an acute triangle has a side length of $8,$ and a side length of $15.$ the third side length is also a positive integer. how many different possible values are there for the third side length?

Answer:

1/14

Step-by-step explanation:

1/4 x 2 divided by 7

Equals 1/2 divided by 7 which is 14

The reflected triangle be R'S'T'

coordinate of R' is (-7, 3) , S' is (-5, -6) and T' is (2, -2)

Reflection is a sort of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. For instance, Triangle P has been reflected to become Triangle Q on the line x = 4 x= 4 x= 4.

A flip is a geometric movement that involves turning an item over in a straight line to create a mirror image. The distance between each point on an item and its corresponding point on the picture is equal. A reflection is another name for a flip.

The x-coordinate and y-coordinate are reversed when a point is reflected over the line y = x. The x-coordinate and the y-coordinate switch places and become negated if you reflect over the line y = -x.

So, the coordinate of RST is

R(-3, 7), S(6,5), T(2, -2)

The reflected triangle be R'S'T'

coordinate of R' is (-7, 3) , S' is (-5, -6) and T' is (2, -2)

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After reflection along the line y is x, the image of the point (5, -3) is (-3, 5).

It is the representation of the point that is situated in the opposite direction of the specified point.

Given

The reflecting line is y = x at the point (5,-3).

The image's center will therefore be about on the line y = x.

If x = 5, then y will have the value of 5.

The value of x will be x = -3 for y = -3.

Consequently, the image's purpose is (-3, 5).

After reflection along the line y is x, the image of the point (5, -3) is (-3, 5).

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Answer:

250, 4000, 20250

Step-by-step explanation:

[tex]\frac{2}{5}a^{4}[/tex]

2/5 × 5^4 = 250

2/5 × 10^4 = 4000

2/5 × 15^4 = 20250

Hope this helps! :)

Answer: Hence we have 6 × 3 = 18 words of this type. Therefore, using the equation (i), (ii) and (iii). Total words with 4 letter are : 1680 + 756 + 18 = 2454 ∴ 2454 different permutations can be formed from the letter of the word EXAMINATION taken four at a time.

The sizes of the the angles x and y in the trapezium are 48° and 115° respectively.

A trapezium is a quadrilateral and the sum of interior angles is 369° and also two angles on the same side are supplementary, that is the sum of the angles of two adjacent sides is 180°.

x + 132° = 180° {adjacent angles}

x = 180° - 132° {subtract 132° from both sides}

x = 48°

y + 65° = 180° {adjacent angles}

y = 180° - 65° {subtract 65° from both sides}

y = 115°

Therefore, the sizes of the adjacent angles x and y of the trapezium are 48° and 115° respectively.

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Answer:

x=52

Step-by-step explanation:

ignore the work at the top of the

Answer: To eliminate x in the system of linear equations, multiply equation 1 by 4 and multiply equation 2 by 5, then subtract both equations.

How to Solve a System of Equations?

Given the system of linear equations as:

Equation 1: 5x − 2y = 10

Equation 2: 4x − 3y = 15

To eliminate x in the system of equations given above, multiply equation 1 by 4 and multiply equation 2 by 5

× 4 Equation 1: 5x − 2y = 10

× 5 Equation 2: 4x − 3y = 15

20x − 8y = 40

20x − 25y = 75

Subtract both equations to eliminate x

17y = -35

In summary, to eliminate x in the system of linear equations, multiply equation 1 by 4 and multiply equation 2 by 5, then subtract both equations.

Step-by-step explanation:

The number of chords drawn in the circle is

A circle's chord is the line segment that connects any two locations on the circle's circumference.

It should be remembered that a circle's diameter is defined as the lengthiest chord that runs across the center of the circle.

Examining the figure the chord are

The line segment RQ is not a chord since it is not touching the circumference of the circle at the two ends.

From the definition the two ends must be touching the circumference of the circle just like  SP and RP the points at the end of both lines are at the circumference of the circle

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The distance between Jordan and Alana will be √5 meters.

Given is that three ballet dancers are positioned on stage. If Vijay is 2 meters straight behind Jordan and 1 meter directly left of Alana.

Let Jordan be at origin (0, 0). Then, Vijay will be at (-2, 0). Alana will be at point (-2, - 1). The distance from Jordan to Alana will be -

r² = (- 1 - 0)² + (- 2 - 0)²

r² = 1 + 4

r = √5

Therefore, the distance between Jordan and Alana will be √5 meters.

