the shorter leg of a right trialbe is 9cm shorter than the longer leb. the hypotenuse is 9cm onger than the longer leg. find the side lengths of the triable.

Answer:

Step-by-step explanation:

There is only one unique triangle that can be made with this information.

The number of general admission seat sold is 842 and the  number of premiere seat sold is 506.

The system of equations that represent the information provided in the question are:

a + b = 1348 equation 1

8.5a + (1.30 x 8.5)b = 12,748.30

8.5a + 11.05b = 12,748.30 equation 2

Where:

The elimination method would be used to solve these equations

Multiply equation 1 by 8.5

8.5a + 8.5b = 11,458 equation 3

Subtract equation 3 from equation 2

1290.30 = 2.55b

b = 1290.30 / 2.55

b = 506

Substitute for b in equation 1 :

a + 506 = 1348

a = 1348 - 506

a = 842

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Answer:

Let F be the number of fragrance samples and L be the number of hand lotion samples.

We know that F + L = 114, since Rika must hand out a total of 114 samples.

We also know that F = (1/3)L and L = (1/4)F, since the number of fragrance samples is 1/3 of the number of hand lotion samples, and the number of hand lotion samples is 1/4 of the number of fragrance samples.

Substituting the second equation into the first equation, we get:

F + (1/4)F = 114

Combining like terms, we get:

(5/4)F = 114

Dividing both sides by (5/4), we get:

F = 92

Substituting this value back into the second equation, we get:

L = (1/4)(92) = 23

Therefore, the system of equations is:

F + L = 114

F = (1/3)L

L = (1/4)F

The solution to this system is F = 92 and L = 23

The relations depicted in graph 1 is a function as every input value has exactly one output value.

A relation called a function is one in which every potential input value results in exactly one possible output value. They are set of ordered pairs.

Relations indicate the relationship between the indicated input and output value.

Graph 1:

In graph 1 each input value has exactly one output hence relations in graph 1 is a function.

Graph 2:

Graph 2 represents a circle, in this each input value does not have exactly one output value and hence it is not a function.

Graph3:

In graph 3, each input value does not have exactly one output value and hence it is not a function.

Graph 4:

In graph 4, each input value does not have exactly one output value and hence it is not a function.

Hence, relations in graph 1 is a function.

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Answer:

2420

Step-by-step explanation:

since it’s an eighth, you need to multiply 300 by 8 but not 320 since it’s separate. so you get 2400 but then add the 20 and get 2420

Answer: irrational number

Step-by-step explanation:

Length of third side = 10 units.

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.

Here, given that,

Height = 7 units

Base = √51 units

And, we have, it is a right angle triangle  

and we have to find the hypotenuse.

By Pythagorean theorem we get,

Hypotenuse = √7²+ 51

                     =√100

                     =10 units.

Hence, Length of third side = 10 units.

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Answer:

p < -7

Step-by-step explanation:

-4p > 28  Divide both sides by -4 and flip the sign

p < -7

Answer:

ok

Step-by-step explanation:

The factorization of the polynomial is ( x - 4 ) ( x + 9 )

factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form.

We are given the function as

x² + 5x - 36

We have to find out the two numbers when multiplied results to 36 & when subtracted results to 5.

The numbers are 9 and 4

x²+ ( 9 - 4)x - 36

Distribute x :

x² + 9x - 4x - 36

Take the common :

x ( x + 9 ) - 4 (x + 9 )

( x - 4 ) ( x + 9 )

Hence, The right answer is of Option C [ ( x - 4 ) ( x + 9 ) ]

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The terms of sequences are u₁ = 4, u₂ = 19 and u₃ = 364.

An ordered list of things is a sequence (or events). Similar to a set, it has members (also called elements, or terms). The length of the sequence is the number of ordered items (potentially infinite).

Given:

A sequence is defined by the term-to-term rule

uₙ₊₁ = u₁² + 3

And  u₀ = 1,

a). The second term

u₁ = u₀² + 3

u₁ = (1)² + 3

u₁ = 4

b). The third term

u₂ = u₁² + 3

u₂= (4)² + 3

u₂ = 19

c). The fourth term

u₃ = u₂² + 3

u₃ = (19)² + 3

u₃ = 364

Therefore, The values, u₁ = 4, u₂ = 19 and u₃ = 364.

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The graph of the equation 30x+6y=180 will be a line in the xy-plane.

An equation is a mathematical statement that expresses the equality of two expressions. It is composed of one or more terms and an equal sign, and can contain constants, variables, and operators. Equations are used to represent relationships between different values, quantities, and objects, and to solve for unknowns. Equations are a fundamental tool of mathematics and can be used to describe physical processes as well as abstract concepts.

