in the number below, how many times greater is the number represented by the digit in the thousands place than the number represented by the digit in the hundreds place?
57,762

a) the exponential equation equivalent to log8 1/64 = 2 is 1/64 = [tex]8^{(-2)}[/tex]

b)  the logarithmic equation equivalent to 3^0 = 1 is log3 1 = 0.

What is exponential equation?

An exponential equation is one in which the exponent contains a variable.

(a) We can rewrite the logarithmic equation as an exponential equation by using the definition of logarithms. The logarithmic equation

log8 1/64 = 2

means that 8 raised to the power of 2 is equal to 1/64:

[tex]8^2 = 1/64[/tex]

Thus, we can write the exponential equation as:

[tex]1/64 = 8^{(-2)}[/tex]

Therefore, the exponential equation equivalent to log8 1/64 = 2 is 1/64 = [tex]8^{(-2)}.[/tex]

(b) We can rewrite the exponential equation as a logarithmic equation by using the definition of logarithms. The exponential equation

[tex]3^0 = 1[/tex]

means that the logarithm of 1 to the base 3 is equal to 0:

log3 1 = 0

Therefore, the logarithmic equation equivalent to 3^0 = 1 is log3 1 = 0.

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Answer:

1/8

Step-by-step explanation:

If "over" refers to (4 * 6) as a whole,

[tex]\frac{3}{4*6}\\\\=\frac{3}{24}\\\\=\frac{1}{8}[/tex]

If "over" refers to division,

[tex]3 \div 4 \times 6\\= 0.75 \times 6\\= 4.5[/tex]

I would suppose it's the first one, so, ignore the second one if you haven't learnt BODMAS yet.

Hope this helps and be sure to mark this as brainliest! :)

Answer: t=2.59

Step-by-step explanation:

This is a matter of clearing out the equation

set 1151=800e^0.14t

1151/800=e^0.14t

ln(1151/800)/0.14=t

t=2.59

The surface area of the pyramid is 113 cm².

A rectangular pyramid is a type of pyramid where the base is a rectangle and the triangular faces meet at a single point called the apex or vertex. It has five faces, including a rectangular base and four triangular faces, and it is a polyhedron with five vertices and eight edges.

The rectangular pyramid has a base of dimensions 7 cm by 5 cm, and the two large triangular faces have a height of 7.6 cm, while the two small triangular faces have a height of 8 cm.

To find the surface area of the pyramid, we need to find the area of each face and then add them up.

Area of the base:

The base of the pyramid is a rectangle with dimensions 7 cm by 5 cm, so its area is:

Area of base = length × width = 7 cm × 5 cm = 35 cm²

Area of the four triangular faces:

Each of the four triangular faces has a base of 5 cm (the width of the rectangle) and a height of either 7.6 cm or 8 cm. Using the formula for the area of a triangle, we can find the area of each face:

Area of each large triangular face = 1/2 × base × height = 1/2 × 5 cm × 7.6 cm = 19 cm²

Area of each small triangular face = 1/2 × base × height = 1/2 × 5 cm × 8 cm = 20 cm²

There are two large triangular faces and two small triangular faces, so the total area of the four triangular faces is:

Total area of four triangular faces = 2 × area of large triangular face + 2 × area of small triangular face

= 2 × 19 cm² + 2 × 20 cm²

= 78 cm²

Total surface area:

Finally, we can find the total surface area of the pyramid by adding the area of the base to the total area of the four triangular faces:

Total surface area = area of base + total area of four triangular faces

= 35 cm² + 78 cm²

= 113 cm²

Therefore, the surface area of the pyramid is 113 cm²

.

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The histogram should be modified as follows:

A histogram is a type of graphical representation that displays the distribution of a dataset. It is a bar graph-like chart where the data is divided into intervals, called "bins", which are represented by adjacent rectangular bars of varying heights.

Then the height of the histogram gives the number of observations into each data interval.

