Do the points (1,2) , (51,27) and (91,48) lie on a straight line? give reason for your answer​

Answer: 2400

Step-by-step explanation:

3000 x 20/100 = 600

Discount = 600

Sale price of the article: 3000-600 = 2400

Answer:

Translation of 3 units to the left.

Vertical stretch by a factor of 2.

Translation of 5 units down.

Step-by-step explanation:

Transformations

For a > 0

[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

Parent function:

[tex]y=x^2[/tex]

Translate 3 units left

Add 3 to the variable of the function

[tex]\implies y=(x+3)^2[/tex]

Stretch vertically by a factor of 2

Multiply the whole function by 2:

[tex]\implies y=2(x+3)^2[/tex]

Translate 5 units down

Subtract 5 from the whole function:

[tex]\implies y=2(x+3)^2-5[/tex]

Please see the attached graphs for the final transformed function (as well as the graphed steps).

Answer:

  a) vertical expansion by a factor of 2; translation 3 units left and 5 units down

  b) see attached

Step-by-step explanation:

Describing transformations is all about matching patterns. The elements of the transformed function are matched with the elements of a transformation.

A function is scaled vertically by multiplying each function value by some scale factor. In generic terms, the function f(x) is scaled vertically by the factor 'c' in this way:

If we want the function f(x) = x² scaled vertically by a factor of 2, then we have

  f(x) = x² . . . . . . . original function

  2·f(x) = 2x² . . . . scaled vertically by a factor of 2

On a graph, each point is vertically twice as far vertically from some reference point (the vertex, for example) as it is in the original function graph.

A function is translated to the right by 'h' units when x is replaced by (x -h).

If we want the function f(x) = x² translated right by 3 units, we will have ...

  f(x) = x² . . . . . . . . . . . original function

  f(x -3) = (x -3)² . . . . . .translated right 3 units

Note that translation left by 3 units would give ...

  f(x -(-3)) = f(x +3) = (x +3)² . . .  . translated left 3 units

On a graph, each point of the left-translated function is 3 units left of where it was on the original function graph.

A function is translated upward by 'k' units when k is added to the function value.

The value of k will be negative for a translation downward.

If we want the function f(x) = x² translated down by 5 units, we will have ...

  f(x) = x² . . . . . . . . . . . original function

  f(x) = x² -5 . . . . . . . . .translated down 5 units

Using all of these transformations at once, we have ...

  f(x) = x² . . . . . . . . . . . . . . . . . original function

  c·f(x -h) +k = c·(x -h)² +k . . . scaled by 'c', translated h right and k up

Compare this to the given function:

 y = 2(x +3)² -5

and we can see that ...

This is the pattern matching that is described at the beginning.

__

When graphing a transformed function, it is often useful to start with a distinctive feature and work from there. The vertex of a parabola is one such distinctive feature.

The transformations move the vertex 3 units left and 5 units down from its original position at (0, 0). The location of the vertex on the transformed function graph will be at (x, y) = (-3, -5).

The graph of the parent function parabola (y= x²) goes up from the vertex by the square of the number of units right or left. That is, 1 unit right or left of the vertex, the graph is 1 unit above the vertex. 2 units right or left, the graph is 2² = 4 units above the vertex.

The scaled graph will have these vertical distances multiplied by 2:

The graph of the transformed function is shown in blue in the attachment.

__

Additional comment

The vertical scale factor 'c' may have any non-zero value, positive or negative, greater than 1 or less than 1. When the magnitude is less than 1, the scaling is a compression, rather than an expansion. When the sign is negative, the graph is also reflected across the x-axis, before everything else.

Answer:

The scale factor from the original triangle to the image is 1/2.  The scale factor from the image to the original is 2.

Step-by-step explanation:

I make a sketch of the information.  Look at the corresponding sides.  Side AC on the big triangle is 8 and A'C' is 4.  It is half of the size of the large triangle.  That is true for each pair of sides.

If I went the other way, the original sides are twice as big as the images sides.

