What is the slope of the linear equation 2y 3x − 1?

The function f(x) = x³ - 7x + 1 for the given f''(x) = 6x, f'(-3) = 20 and f(-3) = -5. By using the antiderivative formula, the required function is evaluated.

The antiderivative formula for indefinite integrals is

[tex]\int f'(x)dx = f(x) + c[/tex]

or we can also write this as

[tex]\int f^n(x)dx = f^{n-1} + c[/tex]

It is given that,

f''(x) = 6x, f'(-3) = 20, f(-3) = -5

Then, by the antiderivative formula, we can write

[tex]\int f''(x)dx = f'(x) + c[/tex] ...(1)

On substituting, we get

[tex]\int f''(x)dx = \int 6x dx = 6\int xdx[/tex]

Since we have the formula for the indefinite integral, [tex]\int x^n dx = \frac{x^{n+1}}{n+1}+c[/tex], we get

[tex]\int f''(x)dx = 6(\frac{x^{1+1}}{1+1})+c[/tex]

⇒ [tex]\int f''(x)dx = 6(\frac{x^2}{2})+c=3x^2+c[/tex]

So, from (1), we get f'(x) = 3x² + c

But we have f'(-3) = 20. So, on substituting x = -3 in the above function f'(x), we get

f'(x) = 3x² + c

⇒ f'(-3) = 3(-3)² + c

⇒ 20 = 3(9) + c

⇒ 20 - 27 = c

∴ c = -7

So, the second derivative function is f'(x) = 3x² - 7.

From the antiderivative expression, we can write

[tex]\int f'(x)dx = f(x) + c[/tex] ...(2)

On substituting f'(x) in the above integral we get

[tex]\int f'(x) dx = \int (3x^2 +-7)dx[/tex]

⇒ [tex]\int f'(x)dx = 3\int x^2dx -7\int dx + c[/tex]

⇒ [tex]\int f'(x) dx = 3(\frac{x^3}{3})-7x+c[/tex]

⇒ [tex]\int f'(x) dx = x^3 - 7x + c[/tex]

From (2), we can write

f(x) = x³ - 7x + c

But we have f(-3) = -5;

Then,

f(-3) = (-3)^3 - 7(-3) + c

⇒ -5 = -27 + 21 + c

⇒ -5 = -6 + c

∴ c = -5 + 6 = 1

Thus, the function f(x) = x³ - 7x + 1.

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The percent error in zookeeper's prediction on baby elephant's weight is 13.79%.

What is percentage error?

Percentage error is the difference between the estimated value and the actual value compared to the actual value, expressed as a percentage. So the percent error is the relative error multiplied by 100.

Uses of percentage error:

The main purpose of calculating percent error is to analyze how close the measured value is to the actual value. This is part of a comprehensive error analysis.

Solution:

Percent error = (Actual weight - Predicted weight/Predicted weight)x100

Percent error = (264 - 232/232) x 100

Percent error = ( 32/232) x 100

Percent error = 0.1379 x 100

Percent error = 13.79%

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Equation y = 3x is parallel to the line y = 3x - 1.

Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other. Perpendicular lines are those that cross at a straight angle of 90 degrees. If two lines have different y-intercepts and equal slopes, they are said to be parallel. In other words, the reciprocals of perpendicular slopes are negative. Pairs of parallel lines cross one another. If they went on, they'd never run into each other. The separation between parallel lines is always the same.

Given

A line that passes through (0,0) has the equation Y=mX, where m is the slope of the line.

Now that this line is perpendicular to the line Y=3X-1, m is equal to 3.

As a result, the line's equation is Y=3X.

Equation y = 3x is parallel to the line y = 3x - 1.

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Answer:

25%

Step-by-step explanation:

[tex](1/2)^2=1/4 \\ \\ \frac{1}{4} \times 100=25\%[/tex]

As per the given stem and leaf plot, the range of the stem and leaf plot is 4.

The term stem and leaf plot in math is referred as a type of table where the stem (or first column) represents the first place values of numbers and the leaves (or second column) represent the final place value of the numbers.

Here we given the following stem and leaf plot data.

Now we have to find the range of the stem and plot.

