What is mathematics. why is it important?​

Answer:

y = x + 1

Step-by-step explanation:

i dont rlly have an explanation, i mean its just that

The value of x round to the nearest 10th is 28.

One of the most significant areas of mathematics is trigonometry, which has numerous applications. The study of the relationship between the sides and angles of the right-angle triangle is the main objective of the branch of mathematics known as "trigonometry." Trigonometric identities, functions, and formulas can be used to determine the angles or sides of a right triangle that are unknown or missing. Angles can be expressed in trigonometry as either degrees or radians. The five most frequently used trigonometric angles in calculations are 0°, 30°, 45°, 60°, and 90°.

In the given right-angled triangle the angle is 41 degrees and the altitude is 32 units.

So, the trigonometry ratio is -

[tex]tan \theta=\frac{32}{x}\\\\x= 32 tan41\\\\x=28[/tex]

the value of x=28

The complete question is'

Find the value of x in a given triangle, and round to the nearest tenth,

image of the triangle is attached,

learn more about trigonometry,

https://brainly.com/question/29002217

#SPJ1

The total cost to fence the rectangular yard is given as follows:

$1,610.28.

The perimeter of a rectangle is the total distance around its outer boundary. To find the perimeter of a rectangle, you need to add up the lengths of all four sides.

If a rectangle has length l and width w, then its perimeter P is given by the equation presented as follows:

P = 2l + 2w

Considering the scale factor of 0.75, the distance represented by each unit on the graph is given as follows:

0.75 x 12 = 9 yards.

Hence the dimensions of the rectangle are given as follows:

The perimeter of the fence is then given as follows:

2 x (72 + 54) = 252 yards.

It costs $6.39 per yard, hence the total cost to fence the yard is given as follows:

252 x 6.39 = $1,610.28.

More can be learned about the perimeter of a rectangle at https://brainly.com/question/24571594

#SPJ1

Therefore, the x-coordinate is 1/2.

A coordinate is a value that represents a point's position in a given system of reference. In two-dimensional (2D) space, coordinates typically consist of two values, x and y, that represent the point's position along the horizontal and vertical axes, respectively.

Given by the question.

To find the x-coordinate of the point where the terminal side intersects the unit circle, we first need to determine the quadrant in which the terminal side lies based on the angle measure of 60 degrees.

Since 60 degrees is in the first quadrant (0 to 90 degrees), the x-coordinate will be positive.

Next, we can use the fact that the terminal side intersects the unit circle, which means its distance from the origin is 1.

Since the angle measure is 60 degrees, we can construct a right triangle with the terminal side as the hypotenuse, and one leg parallel to the x-axis.

The opposite side to the angle t will be sin (60), and the adjacent side to the angle t will be cos (60).

Using the trigonometric identity cos (60) = 1/2, we can see that the x-coordinate of the point where the terminal side intersects the unit circle is: cos (60) = 1/2.

To learn more about parallel:

https://brainly.com/question/16853486

#SPJ1

Therefore, each square has a side length of 1.5 cm. The perimeter of each square is 6 cm.

Perimeter is the distance around the outside of a two-dimensional shape, such as a polygon or a circle. It is the sum of the lengths of all the sides of the shape.

Here,

To calculate the perimeter of the rectangle, we need to first convert the side lengths to the same units. 1 cm 5 mm is equal to 1.5 cm, so the rectangle has dimensions 3 cm by 1.5 cm.

The perimeter of the rectangle is then:

P = 2(3 cm) + 2(1.5 cm)

= 9 cm

To divide the rectangle into two equal squares, we need to find the side length of each square.

The area of the rectangle is:

A = (3 cm)(1.5 cm)

= 4.5 cm²

Since the two squares are equal, each square has area:

A/2 = 2.25 cm²

The side length of each square can be found by taking the square root of the area:

s = √(2.25 cm²)

= 1.5 cm

The perimeter of each square is:

P = 4s

= 6 cm

To know more about perimeter,

https://brainly.com/question/7720055

#SPJ1

The expression is true for all values of a between 0 and -5 (inclusive)

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.

The expression is given as:

|a+5|= -5–a

The absolute value expression is always positive.