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The breakeven points are:

(40, 4500) and (80, 4400)

Coordinates are a pair of integers (Cartesian coordinates), or occasionally a letter and a number, that identify a certain place on a grid, often referred to as a coordinate plane.

Given:

The revenue and cost functions for a product line of running shoes are shown on the graph.

When C(x) = R(x)

And from the diagrams,

the breakeven points are:

(40, 4500) and (80, 4400)

Therefore, the points are (40, 4500) and (80, 4400).

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The distance between two places can be calculated using various methods:

a. Distance = √ ( x₂ - x₁)² + ( y₂ - y₁)²

b. Distance = Speed × time taken

As given in the question,

Distance between two places can be calculated using various techniques:

a. If the coordinates of the two points representing the places are given as (x₁ , y₁) and (x₂ , y₂ ) then

distance between two places  = √ ( x₂ - x₁)² + ( y₂ - y₁)²

b. If the distance travelled between two place with known speed and time taken to cover that distance then

Distance =  Speed × time taken

If the distance between two places is small then it can be calculated using any measuring scale.

Therefore, the distance between the two given places is given by :

a. Distance = √ ( x₂ - x₁)² + ( y₂ - y₁)²

b. Distance = Speed × time taken

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Triangle AFC is the triangle that appears to be consistent with triangle AFD.

Shapes that are identical to one another are said to be congruent. Both the matching sides and the corresponding angles match. There is an obtuse angle, or angle AFD, same like in the give triangle AFD.

Therefore, the opposite triangle must have an obtuse angle in order to be a congruent triangle. Only triangle AFC, out of the three that are given, has an acute angle. Additionally, they both support the same side, increasing the likelihood of congruence. There is no obtuse angle in the triangles BFC and DFE.

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Answer: 5/49

Step-by-step explanation:

The inequality solution for 2/3 | 1/3 x + 3 | < 4 is x > −18 and x < 6.

The correct option is (A).

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

2/3 | 1/3 x + 3 | < 4

Now, solving the inequality

2/3 | 1/2 x + 3 | < 4

| 1/2 x + 3 | < 4 (3/2)

| 1/2 x + 3 | < 6

± (1/2x + 3) < 6

Now, splitting the inequalities

1/2x  + 3 < 6  or -1/2x - 3 < 6

1/2x < 3  or -1/2x < 9

x< 6    or  -x < 18

x< 6    or  x> -18

Hence, the inequality is x > −18 and x < 6.

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Answer:  A

Step-by-step explanation: The person above is right and took the exam on FLVS

The polynomial [tex]x^{3}[/tex] + 8 is equal to (x + 2)([tex]x^{2}[/tex] – 2x + 4).

What is polynomial ?

In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. An example of a polynomial of a single indeterminate x is x2 − 4x + 7.

The given expression is

[tex]x^{3}[/tex] + 8

It can be rewritten as

[tex]x^{3}[/tex] + [tex]2^{3}[/tex]

Formula for sum of cubes:

[tex]x^{3} + y^{3} = (a+b)(x^{2} -xy+y^{2} )[/tex]

For the given expression a=x and b=2.

[tex]x^{3}[/tex] + [tex]2^{3}[/tex] =  (x + 2)([tex]x^{2}[/tex] – 2x + 4).

[tex]x^{3}[/tex] + 8 =  (x + 2)([tex]x^{2}[/tex] – 2x + 4).

Therefore , The polynomial [tex]x^{3}[/tex] + 8 is equal to (x + 2)([tex]x^{2}[/tex] – 2x + 4).

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The graphs of the modulus functions are just a pair of lines drawn simultaneously.

A modulus function is a function which gives the absolute value of a number or variable. It produces the magnitude of the number of variables. It is also termed as an absolute value function. The outcome of this function is always positive, no matter what input has been given to the function.

Given here ; The modulus functions y=|x|-2 , y=|x-1|+1 , y=|x-3|

To plot these, we’ll use the definition of a modulus function, just like for |x|. Let’s start with the first one.

|x–3|={x,, when x≥3

           {  −x  when x<3

That  means, to plot the graph of y = |x – 3|, we have to plot the graph of

y = x – 3, when x ≥ 3

y = 3 – x, when x < 3

That is, for x ≥ 3, we’ll draw a line whose slope is 1 and y-intercept is –3. For x < 3, we’ll draw a line whose slope is –1 and y-intercept is -3.

Similarly for  y=|x|-2 and y=|x-1|+1 we can use the definition of modulus function to plot the pair of  lines (y=x-2 & y=-x-2) & (y=-x+2 & y=x)

as shown in the graph attached.