The z-score of Kimmie is -0.625

The formula for calculating the z-score is expressed as;

z = x-η/s

where

η is the mean

s is the standard deviation

x is the Kimmie score

Substitute the given parameter

z = 85.9-88.4/4.0

z = -2.5/4.0

z = -0.625

Hence the z-score of Kimmie is -0.625

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Using it's concept, there is a 0.0308 = 3.08% probability that a prize ticket with a vowel will be chosen, not replaced, and then another prize ticket with a vowel will be chosen. Since the letter is not replaced, the number of outcomes change, hence they are dependent.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

For the first ticket, since 5 out of 26 letters are vogal, the probability is:

5/26.

For the second ticket, since there is no replacement, the probability is:

4/25.

The probability of both tickets is:

[tex]p = \frac{5}{26} \times \frac{4}{25} = 0.0308[/tex]

0.0308 = 3.08% probability that a prize ticket with a vowel will be chosen, not replaced, and then another prize ticket with a vowel will be chosen. Since the letter is not replaced, the number of outcomes change, hence they are dependent.

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Answer:

[tex]2x^2+1-\dfrac{x}{2x^2-3}[/tex]

Step-by-step explanation:

Use the long division method to divide polynomials:

[tex]\large \begin{array}{r}2x^2\phantom{)))))}+1\phantom{)}\\2x^2-3{\overline{\smash{\big)}\,4x^4-4x^2-x-3\phantom{)}}}\\\underline{-~\phantom{(}(4x^4-6x^2)\phantom{-b))))))}}\\0+2x^2-x-3\phantom{)}\\\underline{-~\phantom{()}(2x^2\phantom{))))}-3)}\\-x\phantom{))))))}\end{array}[/tex]

Therefore:

[tex]\dfrac{4x^4-4x^2-x-3}{2x^2-3}=2x^2+1-\dfrac{x}{2x^2-3}[/tex]

Answer:B & E

Step-by-step explanation:

We can first rearrange the function to isolate y. Then, we can find the slope as the function is in the form y=mx+b.

[tex]3x-4y=7\\-4y=-3x+7\\y=\frac{3}{4}x-\frac{7}{4}[/tex]

Since parallel lines have the same slope, we can put the slope of 3/4 into the point slope form to get the answer.

For reference, the point-slope form is [tex]y-y_1=m(x-x_1)[/tex]

[tex]y+2=\frac{3}{4}(x+4)\\y+2=\frac{3}{4}x+3\\y=\frac{3}{4}x+1[/tex]

The first line is found in option E, so option E is one of the correct options.

We can also move the x to the other side, as two of the 5 options have both variables on the left (B and C).

[tex]-\frac{3}{4}x+y=1[/tex]

If we multiply the whole equation by -4, we can get rid of the fraction.

[tex]-4(-\frac{3}{4}x+y)=-4(1)\\3x-4y=-4[/tex]

Hence, option B is also correct.

Let [tex]C[/tex] be the set of all students in the classroom.

Let [tex]P[/tex] and [tex]M[/tex] be the sets of students that pass physics and math, respectively.

We're given

[tex]n(C) = 60[/tex]

[tex]n(P \cap M') = 17[/tex]

[tex]n(P \cap M) = 25[/tex]

[tex]n((P \cup M)') = n(P' \cap M') = 9[/tex]

i. We can split up [tex]P[/tex] into subsets of students that pass both physics and math [tex](P\cap M)[/tex] and those that pass only physics [tex](P\cap M')[/tex]. These sets are disjoint, so

[tex]n(P) = n(P\cap M) + n(P\cap M') = 25 + 17 = \boxed{42}[/tex]

ii. 9 students fails both subjects, so we find

[tex]n(C) = n(P\cup M) + n(P\cup M)' \implies n(P\cup M) = 60 - 9 = 51[/tex]

By the inclusion/exclusion principle,

[tex]n(P\cup M) = n(P) + n(M) - n(P\cap M)[/tex]

Using the result from part (i), we have

[tex]n(M) = 51 - 42 + 25 = 34[/tex]

and so the probability of selecting a student from this set is

[tex]\mathrm{Pr}(M) = \dfrac{34}{60} = \boxed{\dfrac{17}{30}}[/tex]

Answer:

197.82 m^2

Step-by-step explanation:

The area of a circle is

a = πr^2  The radius is half of the diameter.  They give us the diameter so we need to talk half of that number to use for the diameter.  The diameter is the length from the center of the circle to the edge of the circle.