So, we have:

a +5 = -5 -a or -5 - a = -5 - a

For the expression a +5 = -5 -a we have:

a + a = -5 - 5

Evaluate like terms

2a =- 10

Divide both sides by 2

a = -5

For the expression -5 - a = -5 - a, we have:

0 = 0

So, we have:

0 = 0 or a = -5

This means that, the expression is true for all values of a between 0 and -5 (inclusive)

To learn more about the expression from the given link

https://brainly.com/question/1859113

#SPJ1

The mathematical expression to be evaluated is:

[tex]2 \frac{3}{6} - \frac{1}{3}[/tex]

To simplify the expression, we first convert the mixed fraction to an improper fraction:

[tex]2 \frac{3}{6} = \frac{(2 \times 6) + 3}{6} = \frac{15}{6}[/tex]

Substituting this value back into the original expression, we get:

[tex]2 \frac{3}{6} - \frac{1}{3} = \frac{15}{6} - \frac{1}{3}[/tex]

Now we need to find a common denominator for the two fractions:

[tex]\frac{15}{6} - \frac{1}{3} = \frac{15}{6} \times \frac{2}{2} - \frac{1}{3} \times \frac{2}{2} = \frac{30}{12} - \frac{2}{6}[/tex]

We can simplify the second fraction:

[tex]\frac{30}{12} - \frac{2}{6} = \frac{30}{12} - \frac{4}{12} = \frac{26}{12}[/tex]

Finally, we can simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 2:

[tex]\frac{26}{12} = \frac{13}{6}[/tex]

Therefore, the simplified value of the mathematical expression is:

[tex]2 \frac{3}{6} - \frac{1}{3} = \frac{13}{6}[/tex]

Answer:

[tex]2\frac{1}{6}[/tex]

Step-by-step explanation:

First, write the fractions as improper fractions.

[tex]\sf2\frac{3}{6} -\frac{1}{3} \\\\\sf\frac{15}{6} -\frac{1}{3}[/tex]

To, subtract the fractions make the denominators the same.

For that, multiply both sides of 1/3 by 2.

[tex]\sf\frac{15}{6} -\frac{1*2}{3*2} \\\\\sf\frac{15}{6} -\frac{2}{6}[/tex]

Subtract.

[tex]\frac{13}{6}[/tex]

Write it as a mixed number.

[tex]2\frac{1}{6}[/tex]

The volume of the pyramid is V = (1/3) (3²) (5) = 45 cm³ thus the rate at which the water level is rising when the water level is 3 cm is 45 cm³/sec.

Volume is a measure of the amount of space that an object occupies or contains. It is measured in terms of cubic units, such as cubic metres or cubic centimetres. Volume is a three dimensional measure, which means it takes into account the length, width and height of an object.

The rate at which the water level is rising when the water level is 3 cm can be calculated using the formula for the volume of a pyramid. The formula for the volume of a pyramid is V = (1/3) bh², where b is the area of the base and h is the height. In this case, the base is a square with sides of length 3 cm and the height is 5 cm. Therefore, the volume of the pyramid is V = (1/3) (3²) (5) = 45 cm³.

Since the water is being filled at a constant rate of 45 cm³/sec, then the rate at which the water level is rising when the water level is 3 cm is 45 cm³/sec. This is because the water level is rising at the same rate at which the water is being filled, and since the water is being filled at a rate of 45 cm³/sec, the water level is also rising at the same rate. This is why the rate at which the water level is rising when the water level is 3 cm is 45 cm³/sec.

For more questions related to pyramid

https://brainly.com/question/218706

#SPJ1

Answer:

1st -pentagon -regular

2nd -hexagon -irregular

3rd -octagon -irregular

a)  If I randomly catch any one fish from this tank, the probability of catching a medium-sized fish from the tank is 0.3182.
b) the probability of catching a medium-sized guppy from the tank is 0.1391.

c) the probability of catching a guppy if we randomly select a medium-sized fish from the tank is 0.4375.

d) the probability of catching a medium-sized guppy if we randomly select a guppy from the tank is 0.3206.

e)  the probability of catching a fish that is not a goldfish if we randomly select a fish from the tank is 0.6291.
f) 0.1384 is not equal to 0.1391, which indicates that the two events are not independent

Probability is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, with 0 indicating impossibility and 1 indicating certainty.

