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If Caisse can download a maximum of 1000 mb of songs or movies then the inequality that represents the number of movies and songs that Caisse downloads each month is 85x+4y<1000.

Given that Caisse can download a maximum of 1000 mb of songs or movies to her smartphone each month. the file of each movie is 85mb, and the file of each song is 4mb.

We are required to find the inequality that represents the number movies and songs that Caisse downloads each month.

Inequality is like an equation that shows the relationship between variables that are expressed in greater than, less than , greater than or equal to , less than or equal to sign.

let the number of movies be x and the number of songs be y.

According to question Caisse cannot download more than 1000 mb, so we will use less than towards equation.

It will be as under:

85x+4y<1000.

Hence if Caisse can download a maximum of 1000 mb of songs or movies then the inequality that represents the number of movies and songs that Caisse downloads each month is 85x+4y<1000.

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a. In interval notation, Increasing intervals: (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm). Decreasing intervals: (8am, 9am) U (11am, 12pm). Constant intervals: (9am, 10am) U (10am, 11am)

b. The increase in cost between 12 noon and 3 pm is $2.

c. Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)

Interval notation is used to represent continuous intervals of numbers or values, like ranges on a number line.

The graph shows that from 8-9am, and 11-12pm, the cost from Swift Ride decreases.

We can represent it as (8am, 9am) U (11am, 12pm).

It increases at these times (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm).

And stays constant at : (9am, 10am) U (10am, 11am)

We simply deduct the 12pm's cost from 3pm's cost.

So, we have

Cost increase = $3.5 - $1.5

Evaluate the difference

Cost increase = $2

Hence, the cost increase is $2

When you plot the points provided for Yellow cab, you'll notice that Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)

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\( \frac{5}{2} = \frac{s}{8 } \\ 5 \times 8 = 2s \\ 40 = 2s \\ s = \frac{40}{2} \\ s = 20\)

The H.C.F. of 30, 45, and 60 using the division method is 30.

To find the H.C.F. (Highest Common Factor) of the given numbers using division method, we can follow these steps:

Let's apply this method to find the H.C.F. of 30, 45, and 60.

Step 1: We start by dividing the larger number, 60, by the smaller number, 30.

60 ÷ 30 = 2 with a remainder of 0

Step 2: Now, we divide the smaller number, 30, by the remainder, which is 0.

30 ÷ 0 = undefined

Since the remainder is zero, we stop the process here. The last divisor we obtained is 30. Therefore, the H.C.F. of 30, 45, and 60 is 30.

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Answer:

C. No, because it's determinant is zero

Step-by-step explanation:

\(A= \begin{bmatrix} 16 & - 4\\\\ 8 & - 2\end{bmatrix} \)

\( det(A) =\begin{vmatrix} 16 & - 4\\\\ 8 & - 2\end{vmatrix} \)

\( det(A) = 16\times (-2)-(-4)\times 8\)

\( det(A) = -32+32\)

\( det(A) = 0\)

This matrix have no inverse, because it's determinant is zero.

It is given a 2*2 matrix of order 2.

To find this matrix have an inverse or not.

What is determinant?

A quantity obtained by the addition of products of the elements of a square matrix according to a given rule.

The given matrix is

A= \(\left[\begin{array}{ccc}16&-4\\8&-2\\\end{array}\right]\)

det A=16*(-2)-(-4)*8=0

det A=0

So, this matrix have no inverse, because it's determinant is zero.

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The required of the sidewalk to the nearest square foot is 13.14 ft².

The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth.

A circle's area is the area that it takes up in a two-dimensional plane. It can be simply calculated using the formula A = r2, (Pi r-squared), where r is the circle's radius. The square unit, such as m2, cm2, etc., is the unit of area.

We have,

Length = 5 ft, width = 2 ft, Radius of circle = 2 ft

Now,

Area of sidewalk = area of rectangle + area quadrant

Area of sidewalk = (5×2) + π(2)^2/4

Area of sidewalk = 10 + 3.14

Area of sidewalk = 13.14 ft²

Thus, required area of the sidewalk is 13.14 ft².

