which property is illustrated for all expressions a and b if a=b then b=a

Answer:

⇒   Let marked price be Rs.x.

⇒  Discount = 20% of marked price.

⇒  Discount=  

100

20

​  

×x=  

100

20x

​

⇒  Selling price = Marked price - Discount.

⇒  192=x−  

100

20x

⇒  192=  

100

80x

⇒  x=  

80

19200

=Rs.240

Answer:

S.p = 992

discount = 20%

marked price = S. p + discount

= 992 + 20/100*992

= 992 + 198.4

= 1190.4

The surface area of the triangular prism is 480 square inches and net A is the correct net of the prism

When a triangle is, stretch it out to produce a stack of triangles, one on top of the other. A triangular prism is a name given to this novel 3D object.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have given a triangular prism with its net.

After analyzing the correct net will be net A because the inner rectangle length should be 14 in not 13 in.

The surface area of the triangular prism:

[tex]= 2[\dfrac{1}{2}(5\times12)]+ 5\times 14+ 12 \times 14+ 13\times 14[/tex]

After solving:

The surface area = 480 square inches.

Thus, the surface area of the triangular prism is 480 square inches and net A is the correct net of the prism

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Answer:

x = 9

y = 61

Step-by-step explanation:

let me know if you want an explanation!

Correct answer is option D.

The graph crosses the y-axis at (0, 5), increasing from x = -10 to x = 2 and remaining constant from x = 2 to x = 10.

A function f(x) is said to be increasing on an interval I if for any two numbers x and y in I such that x < y, we have f(x) ≤ f(y).

For this case, the first thing you should observe is that you have a different function in two distinct intervals.

We have then:

For [-10, 2]:

The linear function has a positive slope, therefore it grows and cuts the y-axis at the point (0, 5)

For [2, 10]:

We have a constant function whose equation is:

y = 5

Thus, the correct Answer is:

D. The graph crosses the y-axis at (0, 5), increasing from x = -10 to x = 2 and remaining constant from x = 2 to x = 10.

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Answer:

slope = 5 , y- intercept = - 10

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 5x - 10 ← is in slope- intercept form

with slope m = 5 and y- intercept c = - 10

The slope and y intercept of the function y = 5x - 10 is 5 and -10 respectively.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

Equation of a line in slope intercept form is,

y = mx + b,

where m is the slope of the line and b is the y intercept,

y intercept is the y coordinate of the point where it touches the Y axis.

Given equation is y = 5x - 10.

Comparing with slope intercept form,

m = 5 and b = -10

Hence the slope of the line is 5 and y intercept is -10.

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There 6840 ways  can first, second, and third place be assigned.

A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters.

We will use the concept of permutation

[tex]^{20}P_3[/tex]= 20!/ (20-3)!

     = 20*19*18*17!/ 17!

    = 6840 ways.

Hence, there are 6840 ways.

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The correct option regarding the inverse function is given by:

B.They are reflections of each other.

The inverse function is the reflection of the original function over the line y = x, that is, they are reflections of each other, hence option B is correct.

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Answer:

-2

Step-by-step explanation:

[tex]2(3-4) +3(3)-3^2\\= 2(-1) + 3(3) -3^2\\= -2 + 9 - 9\\= -2[/tex]

Answer:

#1 (4b + 6a) #2  150y

Step-by-step explanation:

#1 :area of right triangle: ab/2

4x2/2 = 4b

area of rectangle: length x width

2 x 3 = 6a

#2:

5y + 2.5y = 7.5y x 2 = 15y

so the top and bottom are both 15 y

the sides are each 5y so thats 10 y

15x10= 150y

The solution to 4sin2xcosx+sin3x=sin<3,14+x> is x = nπ, where n = ±{0, 0.5, 1, 1.5....}

The equation is given as:

4sin2xcosx+sin3x=sin<3,14+x>

Rewrite properly as:

4sin(2x)cos(x)+sin(3x)=sin(3.14+x)

Next, we split the equation as follows:

y = 4sin(2x)cos(x)+sin(3x)

y = sin(3.14+x)

Next, we plot the graph of both equations (see attachment)

From the attached graph, we have:

x = nπ, where n = ±{0, 0.5, 1, 1.5....}

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Answer:

20°

Step-by-step explanation:

Measure of QR is 180 - 108 = 72°

 then using     intercepted arc - external angle theorem:

angle RPQ then equals  1/2 ( 108 - 72) = 20 °

The slope of the line in its simplest form is 3.

