Given that log 2 = 0.3010 and log 3 = 0.4771, find the value of log 108​

Rectangle A is similar to Rectangle B. The solution has been obtained by using concept of similar quadrilaterals.

What are similar quadrilaterals?

When all three matching angles are the same (the fourth angle automatically becomes the same because the internal angle sum equals 360 degrees) and two neighboring sides have the same ratio, two quadrilaterals are said to be similar.

We are given four rectangles with different dimensions.

First considering Rectangle A and Rectangle B

The dimensions of Rectangle A are 2 × 3 and that of Rectangle B are

8 × 12.

For the triangles to be similar, ratio of sides must be equal.

In this, the ratio is equal as the dimensions of Rectangle B are 4 times the dimensions of Rectangle A.

So, the rectangles are similar.

There is no other pair of rectangle which is similar.

Hence, Rectangle A is similar to Rectangle B.

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The discriminant of a quadratic equation in standard form, [tex]ax^2 + bx + c = 0[/tex] , is given by the expression: [tex]b^2 - 4ac[/tex]

The expression gives the discriminant: [tex]b^2 - 4ac[/tex]

This expression is used to determine the nature of the roots of the quadratic equation. Specifically, if the discriminant is positive, then the equation has two real and distinct roots. If the discriminant is zero, then the equation has one real root with a multiplicity of 2. If the discriminant is negative, then the equation has two complex conjugate roots.

A quadratic equation is a second-degree polynomial equation in one variable, typically written in the form:

[tex]ax^2 + bx + c = 0[/tex]

where x is a variable and a, b, and c are constants. The coefficient "a" cannot be zero, since otherwise, the equation would become a linear equation.

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Answer:

To solve the system of equations graphically, you can plot the two lines on a coordinate plane and find the point where they intersect, which represents the solution to the system.

First, let's start by rewriting the equations in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

For the first equation:

3x + y = 15

y = -3x + 15

For the second equation:

3x - 4y = 0

y = (3/4)x

Next, we can plot these two lines on a coordinate plane by using any two points on each line and connecting them with a straight line.

Once the lines are plotted, we can find the point where they intersect, which represents the solution to the system. In this case, the solution is (2, 9), meaning that at x = 2 and y = 9, both equations are satisfied.

So, the solution to the system of equations is (2, 9), which means that the two lines intersect at the point (2, 9).

Answer

2.5

Step-by-step explanation:

have a nice day.

Answer: Let's call the length of the main supporting arm AP = x.

We can use the Pythagorean theorem to find the length of the cable dropping from point A to the ground:

c^2 = x^2 + (46 - 96 + 215)^2

c^2 = x^2 + (175 - 50)^2

c^2 = x^2 + 125^2

c^2 = x^2 + 15625

Since the angle between the main supporting arm and the horizontal is 55°, we can use the trigonometric relationship between the length of the opposite side (the cable) and the length of the adjacent side (the main supporting arm) to find x:

tan 55° = c / x

x / c = tan 55°

x / 215 = tan 55°

x = 215 * tan 55°

The value of x can be calculated using a scientific calculator or by using a table of tangent values. To the nearest centimetre, x = 204 cm.

Step-by-step explanation:

Answer:

Shape of the graph is exponentially decreasing

The horizontal asymptote is y = 0

The y intercept is at x = 0 and is at y = 3/2

Graph attached

Step-by-step explanation:

Not sure what exactly the question is asking for.

Here is what I figured out

Shape of the graph is exponentially decreasing

The horizontal asymptote is y = 0

The y intercept is at x = 0 and is at y = 3/2

We can also rewrite this equation as:

[tex]g(x) = \dfrac{3}{2} \cdot \dfrac{2}{3} \cdot \left(\dfrac{2}{3}\right)^{x-1}\\\\\\= \left(\dfrac{2}{3}\right)^{x-1}[/tex]

The value of 5% of 260 is 13 as it is 5 times of 1% of 260 and the value of 1% of 260 is 2.6.

Percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

so, according to the question

Let 1% of 2600 = X

1/100 * 260 = X

X = 2.6

5% is 5 times of 1% so we can just multiply the value we got after 1% of 260

i.e., 2.6

so 5% of 260 is 5 * 2.6

            = 13.0

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Answer:

  8√2 feet

Step-by-step explanation:

You want the length of the diagonal of a square that is 8 ft on a side.

