Solve each system by elimination.

The average rate of change of function f(x)= [tex]\frac{1}{x+5}[/tex]  on the interval [1,1+h] is [tex]-\frac{1}{36+6h}[/tex]

Given,

The function = [tex]\frac{1}{x+5}[/tex]

We know the average rate of change of the function is [tex]\frac{f(b)-f(a)}{b-a}[/tex]

Where a and b are the intervals

a= 1

b=1+h

f(a) =f(1)= [tex]\frac{1}{1+5}[/tex]

=[tex]\frac{1}{6}[/tex]

f(b)= f(1+h)

=[tex]\frac{1}{1+h+5}[/tex]

=[tex]\frac{1}{6+h}[/tex]

f(b)-f(a)= [tex]\frac{1}{6+h}-\frac{1}{6}[/tex]

[tex]=\frac{6-(6+h)}{6(6+h)} \\=\frac{6-6-h}{36+6h}\\ =-\frac{h}{36+6h}[/tex]

Then,

[tex]\frac{f(b)-f(a)}{b-a} =\frac{-\frac{h}{36+6h} }{1+h-1}[/tex]

[tex]=\frac{-\frac{h}{36+6h} }{h} \\=-\frac{1}{36+6h}[/tex]

Hence, the average rate of change of function f(x)= [tex]\frac{1}{x+5}[/tex]  on the interval [1,1+h] is [tex]-\frac{1}{36+6h}[/tex]

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Answer:

3/5

Step-by-step explanation:

500 is the money she started with if you put that over the money she spent on vegetables it would be 300/500 when simplified it's 3/5

Answer:

The answer is D.

Step-by-step explanation:

Answer:

in this case the answer is D

Step-by-step explanation:

your welcome

It should be noted that solving the system of equations. -5a + 7b = 2 -15a + 21b = 6 will give 0 and this implies that it has no solution

It should be noted that we simply want to solve the equations given:

-5a + 7b = 2 ................ i

-15a + 21b = 6 ............. ii

Divide equation ii through by 3. This will give:

-5a + 7b = 6

Therefore, the equations will be:

5a + 7b = 2 ................ i

5a + 7b = 2 ................ ii

Subtract equation ii from i

This will be (5a + 7b = 2) - (5a + 7b = 2) = 0

Therefore, it should be noted that solving the system of equations. -5a + 7b = 2 -15a + 21b = 6 will give 0 and this implies that it has no solution

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Greetings from Brasil...

The total length will be: 10+10+10+10 = 40

and

(3/4)m = 0.75m

Then, Rule of 3:

QTD             m

  1     ------    3/4

  X     ------   40

X = 53.333

Soon 53 posts will be needed

Answer:

theres a 25% you will grab an apple (work shape is suppose to be circle)

Step-by-step explanation:

Hope this helps

Answer:

2

Step-by-step explanation:

First substitute the values of z and y in the expression.

Use PEDMAS. We have to multiply 5 and 3, which gives 15. Subtract 1 from 15 and then divide the result by 7.

[tex]\sf \dfrac{5z + y}{7}= \dfrac{5*3 + (-1)}{7}\\\\[/tex]

          [tex]\sf = \dfrac{15 - 1}{7}\\\\ = \dfrac{14}{7}\\\\= 2[/tex]

Answer: 3 miles

Step-by-step explanation:

Total = 30 miles per week

Weekly runs in the morning= 3*5 = 15 miles per week

Bikes= 30-15 = 15 miles per week

Bikes each day= 15/5 = 3 miles

tom has 8 cards and sarah has  24 cards .

tom and sarah total baseball cards =32

sarah has three times as many baseball cards as tom

The 2 equations are

1. sarah + tom = 32

2. sarah = [tex]3 \times tom[/tex]

substitute equation 2 in 1.

[tex]3\times tom +tom= 32[/tex]

4 tom = 32

tom = 32/4

tom = 8 cards

sarah = [tex]3\times tom[/tex]

         = [tex]3\times 8[/tex]

sarah = 24 cards

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Answer:

5/4 Quotient[24/5] and 6

Step-by-step explanation:

5/4 Quotient[24/5]

Simplify the following:

(4 + 4/5)/(4/5)

Multiply the numerator of (4 + 4/5)/(4/5) by the reciprocal of the denominator. (4 + 4/5)/(4/5) = ((4 + 4/5)×5)/4:

((4 + 4/5)×5)/4

Put 4 + 4/5 over the common denominator 5. 4 + 4/5 = (5×4)/5 + 4/5:

(((5×4)/5 + 4/5) 5)/4

5×4 = 20:

((20/5 + 4/5)×5)/4

20/5 + 4/5 = (20 + 4)/5:

(((20 + 4)/5)×5)/4

20 + 4 = 24:

(24/5×5)/4

24/5×5 = (24×5)/5:

((24×5)/5)/4

((24×5)/5)/4 = (24×5)/(5×4):

(24×5)/(5×4)

(24×5)/(5×4) = 5/5×24/4 = 24/4:

24/4

The gcd of 24 and 4 is 4, so 24/4 = (4×6)/(4×1) = 4/4×6 = 6:

Answer: 6

Answer:

Step-by-step explanation:

a,d

Answer:ad

Step-by-step explanation:

ad

The new volume of the right circular cylinder is 44 cubic centimeter.