The explanation to the above probability answer are given below:

a)

From the contingency table, we can see that the total number of medium-sized fish is 96. The total number of fish in the tank is 302. Therefore, the probability of catching a medium-sized fish is:

Probability of catching a medium-sized fish = Total number of medium-sized fish / Total number of fish

Probability of catching a medium-sized fish = 96 / 302

Probability of catching a medium-sized fish = 0.3182

Therefore, the probability of catching a medium-sized fish from the tank is 0.3182

b)
From the contingency table, we can see that the total number of medium-sized guppies is 42. The total number of fish in the tank is 302. Therefore, the probability of catching a medium-sized guppy is:

Probability of catching a medium-sized guppy = Total number of medium-sized guppies / Total number of fish

Probability of catching a medium-sized guppy = 42 / 302

Probability of catching a medium-sized guppy = 0.1391

Therefore, the probability of catching a medium-sized guppy from the tank is 0.1391.

c)

From the contingency table, we can see that the number of medium-sized guppies is 42, and the number of medium-sized fish is 96. Therefore, the probability of catching a guppy if we randomly select a medium-sized fish is:

Probability of catching a guppy given a medium-sized fish = Number of medium-sized guppies / Total number of medium-sized fish

Probability of catching a guppy given a medium-sized fish = 42 / 96

Probability of catching a guppy given a medium-sized fish = 0.4375

Therefore, the probability of catching a guppy if we randomly select a medium-sized fish from the tank is 0.4375.

d)
To calculate the probability of catching a medium-sized guppy if we randomly select a guppy from the tank, we need to find the number of medium-sized guppies in the tank and divide it by the total number of guppies in the tank.

From the contingency table, we can see that the number of medium-sized guppies is 42, and the total number of guppies is 131. Therefore, the probability of catching a medium-sized guppy if we randomly select a guppy from the tank is:

Probability of catching a medium-sized guppy given a guppy = Number of medium-sized guppies / Total number of guppies

Probability of catching a medium-sized guppy given a guppy = 42 / 131

Probability of catching a medium-sized guppy given a guppy = 0.3206

Therefore, the probability of catching a medium-sized guppy if we randomly select a guppy from the tank is 0.3206.


e)

From the contingency table, we can see that the total number of non-goldfish is 190 (45 medium goldfish + 70 small guppy + 42 medium guppy + 9 medium gourami + 10 large gourami + 14 small gourami). The total number of fish in the tank is 302. Therefore, the probability of catching a fish that is not a goldfish is:

Probability of catching a fish that is not a goldfish = Total number of non-goldfish / Total number of fish

Probability of catching a fish that is not a goldfish = 190 / 302

Probability of catching a fish that is not a goldfish = 0.6291

Therefore, the probability of catching a fish that is not a goldfish if we randomly select a fish from the tank is 0.6291.

f)

From the contingency table, we can see that the probability of randomly catching a guppy is 131/302, which is approximately 0.4344. Similarly, the probability of randomly catching a medium-sized fish is 96/302, which is approximately 0.3182.

Now, let's consider the joint probability of randomly catching a medium-sized guppy, which we calculated earlier to be 42/302, or approximately 0.1391. To determine if the events are independent, we need to compare the product of the probabilities of the individual events (catching a guppy and catching a medium-sized fish) to the joint probability of the events occurring together.

If the events are independent, then the product of their individual probabilities should be equal to the joint probability:

P(catching a guppy) x P(catching a medium-sized fish)
= P(catching a medium-sized guppy)

0.4344 x 0.3182 = 0.1391

0.1384 is not equal to 0.1391, which indicates that the two events are not independent.

Learn more about probability:
https://brainly.com/question/29381779
#SPJ1

Answer:

3. 216 cm^3

4a. A = 5 ft, B = 4 ft.

4b. 88 ft^3

Step-by-step explanation:

3. Separate into two rectangular prisms:

Volume of first one: 4cm*2cm*3cm = 24cm^3

Volume of second one: 4cm*12cm*4cm = 192cm^3

Add them together: 24 + 192 = 216cm^3

4a.

Length A = 8-3 = 5ft.

Width B = 8-4 = 4ft.

4b. Separate into two rectangular prisms:

Volume of first one: 2ft*3ft*4ft = 24ft^3

Volume of second one: 8ft*4ft*2ft = 64ft^3

Add them together: 24 + 64 = 88ft^3

Answer:

The answer would be $49.01

Step-by-step explanation:

Answer:

x-5=0

10=2x

(1/2)x=10

x>2=25

Step-by-step explanation:

all of these are x=5

the ones that are wrong are 11-x=3 and 1+x=5

answer:

The number is 9

Step-by-step explanation:

9 × 7 = 63

63 - 13 = 50

9×5 = 45

45 + 5 = 50

Answer: We can use the DuPont Model to calculate the total assets turnover and equity multiplier:

ROE = ROA × Equity Multiplier

Equity Multiplier = Total Assets / Total Equity

Profit Margin = Net Income / Sales

Total Assets Turnover = Sales / Total Assets

Given:

ROA = 12%

Profit Margin = 8%

ROE = 19%

To find the Total Assets Turnover:

Profit Margin = Net Income / Sales

0.08 = Net Income / Sales

Net Income = 0.08 x Sales

ROA = 12%

ROA = Net Income / Total Assets

0.12 = 0.08 x Sales / Total Assets

Total Assets Turnover = Sales / Total Assets = 0.08 / 0.12 = 0.67

Therefore, the total assets turnover is 0.67.

