Line segment AC has a length of 120 and contains
point B.If AB=5x+20andBC=6x-10， which
equation shows the relationship between the lengths
of line segments AB， BC， and AC?
A)5x+20=120
B)6x-10=120
lest
C)(5x+20)-(6x-10)=120
D)(5x+20)+(6x-10)=120

The two equations that models the inverse proportion relationship are:

m³ = k/√n

m³√n = k

Inverse proportion is defined as a type of proportionality relationship. Thus, when two quantities are said to be inversely proportional, then it means that as one quantity increases, the other decreases.

We are told that the cube of m varies inversely as the square root of n. Thus:

m³ ∝ 1/√n

If k is the constant of proportionality , then we say that:

m³ = k/√n

We can also cross multiply to get:

m³√n = k

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Step-by-step explanation:

F(x)=2x^3+2

G(x)=2x^2-3x-2

Now,

g(x) - f(x)= 2x^2-3x-2 - (2x^3+2)

= 2x^2-3x-2 - 2x^3-2

=2x^2-3x-2-2-2x^3

=2x^2-3x-4-2x^3

: 3

The lengths of the sides of triangle R'S'T'

R' = (-3.75, 2.25), S' = (2.25, 3) and T' = (2.25, -4.5).

We have the coordinates of triangle RST are given as

R (-5, 3), S(3, 4) and T(3, -6)

and, The scale factor is given as: 3/4

Now, The rule of dilation is

(x, y) = 3/4 (x, y)

Then, we can write

R' = (-5 x 3/4, 3 x 3/4)

R' = (-3.75, 2.25)

S' = (3 x 3/4, 4 x 3/4)

S' = (2.25, 3)

and, T' = (3x 3/4, -6x 3/4)

T' = (2.25, -4.5)

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Answer:

B

Step-by-step explanation:

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21,000 yd² of the field will the farmer grow wheat.

We have,

Length of yard = 210 yd

width of yard = 200 yd

As per the figure the yard is cut in diagonal form in which half portion have wheat and half potion have Cabbage.

So, the resulting shape of field in which what will grow is right angles triangle

= 1/2 x base x height

= 1/2 x 200 x 210

= 100 x 210

= 21,000 yd²

Thus, 21,000 yd² of the field will the farmer grow wheat.

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Answer: Trapezoid, Square, Rhombus, Parallelogram

Step-by-step explanation:

The area of the sector is 36.6 ft².

We have,

To calculate the area of the sector, we need to find the fraction of the entire circle it represents and then multiply it by the area of the entire circle.

The central angle of 260° represents (260/360) or 13/18 of the entire circle.

The area of the entire circle with a radius of 4 ft can be calculated using the formula:

A = πr², where π is approximately 3.14.

Substituting the values,

The area of the entire circle is A = 3.14 x (4 ft)² = 3.14 x 16 ft² = 50.24 ft².

To find the area of the sector, we multiply the area of the entire circle by the fraction represented by the central angle:

Area of sector = (13/18) x 50.24 ft² = 36.64 ft².

Rounded to the nearest tenth

Thus,

The area of the sector is 36.6 ft².

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Approximately 99.7% of scores lie in the shaded region.

We have,

The empirical rule, also known as the 68-95-99.7 rule, provides an estimate of the percentage of scores that lie within a certain number of standard deviations from the mean in a normal distribution.

According to this rule:

Approximately 68% of scores lie within 1 standard deviation of the mean.

Approximately 95% of scores lie within 2 standard deviations of the mean.

Approximately 99.7% of scores lie within 3 standard deviations of the mean.

Now,

In the given scenario, the shaded region represents the area between -2 and 3 standard deviations from the mean on the x-axis.

This encompasses the area within 3 standard deviations of the mean.

And,

Since 99.7% of scores lie within 3 standard deviations of the mean, we can estimate that approximately 99.7% of scores lie in the shaded region.

Therefore,

Approximately 99.7% of scores lie in the shaded region.

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Two sides are congruent to each other. The third side of an isosceles triangle which is unequal to the other two sides is called the base of the isosceles triangle. The two angles opposite to the equal sides are congruent to each other.

In an isosceles triangle, two sides have the same length, making them congruent. These two sides are often referred to as the "legs" of the triangle.

The angles opposite the congruent sides in an isosceles triangle are also congruent. These angles are typically referred to as the "base angles."

The remaining side, called the "base," is not congruent to the legs of the triangle. The base is usually the side that connects the two base angles.

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The perimeter of the rectangle can be shown by Option C.

The perimeter of a rectangle is the total distance around its outer boundary. To calculate the perimeter of a rectangle, you need to know the lengths of its two adjacent sides, typically referred to as length (l) and width (w).