Hence the histogram should be modified as follows:

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Answer:

1629.24m

Step-by-step explanation:

starting with the easy ones

1) Rectangle 1:

Surface area of rectangle=Length x width

SAR= 24x21

= 504m

2) Rectangle 2:

SAR= 19x21

=399

3) Rectangle 3

SAR= 21x8

=168

4) Rectangle 4:

SAR= 21x11

=231

*because the top and bottom are trapeziums the formular for it is

A=1/2(a+b)h

although those trapeziums don't have h(Height)

it needs to be broken down into two triangles and a rectangle. to find the height*

5) side/height of triangle A:

formula: C squared= a squared + b squared

in this case we already have C and A. meaning we have to rearrange the formula to:

x = c^2 - a^2

x = 8^2 - 2.5^2

x = sqrt 57.75

x = 7.61

6) Trapezium

SA= 1/2(a+b)h

SA= 1/2(19+24)7.61

=163.62

7) add all surface area together

which should equal 1629.24m

Answer: The formula for compound interest is:

A = P(1 + R/100)^t

where A is the amount after t years, P is the principal amount, R is the rate of interest per annum, and t is the time period in years.

Here, P = Rs. 3,500, R = 8%, and t = 2 years.

So, the amount after 2 years will be:

A = 3,500(1 + 8/100)^2

= 3,500(1.08)^2

= 3,892.32

Therefore, the compound interest for 2 years will be:

CI = A - P

= 3,892.32 - 3,500

= 392.32

Hence, the compound interest on Rs. 3,500 for 2 years at the rate of 8% per annum is Rs. 392.32.

Step-by-step explanation:

The missing step in the proof is: D. ADCA

In the statements, we are given that AD || BC and ZDAC = ZBCA (alternate interior angles theorem), so we can conclude that triangle ADCA is similar to triangle BCA (by AA similarity criterion).

Therefore, we have the following proportional sides:

DC/AC = AC/BC

Given that DC = BA (given statement), we can substitute BA for DC in the proportion:

BA/AC = AC/BC

Now, we can cross-multiply to get:

BA * BC = AC²

Using the given statement that AC = AC (reflexive property of congruence), we can substitute AC for AC in the equation:

BA * BC = AC * AC

Use the definition of congruent sides to replace BA with DC:

DC * BC = AC * AC

And finally, use the substitution property of equality to replace BC with 6 units (given statement):

DC * 6 = AC * AC

From this equation, we can see that DC = 6 units, which completes the proof. Therefore, the missing step is statement D. ADCA.

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The solution to the equation 3/5x - 4 - 3√7x + 8 = 0 is x = -10√7/9, which is not one of the options provided.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. 2x - 5 and 13 are expressions in this case. These two expressions are joined together by the sign "=".

To solve the equation 3/5x - 4 - 3√7x + 8 = 0:

First, simplify the expression by combining like terms:

3/5x - 3√7x + 4 = 0 + 8

3/5x - 3√7x + 4 = 8

Next, move the constant term to the right side:

3/5x - 3√7x = 8 - 4

3/5x - 3√7x = 4

Factor out x from the left side:

x(3/5 - 3√7) = 4

Divide both sides by (3/5 - 3√7):

x = 4 / (3/5 - 3√7)

To simplify the expression, we can multiply the numerator and denominator by the conjugate of the denominator, which is (3/5 + 3√7):

x = 4(3/5 + 3√7) / [(3/5 - 3√7)(3/5 + 3√7)]

x = 12/5 + 12√7/5 / (9/25 - 63/25)

x = 12/5 + 12√7/5 / (-54/25)

x = -10√7/9

Therefore, the solution to the equation 3/5x - 4 - 3√7x + 8 = 0 is x = -10√7/9, which is not one of the options provided.

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Answer:

B.

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

the description is very confusing and lacks any hint about the behavior of the curve before the change.

but ok, let's assume that the curve (line ?) is in general going up. in other words, if the traveled miles go up, so does the profit.

