2. If you use AB as the base to find the area of ABCD shown at the right, what should you use as the height?

The points on the graph of f(x) = log9x are (20, 4.5), (11/9, 0.087183), (2439, 3.168910), (181, 2.55231), and (2, 1).

The points on the graph of f(x) = log9x can be calculated by substituting the given values of x in the equation. For example,

f(-1/81) = log9(-1/81) = log9(-1) - log9(81) = undefined

f(20) = log9(20) = log9(2*2*2*5) = log9(2) + log9(2) + log9(2) + log9(5) = 1 + 1 + 1 + 1.5 = 4.5

f(11/9) = log9(11/9) = log9(11) - log9(9) = 1.041393 - 0.954210 = 0.087183

f(-13) = log9(-13) = log9(-1) - log9(13) = undefined

f(2439) = log9(2439) = log9(3*13*37) = log9(3) + log9(13) + log9(37) = 0.477121 + 1.11394 + 1.579789 = 3.168910

f(181) = log9(181) = log9(3*3*7*7) = log9(3) + log9(3) + log9(7) + log9(7) = 0.477121 + 0.477121 + 0.84509 + 0.84509 = 2.55231

f(2) = log9(2) = log9(2) = 1

Hence, the points on the graph of f(x) = log9x are (20, 4.5), (11/9, 0.087183), (2439, 3.168910), (181, 2.55231), and (2, 1).

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Step-by-step explanation:

e.g. there fit only max. 55 (< 56) people into a room (like a large conference room or a small movie theater).

or for a mathematical function like

1/(x - 56)

x < 56 can be the domain definition.

or it can be the climate (temperature in Fahrenheit) setting for a certain area at a zoo.

or, or, or ...

Answer:

     [tex]c=\sqrt{61}[/tex]

Step-by-step explanation:

Assuming it's a right triangle, you would have to use the Pythagorean Theorem which states:

[tex]a^{2} +b^{2} =c^{2}[/tex]

Assuming we're looking for the hypotenuse:

[tex]5^{2} +6^{2} =c^{2}[/tex]

[tex]25+36=c^{2}[/tex]

[tex]61=c^{2}[/tex]

[tex]\sqrt{61} =c[/tex]

Answer:

Step-by-step explanation:

85

The slope of the given linear equation y = 2x + 10 is 2.

If we draw the graph of the linear equation y = mx + c. The result is a line with m as the slope, and c as the y-intercept. This form of the linear equation y = mx + c is called the slope-intercept form, and the values of m and c are real numbers.

The slope, m, of the line represents the steepness of a line. This is also termed a gradient, sometimes. The y-intercept, c, of the line y = mx + c represents the y-coordinate of the point where the graph of the line intersects the y-axis.

Now, if we equate the standard slope-intercept form of the equation with the given equation, we get

y = mx + c

y = 2x + 10

m = 2 and c = 10

As we know the m is the slope which is equal to 2.

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During exercise, there was a substantial link between heart rate, coronary flow, and cardiac oxygen consumption. As heart rate increases, so does oxygen consumption, which seems to reach a maximum at very fast heart rates.

Your pulse and heart rate both serve as indicators of how your heart is working. Your heart rate is the number of times it beats in a minute. Your arteries widen as a result of the number of times your heart beats every minute.

In healthy people, heart rate, workload, and oxygen consumption are all linearly connected up to a certain point. The heart's reaction to physical exercise or stress is considered to be controlled by the sympathetic nervous system.

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The end points of the diameter of a circle then we can easily find out the center point of the circle using the midpoint formula given by: Midpoint=(x1+x22,y1+y22).

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The triangle formed by sides 24, 25 and 5 cm is not a right angled triangle.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.

A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Let us consider the triangle is a right angle triangle

so,  

24 and 5 will be the base and heights

[tex]\sqrt{24\x^{2} + 5\x^{2} } = 24.51\\[/tex]

so 25 is not equal 24.51 cm

so the triangle formed by sides 24, 25 and 5 cm is not a right angled triangle.

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Answer:

C

Step-by-step explanation:

the nth term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

the first term a₁ from the table below n = 1, a₂ below n = 2 and so on

here a₁ = 100 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-50}{100}[/tex] = - [tex]\frac{1}{2}[/tex] , then

[tex]a_{n}[/tex] = 100 [tex](-\frac{1}{2}) ^{n-1}[/tex]

Answer:5x to the -4 power

Over

1x to the -9 power

Step-by-step explanation:thankssss

The lengths in the scale drawing are smaller than the corresponding lengths in the original figure.

When the scale factor is less than 1, the image of a shape will be reduced in size compared to the original shape. This means that all dimensions of the shape will be scaled down by the same factor. For example, if a shape is scaled down by a factor of 0.5, its length, width, and height will all be half the size of the original shape. Additionally, the area and volume of the image shape will be scaled down by the square and cube of the scale factor respectively.

