which expressions are equivalent to 7⁴· 9⁸?

the ordered pairs of three points that could each be the other endpoint of the line segment are (10,-7) or (-14,-7) and (-2,5) or (-2,-19)

Define Line segment

A line segment in geometry contains two different points on it that called its boundaries. A line segment is sometimes called as a section of a line that links two places.

Given

One end point=(-2,-7)

Length of the line segment=12unit

Line segment is horizontal

Ordered pair that will be other end of the line segment=(-2+12,-7) or(-2-12,-7)

=(10,-7) or (-14,-7)

Line segment is Vertical

Ordered pair that will be other end of the line segment=(-2,-7+12) or(-2,-7-12)

=(-2,5) or (-2,-19)

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a) The probability that neither fire engine is available when needed is 0.0016. b) The probability that a fire engine is available when needed is 0.9984.

The probability of an event occurring is the likelihood that it will happen. In this case, we are looking at the probability of a specific fire engine being available when needed.

The probability that neither fire engine is available when needed can be found by multiplying the probabilities of each fire engine not being available. The probability of a specific fire engine not being available is [tex]1 - 0.96 = 0.04[/tex]. So the probability that neither is available is [tex]0.04 * 0.04 = 0.0016.[/tex]

The probability that a fire engine is available when needed can be found by subtracting the probability that neither is available from 1. So the probability that a fire engine is available when needed is[tex]1 - 0.0016 = 0.9984.[/tex]

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Answer:

x ≥ 4

Step-by-step explanation:

There are 286 different ways to select 3 players from a 13-player baseball team to visit schools to support a summer reading program.

This is a combination problem, where we want to select 3 players from a team of 13 players, without regard to order.

The number of ways to select r items from a set of n distinct items is given by the combination formula:

C(n, r) = n! / (r!(n-r)!)

where n is the total number of items and r is the number of items to be selected.

In this case, we want to select 3 players from a team of 13 players, so we can use the combination formula:

C(13, 3) = 13! / (3!(13-3)!) = (13 x 12 x 11) / (3 x 2 x 1) = 286

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Answer: a) To find the scale factor, we need to find the ratio of the corresponding lengths of the two prisms, since the volumes of two similar prisms are proportional to the cube of the scale factor. Let x be the scale factor.

(volume of larger prism) / (volume of smaller prism) = (x³) = 27/1

x³ = 27

x = 3

Therefore, the scale factor is 3.

b) The ratio of the areas is equal to the square of the scale factor. Let A1 and A2 be the areas of the larger and smaller prisms, respectively.

(A1) / (A2) = (scale factor)²

A2 = A1 / (scale factor)²

A2 = 153 / 9

A2 = 17 cm²

Therefore, the ratio of their areas is 9:1.

c) The ratio of the volumes is equal to the cube of the scale factor.

(volume of larger prism) / (volume of smaller prism) = (scale factor)³

(volume of smaller prism) = (1 cm³) * (scale factor)³

(volume of smaller prism) = 27 cm³

Therefore, the ratio of their volumes is 27:1.

d) To find the surface area of the smaller prism, we can use the same ratio as in part (b) to find that the surface area of the smaller prism is equal to the surface area of the larger prism divided by the square of the scale factor.

(surface area of smaller prism) = (surface area of larger prism) / (scale factor)²

(surface area of smaller prism) = 153 / 9

(surface area of smaller prism) = 17 cm²

Therefore, the surface area of the smaller prism is 17 cm².

Step-by-step explanation:

Hence, in answering the stated question, we may say that We may now trigonometry compare the two sides and observe that they are equal, demonstrating the provided identity.

Trigonometry is the field of mathematics that explores the connection between triangle side lengths and angles. Owing to the application of geometry in astronomical research, the topic originally originated in the Hellenistic era, beginning in the third century BC. The subject of mathematics known as exact techniques is concerned with certain trigonometric functions and their possible applications in calculations. Trigonometry contains six commonly used trigonometric functions. Their separate names and acronyms are sine, cosine, tangent, cotangent, secant, and cosecant (csc). Trigonometry is the study of triangle characteristics, particularly those of right triangles. As a result, geometry is the study of the properties of all geometric forms.