The diagonal of a square is the hypotenuse of the isosceles right triangle with leg lengths equal to the sides of the square. The ratios of side lengths in such a triangle is ...

  1 : 1 : √2

Then the lengths of the sides of that triangle are ...

  8 ft : 8 ft : 8√2 ft . . . . . multiply ratio values by 8 ft

The diagonal length is 8√2 feet.

__

Additional comment

If you use the Pythagorean theorem to find the diagonal length, you will determine it is ...

  d = √(8² +8²) = 8√(1+1) = 8√2 . . . . feet

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There are a few general reasons why Marcus's results might differ from Zara and Arun's:

In terms of Solubility: Different solutes have different solubilities, which means they will dissolve to different extents in water. It's possible that the solutes Marcus is using have lower solubilities than the solutes used by Zara and Arun, which could lead to differences in the amount of solute that dissolves.

   Amount of solute added: Even if all three individuals add the same amount of solute to their test tubes, the amount of solute that actually dissolves may differ due to differences in solubility. If Marcus is using solutes with lower solubilities, he may be adding the same amount of solute as Zara and Arun, but a smaller proportion of it is dissolving.

  Spatula size: Marcus has the same number of spatulas for all three solutes, but it's possible that the size of his spatulas differs from those used by Zara and Arun. If Marcus's spatulas are smaller, he may be adding less solute to his test tubes, which could explain the differences in his results.

 Lastly, in terms of Experimental error: Finally, it's possible that there is some experimental error that is affecting Marcus's results. For example, he may not be measuring the amount of solute accurately, or he may be adding it to the test tube in a way that doesn't allow it to dissolve as well.

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The unknown sides of the figure are

< KNL = 89.85 degrees

< KJL = 50 degrees

< JKM = 40 degrees

< JML = 80 degrees

A rhombus has it's interior angles equal to 360 degrees and the opposites and angels are equal

hence angle MLK = MJK = 100 degrees

< JML = < JKL = say x

2x + 2(100) = 360

2x = 360 - 200

2x = 160

x = 80

< MJL + < KJL = MJK adjacent angles

50 + < KJL = 100

< KJL = 50 degrees

The sides of a rhombus are equal

JM = KL =  15.6

ML = JK = 15.6

Given that NK = 12 and NL = 10, using cosine rule we solve for < KNL

cos < KNL = (15.6² - 12² - 10²) / -2 * 12 * 10

cos < KNL = 1/375

< KNL = arc cos (1/375)

< KNL = 89.85

< JKM + < JKL +  <JNK = 180 sum of angles on a triangle

<JNK = 180 - 89.85 = 90.15

< JKM + 50 + 90.15 = 180

< JKM = 180 - 50 - 90.15

< JKM = 39.85 approximately 40

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The value of x and y in the quadratic and linear equation are (0.37, -137) and (-3.26 , -6.74) respectively

In the problem given;

2x² + 4x - y = -3 ..eq(i)

-2x + y = -4 ..eq(ii)

From equ(ii)

Using the linear equation;

y = 2x - 4 ...eq(iii)

Put eq(iii) into eq(i)

2x² + 4x - (2x - 4) = -3

2x² + 4x - 2x - 4 = -3

2x² + 2x - 4 = -3

Rearrange the equation;

2x² + 2x - 4 + 3 = 0

2x² + 2x - 1 = 0

Solving the quadratic equation;

x = 0.37 or -1.37

Put the value of x into eq(ii)

-2(0.37) + y = -4

y  = -3.26

or

-2(-1.37) + y = -4

y = -6.74

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No. The statement given by Yuki that 43 is a 2 digit odd number that is composite is not correct.

A composite number is a positive integer greater than 1 that has more than two positive divisors. In other words, a composite number is a number that can be divided by more than just 1 and itself. For example, 4 is a composite number because it can be divided by 1, 2, and 4.

On the other hand, a prime number is a positive integer greater than 1 that has exactly two positive divisors, 1 and itself. For example, 5 is a prime number because it can be divided only by 1 and 5.

