How many whole months will it take for a motorbike valued at £2550 to depreciate to less than £1200 if depreciation is at a rate of 5% per month?

Answer:

y = 2 ± √x is the inverse but it's not a function. (See note below for additional info)

Step-by-step explanation:

Given the quadratic function:

[tex] \displaystyle{y = {x}^{2} + 4x + 4}[/tex]

We can rewrite the function above using perfect square form:

[tex] \displaystyle{y = {(x + 2)}^{2} }[/tex]

Finding an inverse, we swap the terms of x and y:

[tex] \displaystyle{x = {(y + 2)}^{2} }[/tex]

Square root both sides, solving for y:

[tex] \displaystyle{ \sqrt{x }= \sqrt{ {(y + 2)}^{2}} } \\ \\ \displaystyle{ \sqrt{x }= \left| y+ 2\right| } \\ \\ \displaystyle{ \pm \sqrt{x }= y + 2}[/tex]

Subtract both sides by 2:

[tex] \displaystyle{ \pm \sqrt{x } - 2= y+ 2 - 2} \\ \\ \displaystyle{ \pm \sqrt{x } - 2= y} \\ \\ \displaystyle{y = 2 \pm \sqrt{x} }[/tex]

Therefore the inverse of y = x² + 4x + 4 is y = 2 ± √x.

Note: While it's possible to find the inverse of quadratic function, but the inverse version itself is not really a function. So if you want to go by definition or theorem, you can say there's no inverse function. Otherwise, the answer above is the solution.

The amount of rain required would be 2.5 inches.

What is the addition?

Addition is a mathematical operation that represents the process of combining two or more numbers together. The result of this operation is called the sum. The addition operation is often represented using the symbol "+", and it can be used to add any two or more numbers together.

To beat the record by one-tenth of an inch, an additional 0.1 inches of rain must fall.

Currently, the average amount of rain per day is 12 inches / 5 days = 2.4 inches per day.

So, the amount of rain that must fall on Friday to beat the record by one-tenth of an inch is 2.4 inches + 0.1 inches = 2.5 inches

Hence, the amount of rain required would be 2.5 inches.

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The distance that he jumped in the sixth jump nearest to two decimal places will be 0.13.

Let a₁ be the first term and r be the common ratio.

Then the nth term of the geometric sequence is given as,

aₙ = a₁ · (r)ⁿ⁻¹

Every time an insect jump forward, the distance covered is half of the previous jump. If the insect initially jumped 8.4 cm.

The equation is given as,

aₙ = 8.4 · (1/2)ⁿ⁻¹

The distance that he jumped in the sixth jump will be given as,

a₆ = 8.4 · (1/2)⁶⁻¹

a₆ = 8.4 / 64

a₆ = 0.13125

a₆ ≈ 0.13

The distance that he jumped in the sixth jump nearest to two decimal places will be 0.13.

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Answer:

The Sweet and Sour company

Step-by-step explanation:

Convert both types of lemonades into gallons and divide by the price.

For the loving lemon company you divide 24 by 4 and get a unit price of $6 per gallon

For the sweet and sour company change the 8 quarts into 2 gallons and divide 16 by 2, which gets you a unit price of $8 per gallon

Answer:

83°

Step-by-step explanation:

-4m+51-4m+42= 158°

-8m+94= 158

-8m= 64

m= -8

JMK= -4m+51

      = -4(-8)+51

      = 32=51

      = 83°

Considering that the diameter variance of 0.001". If the interior diameter of the pipe is 0.49" and the pipe thickness is 0.005". the maximum allowable pipe diameter is 0.501''

The maximum allowable pipe diameter is calculated by

finding the total thickness of pipe

= interior diameter + 2 * pipe thickness

= 0.49 + 2 * 0.005

= 0.49 + 0.01

= 0.50

The diameter variance gives the range of the allowable diameter to ± 0.001 for maximum allowable pipe diameter we use + 0.001

hence

= 0.50 + 0.001

= 0.501

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When Malia joined a gym 14 weeks after Jane did, the value of b was 5.

Relationships between two variables where their ratios are equal are known as proportional relationships. The fact that one variable is always a constant value multiplied by the other in a proportionate connection is another way to conceive of them.

A car's fuel capacity and efficiency, as well as how far it can go on a single charge of its electric battery, are important considerations. A nonproportional connection can be used to describe this.

a + b = 14

9 + b = 14

b = 14-9 = 5

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Answer:

Complementary

x = 15

Step-by-step explanation:

Answer:

0.02083333333

On solving the provided question, we got to know that - arbitrary number So the money she earns is equal to 10 times w plus 15, which can be expressed as: 10w + 15

A number is considered arbitrary if its only unique characteristic is that it has a high value. You can think of them informally as the numbers that your opponent picked. Any number appears to be worthless intuitively.

Since the question allows us to use any number, we decide to make the money she makes from washing the car equal $10. We'll also assume that she gets paid $15 to wax the car.

So the money she earns is equal to 10 times w plus 15, which can be expressed as:

10w + 15

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Step-by-step explanation:

I said it I knew it I did it I submit for you so I'm the one that is if if you know me.

Answer:

parallel line: y = 8x - 26

perpendicular line: y = -1/8 x - 13/8

Step-by-step explanation:

1.

Lines are parallel, so slopes are equal, and y-intercepts are different.

Given line:

y = 8x - 2

New line:

y = 8x + b

Use point (3, -2) and solve for b.

-2 = 8(3) + b

-2 = 24 + b

b = -26

Equation: y = 8x - 26

2.

Lines are perpendicular, so slopes are negative reciprocals.

Given line:

y = 8x - 2

New line:

m = -1/8

y = -1/8 x + b

Use point (3, -2) and solve for b.

-2 = -1/8 × 3 + b

-2 = -3/8 + b

b = -16/8 + 3/8

b = -13/8

Equation: y = -1/8 x - 13/8

For the given value of domain and range , By observing the figure, The correct answer are options B,C and E.

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

A function's domain and range are the set of all possible inputs and outputs, respectively. A function's domain and range are crucial components. The range includes all of the function's output values, whereas the domain includes all potential input values from the set of real numbers.

domain : (x | x  3/2)

range : (-∞ , 2)

For these values, Option B , C and E holds that they exists when x  3/2 and it's output that is y exists between  (-∞ , 2).

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Answer:

39

Step-by-step explanation:

6a - b = 6 x 8 - 9 = 48 - 9 = 39

Answer: 39

Step-by-step explanation:

Given that a=8 and b=9

The expression is 6a-b

That is; we have to find 6 times a and then subtract b from it.

6a = 6*8=48

b=9

6a-b=48-9=39

Therefore the answer to the question is 39.

Answer: jump off a cliff and shatter your bones

Step-by-step explanation:

The volume of a rectangular box can be found by multiplying the length, width, and height of the box together. So if the volume of the box is x³+x²-4x-4 cubic inches, the length is x+1 inches, and the width is x-2 inches, we can set up the equation h = (x³+x²-4x-4) ÷ (x²-x-2).

The formula for the volume of a rectangular box is V = l × w × h, where l is the length, w is the width, and h is the height of the box. This formula can also be written as V = l×w×h.

In the question you provided, the volume of the rectangular box is given as x³+x²-4x-4 cubic inches, and the length and width are given as x+1 inches and x-2 inches, respectively. With this information, we can set up an equation using the formula for the volume of a rectangular box:

(x+1)(x-2)(h) = x³+x²-4x-4

where h is the height of the box in inches. To solve for h, we can divide both sides of the equation by (x+1)(x-2) to get:

h = (x³+x²-4x-4) ÷ (x+1)(x-2)

And Now we can simplify the expression using standard algebraic operations.

h = (x³+x²-4x-4) ÷ (x²-x-2)

You can now substitute any value of x to find the height of the box.

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Answer:

11/10

Step-by-step explanation:

33/10 - 22/10

Answer:

The answer is 3/20 or 0.15

I wish you luck in your assignments.

Therefore , the solution is circle Part 1: The central idea ( -5 , 7 ). 2nd part: Radius is 6 in part 2,3rd part: FALSE and Parts 4. There are 10 miles between A and B.

A circular shape called a circle is created by following a moving point in a plane so that its distance from a particular point remains constant. The Greek word kirkos, which means hoop or ring, distance is the source of the English word circle.

Here,

The common circle equation is,

( x - h )² + ( y - k ) ( y - k )

6² = r²

where the circle's radius is r and the center's coordinates are (h, k).

Part 1.

Using the common circle equation, we obtain,

Circle's circumference's coordinate is ( -5 , 7 )

Consequently, the second choice is the right one.

Part 2.

Using the common circle equation, we obtain,

circle radius is six.

Consequently, the first choice is the right one.

Part 3.

Using the common circle equation, we obtain,

Circle's circumference's coordinate is ( 2 , 3 )

Therefore False.

Part 1.

In comparison to the common circle equation, we obtain,

Circle's center's coordinates are: ( -5 , 7 )

As a result, the second choice is the right one.

Part 2.

In comparison to the common circle equation, we obtain,

circle's diameter is six.

As a result, the first choice is right.

Part 3.

In comparison to the common circle equation, we obtain,

Circle's center's coordinates are: ( 2 , 3 )

So, False.

Part 1.

Giving the distance between two points,

Distance between A(-5, 3) and B (5, 3), expressed as:

=> [tex]\sqrt{(x2-x1)^{2} + (y2-y1)^{2} )}[/tex]

= >  [tex]\sqrt{(-5-5)^{2} + (3-3)^{2} )}[/tex]

=> 10

Thus, 3rd Option is correct.

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To prove the converse of the Pythagorean theorem, we can define a right triangle Δ DEF with sides a, b, and x.

Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We have,

ΔABC and ΔDEF

To prove the converse of the Pythagorean theorem, we can define a right triangle DEF with sides a, b, and x.

Thus,

ΔDEF is filled in the box.

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Answer:

2.25  

4.5

9

18

36

72

144

288

Step-by-step explanation: you take the number and multiply it by itself. but went it comes to the negative numbers you have to divide the number by 2 then take the answer you get from that and add it by itself so 4.5+4.5=9. its pretty simply when you under stand how to do it.

Answer:

Step-by-step explanation:

3:12 7:28

The means are the second and third terms in the proportion.

The extremes are the two outside terms.

12 and 7 are the means.

(3 and 28 are the extremes.)

So thre answer is D.  12 and 7.

Answer:

3 × 7 = 21

21 - 6 = 15

15 is the answer

Answer:

17/5÷23/8= 1  21/115

The answer is 1  21/115

First, let's find Maura's running speed by using the information that Carlos runs at a rate that is 25% slower than Maura's rate. If Carlos runs at a rate of 6 miles per hour, then Maura runs at a rate of 6 * 1.25 = 7.5 miles per hour.

Next, let's calculate how long it takes for Carlos to finish the marathon. We know that Carlos runs at a rate of 6 miles per hour and the marathon is 26 miles long. So we can use the formula:

time = distance/rate

time = 26/6

time = 4.33 hours

Now let's find how long it takes for Maura to finish the marathon. We know that Maura runs at a rate of 7.5 miles per hour and the marathon is 26 miles long. So we can use the formula again:

time = 26/7.5

time = 3.47 hours

Finally, let's convert Jacob's time of 2 hours and 36 minutes to hours. We can use the formula:

time = 2 + (36/60)

time = 2 + 0.6

time = 2.6 hours

In conclusion, Carlos takes 4.33 hours, Maura takes 3.47 hours and Jacob takes 2.6 hours to finish the marathon.

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Answer:

6chapters per hour

Step-by-step explanation:

Take 48 chapters divided by the no hrs which are 8

Answer: 571.11111...(Fraction: 9/28)

Step-by-step explanation:

5,140÷9 = 571.11111...

The number of tennis ball  fit in the machine are 305 balls.

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Finding an object's volume can help us calculate the quantity needed to fill it, such as the volume of water needed to fill a bottle, aquarium, or water tank.

given dimensions of  machine 15 x 15 x 14

volume of machine is 15 x 15 x 14 = 3150 cubic inches

and shape of ball is spherical,

with dia = 2.7 inches

radius of ball = 2.7/2 = 1.35 inches

volume of sphere is 4/3πr³

V = 4/3πr³

V = 4/3(3.14)(1.35)³

V = 4/3(3.14)(2.46)

V = 10.30 cubic inches

the area covered by 1 ball is 10.30 cubic inches

the number of ball in machine is 3150/10.30

the number of ball in machine  = 305.82 = 305 approx

Hence  305 balls can be fit in machine.

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First, we assume that this conclusion is false. In other words, we assume that the contrary statement "none of the two angles has measure [tex]90^{\circ}[/tex] or greater" is true.

The assumption is equivalent to the following two statements:

(1) [tex]m\angle A\text{ } \boxed{ < 90^{\circ}}[/tex]

(2) [tex]m\angle B\text{ } \boxed{ < 90^{\circ}}[/tex]

Using (1) and (2) and the addition properties of inequalities, we conclude that [tex]m\angle A+m\angle B \text{ } \boxed{ < } \text{ } 180^{\circ}[/tex].

On the other hand, two adjacent angles form a linear pair. Thus, the last statement contradicts the Linear Pair Property, which states that for a linear pair of angles [tex]\angle A[/tex] and [tex]\angle B[/tex], [tex]m\angle A+m\angle B \text{ } \boxed{=} \text{ } 180^{\circ}[/tex].

Therefore, the assumption made is false, and the statement "at least one of the angles [tex]\angle A[/tex] and [tex]\angle B[/tex] has measure [tex]90^{\circ}[/tex] or greater" is true.