The slope of a line is [tex]Slope=\frac{Rise}{Run}[/tex].

We need to find the slope of the line in its simplest form.

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope is often denoted by the letter m; there is no clear answer to the question of why the letter m is used for slope.

Select any two points on the line like A and B.

From the below figure it is clear that

Rise = Change in y = -2-(-5) = 3

Run = Change in x = 9-0 = 9

Now, [tex]\frac{9}{3} =3[/tex]

Therefore, the slope of the line in simplest form is 3.

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Answer:  [tex]\textsf{y = 3/4x - 7.75}[/tex]

-------------------------------------------------------------------------------------------------------------

Given:  [tex]\textsf{Passes through (5, -4) with a slope of 3/4}[/tex]

Find:  [tex]\textsf{The equation in slope-intercept form}[/tex]

Solution:  In order to determine the equation we need to first plug the values into the point-slope form, simplify, distribute, and solve for y to get our final result.

Plug in the values

Simplify the expression and distribute

Subtract 4 from both sides

The equation in slope-intercept form that follows the information that was provided is y = 3/4x - 7.75

They are congruent because the word congruent means the same shape and size and if you look at the picture angle RAM and angle ZMA have the same shape and the same size.

The function that models the horizontal displacement as a function of time in seconds is y = 5cos(2π/3 x)

The given parameters are:

Start by calculating the amplitude, A using:

A = h/2

This gives

A = 10/2

A = 5

Next, we calculate the period using:

B = π/t

This gives

B = π/1.5

Evaluate

B = 2π/3

The pendulum is at the middle.

So, it has no vertical displacement

The function is then represented as:

y = Acos(Bx)

This gives

y = 5cos(2π/3 x)

Hence, the function that models the horizontal displacement as a function of time in seconds is y = 5cos(2π/3 x)

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Answer:

x = 55 degrees

Step-by-step explanation:

The sum of the internal angles of a triangle results in 180°

x + 50° + 75° = 180°

x + 125° =180°

x = 180° - 125°

x = 55°

The value of f(0) is 12.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

By considering the graph we have to find f(0) which means we have to find that point where x- coordinate is zero.

Also, which shows that 12 the function f(x)

So, taking the point is (0,12) we can get f(0)= 12.

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The error from Jorge's arithmetic operation on the given algebraic expression is that he distributed it incorrectly.

An algebraic expression is a mathematical equation that is made up of variables together with arithmetic operations.

From the given expression, we have:

4x - x + 2 + 6 = 6x + 16

Add similar elements together;

3x + 8 = 6x + 16

Using distributive property, subtract 8 from both sides:

3x + 8 - 8 = 6x + 16 - 8

3x = 6x + 8

Simplify

3x-6x = 8

-3x = 8

Divide both sides by -3

-3/-3x = -8/3

x =  -8/3

So from Jorge's calculation, because he distributed incorrectly, we can conclude that could be his error.

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Answer:

B

Step-by-step explanation:

pythagorus theorem

a² + b² = c²

c² - b² = a²

26² - 24² = a²

676 - 576 = a²

a² = 100

a = 10

The equation in slope-intercept form is y = 13/8x -17/8 and the equation in standard form is 13x -8y = 17

A line is the shortest distance between two points. The equation of a line in slope-intercept form is y = mx + b while as a standard notation is Ax+By = C

Given the coordinate points (-3, -7) and (5, 6)

Determine the slope

Slope = 6-(-7)/5-(-3)