Now, let's consider the number 43. 43 is a two-digit odd number, which means it has two digits and is not divisible by 2. However, 43 is a prime number, which means it has exactly two positive divisors, 1 and 43. Therefore, 43 is not a composite number.

To further verify this, we can check the divisors of 43. The divisors of 43 are 1 and 43, because 43 is not divisible by any other positive integer. Therefore, we can conclude that 43 is a prime number and not a composite number.

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Answer:

(-x+2)(2x+1) — first option

Step-by-step explanation:

The rectangles represent an x, red means negative and yellow is positive.

The squares represent a unit (the number 1).

The diagram attached below demonstrates how this works.

Basically the top row of this tile equation is (-x + 2)

And the column is (2x+1).

Expanding this makes -2x²+3x+2

The age of the jane is 565/48 years old.

Problems on ages is a common topic from which questions are asked in almost all Government exams in the quantitative aptitude section.

in this the ages has been found by solving the relationship between the ages given in the question.

the age of rick is = 11 3/4 years old

= 47/4 years old

the age of the lane is 1 3/8 years older than rick

so we add 1 3/8 in the age of rick to find out the age of lane,

so, the age of Lane is = 47/4 + 1 3/8

= 47/4 + 11/8

= (94 + 11)/8

= 105/8 years old .

the age of the jane is 1 1/5 years older than Lane

so we add 1 1/5 in the age of lane to find out the age of jane,

so, the age of jane is = 105/8 + 1 1/5

= 105/8 + 6/5

= (525 + 40)/48

= 565/48 years old .

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If the equation describes the situation is 2x + 40 = 62, then the variable x represents the option (D) number of push ups Noah does

The given statements are

Diego does twice as many push ups as Noah

Therefore, if Noah does x push ups Diego does 2x push ups

Number of jumping jacks that Diego does = 40

Total number of exercises that he does = 62

The linear equation that represents the situation is

2x + 40 = 62

From the given equation

2x = 62 - 40

2x = 22

x = 22/2

x = 11

Here we can see that x is the number of push ups Noah does and 2x is the number of push ups Diego does

Therefore, the variable x is the number of push ups Diego does

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Answer:

since y = 0 when x = 0

Step-by-step explanation:

We can start by solving for y in the equation:

y * x = 3/5 y

Dividing both sides by y:

x = 3/5

So the equation y * x = 3/5 y can be simplified to:

y = 5/3 x

This equation shows that there is a proportional relationship between y and x, where y is always equal to 5/3 times x. This relationship can be represented on a graph by plotting points (x, y) and drawing a line through them. The slope of the line will be 5/3, and the y-intercept will be 0, since y = 0 when x = 0.

Answer:

y = ±1/√5

Step-by-step explanation:

3y = 3/5y

⇒3y×5y = 3

⇒15y² = 3

⇒y² = 3/15

⇒y² = 1/5

⇒y = ±1/√5

Answer: Given the equation V = Sp.v, to solve for v, we need to divide both sides of the equation by Sp.

V / Sp = v

So v = V / Sp

Here, V is the volume of the item being sold, Sp is the price per unit, and v is the number of units being sold. By dividing V by Sp, we can find the number of units being sold (v) at a given price per unit.

Step-by-step explanation:

he possible values for c would be 31 and 41.

Option (D) is correct.

What is the quadratic equation?

A quadratic equation is a polynomial equation of the second degree, which means that it contains a variable raised to the power of two (usually x^2). The general form of a quadratic equation is:

[tex]ax^2 + bx + c = 0[/tex]

where a, b, and c are constants and x is the variable.

We have [tex](ax+2)(bx+7)=abx^2 +7ax+2bx+14=abx^2+(7a+2b)x+14[/tex]

Given, it is equal to 1[tex]5x^2+cx+14[/tex]

⇒ab=15 --- (1)

⇒7a+2b=c

Also given a+b=8 --- (2)

From equations (1) and (2), we can interpret that either of a or b are equal to 3 or 5

When a=3 and b=5, we have c=7(3)+2(5)=21+10=31

When a=5 and b=3, we have c=7(5)+2(3)=35+6=41

Hence, the possible values for c would be 31 and 41.

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-6x+35 = -6x+35 has the same thing on each side: , so this has infinite solutions. Option c is correct.