To find the Equity Multiplier:

ROE = ROA x Equity Multiplier

0.19 = 0.12 x Equity Multiplier

Equity Multiplier = 0.19 / 0.12 = 1.58

Therefore, the equity multiplier is 1.58.

Note: The total assets turnover and equity multiplier are related to each other through the DuPont model. The product of these two ratios should be equal to the ROE. In this case, 0.67 x 1.58 = 1.06, which is approximately equal to 1.9 (ROE in decimal form). This confirms that our calculations are correct.

Step-by-step explanation:

Answer:

To find the volume of Leah's new planter, we need to multiply the length, width, and height of the container:

V = 15 m x 4 m x 8 m x 11 m x 3 m

V = 11,880 cubic meters

Therefore, the total volume of Leah's new planter is 11,880 cubic meters.

Let's represent the volume of the large box as x cubic inches. Since the total volume of both boxes is 212 cubic inches, we can set up the following equation:

8 x 4 x 2 + x = 212

Simplifying the left side, we get:

64 + x = 212

Subtracting 64 from both sides, we get:

x = 148

Therefore, the volume of the large box is 148 cubic inches.

The total area of the garden is 56 square feet and the perimeter of the garden is 30 feet

Given the diagram of a rectangle

The opposite sides of a rectangle are equal

So, the values that complete the missing dimensions are

3 ft and 5 ft

Also, we have the area to be

Area = Sum of area of each garden

This gives

Area = 7 * 3 + 7 * 5

Area = 56

The perimeter is the sum of the lengths

So, we have

Perimeter = 7 + 5 + 3 + 7 + 3 + 5

Evaluate

Perimeter = 30

Hence, the perimeter is 30 feet

Read more about area and perimeter at

https://brainly.com/question/25092270

#SPJ1

In 2012, a company made $410,000 in sales in Seattle but only making $255,000 in sales in Portland. Fulfill each of the following claims:

a. Seattle outsold Portland in sales by 60.78%.

b. Portland's sales lagged Seattle's by 60.78%.

c. Sales in Portland were 62.2% of those in Seattle.

a. Seattle's sales were ___% larger than Portland's.

To calculate the percentage difference between the two sales figures, we can use the following formula:

Percentage difference = ((larger value - smaller value) / smaller value) x 100%

Substituting the values, we get:

Percentage difference = ((410,000 - 255,000) / 255,000) x 100%

Percentage difference = 155,000 / 255,000 x 100%

Percentage difference = 0.6078 x 100%

Percentage difference = 60.78%

Therefore, Seattle's sales were 60.78% larger than Portland's.

b. The sales in Portland were ___% less than those in Seattle.

Since Portland's sales were smaller than Seattle's, we can simply use the percentage difference we calculated above to find the percentage by which Portland's sales were smaller:

Portland sales were 60.78% smaller than Seattle's.

c. Portland sales were ___ % of Seattle's.

To calculate the percentage of Seattle's sales that Portland's sales represent, we can use the following formula:

Percentage = (smaller value / larger value) x 100%

Percentage = 0.62195 x 100%

Substituting the values, we get:

Percentage = (255,000 / 410,000) x 100%

Percentage = 62.2%

Therefore, Portland's sales were 62.2% of Seattle's.

To learn more about percentage difference, refer:-

https://brainly.com/question/30404837

#SPJ1

Therefore, the estimated length of the diagonal is approximately 1.414 units.

The square root of a number is a value that, when multiplied by itself, gives the original number. In other words, the square root of a number "x" is a value "y" such that y multiplied by y equals x. The symbol for square root is √.

For example, the square root of 25 is 5, because 5 multiplied by 5 equals 25. Similarly, the square root of 64 is 8, because 8 multiplied by 8 equals 64. The square root of a negative number is not a real number, as there is no real number that, when squared, equals a negative number.

Using the Pythagorean theorem, we can find the length of the diagonal of the square.

