1. Utilice la función y=0.17% - 3.0 para encontrar lo siguiente.
a) Estime la pendiente de la recta tangente a la curva, donde x = 0,1,2,3.
Pendiente de la recta
Х
tangente
-1
O
1
3
b) ¿en qué intervalos aumenta la función? ¿En qué intervalos está disminuyendo?
c) ¿En qué intervalo o intervalos es positiva la pendiente de la recta tangente? ¿E
intervalo o intervalos es negativa la pendiente de la recta tangente? ¿Cuál es la c
estas preguntas y la parte (b)
c) ¿Dónde parece que la pendiente de la recta tangente es cero? ¿Qué propiedad
gráfica ocurren en estos puntos?
d) ¿Dónde parece la línea tangente aproximarse mejor a la curva? ¿Lo peor? ¿Qu
del gráfico parecen hacer que sea así?

If the length of the rectangle be (3x+2) units and width (4x+10)units then the area of the rectangle be \($x=-\frac{2}{3}, x=-\frac{5}{2}$$\).

The region enclosed by an object's shape is referred to as the area. The area of the shape is the area that the figure or any other two-dimensional geometric shape occupies in a plane.

A rectangle's sides determine its area. In essence, the length and breadth of the rectangle multiplied together gives the area of the rectangle.

Let the length of the rectangle be (3x + 2) units and width of the rectangle be (4x + 10)units.

Area of rectangle = length × breadth

= (3x +2) × (4x +10)

simplifying the above equation, we get

= (3x) × (4x +10) + 2(4x +10)

= 12x² + 30x +8x +20

12x² + 38x + 20 = 0

simplifying the above equation, we get

By using quadratic equation, then

\($x_{1,2}=\frac{-38 \pm \sqrt{38^2-4 \cdot 12 \cdot 20}}{2 \cdot 12}$$\)

simplifying the above equation, we get

\($$\begin{gathered}x_{1,2}=\frac{-38 \pm 22}{2 \cdot 12}\end{gathered}$$\)

Separate the solutions, we get

\($$\begin{aligned}& x_1=\frac{-38+22}{2 \cdot 12}, x_2=\frac{-38-22}{2 \cdot 12} \\& x=\frac{-38+22}{2 \cdot 12}:-\frac{2}{3} \\& x=\frac{-38-22}{2 \cdot 12}:-\frac{5}{2}\end{aligned}$$\)

The solutions to the quadratic equation are:

\($x=-\frac{2}{3}, x=-\frac{5}{2}$$\)

The complete question is:

Find the area of rectangle with length (3x+2) units and width (4x+10)units.

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Answer:

1

Step-by-step explanation:

The value of expression is 1.

An expression in math is a sentence with a minimum of two numbers/variables and at least one math operation in it. Let us understand how to write expressions. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division. The terms involved in an expression in math are:

Constant: A constant is a fixed numerical value.

Variable: A variable is a symbol that doesn't have a fixed value.

Term: A term can be a single constant, a single variable, or a combination of a variable and a constant combined with multiplication or division.

Coefficient: A coefficient is a number that is multiplied by a variable in an expression.

Given:

x²-3y + 12

Now, solving for x= -2 and y= 5

=(-2)²-3(5) + 12

=4 - 15 + 12

=-11 + 12

=1

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C

1) Gathering the data:

2014

X Country 783 miles

2015

X Country

8n

2) Since there were already 783 miles of paved road. We can write the function as:

F(n) =8n +783

The given statement to reduce a rational number to its lowest terms, you first compute the greatest common divisor (gcd) of the numerator and the denominator, using Euclid's algorithm is correct.

What is Euclid's algorithm?

The Euclidean algorithm, also known as Euclid's algorithm, is an effective way to determine the greatest common divisor of two integers, or the biggest number that divides them both evenly without leaving a remainder. It is named after the Greek mathematician Euclid, who first discussed it in his Elements and gave it that name.

A common fraction can be reduced to its simplest terms using the Euclidean algorithm. For instance, the algorithm will demonstrate that the GCD of 765 and 714 is 51, and that 765/714 = 15/14 as a result. Additionally, it has several applications in more complex mathematics.

Hence, the given statement to reduce a rational number to its lowest terms, you first compute the greatest common divisor (gcd) of the numerator and the denominator, using Euclid's algorithm is correct.

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The time needed for Aujah to safely drink her chocolate is given as follows:

101 minutes.

The equation for this problem is defined as follows:

T(x) = 71.1 + 29.4e^(-0.02x).

The chocolate can be safely drank when the temperature is of T(x) = 75ºC, hence the time is obtained as follows:

75 = 71.1 + 29.4e^(-0.02x).

We can solve for x applying the natural logarithm, which is the inverse of the exponential, as follows:

29.4e^(-0.02x) = 3.9

e^(-0.02x) = 3.9/29.4

-0.02x = ln(3.9/29.4)

x = ln(3.9/29.4)/-0.02

x = 101 minutes.

On the graphing calculator, you should input two functions.

The time is the intersection of these points, the value of x in this case.

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Answer:  Approximately 22.62 degrees

===============================================

Work Shown:

cos(angle) = adjacent/hypotenuse

cos(y) = 12/13

y = arccos(12/13)

y = 22.6198649

y = 22.62

Notes:

Answer:

10 m/s

Step-by-step explanation:

Unit stands for one so

120 meters in 12 seconds in 10 meters a sec

Answer:

11

Step-by-step explanation:

2x+3=x+7

x=4

Plug 4 into Ad which is 2x+3 and you get 11

The y-intercept of any function is the value of the function when x = 0.

Therefore, g(x) has the greatest y-intercept.

Answer:

0.0138

Step-by-step explanation:

The probability of getting exactly 4 questions right by guessing can be calculated using the binomial probability formula:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where n is the number of trials (17 questions), k is the number of successes (4 correct answers), p is the probability of success on a single trial (1/5 for guessing), and (n choose k) is the binomial coefficient.

Plugging in the values, we get:

P(X = 4) = (17 choose 4) * (1/5)^4 * (4/5)^13

P(X = 4) ≈ 0.0138 (rounded to four decimal places)

Therefore, the probability that the student will get exactly 4 questions right by guessing is approximately 0.0138.

One solution was found :

                   x = 9

Answer:

Hi,

Step-by-step explanation:

I suppose you want an integer solution.

Let's say

a the number of gallons of 35% alcohol

b the number of gallons of 50% alcohol

\(\dfrac{35}{100}*a+\dfrac{50}{100}*b=\dfrac{40}{100}*6\\\\35*a+50*b=240\\\\7a+10b=48\\\\b=\dfrac{48-7a}{10}\\\\a=4+10*n\\\\b=\dfrac{48-7*(4+10*n)}{10}=2-7*n\\\\As\ b\ must\ be\ a\ positive\ number \ n=0\\\\so\ b=2\ and\ a= 4\)

The product of 83 and 4.5 \times 10^64.5×106 is expressed in scientific notation is 830*10^-12.

Scientific notation can be described as the representation of the large numbers or very small numbers in the standard form which can be seen in the final answer of this question , it do make the handling of numbers to be easier when making a calculation.

From the question, we are asked for the product of 83 and 4.5 \times 10^64.5×10^6,

Then we can multiply 10^6 * 4.5×10^6 which is (4.5*10^11)

Then 4.5/(4.5*10^11) = 10 *10^-12

Then we can found the product  expression as (83* 10 *10^-12) = 830*10^-12.

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For the given expression the value of \((f^{-1})'(3)\) ≈ 0.052.

What is expression?

In mathematics, an expression is a combination of numbers, variables, operators, and symbols that represents a mathematical quantity or relationship.

To find the derivative of the inverse function, we use the formula:

\((f^{-1})'(x) = 1 / f'(f^{-1}(x))\)

First, we need to find the inverse function \(f^{-1(x)\). To do that, we can solve for x in terms of f(x):

\(f(x) = (1/4)x^3 + x - 1\\y = (1/4)x^3 + x - 1\\x^3 + 4x - 4 = 4y\\x^3 + 4x - 4 = 4f^{-1}(x)\\f^{-1}(x) = (x^3 + 4x - 4) / 4\)

Now, we can find the derivative of the inverse function:

\((f^{-1})'(x) = 1 / f'(f^{-1}(x))\\(f^{-1})'(3) = 1 / f'(f^{-1}(3))\)

To find \(f^{-1}(3)\), we plug in x = 3 into the expression for \(f^{-1}(x)\):

\(f^{-1}(3) = (3^3 + 4(3) - 4) / 4 = 8.75\)

To find \(f'(f^{-1}(3))\), we plug in \(f^{-1}(3) = 8.75\) into the expression for f'(x):

\(f'(8.75) = (3/4)(8.75)^2 + 1 = 19.2031\)

Now we can find the derivative of the inverse function at x = 3:

\((f^{-1})'(3) = 1 / f'(f^{-1}(3))\\(f^{-1})'(3) = 1 / f'(8.75)\\(f^{-1})'(3) = 1 / 19.2031\)

\((f^{-1})'(3)\) ≈ 0.052

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Answer:

0.0008032

Step-by-step explanation:

Hope this helps!

Answer:

80,320

Step-by-step explanation:

Answer:

26 in each box

Divide the total of 338 peanuts by 13 boxes (338÷13=26)

Answer:

15.6

Step-by-step explanation:

complementary angles sum up to 90

90-74.4=15.6

therefore the measure of it's complementary angle is 15.6

Step-by-step explanation:

c = number of cars used

v = number of vans used

5c + 12v = 60

as the sum of all students in cars and vans must be 60.

but this does not consider solutions with partly filled cars or vans.

1) Number of participants whose headache remained is: 62

2) The probability of randomly selecting an individual whose headache remained is: 0.4133

3) The probability of randomly selecting an individual whose headache remained and took a placebo is: 0.2933

From the table, we have the parameters as:

Number of participants that took medicine and headache went away = 120

Number of participants that took placebo and headache went away = 68

Number of participants that took and headache remained = 18

Number of participants that took placebo and headache remained = 44

1) Number of participants whose headache remained = 18 + 44 = 62

2) The probability of randomly selecting an individual whose headache remained is:

62/(62 + 120 + 68)

= 62/150

= 0.4133

3) The probability of randomly selecting an individual whose headache remained and took a placebo is:

44/150 = 0.2933

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Answer: c) P(C) = 1/3

Step-by-step explanation:

P(A) + P(B) + P(C) = 1     (100%)

P(A) = P(B) =P(C)

Using substitution:

P(C) + P(C) + P(C) = 1

                 3 P(C) = 1

                    P(C) = 1/3  

The criteria should be used to prove that the pair of triangles are congruent, as mentioned below.

What is congruent of the triangle?

The shapes maintain their equality regardless of how they are turned, flipped, or rotated before being cut out and stacked. We'll see that they'll be placed entirely on top of one another and will superimpose one another. Due to their identical radius and ability to be positioned directly on top of one another, the following circles are considered to be congruent.

Any two figures can be perfectly positioned over one another to demonstrate their congruence. The relationship between two figures that are said to be congruent is described using the word "congruence."

The angle-Side-Angle congruence rule is referred to as ASA. Two triangles are said to be congruent according to this rule if any two angles and the side included between them of one triangle are equal to the corresponding angles and the included side of the other triangle.

Hence, these above criteria should be used to prove that pair of triangle are congruent.

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The value of f(x) when x is 3 is 15

A Function in mathematics is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

For example, if f(x) = x² +2x +5 , the value of f(x) when x is 2 is calculated as;

f(x) = 2² + 2(2) + 5

f(x) = 4 +4+5

= 13

This done by substituting the given value of x into the expression.

Similarly , if f(x) = 5x, the value of f(x) when x is 3 is calculated as;

f(x) = 5(3)

f(x) = 15

therefore the value of f(x) when x is 3 is 15

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Answer:

the slope should be -4

Step-by-step explanation:

to find the slope we use the equation y2 - y1/ x2 - x1

-15 - (-7) / 5 - 3

-15 + 7 / 2

-8 / 2

-4

m=\(\frac{y2-y1}{x2-x1}\)

m=\(\frac{2+3}{4-1} \\\frac{5}{3}\)

So the slope is 5/3

Hope this helps you!

~Just a joyful teen

\(GraceRosalia :)\)

Notice that:

Therefore,

Answer: gh.

To solve the expression 1 - (1 + 0.04/12)^(-12x10), you can follow these steps: Step 1: Simplify the exponent. In this case, -12x10 simplifies to -120.

Step 2: Evaluate the term within the parentheses first. 0.04/12 simplifies to 0.0033333 (approximately).

Step 3: Add 1 to 0.0033333 to get 1.0033333.

Step 4: Raise 1.0033333 to the power of -120.

Step 5: Calculate the value inside the parentheses using a calculator or software. The result is approximately 0.742657.

Step 6: Subtract the value obtained in Step 5 from 1.

1 - 0.742657 = 0.257343 (approximately).

Hence, the value of the expression 1 - (1 + 0.04/12)^(-12x10) is approximately 0.257343.

It's important to follow the order of operations (PEMDAS/BODMAS) when solving mathematical expressions. In this case, the exponent is evaluated first, followed by addition and subtraction. Utilizing a calculator or software that supports exponentiation and parentheses can help simplify complex expressions and obtain accurate results efficiently.

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Answer:

1/12

Step-by-step explanation:

\( - \frac{11}{16} \times - \frac{4}{33} \)

if you know how to cancel, you can cancel the 4 and 16. The 4 becomes a 1 and 16 becomes a 4. Next cancel the 11 and 33. the 11 becomes a 1 and the 33 becomes a 3.

\( - \frac{1}{4} \times - \frac{1}{3} \)

multiply, two negatives make a positive

\( \frac{1}{12} \)

Given the dimensions of the rectangular solid as:

The formula for the surface area of the solid is

The formula for the volume of the solid is

The surface area is 3944 feet^2

The volume is 16800 feet^3