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The points which represents a the solution are: A, C, D and K

What are coordinates?

Coordinates can be defined as the ordered pairs in which it is used to locate any points in 2D.

The given inequalities:  y ≤ −2x + 10 & y > 1/(2x − 2)

The given points: A(-5,4), B(4,7), C(-2,7), D(-7,1), E(4,-2),

F(1,-6), G(-3,-10), H(-4,-4), I(9,3), J(7,-4) and K(2,3).

The attached figure represents the graph of the given inequalities.

The shaded area represents the solution of the inequalities.

So, the points lies in the shaded area represents the solution of the inequalities.

So, points A, C, D and K are a solution to the system of inequalities.

Note only if

If the given inequalities:  y ≤ −2x + 10 & y > (1/2x) - 2

It will be the same solution.

Hence, The  points A, C, D and K are a solution to the system of inequalities.

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Answer:

-18/10

Step-by-step explanation:

I think that is correct

Answer:

1 17/20

Step-by-step explanation:

if you × 8/10 it by 2 = 16/10

The point (-√2,1) can also be represented as (√3, 5.18) in polar coordinates.

To find the polar coordinates of the rectangular coordinates (-√2,1), we can use the following formulas:

r = √(x² + y²)

θ = tan^⁻1(y/x)

Plugging in the given values of (-√2,1), we get:

r = √((-√2)² + 1²) = √(2 + 1) = √3

θ = tan^⁻1(1/(-√2)) ≈ 2.0344 radians

Note that since the point (-√2,1) is in the second quadrant, we need to add π to the value of θ obtained from the inverse tangent in order to obtain an angle in the interval [0,2π). Thus, we have:

θ ≈ 2.0344 + π ≈ 5.1779 radians

Rounding to 2 decimal places as needed, we get the polar coordinates of (-√2,1) as (r,θ) ≈ (√3, 5.18).

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The product of a number y and 12 or 12 times a number y. These are both equivalent expressions to 12y

The cosine of the angle opposite the side of length 5.64 meters is 0.4536.

In a triangle, the cosine of the angle opposite a side is given by the formula:

cos(angle) = (a^2 + b^2 - c^2)/(2ab) where a, b, and c are the lengths of the sides of the triangle and angle is the angle opposite the side of length c. Given the side lengths of the triangle as 3.18 meters, 7.82 meters and 5.64 meters, the side opposite angle we want to find is 5.64 meters.

so we can use the above formula and substitute the values,

cos(angle) = (3.18^2 + 7.82^2 - 5.64^2)/(23.187.82) = 0.4536

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in short, 25% is just 1/4 of anything, we know she's sold 25% which is $600, so her daily goal must be 1/4 + 1/4 + 1/4 + 1/4, or namely 600 + 600 + 600 + 600 = 2400.

After considering the given data we conclude that the perimeter of the given swimming pool is 23 meters which is Option A.

The perimeter of a rectangle is evaluated by adding up all its sides. For the given case, we possess a rectangle with sides
a = 5m,
b = 8m,
c = 8m and
d = 2m.
Perimeter regarding the swimming pool is evaluated as
a + b + c + d
= 5m + 8m + 8m + 2m
= 23 meters
Hence the option regarding the question which satisfy the perimeter is Option A.
Perimeter the counted  measurement regarding the distance around the outside of a two-dimensional shape. In this system  the length of the outline or boundary of any two-dimensional geometric shape is defined as perimeter .
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The complete question is
If a = 5m, b = 8 m, c = 8 m, and d = 2 m, what is the perimeter of the swimming pool?
A.23 m
B. 32 m
C.29 m
D.34 m

\(\bold{\huge{\underline{ Solution }}}\)

- I have used different colours for indicating different process

- I used brown colour to indicate steps

- I used green colour for explaining solution

- Pink colour for known properties of integration

- Purple colour for the middle steps that are optional.