The first stage in Rita's evidence would be determined by the method she uses to verify her identity. Nonetheless, one alternative method to begin the proof is to use the trigonometric identities:

sin(-θ) = -sin(θ) and cos(-θ) = cos(θ)

Applying these identities, we can rewrite the given equation's left side as:

sin(-) cos(-) = cos() (-sin())

After that, we may employ the following identity:

tan( ) = sin( )/cos( )

to rewrite the following equation's right side as:

-1 tan() = -sin()/cos()

We may now compare the two sides and observe that they are equal, demonstrating the provided identity.

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The correct situation which can be modeled with a periodic function is,

⇒ The height of a pebble stuck in the tread of a tire.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Now, The situations that can be modeled with a periodic function is that,

The height of a pebble stuck in the tread of a tire.

And, A function is said to be periodic if it gives same value after a same period. And functions which are not periodic are called aperiodic.

Thus, The correct situation which can be modeled with a periodic function is,

⇒ The height of a pebble stuck in the tread of a tire.

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The 5 number summary for the given dataset (40, 42, 46, 48, 51, 55, 58, 66, 67, 68, 69) is: Minimum: 40, Q1: 47, Median (Q2): 55, Q3: 66.5, Maximum: 69.

What is statistics ?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the use of quantitative methods to gather, describe, and draw inferences from data, which can be used to make decisions, predictions, or conclusions about a population or a phenomenon.

To find the 5 number summary, we need to find the minimum, maximum, and the three quartiles of the given dataset:

The minimum value is 40.

To find the quartiles, we first need to sort the data in ascending order:

40, 42, 46, 48, 51, 55, 58, 66, 67, 68, 69

The median (quartile 2) is the middle value of the dataset, which is 55.

Quartile 1 (Q1) is the median of the lower half of the dataset, which includes the values 40, 42, 46, 48, and 51. The median of this lower half is (46+48)/2 = 47.

Quartile 3 (Q3) is the median of the upper half of the dataset, which includes the values 58, 66, 67, 68, and 69. The median of this upper half is (66+67)/2 = 66.5.

The maximum value is 69.

Therefore, the 5 number summary for the given dataset is:

Minimum: 40

Q1: 47

Median (Q2): 55

Q3: 66.5

Maximum: 69

Therefore, the 5 number summary for the given dataset (40, 42, 46, 48, 51, 55, 58, 66, 67, 68, 69) is: Minimum: 40, Q1: 47, Median (Q2): 55, Q3: 66.5, Maximum: 69.

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The side of the right triangle can be found as follows:

b = 4√2 units

d = 7√3 / 2 units

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, let's use trigonometric ratios to find the side of the right triangle as follows;

Let's find b as follows:

sin 45 = opposite / hypotenuse

sin 45° = b / 8

cross multiply

b = 8 sin 45

b = 8 × √2 / 2

b = 8√2 / 2

b = 4√2 units

Let's find d as follows:

sin 60° = d / 7

cross multiply

d = 7 sin 60

d = 7 × √3 / 2

d = 7√3 / 2 units

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The tax rate used to calculate a person's payable tax in South Africa is not a fixed rate, but rather a combination of different rates that apply to different income brackets

As of the 2021/2022 tax year, the tax rates for individuals in South Africa are as follows:

For taxable income up to R216,200: 18% of taxable income

For taxable income between R216,201 and R337,800: R38,916 plus 26% of taxable income above R216,200

For taxable income between R337,801 and R467,500: R70,532 plus 31% of taxable income above R337,800

For taxable income between R467,501 and R613,600: R110,739 plus 36% of taxable income above R467,500

For taxable income between R613,601 and R782,200: R163,335 plus 39% of taxable income above R613,600

For taxable income above R782,200: R229,089 plus 41% of taxable income above R782,200

Based on the above tax rates, if a person's annual taxable income is R450,090, their payable tax would be calculated as follows:

18% of the first R216,200 = R38,916

26% of the amount above R216,200 up to R337,800 = R26,890

31% of the amount above R337,800 up to R450,090 = R34,754

Total payable tax = R38,916 + R26,890 + R34,754 = R100,560

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The average cost of a letter was 7.11.

