The function y = f(x) is graphed below. What is the average rate of change of the function f(x) on the interval -5 < x < -4?

Under the < is a _ thing

The integral ∫1/√1 +(lnx) 2dx is -x+2xln(x)+c

An integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data

The given integral is ∫1/√1 +(lnx) 2dx

= ∫1 +2(lnx)dx

Apply the sum rule

∫f(x)±g(x)=∫f(x)±∫g(x)

= ∫1dx +2∫(lnx)dx

=x+2(xln(x)-x)+c

=-x+2xln(x)+c

Hence, the integral ∫1/√1 +(lnx) 2dx is -x+2xln(x)+c

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Answer:

m∠C = 67°, a = 7.37, b = 15.13

Step-by-step explanation:

There are 180° in a triangle. We know two angles in the triangle, so we can calculate the third angle.

Since this is not a right triangle, we will use the Law of Sines.

SinA/a = SinB/b = SinC/c

see image.

The volume of the storage shed is 125600 ft³.

The storage shed will be refilled after using 125600 ft³ of salt.

The cylindrical storage shed shown below is completely filled with road salt to make a town's roads safer during snow storms.

The volume of the storage shed can be found as follows;

volume of a cylinder = πr²h

where

Therefore,

r = 40 / 2  =20 ft

h = 100 ft

volume of the storage shed = 3.14 × 20² × 100

volume of the storage shed = 3.14 × 400 × 100

volume of the storage shed = 125600 ft³

Therefore, the storage shed can handle 125600 ft³ of salt before it needs to be refilled.

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Answer:

[tex]\frac{27}{8}[/tex]

Step-by-step explanation:

using the rules of  exponents/ radicals

• [tex](\frac{a}{b}) ^{-m}[/tex] = [tex](\frac{b}{a}) ^{m}[/tex]

• [tex]a^{\frac{m}{n} }[/tex] = [tex](\sqrt[n]{a}) ^{n}[/tex]

then

[tex](\frac{16}{81}) ^{-\frac{3}{4} }[/tex]

= [tex](\frac{81}{16}) ^{\frac{3}{4} }[/tex]

= [tex]\frac{(\sqrt[4]{81})^3 }{(\sqrt[4]{16})^3 }[/tex]

= [tex]\frac{3^3}{2^3}[/tex]

= [tex]\frac{27}{8}[/tex]

Table (x, y) equals (0, 0), (6, 3), and (12, 6) represents a linear relationship that is also proportional.

In its most basic form, a ratio is a comparison between two comparable quantities.

There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.

If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.

The first option is linear but not proportional as 3 ×2 = 6 and 6×2 = 12.

By observing the given options we conclude that the third option is linear and proportional as,

6 ÷ 2 = 3 and 12 ÷ 2 = 6.

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The side of  the initial cube is 42 cm.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Rick melted a cube and made a cone with it.

The amount of melted liquid left after making the cone was 49 cm

6/7 of the melted liquid was used in making the cone

We need to find the side of the initial cube.

Cube =a³

Le us the whole liquid be 1.

6/7 of the melted liquid was used in making the cone

1/6/7=7/6 is the left out liquid after making cone.

7/6x=49

x=42 cm

Hence, the side of  the initial cube is 42 cm.

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The property that could be used to determine that the triangles are congruent is the SSA congruent theorem

From the question, we have the following parameters that can be used in our computation:

Triangles = QRP and XWY​

On the triangles, we can see that:

This means that we make use of the SSA congruent theorem

The SSA congruent theorem implies that  if two sides and an angle not included between them are respectively equal to two sides and an angle of the other than the two triangles are equal.

In this case, we have

Congruent sides: RQ and HG & PR and HF

Congruent angles: Angles Q and G

Hence, the additional information on the congruency of the triangles is the SSA theorem

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Answer:

sq root of 21=7

Step-by-step explanation:

we need to use Pythagoras theorem

so distance(isa-jul)^2 +distance(ele-jul)^2= distance(isa-ele)^2

now just do the square root and there you go.

Answer:

To solve this problem, you need to use the distributive property, which states that for any two numbers a and b, and for any numbers x and y, (a + b) * x = ax + bx and x * (a + b) = xa + xb.

Applying the distributive property, we have:

(-5i)(7 + i) = (-5i) * 7 + (-5i) * i

= -35i + (-5i) * i

Now, you need to use the fact that i * i = -1:

(-5i)(7 + i) = -35i + (-5i) * i

= -35i + (-5) * (-1)

= -35i - 5

= -40i - 5

So the final result is -40i - 5.

