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The proportion 16 over 12 equals 12 over 9 shows the corresponding sides are proportional, so the triangles are similar by the SAS similarity postulate.

What is SAS similarity theorem?

According to the Side-Angle-Side Postulate (SAS) postulate, triangles are congruent if two sides of one triangle and the angle that connects them are congruent with two sides and the included angle of a second triangle. According to the SAS criteria for triangle similarity, two sides of one triangle are comparable to two sides of another triangle if their included angles are congruent.

The proof showing that ΔWXZ ~ ΔXYZ is presented as follows;

Segment XZ is perpendicular to segment WY

∠WZX and ∠XZY are right angles by definition of XZ  perpendicular to WY

∠WZX in ΔWXZ = ∠XZY in ΔXYZ = 90° (definition)

Given that two sides of ΔWXZ are proportional to two sides of ΔXYZ, and

that the included angles between the two sides, ∠WZX and ∠XZY are

congruent, the two triangles, ΔWXZ and ΔXYZ are similar by Side-Angle-

Side, SAS, similarity postulate.

The option that best completes the proof is therefore;

which is; 16 over 12 equals 12 over 9

The SAS similarity test determines whether two triangles are similar if the ratio of the lengths of two sides of one triangle equals the ratio of the lengths of two sides of another triangle, and the included angles are equal.

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Completed question :

Which of the following best completes the proof showing that ΔWXZ ~ ΔXYZ?

Since segment XZ is perpendicular to segment WY, angles WZX and XZY are both right angles and congruent. The proportion ________ shows the corresponding sides are proportional, so the triangles are similar by the SAS Similarity Postulate.

16 over 12 equals 9 over 12

16 over 12 equals 12 over 9

12 over 12 equals 16 over 9

12 over 16 equals 16 over 9

Following that, the Pythagorean theorem states that the separation between the two points is equal to the square root of the sum of the squares on the horizontal and vertical sides: distance=√(Δx)2+(Δy)2=√(x2−x1)2+(y2−y1) 2.

As per the a sphere, a straight line connects any two points at their closest distance. The earth resembles a spherical in form. The distance between any two places on Earth is calculated using the perpendicular distance or a straight line between the two spots because the radius of the sphere is so large that humans see it as a plane. In the case of in the earth, the arc length and the perpendicular distance are about identical.

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Two line segments are the diagonals. The name of the line segments is KE and JD.

What is the right rectangular prism?

The right rectangular prism has two parallel end faces and four lateral faces, each of which is a rectangle; the faces are perpendicular to the bases of the prism. Parallelograms are the faces of a non-right rectangular prism (oblique prism). A cuboid is another name for a right rectangular prism.

The diagonal length of a right rectangular prism is calculated as √(l² + w² + h²) units. So, the formula for the length of a right rectangular prism's diagonal is √(l²+w²+h²), where l is the length, b is the breadth, and h is the height.

The diagonals are line segments that are in contact with opposite vertices.

The diagonals are KE, JD, IG and HF.

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In order to have an average speed of 6 miles per hour over the entirety of the trip, the man would need to travel 15 miles in the next 2 1/2 hours. This means that he would need to travel at a speed of 6 miles per hour for the remainder of the trip.

Properties of Special right angled triangle,

a) If the leg of a 45°-45°-90° right triangle is x units, then the length of hypotenuse is x√2 units.

b) If a 30°-60°-90° right triangle the hypotenuse is twice the shorter leg, then longer leg is √3 times the shorter leg.

We have to discuss properties of special Right Triangles :

a) Properties of 45°-45°-90° Triangles : The sides of a 45°-45°-90° right triangle have a special relationship.

Example 1: If the leg of a 45°-45°-90° right triangle is x units, show that the hypotenuse is x√2 units.

Using the Pythagorean Theorem with

a = b = x, then c² = a² + b²

=> c² = x² + x²

=> c² = 2x²

=> c = √2x²

=> c = x√2

Thus, hypotenuse is x√2 units.

b) The sides of a 30°-60°-90° right triangle also have a special relationship.

Example 1: In a 30°-60°-90° right triangle the hypotenuse is twice the shorter leg. Show that the longer leg is √3 times the shorter leg.