We know that the perimeter can be given by;

P = 2(l + b)

P = 2[(2.4x + 3.5) + (1.2x + 6.8)]

P = 2[2.4x + 3.5 + 1.2x + 6.8]

P = 2[2.4x +  1.2x + 3.5 + 6.8]

P = 2[3.6x + 10.3]

P = 7.2x + 20.6

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Group-B secured more marks than group-A by a margin of 20 marks

(i) To calculate the marks secured by group-A, we need to multiply the number of correct answers by the marks awarded for a correct answer and subtract the product of the number of incorrect answers and the penalty for each incorrect answer.

Group-A secured:

Marks = (Number of correct answers * Marks for correct answer) - (Number of incorrect answers * Penalty for incorrect answer)

      = (6 * 10) - (4 * 5)

      = 60 - 20

      = 40 marks

Therefore, group-A secured 40 marks.

(ii) For group-B, we need to consider the number of correct answers, incorrect answers, and unanswered questions to calculate the total marks.

Group-B secured:

Marks = (Number of correct answers * Marks for correct answer) - (Number of incorrect answers * Penalty for incorrect answer) + (Number of unanswered questions * Marks for not supplying answers)

      = (7 * 10) - (2 * 5) + (1 * 0)

      = 70 - 10 + 0

      = 60 marks

Hence, group-B secured 60 marks.

(iii) To determine which group secured more marks and by how many, we compare the marks obtained by group-A and group-B.

Group-A secured 40 marks, while group-B secured 60 marks.

The difference in marks secured by group-B compared to group-A is:

60 - 40 = 20 marks.

Therefore, group-B secured more marks than group-A by a margin of 20 marks.

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The solution to the given scatter plot is:

a)  Exponential

b) y = 587.52x

c) 894

Scatter plots are basically al type of data visualization that shows us the relationships that exists between variables.

a) The best model for the given scatter plot is definitely exponential because of the nature of the points and curve.

b) The regression equation for the model has the general formula:

Y = a + bx

Thus, from the given scatter plot, we can say that the equation is:

y = 587.52x

c) Using the equation that you found, in part B, using an online regression equation calculator, we can say that the prediction of the point total in the 10th level is: 894

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Answer:

3n+5.3

Step-by-step explanation:

(1.1×n+1.9n)+(−3.8+9.1) = 3n+5.3

Answer:

no

Step-by-step explanation:

(I'll assume you're talking about a rectangle)

If the width is zero, the shape would be a line. Therefore, the width cannot be zero.

Feel free to tell me if I did anything wrong! :)

The exact value of the given expression of tan 15 ° can be found to be 1 / √3.

When given a tangent degree, you can find the exact value by relating it to the Sine and Cosine values as shown below :

tan ( x ) = sin ( x ) / cos ( x )

Given that x is 15 degrees, we have :

tan ( 15 ) = sin ( 15 ) / cos ( 15 )

The values of sine and cosine :

sin(30) = 1/2

cos(30) = √3/2

This means the relation is:

tan ( 15 ) = sin ( 15 ) / cos ( 15)

= ( 1 / 2 ) / (√3 / 2 )

= 1 / √3

=  0.2679

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Answer: About two angles are congruent

Step-by-step explanation:

The price at which Berkshire Hathaway close on the previous day based on the table is $199,740.

The closing price of stock means the final trading price at which a particular stock or security is traded on given trading day. It is the last recorded price of a stock when market closes for the day.

The closing price is an important indicator used in financial markets to evaluate the performance and value of a stock. It serves as a reference point for investors, analysts and traders to assess the overall market sentiment and make investment decisions.

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The equation A = (x + 15)(x + 10) − 5 represents the area of the patio that will be painted, where A is the total area.

Option C is the correct answer.

We have,

The equation A = (x + 15)(x + 10) − 5 represents the area of the patio that will be painted.

The dimensions of the rectangular patio are given as (x + 15) for the length and (x + 10) for the width.

These values account for the extra length and width added to the original dimensions (x) to include the bench area.

To determine the total area of the patio that will be painted, we calculate the product of the length and width, which is (x + 15)(x + 10).

However, we need to subtract the area of the bench, which has a length of 5 and a width of 1.

Hence, we subtract 5 from the product to exclude the bench area.

Therefore,

The equation A = (x + 15)(x + 10) − 5 represents the area of the patio that will be painted, where A is the total area.

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Answer:

C

Step-by-step explanation:

i took the test :)

have a great day.!

Yes, because EFGH is a parallelogram and its diagonals are congruent.

To prove the statement, we have to know the properties of a rectangle.

The properties of a rectangle are listed thus;

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The triangle that has been shown is a scalene obtuse triangle.

A triangle called a scalene triangle has three sides that are all different lengths. In other words, a scalene triangle has three different angles and no two of its sides have the same length.

A triangle with one obtuse angle is referred to as an obtuse triangle. Any angle that is greater than 90 degrees but less than 180 degrees is referred to as an obtuse angle.

Thus we have a scalene obtuse triangle.

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The slope of the points in this table is equal to -3.