If we draw a diagonal from one corner of the square to the opposite corner, we create a right triangle. The two legs of the right triangle are the sides of the square, which have a length of 1. The hypotenuse, which is the diagonal of the square, is the side we are trying to find.

Using the Pythagorean theorem, we can write:

[tex]d^2 = 1^2 + 1^2[/tex]

where d is the length of the diagonal.

Simplifying, we get:

[tex]d^2 = 2[/tex]

Taking the square root of both sides, we get:

d ≈ 1.414

To know more about right triangle, visit

https://brainly.com/question/15490304

#SPJ1

The correct graph of the inequality -0.4x - 2 < - 1.2 is option 2.

Equation containing a relational operator and a linear expression is known as a linear inequality. In a coordinate plane or space, regions that satisfy a linear inequality are defined. A linear inequality defines a half-plane in two dimensions, which, depending on the inequality, can be either above or below a line. A linear inequality defines a half-space in three dimensions, which, depending on the inequality, is either above or below a plane. The goal of optimization problems is to determine the maximum or minimum value of a linear function under a set of constraints, which are typically represented by linear inequalities.

The given inequality is -0.4x - 2 < - 1.2.

-0.4x - 2 < - 1.2

Adding 2 on both sides of the equation we have:

-0.4x < -1.2 + 2

-0.4x < 0.8

-x < 2

x > -2

Hence, the correct graph of the inequality is option 2.

Learn more about inequality here:

https://brainly.com/question/30231190

#SPJ1

1. {0, 1, 3, 4, 6}; 2. {4, 6}.

Step-by-step explanation:

1. А={0, 1, 2, 3}, B={2, 4, 5, 6}, C={2, 5, 7, 9}; (A∪B)-(B∩C)-?

a) A∪B⇔{0, 1, 2, 3, 4, 5, 6};

b) B∩C⇔{2, 5};

c) (A∪B)-(B∩C)⇒{0, 1, 3, 4, 6}.

2. A={4, 6, 8, 10}, B={4, 6, 8}, C={1, 2, 3, 4, 7}, D={3, 5, 6, 7}; A∩(D∪(B∩C))=?

a) B∩C⇔{4};

b) D∪(B∩C)⇔{3, 4, 5, 6, 7};

c) A∩(D∪(B∩C))⇒{4, 6}.

Answer:

Step-by-step explanation: To find (f+g)(x), we simply add the two functions:

(f+g)(x) = f(x) + g(x)

= (3x - 5) + (7x - 3)

= 10x - 8

Therefore, (f+g)(x) = 10x - 8.

To find (f-g)(x), we subtract g(x) from f(x):

(f-g)(x) = f(x) - g(x)

= (3x - 5) - (7x - 3)

= -4x - 8

Therefore, (f-g)(x) = -4x - 8.

The perimeter of the figure is approximately 63.6 meters, since the lengths of all the sides add up to the figure's perimeter.

Perimeter is the total length of the boundary of a closed 2-dimensional shape. In other words, it is the distance around the edge of a shape. The perimeter is usually measured in units such as meters, centimeters, feet, or inches depending on the measurement system used. The perimeter can be calculated by adding up the lengths of all the sides of the shape.

Since opposite sides of a parallelogram are equal in length, the length of the straight side of the first parallelogram is:

Length of first parallelogram = 9m

Similarly, the length of the straight side of the second parallelogram is:

Length of second parallelogram = 11m

Now, let's find the length of the straight side of the semicircle segment. We are given that the other side of each parallelogram gets half of the diameter, which is 17m. Therefore, the length of the straight side of the semicircle segment is:

Length of semicircle segment = 17m / 2 = 8.5m

The lengths of all the sides add up to the figure's perimeter. Let's use P to represent the perimeter. Then:

P = 2 (parallelogram length) + semicircle length

When we replace the values we discovered earlier, we obtain:

P = 2(9m + 11m) + π(17m)/2

= 38m + 8.5πm

≈ 63.6m (using π ≈ 3.14)

To know more about parallelogram, visit:

https://brainly.com/question/29147156

#SPJ9

Answer: He has one left

Step-by-step explanation: 2-1=1

Answer:

Parameter estimates

The coefficient for Px (-5) suggests that there is an inverse relationship between the price of the fruit drink and the quantity demanded. In other words, as the price of the drink increases, the quantity demanded decreases.

The coefficient for M (0.001) suggests that there is a positive relationship between the median annual family income and the quantity demanded. In other words, as the median income increases, the quantity demanded also increases.