As we all know that range is defined as the maximum and minimum number in the data set.

While we looking into the given data, we have identified the the minimum number is 14 and the maximum number is 18.

Then the range is calculated as,

=> 18 - 14 = 4.

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The factorized form of the formula is (3x+9)(x+9) of [tex]3x^{2}[/tex]+ 36x + 81 = 0 . Quadratics can be defined using a polynomial equation of the second degree.

The mathematical action known as "squaring," which is typically used to describe a quadratic problem, involves multiplying a variable by itself. This lexicon is based on the idea that the area of a square is equal to the product of the lengths of its sides. The Latin term quadratum, which means square, is where the word "quadratic" comes from.

here ,

=  [tex]3x^{2}[/tex] + 36x + 81 = 0

= 3x² + 27x + 9x + 81

= 3x(x+9) + 9(x+9)

= (3x+9)(x+9)

= 3(x+3)(x+9)

The factorized form of the formula is (3x+9)(x+9) of [tex]3x^{2}[/tex]+ 36x + 81 = 0 .

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The solution to the evaluation of the expression x(y² - z) x = 6, y = 4 and z = 1 is 90

Evaluate:

x(y² - z)

When

x = 6, y = 4 and z = 1

x(y² - z)

substitute the value of x, y and z

= 6(4² - 1)

Applying PEMDAS:

P = parenthesis

E = Exponential

M = Multiplication

D = Division

A = Addition

S = Subtraction

= 6(16 - 1)

= 96 - 6

= 90

In conclusion, the expression x(y² - z) when evaluated gives 90.

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The critical value that should be used in constructing the confidence interval is (0.150 , 0.166).

The given parameter is as follows,

t\alpha /2,df = 2.473

Margin of error = E = t\alpha/2,df * (s sqrt n)

= 2.473 * (0.0171 / \sqrt28)

Margin of error = E = 0.008

If the populace preferred deviation (σ) is known, a speculation take a look at carried out for one populace imply is known as one-imply z-take a look at or definitely z-take a look at. A z-take a look at is a speculation take a look at for trying out a populace imply, μ, in opposition to a intended populace imply, μ0.

The 98% confidence interval estimate of the population mean is,

\bar x - E < \mu < \bar x + E

0.158 - 0.008 < \mu < 0.158 + 0.008

0.150 < \mu < 0.166

(0.150 , 0.166)

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The equations m = 2d and m+d = 120 represent this situation.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

d = kilograms of dark chocolate

m =kilograms of milk chocolate

So, her recipe calls for twice the amount of dark chocolate as milk chocolate.

Mathematically speaking:

m = 2d

She needs to buy 120 kg, of chocolate in total. So;

m + d = 120

The following system of equations represents the situation:

m = 2d

m+d = 120

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The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

So, her recipe calls for twice the amount of dark chocolate as milk chocolate.

m = 2d

She needs to buy 120 kg, of chocolate in total. So;

m + d = 120

The following system of equations represents the situation:

m = 2d

m+d = 120

Answer:

k = 48 , y = 48x

Step-by-step explanation:

given y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation

to find k use the condition y = 12 when x = [tex]\frac{1}{4}[/tex] , then

12 = [tex]\frac{1}{4}[/tex] k ( multiply both sides by 4 to clear the fraction )

48 = k

constant of variation is then k = 48 , so

y = 48x ← equation of variation

During the first 10 seconds, in the intervals (0, 2) and (6, 10) the acceleration is increasing.

The acceleration is: y = 7*sin( x*pi/4).

Sin(θ) increases between -pi/2 and pi/2

Sin(θ) decreases between pi/2 and (3/2)*pi.

And so on.

Here we have:

θ = x*(pi/2)

When x = 0, θ = 0.

And sin(θ) is increasing in θ = 0.

Then we must choose one of the options that start with x = 0.

now it will stop increasing when:

θ = pi/2 = x*(pi/4)

x = 2.

So the acceleration is increasing in the segment (0,2)

And it will start increasing again when:

θ = (3/2)*pi = x*(pi/4)

(3/2)*pi*(4/pi) = 6 = x.