I also don't know how they could drive the miles without paying the driver, but again, let's assume they did.

now they pay the driver. $0.25 per mile.

this has to come out of their profit.

so, the Y (profit) values all go down by 0.25.

therefore, the y-intercept is going down too.

that eliminates C. and D.

for this to be true they have to have some overhead costs that apply even if there are 0 miles traveled (which is the meaning of the y-intercept : the y-value when x = 0).

so, the line must be in a form

y = ax + b

with "b" <> 0.

and since we assumed the line to go up (positive slope), a "sinking" line means that the x-intercept (the break-even point, where the line goes from below the x-axis and therefore negative (y) profit up into positive profit) will move to the right (become greater).

because now that they have additional costs (paying the driver), it takes longer (more driven miles) to make a positive profit.

and that eliminates A, leaving B. as the right answer.

Answer: 0.0295

Step-by-step explanation: To solve for r in the equation $425.83=400(1+r)^5$, we can rearrange the equation to isolate the variable.

Dividing both sides by 400 gives $(1+r)^5=1.064575$, and taking the fifth root of both sides gives:

$1+r=\sqrt[5]{1.064575}$.

Subtracting 1 from both sides gives $r\approx 0.0295$.

Therefore, your answer would be 0.0295.

Answer:

5.4

Step-by-step explanation:

square of 29 = 5.385164807

5.385164807 estimated is 5.4

Answer:

40 units

Step-by-step explanation:

a = 8

b = 15

To find c, we can use the formula: [tex]a^{2} +b^{2} =c^{2}[/tex]

[tex]8^{2} +15^{2} =x^{2}[/tex]

64 + 225 = c^2

289 = c^2

c = 17

a + b + c = perimeter

8 + 15 + 17 = 40

Answer:

  40 units

Step-by-step explanation:

You want the perimeter of the triangle shown in the graph.

You can count the grid squares to find the horizontal and vertical dimensions of the triangle. You find they are 8 units and 15 units, respectively.

The length of the slant side is the hypotenuse of a right triangle with sides 8 and 15. If you don't recognize this {8, 15, 17} Pythagorean triple, you can find the hypotenuse using the Pythagorean theorem:

  c² = a² +b²

  c² = 8² +15² = 64 +225 = 289

  c = √289 = 17

The long side of the triangle is 17 units.

The perimeter of the triangle is the sum of the lengths of its sides:

  P = 8 + 15 + 17 = 40

The perimeter is 40 units.

__

Additional comment

A "Pythagorean triple" is a set of three integer side lengths that form a right triangle. The triple is "primitive" if the numbers have no common factor. There are a few Pythagorean triples that regularly show up in algebra, trig, and geometry problems. Some of them are ...

  {3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41}

You will also see multiples of these, for example, 2·{3, 4, 5} = {6, 8, 10}.

The smallest is {3, 4, 5}, and it is the only set that is an arithmetic sequence (has constant differences between lengths). In every case, the sum of the numbers is even. (A right triangle cannot have integer side lengths and an odd perimeter value.)

The expression that has the greatest value when n is equal to 4 is option B, n + 30, with a value of 34.

To determine which mathematical expression has the greatest value when n is equal to 4, we can simply substitute 4 for n in each expression and compare the results.

A. 5n = 5(4) = 20

B. n + 30 = 4 + 30 = 34

C. 50 - n = 50 - 4 = 46

D. 80 ÷ n = 80 ÷ 4 = 20

The complete question is: Which expression has the greatest value when n is equal to 4? A. 5n B. n + 30 C. 50 – n D. 80 ÷ n

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Answer:

  (d)  25 feet and 20 feet​

Step-by-step explanation:

You want the possible dimensions of a pool with an area of 500 square feet and a perimeter of 90 feet.

The area is the product of the length and width. The area of the pools offered in the answer choices are ...

  (a)  15·30 = 450 . . . square feet

  (b)  10·35 = 350 . . . square feet

  (c)  50·10 = 500 . . . square feet

  (d)  25·20 = 500 . . . square feet

The area requirement eliminates answer choices A and B.

The perimeter is twice the sum of length and width. The perimeters of the possible pools are ...

  (c) 2(50 +10) = 120 . . . feet

  (d) 2(25 +20) = 90 . . . feet

The perimeter requirement eliminates answer choice C.

The pool's possible length and width are 25 feet and 20 feet, choice D.

__

Additional comment

You could write a quadratic equation for the pool dimensions, but doing that will generally involve more work than checking the given answer choices.