In other words, when the scale factor is between 0 and 1 it will be a reduction and if it's greater than 1 it will be an enlargement.

As can be seen from the question, the scale factor is less than one as it is 1 / 3. This means that the lengths on the scale drawing would be smaller than the lengths on the original drawing.

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Answer:

I believe its A, correct me if i'm wrong.

Step-by-step explanation:

A hypothesis test involves a comparison between research results from a sample and a hypothesis about a population.

Thus, option (A) is correct.

In hypothesis testing, a researcher starts with a null hypothesis, which represents the assumption of no difference or no effect in the population.

The researcher collects data from a sample and performs statistical analysis to determine whether the evidence supports or rejects the null hypothesis in favor of an alternative hypothesis.

The research results obtained from the sample are compared to the hypothesis about the population to determine whether there is enough evidence to reject the null hypothesis and accept the alternative hypothesis.

Thus, option (A) is correct

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Answer:

Step-by-step explanation: By using linear inequation, it can be calculated that-

After 50 hours,  Plan B be more profitable than Plan A for the painter

What is linear inequation?

Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by >, <, ≥, ≤

A one degree inequation is known as linear inequation.

Here, a linear inequation needs to be solved

Let after t hours,  Plan B be more profitable than Plan A for the painter

For plan A

A painter Charges $500 plus $45 per hour

Cost after t hours = $(500 + 45t)

For plan B

A painter Charges  $55 per hour

Cost after t hours = $55t

By the problem,

55t > 500 + 45t

55t - 45t > 500

10t > 500

t >

t > 50

After 50 hours,  Plan B be more profitable than Plan A for the painter

The first step to solve the equation 3x/5 + 5 = 20,

3x/5 + 5 - 5 = 20 - 5

3x/5 (5/3) = 15 (5/3)

is known as Subtraction property of equality, So option B is correct.

It is a property of mathematics, in which we subtract the same number on both the sides of any equation.

for example, ax+b = c  ⇒ ax+b-5 = c-5

Given math equation,

3x/5 + 5  = 20

here we apply, Subtraction property of equality

So, we are subtracting -5 both the sides

3x/5 + 5 - 5 = 20 - 5

Hence, Used property is subtraction property of equality

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Answer: To find the inverse of a function f(x), we need to switch the x and y variables and then solve for y.

So, the inverse function f^-1(x) of f(x) = 2x - 3 is:

f^-1(x) = (x+3)/2

This is the inverse of the function, and it can be denoted by f^-1(x) = (x+3)/2

Step-by-step explanation:

Yes, it is possible to form a triangle with sides of 3.5cm, 4.5cm, and 7.5cm. This is because these triangle's sides adhere to the triangle inequality theorem.

The triangle inequality theorem which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This is because in order to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side, otherwise it would be impossible to connect the three sides and form a closed shape.

In this case,

3.5 cm + 4.5 cm = 8 cm > 7.5 cm

3.5 cm + 7.5 cm = 11 cm > 4.5 cm

4.5 cm + 7.5 cm = 12 cm > 3.5 cm

So it is possible to form a triangle with these side lengths.

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Answer: y= 120

Step-by-step explanation: y= 180 -2x30

=180-60

=120

The degree of a polynomial is the highest power of the variable in the equation. In this case, the equation 2x² 5x³ 7 has the highest power of x being 3, so the degree of the polynomial is 5.

Step 1: Identify the highest power of the variable (x).

Step 2: Count the number of terms in the equation.

Step 3: The degree of the polynomial is the highest power of the variable plus the number of terms minus one.

Step 4: In this case, the highest power of x is 3 and the number of terms is 3, so the degree of the polynomial is 3 + 3 - 1 = 5.

The degree of the polynomial 2x² 5x³ 7 is 5. This can be calculated by taking the highest power of the variable (x) and adding it to the number of terms in the equation (3), and then subtracting 1.

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Answer:

See below

Step-by-step explanation:

The purple is the pre-image.  The orange is the image.  The green is showing that the pre-image and the image are the same difference by the y axis.

Answer:

[tex]a_{73}=367[/tex]

Step-by-step explanation:

[tex]a_n=a_1+(n-1)d\\a_{73}=7+(73-1)(5)\\a_{73}=7+(72)(5)\\a_{73}=7+360\\a_{73}=367[/tex]

Colin will have a total amount of $ 675.90 with Colin.

The interest charged on a loan or deposit is known as compound interest. It is the idea that we used the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest. 

The formula for compound interest is given by

Here we have

Colin invests $600 at a rate of 1.5% per year compound interest for 8 years

Here principal amount, p = $ 600

Rate of interest, r = 1.5% =

Number of compounds per year = 1

Time period, t = 8

By the Compound interest formula A = P (1 + r/n)^nt

A = 600( 1 + 0.015/1)⁽¹⁾⁽⁸⁾  

A = 600(1.015)⁸

A = $675.90  

Therefore,

Colin will have a total amount of $ 675.90.