Slope = 13/8

For the y-intercept

6 = 13/8(5) + b

6 = 65/8 + b

b = 6 - 65/8

b = -17/8

The equation in slope-intercept form is y = 13/8x -17/8

Write in standard form

Recall y = 13/8x - 17/8

Multiply through by 8

8y = 13x - 17

-13x + 8y = -17

13x -8y = 17

Hence the equation in standard form is 13x -8y = 17

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Answer: $329.8

[tex]3298-(\frac{90}{100} *3298)\\= 3298 - 2968.2\\= 329.8[/tex]

The amount Keiko pays annually is $329.8

To answer the question, we need to know the amount Keiko pays annually

Since Keiko health insurance premium annually is $3298 and if his employer pays 90% of the premium, we want to know how much Keiko pays.

Since the employer pays 90% of the premium, the employer pays x = 90% of $3298

= 0.9 × 3298

= $2968.2

So, the amount Keiko pays annually is y = premium - amount employer pays, x

= $3298 - $2968.2

= $329.8

So, the amount Keiko pays annually is $329.8

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Answer:

a. 700

b. 1000

c. 80

d. 700

e.

Answer:

$75

[It is easy to say $60, but don't forget to add Samuel to the total]

Step-by-step explanation:

There are 5 people in total:

1  Samuel

4 friends

5 people who can spend up to $15 each.

(5 people)*($15/person) = $75 total spent on supplies

Answer:

£11.50

Step-by-step explanation:

7litres of petrol cos t £3.50. The cost of 1 liter will be:

= £3.50/7

= £0.50

The cost of 23 litres of petrol of the same grade will be:

= £0.50 × 23

= £11.50

An expression is defined as a set of numbers, variables, and mathematical operations. The given statement can be modeled as (3m+7)/27 < n.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given statement "The quotient of 7 more than three times a number m and the number 27 less than n" can be modeled as an algebraic expression as shown below.

(3m+7)/27 < n

Hence, the given statement can be modeled as (3m+7)/27 < n.

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The values of x does f(x) = 0 will be -4,0,2.Option A is corect.

A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.

The graph shows the cubic polynomial equation found as;

⇒(x+4)(x)(x-2)

The points f(x) = 0 is;

⇒(x+4)(x)(x-2)

⇒(-4+4)(0)(2-2)

⇒0

The values of x does f(x) = 0 will be -4,0,2.

Hence, option A is corect.

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The correlation between variables (r) = 0.959, and signifies a positive relationship between the variables.

The correlation of two pairs of data values tells about the degree of movement(along or opposite) that can occur in one of the data values when other data value is increased or decreased respectively.

The pertinent data are:

Period Fertilizer Sales Number of Mowers Sold

1 1.6 12.0

2 1.3 10.0

3 1.8 13.0

4 2.0 15.0

5 2.2 15.0

6 1.5 11.0

7 1.6 12.0

8 1.4 10.0

9 1.8 13.0

10 1.4 10.0

11 1.9 15.0

12 1.4 11.0

13 1.7 14.0

14 1.4 13.0

To determine the correlation between the two variables

Regression equation ( y ) = a + bx

y = dependent variable ( mower )

x = independent variable ( fertilizer)

a = intercept point ( y-axis and regression line )

b = slope ( regression line )

From the given data;

N = 14 ,    Σ x = 22.8,  

Σy = 131,   Σy^2 = 1269,

Σx^2 = 38.18,      (Σx)^2 = 519.84

Σxy = 219.8,       (Σy)^2 = 17161

Hence, The correlation between variables (r) = 0.959, and signifies a positive relationship between the variables.

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Answer:

r = - 3.25, p = -1.5

Step-by-step explanation:

→ Rearrange p - 2r = 5

p = 5 + 2r

→ Substitute into 6p - 4r = 4

6 ( 5 + 2r ) - 4r = 4

→ Expand

30 + 12r - 4r = 4

→ Simplify and solve

r = - 3.25

→ Substitute into p - 2r = 5

p + 6.5 = 5

→ Minus 6.5 from both sides

p = -1.5

Answer:

Ox=4 is the answer for the question