[Note :- For solving such questions it is mandatory that you should know all the functions and it's derivatives ]

\(\sf{=}{\sf{\dfrac{ x^{2}}{2}}}{\sf{ + 7x + 67x .In| x - 4 | - 30.In| x - 3 | + c }}\)

Answer:

\(\displaystyle \large{\frac{x^2}{2}+7x+67\ln |x-4|-30\ln |x-3| + C}\)

Step-by-step explanation:

To find an integration of this function, first, you must know these integration methods and differences of them.

These methods above are common when it comes to integrating fractional functions, except there are differences when to use these methods.

Examples (of these integrands that require partial fraction technique)

\(\displaystyle \large{\int \frac{3}{x^2-5x+6} \ dx}\\\displaystyle \large{\int \frac{x+2}{x^2-4} \ dx}\)

Examples (of these integrands that require long division)

\(\displaystyle \large{\int \frac{x^2+5x+6}{x+2} \ dx}\\\displaystyle \large{\int \frac{x^4+3}{x} \ dx }\)

Therefore, from the given integral, the integrand requires long division method. (See attachment for long division.)

After long division, we should get:

\(\displaystyle \large{\int x+7+\frac{37x-81}{x^2-7x+12} \ dx}\)

Recall important properties of integral such as:

\(\displaystyle \large{\int [f(x) \pm g(x)] \ dx = \int f(x) \ dx \pm \int g(x) \ dx}\)

Hence:

\(\displaystyle \large{\int x \ dx + \int 7 \ dx + \int \frac{37x-81}{x^2-7x+12} \ dx}\)

Recall important integration formula for polynomial and constant:

\(\displaystyle \large{\int x^n \ dx = \frac{x^{n+1}}{n+1} + C}\\\displaystyle \large{\int x \ dx = \frac{x^2}{2} + C}\\\displaystyle \large{\int k \ dx = kx + C \ \ \tt{(k \ \ is \ \ a \ \ constant.)}\)

Therefore:

\(\displaystyle \large{\frac{x^2}{2}+7x+\boxed{\int \frac{37x-81}{x^2-7x+12} \ dx}}\)

From the boxed integral above, we cannot evaluate it by default. From what I said, if the degree of numerator is less than the degree of denominator, we’ll use partial fraction technique.

Therefore, factor the denominator:

\(\displaystyle \large{\frac{37x-81}{(x-4)(x-3)}}\)

Set to A/x-4 and B/x-3

\(\displaystyle \large{\frac{37x-81}{(x-4)(x-3)} = \frac{A}{x-4} + \frac{B}{x-3}}\)

Multiply both sides by (x-4)(x-3).

\(\displaystyle \large{\frac{37x-81}{(x-4)(x-3)} \cdot (x-4)(x-3)= \frac{A}{x-4} \cdot (x-4)(x-3) + \frac{B}{x-3} \cdot (x-4)(x-3)}\\\displaystyle \large{37x-81= A(x-3) + B(x-4)}\\\displaystyle \large{37x-81= Ax-3A+Bx-4B}\\\displaystyle \large{37x-81= (A+B)x-(3A+4B)}\)

Then compare the coefficients:

\(\displaystyle \large{\left \{ {{A+B=37} \atop {3A+4B=81}} \right}\)

Solve the simultaneous equation for A and B.

\(\displaystyle \large{\left \{ {{A=37-B} \atop {3A+4B=81}} \right}\\\displaystyle \large{\left \{ {{A=37-B} \atop {3(37-B)+4B=81}} \right}\\\displaystyle \large{\left \{ {{A=37-B} \atop {111-3B+4B=81}} \right}\\\displaystyle \large{\left \{ {{A=37-B} \atop {111+B=81}} \right}\\\displaystyle \large{\left \{ {{A=37-B} \atop {B=81-111}} \right}\\\displaystyle \large{\left \{ {{A=37-B} \atop {B=-30}} \right}\\\displaystyle \large{\left \{ {{A=67} \atop {B=-30}} \right}\\\)

Therefore, A = 67 and B = -30. Substitute the values in:

\(\displaystyle \large{\int \frac{67}{x-4}-\frac{30}{x-3} \ dx}\\\displaystyle \large{\int \frac{67}{x-4} \ dx -\int \frac{30}{x-3} \ dx}\)