The coefficient for Py (10) suggests that there is a positive relationship between the price of the competing brand of fruit drink and the quantity demanded for this brand. In other words, as the price of the competing brand increases, the quantity demanded for this brand also increases.

Step-by-step explanation:

To calculate the monthly consumption of the fruit drink, we plug in the given values into the demand equation,

Qx = 10 - 5(2) + 0.001(20,000) + 10(2.5)

Qx = 10 - 10 + 20 + 25

Qx = 45 liters per family per month.

Therefore, the monthly consumption of the fruit drink per family is 45 liters.

If the median annual family income increased to $30,000, then the new monthly consumption of the fruit drink per family can be calculated as follows,

Qx = 10 - 5(2) + 0.001(30,000) + 10(2.5)

Qx = 10 - 10 + 30 + 25

Qx = 55 liters per family per month.

Therefore, the monthly consumption of the fruit drink per family would increase from 45 liters to 55 liters per family per month.

To determine the demand function, we need to solve for Qx in terms of the other variables,

Qx = 10 - 5Px + 0.001M + 10Py

Qx - 10Py = 10 - 5Px + 0.001M

Qx = (10 - 5Px + 0.001M) / 10Py

Therefore, the demand function is:

Qx = (10 - 5Px + 0.001M) / 10Py

To find the inverse demand function, we need to solve for Px in terms of Qx.

Qx = 10 - 5Px + 0.001M + 10Py

5Px = 10 - Qx - 0.001M - 10Py

Px = (10 - Qx - 0.001M - 10Py) / 5

Therefore, the inverse demand function is,

Px = (10 - Qx - 0.001M - 10Py) / 5

Answer:

This should be a permutation

Step-by-step explanation:

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

P (12,5) = 12!/(12-5)!

P (12,5) = 12!/7!

P(12,5) = 95040

It's tough to know for sure what a black dot on the sea might mean without more information. A ship, boat, or other watercraft may occasionally be indicated by a black dot on the water.

Depending on the situation, a black dot on the sea could mean a variety of various things. Here are some potential examples:

A black dot on a nautical chart could represent a buoy, beacon, marker, or other navigating aid.

A black dot in the ocean may be the result of a bird, a fish jumping out of the water, or other marine life, depending on your distance.

A black dot may represent the existence of a microscopic organism or particle if you are using a microscope or other scientific equipment to see the ocean.

Therefore, 1. Pacific Ocean 2. South Carolina 3. Georgia 4. Alabama 5. (x,y) ----> (x+4,y-10) 6. Colorado 7. Pennsylvania 8. Minnesota and Wisconsin, 8. Missouri 9. Reflect over y-axis and then reflect over x-axis.

10. Oregon 11. Kansas or Oklahoma, 12. Tennessee

Learn more about sea here:

https://brainly.com/question/3762397

#SPJ1

Answer:

Option (C)

-0.46 brother

Answer:

Option (C)

-0.46

Step-by-step explanation:

The wrestler's weight before he went on his diet was 78.0 kilograms.

What is y-intercept?

In the context of a graph of a function, the y-intercept is the point where the graph intersects the y-axis. It is the value of the dependent variable (y) when the independent variable (x) is zero. Geometrically, the y-intercept is the value of the function at the point where it crosses the y-axis.

To determine the wrestler's weight before he went on his diet, we need to find the y-intercept of the linear function that represents his weight gain over time. This is because the y-intercept corresponds to the initial weight of the wrestler, i.e., his weight before he started his diet.

We can use the two data points where the time is 0 (i.e., at the start of the diet) to find the slope of the linear function:

(1.5, 85.8) and (3.0, 93.6)

The change in weight over the time interval of 1.5 to 3.0 months is:

93.6 - 85.8 = 7.8

The change in time over that interval is:

3.0 - 1.5 = 1.5

So the slope of the linear function is:

7.8 / 1.5 = 5.2

Now we can use the point-slope form of a linear function to write an equation for the wrestler's weight gain over time:

y - 85.8 = 5.2(x - 1.5)

where y represents the wrestler's weight and x represents the time in months.

To find the wrestler's weight before he went on his diet, we need to evaluate this equation at x = 0:

y - 85.8 = 5.2(0 - 1.5)

y - 85.8 = -7.8

y = 78.0

Therefore, the wrestler's weight before he went on his diet was 78.0 kilograms.

To learn more about y-intercept, visit the link:

https://brainly.com/question/29501432

#SPJ9