Santiago creates a playlist of Latin dance music. The playlist contains bachata, salsa, and mambo tracks, as shown in the table. Santiago puts the playlist on shuffle mode. What is the probability that the first track he hears is a salsa track?

The value of the x would be 9.

Option (A) is correct.

What is a complementary angle?

A complementary angle is an angle that, when added to another angle, forms a right angle (90 degrees). Complementary angles are pairs of angles that add up to 90 degrees.

Angle JKM and angle MKN are complementary angles

so

   (3x + 2) + (6x + 7) = 90

  9x + 9 = 90

  9(x + 1) = 90

     x + 1 = 10

    x = 9

Hence, the value of the x would be 9.

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After solving the equation the value of the x would be 9. Therefore, the correct option is A.

What is a complementary angle?

A complementary angle is a pair of angles that add up to 90 degrees. Complementary angles can be adjacent angles, or angles that share a common vertex and side, or they can be nonadjacent angles that have no common points or sides. Complementary angles are usually referred to by their sum, such as "90-degree angles" or "angles that add up to 90 degrees." Complementary angles can also be called supplementary angles when they add up to 180 degrees.

Angle JKM and angle MKN are complementary angles

so   (3x + 2) + (6x + 7) = 90

 9x + 9 = 90

 9(x + 1) = 90

    x + 1 = 10

   x = 9

Hence, the value of the x would be 9.

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It will take 38 weeks a student to save enough money for the ticket.

Mathematical operations come in several types, with division being one. The phrases or numbers are divided into the same number of components during this operation.

Given,

a student must save at least $675 plus 3% tax to buy a round-trip ticket to London.

3% of 675

= 3 x 675 / 100

= 20.25

The student has $98 saved already.

Now student needs ($675 - $98) + 20.25 = $577 + 20.25

= $597.25

If the student earns $32 per week and plans to save half of the earnings each week toward the ticket cost.

That means, $32 / 2 = $16 per week.

To find the amount of enough money:

Divide $597.25 by $16.

597.25 /16

= 37.328125

≈ 38 weeks

Therefore, student will save for 38 weeks.

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The solution to the equation f(x)=g(x) are x=-2 and x=1.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

The given functions are f(x)=-x+6 and g(x)=-x²-2x+8.

Now, f(x)=g(x)

-x+6=-x²-2x+8

⇒ x²+x-2=0

⇒ x²+2x-x-2=0 (Splitting middle term method)

⇒ x(x+2)-1(x+2)=0

⇒ (x+2)(x-1)=0

⇒ x+2=0 and x-1=0

⇒ x=-2 and x=1

Therefore, the solution for the obtained equation are x=-2 and x=1.

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Yes , the triangles ΔSTU and ΔSRQ are similar triangles

What are similar triangles?

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the first triangle be ΔSTU

Let the second triangle be ΔSRQ

Now , for the triangles to be similar , the corresponding sides of the triangles should be in the ratio

So , on simplifying , we get

The measure of side ST = 21

The measure of side SU = 35

The measure of side SQ = 6

The measure of side SR = 10

Now , for similar triangles ,

ST / SQ = SU / SR

Substituting the values in the equation , we get

21 / 6 = 35 / 10

3.5 = 3.5

Therefore , the corresponding sides of the triangles are equal

Hence , the pair of triangles are similar triangles

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a. 4(x - 5)^2

= 4 * (x - 5)^2

= 4 * ((x - 5) * (x - 5))

= 4x^2 - 40x + 100

b. 3(x + 1) (2x - 9)

= (3(x + 1)) (2x + −9)

= (3(x + 1))(2x) + (3(x + 1))(−9)

= 6x^2 + 6x − 27x − 27

= 6x^2 − 21x − 27

c. -2(4x + 2)^2

= -2 * (4x + 2)^2

= −2 * ((4x + 2) * (4x + 2))

= 32x^2 − 32x − 8

or d. -2(4x + 2)^2 - 5 (with subtracting 5)

= −32x^2 + −32x + −8 + −5

= (−32x^2) + (−32x) + (−8 + −5)

= −32x^2 + −32x + −13

d. -3(5x - 2)^2 + 5 (with negative)

= 75x^2 + −60x + 12 + 5

= 75x^2 + −60x + 12 + 5

= (75x^2) + (−60x) + (12 + 5)

= 75x^2 + −60x + 17

or d. 3(5x - 2^2 + 5 (without negative)

= (3)(5x + −4 + 5)

= (3)(5x) + (3)(−4) + (3)(5)

= 15x − 12 + 15

= 15x + 3

Hello,

I hope you and your family are doing well!