We will find the area of the big circle and  subtract out the area of the little circle to bind the blue area.

Outer circle

a = πr^2

a = 3.14(12)^2

a = 3.14(144)

a = 452.16

Inner Circle:

a = πr^2

a = 3.14(9)^2

a = 3.14(81)

a =254.34

Lastly, subtract 254.34 from 452.16 to get  197.82

The best option that would be used to show the data would be the line graph.

The reason  I chose the line graph is that it would show us the trend in the data. This is in a way that we would see the periods there was a high bills.

Also the line graph is very simple to understand. The relationship and the changes in the data is easily seen.

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Answer:

Step-by-step explanation:

The given relation can be used with the formula for the area of a triangle to give an equation for the altitude or base.

Let b represent the length of the base. Then the altitude (height) is (b+4). The area formula tells us the area is ...

  A = 1/2bh

Using given values, the equation becomes ...

  96 = 1/2b(b +4)

Simplifying the equation and multiplying by 2, we have ...

  192 = b² +4b

Adding (4/2)² = 4 will complete the square.

  196 = b² +4b +4 = (b +2)²

Taking the square root gives ...

  14 = b +2 . . . . . . we are not interested in the negative root

  12 = b . . . . . . . . subtract 2

  16 = b+4 . . . . . find the altitude

The base is 12 cm; the altitude is 16 cm.

For the square with side length n, the diagonal measures:

[tex]d = \sqrt{2} *n[/tex]

The sidelength of the square is n, and we want to get the length of the diagonal d.

Notice that the diagonal is the hypotenuse of a right triangle whose catheti measure n.

Then we can use the Pythagorean theorem, which says that the square of the hypotenuse is equal to the sum of the squares of the cathetus;

[tex]d^2 = n^2 + n^2\\\\d^2 = 2n^2\\\\d = \sqrt{2n^2} \\\\d = \sqrt{2}*n[/tex]

That is the length of the diagonal.

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Answer:

2:7

Step-by-step explanation:

If 2 of the puppies are brindle that leaves 7 that are not out of the nine making the ratio 2:7.

The probability will be:

Case 1  matches with 5/48.

Case 2 matches with 1/12.

Case 3 matches with 1/4.

Case 4 matches with 1/8.

Case 5 matches with 5/16.

We have a total sample space of six-sided die and an eight  sided die.

(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8)

(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8)

(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(3,7),(3,8)  

(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(4,7),(4,8)

(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(5,7),(5,8)

(6,1),(6,2),(6,3),(6,4),(6,5),(6,6),(6,7),(6,8)  

Case 1: The Probability that both numbers are odd numbers and their product is greater than 10. are:  (3,5),(3,7),(5,3),(5,5),(5,7)

And the total number of outcomes are: 48.

The required probability is 5/48.

Case 2: The probability that the second number is twice the first number are:

(1,2),(2,4),(3,6),(4,8)

And the total number of outcomes are 48.

So, the required probability is 1/12.

Case 3: The probability of a number whose sum is a multiple of 4 are:

(1,3),(1,7),(2,2),(2,6),(3,1),(3,5),(4,4),(4,8),(5,3),(5,7),(6,2),(6,6).

And the total number of outcomes are: 48.

The required probability is 12/48 = 1/4

Case 4: The probability that the sum of two numbers is greater than 11.

(4,8),(5,8),(6,7),(6,8),(5,7),(6,6)

And a total number of outcomes are 48.

So, the required probability is 6/48 = 1/8.

Case 5: The probability that the second number rolled is less than the first number are:

(2,1),(3,1),(3,2),(4,1),(4,2),(4,3),(5,1),(5,2),(5,3),(5,4),(6,1),(6,2),(6,3),(6,4),(6,5)

And the total number of outcomes are: 48.

The required probability is 15/48 = 5/16.