The average cost of a letter can be calculated using the following formula:

Average cost per letter = Total Cost / Number of Letters

In this instance, the average cost of a letter is 7.11 (rounded to the nearest cent):

Average cost per letter = 3,455 / 485

Average cost per letter = 7.11

To calculate the average cost of a letter, we used a simple formula. The total cost was divided by the total number of letters to get the average cost per letter. This amount was then rounded to the nearest cent to get the final answer of 7.11.

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Answer:

The missing measures in triangle STU are:

SU = 14, ST = (2/3)TU, TU = (4/3)ST, m∠S = 70 degrees, m∠T = 64 degrees, m∠U = 46 degrees.

Step-by-step explanation:

Since triangles PQR and STU are similar, their corresponding sides are in proportion, and their corresponding angles are congruent. We can use this information to find the missing measures in triangle STU:

Since side PQ corresponds to side ST, we have:

ST/PQ = TU/PR

Substituting the given values, we get:

ST/14 = TU/21

Cross-multiplying, we get:

ST × 21 = 14 × TU

ST = (14/21)TU

Simplifying, we get:

ST = (2/3)TU

Since side QR corresponds to side TU, we have:

TU/QR = ST/RP

Substituting the given values, we get:

TU/28 = ST/21

Cross-multiplying, we get:

TU × 21 = 28 × ST

TU = (28/21)ST

Simplifying, we get:

TU = (4/3)ST

Since angle P corresponds to angle S, we have:

m∠S = m∠P = 70 degrees

Since angle R corresponds to angle U, we have:

m∠U = m∠R = 46 degrees

To find m∠T, we can use the fact that the angles in a triangle add up to 180 degrees:

m∠S + m∠T + m∠U = 180

Substituting the given values, we get:

70 + m∠T + 46 = 180

Simplifying, we get:

m∠T = 64 degrees

To find SU, we can use the fact that the corresponding sides are in proportion:

SU/PR = ST/PQ

Substituting the given values, we get:

SU/21 = (2/3)

Cross-multiplying, we get:

SU = 14

Therefore, the missing measures in triangle STU are:

SU = 14

ST = (2/3)TU

TU = (4/3)ST

m∠S = 70 degrees

m∠T = 64 degrees

m∠U = 46 degrees.

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Sensitivity 67% specificity 86%

Positive predictive values 67% Negative predictive values 86%

Probability of the correct diagnosis 80%

The following can be calculated from the data given:1. Sensitivity and Specificity2. Positive and Negative Predictive Values.3. The probability of the correct diagnosis1. Sensitivity and Specificity:Sensitivity is the proportion of positive cases correctly identified by a screening test or diagnosis test. Sensitivity = Number of true positives / (Number of true positives + Number of false negatives) = 20 / (20 + 10) = 20 / 30 = 67%Specificity is the proportion of negative cases correctly identified by a screening test or diagnosis test. Specificity = Number of true negatives / (Number of true negatives + Number of false positives) = 60 / (60 + 10) = 60 / 70 = 86%2. Positive and Negative Predictive Values.Positive Predictive Value (PPV) is the proportion of positive test results that are true positives.Positive predictive value (PPV) = Number of true positives / (Number of true positives + Number of false positives) = 20 / (20 + 10) = 20 / 30 = 67%.Negative Predictive Value (NPV) is the proportion of negative test results that are true negatives.Negative predictive value (NPV) = Number of true negatives / (Number of true negatives + Number of false negatives) = 60 / (60 + 10) = 60 / 70 = 86%.3. Probability of the correct diagnosisThe probability of correctly diagnosing a diseased individual would be the proportion of true positives and true negatives among the total tested.Probability of correctly diagnosing a diseased individual = (Number of true positives + Number of true negatives) / (Number of true positives + Number of false positives + Number of true negatives + Number of false negatives) = (20 + 60) / (20 + 10 + 60 + 10) = 80 / 100 = 80%.