The formula for the volume of the cylinder is given as

         V = Πr^2h              (1)

We have been given that,   V = 22 cubic centimeters

Now we need to find the volume of the cylinder which is denoted by V’ whose,

                  r = 2r

          and, h = h/2

Now putting the required values in equation (1) we get

 V’ = Π(2r)^2(h/2)

 V’ = Π4r^2(h/2)

V’ = 4/2(Πr^2h)

V’ = 2V   [as V = Πr^2h]

V’ = 2*22 cubic centimeter

V’ = 44 cubic centimeter

Hence the new volume of the right circular cylinder is 44 cubic centimeter

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Earning of each = $33.75

Let's take the earnings of each person to be x.

Total person working at the theater = 16 + 4 + 12

                                                          = 32

Now the total earnings of the people = 32x

Which is given = $1080

So we get an equation

              32x = 1080

                 x = $33.75

Hence we get the earnings of each person = $33.75

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A measurement that can be repeated is said to be precise and one that is close to the accepted or actual value is approximate.

Given that,
The incomplete statement is given we have to complete the statement.

All over the world, most things are in use as of common quantity, so people all over the world agree that they have to follow a common system of measurement and that the common system of measurement is called standard measurement.

Here,

A measurement that can be repeated is said to be precise values
A measurement that is close to the accepted or actual value is approximate.

Thus, the required words are precise and approximate.

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Let f(x) be the integrand.

[tex]f(-2)=-8 \\ \\ f(0)=0 \\ \\ f(2)=8 \\ \\ f(4)=64 \\ \\ \implies \int^{4}_{-2} x^3 \text{ dx}=\approx \frac{1}{2}(2)[-8+64+2(0+8)] \\ \\ =\boxed{72}[/tex]

A> The equation for the line is y = -0.1x + 2600

B> The value of the car is $16,500

From the table, we know that for every 6000 miles added there is a decrease in the value by $600.

A> So it is the function of one order

y = kx + b

25500 = 5000k + b

24800 = 12000k + b

After equating it we get

b = 26000 and k = -0.1

Now put the value of b and k in the equation, and we get

y = -0.1x + 26000

Therefore the equation is y = -0.1 + 26000

B> When we put the value of x = 95000, we get

y = -0.1 × 95000 + 26000

  = 16500

Therefore the cost of the car is $16,500

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Answer:

The two in the middle?

Solving a system of equations, we conclude that the largest number on a hat is 14.

We have 3 hats, each one with a number that we will define as:

x, y, and z.

We know that by adding pairs of these numbers we get 11, 17 and 22, then we can write a system of equations:

x + y = 11

x + z = 17

y + z = 22

Clearly z is the largest number, so we want to find z.

First, we can isolate x on the first equation so we get:

x = 11 - y

Replacing that in the second equation giveS:

x + z = 17

(11 - y) + z = 17

Now our system is:

y + z = 22

(11 - y) + z = 17

Isolating y in the first one we get:

y = 22 - z

Now we can replace that in the other equation:

(11 - (22 - z)) + z = 17

Now we can solve this for z.

11 - 22 + z + z = 17

-11 + 2z = 17

2z = 17 + 11 = 28

z = 28/2 = 14

z = 14

We conclude that the largest number on a hat is 14.

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Given lines CD and EF are parallel. Therefore answer is (a)

How to find slope of  two lines and check whether they are parallel or perpendicular

Given are two points P (x₁, y₁) and Q ( x₂, y₂)

Then slope of the line  PQ is given by  (y₂-y₁)/(x₂-x₁)

If two lines have slopes m₁ and m₂ respectively

Then the lines are parallel when their slopes are equal i.e. m₁=m₂

and  the lines are perpendicular when m₁*m₂= -1

Given C(5,2), D(8,3),E(3,8) F(-6,5)

Then,

Slope of CD = (3-2)/(8-5)= 1/3

Slope of EF = (5-8) / (-6-3)  = 1/3

Slope of CD=Slope of EF

Therefore CD and EF are parallel

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Answer:

if you just want to simplify, -6a^2 m^7 n

Step-by-step explanation:

The time at which the truck will pass the car is 2.5 hours and the distance at which the car and truck meet is 200km.

Velocity is defined as the ratio of the distance moved by the object at a particular time. The velocity is a vector quantity so it needs both the magnitude and the direction.