∆MNQ is a 30°-60°-90° right triangle, and the length of the hypotenuse MN is two times the length of the shorter side NQ. Use the Pythagorean Theorem, c² = a²+ b²

let length of shorter side of ∆MNQ, NQ= x units, so, length of hypotenuse,MN = 2x

=> MN² = NQ² + MQ²

=> MQ² = MN² - NQ²

=> MQ² = (2x)² - x²

=> MQ² = 4x² - x² = 3x²

=> MQ = √3x²

=> MQ = √3 x = √3 NQ

So, longer side of right angled triangle is √3 times the short side.

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Complete question:

8-3 study guide and intervention special right triangles

a) Properties of 45°-45°-90° Triangles

b) Properties of 30°-60°-90° Triangles

If k = 0, there is just one distinct solution, sometimes called a double solution.

Depending on the sign of the discriminant, a quadratic equation will always have one of three real solutions: 0, one, or two. Only 2 actual solutions exist if the discriminant is positive.

If you get to the finish with 0=0, it signifies that the left and right sides of the equation are equal to each other regardless of the values of the variables involved. As a result, the solution set for this equation is made up entirely of real numbers for each variable.

There is just one distinct solution, occasionally referred to as a double solution, if k = 0.

The graph shifts upward if k is greater than 0. The graph is moved downward if k is less than 0.

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Answer: The slope of Line B is 1/-4 = -1/4.

Step-by-step explanation:

When two lines are perpendicular to each other, the product of their slopes is -1. If the slope of Line A is -4, the slope of Line B must be 1/-4 = -1/4 in order for the two lines to be perpendicular.

Answer: As x approaches positive infinity, y approaches positive infinity

As x approaches negative infinity, y approaches positive infinity.

Step-by-step explanation:

The key thing to keep in mind is the type of function. This is an absolute value graph that in general has a V shape. This one in specific is a V shape shifted to the right 7 unites from the origin, with positive and negative slopes for each piece-wise line.

Answer:

Step-by-step explanation:

wait a minute

Answer:

Direct Proportion

Step-by-step explanation:

It is linear, meaning that the ratio between the mass and gravity is proportional.

The term known as K-value is a constant. The proportionality constant, k, is represented in the direct variation equation y = kx. Similar to this, k is the variational constant in the equation for inverse variation, y = kx.

Which variant of K?

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Answer:

the sun because u can't get energy from a bicycle yea kettle or a faucet.

The derivative of x² log x is 2x log x + x/ ln(10).

The derivative of a function f(x) is usually represented by d/dx (f(x)) (or) df/dx (or) Df(x) (or) f'(x). Let us see what a derivative technically means. Consider a curve of function f(x) and let two points on it be (x, f(x)) and ((x + h), f(x + h)). Then the slope of the secant line through these points is given by [f(x + h) - f(x)]/(x + h - x) = [f(x + h) - f(x) / h. See the figure below and observe that when the distance between two points is closely equal to 0 (i.e., as h approaches 0), the second point overlaps the original point and the secant line becomes the tangent line. In calculus, the slope of the tangent line is referred to as the derivative of the function.

The derivative of a function at a point is the slope of the tangent drawn to that curve at that point.

It also represents the instantaneous rate of change at a point on the function.

The velocity of a particle is found by finding the derivative of the displacement function.

The derivatives are used to optimize (maximize/minimize) a function.

They are also used to find the intervals where the function is increasing/decreasing as well as the intervals where the function is concave up/down.

Given equation: y = x² log x

Differentiating this equation with respect to x, we get

dy/dx = 2x log x + x/ ln(10)

Thus, the derivative of x² log x is 2x log x + x/ ln(10).

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The zero slope means for every unit change in the horizontal distance there is no change of vertical distance.

We know that the slope of a line is nothing but the change in y coordinate with respect to the change in x coordinate.

The slope of the line describes the steepness of a line.

Also,  if a line makes an angle θ with the positive direction of the x-axis, then the slope of the line will be tangent of angle θ

m = tan θ

If the slope is zero, i.e., m = 0 then,

tan θ = 0

θ = arctan(0)

θ = (nπ)                where n = 0, 1, 2, . . .