So at x= 6 the acceleration starts increasing again, and the acceleration is only defined until x = 10, then

the correct option is: (0, 2) and (6, 10)

Thus, during the first 10 seconds, in the intervals (0, 2) and (6, 10) the acceleration is increasing.

Complete question:

The acceleration y, in meters per second squared, of an object after x seconds is given by y = 7 sin (pi/4 x). During the first 10 seconds, over which intervals is the acceleration increasing?

(2, 6)

(4, 8)

(0, 2) and (6, 10)

(0, 4) and (8, 10)

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The acceleration is: y = 7*sin( x*pi/4).

Sin(θ) increases between -pi/2 and pi/2

Sin(θ) decreases between pi/2 and (3/2)*pi.

And so on.

Here we have:

θ = x*(pi/2)

When x = 0, θ = 0.

And sin(θ) is increasing in θ = 0.

θ = pi/2 = x*(pi/4)

x = 2.

θ = (3/2)*pi = x*(pi/4)

(3/2)*pi*(4/pi) = 6 = x.

So at x= 6 the acceleration starts increasing again, and the acceleration is only defined until x = 10, then

Thus, during the first 10 seconds, in the intervals (0, 2) and (6, 10) the acceleration is increasing.

(2, 6)

(4, 8)

(0, 2) and (6, 10)

(0, 4) and (8, 10)

Answer:

3.50x + 2.25y smaller than or equal 7

Step-by-step explanation:

Let x represent the resistor and y represent the circuit board

Resistor: $3.50

Circuit board: $2.25

We know it can be bought at most for $7, so it will be smaller than or equal to $ 7. So, we have equation

3.50x + 2.25y smaller than or equal 7

Answer is 1. Polynomial Function is a quadratic, cubic, and of any degree function. It involves only a non - negative powers of x.

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Answer:

Step-by-step explanation:

domain

all real numbers, because the graph keeps going to the left and to the right

range

y ≥ 1 because the function starts in y = 1 and then keeps going up

Answer:

To solve this problem, we can use the formula for the area of a triangle, which is A=1/2bh, where b is the base and h is the height. In this problem, we are given that the area of the triangle is 128 square centimeters, so we can set up the following equation:

A = 1/2bh

128 = 1/2bh

We are also given that the height of the triangle is 8 centimeters greater than three times the base, so we can set up the following equation:

h = 3b + 8

We can substitute the second equation into the first equation to get the following:

128 = 1/2bh

128 = 1/2(3b + 8)b

128 = 3/2b^2 + 4b

We can then use the quadratic formula to solve for b, the base of the triangle:

b = (-4 +/- sqrt(4^2 - 4(3/2)(128)))/(2(3/2))

b = (-4 +/- sqrt(64 - 192))/3

b = (-4 +/- sqrt(-128))/3

Since the square root of a negative number is not a real number, we know that there is no solution to this equation, which means that the given information is not sufficient to determine the base of the triangle.

Therefore, the correct answer is that the base of the triangle cannot be determined from the information given.

To solve this problem, we can use the formula for the area of a triangle, which is A=1/2bh, where b is the base and h is the height. In this problem, we are given that the area of the triangle is 128 square centimeters, so we can set up the following equation:

A = 1/2bh

128 = 1/2bh

We are also given that the height of the triangle is 8 centimeters greater than three times the base, so we can set up the following equation:

h = 3b + 8

We can substitute the second equation into the first equation to get the following:

128 = 1/2bh

128 = 1/2(3b + 8)b

128 = 3/2b^2 + 4b

We can then use the quadratic formula to solve for b, the base of the triangle:

b = (-4 +/- sqrt(4^2 - 4(3/2)(128)))/(2(3/2))

b = (-4 +/- sqrt(64 - 192))/3

b = (-4 +/- sqrt(-128))/3

Since the square root of a negative number is not a real number, we know that there is no solution to this equation, which means that the given information is not sufficient to determine the base of the triangle.

Therefore, the correct answer is that the base of the triangle cannot be determined from the information given.

Yuki would have typed more than Neil at 10:30 AM and the inequality is 45×90+45 × x < 90 × x

We know that Neil started 90 minutes earlier than Yuki by subtracting the time difference So that tells us that

at 10:30 AM Neil would have typed 45 times 90. After x minutes he would have typed 45*90+45*x and Yuki would have typed 60*x.

Words typed by Yuki will be greater than those that will be Words typed by Neil

45×90+45 × x < 90 × x

When we will try in  Solving the above inequality would give us

x >90

it means that 90 minutes after 10:30 AM

Yuki would type more than Neil.

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The Median for n = 11 numbers will be 6th term of the Observation set.

One measure of central tendency is the median. The median is the number that lies in the middle of the specified range of integers. It separates the higher half from the lower half of a particular data sample. At least half of the observations are above or equal to the median, and at least half of the observations are below the median.

The median can be calculated as follows when there are odd numbers of observations in a data collection:

Step 1: Arrange the sample of data in ascending or descending order.

Step 2: If the number of observations (let's say n) is odd, the middle observation is the median of the given data.

Median = [tex](\frac{n+1}{2} )^{th}[/tex] term.

Here n = 11, So median will be 6th term of Observation set.

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As per the given origin, the potential at x = 3.0m is 143.0V

The term origin in math is referred as the initial point or the starting point from where we begin our calculations or measurements.

Here we have given that the potential at the origin is -140 V.

And we need to find the potential at x = 3.0m.

While we looking into the given question, we have identified that the region of space has a non-uniform electric field that points in the +x-direction and has magnitude and as the reference point, it take the potential at the origin to be -140 V .

Then the electric potential at x=3.0m is calculated as,

=> V(3) - 140 = 3.0

=> V(3) = 143.0

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The probability of both events occurring is 0.18.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true.

Since the person goes to store to buy clothes. the probability of the events are independent. the probability of buying a hat is 0.25. the probability of buying a pair of gloves is 0.72.

The probability of both events occurring will be:

= P(hat) × P(glove)

= 0.25 × 0.72

= 0.18

The probability is 0.18.

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Step-by-step explanation:

a linear function is defined as

y = ax + b

the variable x is only occurring with the exponent of 1.

this represents a straight line in a graphic representation (hence the name "linear").

if the exponent of the variable x is not 1, then it is not a linear function

P : y = 3/x + 2³

it is not linear.

the exponent of x = -1, as 1/x = x^-1. -1 is different to 1, which would be needed as exponent of x to make it linear.

Q : y = (1/3)x² + 3

it is not linear.

the exponent of x = 2. and 2 is different to 1, which would be needed as exponent of x to make it linear.

Therefore , the relationship of square root can be illustrated as [tex]y^{2}[/tex] = x.

A number's square root is that factor of the number that, when multiplied by itself, yields the original number. Specifically, squares and square roots are exponents. Think of the number nine. This can be expressed as [tex]3^{2}[/tex] or as 3 x 3.

Here,

In math, the square root of a number x is a number y such that y2 = x, or a number y whose square

(the result of multiplication by itself, or y), is x.

As an illustration, 4 and 4 are the square roots of 16, since 42 = (4)2 = 16.

Therefore , the relationship of square root can be illustrated as [tex]y^{2}[/tex] = x

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Answer:

$25000

Step-by-step explanation:

100% - 34% = 66%

We know that

66% = $16,500

We have to find 1%

16500 divided by 66 = $250

Then we have to find the 34%

250 times 34 = $8500

Then we add both numbers to find their previous year's revenue

$16500 + $8500 = $25000

So, their previous year's revenue is $25000

An asymptote is not the same as discontinuity.

An asymptote is a line or curve to which a function's graph draws closer without touching it. A vertical asymptote is a line that a function approaches but never quite touches. A vertical asymptote isn't always a discontinuity. It only matters if there's something "on the other side" since then how are you supposed to get across that gap without picking up your pencil? For instance ln(x) has a vertical asymptote at x=0 but it's no big thIng. But ln(|x|) (which is just ln(x) together with its "mirror image" on the negative side) is discontinuous.

An asymptote is not the same as discontinuity.

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The value of x for the congruent triangles will be equal to 10.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other. The meaning of congruency is that the two shapes are similar as well as equal in size.

Given that the angles are ∠E = 95, ∠F = 32 and ∠R=4x +13. The value of x will be calculated as,

Calculate the value of angle ∠G,

∠G = 180 - 32 - 95

∠G = 53

The value of x will be,

4x + 13 = 53

4x = 40

x = 10

Therefore, the value of x for the congruent triangles will be equal to 10.

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Answer: 7 dollars

Step-by-step explanation:

i think

Answer: A dollar is 100 cents, so you would add the 5 dimes and 12 quarters together. A dime is 10 cents so 10x5 is 50, so you would have 50 cents in dimes. A quarter is 25 cents, so you would multiply 12x25 and you would get 300 and you add those both together to get 350 cents. A dollar is 100 cents so you would have 3 dollars and the remaining 50 cents would stay 50 cents! <33

Step-by-step explanation:

The correct Inequality that shows the above situation is 55 + 9h ≥ 199, the error in the given expression is taking less than or equal to.

Inequality simply means that two things aren't equal. One of the items might be lower too, greater than, or equivalent to the others.

Mathematical expressions with inequalities are those in which the two sides are not equal.  

the signs we use in Inequalities are

 ≠ means not equal to

< means less than  

> means greater than  

≤ means less than or equal to

≥ means greater than or equal to                  

Here we have

The student already saved $ 55

She earns $ 9 per hour

The money that she needs to buy the bicycle is at least $ 199

Let's assume that she worked for h hours to earn at least $ 199

The amount that she earned after h hours = 9h

As we know she already saved $ 55

Finally the amount that she had = 55 + 9h

She wants at least $ 199 but not less than that, so the amount 55 + 9h must be greater than $ 199

=> 55 + 9h ≥ 199  

The expression that the student used is 55 + 9h ≤ 199, here error is taking less than or equal to.

Therefore,

The correct Inequality that shows the above situation is 55 + 9h ≥ 199, the error in the given expression is taking less than or equal to.  

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Answer:

Step-by-step explanation:

[tex]\displaystyle\\\frac{tan32^0+tan88^0}{1-tan32^0tan88^0} \ \ \ \ (1)\\\\Let\ \alpha =32^0\ and\ \beta =88^0\\\\Hence,\ expression\ (1)\ will \ look\ like\ this:\\\\\frac{tan\alpha +tan\beta }{1-tan\alpha tan\beta }\\[/tex]

The trigonometric formula for adding angles for a tangent is as follows:

                              [tex]\displaystyle\\\\\boxed {tan(\alpha +\beta )=\frac{tan\alpha +tan\beta }{1-tan\alpha tan\beta }}[/tex]

Thus,

[tex]\displaystyle\\\frac{tan32^0 +tan88^0 }{1-tan32^0 tan88^0 }=tan(32^0+88^0)\\\\\\\frac{tan32^0 +tan88^0 }{1-tan32^0 tan88^0 }=tan120^0[/tex]

Calculate the value of tan120°:

[tex]tan120^0=tan(90^0+30^0)\\\\tan120^0=-cot30&^0\\\\tan120^0=-\sqrt{3}[/tex]

So,

[tex]\displaystyle\\\frac{tan32^0 +tan88^0 }{1-tan32^0 tan88^0 }\equiv-\sqrt{3}[/tex]

The next three number is 1/125, 1/625, 1/3125.

What is pattern?

A recurring arrangement of numbers, forms, colours, and other elements constitutes a pattern in mathematics. The Pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern. Patterns can also occasionally be referred to as a series.

Given pattern is 25, 5, 1, 1/5,  1/25.

Assume first term is a₁ = 25

The second term is a₂ = 5

The third term is a₃ = 1

The fourth term is a₄ = 1/5

The fifth term is a₅ = 1/25

The ratio of each consecutive term is

a₂/a₁= a₃/a₂ = a₄/a₃ = a₅/a₄ = 1/5.

The 6th term is a₆ = (1/25)× (1/5) = 1/125

The 7th term is a₇ = (1/125) × (1/5) = 1/625

The 8th term is a₈ = (1/625) × (1/5) = 1/3125

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Answer:

3. B

4. C

Tell me if you need an explanation, I can add it for you :D