To solve this problem, we can use the formula:

total cost = set-up fee + (cost per copy * number of copies)

In this case, we know the total cost and the set-up fee, and we want to find the number of copies. We can substitute these values into the formula and solve for the number of copies:

$32.20 = $14.95 + ($0.03/copy * number of copies)

Subtracting the set-up fee from both sides of the equation gives:

$17.25 = $0.03/copy * number of copies

Dividing both sides of the equation by the cost per copy gives:

number of copies = $17.25 / $0.03/copy = 575 copies

So Emilio was charged $32.20 to print 575 copies of the brochures.

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Happy Holidays!

Answer:

i think that answer is correct

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

(7+-6)/2

(7-6)/2

1/2

(-6+(-8)/2

(-6-8)/2

-14/2

-7

(.5,-7)

The required solution of the given inequality is given as x > 4, and the answer for the blanks is to Divide both sides by -8 and change the inequality sign.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
Given inequality,
-8x < 32
Divide both sides by -8
x > 4

The sign of the inequality change because multiplication with the negative value changes the inequality sign and the higher negative value is the least value.

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Answer: 59

Step-by-step explanation:

a. Harold's monthly payment is given as follows: $164.13.

b. The total amount paid is given as follows: $9,847.8.

c. The finance charge is of: $847.8.

The monthly payment formula is defined as follows:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which the parameters are listed as follows:

The values of these parameters for this problem are given as follows:

P = 9000, r = 0.036, n = 5 \times 12 = 60.

Then:

r/12 = 0.036/12 = 0.003.

Then the monthly payment is calculated as follows:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]A = 9000\frac{(0.003)(1.003)^{60}}{(1.003)^{60} - 1}[/tex]

A = $164.13.

Then the total amount paid is of:

Total = 60 x 164.13 = $9,847.8.

Meaning that the finance charge is given as follows:

9847.8 - 9000 = $847.8.

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The point of the compass located in order to make the arcs is points X and Y.

An "arc" in mathematics is a straight line that connects two endpoints. An arc is typically one of a circle's parts. In essence, it is a portion of a circle's circumference. A curve contains an arc. A circle contains an arc. For instance, a quarter-circle and a semicircle are both examples of arcs. A minor arc is one that is smaller than half of the circle it is a part of, or less than a semicircle, whereas a major arc is one that is more than half of its circle.

Given

The following figure was drawn using a straightedge and a compass.

The point of the compass located in order to make the arcs:

1. points X and Y

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Answer:

-2

Step-by-step explanation:

Given,

g(x) = f(4)

or, 2 - 4x = 3*4 - 2

or, 2 - 4x = 10

or, 2 - 10 = 4x

or, -8 = 4x

or, x = -2

The equation Sharon can use to find c, the average amount the cable company charges per channel is 300(c - 0.20) = 180.

The cable company charges an average of $0.80 per channel.

An equation involves two expressions or statement on two sides connected with an equal sign.

Total number of channels = 300

Let c be the cable company charges per channel.

Then the charge satellite company charges per channel = c - 0.20

Monthly charge of satellite company = 300(c - 0.20)

Monthly satellite bill = $180

So,  300(c - 0.20) = $180

⇒ c - 0.20 = 180/300

⇒ c - 0.20 = 0.60

⇒ c = 0.60 + 0.20

⇒ c = 0.80

Hence the equation used to find the cable company charge per channel is 300(c - 0.20) = 180 and the cable company charge per channel is $0.80.

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Answer:

D.  b + c = 68

    0.08b + 0.15c = 6.00

Step-by-step explanation:

The total cost is $6.00

The total amount of copies is 68

To find the total cost, we multiply the amount of copies by the individual price. So we get

0.08b + 0.15c = 6.00

We add the amount of copies bought to get a total of 68, so we get this equation:

b + 6 = 68

The number of petals that the flower should have is of:

8 petals.

A figure has rotational symmetry when it can be rotated by an angle measure which is greater than 0º and less than 360º and the rotated image is equals to the original figure, that is, the image is equals to the pre-image.

In this problem, we want the flower to have a rotation symmetry of 45 degrees.

The total angle measure of the flower is given as follows:

360º.

Then the number of petals needed for the flower to have a rotational symmetry of 45º is calculated as follows:

360/n = 45.