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Function describing following curve in which a circle of radius 6 centered at (4,3,0) that lies in the plane y = 3 is [tex]r(t) = (6 cos t +4,6 sin t +3,0)[/tex], for Osts 21. Therefore the correct answer is Option c.


A circle of radius 6 centered at (4,3,0) that lies in the plane y = 3 can be described by the following function:
[tex]r(t) = (6 cost +4,6 sint +3,0), for Osts 21[/tex]
This function describes the position of a point on the circle at any given time t.

The x and z coordinates are determined by the cosine and sine function, respectively, with a radius of 6. The y coordinate is constant at 3, since the circle lies in the plane y = 3. The center of the circle is shifted by adding 4 to the x coordinate and 3 to the y coordinate.

Therefore, the correct answer is Option c. [tex]r(t) = (6 cost +4,6 sint +3,0),[/tex] for Osts 21.

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Answer:

total cost equation = ( 9+x) times 4 = 724. Total,price of a ticket is 162$

Step-by-step explanation:

Since insurance for each ticket costs 19$ and the family bought four and the ticket itself costs x, the costs of the four tickets is (19+x) times 4. If thr total cost is 724 then we can take 19 times4 and subtract that from it because 19times 4 + x times 4 is the same as (19+x) times 4. From this we fet 648. Now we have x4 or x times 4 = 648 leftover, so divided 648 by 4 to get one x out of it since it is made up of four x. You get 162 from this, so the price of a ticket without insurance is 162$

cos^2(x) - cos^4(x)

sin^2 (x) cos^2 (x) can be written as sin^2 (x) cos^2 (x) = (1-cos^2(x)) cos^2(x)Expanding (1-cos^2(x)) cos^2(x) gives - cos^4(x) + cos^2(x)Therefore, sin^2 (x) cos^2 (x) in expanded form, with no powers, parentheses or products is cos^2(x) - cos^4(x).

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The equatiοn οf the circle is [tex](x + 5)^2 + (y + 6)^2 = 25[/tex].

The standard fοrm equatiοn οf a circle with radius "r" and center (a, b) is:

[tex](x - a)^2 + (y - b)^2 = r^2[/tex]

In this case, the center is (-5, -6) and the radius is 5. Sο, we can substitute these values intο the standard fοrm equatiοn and get:

[tex](x - (-5))^2 + (y - (-6))^2 = 5^2[/tex]

Simplifying the equatiοn, we get:

[tex](x + 5)^2 + (y + 6)^2 = 25[/tex]

Therefοre, the equatiοn οf the circle is [tex](x + 5)^2 + (y + 6)^2 = 25.[/tex]

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Answer:

x = -12 and x = 12.

Step-by-step explanation:

To solve for x, we need to take the square root of both sides of the equation:

x² = 144

√(x²) = √144

since sqaure root gives both positive and neagtive value, so

x = ±12

So the solutions for x are x = -12 and x = 12.

The density of the lead cuboid is approximately 11.3 g/cm³.

What is density?

Density is a physical property of matter that describes how much mass is contained within a certain volume. It is defined as the amount of mass per unit of volume, and is typically measured in grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³).

The formula for density is:

density = mass / volume

where mass is the amount of matter in an object, and volume is the amount of space that the object occupies.

The volume of the cuboid can be calculated using the formula V = lwh, where l, w, and h are the length, width, and height of the cuboid, respectively.