If x is the width, then 45-x is the length, and the area is ...

  x(45 -x) = 500

  x² -45x +506.25 = -500 +506.25 . . . multiply by -1, complete the square

  x = 22.5 -√6.25 = 20 . . . . take the square root; width is the smaller dimension

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Step-by-step explanation:

to find the interest she needs to pay back every month, we need to use this formula:

I = PRT/12

in this case the principle is $300,000, the rate is 7% p.a. and the amount of time is 1 year, if we substitute in our values we:

I = (300,000)(7)(1)/12 = $17,500 in interest every month

to find her yearly income from rent, we have to multiply the monthly rent by 12

1500 × 12 = $18,000

to calculate her loss percentage in a year, we have to subtract 18,000 from 3000 which is 15,000

she said that she hopes the property's value will increase to cover the loss she made.

to cover the loss of $15000 per year, the property needs to increase in value by at least $15000. the percentage increases value can be written as

Percentage increase = (difference in increase/Original price) × 100

so

percentage increase = (15000/300000) × 100 = 5%

so the property needs to increase in value by at least 5% per year to cover the loss.

The woman needs to pay $1750 monthly as interest. Her yearly income from the rent is $18,000. After considering all other costs, she is at a loss of $6000 per year, so the property needs to increase in value by 2% per year to cover this loss.

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Answer: The area of the door can be calculated as:

Area of door = width x height

= 0.9 m x 2.1 m

= 1.89 square meters

The area of one window can be calculated as:

Area of window = width x height

= 1.5 m x 1.2 m

= 1.8 square meters

Since there are four windows, the total area of the four windows is:

Total area of four windows = 4 x Area of window

= 4 x 1.8 square meters

= 7.2 square meters

Therefore, the total area of the door and the four windows is:

Total area = Area of door + Total area of four windows

= 1.89 square meters + 7.2 square meters

= 9.09 square meters

Hence, the total area of the door and the four windows is 9.09 square meters.

Step-by-step explanation:

By answering the presented question, we may conclude that As a result, the linear function denoted by the table is y = 2x - 2.

A line's slope shows how steep it is. A mathematical equation for the gradient is referred to as "gradient overflow" (the change in y divided by the change in x). The slope is defined as the ratio of vertical change (rise) to horizontal change between two points (run). The slope-intercept form of an equation is used to represent the equation of a straight line, which is written as y = mx + b. The y-intercept is located where the line's slope is m, b is b, and (0, b). The slope and y-intercept of the equation y = 3x - 7 are two examples (0, 7). The line's slope is m. b is b at the y-intercept, and (0, b).

To obtain the slope and y-intercept of a linear function in slope-intercept form, we must first establish the slope and y-intercept.

With two locations on the line, we can first determine the slope. Let us start with the first and last points in the table:

slope = (y change) / (change in x)

slope = (16 - (-8)) / (9 - (-3))

slope = 24 / 12

slope = 2

We can now use the slope and one of the points to get the y-intercept. Let's take the point (1, 0) as an example:

y = mx + b 0 + b b = 2(1) + b b = -2

Hence the linear function's slope-intercept equation is:

y = 2x - 2

As a result, the linear function denoted by the table is y = 2x - 2.

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One per 2,500 can be used to represent the rate of 80cm to 2km.

To write 80cm to 2km as a rate, we need to convert the units to the same system. We can convert 80cm to kilometers by dividing by 100,000 (since there are 100,000 centimeters in a kilometer):

80 cm/100,000 = 0.0008 km

Now we can express the rate as:

0.0008 km per 2 km

Or we can simplify it by dividing both the numerator and denominator by 0.0008:

1 per 2,500

Therefore, 80cm to 2km can be expressed as a rate of 1 per 2,500.

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The student's is incorrect because the greatest common factor of 12 and 8 is 2z, so the correct expression is 2x (6x+4).

Expression is the communication of emotion or ideas through words, art, music, or other forms of communication. It is the way in which a person or artist conveys their thoughts and feelings in a creative and meaningful way. Expression can be seen in the form of art, writing, music, dance, and other creative outlets. Expression is a powerful tool that can be used to communicate a message or to evoke a feeling in the audience. Expression can be used to inspire, educate, motivate, and even to heal. Expression is a way to connect people and cultures, and a way to share stories and experiences. It is a way to express oneself in a meaningful and powerful way.