Hence, The graphs of the modulus functions are just a pair of lines drawn simultaneously.

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Therefore , as a result, the ratio of the corresponding sides of the triangle ABC and XYZ will be identical.

Since a triangle has four points or segments, it is regarded as a polygon. It is a fundamental geometric shape. A triangle with sides A, B, or C is referred to as triangle ABC. So when sides are not collinear, a single plane and square are generated in Euclidean geometry. If a triangle has three sides and three corners, it is a polygon. The corners of a triangle are the places where its three sides converge. The sum of the three triangle angles is 180 degrees.

Here,

A dilation is a modification that yields an image with a different size but the exact shape as the original. The initial figure can stretches or contracts by a specific amount.

We can observe that ABC contracts to form XYZ in the problem due to a 5x dilation.

As a result, the ratio of the corresponding sides of the triangles ABC and XYZ will be identical.

AB/CD = AC/XY= BC/YZ= 5

Therefore , as a result, the ratio of the corresponding sides of the triangles ABC and XYZ will be identical.

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∠u,∠x→ Alternative interior angle.

∠w,∠s→Corresponding angle

∠t,∠y→Alternative exterior angle.

∠s,∠t→Supplementory angle

∠w,∠y→Supplementory angle

∠t,∠x→Corresponding angle

∠w,∠z→vertical angle

∠v,∠w→ Alternative interior angle.

∠v,∠z→Corresponding angle

∠s,∠z→Alternative exterior angle.

∠t,∠u→Vertical angle

∠w,∠x→Supplementory angle

∠w,∠s→Corresponding angle

∠s,∠v→Vertical angle

∠x,∠z→Supplementory angle

What is the supplementary angle?

When two angles add up to 180 degrees, they are called supplementary. To avoid confusion, remember that s comes after c in the alphabet and that 180 is greater than 90.

supplementary angles:

∠x,∠z; ∠w,∠x; ∠w,∠y;∠s,∠t

Corresponding angles:When two parallel lines intersect any other line, corresponding angles are formed in matching corners or corresponding corners with the transversal (i.e. the transversal). Angles p and w, for example, are the corresponding angles in the figure below.

Corresponding angles are ∠w,∠s; ∠v,∠z; ∠t,∠x.

Vertical angles: Vertical angles are the angles formed when two lines intersect. The term "vertical" in this context refers to the fact that they share the same Vertex (corner point), rather than the usual meaning of up-down.

∠s,∠v; ∠t,∠u; ∠w,∠z

Alternate interior angles :When two lines are cut by a third line, a transversal, the term alternate interior angles is frequently used. If k and l are parallel, then the pairs of alternate interior angles are congruent, according to the Alternate Interior Angles Theorem.

Alternate Interior Angles: ∠u,∠x; ∠v,∠w.

Similarly alternative exterior angles are: ∠s,∠z; ∠t,∠y.

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The probability that a household subscribes to cable tv and netflix is 0.32.

Given data :

We know that from they gave us, cable tv have 70% , Netflix have 55%

so,   C = 70% / 100% = 0.7

N = 55% / 100% = 0.55

The probability of both C and N is ;

   = [tex]\frac{42}{70 + 55}[/tex] %  = 0.318 ≅ 0.32

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Answer:

its a you did got it correct

Step-by-step explanation:

had that test 2 years ago

The weight of three square yards of wood equals the weight of three square yards of wood =3×22.5=67.5 lb.

a. A sample of wood measuring 1/5 square foot weighs 1/2 lb.

5 is multiplied on both sides to get,

1 square foot of wood sample weighs 1/2/5=5/2 pounds.

A square yard now equals nine square feet.

Therefore, the weight of a sample of wood in a square yard is nine pounds, and the weight of a sample of wood in a square foot is nine plus five divided by two is forty-five divided by two is twenty-five pounds.

b. The weight of three square yards of wood equals the weight of three square yards of wood.

=3×22.5=67.5 lb.

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There are 24 ways for the vote of the favorite, second favorite, and third favorite band to be cast.

The list contains 4 bands.

Out of these 1 band is Alonzo's favorite, 1 is his second favorite and another is his 3rd favorite

Now to choose his favorite Alonzo has 4 choices. Hence there are 4 ways to cast this vote.

Now since one band has been chosen, Alonzo is left with 3 bands on the list, hence he has 3 ways to cast the vote for the second favorite.

For the last vote of 3rd favorite, there are2 options available, hence this can be done in 2 ways.

