What are the 4 properties of logarithm?.

The slope of the line 3x - 4y = -12 is 3/4, obtained by dividing -3 by -4 after isolating y.

What is slope ?

Slope, also known as gradient, is a measure of the steepness of a line. It is the ratio of the change in the y-coordinate to the change in the x-coordinate between any two distinct points on the line. It is represented by the letter "m" in the slope-intercept form equation of a line y = mx + b, where m is the slope, x is the independent variable, y is the dependent variable and b is the y-intercept, the point where the line crosses the y-axis.

The slope of a line can be found by rearranging the equation to the slope-intercept form y = mx + b. To find the slope of the equation 3x - 4y = -12, you can divide both sides by -4 and then divide by 3.

3x - 4y = -12

-4y = -3x -12

y = (3/4)x +3

So , The slope of the line 3x - 4y = -12 is 3/4, obtained by dividing -3 by -4 after isolating y.

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F(-1)=-6

Substitute x=-1 into the function

f(-1)=3(2)x,x=-1

F(-1)=3x2x(-1)

Answer:This is a mathematical expression. To solve it, we can use the order of operations (PEMDAS)

First, we simplify the expressions inside the parentheses.

5+7 = 12

Then, we simplify the multiplication

12 * 200 = 2400

So the result of (5+7)*200 is 2400.

A region in the first quadrant defined by the x-axis, the graph of x=y2+2, and the line x=4 is called R then the area of R be [tex]$-\frac{2 \sqrt{2}}{3}+2 \sqrt{2}$$[/tex]

A parabola is a U-shaped plane curve in which every point is situated at an equal distance from both the focus, a fixed point, and the directrix, a fixed line. A parabola is a U-shaped curve that represents the graph of a quadratic function.

Students are able to fill in the gap between the mathematics they learn in class and the things they see in real life by drawing a comparison between the equation of a parabola and a shape found in the real world (the parabaloid). They can conceive difficult ideas that they might otherwise find repugnant by doing this.

Sketch the graph of [tex]$x=y^2+2$[/tex] by sketching the sideways parabola [tex]$x=y^2$[/tex] then adding 2 to the x coordinates (translate 2 to the right).

Add the x axis and the vertical line x = 4.

The area can be found by either

[tex]$\int_2^4 \sqrt{x-2} d x$$[/tex] or [tex]$\int_0^{\sqrt{2}}\left(4-\left(y^2+2\right)\right) d x$$[/tex]

[tex]$=\int_0^{\sqrt{2}}-x^2+2 d x$$[/tex]

Apply the Sum Rule: [tex]$\int f(x) \pm g(x) d x=\int f(x) d x \pm \int g(x) d x$[/tex]

[tex]$=-\int_0^{\sqrt{2}} x^2 d x+\int_0^{\sqrt{2}} 2 d x$$[/tex]

simplifying the equation, we get

[tex]$\int_0^{\sqrt{2}} x^2 d x=\frac{2 \sqrt{2}}{3}$$[/tex]

[tex]$\int_0^{\sqrt{2}} 2 d x=2 \sqrt{2}$$[/tex]

[tex]$=-\frac{2 \sqrt{2}}{3}+2 \sqrt{2}$$[/tex]

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Test score of a student who does not study for the test 70%.

A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.

The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The sign "%" is used to denote it.

Out of a hundred is what the word "percent" refers to. Percentages are used in mathematics to represent subsets of a whole, just like fractions and decimals are. The whole is thought of as being composed of 100 equal parts when using percentages. As a less common alternative, the abbreviation "pct" may be used to indicate that a number is a percentage.

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The sum of two sides is always greater than the third side. So the side lengths 5, 12 and 13 can form a right triangle.

In the given question, we have to define the side lengths 5, 12 and 13 form a right triangle.

A side can form a right triangle if the sum of two sides is greater than the third side.

To check the given sides can from a right triangle or not we add them.

5 + 12 > 13

17 > 13 (True)

5 + 13 > 12

18 > 12 (True)

12 + 13 > 5

25 > 5 (True)

Hence, we can see that the sum of two sides is always greater than the third side. So the side lengths 5, 12 and 13 can form a right triangle.

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Calculating the total number of factors for a given number is done by using the formula total number of Factors for N=(a+1)(b+1)(c+1). A prime factor is any non-zero natural integer that can be divided only by itself and by 1.

Actually, some of the first prime numbers are 2, 3, 5, 7, 11, and so forth. a sum that has been multiplied to yield a new sum. By dividing 15 by 3 and 5, for instance, we obtain 3 5=15. major components: All prime but non-composite components are referred to as prime factors. 2, 3, and 5 are a handful of the prime factors of 30. The only prime factors of 12 are 2 and 3, therefore listing 2 twice as in mathematics.