The line will pass through the origin, since the equation is satisfied when both x and y are 0. The intercepts of the line on the x-axis and y-axis represent the values of x and y that will make the equation true, regardless of the values of the other variable.

For this equation, the y-intercept is 30, since when x=0, the equation becomes 30(0)+6y=180, and so y=30. This means that if you do not board your dog, you would need to play with it for 30 hours in order to meet the requirement of spending a total of 180 dollars.

The x-intercept is 6 since when y=0, the equation becomes 30x+6(0)=180, and so x=6. This means that if you do not play with your dog, you would need to board it for 6 nights in order to meet the requirement of spending a total of 180 dollars.

Therefore, the graph of the equation 30x+6y=180 shows that it is possible to meet the requirement of spending a total of 180 dollars either by boarding your dog for 6 nights or by playing with it for 30 hours, regardless of the values of the other variable.

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The option (A) (7,-7), (-7,-5), (-7,-3), (-7,-1) ordered pair is y a function of x.

What is a function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range.

In a mathematical relation, for a given value of x, there can only be one unique value of y.

It is a requirement that a function must follow.

In option A, the x values are all different, so y is a function of x

In option B, there are two (0,0) and (0,9) which means for x=0 there are two possible values of y, thus y is not a function of x.

In option C, there is a repetition of the x-value, 15, so y is not a function of x

In option D, there is a repetition of the x-value, 13, so y is not a function of x.

So, the correct option is A (7,-7), (-7,-5), (-7,-3), (-7,-1)

Hence, the option (A) (7,-7), (-7,-5), (-7,-3), (-7,-1) ordered pair is y a function of x.

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Answer:

Answer: 27:8

Step-by-step explanation:

There are 24 + 16 + 14 = 24+16+14= 54

54 marbles in total.

The ratio of total marbles to red marbles is 54 : 16, which simplifies to 27 : 8.

Answer: 27:8

The focus is at (3,3+1/4) and the directrix is the equation of a line is 2.75.

A parabola is defined as the set of all points that are equidistant to the focus (F) and the directrix (d).

In the case of this parabola represented by the equation (y-3)² = 4(x-3), the vertex is located at the point (3,3) which means that this parabola opens horizontally to the left. Since the coefficient of x² is positive the parabola opens up.

The focus is located at the point (3,3+1/4) which is (3,3.25) and the directrix is the line x = 2.75. These two elements are crucial in understanding the shape and behavior of the parabola, The focus is where the parabola bends, and the directrix is where it opens.

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The value of the ratio x : y : z is 1/2 : /3 : 5/18

From the question, we have the following parameters that can be used in our computation:

x:y = 1/2:1/3 and y:z = 1/5:1/6

Express the ratio properly

So, we have the following representation

x : y = 1/2 : 1/3 and y : z = 1/5 : 1/6

Multiply the ratio y : z = 1/5 : 1/6 by 5/3

So, we have

y : z = 1/3 : 5/18

So, we have

x : y : y : z = 1/2 : 1/3 : 1/3 : 5/18

Remove the repetition

This gives

x : y : z = 1/2 : /3 : 5/18

Hence, the ratio is 1/2 : /3 : 5/18

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Answer:

8 dm decreased 60%

Step-by-step explanation:

8-3.2=4.8

4.8/8=0.6

0.6=60%

The solution to the system of equations are

The number of adult tickets x = 85

The number of children's ticket y = 65

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first equation be represented as A

Let the number of adult tickets be = x

Let the number of children's tickets be = y

A total of 150 tickets were sold

Substituting the values in the equation , we get

x + y = 150   be equation (1)

And , Adult tickets cost $7 each and children's tickets cost $4 each

So , 7x + 4y = 855   be equation (2)

Multiply equation (1) by 7 , we get

7x + 7y = 1050   be equation (3)

Subtracting equation (2) from equation (3) , we get

3y = 1050 - 855

3y = 195

Divide by 3 on both sides of the equation , we get

y = 65

Substitute the value of y in the equation (1) , we get

x + 65 = 150

Subtracting 65 on both sides of the equation , we get

x = 150 - 65

x = 85

Hence , the number of adult tickets x is 85 and the number of children's ticket y is 65

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Answer:

2x + 1 = 79 (being alternate angel )

2x = 79-1

2x = 78

x = 78/2

x = 39

The given figure is a polygon, a quadrilateral and a trapezoid.

A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.

Given is a figure,

The figure is a polygon, a quadrilateral and a trapezoid.

It can not be a parallelogram, rhombus or a rectangle, because none of their properties are shown in the figure.

Hence, the given figure is a polygon, a quadrilateral and a trapezoid.