Given that the length (l) of the cuboid is 5cm, the width (w) is 3cm, and the height (h) is 2cm, we can calculate the volume as:

V = lwh = 5cm x 3cm x 2cm = 30 cm³

The density (ρ) of an object is defined as its mass (m) per unit volume (V), or ρ = m/V.

Given that the mass of the cuboid is 339 g and its volume is 30 cm³, we can calculate the density as:

ρ = m/V = 339 g / 30 cm³ ≈ 11.3 g/cm³ (to 1 decimal place)

Therefore, the density of the lead cuboid is approximately 11.3 g/cm³.

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The acceleration of a bus his speech changes from 126M/S to 3097 m/s over a period of three seconds is 990. 3 m/s^2

Acceleration is can be defined as the rate of change of the velocity of an object with respect to time.

It is also defined as the rate at which velocity changes with time, that is, in both speed and direction.

Accelerations are vector quantities because they are known to have both magnitude and direction.

The orientation of an object's acceleration is determined by the configuration of the net force acting on that object.

The formula for acceleration is given as;

Acceleration = change in velocity/time

Substitute the values

Acceleration = 3097 - 126 (m/s)/3 s

Divide the values

Acceleration = 990. 3 m/s^2

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The given polynomial is x⁵ + (1/5)x³ - x⁵ - x + 5 + x³, Combining the like terms, we get: 2x⁵ + (6/5)x³ - x + 5 This is the polynomial in standard form.

To rewrite the given polynomial in standard form, we first need to combine the like terms. The polynomial can be simplified by adding the coefficients of the same degree terms. After combining like terms, we get -2x⁵ + (6/5)x³ - x + 5. This is the standard form of the polynomial, where the terms are arranged in descending order of degree, and each term has a coefficient multiplied by a power of x. In this case, the highest degree term is -2x⁵, followed by (6/5)x³, -x, and finally, the constant term 5.

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Complete Question

Rewrite the following polynomial in standard form. -x⁵ + (1/5)x³ - x⁵ - x + 5 + x³

Simone will need approximately 429.4 square feet of glass to cover the entire pyramid.

Calculating the surface area of a square pyramid

The surface area of a square pyramid can be calculated by using the following formula: S = l² + 2lw

where, S = surface areal = length of one side of the bases = 10 feet

w = slant height of the pyramid

We need to find the slant height of the pyramid to calculate the surface area of the pyramid.

The slant height of the square pyramid can be calculated using the Pythagorean theorem. We can draw a triangle by joining the midpoint of one of the sides of the base and the apex of the pyramid.

This will divide the pyramid into two right triangles. Using the Pythagorean theorem, we have; l² + h² = sl²

where, h = height of the pyramid = 14 feet

l = half the length of one of the sides of the base = 5 feet

Substituting the given values into the above formula, we get;

5² + 14² = s²

25 + 196 = s²

221 = s²s = √221 ≈ 14.87 feet

Now that we have the slant height of the pyramid, we can substitute the values into the surface area formula we had earlier: S = l² + 2lw

S = 10² + 2(10)(14.87)S ≈ 429.4 square feet

Therefore, Simone will need approximately 429.4 square feet of glass to cover the entire pyramid.

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The equivalent ratio to tan F  in  right angles triangle, △EFD is tan F = DE / DF.

For the stated question:

△EFD∼△GHD

So, in right angles triangle, △EFD

Sin Ф = perpendicular / hypotenuse.

Sin E = DF / EF

And,

The ratio is equivalent to tan F = perpendicular / base

tan F = DE / DF

Thus, the equivalent ratio to tan F  in  right angles triangle, △EFD is tan F = DE / DF.

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The complete question is attached:

Option (a) [tex]y=\frac{3x}{2} -5[/tex] can be used as a the model line on the graph for the Linear function.

A linear function in mathematics is one that has either one or two variables but no exponents. It is a function with a straight line as its graph.

A straight line on the coordinate plane is described by a linear function.

