Donner un encadrement d’amplitude 10^-p des réels donner, l’entier p étant précisée pour chaque cas

The equation of the line that goes through the points (-1,-3) and (3, 5) is y = 2x -2.

What is the equation of the line?

A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.

We have given:

the line that goes through the points (-1,-3) and (3, 5).

The two-point form of a line passing through these two points is:

y − y1 = (y2-y1)/(x2-x1) * (x - x1)

Here, (x, y) represents any random point on the line and we keep 'x' and 'y' as variables.

So,

y − (-3) = (5-(-3))/(3-(-1)) * (x - (-1))

y +3 = (5+3)/(3+1) * (x+1)

y +3 = 8/4 * (x+1)

y = 2x + 1 -3

y = 2x -2

hence, the equation of the line that goes through the points (-1,-3) and (3, 5) is y = 2x -2.

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The amount of the drug present in the bloodstream after 10 hours is approximately 239 mg.

The amount of the drug A(t), in mg, present in the bloodstream t hours after being intravenously administered can be approximated by the exponential function,

A(t) = −1000e^−0.3t + 1000.

According to the given function,

A(t) = −1000e^−0.3t + 1000.

The amount of the drug present in the bloodstream after 10 hours can be found by substituting t = 10 in the given function.

A(10) = −1000e^−0.3(10) + 1000

= −1000e^−3 + 1000

≈ 239mg (rounded to the nearest whole number).

Therefore, the amount of the drug present in the bloodstream after 10 hours is approximately 239 mg.

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Answer:

ok

Step-by-step explanation:

Answer: 9424.78

Step-by-step explanation V=πr2h=π·102·30≈9424.77796

The basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.

The given piecewise-defined function f(x) has different expressions for different intervals. For x greater than or equal to zero, f(x) takes the value of x. For x less than zero, f(x) is equal to -x. We need to find a basic function that captures this behavior.

Among the options provided, f(x) = |x| is equivalent to the given piecewise function. The absolute value function, denoted by |x|, returns the positive value of x regardless of its sign. When x is non-negative, |x| equals x, and when x is negative, |x| is equal to -x, mirroring the conditions of the piecewise-defined function.

The function f(x) = |x| represents the absolute value of x and matches the behavior of the given piecewise-defined function, making it the equivalent basic function.

In summary, the basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.

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The equation of the function is y = 10 * sin(x/2pi) + 5.

What is the sinusoidal function?

The period of a sinusoidal function is the time it takes for the sinusoidal function to complete one cycle of revolution.

The graph of a sinusoidal function can be represented by the equation:

y = A * sin(B(x - C)) + D

where A is the amplitude, B is the frequency, C is the horizontal shift, and D is the vertical shift.

From the information given, we know that the maximum point is at (0,5) and the minimum point is at (2pi,-5). We can use this information to find the values of A, B, C, and D.

The amplitude is the distance between the maximum and minimum points. In this case, it is 5 - (-5) = 10. So A = 10.

The period of the function is the distance between two consecutive maximum or minimum points. In this case, it is 2π.

So the frequency is 1/2π.

The horizontal shift is the amount by which the function is shifted along the x-axis. In this case, the maximum point is at x = 0, so the function is not shifted horizontally. So C = 0.

The vertical shift is the amount by which the function is shifted along the y-axis. In this case, the maximum point is at y = 5, so the function is shifted upward by 5. So D = 5.

So the equation of the function is:

y = 10 * sin(1/2pi (x - 0)) + 5

y = 10 * sin(x/2pi) + 5

where x is entered in radians.

Hence, the equation of the function is y = 10 * sin(x/2pi) + 5.

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The probability that at most two customers purchase the investment is 0.1875 or 18.75%.

To calculate the probability that at most two customers purchase the investment,  to calculate the probabilities for each possible outcome: 0, 1, and 2 customers purchasing the investment, and then sum them up.

Let's consider the customers as A, B, C, and D, with D being the fourth customer.

