Recopier et compléter les égalités suivantes :

a.26/....=13/6
b..../15=19/3
c...../27=7/3
d.17/....=85/95

The definition of the piece-wise function is:

A piece-wise function is a function that has different definitions, depending on the input.

In this problem, for inputs between -2 and 2, the function is a line that goes through (-2,-4) and (2,6). The slope is:

m = (6 - (-4))/(2 - (-2)) = 2.5.

The y-intercept is of b = 1, hence the rule is:

\(f(x) = 2.5x + 1, -2 \leq x \leq 2\)

For x greater than 2 and less than 6, the function is constant at -3, hence the rule is:

\(f(x) = -3, 2 < x < 6\).

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Answer:

\(y = 5\)

Step-by-step explanation:

Given function:

\(y=\dfrac{5x}{x+6}\)

\(\implies y=5 \left( \dfrac{x}{x+6}\right)\)

\(\textsf{As }x \rightarrow +\infty, \ \dfrac{x}{x+6} \rightarrow1\)  

\(\implies y\rightarrow5\)

\(\textsf{As }x \rightarrow -\infty, \ \dfrac{x}{x+6} \rightarrow1\)  

\(\implies y\rightarrow5\)

As \(x\) approaches infinity and negative infinity, \(y\) approaches 5 (but never gets there).    Therefore, the horizontal asymptote is \(y=5\)

Answer:

slope = \(\frac{2}{3}\)

Step-by-step explanation:

calculate the slope m using the slope formula

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

with (x₁, y₁ ) = (0, - 4) and (x₂, y₂ ) = (6, 0) ← 2 points on the line

m = \(\frac{0-(-4)}{6-0}\) = \(\frac{0+4}{6}\) = \(\frac{4}{6}\) = \(\frac{2}{3}\)

\(4x^2+20x-24 = 4x^2-4x+24x-24 = 4x(x-1)+24(x-1) = (4x + 24)(x-1)\\\)

\(= 4(x+6)(x-1)\)

Answer:

village market

Step-by-step explanation:

5 times 2.30 =11.5

10 times 5.10 =51

11.5 times 2 =23

51 to 23

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Answer:

Answer vary:

The better buy is 5 cans of green beans at the Village Market.

Step-by-step explanation:

honestly in my opinion that‘s my answer.

if 10 cans cost $5.10 and 5 cans cost $2.30, think about if you add another $2.30 for another 5 cans the cost is $4.60 and you get 10 cans. and that’s obviously cheaper than the other buy.

10 cans = $5.10

5 cans = $2.30.    

(the 5 can offer)

2.30+2.30= $4.60

The measure of angle K and L in the first figure is ∠L = 23 degrees and ∠K = 157. Second figure, the measure of ∠K = ∠L = 70 degrees.

A polygon's interior angle is the angle created between its two adjacent sides. Alternately, we may state that the internal angle of a polygon refers to the angle measured at the interior portion of a polygon.

For figure 2 the two lines are parallel to each other, and the line that meets the parallel line at points at M and L are from two equal lines.

Hence, the angle suspended by both are equal, that is:

∠L = ∠M

∠L = 23 degrees.

Now, the ∠K and ∠J are created by two parallel lines; hence they are equal:

∠K = ∠J = x

The sum of interior angles of a quadrilateral is 360, so:

∠L + ∠M + ∠J + ∠K = 360

23 + 23 + x + x = 360

46 + 2x = 360

2x = 360 - 46

x = 157

Hence, the measure of angle K and L is 157 and 23 respectively.

For the second figure, the angle K and L are created by equal length of segments.

∠K = ∠L = x

The sum of interior angles of a quadrilateral is 360, so:

∠L + ∠M + ∠J + ∠K = 360

x + 90 + 130 + x = 360

2x + 220 = 360

2x= 360 - 220

x = 70

Hence, the angle of K and L is 70 degrees.

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Answer:

Let the number of shirts he sold the first week = x    and the number sold the second week = 100 - x

So we have      

[Sales] - [Cost] = Profit

[25x + 20(100 - x)] - [15 * 100]  = 600     simplify

25x + 2000 - 20x - 1500 = 600

5x + 500  = 600      subtract 500 from both sides

5x = 100          divide both sides by 5

x = 20 =   the number of shirts sold the first week

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

Let x = number of shirts sold in Week 1

Let y = number of shirts sold in Week 2

Profit = Selling price - cost price

If Billy purchased the shirts at a cost of $15 each, then

Equation 1

Total of 100 shirts purchased:

⇒ x + y = 100

Equation 2

Total profit of $600:

⇒ 10x + 5y = 600

Rewrite Equation 1 to make y the subject:

⇒ y = 100 - x

Substitute this into Equation 2 and solve for x:

⇒ 10x + 5(100 - x) = 600

⇒ 10x + 500 - 5x = 600

⇒ 10x - 5x + 500 = 600

⇒ 5x + 500 = 600

⇒ 5x = 600 - 500

⇒ 5x = 100

⇒ x = 100 ÷ 5

⇒ x = 20

Therefore, Billy sold 20 shirts in his first week.