Particularly in statistics, there are many different mean types.Each mean is used to summarise a particular set of data, typically in order to assess the overall importance of that data set. A statistic known as the standard deviation describes the degree of variance or dispersion in a group of values. A low standard deviation indicates that the values often tend to be close to the set mean, whereas a large standard deviation denotes that the values are distributed over a wider range.

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The shaded areas therefore cover a total area of 86.84 cm2.

Let's calculate the whole trapezoid's area. You multiply by the height after adding the top and bottom sides and dividing the result by two.

To get the length of the top side, we sum the values that make up that side.

6.4+5.2+9.6=21.2

The underside is 5.2.

The top and bottom sides are added.

21.2+5.2=26.4

We multiply by 2.

26.4/2=13.2

We increase by the height, which is 6.2 as we can see.

13.2×9.1=120.12

Next, we locate the rectangle's unlit portion.

6.4×5.2 = 33.28

To get the total area of the two shaded triangles, we deduct this from the trapezoid's overall area.

120.12 - 33.28 = 86.84

The shaded areas therefore cover a total area of 86.84 cm2.

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The true statement is "No, you cannot prove that the two right triangles are congruent with the information given."

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

As a general rule, congruent triangles would have same dimensions and angles

In the scenario, we understand that Sidewalk B and Sidewalk A form a right angle.

This and the other information does not provide information to determine the congruency because the lengths of the sides of either triangle or the angles are missing.

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$656.25 is the difference between  the investor paid for the share and  the investor sold the share.

Two or more expressions with an Equal sign is called as Equation.

Given that At the beginning of 2017, the share was worth $1050.

From the beginning of 2015 to the beginning of 2017 the value of the share halved each year.

In 2017 it is 1050.

In 2016 , it is 2100

In 2015, it is 4200

Beginning of 2017 to the beginning of 2019, the value of the share increased by 1.5 times each year.

In 2017, 1050×1.5=1575

In 2018, 1575×1.5=2362.5

In 2019, 2362.5×1.5=3543.75

The investor paid for share is 4200 and the investor sold is 3543.75.

Difference =4200-3543.75

=656.25

Hence, $656.25 is the difference between  the investor paid for the share and  the investor sold the share.

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The congruency postulates for each question is;

1) SSS

2) Not enough information

3) Not enough information

4) SAS

5) ASA

6) Not enough information

In mathematics, when it comes to triangles, there are different postulates or theorems that are used to prove congruency and they include;

SAS which stands for Side- Angle - Side Congruency

SSS which stands for Side- Side - Side Congruency

ASA which stands for Angle- Side - Angle Congruency

AAS which stands for Angle - Angle - Side Congruency

HL which stands for Hypotenuse Leg Congruency

1) We see that we are given three congruent sides to the other triangle and as such the congruence postulate is SSS.

2) We are given two congruent sides and the non-included angle and this is not enough information to prove the congruency.

3) We are given two congruent sides and the non-included angle and this is not enough information to prove the congruency.

4) We are given two congruent sides and the included angle and this is SAS congruency.

5) We are given two congruent angles and the included angle and this is ASA congruency.

6) We are given two congruent sides and the non-included angle and this is not enough information to prove the congruency.

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The final expression of the algebraic expression is; (30√2)/2

The algebraic expression is expressed as;

(18/√2) - 12/√32

Now, we know that √32 can be expressed as;

√(16 * 2) = √16 * √2

= 4√2

Thus, the expression is now;

(18/√2) - 12/4√2

= (18/√2) - (3/√2)

Factorizing common factor gives;

(1/√2)(18 - 3)

= 15/√2

Rationalizing the denominator gives;

(30√2)/2

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The value of x = 10 and y = 8.

The method of elimination is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with multiplication or division of coefficients of the variables.

Equation 1
-2y = 2 - 3x
-2y + 3x = 2
3x - 2y = 2 .....(1)


Equation 2
-5y = 10 - 5x
-5y + 5x = 10
5x - 5y = 10
Taking 5 common we get,
5(x - y) = 5(2)
x - y = 2 .....(2)

On multiplying equation (2) by 3, we get

3x - 3y = 6 .....(3)

Adding equation (1) and (3),
 
       3x - 2y = 2
       3x - 3y = 6
     _____________
                y = 8
       
Putting the value of y in equation (2) we get,
x - 8 = 2
x = 2 + 8
x = 10

So, the value of x = 10 and y = 8.

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The number of bacteria of type 3 that will be found on the Petri dish will be 36.84%.

The percentage of bacteria of type 3 on the Petri dish can be calculated using the percentage formula:

In this case, the final value is the number of bacteria of type 3 in the Petri dish, which is 7. The initial value is the total number of bacteria in the Petri dish, which is the sum of all the bacteria of all types, which is:

Hence:

Therefore, 36.84% of the bacteria in the Petri dish are of type 3.