Probability of 0 customers purchasing:

P(0 customers) = (1 - probability of sale)²number of customers

= (1 - 0.5)²4

= 0.0625

Probability of 1 customer purchasing:

P(1 customer) = (probability of sale)²1 ×(1 - probability of sale)²3 (since 3 customers won't purchase)

= 0.5²1 ×0.5²3

= 0.5 × 0.125

= 0.0625

Probability of 2 customers purchasing:

P(2 customers) = (probability of sale)²2 × (1 - probability of sale)²2 (since 2 customers will purchase)

= 0.5²2 ×0.5²2

= 0.25 × 0.25

= 0.0625

Now  sum up these probabilities to find the probability that at most two customers purchase the investment:

P(at most 2 customers) = P(0 customers) + P(1 customer) + P(2 customers)

= 0.0625 + 0.0625 + 0.0625

= 0.1875

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Answer:

11.75$

Step-by-step explanation:

do 94 divided by 8. You get 11.75, so each ticket costs 11 dollors and 75 cents

Anorexia nervosa is a serious eating disorder characterized by a distorted body image, an intense fear of gaining weight, and an obsession with food, dieting, and weight loss.

Some of the common traits that may be displayed by a person with anorexia nervosa include:

Severe weight loss

Refusal to maintain a normal body weight

Distorted body image

Obsessive thoughts about food, calories, and weight

Preoccupation with food preparation and rituals around eating

Avoidance of social situations that involve food

Excessive exercise

Perfectionism and high achievement orientation

Anxiety, depression, and other emotional disorders

It is important to note that anorexia nervosa is a complex disorder that can manifest differently in different people, and not all individuals with anorexia nervosa will display all of these traits. It is also important to seek professional help if you or someone you know is struggling with an eating disorder.

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Answer:

8 and -18

Step-by-step explanation:

Answer:

1.20

Step-by-step explanation:

5 bars = 3.00

1 bar = 0.60

2 bars = 0.60 x 2 =1.20

The relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”.

Now, According to the question:

What is inequality?

A statement involving the symbols '>', '<', ' ≥', '≤' is called an inequality. For example 5 > 3, x ≤ 4, x + y ≥ 9.

(i) Inequalities which do not involve variables are called numerical inequalities. For example 3 < 8, 5 ≥ 2.

We use the equal sign "=" to say that two things are the same. However, sometimes we just want to show that something is bigger or smaller than something else. Or maybe we just want to say that two things are not equal. These cases are called inequalities.

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Step-by-step explanation:

18/24=>9/12=>3/4

=>3:4

Answer:

Step-by-step explanation:

18 = 2 * 3 * 3

24 = 2 * 2 * 2 * 3

GCF = 2*3 = 6

18: 24 = 18÷6  : 24÷6

           = 3 :  4

Using Algebra operation,

the total revenue from ticket sales on that day is $ 3444..

We have given the following information,

timing of museum for entry is 9:00 am to 5:55pm. i.e 8 hours 55 minutes .

price of ticket for a regular admission= $10

price of ticket for a student admission = $6

30 people's admission in every 5 minutes so,

inclusive there are 9×12=108 five-minute intervals, total of tickets were sold = 108× 30

= 3240

let x student and 3x regular tickets were sold on that day.

then, x+3x= 108× 30 –> x= 3240/4 = 810

put x= 7560 in above formula, for regular admission, 3x=3× 81 = 243

So, the total revenue from ticket sales that day was 243×$10 + 810×$6 = $2430 + $4860

= $7290

Hence, total revenue from tickect sales is $7290.

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Performing a change of scale we will see that the actual distance is 4 miles.

We know that the scale is:

3/4 inch = 2 miles.

And the distance that Nicole found on the map is (1 + 1/2) inches.

We can rewrrite the scale as:

1 inch = (4/3)*2 miles

1 inch = (8/3) miles.

Then the actual distance will be:

distance = (1 + 1/2) inches = (1 + 1/2)*(8/3) miles = 4 miles.

The correct option is A.

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Answer:

\(\boxed{9}\)

Step-by-step explanation:

\(\sf of \ refers \ to \ multiplication.\)

\(12.5\% \times 72\)

\(\frac{12.5}{100} \times 72\)

\(\sf Multiply.\)

\(\frac{900}{100} =9\)

Answer:

\(7n-6, \: 4n+8\)

Step-by-step explanation:

\(+7\) difference.

So it becomes \(7n\).

\(7(1)+c=1\)

\(c=-6\)

Therefore, the nth term becomes:

\(7n-6\)

\(+4\) difference.

So it becomes \(4n\).

\(4(1)+c=12\)

\(c=8\)

Therefore, the nth term becomes:

\(4n+8\)

Answer:

a) 7n-6

b) 4n+8

Explanation:

a) 7 times tables but take away 6 for the start

b) 4 times tables but add 8 for the start

The four triangle congruence theorems are SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle) and AAS (Angle-Angle-Side).

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The length of a vector 'v' in an n-dimensional Euclidean space is calculated as the square root of the dot product of the vector with itself, or ‖v‖ = \(\sqrt{(v.v)}\) = \(\sqrt{(v1^{2}+v2^{2} +.... + vn^{2} )}\).

The length of a vector 'v' in an n-dimensional Euclidean space is denoted as ‖v‖ and can be calculated asthe vector's dot product with itself, square root:

‖v‖ = \(\sqrt{(v.v)}\) = \(\sqrt{(v1^{2}+v2^{2} +.... + vn^{2} )}\)

So, to find the length of the vector 'v', we simply substitute its components in the above equation.

The length of a vector, also known as its magnitude or norm, is a scalar value that represents the magnitude of the vector in a given space. In the context of an n-dimensional Euclidean space, the length of a vector can be calculated as the square root of the dot product of the vector with itself. This calculation is based on the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares formed by the other two sides' lengths.

In mathematical terms, the length of a vector 'v' in an n-dimensional Euclidean space is calculated as follows:

‖v‖ = \(\sqrt{(v.v)}\) = \(\sqrt{(v1^{2}+v2^{2} +.... + vn^{2} )}\)

where 'v' is the vector, and 'v1', 'v2', ..., 'vn' are its components in the n-dimensional space. The dot product of the vector with itself (v · v) is equivalent to the sum of the squares of its components. The square root of this sum is the final length of the vector.

The length of a vector is an important concept in linear algebra and geometry. It is used to measure the distance between two points in a space, to calculate angles between vectors, to normalize vectors, and for various other mathematical and practical applications.

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It is of the form, ax +by +c = 0, where a, b and c are real numbers, and both a and b not equal to zero. Equations of the form ax + by = 0; where a and b are real numbers, and a, b ≠ 0, is also linear equations in two variable.

Now, According to the question:

Equations of degree one and having two variables are known as linear equations in two variables. It is of the form, ax +by +c = 0, where a, b and c are real numbers, and both a and b not equal to zero.

Equations of the form ax + by = 0; where a and b are real numbers, and

a, b ≠ 0, is also linear equations in two variable.

Solution of a Linear Equation in Two Variables:

The solution of a linear equation in two variables is a pair of numbers, one for x and one for y which satisfies the equation. There are infinitely many solutions for a linear equation in two variables.

For example,  x+2y =6 is a linear equation and some of its solution are (0,3),(6,0),(2,2) because, they satisfy  x+2y=6.

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Answer:

2

Step-by-step explanation:

The Y intercept is 2.

You can figure this out by looking at the Y line (the vertical one) and seeing theres a point exactly on 2, when the X number is at 0.

2

Hope it helps.

Do comment if you have any query.

The resulting matrix after scalar multiplication by -24 is a 3x3 matrix with elements -24, -48, -72, -96, -120, -144, -168, -192, and -216.

To perform scalar multiplication, each element of the matrix is multiplied by the scalar value -24. This results in the following calculation:

-24 * [1 2 3; 4 5 6; 7 8 9] = [-24 * 1 -24 * 2 -24 * 3; -24 * 4 -24 * 5 -24 * 6; -24 * 7 -24 * 8 -24 * 9]

Simplifying the expression gives us:

[-24 -48 -72; -96 -120 -144; -168 -192 -216]

Therefore, the resulting matrix after scalar multiplication by -24 is a 3x3 matrix with elements -24, -48, -72, -96, -120, -144, -168, -192, and -216. Each element in the original matrix is multiplied by -24 to obtain the corresponding element in the resulting matrix.

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The equation of the line that passes through the point (5,3) and has a slope of -4/5 is,

⇒ 4x + 5y = 35

Here,

The given point is (5, 3) and slope is -4/5.

We have to find the equation of the line that passes through the point (5,3) and has a slope of -4/5.

What is Equation of line?

The equation of the line that passes through the point (a, b) and has a slope of m is;

⇒y - a = m (x - b)

Now,

The given point is (5, 3) and slope is -4/5.

Hence, The equation of the line that passes through the point (5,3) and has a slope of -4/5 is;

y - 3 = -4/5 (x - 5)

5 (y - 3) = -4 (x - 5)

5y - 15 = -4x + 20

4x + 5y = 20 + 15

4x + 5y = 35

Therefore, The equation of the line that passes through the point (5,3) and has a slope of -4/5 is

⇒ 4x + 5y = 35.

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Answer:

9/14

Step-by-step explanation:

2/7÷4/9=9/14

Solution with Steps

2/7÷4/9=?

Dividing two fractions is the same as multiplying the first fraction by the reciprocal (inverse) of the second fraction.

Take the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes

2/7×9/4=?

For fraction multiplication, multiply the numerators and then multiply the denominators to get

2×9/7×4=1/8 2/8

This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 18 and 28 using

GCF(18,28) = 2

1/8÷2 2/8÷2=9/14

Therefore:

2/7÷4/9=9/14

The result of 2/7 divided by 4/9 in simplest form is 9/14 .

Hence option D is correct.

Division: It is one of the four basic mathematical operation, the other three being addition, subtraction, multiplication.

Given, that 2/7 divided by 4/9 .

Division of fractional terms :

= \(\dfrac{\frac{a}{b}}{\frac{c}{d}}\)

= \(a \times d/b\times c\)

Apply division process on fractional terms,

= \(\dfrac{\frac{2}{7}}{\frac{4}{9}}\)

= \(2 \times 9/ 7 \times4\)

= \(\frac{18}{28}\)

= \(\frac{9}{14}\)

Thus option D is correct.

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Answer:

\(y = -2x + 10\)

Step-by-step explanation:

Slope: \(m = \frac{y_{2}-y_{1} }{x_{2}-x_{1}}\)

Slope-Intercept Form: \(y=mx+b\)

\(m=\frac{8-0}{1-5}\)

\(m = -2\)

\(y = -2x + b\)

\(0 = -2 (5)+b\)

\(0=(-10)+b\)

\(b = 10\)

\(y = -2x + 10\)

Answer:

(f - g)(x) = -x² + 2x + 8

Step-by-step explanation:

Step 1: Plug in variables

2x + 1 - (x² - 7)

Step 2: Distribute the negative

2x + 1 - x² + 7

Step 3: Combine like terms

-x² + 2x + 8

Answer:

  -x^2 +2x +8

Step-by-step explanation:

F(x) = 2x+1

g(x) =x^2-7

(f-g) (x) =2x+1  - ( x^2 -7)

   Distribute the minus sign

           = 2x+1 -x^2 +7

           -x^2 +2x +8

Answer:

Step-by-step explanation:

To find the x-intercept and y-intercept of the equation we need to understand what is an intercept. Intercept means to intersect/cut so x-intercept means the equation cuts the x-axis and y-intercept means the equation cuts the y-axis.

So if the equation cuts the x-axis the coordinate should be \((x,0)\)  and if the equation cuts the y-axis the coordinate should be \((0,y)\) , and since the equation satisfies these both points in other words these two points lie on the line they can be put into the equation. So here we go,

For x-intercept

\(x+2y=10\\x+2(0)=10\\x=10\)

so the x-intercept is (10,0)

For y-intercept

\(x+2y=10\\0+2y=10\\2y=10\\y=10/2\\y=5\)

so the y-intercept is (0,5)

I also have attached an example of how intercepts looks like you can take a look i plotted the graph an you can see our answers check out.