Step-by-step explanation:

please refer to the sketch

The system of the equations to be used to graph the solution of the equation given is y = x² and y = 2x+3

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given that, is an equation, x² = 2x+3, we need to find a system of equations that can be graphed to give the solution of the equation given,

So, the equation is x² = 2x+3

We can write this as,

x²-2x-3 = 0

Now, factorize to find the solution of the equation,

x²-3x+x-3 = 0

x(x-3)+1(x-3) = 0

(x+1)(x-3) = 0

x = -1 and x = 3

So, the solution of the equation is -1 and 3

However, if we consider the equation to be two different systems combined, that is the equation of the straight line and the equation of the basic quadratic function,

y = x² and y = 2x+3

Then the solution to is the intersection of the graph of the straight line and the graph of the quadratic curve.

That is the x-coordinates of the points of intersection are the solutions.

Since, the graphs are intersecting at (3, 9) and (-1, 1) [see the graph]

Therefore, the system of equation is y = x² and y = 2x+3

Hence, the system of the equations to be used to graph the solution of the equation given is y = x² and y = 2x+3

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The probability that the team will win more than 9 games this season, given the average number of wins for the team, is 4 %

The Z-score formula is:

Z = (x - mean) / standard deviation

Where x is the number of wins we're interested in (9), mean is the average number of wins (7.6), and standard deviation is the standard deviation of the number of wins (1.3)

Z = (9 - 7.6) / 1.3

= 2.3 / 1.3

= 1.77

This means that 9 wins is 1.77 standard deviations above the mean. The result is the probability of a team winning more than 9 games this season, which is around 0.04 or 4% from the standard normal distribution table.

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Answer:

x = 45

Step-by-step explanation:

2x + 6 and 96 are vertically opposite angles and are congruent , then equation is

2x + 6 = 96 ( subtract 6 from both sides )

2x = 90 ( divide both sides by 2 )

x = 45

Answer:

can you just give me the brainliest.

the answer is in the attached document

Step-by-step explanation:

On solving the provided question, we cans ay that - here in triangles, triangle ABC is congruent to triangle A`B`C`

Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.

Here,

two triangles are there

triangle ABC and triangle A`B`C`

AB =A`B`

BC = B`C`

AC =A`C`

So, by sss property

both are congruent

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Answer:

200

Step-by-step explanation:

[tex]\frac{2}{5}[/tex] = [tex]\frac{80}{x}[/tex]

2 x 40 = 80, so

5 x 40 = 200

Answer:

200 houses

Step-by-step explanation:

Flat: 2 parts = 80 flats
1 part => 80 : 2 = 40 flats
Houses: 5 parts = 40 x 5 = 200 houses

Answer:

7/

Step-by-step explanation:

3/4 * 7/

3 can be crossed

Leaving 7/

Answer:

[tex]y=3x-7[/tex]

Step-by-step explanation:

Parallel lines, by definition, never intersect. They have the same slope but different y-intercepts (otherwise they would be the same line) on a graph.

Slope-Intercept Form:

Slope-Intercept form is expressed as: [tex]y=mx+b[/tex], where

This form is super useful for linear equations as it gives us the two key features of a linear equation. It's how each of the options are formatted, so we know we'll have to use this form.

The line is parallel to [tex]y=3x-4[/tex], meaning it has a slope of 3, but also a y-intercept other than -4 (otherwise they would be the same equation).

So we can generally form an equation: [tex]y=3x+b\text{, }b\ne-4[/tex], so we can plug any value for "b" here (except -4) and have a parallel line

Since we not only want to find a parallel line, but also one that passes through a specific point, we can use our general parallel equation: [tex]y=3x+b\text{, }b\ne-4[/tex], and plug in known values. We of course already have the slope plugged in, but now we have a (x, y) coordinate, which we can plug in for x and y in the equation.

Original Equation:

[tex]y=3x+b[/tex]

Point given: (3, 2), substitute in x=3 and y=2:

[tex]2=3(3)+b[/tex]

Simplify:

[tex]2=9+b[/tex]

Subtract 9 from both sides:

[tex]-7=b[/tex]

Now we can take this value. and plug it back into the general equation:

[tex]y=3x+(-7)\implies y=3x-7[/tex]

Now we have our answer!

Divide 228/5 into 45, leaving a residue of 3, and divide 1,487 by 4 to get 371.75 . 2.28 divided by 5 using partial quotients = 40 + 5 = 45

The quotient is a whole number when a number is entirely divisible by another integer.For instance, 15 x 3 = 5. (whole number)The quotient is a decimal number when a number is not entirely divisible by another integer. For instance, 15 x 2 equals 7.5 (decimal number)

given

2.28 divided by 5 using partial quotients = 40 + 5 = 45

after all partial quotients are added up. 1.72 divided by 3 using sharing to divide = 1.72 / 3 = 0.58

Divide 228/5 into 45, leaving a residue of 3, and divide 1,487 by 4 to get 371.75 .