Recall the integration formula for above:

\(\displaystyle \large{\int \frac{k}{x-a} \ dx = \int k \cdot \frac{1}{x-a} \ dx = k\ln |x-a| + C}\)

Therefore:

\(\displaystyle \large{\int \frac{37x-81}{x^2-7x+12} \ dx = \int \frac{67}{x-4}-\frac{30}{x-3} \ dx = 67\ln |x-4| - 30\ln |x-3|}\)

Back from this:

\(\displaystyle \large{\frac{x^2}{2}+7x+\boxed{\int \frac{37x-81}{x^2-7x+12} \ dx}}\)

Substitute in:

\(\displaystyle \large{\frac{x^2}{2}+7x+67\ln |x-4|-30\ln |x-3| + C}\)

Therefore the solution is:

\(\displaystyle \large \boxed{\frac{x^2}{2}+7x+67\ln |x-4|-30\ln |x-3| + C}\)

Answer:

The measure of angle ADE is equal to 62 degrees.

Step-by-step explanation:

Firstly, I want to remind you that the sum of the interior angles in a quadrilateral are 360 degrees. Now, we are given that CD || BA and CB || DA, which means that this quadrilateral is a parallelogram. This is important because we know that the opposite angles in a parallelogram are congruent, which means that angle C is congruent to angle A and angle B is congruent to angle D. Therefore, the measure of angle A is also 73 degrees. Next, we can represent angle D as x, which means that angle B is equal to x, so the sum of angle D and B is 2x. Finally, we can set up an equation where we solve for the value of x, and then subtract it with 45 degrees:

2x + 2(73) = 360

2x + 146 = 360

2x = 214

x = 107 = B = D

Now, we can subtract the measure of angle D with 45 degrees to get the measure of angle ADE:

ADE = 107 - 45

ADE = 62

Answer:

The solution to the equation x + 9 = 18 + -2x is x = 3.

Step-by-step explanation:

To solve this equation for x, you can first simplify both sides of the equation by combining like terms.

x + 9 = 18 + -2x

Add 2x to both sides:

x + 2x + 9 = 18

Combine like terms:

3x + 9 = 18

Subtract 9 from both sides:

3x = 9

Finally, divide both sides by 3 to solve for x:

x = 3

Therefore, the solution to the equation x + 9 = 18 + -2x is x = 3.

HOPE THIS HELPED:)))

Answer:

3

Step-by-step explanation:

replace the + with - signs

x+9=18−2x

add the 2x to both equations and x becomes a 1 since we dont know its value.

3x+9=18

then you got to subtract 9 by 18 and that equals to 9 then

3x=9 3 divided by 9 is 3 and when simplified

and the answer is 3

Answer:

240 cm

Step-by-step explanation:

18*12= 216

+

4*3*2= 24

216*24= 240

Answer:

y + -24.8 = -13

Step-by-step explanation:

y + 6.2x(-4) = -13

y + -24.8 = -13

To determine the final answer you would need to figure out the value of Y.

The point (60, 720) means that the break even is when 60 cakes are produced. That is when 60 cakes are sold, the revenue is equal to the cost of $720

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

The slope intercept form of the linear equation is:

y = mx + b

where m is the slope and b is the initial value.

A baker uses the equation y = 12x to predict the revenue generated from selling cakes. She uses equation y = 450+4.5x to model the cost to produce a cakes.

The solution to the system y = 12x and y = 450 + 4.5x represent the point at which there is break even, that is cost is equal to revenue

The point (60, 720) means that the break even is when 60 cakes are produced. That is when 60 cakes are sold, the revenue is equal to the cost of $720

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Answer:

58.07 > 58.4 is false.

29.6 = 29.600 is true.

140.23 < 140.203 is false.

108.505 > 108.5 is true.

Answer:

correct choice is the last one

Step-by-step explanation:

let h = cost of 1 hamburger meal

let c = cost of 1 chicken nugget meal

5h + 6c = 39

9h + 2c = 35