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The three types of loops that can be built using the while statement and other statements are The While Loop,The For Loop,The Do-While Loop.

Loop in math is a path or line that starts and ends at the same point. It can refer to a continuous curve, like a circle, or to a sequence of discrete points, like a polygonal line. It is a fundamental concept in mathematics, used to study various topics such as curves, surfaces, and solids. Loops are also used in graph theory to study networks.

1. The While Loop: This allows you to execute a set of instructions until a certain condition is met.
2. The For Loop: This is a pre-defined loop that is used to iterate through a list of elements and execute a set of instructions for each element.
3. The Do-While Loop: This is similar to the While Loop, but the set of instructions are executed at least once before the condition is checked. This allows for a set of instructions to always be executed at least once.

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The value of 625 is the numerical representation of the quantity.

It is a composite number, meaning it can be divided evenly by more than just 1 and itself (5 x 5 x 5 = 625). It is also a perfect cube, as it can be represented as 5 cubed (5³).

In mathematical operations, it can be used as a constant or as a variable in equations and formulas. It can also be represented in scientific notation as 6.25 x 10².

In terms of real-world applications, it may be used in measurements, such as area or volume, or as a quantity in various calculations or formulas.

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The measures of angles m∠ABC = 36° and m∠CBD = 84°.

Geometry is a branch of mathematics that deals with shapes, sizes, angles, and dimensions of objects.

The angle m∠ABD = 120° is the result for the sum of the two angles m∠ABC and m∠CBD so;

m∠ABC + m∠CBD = m∠ABD

2x + 5x - 6 = 120°

7x - 6 = 120° {add 6 to both sides}

7x = 120° + 6°

7x = 126° {divide through by 7}

x = 126°/7

x = 18

2x = 2(18) = 36°

5x - 6 = 5(18) - 6 = 84°

Therefore, the geometry question have the measure of angles m∠ABC = 36° and m∠CBD = 84°.

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Possible Question:

Find m∠ABC and m∠CBD if m∠ABD =120°, m∠ABC = 2x, m∠CBD = (5x - 6)°, and the angle m∠ABD is the sum of m∠ABC and m∠CBD.

Answer:

it will the the same shape you esrased but two more squares to the left

points (-3,1)(-5,1)(-4.5,3)(-6,5)

The hypothetical value of the sum of the geometric series is 1

The first term that we have in this progression is given as 1/2. Next we have to find the common ratio that lies between the values.

The sum of the infinite geometric series can be gotten by

a / (1 -r)

where a is the first term in the series = 1/2

r is the common ratio of the progression = 1/2

we would have to input the values. such that we would have:

1/2 / (1- 1/2)

(1/2) / (1/2)

= 1

The sum of the series is 1.

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The function g(n+4) = 10 + n/23 + 4n.

A function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. Let A & B be any two non-empty sets; mapping from A to B will be a function only when every element in set A has one end, only one image in set B.

g(x)=6+x/7+4x

g(n+4) = 6+n+4/7+4(n+4)

g(n+4) = 10 + n/7 + 4n + 16

g(n+4) = 10 + n/23 + 4n

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We can start by using the following equation to determine the number of yards of red fabric r she will need for each costume:

1 + r = y (y represents the total number of yards of fabric for each costume)

We know that the total number of yards for all the costumes is 8 and there are 5 costumes, so we can use this information to set up another equation:

5y = 8 (y represents the total number of yards of fabric for each costume)

Now we can substitute the first equation into the second equation to get:

5(1 + r) = 8

Expanding the left side of the equation:

5 + 5r = 8

Subtracting 5 from both sides:

5r = 3

Dividing both sides by 5:

r = 3/5

So, Mrs. Byers will need 3/5 yards of red fabric for each costume.

Longitudes: The vertical lines running north-south, join the two poles. They are called the meridians of longitude. They are spaced farthest apart at the equator and converge at a point at each pole.

Horizontal lines called latitudes are used to measure distances north or south of the equator. Vertical lines known as longitudes are used to determine the west or east of the meridian in Greenwich, England. Latitude and longitude work together to help cartographers, geographers, and others find specific locations on the globe.

What is the uses of latitude?

Any location's distance from the equator may be determined using its latitude, which is based on its degree. We can locate any point on Earth using longitude and latitude. The GPS or Global Positioning System uses these coordinates.

The grid system that enables us to locate absolute or precise places on the surface of the Earth is made up of latitude and longitude. Latitude and longitude can be used to pinpoint certain locations. Landmark identification also benefits from knowledge of latitude and longitude.

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Our point A(x,y) rotates 270 degrees anticlockwise around the origin to become A' (y,-x). This implies that we reverse x and y and turn x negative.

A figure can be rotated 90 degrees anticlockwise by rotating it 270 degrees clockwise. It would now be (x, y) = (-y, x)

A translation in geometry is a type of transformation that shifts a geometric figure in a specific direction without altering its size or orientation. The figures are congruent before and after the transformation because it is a type of rigid transformation.

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