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For this problem, we know that the line's function is equal to 3 if X isn't 0. That means that for every X that isn't 0, we'll have a line at y = 3 (since we know that g(x) is just fancy for y!). We're also given that if X is equal to 0, it must be at y = 4.

Therefore, your graph should have a straight line through y = 3 EXCEPT at x = 0! At x = 0 you should just have a shaded dot at y = 4.

Answer: look it up :)

Step-by-step explanation: click new tab. then type 'the sum of a number and 9'. the first or second result will come up with your answer, n+9 is the one I got.

Answer: x+9 or n+9

Step-by-step explanation: sum refers to addition you can put x for "a number"  thus you get x+9 as your expression or n+9 for your teacher but both are variables so it doesn't matter if it's j, y, u, or p what's there functionality wise but your teacher might want it a certain variable like n

Answer:

24,241 people

Step-by-step explanation:

To determine the attendance at the festival in the fifth year, we need to calculate the cumulative increase in attendance over five years.

1st year: 20,000

2nd year: 20,000 * 1.05 = 21,000 (5% increase from the first year)

3rd year: 21,000 * 1.05 = 22,050 (5% increase from the second year)

4th year: 22,050 * 1.05 = 23,127.50 (5% increase from the third year)

5th year: 23,127.50 * 1.05 = 24,241.38 (5% increase from the fourth year)

So, in the fifth year the festival will be attended by approximately 24,241 people.

Answer:

50%

Step-by-step explanation:

16 litres = (16 x 1000) cm^3

             = 16000 cm^3

Hence,

Percentage = 8000/16000 x 100%

                    = 1/2 x 100%

                    = 50%

Therefore ,the value of a given fraction is equal to 10/12, which equals 5/6, after resolving the given problem.

To represent a whole, divide it into any number of comparable parts, or fractions. How many units of a particular size there are is expression using fractions in standard English. 8, 3/4. Parts of a whole are included. Numbers in mathematics are stated as a ratio of the excess to the denominator. These are each simple fractions that represent an integer. A fraction is contained in the fraction or reduction of a complex fraction. When a fraction is true, its numerators are less than its denominators. An amount that makes up a fraction of a whole is called a fraction. You can assess the whole by dissecting it into smaller pieces.

Here,

Given : 5/8 X 4/3

=> 5/8 X 4/3 = 20/24

on condensing,

10/12 = 5/6

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Answer:

no solutions

Step-by-step explanation:

   -9x-2y=5

- (-9x-2y=11)

-9x-(-9x) - 2y-(-2y) = 5 - 11  ==> subtract the top two equations

-9x + 9x - 2y + 2y = -6  ==> subtracting by a negative number is equivalent

                                       to adding by a positive number

(-9x + 9x) - 2y + 2y = -6

0 - 2y + 2y = -6

0 - 0 = -6

0 [tex]\neq[/tex] -6  ==> Hence, there is no solutions.

The pound of cement used based on the information will be C. 2 pounds.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

In this case, for each pound of sand, he uses 1 2/3 pounds of gravel and for each pound of gravel, he uses 2/5 pound of cement.

The pound of cement used will be:

Gravel = 1 2/3 × 3

= 5 pounds

Cement used will be:

= 2/5 × 5.

= 2 pounds.

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Answer:

(2m + 1) * x ^ 2 - (2m + 5) * x + (2m + 1) = 0

2mx^2+x^2-2mx+5x+2m+1=0

3mx^2+5x+1=0

That's as far as you can get simplifying it.

Step-by-step explanation:

Answer:

$10.80

Step-by-step explanation:

9 times 0.20 equals 1.80

9 + 1.80 = $10.80

Answer:

no

Step-by-step explanation:

The amount of white paint used by Tamara to paint the bedroom walls is 2.125.

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

Total amount of paint = 8.5

Three fourths of this amount is blue paint.

Amount of blue paint = (3/4) × 8.5 = 6.375

Rest is white paint.

Amount of white paint = Total paint - Amount of blue paint

                                     = 8.5 - 6.375

                                     = 2.125

Hence the amount of white paint used to paint bedroom walls is 2.125.

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Answer:

40/20 & 22/11

Step-by-step explanation:

To find an equivalent fraction to 4/2, or to any other fraction, you just need to multiply (or divide, if the fraction is not yet reduced), both the numerator and the denominator of the given fraction by any non-zero natural number. For example:By dividing the original fraction by 2, we get:4 ÷ 2 / 2 ÷ 2 = 21. By multiplying the original fraction by 2, we get:4 × 2 / 2 × 2 = 8/4. Here is the full list of equivalent fractions to 4/2. 2/1, 4/2, 6/3, 8/4, 10/5, 12/6, 14/7, 16/8, 18/9, 20/10, 22/11, 24/12, 26/13, 28/14, 30/15, 32/16, 34/17, 36/18, 38/19, 40/20...