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The solution to the given fraction 7/11 = x/9 to the nearest tenth is 5.7

7/11 = x/9

7 × 9 = 11 × x

63 = 11x

x = 63/11

x = 5.72727272727272

Approximately,

x = 5.7

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Answer:

The second option, 3x^2(x+3)(4x+1)

Step-by-step explanation:

Factor out the common term, which is 3x^2

This then becomes 3x^2(4x^2+13x+3)

Factor the inside term and it becomes

(3x^2)(x+3)(4x+1)

Answer:

Step-by-step explanation:

hello :

The graph of y =-3x+4 is the line

The cost per person if number of students is 100 given the inverse variation is $46.75

C = k / n

where,

k = constant of proportionality

If n = 55 and C = $85

C = k / n

85 = k / 55

85 × 55 = k

4,675 = k

Find C if n = 100

C = k / n

= 4,675 / 100

C = $46.75

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Answer:

C = $46.75

Step-by-step explanation:

85 × 55 = k

4,675 = k

4675/100=46.75

therefore the answer is 46.75

The equivalent expressions indicated are;

1) 1/a^6b^4

2) a^6/b^6

3) a^6/b^5

4) b^6/a^6

5) a^5b^3

We have to note that when we talk about the equivalent expressions, we mean the expressions that we have to get from each other when we carry out a little computational work on the original expression.

Thus, the equivalent expression has shown that the expression that is in the bracket is the same as the original expression by the use of the laws of exponents.

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The measure of m<1, m<2 and m<3 are 90, 63 and 63 degrees respectively

A kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other.

The given figure is a kite with two intersecting lines that are perpendicular to each other.

Since the lines are perpendicular to each other, hence;

m<1 = 90 degrees

For the measure of m<2

m<2 + 90 + 27 =180

m<2 + 117 = 180

m<2 = 180 - 117

m<2 = 63degrees

Since the opposite sides are congruent, hence the measure of m<2 is congruent to m<3. Hence m<3 = 63 degrees

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Answer + Step-by-step explanation:

Recall That the number of solution

of a quadratic equation ax² + bx + c = 0

depends on the discriminant b² - 4ac :

if b² - 4ac > 0 , the equation has two distinct solutions.

if b² - 4ac = 0 , the equation has only one solution.

if b² - 4ac < 0 , the equation has no solutions.

=======================================

System 1 :

y = x² + 4x + 7  and y = 2

⇔ x² + 4x + 7 = 2

⇔ x² + 4x + 5 = 0

→ b² - 4ac = 4² - 4×1×5 = 16 - 20 = -4 < 0

Then the quadratic equation has no solutions

Therefore the system has no solutions.

System 2 :

y = x² - 2  and y = x + 5

⇔ x² - 2 = x + 5

⇔ x² - x - 7 = 0

→ b² - 4ac = (-1)² + 4×7 = 29 > 0

Then the quadratic equation has two solutions

Therefore the system has two solutions.

System 3 :

y = -x² - 3  and y = 9 + 2x

⇔  -x² - 3 = 9 + 2x

⇔ -x² - 2x - 12 = 0

→ b² - 4ac = (-2)² - 4×(-1)×(-12) = 4 - 48 = -44 < 0

Then the quadratic equation has no solutions

Therefore the system has two solutions.

System 4 :

y = -3x - 6  and y = 2x² - 7x

⇔  -3x - 6 = 2x² - 7x

⇔ 2x² - 4x + 6 = 0

→ b² - 4ac = (-4)² - 4×(2)×(6) = 16 - 48 = -32 < 0

Then the quadratic equation has no solutions

Therefore the system has two solutions.

System 5 :

y = x² and y = 10 - 8x

⇔ x² = 10 - 8x

⇔ x² + 8x - 10 = 0

→ b² - 4ac = 8² - 4×1×(-10) = 64 + 40 = 104 > 0

Then the quadratic equation has two solutions

Therefore the system has two solutions.

Answer:

7

Step-by-step explanation:

1, 1, 2, 4, 7, 8, 10, 15, 20

median = 7

The complete table is

x     y

-1     -2

0     3

1     8

2    13

The function is given as:

y = 5x + 3

On the table, we have

x = -1, 0, 1 and 2

Using the above values, we have:

y = 5(-1) + 3 = -2

y = 5(0) + 3 = 3

y = 5(1) + 3 = 8

y = 5(2) + 3 = 13

So, the complete table is

x     y

-1     -2

0     3

1     8

2    13

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                                                                  n=8

                                                                  n=-6

A number line is a horizontal line with evenly spaced number increments. The numbers on the line will determine how the number on the line can be answered.

