Find the slope of the line passing through the points (4, -2) and (9, -2).
slope:
Find the slope of the line passing through the points (2, 9) and (2, - 7).
slope:

Perimeter of the parallelogram is 20 units.

According to question,

3 + x = 2a - 4

     x = 2a - 4 - 3

    x = 2a - 7

Diagonals in a parallelogram bisects each other.

Therefore, 2a - 7 = 3

                       2a = 3 + 7

                       2a = 10

                          a = 10/2

                          a = 5

a - 1 = 4b - 6

5 - 1 = 4b - 6

    4 = 4b - 6

  4b = 4 + 6

   4b = 10

     b = 10/4

     b = 5/2

Opposite sides of a parallelogram are equal.

Therefore, c - 2 = 2b

                  c - 2 = 2(5/2)

                  c - 2 = 5

                       c = 5 + 2

                       c = 7

Sides of parallelogram,

Side 1 = 12 - c

          = 12 - 7

          = 5

Side 2 = c - 2

           = 7 - 2

           = 5

Perimeter of parallelogram = 2(length of side 1 + length of side 2)

                                             = 2(5 + 5)

                                             = 2 * 10

                                             = 20

Hence, perimeter is 20 units.

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Answer:

y = (2/3)y - 2

Step-by-step explanation:

Linear equations of the form y=mx+b, describe the slope, m, and the y-intercept, b (the value of y when x=0).  

Line K

y = -(3/2)x + 1 tells us that it has a slope of -(3/2) and crosses the y axis (x=0) at y = 1.  

Perpendicular Lines

Perpendicular lines have a useful property in that they have a slope that is the "negative inverse" of the line they are perpendicular to.  If, for example, we were ever asked  what is the slope of a line perpendicular to Line L (yes, it happens), we could, with minimal effort, respond "It is the negative inverse of -(3/2)," which is a slope of (2/3).

Line L

We just accidently answered a key question when we found the negative inverse of the slope for Line K, (2/3).  That will be the slope of Line L that will make it perpendicular to Line K.

Line L will have the form y = (2/3)x + b

This line will be perpendicular to Line K, no matter the value of b.  But we want a perpendicular line that goes through point (6,2), so we need to find a value of b that will force it to go through that point.

The role b has in our equation is simply moving it up or down.  If b were 0, the line will go through the origin (0,0).  If b were 5, it would interect the y axis at 5 (0,5).  We could draw a graph and get a pretty good idea what b would have to be for the line to go throgh (6,2), but most prefer the easier route:  Use the (x,y) value in the above equation and solve for b.  Its easy, and works great:

   y = (2/3)x + b for (6,2)

  2 = (2/3)(6) + b

   b = 2 - (2/3)*(6)

   b = 2 - 4

    b = -2

The equation for Line L is thus:  y = (2/3)y - 2

See the attached graph.  Included are equations [marked Demo Line 1 and 2] with 2 random values of b (1 and 0), in order to:

According to the solving the area of the square is 68.0625.

As is common knowledge, a square is a four-sided, two-dimensional figure. It is also referred to as a quadrilateral. The total quantity of unit squares forming a square is referred to as the square's area. In other words, it is described as the area that the square takes up.

The box formed after cutting the square from each corner will have the dimensions as,

length = 104 - 2x, width = 39 - 2x, height = x.

∴ volume of the box = length × width × height

∴ v = (104 - 2x)(39 - 2x)(x) -----(i)

∴ v = (104 - 2x) (39x - 2[tex]x^{2}[/tex])

∴ v = 104(39x - 2[tex]x^{2}[/tex]) -2x(39x - 2[tex]x^{2}[/tex])

∴ v = 4056x - 208[tex]x^{2}[/tex] - 78[tex]x^{2}[/tex] + 4[tex]x^{3}[/tex]

∴ v = 4[tex]x^{3}[/tex] - 286[tex]x^{2}[/tex]  + 4056x

let f(x) =  4[tex]x^{3}[/tex] - 286[tex]x^{2}[/tex]  + 4056x  -----(ii)

To, find x for which f(x) is maximum,

⇒we should apply second derivative test ,

According to this test, first we should find critical points at which f'(x) = 0.

then if f''(x) < 0 for that critical point then f(x) is maximum at that critical point.

∴ let us consider, f'(x) = 0.

now, f(x) =  4[tex]x^{3}[/tex] - 286[tex]x^{2}[/tex]  + 4056x

⇒ f'(x) = 12[tex]x^{2}[/tex] - 572x + 4056.  -----(iii)

⇒ f'(x) = 4(3[tex]x^{2}[/tex] - 143x + 1014)

⇒ f'(x) = 0.

⇒  f'(x) = 4(3[tex]x^{2}[/tex] - 143x + 1014) = 0

⇒ x = (-b ± [tex]\sqrt{b^{2} - 4ac }[/tex])/2a    ; where a = 3, b = -143, c = 1014.

∴ x = (-(-143) ± [tex]\sqrt{(-143)^{2} -4(3)(1014)}[/tex])/2×3

∴ x = (143 ± [tex]\sqrt{8281}[/tex])/6.

∴ x = [tex]\frac{143 + 91}{6}[/tex]  , x = [tex]\frac{143 - 91}{6}[/tex]

⇒ x = 39, 8.25

the square of length 8.25 inch should be cut from each side to det contained with the maximum volume.

Area of the square is = [tex]x^{2}[/tex] = [tex]8.25^{2}[/tex]

∴ Area = 68.0625

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Answer:

x

Step-by-step explanation:

The numerical coefficient is x.

The expression that shows the distance you would drive from the library to the grocery store along this road is; |-5|+|7|

An absolute value inequality is defined as an expression that has absolute functions as well as inequality signs. For example, the expression |x + 5| > 1 is an absolute value inequality that contains a greater than symbol.

Now, from the inequality line graph attached, we see that the point of the library is at -5 on the line graph.

Similarly, we also see that the point of the grocery store which i will liken to the maths class is at the point 7.

Thus, the distance between both points when we take absolute values into consideration is; |-5|+|7|

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Answer:

The number is -7.5

Step-by-step explanation:

Creating an equation:

5x+7=3x-8

-> 5x = 3x-15

-> 2x=-15

-> x=-7.5

All the angles in a triangle add up to 180 degrees.

40 + x + (5x + 14) = 180

54 + 6x = 180

6x = 126

x = 21 degrees

Answer:

x=21

Step-by-step explanation:

a triangle adds up to 180 degree so to find x we will use the formula

(5x+14)+x+40=180

subtract 40 from each side so we have

(5x+14)+x=140

we have 2 terms with the same factor (x) so combine like terms

6x+14=140

subtract 14 from both sides

6x=126

divide both sides by 6

x=21

check your answer

5(21)+14

105+14=119

119+ 21+40=180

so x is equal to 21

Answer:

10.8 cm

Step-by-step explanation:

To solve this answer, we should use sine law.

[tex]\frac{SinA}{a}[/tex]=[tex]\frac{SinB}{b}[/tex]

[tex]\frac{Sin40}{7}[/tex]=[tex]\frac{Sin81}{x}[/tex]   (cross multiply)

xSin40 = 7Sin81

xSin = [tex]\frac{7Sin81}{40}[/tex]

x= [tex]\frac{7Sin81}{Sin40}[/tex]

x= 10.8 cm

Answer:10.75

Step-by-step explanation:

3/4 as a decimal is 0.75. add that to the 10 gives you 10.75

Answer:

Rs 80,0000 and Rs 100,000

Step-by-step explanation:

sum the parts of the ratio, 4 + 5 = 9 parts

divide the amount by 9 to find the value of one part.

Rs 1,80,000 ÷ 9 = Rs 20,000 , then

4 parts = 4 × Rs 20,000 = Rs 80,000 ← amount son receives

5 parts = 5 × Rs 20,000 = Rs 100,000 ← amount daughter receives

The sum obtained by the son is Rs. 80,000 and the daughter is Rs. 1,00,000.

Mr. Karki divided Rs. 1,80,000 in a ratio of 4:5 between his son and daughter.

Let the common multiple be x

∴ The son obtained Rs. 4x        --------1

And daughter obtained Rs. 5x        --------2

As the total sum is Rs. 1,80,000

∴ 4x + 5x = 180000

9x = 180000

x = 180000/9

∴ x = Rs. 20000

Putting the value of x in 1 and 2 we get,

The sum obtained by son = 4x = 4*20000 = Rs. 80000

And the sum obtained by daughter = 5x = 5*20000 = Rs. 100000

Thus, the son obtained Rs. 80,000 while the daughter obtained Rs. 1,00,000 which is in the ratio of 4:5.

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Answer:

part b

y + 1 = 5/4(x - 2)  

part c

y - 5 = 3(x - 0) or y - 5 = 3(x)

Step-by-step explanation:

Answer:

2 [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

2 + [tex]\frac{3}{4}[/tex]

= 2 [tex]\frac{3}{4}[/tex] ← as a mixed number

Answer:

-18 + -5

Step-by-step explanation:

Because -18 - 5 is an inverse equation, that means that we are doing one equation that looks like something it usually doesn't. When subtracting a negative and a positive in that order, the result will be the sign of the greater value(-18), so the result will be negative. Subtracting a big number that's a negative by a smaller number that's a positive is the same as adding the same numbers together as if they are both negatives. E.g, -4 - 2 = -4 + -2.

Hope this helps!

Answer:5.3

Step-by-step explanation:

using the Pythagorean theorem 8²-6²=28    √28=5.3

5

Step-by-step explanation:

Pythagoras theorem states that

a²+b²=c²

therefore a²=b²-c²

a²=8²-6²

a=√8²-6²

=√64-36

=√28

=5.3 or approximately 5

The angle formed by 7th Avenue and Broadway at The Shake Hut's corner measures 126°.

An expression that depicts the relationship between two or more numbers and variables is called an equation.

If we consider x to be the angle opposite the Pizza Palace, then x = 54°

Also:

The snake hut plus x equals 180

54 plus The Snake Hut = 180

126° is the snake hut.

The angle formed by 7th Avenue and Broadway at The Shake Hut's corner measures 126°.

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The average rate of change of function [tex]g(x)=5(2)^{x}[/tex] from x = 3 to x = 4 is 4 times that from x = 1 to x = 2.

The correct option is (A).

What is the average rate of change of a function?

The average rate at which one quantity changes in relation to another's change is referred to as the average rate of change function.

Using function notation, we can define the Average Rate of Change of a function f from a to b as:

                                     [tex]rate(m) = \frac{f(b)-f(a)}{b-a}[/tex]

The given function is  [tex]g(x) = 5(2)^{x}[/tex],

Now calculating the average rate of change of function from x = 1 to x = 2.

                               [tex]m = \frac{g(b)-g(a)}{b-a}\\ m = \frac{g(2)-g(1)}{2-1}\\\\m=\frac{5(2)^{2}-5(2)^1}{2-1}\\ m=\frac{10}{1} \\m=10[/tex]

Now, calculate the average rate of change of function from x = 3 to x = 4.

                                 [tex]m = \frac{g(b)-g(a)}{b-a}\\ m = \frac{g(4)-g(3)}{4-3}\\\\m=\frac{5(2)^{4}-5(2)^3}{4-3}\\ m=\frac{40}{1} \\m=40[/tex]

The jump from m = 10 to m = 40 is "times 4".

So option (A) is correct.

Hence, The average rate of change of function [tex]g(x)=5(2)^{x}[/tex] from x = 3 to x = 4 is 4 times that from x = 1 to x = 2.

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Applying the definition of angle bisector, the value of x is: x = 3.

An angle bisector can be defined as a ray or line that divides an angle into two parts that are congruent or equal to each other in measure.

Since TR is the angle bisector that bisects angle ATS, it implies that angle ATS is divided into equal parts.

Given the following:

Measure of angle RTS = (17x - 5)°

Measure of angle ATS = (28x + 8)°

Therefore:

Measure of angle ATS = 2(measure of angle RTS) [definition of angle bisector]

Substitute

28x + 8 = 2(17x - 5)°

28x + 8 = 34x - 10

Combine like terms

28x - 34x = -8 - 10

-6x = -18

Divide both sides by -6

-6x/-6 = -18/-6

x = 3

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By probability , 7 is degrees of freedom are there .

Describe probability using an example?

825 Observations and 8 categories .

Degree of freedom = k - 1

     df = 8 - 1

     df = 7

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The quotient of the polynomial is 4x - 9 and the remainder is 20

The resultant of the division is called the quotient while the Remainder is the number that is left after division.

In long division, the terms on top of the division symbol are called the quotient while that at the bottom is called the remainder.

When a division has no remainder it means that the polynomial is divisible by the divisor.

The body of the calculation is found in the attached file below.

In conclusion, the Quotient and remainder are 4x - 9 and 20 respectively.

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The sum of the numbers they wrote on the piece of paper is 2,305,843,009,213,693,954

What is Pythagoras's theorem?

The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle or in standard algebraic notation, a² + b² = c², is equal to the squares on the legs.

What is the sum of numbers?

The outcome or conclusion we arrive at when we add two or more integers is known as the sum. Addends are the numbers that are added.

Here, we calculate the sum of the given numbers

= (1³)^²⁰  +  (1³)²⁰  +  (2³)²⁰  +  (-2³)²⁰

= 2,305,843,009,213,693,954

Hence, the sum of the numbers they wrote on the piece of paper is 2,305,843,009,213,693,954.

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If a coin is weighted so that the probability of heads is five times the probabily of tails, that means :

+) P(head) + P(tail) = 1
+) P(head) = 5P(tail)

Therefore, P(head) = 5/6 ; P(tail) = 1/6

For both head and tail to be flipped, the events must happen together.

Therefore, we have the probabilty that both head and tail is flipped = 5/6 x 1/6 = 5/36.

If shipments increased by 7% (which is the same as 0.07) per year, then the shipment in a year can be found by multiplying the shipments in the previous year by 1.07.

Therefore, if [tex]x[/tex] represents the number of years since 2000 and [tex]f(x)[/tex] represents the number of shipments, then [tex]f(x)=3173000(1.07)^x[/tex].

Answer:

It would be the last graph (c). It would look like the image below.

Explanation:

Since 3 is negative the answer would have a graph with a line going like this \.

In 40 months, so that the manufacturer will not have more than 7% of the rice cookers returned.

A p-value calculates the likelihood of getting the outcomes that were observed, presuming that the null hypothesis is correct. The statistical significance of the difference that was found increases with decreasing p-value. Statistical significance is commonly defined as a p-value of 0.05 or less. The sample data, test type, and sampling distribution of the test statistic under the null hypothesis are used to determine the p-value (lower-tailed test, upper-tailed test, or two-sided test).

Given,

Cook-it rice cooker has a mean time before failure of 38 months with a standard deviation of 4 months, and the failure times are normally distributed.

The 7th percentile, or X when Z has a p-value of 0.08, or X when Z = 0.4720, should serve as the warranty period.

Z = X - Mean/ standard deviation

0.472 = x - 38/4

0.472 (4) - x - 38

1.888 = x - 38

x = 39.88

x = 40

In 40 months, so that the manufacturer will not have more than 7% of the rice cookers returned.

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Answer:

x/2 = any number

Step-by-step explanation:

The value of r is -10 for line with slope 2/5 .

What is slope?

A line's slope, often known as its gradient, is a numerical representation of the line's steepness and direction.

Main Body:

We know that the slope of line in two point form is

(y₂-y₁)/(x₂-x₁) = m where m = slope

given points are (-3,r) and (7,-6) m= 2/5

(-6-r)/(7+3)= 2/5

(-6-r)/10 =2/5

therefore value of r= -10

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