Answer:

Hmmm... let me see about this...

The macrostate s of two six-sided dice can be defined as the sum of the top faces of the dice.

The macrostate of a system refers to a comprehensive description of the system in terms of its properties and variables that are used to characterize it. In the case of two six-sided dice, the macrostate is described by the sum of the numbers on the top faces of the two dice, which determines the total score or outcome. This macrostate, represented by the variable "s", is a measurable quantity that summarizes the state of the system, providing information about the distribution of the outcomes over all possible configurations of the two dice.

It's important to note that a macrostate does not specify the exact configuration of the system, but rather provides a probabilistic description of it. In other words, the macrostate "s" only describes the sum of the two dice and does not specify which number is on each die. In thermodynamics, macrostates are used to characterize the thermodynamic properties of a system, such as its temperature, pressure, and entropy. The study of macrostates and their distributions helps us to understand the behavior of complex systems and make predictions about their future behavior.

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Answer:

C. Check the intersecting lines with the corner of a piece of paper to ensure the lines create 90° angles. Took the test just now and got it right

Step-by-step explanation:

Since the line that we need to figure out is perpendicular to the one given, the slope of the line in question is going to be the opposite-reciprocal of the slope of the given line.

Slope of the given line = -12

Slope of the new line = \(\frac{1}{12}\)

We will use the point given and the new slope to determine the y-intercept using slope-intercept form.

\(4 = \frac{1}{12}(0) + b\\\\4 = 0 + b\\\\4 = b\)

Formula for this line

\(y = \frac{1}{12}x + 4\)

We can graph the lines to check our work.

Both lines are perpendicular.

False, because the determinant of a triangular matrix is the product of the entries along the main diagonal.

What is cofactor expansion?

The Laplace expansion, also known as the cofactor expansion in linear algebra, expresses the determinant of a n n matrix B as a weighted sum of minors. It is named after Pierre-Simon Laplace.

a. The correct answer is A: True, because cofactor expansion across a row adds each of the cofactors together. Cofactor expansion down a column subtracts each cofactor from one another. This causes the two cofactor expansions to have opposite signs.

To see why this is true, let's consider an example.

Let A be the 3x3 matrix:

   \(size(8cm); \\real\ ticklen=3;\\ pen\ axispen=black+1.3bp; \\pen \ gridpen=gray(0.22);\\ pen\ tickpen=black+0.8bp;\\ pen \ ticklabelpen=black;\\ pen\ vectorpen=black;\\ x\ axis(extend)=true\)

The determinant of A can be computed using cofactor expansion along the first row:

det A = 2 * C_{12} - 3 * C_{13} + 4 * C_{14}

= 2 * (-6) - 3 * (5) + 4 * (-4)

= -12 - 15 + 16

= -11

Alternatively, we can compute the determinant using cofactor expansion down the first column:

det A = 8 * C_{21} - 5 * C_{31} + 2 * C_{41}

= 8 * (-6) - 5 * (5) + 2 * (-4)

= -48 + 25 -8

= -31

b. For part b,

The correct answer is C: False, because the determinant of a triangular matrix is the product of the entries along the main diagonal.

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Answer:

x = 15

Step-by-step explanation:

Consider the right triangle on the left with hypotenuse h₁  , then

Using Pythagoras' identity

h₁² = x² + 9²

Consider the right triangle on the right with hypotenuse h₂ , then

h₂² = x² + 25²

Now consider the large right triangle with legs h₁ and h₂ , then

h₁² + h₂² = (9 + 25)² , substitute values

x² + 9² + x² + 25² = 34² , that is

2x² + 81 + 625 = 1156

2x² + 706 = 1156 ( subtract 706 from both sides )

2x² = 450 ( divide both sides by 2 )

x² = 225 ( take the square root of both sides )

x = \(\sqrt{225}\) = 15

Options :

B) ACT scores account for 57.74% of the total fluctuation in GPA.

B) ACT scores account for 57.74% of the total fluctuation in GPA.

C) GPA accounts for 57.74% of the variability of ACT scores.

D) None of the above.

Answer:

B) ACT scores account for 57.74% of the total fluctuation in GPA.

Step-by-step explanation:

The R-squared value, called the Coefficient of determination gives the percentage or proportion of variation in the dependent variable which is due to or caused by the independent variable.

In the study above, the independent variable is the ACT score, is used to draw a regression relationship between the GPA of students, with GPA being the dependent variable.

The R² :value being 0.5774 means that (0.5774 * 100%) = 57. 74 % of variation in students GPA is caused by the regression line (independent variable which is the ACT SCORE).