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Answer:

The first inequality can be solved by combining like terms and isolating x on one side:

-2(6x + 36) - 7x <= 23

-12x - 72 - 7x <= 23

-19x - 72 <= 23

-19x <= 95

x >= -5

The second inequality can be solved by subtracting 10 from both sides:

6x + 10 > 40

6x > 30

x > 5

The solution to both inequalities is x >= -5 and x > 5, which means that x is a real number greater than 5.

Answer:

As far as I know

Mode: The most frequent number—that is, the number that occurs the highest number of times. Example: The mode of {4 , 2, 4, 3, 2, 2} is 2 because it occurs three times, which is more than any other number.

The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.

The rate of change is $2.33 per visitor

Rate of change refers to how quickly something changes over time. For example, acceleration is the rate of change of velocity with time.

Velocity is also the rate of change in position with time.

Rate of change means difference or changes with time.

It cost $31 for 3 visitor. This means that the cost per visitor is $31/3 = $10.33

It cost $80 for 10 visitor. This means that the cost for one visitor is 80/10 = $8

The rate of change is the difference in rate. This means that rate of change = $10.33 - $8

= $2.33/visitor

Therefore the rate of change is $ 2.33 per visitor.

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the value of the Perpendicular distance of F from Chord AB is 10.

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.

Given a circle, Where F makes a right angle triangle with the chord CD and also with Chord AB.

We know that,

Equal chords of a circle are equidistant from the center of a circle.

Here,

Chords AB and CD are equal to 18.

So, Chords AB and CD are equidistant from F(center of the circle).

Thus, x = 10

therefore, the value of the Perpendicular distance of F from Chord AB is 10.

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The given inequality can be correctly shown in the graph containing all the numbers greater than or equal to 3. The correct option is (D).

A number line is a graphical representation of numbers on a line.

The number line has one convention that the positive numbers are always on the right side of the origin and the negative numbers are on the left side.

The inequality is given as below,

[tex]\frac{7x-3}{9} \geq 8 - 2x[/tex]

It can be solved as follows,

[tex]\frac{7x-3}{9} \geq 8 - 2x[/tex]

Multiply both sides by 9 to get,

⇒ 7x - 3 ≥ 9(8 - 2x)

⇒ 25x ≥ 75

⇒ x ≥ 3

It implies that the solution is the set of numbers greater than or equal to 3.

Hence, the solution of inequality is obtained as number line satisfying x ≥ 3.

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It can be concluded that the given coordinates of A(2,3), B(4,6), C(7,4) and D(a,b) can be used to determine the length of the sides as well as the angles of the quadrilateral ABCD.

A quadrilateral is a four-sided polygon with four angles. It is a two-dimensional shape that is bounded by four line segments, each of which is called a side. The sum of the angles of a quadrilateral is 360 degrees. Types of quadrilaterals include rectangles, squares, trapezoids, parallelograms, and kites.

First of all, ABCD is a quadrilateral, which means it has four sides and four vertices. A, B, C and D are the vertices of this quadrilateral. It can be seen that A(2,3), B(4,6), C(7,4) and D(a,b) given in the question are coordinates of the vertices. Therefore, from these coordinates, we can conclude that A, B, C and D are the vertices of the quadrilateral ABCD.

Moreover, these coordinates can also be used to determine the length of the sides of the quadrilateral. The distance between A and B can be calculated by using the Pythagorean theorem. Similarly, the lengths of other sides can also be calculated by using the same theorem. Furthermore, the coordinates will also help us to calculate the angles formed by the sides of the quadrilateral ABCD.

Therefore, it can be concluded that the given coordinates of A(2,3), B(4,6), C(7,4) and D(a,b) can be used to determine the length of the sides as well as the angles of the quadrilateral ABCD.

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complete questions as follows-

If A(2,3),B(4,6),C(7,4) and D(a,b) are vertices of quadrilateral prove its true.

Answer:

9

Step-by-step explanation:

The answer is 9

Answer: 8

Step-by-step explanation:

20=r+11

-11     -11

   8=r    

Answer: #1 a=226

Step-by-step explanation:#1, split the shale into 2 parts. A small square with the 6 and 16. Then subtract six from sixteen and you have the height of the rectangle. Then take your difference (10) and multiply it with your width (19)= 190

Then do the little square which is 6x6=36. Add 190 and 36

Answer:

The area and the perimeter is 225 and 152. I'll show you how to do the rest below:

Step-by-step explanation:

For the Area you Multply all the numbers together

And for the perimeter you multiply the numbers by four

I hope you understand! let me know in the reply box

On solving the provided question, we can say that - the value of the following equations is 6(0) + 2y = 10y = 5

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

here,

6x + 2y = 10

so, x = 0;

6(0) + 2y = 10

y = 5

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