Option (a) [tex]y=\frac{3x}{2} -5[/tex] satisfy with all point as below,

If we take, x = 0, we get y = -5

If we take, x = 2, we get y = -2

If we take, x = 4, we get y = 1

If we take, x = 6, we get y = 4

If we take, x = 8, we get y = 7

So, here we see all the value are match according to the graph.

Therefore, [tex]y=\frac{3x}{2} -5[/tex] can be used as a the model line on the graph for the Linear function.

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domain of the function is (-∞, ∞)

When answering questions on the Brainly platform, it is important to always be factually accurate, professional, and friendly. In addition, you should be concise and provide a step-by-step explanation in your answer. Irrelevant parts of the question should be ignored, and the following terms should be used in your answer.To solve the inequality 72 - 72 > 1 X-1 X, we need to simplify the inequality as shown below:72 - 72 > 1 X-1 X0 > X - 1Since we want to get X alone on one side of the inequality, we need to add 1 to both sides:0 + 1 > X - 1 + 1X > 0Thus, the solution to the inequality 72 - 72 > 1 X-1 X is (0, ∞).To find all values of x for which the graph of f(x) = x² flies above the graph of g(x) = 2x + 48, we need to solve the inequality:f(x) > g(x)x² > 2x + 48We can rearrange this inequality as follows:x² - 2x > 48Now, we need to factor the left-hand side of the inequality:x(x - 2) > 48The inequality will be satisfied if x > 0 and x - 2 > 0 (i.e. x > 2), so the solution to the inequality is x > 2.The domain of the given function f(x) = 72 + x - x² is all real numbers, since there are no restrictions on the input value x. Therefore, the domain of the function is (-∞, ∞).

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Answer:

3

Step-by-step explanation:

in a three - dimensional scenario a plane consists of three points and also they are not on the same line.

When 25 percent of doctors make less than $180k and 25% make more than $320k, a. Approximately 13.14% of physicians earn less than $200,000. and b. Approximately 7.75% of physicians earn between $280,000 and $320,000.

a. The fraction of physicians who earn less than $200,000 can be estimated using the given information as follows:

Let's denote the mean salary of physicians in this specialty by μ and the standard deviation by σ. Since the salaries are approximately normally distributed, we can use the properties of the standard normal distribution to solve this problem.

We know that 25% of the physicians earn less than $180,000, which means that their z-score (number of standard deviations from the mean) is: z = (180,000 - μ) / σ

Using a calculator, we can find the z-score corresponding to the 25th percentile, which is approximately -0.674. Therefore: -0.674 = (180,000 - μ) / σ

Similarly, we know that 75% of the physicians earn more than $180,000, which means that their z-score is: z = (320,000 - μ) / σ

Using the calculator, we can find the z-score corresponding to the 75th percentile, which is approximately 0.674. Therefore: 0.674 = (320,000 - μ) / σ

Solving these two equations simultaneously, we can find μ and σ:

μ = $250,000

σ = $53,333

Now, to find the fraction of physicians who earn less than $200,000, we need to calculate the z-score corresponding to this salary: z = (200,000 - μ) / σ = -1.125

Using the calculator, we can find that the fraction of physicians who earn less than $200,000 is approximately 0.1314.

b. The fraction of physicians who earn between $280,000 and $320,000 can be estimated using the same method as above. We need to calculate the z-scores corresponding to these salaries:

z1 = (280,000 - μ) / σ = 0.596

z2 = (320,000 - μ) / σ = 0.674

Using the calculator, we can find the area between these two z-scores, which represents the fraction of physicians who earn between $280,000 and $320,000. This area is approximately 0.0775.

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Answer:

x= -3/5+4y/5

x= -3/5 or -0.6 in decimal form

Step-by-step explanation:

I hope this helps :)

The value of the n for the given algebraic equation is=12.

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added to a variable before being multiplied by it.

The given algebraic expression is

-4.3+1.2n=10.1

Add 4.3 on both sides

1.2n=10.1+4.3

1.2n=14.4

divide 1.2 into both sides

n = 14.4÷1.2

n = 12

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