The numbers on the number line increase as one moves from left to right and decrease as one moves from right to left.

A modulus function is a function that returns the absolute value of a number or variable. It yields the magnitude of the number of variables. It is also known as an absolute value function. This function's output is always positive, regardless of the input.

Open modulus with a positive sign.

                 5-|n-1|=-2

                -|n-1|=-2-5

                 n+1= 7

                 n= 8

Open modulus with a  negative sign.

                5-|n-1|=-2

                -|n-1|=-2-5

                 n-1= -7

                 n= -6

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The measure of the length and width of the rectangle is given as 135 feet and 92 feet respectively.

From the information given, we have the following proofs;

Length, l = 2x + 30 - 49

Length = 2x - 19

The formula for perimeter of a rectangle is given as;

Perimeter = 2( length + width)

Substitute the expressions into the formula

Perimeter =  2 ( x+ 15 + 2x - 19 )

Perimeter = 2 (3x - 4)

Perimeter = 6x - 8

We have that the area is  162 more than 27 times the perimeter, which is Area = 27 (perimeter )+ 163

Area = 27(6x-8) + 162

Expand the bracket

Area= 162x - 216 + 162

Area = 162x - 54

But we know that

Area = length × width

Substitute the expressions

Area = (x+15)(2x-19)

Area =  2x² - 19x +30x - 285

Area = 2x² + 11x - 285

Equate the two formulas for area

162x - 54 = 2x² +11x - 285

Collect like terms

2x² + 11x - 285 - 162x + 54 = 0

2x²  - 151x - 231 = 0

Solve the quadratic equation

(2x + 3)(x-77) = 0

Let's solve for x

x - 77 = 0

x = 77

The expression for the width;

Width = x+15

Width = 77 + 15

Width = 92 feet

The expression for the length

Length = 2(x+15) - 49

Length = 2 ( 77 + 15) - 49

Length = 154 + 30 - 49

Length = 184 - 49

Length = 135 feet

Thus, the measure of the length and width of the rectangle is given as 135 feet and 92 feet respectively.

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Answer:

The answers are in the image

Step-by-step explanation:

The solution is in the attached image

The sequence of transformation will be;

Rotate 120 degrees Counterclockwise around B, then Translate B to B' and reflect over segment BA.

We want to find the transformation that maps Quadrilateral ABCD onto Quadrilateral A'B'C'D'.

Looking at the given image, the sequence of transformation will be;

Rotate 120 degrees Counterclockwise around B, then Translate B to B' and reflect over segment BA.

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The amount of rim needed for each window is 141.4 in

Since the outer rim is the length of an arc, we use the formula for length of an arc of a circle.

An arc is part of section of the circumference of a circle

So, length of arc, L = Ф/360 × 2πR where

Gven that for the window rim

Substituting the values of the variables into the equation for L, we have

L = Ф/360 × 2πR

L = 270°/360° × 2π × 30 in

L = 3/4 × 2π × 30 in

L = 3/2 × π × 30 in

L = 3 × π × 15 in

L = 45π in

L = 141.37 in

L ≅ 141.4 in

So, the amount of rim needed for each window is 141.4 in

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Simplifying the expression gives 36x^2 - 82x - 10 = 0

Given the expression;

4x-5/3+2x=7+2/9x+2

[tex]\frac{4x - 5}{3 + 2x} = \frac{9}{9x + 2}[/tex]

Cross multiply

[tex]4x - 5( 9x + 2) = 9 (3 + 2x)[/tex]

Expand the bracket

[tex]36x^2 + 8x - 45x - 10 = 27x + 18x[/tex]

Collect like terms

36x^2 + 8x - 45x - 27x - 18x = 0

Add the like terms

36x^2- 82x - 10 = 0

Thus, simplifying the expression gives 36x^2- 82x - 10 = 0

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