This is because 12z+8 can be written as 2z(6x+4), where the greatest common factor of 12 and 8 (2z) is factored out.

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Complete Question:
The expression 12z+8 is equivalent to the expression a (bx + c), where b and c are constants and have no common factors. A student wrote the answer as 2 (6x+4).

Which statement best explains whether the student's answer is correct or incorrect?

OA. The student's answer is incorrect because the greatest common factor of 12 and 8 is 2z, so the correct expression is 2x (6x+4).

OB. The student's answer is incorrect because the greatest common factor of 12 and 8 is 4z, so the correct expression is 4z (3x+2).

C. The student's answer is incorrect because the greatest common factor of 12 and 8 is 4, so the correct expression is 4 (3x+2).

OD. The student's answer is incorrect because the greatest common factor of 12 and 8 is 8, so the correct expression is 8 (4x+1).

Answer:

-2.5

Step-by-step explanation:

follow BIMDAS.

like my answer if you find it helpful

Using the total area of the rectangular pool we know that the required width of the pathway is 3.6 ft respectively.

In the Euclidean plane, a rectangle is a quadrilateral with four right angles.

A parallelogram with a right angle or an equiangular quadrilateral, where equiangular means that all of its angles are equal, are other ways to define it.

A rectangle with four equal-length sides is a square.

Squares are not always rectangles, but rectangles are always squares.

So, the pool and walkway together have a 360 square foot total space.

Assume that the walkway is w feet in width.

Since the pool has an additional w feet of width on both sides, the total area's measurements can be expressed as (8 + 2w) by (10 + 2w).

Thus, we can construct the following equation:

(8 + 2w) x (10 + 2w) = 360

By enlarging and condensing the left side, we obtain:

4w² + 36w - 80 = 0

Using the quadratic formula, we can find w:

w = (-b ± √(b² - 4ac)) / 2a

Here, an equals 4, b equals 36, and c equals -80. When these values are added to the formula, we obtain:

w = (-36 ± √(36² - 4(4)(-80))) / 8

w = (-36 ± √(1872)) / 8

w ≈ -5.6 or w ≈ 3.6

We can ignore the first option because the width cannot be negative. Consequently, the pathway should be around 3.6 feet wide.

Therefore, using the total area of the rectangular pool we know that the required width of the pathway is 3.6 ft respectively.

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The appropriate measurement unit for force is  kg.m/s²

A force is simply referred to as either a push or pull of an object resulting from the object's interaction with another object.

From Newton's Second Law, force is expressed as;

F = m × a

Where is mass of object and a is the acceleration

One Newton is defined as the force required to accelerate a mass of one kilogram at a rate of one meter per second squared.

Since F = m × a

Plug in m = kg and a = m/s²

F = kg × m/s²

F = kg.m/s²

Therefore, the unit of measurement is kg.m/s².

Option B is the correct answer.

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Answer: Let's say that the width of the rectangle is x meters. Then, according to the problem, the length of the rectangle is 6 meters longer than the width, which means that the length is (x + 6) meters.

The formula for the area of a rectangle is:

Area = Length x Width

We are given that the total area of the rectangle is 16m². Substituting the expressions for length and width, we get:

(x + 6) x = 16

Expanding the product and rearranging, we get a quadratic equation:

x² + 6x - 16 = 0

We can solve this equation by factoring or by using the quadratic formula. Factoring, we get:

(x + 8) (x - 2) = 0

This equation is satisfied when either x + 8 = 0 or x - 2 = 0. Therefore, the possible values for the width are x = -8 or x = 2. However, since the width of a rectangle cannot be negative, we reject the solution x = -8.

Therefore, the width of the rectangle is x = 2 meters. The length is 6 meters longer than the width, so the length is (2 + 6) = 8 meters.

Therefore, the dimensions of the rectangle are 2 meters by 8 meters.

Step-by-step explanation:

The correct option -D. 5;  Thus, the value of x for the given external secant segment and the tangent on the circle is found as:x = 5.