Hence we get the total number of ways to be

4 X 3 X 2 ways

= 24 ways

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The additive inverse of -4 is 4.

In mathematics, the additive inverse of a number is the number that, when added to the original number, results in a sum of zero. So for any number x, the additive inverse of x is -x. Therefore, the additive inverse of -4 is 4 because (-4) + 4 = 0.

The concept of additive inverse is used in many areas of mathematics, such as algebra, where it is used to solve equations and simplify expressions.

For example, if you have an equation such as x + (-4) = 0, you can simplify it by adding 4 to both sides, which results in x = 4. This is because 4 is the additive inverse of -4, and when added to -4, the sum is zero.

Another application of additive inverse is in linear algebra when working with vector space. Additive inverse is also used in cryptography and error correction codes.

It also could be used in many other fields like physics, finance and engineering.

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Since, Mario correctly applies the ratio test to determine whether the series converges or diverges. Mario's conclusion would be that the series converges if the limit of (an+1/an) as n approaches infinity is less than 1.

If Mario correctly applies the ratio test to determine whether the series converges or diverges, he would find that the series converges if the limit of (an+1/an) as n approaches infinity is less than 1, and diverges if the limit of (an+1/an) as n approaches infinity is greater than or equal to 1.

So, Mario's conclusion would be that the series converges if the limit of (an+1/an) as n approaches infinity is less than 1.

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The product of 4 5x3 7 is 420. To fully express the calculation, we can write it as 4 x (5 x 3) x 7 = 420. In other words, four multiplied by the product of five times three multiplied by seven equals 420.

First, multiply 5 and 3 to get 15.

Next, multiply 4 and 15 to get 60.

Lastly, multiply 60 and 7 to get 420.

4 x (5 x 3) x 7 = 420

First, we need to multiply the 5 and the 3 together in order to get the product of 15. Then, we need to multiply 4 and 15 in order to get the product of 60. Finally, we will multiply 60 and 7 together to get the final product of 420. To fully express the calculation, we can write it as 4 x (5 x 3) x 7 = 420. In other words, four multiplied by the product of five times three multiplied by seven equals 420.

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Log log scale is used to visualize data with large ranges of values, as it allows for the comparison of data with vastly different scales.

Log log scale is a type of graph which uses a logarithmic scale on both the x-axis and the y-axis, which allows for data with vastly different scales to be compared. This is especially useful when dealing with data which has very large ranges, as it allows us to zoom in on the data and compare it more easily. For example, if we are looking at data that ranges from 1 to 1000, a log log scale would allow us to see the entire range on one graph, instead of having to break it down into multiple graphs. This can be very helpful in visualizing data which spans a wide range of values, as it allows us to compare and analyse the data more effectively.

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By understanding the definition of the statistics method, it can be concluded that 57% is an example of the result of inference statistics.

In statistics, the population is defined as the entire research subject, while the sample is a representative or part of the population, which has the same characteristics that can describe and represent the entire population.

There are two methods used to perform data analysis:

a. Descriptive statistics: an analytical method used to describe the characteristics of data. The end result of this method is in the form of tables, charts, graphs, etc.

b. Inference statistics: an analytical method used to draw conclusions about a population based on a sample. The end result of this method is in the form of a possibility or probability and is expressed in percent units.

If we look at the given problem, it is stated that "in a sample of 1,600 registered voters, 912 or 57% approve of the way the president is doing his job"

By understanding the definition of descriptive and inference statistics, it can be concluded that 57% is an example of the result of Inference statistics.

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To complete the two-column proof, the required statement and reason are explained below.

A parallelogram is a given plane figure which has its opposite sides to be parallel and equal in length. It has its unique identifying properties.

Supplementary angles are two or more angles which add up to 180^o.

To complete the two-column proof, we have;

                 STATEMENT                                        REASON

1. ABCD and GDEF are parallelograms                Given

2. <C and <CDA are supplementary angles         m<C + m<CDA = 180^o

3. m<C + m<F = 180^o                      Definition of supplementary angles

4. <EDG ≅ <F                                    Definition of congruent angles

5. <EDG = <F                                    Parallelogram opposite angles theorem          

6. m<CDA = m<EDG                        Vertical angles congruence theorem

7. m<CDA ≅ m<EDG                        Definition of congruent angles

8. m<CDA ≅ m<F                             Given

9. m<C + m<CDA = m<C + m<EFG     Substitution property of equality

10. <C and <F are supplementary angles          Parallelogram consecutive

                                                                             angles theorem

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Answer:

rhombus

Step-by-step explanation: