The length of a rectangle is four meters less than twice it's width. If the area of the rectangle is 96 square meters what is the width?

Answer:

DQ = [tex]\frac{5}{(2-\sqrt{x})(2-\sqrt{x+h})(\sqrt{x}-\sqrt{x+h})}[/tex]

Step-by-step explanation:

Given function is f(x) = [tex]\frac{5}{2-\sqrt{x}}[/tex]

f(x + h) = [tex]\frac{5}{2-\sqrt{x+h} }[/tex]

Therefore, indicated difference quotient will be,

DQ = [tex]\frac{f(x+h)-f(x)}{h}[/tex]

Now we substitute the values in the difference quotient,

DQ = [tex]\frac{\frac{5}{2-\sqrt{x+h} }-\frac{5}{2-\sqrt{x}}}{h}[/tex]

      = [tex]\frac{5(2-\sqrt{x})-5(2-\sqrt{x+h})}{h(2-\sqrt{x})(2-\sqrt{x+h})}[/tex]

      = [tex]\frac{10-5\sqrt{x}-10+5\sqrt{x+h}}{h(2-\sqrt{x})(2-\sqrt{x+h})}[/tex]

      = [tex]\frac{-5\sqrt{x}+5\sqrt{x+h}}{h(2-\sqrt{x})(2-\sqrt{x+h})}[/tex]

      = [tex]\frac{5(-\sqrt{x}+\sqrt{x+h})}{h(2-\sqrt{x})(2-\sqrt{x+h})}[/tex]

      = [tex]\frac{5(-\sqrt{x}+\sqrt{x+h})(\sqrt{x}+\sqrt{x+h})}{h(2-\sqrt{x})(2-\sqrt{x+h})(\sqrt{x}+\sqrt{x+h})}[/tex]

      = [tex]\frac{5[(x+h)-x]}{h(2-\sqrt{x})(2-\sqrt{x+h})(\sqrt{x}+\sqrt{x+h})}[/tex]

      = [tex]\frac{5h}{h(2-\sqrt{x})(2-\sqrt{x+h})(\sqrt{x}+\sqrt{x+h})}[/tex]

      = [tex]\frac{5}{(2-\sqrt{x})(2-\sqrt{x+h})(\sqrt{x}+\sqrt{x+h})}[/tex]

Answer:

?

Step-by-step explanation:

The temperature in Fahrenheit, x, is converted into the temperature in Celsius with the formula . What transformations are used in transforming the parent graph y = x, to obtain the graph of blank. The answers would be:

To obtain the graph of c(x) = (5/9){ x - 32 } we need as horizontal transformation. The correct option is A.

A function is defined as the expression that set up the relationship between the dependent variable and independent variable. 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.

Given function of temperature is c(x) = (5/9){ x - 32}. The two graphs are plotted on the x-y plane. It is observed that y = x is transformed to the horizontal direction.

The graph of the two functions y = x and c(x) = (5/9){ x - 32 } is attached with the answer below.

Therefore, to obtain the graph of c(x) = (5/9){ x - 32 } we need as horizontal transformation. The correct option is A.

To know more about a function follow

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Answer:

180000

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

sawarasenaaa kimi wa-

The GCF of 45 and 75 is 15.

So, divide both numbers by 15.

45/15 = 3

7515 = 5

Therefore, the simplified version of the ratio is 3 to 5

Best of Luck!

Answer:

64 Divided by 8

Step-by-step explanation:

Answer:

7/16

Step-by-step explanation:

3/8 = 6/16

7/16 is greater than 6/16

Hope This Helps :)

Answer:

7/16

Step-by-step explanation:

Simplified 7/16 is 3.5/8, which is more than 3/8. The rest of the answers are less than 3/8.

Answer:

4-5<-2 is false it should be 4-5>-2

Step-by-step explanation:

Answer:b

Step-by-step explanation:

Answer:

9.9924 liters

Step-by-step explanation:

there are 3.785 liters in one gallon

multiply 3.785 liters times 2.64

that comes out to 9.9924 liters

Answer:

x = -7

Step-by-step explanation:

This isn't a quadratic.

Step 1: Write out equation

3x - 5 = -26

Step 2: Add 5 to both sides

3x = -21

Step 3: Divide both sides by 3

x = -7

Step-by-step explanation:

[tex]\sf \bf We \: have,[/tex]

[tex]\sf 3x - 5 = -26[/tex]

[tex]\sf : \implies \bf 3x - 5 \green{+5}= -26\green{+5}[/tex]

[tex]\sf : \implies \bf 3x =-21[/tex]

[tex]\sf : \implies \bf 3x× \green{\dfrac{1}{3}}=-21× \green{\dfrac{1}{3}}[/tex]

[tex]\sf : \implies \bf \underline{\boxed{\sf \bf x = -7}}[/tex]

Answer:

The answer is 18.

Step-by-step explanation:

You just need to plug in -7 to the equation 2x-4. You get -18, but absolute value is always positive, so its 18.

The answer is 18.

Sorry no explanation im soooo sorry

Answer:

The answer is 3.

Step-by-step explanation:

The equation would be: x = 14.95 divided by 4.99, rounded to the nearest one:

14.95 divided by 4.99 = 2.99599...

Normally, I would not round the number to the nearest digit in problems like these, but 2.99599 is quite close to 3, so this might be an exception.

Anyways, that's how I got my answer.

Hope this helped.

Answer:

The answer could be any number above -7.

So, it could be...

(-8)

(-9)

(-10)

etc.

Step-by-step explanation:

The bigger the negative number, the lower the value.

Answer:

5pi/3x180grados/piradianes

900/3=300 grados

Step-by-step explanation:

Answer:

I think it would be 50 even numbers

no the frame will not fit

7 6/11 =7.545454

7.545454 is larger than 7.5

Answer:

3 hours

Step-by-step explanation:

369 divided by (58+65)

Answer:

The standard equation of the sphere is [tex](x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53[/tex]

Step-by-step explanation:

From the question, the end point are (3,-2,4) and (7,12,4)

Since we know the end points of the diameter, we can determine the center (midpoint of the two end points) of the sphere.

The midpoint can be calculated thus

Midpoint = [tex](\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})[/tex]

Let the first endpoint be represented as [tex](x_{1}, y_{1}, z_{1})[/tex] and the second endpoint be [tex](x_{2}, y_{2}, z_{2})[/tex].

Hence,

Midpoint = [tex](\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})[/tex]

Midpoint = [tex](\frac{3 + 7 }{2}, \frac{-2+12 }{2}, \frac{4 + 4 }{2})[/tex]

Midpoint = [tex](\frac{10 }{2}, \frac{10}{2}, \frac{8 }{2})\\[/tex]

Midpoint = [tex](5, 5, 4)[/tex]

This is the center of the sphere.

Now, we will determine the distance (diameter) of the sphere

The distance is given by

[tex]d = \sqrt{(x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} + (z_{2}- z_{1})^{2} }[/tex]

[tex]d = \sqrt{(7 - 3)^{2} +(12 - -2)^{2} + (4- 4)^{2}[/tex]

[tex]d = \sqrt{(4)^{2} +(14)^{2} + (0)^{2}[/tex]

[tex]d = \sqrt{16 +196 + 0[/tex]

[tex]d =\sqrt{212}[/tex]

[tex]d = 2\sqrt{53}[/tex]

This is the diameter

To find the radius, r

From [tex]Radius = \frac{Diameter}{2}[/tex]

[tex]Radius = \frac{2\sqrt{53} }{2}[/tex]

∴ [tex]Radius = \sqrt{53}[/tex]

r = [tex]\sqrt{53}[/tex]

Now, we can write the standard equation of the sphere since we know the center and the radius

Center of the sphere is [tex](5, 5, 4)[/tex]

Radius of the sphere is [tex]\sqrt{53}[/tex]

The equation of a sphere of radius r and center [tex](h,k,l)[/tex] is given by

[tex](x-h)^{2} + (y-k)^{2} + (z-l)^{2} = r^{2}[/tex]

Hence, the equation of the sphere of radius [tex]\sqrt{53}[/tex] and center [tex](5, 5, 4)[/tex] is

[tex](x-5)^{2} + (y-5)^{2} + (z-4)^{2} = \sqrt{(53} )^{2}[/tex]

[tex](x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53[/tex]

This is the standard equation of the sphere

Answer:

The pump should be added by 8PM

Step-by-step explanation:

An oil tanker can be emptied by the main pump in 4 hours.

An auxiliary pump can empty the tanker in 11 hours.

the main pump is started at 7 PM,and we have 10 PM - 7PM = 3 hours to empty the tank.

So we have to look for the combined rate of the both pumps .

Let's say the volume= x

Rate of first pump= x/4

Rate of second pump= x/11

The rate will be added together

Combined rate= x/11 + x/4

Combined rate= 15x/44

But they have three hours to complete their pump

15x/44 = 3

X=1.0227

The pump should be added by 8PM

Answer:

[tex]-\frac{19}{8}[/tex]

Step-by-step explanation:

[tex]\frac{1}{4}-\frac{21}{8}=\frac{2}{8}-\frac{21}{8}=\frac{2-21}{8}=-\frac{19}{8}[/tex]

The required number line represents 2 whole intervals (16/8) and then 7 more parts (7/8) from 0, and ends up at the point marked 2 3/8.

In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.

To add fractions with different denominators, we need to find a common denominator. In this case, we can use 8 as the common denominator:

1/4 + -21/8

1/4 - 21/8

2/8 - 21/8

-19/8

-2 3/8

To represent 19/8 on a number line, we need to divide the interval between 0 and 3 into 8 equal parts, and then count 23 of these parts from 0.

The number line would look something like below as shown.

Thus, the required number line represents 2 whole intervals (16/8) and then 7 more parts (7/8) from 0, and ends up at the point marked 2 3/8.

Learn more about the number line here:

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Proof by induction

Base case:

n=1: 1*2*3=6 is obviously divisible by six.

Assumption: For every n>1 n(n+1)(n+2) is divisible by 6.

For n+1:

(n+1)(n+2)(n+3)=

(n(n+1)(n+2)+3(n+1)(n+2))

We have assumed that n(n+1)(n+2) is divisble by 6.

We now only need to prove that 3(n+1)(n+2) is divisible by 6.

If 3(n+1)(n+2) is divisible by 6, then (n+1)(n+2) must be divisible by 2.

The "cool" part about this proof.

Since n is a natural number greater than 1 we can say the following:

If n is an odd number, then n+1 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.

If n is an even number" then n+2 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.

Therefore by using the method of mathematical induction we proved that for every natural number n, n(n+1)(n+2) is divisible by 6. QED.

Answer:

102.2 miles

Step-by-step explanation:

First, convert the minutes to hours:

101.5/60

= 1.69 hours

Multiply this by 60.4 to find how many miles it covered:

= 102.2 miles

Answer:

c

Step-by-step explanation:

just plug each coordinates

5=x

18=y

if its tru for both then thats the answer

Answer:

5,8

Step-by-step explanation:

y=4x-2-----(i)

y=x+13----(ii)

Equating equation i and ii we get,

[tex]4x - 2 = x + 13[/tex]

[tex]4x - x = 13 + 2[/tex]

[tex]3x = 15[/tex]

[tex]x = 3[/tex]

[tex]substitutin \: the \: value \: of \: x \: in \: equation \: (i)[/tex]

[tex]y = 4x - 2[/tex]

[tex]y = 4 \times 5 - 2[/tex]

[tex]y = 20 - 2[/tex]

[tex]y = 18[/tex]

Marks this as a brainest answer ok.

This is basically saying [tex]1 \le x < 4[/tex]

The square bracket says "include this endpoint" while the curved parenthesis means "exclude this endpoint". We can tell what is included/excluded based on how the endpoint is drawn.

Open circle = exclude endpoint

Closed/filled in circle = include endpoint

Your teacher has also drawn a square bracket at the left endpoint, and a curved parenthesis at the right endpoint. This style of drawing the endpoints helps set up [1, 4). Though sometimes you might see the use of open/closed circles instead for the endpoints. I'm referring to the number line portion.

We want to express the shaded set of numbers on the x-axis with interval notation.

The interval notation is:

[1, 4)

Let's start by analyzing the graph.

We have two ends, one at x = 1, with a colored dot, which means that that value belongs to the set.

We have the other end at x = 4, with a white dot, which means that the value does not belong to the set.

Then the interval notation is:

[1, 4)

Where [] are used for colored dots.

() are used for white dots.

If you want to learn more, you can read:

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Answer:

4cm - 4mm = 3.6 cm

So, B and C equals 3.6 cm

Answer:$12

Step-by-step explanation:

Answer:

months of game play (m) =$11

Step-by-step explanation:

Answer:x=8

Step-by-step explanation:Reorder the terms:

10x + -2(6 + x) = 52

10x + (6 * -2 + x * -2) = 52

10x + (-12 + -2x) = 52

Reorder the terms:

-12 + 10x + -2x = 52

Combine like terms: 10x + -2x = 8x

-12 + 8x = 52

Solving

-12 + 8x = 52

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '12' to each side of the equation.

-12 + 12 + 8x = 52 + 12

Combine like terms: -12 + 12 = 0

0 + 8x = 52 + 12

8x = 52 + 12

Combine like terms: 52 + 12 = 64

8x = 64

Divide each side by '8'.

x = 8

Simplifying

x = 8

Answer:

x=5

Step-by-step explanation:

Answer:

So in this sequence, we are adding by 9 in each term

So our pattern is: 7 , 7 +9 , 7 + 2(9) , 7 + 3(9) .....

hence, we can write it as: 7 + [tex]9^{n-1}[/tex] where n is the number of the term you want