This question should be provided as:

There are nine different types of bacteria on the Petri dish. A drawing shows some colonies of bacteria on the Petri dish. The number of bacteria in different colonies is as follows:

Colony  bacteria

   1          2

   2          1

   3          7

   4          4

   5          1

   6          1

   7          1

   8          1

   9          1

What percent of the bacteria on the Petri dish is of type 3?

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The value L that a function f(x) approaches when its input value x approaches a predetermined value c is referred to as the function's limit.

The limit of f(x) as x approaches c does not exist if, at the value c, there is no single value L that the function f(x) can be considered to approach.

The behavior of the function as it approaches c from both the right and the left must be examined in order to ascertain whether this is true of the function (that is, from x values that are larger and smaller than c, respectively).

A fundamental idea in calculus is the concept of limits. Limits help one to comprehend the connection that a function creates between its variables.

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Answer:

(0, 3 )

Step-by-step explanation:

y = 2x + 3 → (1)

3x + 2y = 6 → (2)

substitute y = 2x + 3 into (2)

3x + 2(2x + 3) = 6 ← distribute parenthesis and simplify left side

3x + 4x + 6 = 6

7x + 6 = 6 ( subtract 6 from both sides )

7x = 0 , then

x = 0

substitute x = 0 into (1) for y

y = 2(0) + 3 = 0 + 3 = 3

solution is (0, 3 )

Answer:

  82°

Step-by-step explanation:

You want the unmarked remote interior angle of a triangle, given that one of them is 61°, and the exterior angle opposite is 143°.

The exterior angle is the sum of the remote interior angles:

  143° = 61° +∠B

  ∠B = 143° -61° . . . . subtract 61°

  ∠B = 82°

__

Additional comment

In case you don't remember the remote interior angles theorem, you can get the same result using angle relations you do remember:

The interior angle at A is the supplement of the exterior angle:

  ∠A = 180° -143°

When ∠A is added to the other two interior angles, the total is 180°:

  ∠A +∠B +61° = 180°

  (180° -143°) +∠B +61° = 180° . . . . . . use the above expression for ∠A

Rearranging this to give the value of angle B, we have ...

  ∠B = 180° -180° +143° -61°

  ∠B = 143° -61° = 82° . . . . . . as above

Another way to get there is to consider ...

  The sum of ∠B and 61° is supplementary to interior angle A (their total is 180°). The exterior angle 143° is supplementary to interior angle A. Two angles supplementary to the same angle are equal, so the sum of ∠B and 61° is equal to the exterior angle 143°.

Answer: The answer is D

Step-by-step explanation:

Couldn't see the full graph but one of the points I got was (2,4) and I saw that in the picture. But the correct answer is D.

Hope this helps! Good luck!

Leslie's survey found that 58.75% of students had a dog, 21.25% had a cat, and 11.25% had neither.

This can be visualized in the following table:

Dog | Cat | Neither

 47  |   17  |   24

  9   |   0   |   0

Leslie's survey results showed that out of the 80 students surveyed, 47 of them had a dog, 17 of them had both a dog and a cat, 24 of them had a cat but no dog, and 9 of them had neither a dog nor a cat.

This shows that a higher percentage of students surveyed had a dog (58.75%) than a cat (21.25%). Furthermore, a higher percentage of students surveyed had either a dog or a cat (79%) than those that had neither (11.25%).

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The car unit rate of the race car is 6 miles/minute.

A unit rate specifies how many units of the first type of quantity equal to one unit of the second type of quantity. Examples of unit rates are km/hour, m/sec, cost/litre, and so on.

The denominator of a unit rate is always 1. To calculate the unit rate, divide the denominator by the numerator so that the denominator equals 1. For example, if 50km is covered in 5.5 hours, the unit rate will be 50km/5.5 hours = 9.09 km/hour.

Given that,

Quantity = 48 miles

Time taken = 8 minutes.

Thus, The car unit rate of the race car is 6 miles/minute.

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Answer:

0.4863

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Angle A=Angle X

AB=XY

AC=XL

The 29.9-ounce package has a lower unit price of $0.2669 per ounce, making it the better buy.

To determine the unit price for the 10.5-ounce package, you would divide the cost of the package ($2.99) by the weight of the package (10.5 ounces). So:

$2.99 ÷ 10.5 ounces = $0.2847 per ounce

To find the unit price for the 29.9-ounce package, you would divide the cost of the package ($7.98) by the weight of the package (29.9 ounces). So:

$7.98 ÷ 29.9 ounces = $0.2669 per ounce

So, the 29.9-ounce package has a lower unit price of $0.2669 per ounce, making it the better buy.

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The range is the set of possible outcome values, which are shown on the y-axis.

The range of a function directs to all the possible values y could be. The formula for finding the range of a function is y = f(x). It is a function of every x value that corresponds to only one y value.