Given that at 2 p.m., a car is 100 km east of Toronto, driving eastward at 80 km/h. A truck leaves Toronto at 2 p.m. and is driving eastward at 120 km/h.

The time will be calculated as:-

Relative velocity = Distance / Time

Time = Distance /  Relative velocity

Time = 100 / 120 - 80

Time = 2.5 Hours

Distance of car = Speed x time = 80 x 2.5

Distance of car = 80 x 2.5

Distance of car = 200 Km

Therefore, the time at which the truck will pass the car is 2.5 hours and the distance at which the car and truck meet is 200km.

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Answer:

79

Step-by-step explanation:

Let the numerator of the original fraction be 'x' and the denominator be 'y'. So, the original fraction becomes xy

According to the question,

Condition I,

If 4 is subtracted from the numerator of a fraction, its value becomes 1/3.

or,x−4y=13

or,3(x−4)=y

or,y=3x−12

Condition II,

If 5 is added to the denominator of the original fraction, the value becomes 1/2.

or,xy+5=12

or,2x=y+5

Put value of y from equation (i) in equation (ii), we get,

or,2x=(3x−12)+5

or,2x=3x−12+5

or,3x−2x−7=0

∴x=7

Put value of x in equation (i), we get,

or,y=3×7−12

or,y=21−12

∴y=9

So, (x,y) = (7,9)

Therefore, the required original fraction is 79.

Shawn earn 11 per hour.

Hannah travel 25 miles in one gallon of gas.

A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.

given:

According to the graph the y- axis shows the earnings.

So, we have the coordinates are

(1, 11), (2, 22) and (3, 33)

So, Shawn earn = 22 - 11 / 2 -1 = 11 per hour.

Now, in second case

The coordinates are

(3, 75), (5, 125), (6, 150), (10, 250)

So, m= (125 - 75) / (5-3)

m= 50/2

m=25

So, Hannah travel 25 miles in one gallon of gas.

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Answer:

Step-by-step explanation:

The sides of the triangle are:

Its perimeter is the sum of the three sides:

Step-by-step explanation:

we are calculating miles.

when we have speed, which is mph or miles/hour. what do we have to multiply it with to get miles ? hours !

miles/hour × hour = miles

so, in the function D(x) the speed 60 mph has to be multiplied by the hours spent driving to get the driven miles.

x = hours spent driving

the domain is the interval or set of all valid x (input) values. the range is the interval or set of all valid y (function result) values.

so what are valid x (number of driving hours) values ?

it starts with 0, if course (before actually driving). and it goes up to 4 (after 4 hours the 240 miles are "done").

the domain is

0 <= x <= 4

and the range ? that is all the function result values for the valid x values.

for x = 0 this starts at 240.

and goes down for x = 4 to 0.

the range is

0 <= y (= D(x)) <= 240

Answer:

−3 < x ≤ 0

Step-by-step explanation:

1 < x + 4 ≤ 4

Add -4 to all parts

1 + −4< x + 4 + −4 ≤ 4 + −4

Put pairs in bracket to avoid confusion

(1 + −4) < x (+ 4 + −4) ≤ (4 + −4)

−3 < x ≤ 0

The ratio of the area of the smaller square to the area of the larger square = 4 : 49

Let the perimeter of the small square be [tex]P_1[/tex]

Lethe the perimeter of the large square be [tex]P_2[/tex]

Perimeter of a square = 4 Length

[tex]P_1=4L_1\\\\P_2=4L_2[/tex]

The ratio of the perimeters = 2:7

[tex]\frac{4L_1}{4L_2} =\frac{2}{7} \\\\\frac{L_1}{L_2} =\frac{2}{7}[/tex]

The area of a square = L^2

[tex](\frac{L_1}{L_2} )^2=(\frac{2}{7} )^2\\\\\frac{L_{1} ^{2} }{L_{2} ^{2}} =\frac{2^2}{7^2} \\\\\frac{L_{1} ^{2} }{L_{2} ^{2}} =\frac{4}{49}[/tex]

Therefore, the ratio of the area of the smaller square to the area of the larger square = 4 : 49

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Answer:

[tex] \sf \large( \frac{2}{5} ) {}^{14} [/tex]

Step-by-step explanation:

=((2/5)^4(2/5)^3)^2

=((2/5^4+3))^2

=((2/5^7))^2)

=(2/5)^14

Using a geometric sequence, we have that:

Graph 1 models the situation.

The end behavior of the graph is given as follows:

As x decreases, y approaches the line y = 2.

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q, hence the second term is the first multiplied by q, the third is the second multiplied by q, and so on.

For item 4, we have that:

This means that the first graph is correct.

The end behavior of a function is given by the limits of the function when x goes to infinity.

Hence, from the final graph, we have that:

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