A line that precisely intersects a circle at two points is said to be a secant.

The size of the angle created when two tangents, two secants, or two tangents cross outside of a circle is equal to one-half a positive difference between the sizes of the intercepted arcs.

Using the Theorem:

The square of a length of tangent is equal the the product of such external secant segment and the overall length of the secant if one secant and one tangent both drawn to a circle from a single exterior point:

4(4 + x) = 6²

16 + 4x = 36

4x = 36 - 16

4x = 20

x = 20/4

x = 5

Thus, the value of x for the given external secant segment and the tangent on the circle is found as:x = 5.

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The value of GH in the right angle triangle, given FH and Angle FHG is 22.46 inches.

Since we have the adjacent side (FH) and want to find the hypotenuse (GH), we can use the cosine function.

cos(35°) = adjacent side (FH) / hypotenuse (GH)

We know that FH = 18.4 in. So, we can write the equation as:

cos(35°) = 18.4 / GH

GH = 18.4 / cos(35°)

GH = 18.4 / 0.81915

=  22.46 inches

So, the length of GH, the hypotenuse, is approximately 22.46 inches.

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The coordinates of the vertices of the image rectangle M'P'A'T' are:

M'(2,1), P'(3,1), A'(3,3), T'(2,3).

What is rectangle?

A rectangle is a geometric shape that has four sides and four right angles (90 degrees) with opposite sides being parallel and equal in length.

To find the coordinates of the vertices of the image rectangle M'P'A'T', we need to apply a transformation to each vertex of the original rectangle MPAT.

We can see that the original rectangle MPAT has sides parallel to the x and y-axes, which suggests that it is aligned with the coordinate axes. We can also see that the length of its sides are equal, which means it is a square.

To transform this square, we can use a combination of translations, rotations, and reflections. However, since we don't have any information about the type of transformation that is being applied, we can assume that the simplest transformation is a reflection across the line y=x.

To reflect a point (x,y) across the line y=x, we swap its x and y coordinates to get the reflected point (y,x). Therefore, the coordinates of the vertices of the image rectangle M'P'A'T' are:

M'(2,1)

P'(3,1)

A'(3,3)

T'(2,3)

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The volume of air passing through the filter is 800 cubic feet per minute. It is calculated by multiplying the air flow speed (100ft/min) by the area of the filter (8ft²).

The volume of air passing through the HEPA filter can be calculated using the formula for the speed of air flow multiplied by area. The speed of the air flow is given as 100ft/min and the area of the filter is given as 4ft x 2ft, which equals 8 square feet. Therefore, the volume of the air passing through the filter can be calculated as 8ft2 x 100ft/min = 800 cubic feet per minute.

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Answer:

Phn10x12

Step-by-step explanation:

PEANUTS CASHEWS MIXTURE Number of Grams (g) 12 X 12+ X Price per grams Php 10.00 Php 8.00 Php 9.00 Total Price Phn10x12 = Php 120 8x 9 [12+x]​

The statements that provide support for Chloe's claim are A<0 because A is to the left of zero, B>0 because B is to the right of zero. So correct option is A and F.

Comparison algebra is a branch of algebra that deals with inequalities and comparisons between different quantities or expressions. In comparison algebra, the goal is to determine the relationships between different expressions or quantities, such as whether one expression is greater than, less than, or equal to another expression.

Comparison algebra involves the use of comparison symbols, such as "<" (less than), ">" (greater than), and "=" (equal to), to express these relationships. For example, if we have two expressions, A and B, we can use the "<" symbol to express the relationship that A is less than B, as in A < B.

In comparison algebra, we can also manipulate inequalities and equations in similar ways as we do with regular algebraic expressions. For instance, we can add, subtract, multiply, or divide both sides of an inequality or equation by the same number or expression, while maintaining the inequality's direction.

The statements that provide support for Chloe's claim are:

A. A<0 because A is to the left of zero.

F. B>0 because B is to the right of zero.

Statement A supports Chloe's claim because Point A is to the left of zero on the number line, which means its value is negative. Statement F also supports Chloe's claim because Point B is to the right of zero on the number line, which means its value is positive.

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