Applying cross multiplication, we have that:

45n = 360

n = 360/45

n = 8 petals.

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Answer:

 (a) A  and B are similar but not congruent

Step-by-step explanation:

All of the rectangles have sides in the ratio of 2:1, so are all similar. Only the rectangles that are the same size are congruent: A and C.

1. f(x) - cubic function -- polynomial , g(x) - linear function

similar

The function f(x) = x³+x²-3x+4 is a polynomial function and g(x) = 2ˣ-4 is an exponential function.

Domain: -∞ < x < ∞

Range: -∞ < y < ∞

y-intercept = 4

x - intercepts = -2.68

Function g(x)

Domain: x > 0

Range: -4 < y < ∞

y - intercept = -4

x - intercepts = none

By comparing the key features above, we can conclude that the common features in both functions are their range

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Answer:

Step-by-step explanation: To solve the problem, we can use the given information to set up a system of equations and solve for the values of $x$ and $y$. Specifically, we are given that one number is 4 less than 3 times a second number, and that two times the first number decreased by two times the second is 8.

Let $x$ represent the larger number, and $y$ represent the second number. We can write the given information as a system of equations as follows:

x &= 3y - 4

2x - 2y &= 8

Solving this system of equations, we find that $x = 12$ and $y = 2$. Therefore, the value of the larger number is 12

Answer:

x + x - x = x

explanation:

give us the actual formula lol

Answer:

me either

Step-by-step explanation:

Answer:

x ≥ 72/5

8.6 ≤ x -5 4/5= 8.6 ≤ x -29/5

8.6 ≤ x -29/5= x ≥ 72/5

The Co-ordinates of the point C that divides the line in the ratio of 3:4 is (-20/7, -17/7)

What is Section Formula?

The Section formula is used in coordinate geometry to compute the ratio of a line segment split by a point, either internally or externally. It determines the centroid, incenter, and excenters of a triangle. It is used in physics to determine the centre of mass of systems, equilibrium locations, and so on.

Solution:

A(-8, 1) and B(4, -7)

Ratio is 3:4

Section Formula is (mx2 + nx1/ m + n), (my2 + ny1/ m + n)

m = 3 and n = 4

Co-ordinates of C are (3*4 + 4*(-8)/ 3+4), (3*(-7) + 4*1 / 3+4)

= (12 - 32 / 7), (-21 + 4 / 7)

= (-20/7, -17/7)

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Step-by-step explanation:

please refer to the attached sketch for the answer.

The needed 3rd-degree polynomial function with real coefficients matching the specified constraints will be y=-5x³+10x²-45x+90.

A polynomial is a mathematical statement made up of indeterminates and coefficients that solely includes the operations of addition, subtraction, multiplication, and positive-integer powers of variables. x2 4x + 7 is an example of a polynomial with a single indeterminate x. Polynomials are sums of k-x^n terms, where k can be any number and n can be any positive integer. 3x+2x-5, for example, is a polynomial. Polynomials are introduced. This video defines words such as degree, standard form, monomial, binomial, and trinomial.

Here,

y=-5(x-2)(x-3i)(x+3i)

y=-5(x-2)(x²+9)

y=-5(x³-2x²+9x-18)

y=-5x³+10x²-45x+90

The required 3rd-degree polynomial function with real coefficients satisfying the given conditions will be y=-5x³+10x²-45x+90.

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The coordinate location of the hill halfway between them is  (1, -1).

Jack's house is located at the point (-2, 3) and Jill's house is located at the point (4, -5).  They plan to meet up at the hill located halfway between there two houses.

The coordinate location of the hill can be calculated as follows:

using mid point formula,

(x, y) = (x₁ + x₂ / 2, y₁ + y₂ / 2)

using the end points (-2, 3) and (4, -5)

(x, y) = (-2 + 4 / 2, 3 - 5 / 2)

(x, y) = (2 / 2. -2 / 2)

(x, y) = (1, -1)

Therefore, the coordinate location of the hill is (1, -1).

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the area of the generic rectangle will be x²-2x-15.

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A quadrilateral with equal angles and parallel opposite sides is referred to as a rectangle. Around us, there are a lot of rectangle items. The length and width of any rectangle form serve as its two distinguishing attributes. The width and length of a rectangle, respectively, are its longer and shorter sides.

Area of rectangle is A = a*b

(x + 3)(x - 5) in a generic rectangle

The product will give the area

x²-2x-15

hence the area of the generic rectangle will be x²-2x-15.

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