An equation will have infinite solutions if both sides of the equal sign are the exact same thing, for instance . (You can test this with any value of x and find that they all work!)

So to find the equations that have infinite solutions, we need to see which have the same exact sides.

(Choice A)

-6x+35 = -6x-35 have the different thing on each side: , so this has no solution.

(Choice B)

6x+35  = -6x-35 does not have the same thing on each side, so it doesn’t have infinite solutions (it has 1).

(Choice C)

-6x+35 = -6x+35 has the same thing on each side: , so this has infinite solutions.

(Choice D)

6x+35=-6x+35 And finally,  has the different thing on each side: , so it has one solution.

Hence , -6x+35 = -6x+35 has the same thing on each side: , so this has infinite solutions.

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Answer:

Area = 91 square inches

Step-by-step explanation:

Let

L = length of the rectangle in inches

W = width of rectangle in inches

We are given:
The length of a rectangle is one inch less than twice the width

In math terms this is equivalent to:
L = 2W - 1

he perimeter of the rectangle is 40 in.
The perimeter of the rectangle = 2(L+ W)

So in math terms;
2(L + W) = 40

L + W = 40/2

L + W = 20

Since L = 2W - 1 we can substitute for L in terms of W in the above equation:
L + W = 2W - 1 + W = 3W - 1

Equating it to 20 gives
3W - 1 = 20

Add 1 both sides:
3W = 21

W = 7

Which gives

L = 2W - 1 = 2(7) - 1 = 14 - 1 = 13

So L = 13

The area of the rectangle = L x W

= 13 x 7

= 91 square inches

Answer:

Step-by-step explanation:

You want the missing side and the angles for the right triangle with leg BC = 2.7 cm and hypotenuse AB = 3.1 cm.

The cosine of angle B is given by ...

  Cos = Adjacent/Hypotenuse

  cos(B) = CB/AB = 2.7/3.1

Then the angle is ...

  B = arccos(2.7/3.1) ≈ 29.429°

  B ≈ 29°

Angle A is the complement of angle B:

  A = 90° -29°

  A = 61°

The sine ratio is ...

  Sin = Opposite/Hypotenuse

Then side AC can be found from ...

  sin(B) = AC/AB

  AC = AB·sin(B) = 3.1·sin(29.429°) ≈ 1.523

  AC ≈ 1.5 . . . . cm

The triangle solution is ...

__

Additional comment

The mnemonic SOH CAH TOA is intended to help you remember the trig ratios above, in addition to ...

  Tan = Opposite/Adjacent

Understand the strengths and weaknesses of the tools, eliminate the outliers, critically analyze the correlations, and look at the context are all methods that help to consider any limitations of the data.

When preparing for a question-and-answer session after a presentation, it is important to consider any limitations of the data used. To do this, it is important to understand the strengths and weaknesses of the tools used to collect and analyze the data. Eliminating outliers from the data can help to ensure accuracy, as outliers can skew the results. It is also important to critically analyze any correlations that may be present in the data, as these could be indicative of a limitation in the data. Additionally, looking at the wider context of the data can help to identify any potential limitations, as certain factors may not have been taken into account when collecting the data. All of these methods can help to ensure accuracy and validity of the data used in the presentation.

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Answer:

395.8406(answer depends on what place you round to)

Step-by-step explanation:

The equation is A=2πrh+2πr^2. Plug it what you know, and it'd look like this: A=2π(7)(2)+2π(7)^2. Use your calculator and you get the answer.

A statement which best describes the reflection include the following: C. a reflection over the line x = 3.

In Mathematics, a reflection can be defined as a type of transformation which moves every point of the geometric figure such as a triangle, by producing a flipped, but mirror image of the geometric figure.

Based on the graph of triangle ABC and triangle ΔA’B’C’, we can logically deduce the following coordinates after a reflection over the line x = 3:

A = (-2, 2)   → A' = (8,2)

B = (0, 4)    → B' = (6, 4)

C = (2,2)     → C' = (4, 2)

Therefore, the two triangles are identical (similar) because they are reflections of each other. Also, the distance between the point C and point C' is 2 units, therefore, with a line that is parallel to the y-axis and lies at point x = 3, as shown in the image attached below.

