 takes to reach the point of intersection from the time that Bus 1 takes to reach the same point.

6.875 hours (or 6 hours and 52.5 minutes) - 11 hours = -4.125 hours (or -4 hours and 7.5 minutes)

Since Bus 2 leaves Harare at 8:30AM, you can subtract -4.125 hours from 8:30AM to find the time the buses will meet.

8:30AM - -4.125 hours = 12:37:30 PM

So the buses will pass each other at 12:37:30 PM

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Answer: To keep both sides of the equation balanced

Step-by-step explanation:

The Golden Rule states that what you do to one side of an equation, that side being what is on one side of the equal sign, you must do to the other side. This is very important.

I decided to use Gallon Of Gas

The rate of change is 19.8 cents annually.

The average cost of a gallon of gas is $3.744 this year (2021).

Gas prices increased significantly in 2021, almost by $2 in some states, due to disease.

Gas prices forecast for the coming year!

Capital price at the average rate of change and economic fixtures: $4 per gallon (Real-Life Problems)

Detailed explanation:

Determine the average rate of change from 1960 to 2000 by computing the percentage change in the item's price for each decade.

A simple reveals the anticipated rise in petrol prices over the coming ten years.

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I made the decision to utilise a gallon of gas. The annual change is 19.8 cents. This year, a gallon of gasoline costs on average $3.744. (2021).

Disease caused a substantial rise in gas prices in 2021, almost by $2 in some places. Future gas prices, the average rate of change in capital prices, and economic indicators: At $4 per gallon (Real-Life Problems). By calculating the price change percentage for each decade, you can calculate the overall rate of change between 1960 and 2000.

A quick calculation shows how much gasoline prices are expected to climb over the next ten years. Subtract the original price from the new price to determine the percent change, then divide the result by the original price and multiply by 100. We must now calculate the percentage change when 25 is raised to 45. To determine the percentage change, we can easily use the formula.

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Answer:

(2x-5)^3

Step-by-step explanation:

(((8 • (x3)) -  (22•3•5x2)) +  150x) -  125

 ((23x3 -  (22•3•5x2)) +  150x) -  125

3.1    8x3-60x2+150x-125  is not a perfect cube

Factoring:  8x3-60x2+150x-125

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  150x-125

Group 2:  -60x2+8x3

Pull out from each group separately :

Group 1:   (6x-5) • (25)

Group 2:   (2x-15) • (4x2)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

The equivalent expressions are 7(4c - 8), 28(c - 2), - 7(8-4c). Options A, B, E

Algebraic expressions are described as expressions that are made up of terms, variables, coefficients, factors and constants.

They are also composed of mathematical operations, such as;

Equivalent expressions are those with the same solution but different arrangement of values, we have the expression;

28c-56

Let's factor the terms, we get;

7(4c - 8)

Also,

28(c - 2)

Hence, the expressions are 7(4c - 8), 28(c - 2), - 7(8-4c)

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Answer:

Another name for factorization method Mcq is Doolittle's Method

Step-by-step explanation:

Hope it helps!

Therefore , as a result, the x, y, and z axes are the axis that the supplied coordinate plane problem is solved with.

The phrase "coordinate plane" describes a two-dimensional area made up of two rational numbers. It appears at the point where the X and Y axes connect, called the origin. A coordinate grid's numbers can be used to find points.

Here,

The x, y, and z axes of the Cartesian coordinate system,

which is used to represent three-dimensional space, are three axes that are mutually perpendicular to one another.

The origin is the location where the three axes converge.

Therefore , as a result, the x, y, and z axes are the axis that the supplied coordinate plane problem is solved with.

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The constant f(a) is the result of dividing a polynomial f(x) by xa, and f(x)=q(x)(xa)+f(a), where q(x) is a polynomial of degree one lower than f(x )'s.

Algebraic expressions called polynomials include constants and indeterminates.

Polynomials can be thought of as a type of mathematics.

Nearly all branches of mathematics employ them to express numbers, and calculus is one of those branches where they play a crucial role.

A specific kind of expression is a polynomial.

A mathematical statement without the equals symbol (=) is called an expression. Let's examine the definition and usage of polynomials as they are described below.

An algebraic expression known as a polynomial requires that all of its exponents be whole numbers.

Any polynomial must have variable exponents that are non-negative integers. Although a polynomial contains variables and constants, we are unable to divide a polynomial by a variable.

Hence, The constant f(a) is the result of dividing a polynomial f(x) by xa, and f(x)=q(x)(xa)+f(a), where q(x) is a polynomial of degree one lower than f(x )'s.

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The remainder theorem helps us find the remainder when dividing a polynomial by a linear expression, using the formula R = f(a), where a is the root of the linear expression. Using this formula, we can easily calculate the remainder without performing long division.

The remainder theorem is a concept in algebra that helps us find the remainder when we divide a polynomial by a linear expression. The formula for the remainder theorem can be stated as follows:

If we have a polynomial f(x) and we divide it by a linear expression x - a, then the remainder R is given by the formula:

R = f(a)

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The change of base property is a formula that makes it possible to express a logarithm in terms of logs expressed in a different base.

It is possible to express a logarithm in terms of logs stated in a different base using the change of base property formula. This is especially useful when evaluating a log to a base other than 10 or e using a calculator. X, a, and b are all taken to be positive. The base change property can be used to simplify equations with different bases for the logarithmic terms. All the logarithmic terms of an equation with logarithmic functions should have the same base in order to be solved.

Examples given below:

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When numbers are substituted into an equation, they typically produce a set of ordered pairs called a table of values (relation). Each ordered pair of numbers in the values table's table of values is related to one another according to the equation.

In math, what is a value?

Each digit's value varies based on where it is in the number, and this is referred to as the value. We figure it out by multiplying the digit's place value by its face value.

               Value is composed of Place Value and Face Value. Honesty, integrity, benevolence, kindness, courage, and self-assurance are a few examples of values.

What does a table of values example mean?

You can choose two or more points to include in your graph by using a table of data, a graphic organizer or chart. For the equation y= 2x + 1, an example table of values is shown here.

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If Ahmad works at a constant rate, he will take 90 minutes in finishing his exam, and he will finish it at around 1:15 pm.

We know that Ahmad answers at a constant rate, and he takes around 1.5 minutes to answer each answer.

The total time that it will take him to answer the 60 questions is equal to the number of questions times the time that it took him to answer each one, then the total time is:

T = (1.5 min)*60  = 90 minutes

So it will take him an hour and a half.

And e know that the exam starts at 11:45 am

After one hour, it will be:

0:45 pm

And after 30 minutes, it will be:

1:15 pm

Ahmad will finish his exam at 1:15 pm.

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The value of x is 27

From the information given, we have that the triangle is an isosceles triangle.

The properties of an isosceles triangle are;

We have that;

First side = x + 2

Second side = 2x - 25

Equate the two sides, we get;

x+ 2 = 2x - 25

collect like terms

x - 2x = - 25 - 2

subtract like terms

-x= -27

make 'x' the subject

x = 27

Hence, the value is 27

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Answer: to sum up

Step-by-step explanation:

In seventh grade, you received an A+:

1. Immediately after class, go through your notes.

2. Spend the most of your time studying throughout the day.

3. Read ahead rather than catching up.

4. Instruct someone else on the material.

5. Establish a study schedule from the start.

Grading in education is the practice of assigning standardized grades to students based on their degree of success in a course. Grades can be assigned in the form of letters, a range, a percentage, or a number out of a potential total. Grades are averaged in certain countries to get a grade point average. A 10-point grading scale is commonly used in Indian institutes (though some use a 4-point scale). Your GPA is derived by dividing the entire amount of your grades by the number of credits you took.

Here,

You get A+ in 7th grade:

1. Review your notes from class immediately after.

2. Do the bulk of your studying during the day.

3. Try to read ahead rather than play catch-up.

4. Teach the material to someone else.

5. Create a study schedule from day one.

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Answer: AB : secant

OC : radius

AC : tangent

CD : chord

Point C : center

Point O : Point of tangency

D B You Try A : Not enough information provided to match the notation.

Step-by-step explanation:

The null hypothesis is H0: p = 403

The alternative hypothesis is given as: H1: p < 403

The null hypothesis is a statement that there is no significant difference or relationship between two groups or variables. It represents the status quo or the default assumption that there is no effect.

The alternative hypothesis is the statement that there is a significant difference or relationship between the groups or variables. It is the opposite of the null hypothesis and represents the research hypothesis or the claim that you are trying to test.

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Note that the above problems are solved using the knowledge of the sum of angles in a triangle.

10) when computed, x = 13°
11) when computed m∠S = 158°

12) when computed, ∠P = 115.625°; ∠Q = 21.125°; ∠R = 43.25°

13) when computed, angles L, J, K is 52°, 45°, 83° respectively.
14) When computed,

∠b = 108°

∠c = 36°

∠d = 36°

Note that the Triangles Theorem posits that the sum of Angles in a Triangle = 180°

10) To solve for x, we know that:

Given the above, we can state:

8x-44 = 180/3
8x-44 = 60

8x = 60 +44

x = 104/8

x = 13°

Thus x = 13°

11) For this problem, the key to solving for x is to note that the triangle is isosceles.

This means that,

15x - 31 = 9x + 11

Thus, collecting like terms, we have:

15x-9x = 11+ 31

24x = 42

x = 42/24

Thus,

x = 1.75

Since we are looking for m∠S, we can arrive at this by removing (15x - 31 ) + (9x + 11) from 180° based on the rule of the Sum of Angles in a triangle.
That is:

180 -  (15x - 31 ) + (9x + 11) = m∠S

To do this, we must impute the value of x in to the above equation:
⇒ m∠S = 180 -  ((15 * 1.75) - 31 ) + ((9 * 1.75) + 11)
⇒ m∠S = 180 -  (-4.75) + 26.75
m∠S = 180 -  22; thus

m∠S = 158°

12) <M, <P, <R, recall that the sum of the interior angles of triangle MPR will add up to 180 degrees

so <M + <P + <R = 180

We have ∠P is 14 less than five times x = 5x-15

∠Q is five less than x = x - 5

∠R is nine less than twice x =2x - 9

Recall the angle sum property of the triangle: The sum of all angles of a triangle is 180°

So, 5x -15 + x - 5 + 2x - 9 = 180°

Collect like terms to get

8x - 29 = 180

8x = 180+29

Thus,

x= 26.125

So,∠P  = 5x-15

=5 (26.125) -15

∠P = 115.625°

∠Q =x-5

=26.125 - 5

∠ Q =21.125°

∠R = 2x - 9

=2(26.125)-9

Thus

∠R = 43.25°

To confirm, if the above ∠ sum up to 180°, we say

Check 43.25+21.125+115.625

⇒ 43.25+21.125+115.625 = 180° is TRUE.

13) To solve for ∠J, ∠K  and ∠ L, recall that

The sum of the interior angles of triangle JKL will add up to 180 degrees

so <J + <K + <L = 180

L = measure of angle L

J = measure of angle J = L - 7

K = measure of angle K = 2L - 21

Thus, L + L-7 + 2L - 21 = 180; Collect like terms and we have

4L - 28 = 180

4L = 208

L = 52°,

If L is 52 then

J = L - 7 = 52 - 7

= 45°

K = 2L - 21 = 2(52) - 21

= 83

To check that they all sum up to 180° we say:

52+ 45+83

= 180°


14)

The sum of angle in a triangle is 180 degrees

Hence <b + <c + <d = 180

13x-35 + 5x - 19 + 2x + 14 = 180

13x+5x+2x-35-19+14 = 180

20x-40 = 180

20x = 180 + 40

20 x = 220

x = 220/20

x = 11

Get <b

<b = 13x-35

<b = 13(11) - 35

<b = 143-35

<b = 108 degrees

Get <c

c =5x-19

<c = 5(11)-19

<c = 55-19

<c = 36degrees

Get <d

<d = 2x+14

<d = 2(11) + 14

<d = 22+14

<d = 36 degrees

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Full Question for Number 14:
In ΔBCD if bc =bd angle b = 13x-35 angle c =5x-19 and angled d = 2x+14 find x and the measure of each angle

The 68-95-99.7 rule, also known as the empirical rule, is a shorthand for remembering the percentage of values in a normal distribution that lie within an interval estimate: 68%, 95%, and 99.7% of values lie within one, two, and three standard deviations of the mean, respectively.

The empirical rule, also known as the three-sigma rule or the 68-95-99.7 rule, is a statistical rule stating that for a normal distribution, nearly all observed data will fall within three standard deviations (denoted by σ) of the mean or average (denoted by µ).

The Empirical Rule states that 99.7% of data from a normal distribution is within 3 standard deviations of the mean.

68% of the data is within one standard deviation of the mean, 95% is within two standard deviations, and 99.7% is within three standard deviations, according to this rule.

Three-sigma limits that follow the empirical rule are used to define the upper and lower control limits in statistical quality control charts and risk analysis such as VaR.

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Answer:

[A] ((-2,5), (7, 5), (4, 0), (3, 1), (0,6))

Step-by-step explanation:

Given:

Which of the relations given by the following sets of ordered pairs is a function?

A. ((-2,5), (7, 5), (4, 0), (3, 1), (0,6))

B. ((1,2), (2, 3), (3,4), (2, 1), (1, 0))

C. ((2-8), (6, 4), (-3, 9), (2, 0), (5, 3))

D. ((1,3), (1, 1), (1, 1), (1,3), (1,5)}

Solve:

Knowing that; In order to know if a set of ordered pairs is a function or not we must see that if every x value have one or more than one y value that a function. If there is more than one same x value then it isn't a function.

Summary:

x value can't be duplicate but y can - in a working function

Hence, based on what we see in the answer choices;

[A] ((-2,5), (7, 5), (4, 0), (3, 1), (0,6)) is a function. Due to none repeat x values.

[B]((1,2), (2, 3), (3,4), (2, 1), (1, 0)) isn't a function. Due to repeat x -values (1 and 2)

[C] ((2-8), (6, 4), (-3, 9), (2, 0), (5, 3)) isn't a function. Due to repeat x-values (2)

[D]  ((1,3), (1, 1), (1, 1), (1,3), (1,5)} isn't a function. Due to repeat x-values (1)

RevyBreeze

The domain and range of the given function are (-∞,∞),{x|x∈R} and (-∞,-28],{y|y≤-28} respectively.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given functions are h(z)=-3(z+13)²-28.

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

x-intercept(s): None

y-intercept(s): (0,-535)

Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.

Domain: (-∞,∞),{x|x∈R}

Range: (-∞,-28],{y|y≤-28}

Therefore, the domain and range of the given function are (-∞,∞),{x|x∈R} and (-∞,-28],{y|y≤-28} respectively.

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