In Mathematics and Geometry, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided in the table, we can logically deduce the following data points on the line:

By substituting the given points into the slope formula, we have the following;

Slope, m = (4 - 7)/(1 - 0)

Slope, m = -3/1

Slope, m = -3.

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The value of sin of θ given in the unit circle using the coordinates is -√13/7.

Given a unit circle.

We know that any point on the unit circle can be represented in terms of the angle that the point makes with the positive X axis as,

x = cos θ and y= sin θ

Here θ is the angle formed by the positive X axis with the point.

Here also given a unit circle.

So using the coordinates, we get

cos (θ) = -6/7

sin (θ) = -√13/7

Hence the value of sin of θ is -√13/7.

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The surface area for each rectangular prism is given as follows:

3) S = 195.5 mm².

4) S = 158.1 m².

The surface area of a rectangular prism of height h, width w and length l is given by:

S = 2(hw + lw + lh).

This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.

Hence, for item 3, the surface area is given as follows:

S = 2 x (8.2 x 5 + 8.2 x 4.3 + 5 x 4.3)

S = 195.5 mm².

For item 4, the surface area is given as follows:

S = 2 x (4.1 x 3 + 4.1 x 9.4 + 3 x 9.4)

S = 158.1 m².

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The graph of the system of equations on the image at the end, there we can see that the solution is (110, 95).

Here we want to solve the given system of equations:

2x + 3y = 505

5x + 3y = 835

Using a graphing tool.

To solve the system graphically we just need to graph both equations on the same coordinate axis and find the point where the graphs intercept.

On the image at the end, you can see the graph of the system of equations. On that image we can see that the solution of the system of equations is (110, 95).

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The volume of the sphere is 196 cm³

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is measured in units³

The sphere is a geometrical three-dimensional solid having a curved surface.

The volume of a sphere is expressed as;

V = 4/3 πr³

where r is the radius.

π = 3

r = 7

V = 4/3 × 3 × 7²

V = 4 × 49

V = 196 cm³

Therefore the volume of the sphere is 196 cm³

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Answer:

Step-by-step explanation:

Graph a straight line, slanting down, with a y-intercept of 4  (the point (0,4)) and an x-intercept of 8 (the point (8,0)).  Your line should slope down-1-over-2.  Line should be solid and shade everything below the line.

(sorry, Brainly doesn't offer graphing tools, so I had to just describe the line.  Hope this helps you!)

We have shown that E₀ cos⁴θ = E₀ (1/2 + (cos2θ)/2)².

Let's start by condensing the supplied equation, E₀ cos⁴θ:

E₀ cos⁴θ = E₀ (cos²θ)²

Now, we can rewrite cos²θ in terms of Sin²θ using the identity sin²θ = 1 - cos²θ:

cos²θ = 1 - sin²θ

Reintroducing this into the expression:

E₀ (cos²θ)² = E₀ (1 - sin²θ)²

Expanding the square:

E₀ (1 - sin²θ)² = E₀ (1 - 2sin²θ + sin⁴θ)

Now, let's simplify the expression (1 - 2sin²θ + sin⁴θ):

1 - 2sin²θ + sin⁴θ = (1 - sin²θ)²

Using the identity given in the hint,

(1 - sin²θ)² = (2sin²θ)²

Expanding the square:

(2sin²θ)² = 4sin⁴θ

Let's now reintroduce this outcome into the preceding expression:

E₀ (1 - 2sin²θ + sin⁴θ) = E₀ (2sin²θ)² = E₀ (4sin⁴θ)

Therefore, we have shown that E₀ cos⁴θ = E₀ (1/2 + (cos2θ)/2)².

Hence verified.

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Answer: on the line y = x-3 and above the line y = -x + 2.

Step-by-step explanation:

The first inequality, y ≤ x-3, represents a shaded region below or on the line y = x-3. This line has a slope of 1 and y-intercept of -3. It is a straight line that slants upward from left to right.

The second inequality, y > -x + 2, represents a shaded region above the line y = -x + 2. This line has a slope of -1 and y-intercept of 2. It is a straight line that slants downward from left to right.

To determine which graph represents the system of linear inequalities, we need to look for a graph that shows the shaded region below or on the line y = x-3 and above the line y = -x + 2.

The probability of two heads when a biased coin is spun twice is 0.16.

The first time you flip the coin, the probability of seeing a heads is 2/5. The second time you flip the coin, the probability of seeing a heads is still 2/5 because the probability of a biased coin has not changed over the course of the two flips.

Since each flip is an independent event, you multiply the probabilities together.

The probability of two heads when a biased coin is flipped twice is (2/5) × (2/5) = 4/25 = 0.16.

Therefore, the probability of two heads when a biased coin is spun twice is 0.16.

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Answer:

Step-by-step explanation:

El peso de un objeto se calcula multiplicando su masa por la aceleración debida a la gravedad. En el caso de Guadalupe, su peso en la Tierra sería 50 kg * 9.8 m/s² = 490 N (newtons).