This means, the line with zero slope must be coincident or parallel to the x-axis.

Sometimes zero slope term is used to describe a line that has a constant rise.

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Explicit formula of the sequence: T(n) = 10240(1/4)ⁿ⁻¹.

To get the nth phrase in a series, we can use an explicit formula. Exact or definite is the simplest definition of explicit. The reason the formula is explicit is because it allows for the easy determination of the nth term when used appropriately.

Each sequence in which the ratio of any term to the one before it is constant is said to be geometric. A geometric sequence can be expressed explicitly using the formula a = a₁r⁻¹, where r is the common ratio.

here T₁ = 10240

Explicit formula of the sequence:  T(n+1) = T(n)(0.25)

If a sequence is in the form of ar, ar², ar³,.....,arⁿ terms

Sequence will be the geometric sequence and the explicit formula of the sequence will be: T(n) = arⁿ⁻¹

Here,  

a = First term

r = Common ratio

n = Number of terms

From the table attached,

There is common ratio between the successive term and previous term under the column (height after the bounce) is:

T₂/T₁ = 2560/10240 = 1/4

T₂/T₃ = 064/2560 = 1/4

Therefore, height of the ball after each bounce will represent a geometric sequence.

Explicit formula of a geometric sequence will be given by the expression:

T(n) = 10240(1/4)ⁿ⁻¹

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The list of most commonly used graph types are as follows:

Now, According to the question:

Types of Graphs and Charts

The list of most commonly used graph types are as follows:

All these graphs are used in various places to represent a specific set of data concisely. The details of each of these graphs (or charts) are explained below in detail which will not only help to know about these graphs better but will also help to choose the right kind of graph for a particular data set.

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The equation for g(x) that matches the graph is g(x) =| -x - 3| +3

There are many tools we can use to find the information of the relation which was used to form the graph.

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

If we know that the function crosses x-axis at some point, then for some polynomial functions, we have those as roots of the polynomial.

We are given that function, g(x), is shown below. It is a shifted graph of y = |x|.

The vertex of the square root function f(x) = √x is located at (0, 0). In the given graph, it has moved to (2, 4). The vertical and horizontal scale factors remain unchanged.

The equation for g(x)  is g(x) =| -x - 3| +3

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Answer:

8 Tickets

Step-by-step explanation:

40 / 5 = 8

Answer:

x = -0.85

Step-by-step explanation:

First, you divide 3 by 3, so that means you also divide 5 by 3, which is 1.66666666666... Now it is -2x =1.66666666666... Technically, it is 1.7, or 1.66666666666..., 1.7 divided by -2 is -0.85. Or if you want to keep 1.66666666666... it will equal -0.8499999999999...

On solving the provided question, we can say that x is an acute angle., cos(x) = 12 => x = cos^{-1}1/2=> x = 60

In Euclidean geometry, an angle is a shape made up of two rays, referred to as the angle's sides, that meet at a point in the middle known as the angle's vertex. Two rays can generate an angle that is in the plane where the rays are located. The meeting of two planes also creates an angle. They are referred to as dihedral angles. An angle is the shape created by two rays or lines that have a shared termination in plane geometry. The Latin word "angulus," which meaning "horn," is the source of the English term "angle." The vertex is the common terminal of the two rays, which are referred to as the sides of the angle.

here,

x is an acute angle.

cos(x) = 12

x = cos^{-1}1/2

x = 60

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The speed of the moving body that is being referred to here is 80 kilometer per hour.

The given problem is a straightforward one based on the idea of the universal law of motion. According to the universal law of motion, any uniformly traveling body's distance traveled is determined by the product of its speed and the time elapsed. Distance is calculated as speed * time. Therefore the body is going at a speed of 80 kilometers per hour, according to the same relation as above, assuming that it is moving at a constant speed.

                                [tex]Distance = speed * time[/tex]

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Plane X contains point C. Plane Y contains points A andB. there are three planes that pass through points A, B, and C.To find these planes, we need to draw a triangle connecting points A, B, and C.