To find the range of a function on a graph, draw (or plot) the domain (x) and range (y) coordinates on a piece of graph paper using small dots. This can assist you to see the shape of the function. You will notice a straight line, a curved line shaped like a "u" or "n", or something that looks like waves.

When making a graph, move left or right on the x-axis, depending on whether the x-coordinate is negative or positive. Then, move up or down on the y-axis, depending on whether the y-coordinate is positive or negative.

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Before any taxes, deductions, and other adjustments, she earns $98.40 per week.

To calculate Talia's gross pay for a week, we need to know how many hours she works per day and her pay rate.

Gross pay refers to the total amount of money an employee earns before any deductions or taxes are taken out. It is the total amount of money earned by an employee for the hours worked, including any overtime or bonuses.

You've provided that information:

Talia works 6 hours per day on Fridays and Saturdays each week.

Her pay rate is $8.20 per hour.

First, we need to find out how many hours she works a week. As she works 6 hours on Friday and 6 hours on Saturday, the total hours she works in a week is 6 hours/day x 2 days/week = 12 hours/week.

Next, we need to multiply her hourly rate by the number of hours she works per week to find her gross pay. Her pay rate is $8.20/hour and she works 12 hours/week, so her gross pay is:

$8.20/hour x 12 hours/week = $98.40/week

So, Talia's gross pay for a week is $98.40.

Therefore, before any taxes, deductions, and other adjustments, she earns $98.40 per week.

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A polygon with 6 angles is called hexagon

The regular hexagon is a convex polygon with six equal sides and six equal angles, always divided into symmetric or asymmetric triangles. It is closely related to equilateral triangles: By joining each vertex with its opposite, the regular hexagon is divided into six equilateral triangles.

The sum of the interior angles of a hexagon is 720°

Sum of Interior Angles = (n-2) x 180°

Sum of Interior Angles = (6-2) x 180°

Sum of Interior Angles = 4 x 180°

Sum of Interior Angles = 720°

An angle is the opening formed by two half-straights (sides) with the same origin called vertex. For example, within a triangle there are three angles, which in total add up to 180°.

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About once every 126 years, or every 31,560 days, there will be a 4-sigma event; A 5-sigma event occurs approximately once every 13,932 years (!!) or every 3,483,046 days.

The geniuses, or approximately 0.1 percent of the population, are 4 standard deviations from the mean. When attempting to determine a hypothesis's likelihood, the standard deviation emerges as an essential instrument.

4 Standard Deviations From The Mean: 99.99% (9999 out of 10000) of values in a data set with a normal distribution will be within 4 standard deviations of the mean. Therefore, the interval (S – 4E, S + 4E) will cover 9999 of the 10000 data points in the set.

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It will take 36 months for the populations of Rock Hill and Greenville to be the same.

What is the Division?

Division is a mathematical operation used to find the number of times one number, known as the dividend, is contained within another number, known as the divisor. It is represented by the symbol "/" or the word "divided by". It is the inverse operation of multiplication.

To determine when the populations of Rock Hill and Greenville will be the same, we need to find the difference in population growth between the two cities and divide it by the difference in population growth rate. We can use the following formula:

(Population of Rock Hill - Population of Greenville) / (Population growth rate of Rock Hill - Population growth rate of Greenville) = Number of months until populations are equal

First, we will calculate the population growth rate of Rock Hill and Greenville:

Population growth rate of Rock Hill = (100 people move in) - (150 people move out) = -50 people/month

Population growth rate of Greenville = 200 people move in/month

Now we can use this information to calculate the number of months until the populations are equal:

(70,000 - 61,000) / (-50 - 200) = (9,000) / (-250) = 36

It will take 36 months for the populations of Rock Hill and Greenville to be the same.

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The difference in cost between Plumber W and Plumber T if the repair takes 5 hours will be $36.

From the information, Plumber W charges $95 per hour and an additional $32 for parts. Plumber T charges $86 per hour and an additional $41 for parts.

The difference in cost between Plumber W and Plumber T if the repair takes 5 hours will be:

= 86 + (41 × 5) - 95 + (32 × 5)

= 86 + 205 - 95 + 160

= 291 - 255

= 36

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Complete question

Plumber W charges $95 per hour and an additional $32 for parts. Plumber T charges $86 per hour and an additional $41 for parts.

What is the difference in cost between Plumber W and Plumber T if the repair takes 5 hours?

The Gardener's rate per hour if he charged $450 for 9 hours is $50 per hour.

Number of days the Gardener worked = 5 days

Amount charged for 9 hours = $450

Fixed amount charged by the Gardener = $325

The gardener's rate per hour = Total amount charged for hours worked / Number of hours worked

= $450 / 9

= $50 per hour

Therefore, the Gardener charges $50 per hour

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