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Complete Question:

ΔA’B’C’ is a reflection of ΔABC. Which best describes the reflection?

A coordinate plane showing triangles A B C and A prime B prime C prime. The coordinates of the first figure are A negative 2 comma 2, B zero comma 4, and C 2 comma 2. The coordinates of the second figure are A prime 8 comma 2, B prime 6 comma 4, and C prime 4 comma 2.

a.)A reflection over the line x = 2

b.)A reflection over the line y = 3

c.)A reflection over the line x = 3

d.)A reflection over the y-axis

Answer:

The correct answer is:

You can map ABC to A'B'C' by translating it 6 units left and reflecting it across the x-axis, which is a series of rigid motions.

Explanation:

In ABC, the coordinates are:

A(1, -3)

B(5, 3)

C(4, -1).

In A'B'C', the coordinates are:

A'(-5, 3)

B'(-1, -3)

C'(-2, 1)

Each point is mapped to its image:

A(1, -3)→A'(-5, 3)

B(5, 3)→B'(-1, -3)

C(4, -1)→C'(-2, 1

Comparing the x-coordinates in the pre-image and image, we notice that the image has an x-coordinate that is 6 less than that of the pre-image:

1-6 = -5

5-6 = -1

4-6 = -2

This means that the figure must be translated 6 units left; that is the only way to have this change on the pre-image to form the image.

Comparing the y-coordinates of the pre-image with those of the image, we notice that they are negated:

-(-3) = 3

-(3) = -3

-(-1) = 1

This means the pre-image was reflected across the x-axis; this is the only way to negate the y-coordinate and not change the x-coordinate.

These are rigid motions because they do not change the shape or size, they simply move it and change its orientation.

Step-by-step explanation:

Hope this will help u

Only one decimal place in the product of 8x0. 5 because the final zeros in the product do not change the value of the number.

One decimal place to the left of the decimal point is the ones place. One decimal place to the right of the decimal place is the tenths place.

This is a result of the rules of significant figures. These are the digits of the numbers that matter. For operations involving multiplication, the product should have the same significant numbers with the least significant numbers of the given data. In this case, that would be 0.5. Since 0.5 has one significant figure, then the product should be reported with one significant number. That should be 4.0.

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Answer:

Step-by-step explanation:

Answer:

5s + 4j where s is the cost of shirts and j is the cost of jeans

Step-by-step explanation:

for shirts, we can represent it with s

for jeans, we can represent it with j

steve is buying two shirts (s) and three jeans (j), so we can write Steve's cost as 2s+3j

his brother buys three shirts (s) and one pair of jeans (j), so we can write his brothers cost as 3s+1j

now, steve's cost is 2s+3j

and his brother's is 3s+1j

we can add these together to find the total cost

2s + 3j + 3s + 1j

combine like terms

5s + 4j

The total cost of the shirts and jeans are,

⇒ 5x + 4y

Where, x is cost of each shirt and y is cost of each jeans.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that;

For the summer, Steve buys 2 shirts and 3 pairs of jeans. His brother buys 3 shirts and 1 pair of jeans.

Let the cost of each shirt = x

And, The cost of each jeans = y

Hence, We get;

Cost of Steve shirts and jeans = 2x + 3y

And, Cost of his brother shirts and jeans = 3x + y

Thus, The total cost of the shorts and jeans are,

⇒ 2x + 3y + 3x + y

⇒ 5x + 4y

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The t-test yields the probability (p value) that the null hypothesis is option (B) incorrect

The p-value in a t-test represents the probability of obtaining the observed test statistic (or one more extreme) assuming that the null hypothesis is true. The null hypothesis is typically a statement of "no effect" or "no difference" between two groups being compared in the test.

Therefore, a low p-value (generally less than 0.05) indicates that the observed data is unlikely to have occurred by chance under the null hypothesis and suggests that the null hypothesis is likely to be false.

In other words, a low p-value provides evidence against the null hypothesis and in favor of the alternative hypothesis (which typically represents the hypothesis that the researchers are interested in testing).

Thus, the p-value does not directly tell us whether the null hypothesis is correct or incorrect, but rather whether the evidence supports rejecting it or not.

Therefore, the correct option is (B) incorrect

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