show algebraically the sum of two consecutive numbers is always odd

The table of solutions should be completed based on the given equation (y = 2x²) as follows:

x                    y_

-2                  8

-1                   2

0                   0

1                    2

2                   8

Also, a graph of the solution to the given equation is shown in the image attached below.

In Mathematics, a graph can be defined as a type of chart that is commonly used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate.

Next, we would complete the table based on the given equation as follows:

When x = -2, the value of point y is given by:

y = 2x²

y = 2(-2)²

y = 2 × 4

y = 8

When x = -1, the value of point y is given by:

y = 2x²

y = 2(-1)²

y = 2 × 1

y = 2

When x = 0, the value of point y is given by:

y = 2x²

y = 2(0)²

y = 2 × 0

y = 0

When x = 1, the value of point y is given by:

y = 2x²

y = 2(1)²

y = 2 × 1

y = 2

When x = 2, the value of point y is given by:

y = 2x²

y = 2(2)²

y = 2 × 4

y = 8

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Answer:

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

Answer:

Difference = 6 inches

Step-by-step explanation:

Given information,

→ Meg measured the length of some pieces of the wire.

Now we have to,

→ find the difference between the longest and shortest piece of wire.

Then the difference will be,

→ Longest wire - Shortest wire

→ 9 - 3

→ 6 inches

Hence, the difference is 6 inches.

The length of the shortest ladder that will reach from the ground over the fence to the wall of the building is 11.31 feet

Let L stand for the ladder's overall length.

Right angled triangle ΔAGB contains the following:

L² = h² +(x+4)²

( Since by using Pythagorean Theorem)

Triangles AGB and CDB also have similarities.

As a result, the corresponding sides' ratio is equal.

Hence, we have:

h/4 = (x+4)/x

h = 4(x+4)/x

As a result, when we enter the value of h in equation (1), we obtain:

L² = h² +(x+4)²

L² = (4(x+4)/x)² +(x+4)²

L² = (16(x+4)²/x²)+(x+4)²

L² = (x+4)²(16/x² + 1)

We now have to reduce L.

Therefore, we employ the differentiation method.

We distinguish in relation to x as follows:

L² = (x+4)²(16/x² + 1)

2L dL/dx =2(x+4)(16/x² + 1) + (x+4)² (-32/x³)

2L dL/dx =2(x+4){ (16/x² + 1) + (x+4) (-16/x³)

2L dL/dx =2(x+4){ (16/x² + 1 -16/x²-64/x³)

2L dL/dx =2(x+4){ (1-64/x³)

when the derivative is zero we have:

2(x+4){ (1-64/x³) = 0

x= -4 and x³ = 64 and x =∛64 = 4

But x can't be negative.

Hence, we have:

x = 4

After solving equation (2) with this value of x, we get the following result:

L² = (x+4)²(16/x² + 1)

L² = 128

L = 11.313 feet

Hence,

L = 11.313 feet

which on rounding to two decimal places is: 11.31 feet

As a result, the shortest ladder's length, measured from the ground to the building's wall over the fence, is 11.31 feet.

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Answer:

Step-by-step explanation:

Find x:-

[tex]\sf 11x-9+72+6x-2=180[/tex]

[tex]\sf 17x+61=180[/tex]

[tex]\sf 17x=119[/tex]

[tex]\sf x=7[/tex]

Find y:-

[tex]\sf 30+11(7)-9+5y-8=180[/tex]

[tex]\sf 5y+90=180[/tex]

[tex]\sf 5y=90[/tex]

[tex]\sf y=18[/tex]

So, therefore, x = 7° & y = 18°!!

____________________

Hope this helps!

Have a great day! :)

Answer:

1 ; -5 ; 2x

Step-by-step explanation:

1. We must have 0x equal to a number that is not 0

example = 1

5x - 5x = 5 + 1

0 = 6 (false)

2 we must have 0 = 0

-5

5x - 5x = 5 - 5

0 = 0

3 the x must stay

example = 2x

5x - 5 = 5x + 2x

2x = -5

2/2 x = -5/2

x = -5/2

a) a/5 + 3 = 8

Step 1 : Minus both sides by 3

a/5 + 3 - 3 = 8 - 3 -> a/5 = 5

Step 2 : Multiply both sides by 5

a/5 x 5 = 5 x 5 -> a = 25.

b) (3b)/7 - 1 = 5

Step 1 : Add both sides by 1

(3b)/y - 1 +1 = 5 + 1 -> (3b)/7 = 6

Step 2 : Multiply both sides by 7

(3b)/7 x 7 = 6 x 7 -> 3b = 42

Step 3 : Divide both sides by 3

3b : 3 = 42 : 3 -> b = 14.

After the use of fractional exponents give us the value 8√(x²y⁴) is 2³(x²y⁴)¹/₂.

Exponent:

Exponent is refers the way of writing the words, "raised to the power". And it is used to show that a number has been raised to a certain power.

Given,

Here we have the expression 8√(x²y⁴).

Now, we need to simplify the fractional exponents.

When we rewritten the expression like the following,

=> 8√(x²y⁴)

While we looking at these expression we know that, the number 8 can be written as the multiple of 2,

So, it can be written as,

=> 8√(x²y⁴) = 2³√(x²y⁴).

So, in the simplified form it can be written as,

=>8√(x²y⁴) =  2³(x²y⁴)¹/₂.

Therefore, the simplified form is 2³(x²y⁴)¹/₂.

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The measurements of the rectangle are 10 cm and 5cm.

What is rectangle?

A rectangle could be a quadrilateral with four right angles in geometer geometry. It may be outlined as an angulate quadrilateral as a result of all of its angles square measure equal; or a quadrangle with a right angle.

Main Body:

Let the width be x.

According to question :

width is 5 more than 1 times the length(l), so

length (l) = width -5

Area if rectangle = 50 cm²

Formula for area of rectangle = length * width

⇒50 = x*(x-5)

⇒50 = x² - 5x

⇒x² - 5x - 50 =0

splitting the middle term

⇒x²- 10x +5x -50 = 0

⇒x(x-10) +5(x-10)

⇒(x-10)(x+5)

Hence the value for x = 10 or -5 .

but length can never be -ve so x= 10.

Width = 10 cm

length = width -5

length = 10 -5

l = 5cm

Hence Measurements of rectangle are 10cm and 5cm.

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Answer:

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

Since both points have same y-coordinate, the distance between the points is the difference of x-coordinates:

Answer:

  5 5/6 yards

Step-by-step explanation:

You want the perimeter of a rug that is 2 yards by 11/12 yards.

The formula for the perimeter of a rectangle is ...

  P = 2(L+W)

Using the given values, we find the perimeter to be ...

  P = 2(2 yd + 11/12 yd) = 4 22/12 yd = 5 5/6 yd

The perimeter of the rug is 5 5/6 yards.

Answer:

5 11/16 as a decimal = 5.6875

7 24/25 as a decimal is 7.96

Step-by-step explanation:

Answer:

5 11/16 = 5.6875

7 24/25 = 7.97

Step-by-step explanation:

you keep the whole numbers then you turn the fractions into decimals so to do that you divide 100 by the denominator and whatever the answer is you multiply it by the numerator to get your answer, 100 divided by 16 is 6.25 and 6.25 multiplied by 11 is 68.75 but since the 5 is already the whole number you basically just forget the decimal in 68.75 ( I hope that makes sense)

And for 7 24/25 you do 100 divided by 25 and that’s 4 so now you multiply 24 by 4 and that’s 96 so that goes after the decimal so it’s 7.96 (I hope that helped and all made sense.)

An equation is a mathematical statement showing the equality of two

opposite variables

How to determine the equation of the circle using coordinates?

The equation of a circle is determined by the function r²=(x-x1)² +(y-y1)²

where :

then, the last thing is to write the equation of the circle and input the values of the coordinates to arrive at your answer,

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Answer:

d = 3h - 6

Step-by-step explanation:

h = [tex]\frac{d}{3}[/tex] + 2 ( multiply through by 3 to clear the fraction )

3h = d + 6 ( subtract 6 from both sides )

3h - 6 = d

Answer:

24%

Step-by-step explanation:

6/25 is also the same as 24/100 because

(6/25)*(4/4)=24/100

Since the denominator is 100, the numerator is the percentage.

6/25=24%

Answer:

24%

Step-by-step explanation:

One way to figure this out is to multiply the denominator by 4 so that it becomes 100. This makes it easy to see what the percentage will be.

6/25 x 4/4 = 24/100

6/25 = 24%

Answer:

So, the probability of selecting a number from 1 to 100 that is divisible by 5 or 7 is 0.32.

Hope this helped!

Answer:

<ABD = 67.17

Step-by-step explanation:

Comment

This requires 2 steps.

Finding <A

<A is found by taking the inverse tangent of the ratio 8/19.

<A = tan-1*(8/19)

<A = 22.83 degrees. We'll round it later.

Finding <ABD

You have to use 2 facts here.

All triangle angles add up to 180 degrees.

You find the third angle by subtracting the other 2.

<A = 22.83                                       Found above

<ADB = 90 degrees                        Given

<ABD = ?

Equation

< A + <ADB + <ABD = 180

Solution

22,83 + 90 + <ABD = 180                 Combine the left

112.83 + <ABD = 180                         Subtract 112.83 from both sides.

112.83-112.83 +<ABD = 180 - 112.83  Combine

<ABD = 67.17

The answer to the nearest degree is 67.

The quiz consists of 40 problems and it solved by a linear equation.

What is the linear equation?

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.

Assume that the quiz consists of n problems.

Denise did 7/8 of the problems correctly.

If the total number of problems of the quiz is n, the number of answers that are correct is (7/8)× n.

The number of incorrect problems are 5.

Total number of problems those are done by Denise is { (7/8)× n}+5.

Assume that Denise attempts all problems.

Now making a linear equation:

{ (7/8)× n}+5 = n

(7n)/8+5 = n

(7n+40)/8 = n

(7n+40) = 8n

Subtract 7n from both sides:

7n+40 -7n = 8n - 7n

40 = n

The number of problems in the quiz is 40.

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The length of the line segment with points (-5, 5) (3, -1) is 10 units

The length of line in an ordered pair is calculated using the formula

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

where

d = distance between the points

x₂ and x₁ = points in x coordinates

y₂ and y₁ = points in y coordinates

distance between points  (-5, 5) and (3, -1) is calculated as follows

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

d =√{(-5 - 3)² + (5 - -1)²}

d =√{64 + 36}

d = √100

d = 10 units

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Answer:

a) He didn't add 2.

b) 38/3

The information illustrated regarding the numbers shows that it's a C. Direct variation.

A direct variation means the variation that has a constant of proportionality.

In this case, when x is 256, y is 32. The constant is 32/256 = 1/8

When y = 6, x = 48. The constant is also 6/48 = 1/8.

Therefore, it's a direct variation.

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The distance between the two cars varies at a speed of 65 m/h after two hours.

Let y represent the car's southward travel distance.

Let x be the distance traveled by the westbound automobile.

Allow a to be the distance between the two vehicles.

A right-angled triangle can be used to symbolize these three distances. So, we can state:

a^2 = x^2 + y ^2

Given that the distances vary with respect to time, let's make a distinction.:__________(1)

2a da/dt = 2x dx/dt +2y dy/dt

Rate of distance change between two cars, da/dt

The car is traveling west (dx/dt) at 25 m/h, while the car traveling south (dy/dt) is traveling at 60 m/h.

Therefore:

dy/dt = 60 m/h and dx/dt  = 25 m/h

The separation between the two cars will be after two hours:

y = 3* 60 = 180 miles

x = 3 * 25 = 75 miles

Therefore:

a^2 = x^2 + y ^2

a^2 = 75 ^2+ 180 ^2

a= [tex]\sqrt{5625 + 32400}[/tex]

a= 195

From (1):

195(da/dt) = 75(25) + 180(60)

195(da/dt) = 1875 + 10800 = 12675

da/dt = 12675 / 195 = 65 m/h

As a result, after two hours, the two automobiles' separation is varying at a speed of 65 m/h.

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The missing base for the expression x² = 100 is given by:

± x = 10.

The expression in this problem is given as follows:

x² = 100.

The missing base is represented by the variable x, hence we have to solve the above expression x² = 100 for the variable x.

To solve for x, we need to isolate the variable x, applying the inverse operation to the second power, which is the square root, hence the variable x is isolated as follows:

x = plus/minus square root of 100.

The plus/minus sign is necessary because the x-squared function is even, then the missing base is obtained as follows:

x = ± 10.

Plus/minus 10 because both of these statements are true:

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Function [tex]-3x^2+18x+3[/tex] has maximum value at x = 3 and its maximum value is 30.

How do you find the maximum and minimum value of the function?

Calculus can be used to find the critical point, or the x-value of the vertex, by taking the derivative of the function, or f'(x). To determine the critical point, we shall set the function's first derivative to zero and solve for x. This point's maximum or minimum value can be determined by taking the second derivative, or f"(x). The second derivative will have a minimal value if it is positive. The second derivative will be the highest value if it is negative.

Given function:

[tex]-3x^2+18x+3[/tex]

To find the maximum and minimum value of the function use second derivative test.

On differentiating the above function we get,

-6x + 18

Now, find critical point

-6x + 18 = 0

-6x = - 18

x = - 18/-6 = 3

x = 3

Here, x = 3 is the critical point. Now again differentiate the above function we get,

-6

As , [tex]f^{''}(x)[/tex] < 0 , therefore x = 3 will given a maximum value of function and maximum value is

f(3) = [tex]-3(3)^2+18x+3 = -3(9) + 18(3) + 3 = -27 + 54 + 3 = 27 + 3 = 30[/tex]

Hence , function [tex]-3x^2+18x+3[/tex] has maximum value at x = 3 and its maximum value is 30.

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There is a 0.97541 or 97.541% probability that at least one student will choose a president who passed away in office.

Take into account the details offered.

43 US presidents are listed by Mr. Bray, 8 of them passed away while in office.

Consequently, p= 8/43.

If 8 of the 43 presidents died while in office, then 43-8=35 presidents survived.

q= 35/43

Let X represent how many presidents have passed away while in office.

The probaility that at least one student will choose a president who passed away in office is:

P(X[tex]\geq[/tex]1 ) = 1 -P(X=0)

P(X[tex]\geq[/tex]1 ) = 1 -¹⁸c₀(8/43)⁰(35/43)¹⁸

By using  Combinations Formula,

By solving we get,

P(X[tex]\geq[/tex]1 ) = 0.97541

As a result, there is a 0.97541 or 97.541% chance that at least one student will choose a president who passed away in office.

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Answer:

$72 / hr

Step-by-step explanation:

$36 / (1/2 hr ) =  $72 per hour

Answer:

The rocket reaches its maximum height at 2.25 seconds.

It’s maximum height is 88 feet.

This can be found by finding the derivative of the function and setting it to zero.

-16x² +72x + 7

Taking first derivative and setting to zero:

-32x + 72 = 0

x = -72/-32=2.25

Find the height when x is 2 seconds by substituting this value into the original function:

-16 * (2.25)² + 72 * 2.25 + 7 = 88

Therefore the maximum turning point of the parabola will be (2.25, 88)

Answer:

y=2x+8

Step-by-step explanation:

The slope must be the same so the equation so far is y=2x+b

To find b, you have to multiply the given x value (-1 is the given x value) and then see how much you have to add to reach the given y value (aka 6)

-1*2=-2

6--2=8

b=8

That means that the equation is y=2x+8

Answer: 11 months

Step-by-step explanation:

You do this by 73 times 11 equals 803

Then 49 times 11 equals 539 then add on the registration fee and it equals to 779 which is less than 803

The value of test statistic is  -1.14

Define Standard error.

The standard error (SE)of a statistic (usually an estimate of a parameter) is the standard deviation of its sampling distribution or an estimate of that standard deviation. If the statistic is the sample mean, it is called the standard error of the mean (SEM).

Null Hypothesis

P = 0.54

Alternate Hypothesis

P < 0.54

For 0.05 level , the value of Z = 1.645

Decision rule ,

reject null Hypothesis if test statistic Z < -1.645

sample size (n) = 200

sample success (x) = 100

Standard error SE = √(p * (1 - p) / n

                         = √0.54 * (1 - 0.54) / 200

Standard error SE= 0.0352

Sample proportion (р)  = x/n

                               = 100 / 200 ⇒ 0.5

test statistic  Z = (р - P) / SE

                         = (0.5 - 0.54) / 0.0352

test statistic  Z = -1.136 or -1.14

Therefore, the value of test statistic is  -1.14

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The true statement about the change of scale is 1 cm represented 5 m in the first scale, but now 1 cm represents 4 m in the second scale.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

Given that, Tran planned a rectangular pool and made a scale drawing using cm as the unit of measurement. He originally planned for the length of the pool to be 40 m but decided to change it to 32 m. If the length of the pool in his scale drawing is 8 cm,

The scale factor of drawing to original pool was 1/5 before changing the length but when length changed to 32 m scale factor now is 1/4

Hence, The true statement about the change of scale is 1 cm represented 5 m in the first scale, but now 1 cm represents 4 m in the second scale.

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