The three planes that pass through A, B, and C are the planes that are parallel to the sides of the triangle and that contain points A, B, and C. These planes divide the space into three sections. Each plane will contain one of the points of the triangle. The three planes together form a three-dimensional space that is bounded by the three planes. This space contains all the points A, B, and C, and all the points in the triangle. Therefore, there are three planes that pass through points A, B, and C.

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When adding two rational numbers with different signs, you can determine the sign of the sum by comparing the magnitudes of the numbers.

•   If the absolute value of the first number is greater than the absolute value of the second number, the sum will have the same sign as the first number.

•   If the absolute value of the second number is greater than the absolute value of the first number, the sum will have the same sign as the second number.

To determine whether the sum will be positive or negative, you can also compare the signs of the numbers:

•   If one number is positive and the other is negative, the sum will be negative if the positive number is smaller than the negative number and positive if it is greater.

•   If the numbers have different signs, the sum will be positive if the numbers have opposite signs and negative if they have the same sign.

•   If the sum of the two rational numbers is zero, it means that the two numbers cancel each other out, which happens when the absolute value of the first number is equal to the absolute value of the second number with opposite signs.

It's important to note that if you are adding two rational numbers with different signs, you also have to keep in mind that the order of the numbers matters and you might get different results depending on the order.

I hope this helps :)

The value of expression in the form of fraction is, 13/15.

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

We have to given that;

The expression is,

⇒ 7/10 + 1/6

Now, We can solve as;

⇒ 7/10 + 1/6

⇒ (7 × 6 + 1 × 10) /60

⇒ (42 + 10) / 60

⇒ 52/60

⇒ 26/30

⇒ 13/15

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Answer:

195

Step-by-step explanation:

Since: d / 13 = 15, we need to do the inverse which is multiplication:

15 x 13 = 195

Answer:

Step-by-step explanation:

To calculate the interest rate on Selena's debt, we may utilize the formula for continuous compounding of interest. A = P * e is the formula (rt)

Where:

A = the total amount (including interest)

P denotes the original principal (loan amount)

r denotes the interest rate (as a decimal)

t = time (in years)

We know Selena's total (A) is 8,000 + 2,292.77 = 10,292.77.

8,000 is the initial primary (P).

6 years have passed.

The interest (I) is calculated as A-P = 2,292.77.

We may use the formula for continuous compounding of interest to compute the interest rate on Selena's debt. The formula (rt) is A = P * e.

A denotes the whole sum (including interest)

P stands for the original principle (loan amount)

r represents the interest rate (as a decimal)

t = time (in years)

Selena's total (A) is 8,000 plus 2,292.77 = 10,292.77.

The initial primary is 8,000. (P).

6 years have gone by.

A-P = 2,292.77 is the interest (I) calculation.

Cesar's reasoning is incorrect because the degree of a polynomial is determined by the highest exponent of the variable in the polynomial, not the number of terms.

In the example given (2×2 = 3+1 = 4), the degree of the polynomial is not given. Therefore, it is not possible to determine the correct degree without more information about the polynomial in question.

The degree of a polynomial is a measure of the highest power of the variable in the polynomial. For example, the degree of the polynomial 3x2 + 2x - 4 is 2 (the highest power of x is 2), whereas the degree of the polynomial 4x3 + 3x2 - 2x + 1 is 3 (the highest power of x is 3).

Cesar's statement that the degree of the polynomial is 4 because 2×2 = 3+1 = 4 is not a valid way to determine the degree of a polynomial, as it is not related to the powers of the variables in the polynomial. To determine the correct degree of the polynomial, we need more information about the polynomial.

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The probability of getting the number 10 is 0.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

Given that, a die has six faces numbered 1 to 6.

A) Getting the number 6

Probability of getting the number 6 = 1/6

B) Getting the number 10

Probability of getting the number 10 = 0/6

C) Not getting the number 6

Probability of not getting the number 6 = 1-1/6

(6-1)/6 =5/6

D) Getting one of the numbers 1,2,3,4,5 or 6

Here, P(E) = 5/6 + 1/6

= 6/6

= 1

Therefore, the probability of getting the number 10 is 0.

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