HENCE, we can conclude that ACT Score is responsible of 57. 74 % variation in GPA while the remaining percentage is due to other factors.

In order for the relationship zyx ~ wvu to be correct, the following conditions must be true:

Corresponding angles are congruent: The angles formed by matching vertices should have the same measures in both triangles. This ensures that the corresponding angles are equivalent.

Corresponding sides are proportional: The lengths of the sides that connect the corresponding vertices of the triangles should have a consistent ratio. This implies that the corresponding sides are proportional to each other.

These conditions are based on the definition of similarity between two triangles. If both the corresponding angles are congruent and the corresponding sides are proportional, then the triangles zyx and wvu are considered similar (denoted by ~).

Therefore, in order for zyx ~ wvu to be correct, the congruence of corresponding angles and the proportionality of corresponding sides must hold true.

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The answer is A.) 25

The previous answer of 87 is wrong, and there is me to prove it below.

The deli can expect to approximately sell 25 flavored bagels during an hour when 50 plain bagels are sold.

A scatter plot is a plot containing points that are made using different cartesian coordinates. The line that passes approximately through these points is called the regression line.

To find the number of flavored bagels which is x, we have to substitute the value of y which is the number of plain bagels sold.

The equation is given as:

y = 1.731x + 6.697

Now substitute the value of y = 50:

50 = 1.731x + 6.697

43.303 = 1.731x

x = 43.303/1.731

= 25.016 ≈ 25 falvored bagels

Therefore, the deli can expect to approximately sell 25 flavored bagels during an hour when 50 plain bagels are sold. The correct answer is option A.

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Solving a system of equations we can see that there are 13 pieces of fruit ina  large basket and 7 on a smaller one.

Let's define the variables:

x = number of pieces in a small basket.

y = number of pieces in a large basket.

With the given information we can write a system of equations:

10x + 6y = 148

10x + 7y = 161

If we take the difference between the two equations we get:

(10x + 7y) - (10x + 6y) = 161 - 148

y = 13

So there are 13 pieces of fruit on a large basket, and we can find the value of x by evaluatin one of the equations in y = 13.

10x + 6*13 = 148

10x = 148 - 6*13

10x = 70

x = 70/10 = 7

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Answer:

x = -2 and 6

Step-by-step explanation:

To find vertical asymptote, set the denominator equal to 0 and solve for x. See the guidelines below for determining VA

\(y=\frac{x-5}{x^{2} -4x-12}\)

\(x^{2} -4x-12=0\)

\(x^{2} -6x+2x-12=0\)

\(x(x-6)+2(x-6)=0\)

\((x+2)(x-6)=0\)

\(x=-2,6\)

Hope this helps and God bless!

The integral\int(1/x^4 + 9x^2) dx converges by comparison to a convergent integral, and its value is 1/3

To determine whether the integral converges or diverges, we can use the limit comparison test with the integral:

Since for all x > 0, we have:

Thus, by the limit comparison test:

converges if and only if converges.

We can evaluate  using the power rule of integration:

where C is the constant of integration. Evaluating this integral from 1 to infinity, we get:

∫(1/x^4) dx from 1 to infinity = lim as b → infinity

=>

=> 0 - (-1/3)

=> 1/3

Since the integral  dx converges by comparison to a convergent integral, and its value is 1/3.

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Note: The full question is

Determine whether the integral converges or diverges; if it converges, evaluate. (If the quantity diverges, enter DIVERGES. Do not use the [infinity] symbol in your answer.) [infinity] dx x4 + 9x2 1

Answer:The equation that can be paired with x + 2y = 5 to create an inconsistent system is given by:

2x + 4y = 3.

Step-by-step explanation:

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

An inconsistent system is a system that has no solutions, and it happens when the coefficients of x and y are multiples, and the independent terms are not.

Hence:

x + 2y = 5.

2x + 4y = 3.

Is inconsistent, as the variables are each multiplied by 2, but the independent term is not.

Answer:

f(-1) = 2-3(-1) +1

= 7

f(-3)= 2-3(-3)+1

= 12

f(-1) = -1-1

= -2

f(-3) = -3-1

= -4

Answer:

-14x² - x + 4

Step-by-step explanation:

(-10x² + 5x - 3) - (4x² + 6x - 7)

= (-10x² + 5x - 3) - (+4x²) - (+6x) - (-7)

= (-10x² + 5x - 3) -4x² -6x +7

= -10x²-4x² +5x-6x -3+7

= -14x²  - x + 4

Answer:

The answer is -10x + 9

Step-by-step explanation:

Combine like terms.

-10x + 9

Hoped this helped!

Could I get brainly?

Step-by-step explanation:

S.i =principal x rate x time/100

7,50000x4x4.5/100

13500000/100

135000

Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation: