-59=-3b-32 love for b

The expression for the total amount Tristan paid is 1.1342x.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Total bill = $x

Tax = 7%

This means,

= (7/100)x

= 0.07x

Tip = 16%

This means,

= (6/100) x (x + 0.07x)

= 0.06 x (1.07x)

= 0.0642x

The total amount paid.

= total bill + tax + tip

= x + (7% of x) + 16% of (x + 7% of x)

= x + 0.07x + 0.0642x

= 1.1342x

Thus,

The total amount paid is 1.1342x.

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The Scottish mathematician John Napier reported his findings on logarithms in 1614.

The comparison of arithmetic and geometric series predicted the development of logarithms. He was there to aid with the multiplication of quantities known as sines at the time.

The value of the entire sine was equal to the length of the hypotenuse in a right-angled triangle with a hypotenuse of, say, 107 units. He provided a definition in terms of relative rates.

Because both motions are equally spaced apart in time and have an equal shift at the beginning, the logarithm of any sine is a number that comes very close to expressing the line that increased equally over the course of time while the line of the entire sine decreased proportionately into that sine.

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The inverse operation of log is antilog.

Mathematicians use the logarithm to express the inverse function of exponentiation. That is, the logarithm of a given number p is the exponent to which another fixed number, the base b, must be raised in order to obtain that number p. In the simplest case, the logarithm counts how many times the same factor appears in repeated multiplication.

The sum of the logarithms of two numbers says a and b, is the logarithm of the product of the two numbers. Both numbers must have the same base. In other words, this theorem is known as the “product rule for logarithms”.

The difference of the logarithms of two numbers, such as a and b, is equal to the logarithm of their division. Even in this case both numbers should have the same base. There is another name for this theorem, which is the “quotient rule for logarithms”.

Let f(x) = logₐx

y = logₐx

Now, to find the inverse of the function, swap the variables x and y.

x = logₐy

y = aˣ

Thus, the inverse operation of log is antilog.

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Answer:

The first step is to simplify the double radical.

√√189² = √(189²) = √(189*189) = √(35281)

Now, we simplify the radical by finding the prime factorization of 35281:

35281 = 189² = (189)(189) = (363)(363) = (3²*63²)

So, we can simplify the radical as:

√35281 = √(3²63²) = 3√(63²) = 3√(6363) = 3√3969 = 3√(31323) = 3√(3²1323) = 3*63 = 189

Therefore, √√189² = √(189*189) = √35281 = 189

Step-by-step explanation:

So the relative frequencies of the five classes are:

A: 10.25%

B: 35.89%

C: 38.46%

D: 12.82%

F: 2.56%

What is the Frequency?

Frequency refers to the number of times a specific event or value occurs within a set of data. It is a measure of how often something happens or occurs.

A relative frequency is a measure of how often a certain event or value occurs within a set of data, expressed as a proportion or percentage of the total number of events or values.

To find the relative frequencies of the five classes in percentage, you need to divide the frequency of each class by the total number of observations, and then multiply by 100 to express the result as a percentage.

The total number of observations can be found by adding up the frequencies of all five classes: 4 + 14 + 15 + 5 + 1 = 39

To find the relative frequency of class A, divide the frequency of class A (4) by the total number of observations (39) and then multiply by 100: 4/39 * 100 = 10.25%

Similarly, you can find the relative frequencies for the other classes:

Class B: 14/39 * 100 = 35.89%

Class C: 15/39 * 100 = 38.46%

Class D: 5/39 * 100 = 12.82%

Class F: 1/39 * 100 = 2.56%

So the relative frequencies of the five classes are:

A: 10.25%

B: 35.89%

C: 38.46%

D: 12.82%

F: 2.56%

It's worth noting that the sum of all relative frequencies should be equal to 100%.

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The complex number given above expressed as a + ib is 2i

Complex numbers are the numbers that are stated in the form of a+ib where, a,b are real numbers and I is an imaginary number termed "iota". The value of i = (√-1).

To solve the above problem, first, we must reduce imaginary units using the property i² = -1

(i)⁹ - 1 (i)¹⁹

i - 1 (i) ¹⁹

i - 1 (-1)

Subtract the complex numbers

i - (-i)

Identify the components of the numbers and add the real and imaginary parts separately.

(1 + 1)i

Identify the components of the numbers and add the real and imaginary parts separately

(1 + 1)i

(2)i

Thus, the solution to the imaginary number given above is 2i.

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Full Question:

Express the given complex number in the form a + ib: i⁹ - i¹⁹

Since the value is a numerical measurement representing a property of a sample, it is statistical.

Given that a sample of workers is chosen, and it is discovered that 55% of them possess a car.

Let's first clarify the distinction between a parameter and a statistic before moving on to the questions.

Parameters are numerical summaries of population statistics. However, statistics are numerical summaries of sample data.

Sample is a subset of the population; as such, it is just a small percentage of the whole population.

The percentage of the sample of employees in this case is 55%. Statistic refers to a numerical representation of data about a sample.

The value is statistical since it is a numerical measurement that describes a property of a sample.

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Answer:

(-3,0)

Step-by-step explanation:

Step-by-step explanation:

Bottom line point

( -5, -3 )

( -1, 3 )

Midpoint:

( -3, 0 )

Answer:

$60

Step-by-step explanation:

19 times 15 = 285
1425-285=1140
1140 divided by 19 = 60

To check: Divide 1425 by 75 to get 19.

Answer:

Step-by-step explanation:

Given GH₵960 contributed by 80 students of which 68 are girls who contributed a total of GH₵714, you want to know the amount per girl and the amount per boy that was contributed.

The amount per girl or boy is found by dividing their total contribution by the corresponding number of girls or boys.

If 68 girls contributed GH₵714, then the amount per girl is ...

  (GH₵714)/(68 girls) = GH₵10.50 /girl

Each girl contributed GH₵10.50.

The remaining 12 students were boys, and the amount they contributed was (GH₵960 -714) = GH₵246. Then the amount per boy is ...

  (GH₵246)/(12 boys) = GH₵20.50 /boy

Each boy contributed GH₵20.50.

Their recipe contains 88.6% sand.

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Applying the trigonometric ratios, the values of x are:

1. x = 7.3

2. x = 33.3

3. x = 21.3

4. x = 31.9

5. x = 25.6

6. x = 11.0

7. x = 41.8°

8. x = 64.2°

These ratios include:

1. ∅ = 63

adj. = x

hyp. = 16

Therefore,

cos 63 = x/16

x = cos 63 * 16

x = 7.3

2. ∅ = 39

opp. = 27

adj. = x

Therefore,

tan 39 = 27/x

x = 27/tan 39

x = 33.3

3. ∅ = 49

adj. = 14

hyp. = x

Therefore,

cos 49 = 14/x

x = 14/cos 49

x = 21.3

4. ∅ = 15

adj. = x

hyp. = 33

Therefore,

cos 15 = x/33

x = cos 15 * 33

x = 31.9

5. ∅ = 52

opp. = x

adj. = 20

Therefore,

tan 52 = x/20

x = tan 52 * 20

x = 25.6

6. ∅ = 27

hyp. = x

opp. = 5

Therefore,

sin 27 = 5/x

x = 5/sin 27

x = 11.0

7. ∅ = x

opp. = 4

hyp. = 6

Therefore,

sin x = 4/6

x = sin^(-1)(4/6)

x = 41.8°

8. ∅ = x

adj. = 14

opp. = 29

Therefore,

tan x = 29/14

x = tan^(-1)(29/14)

x = 64.2°

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So, option (a) is the correct answer.

(a) Triangle with lengths of sides 7 cm, 8 cm and 9cm is a right triangle. This is because the Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, 9^2 = 7^2 + 8^2, which is true, hence the triangle has a right angle.

(b) ABC with AB = 8.7 cm, AC = 7 cm and BC = 6cm can't be determined as it depends on the angles, as the sides are given but the angles are not.

(c) PQR such that PQ = QR = PR = 5cm is an equilateral triangle. This is because in an equilateral triangle all three sides are of equal length.

(d) DEF with D = 90 degrees can't be determined as only the angle is given, we need the length of the sides as well

(e) XYZ with Y = 90 and XY = YZ can't be determined as the angle and the sides are not enough information

(f) LMN with L = 30, M = 70 and N = 80 is not a triangle as the sum of two sides is less than the other side, hence the triangle inequality theorem is violated.

Therefore, Option (a) is the correct answer.

It's worth noting that a triangle can be defined by its three sides as well as by its three angles, but in any case, we need enough information to determine the type of triangle.

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The total volume in cubic centimeters of the boxes in the display is 4608√6.

Therefore the answer is 4608√6.

The formula for finding surface area of a cube of side a is

A = 4a²

The formula for finding volume of a cube of side a is

V = a³

Given that surface area of a cube is 384 cm², that is

4a² = 384 cm²

a² = (384/ 4) cm²

Therefore, a = 4√6 cm

Now volume of a single cube can be found by

V = a³

V = (4√6 cm)³

V = 384√6 cm³

Therefore volume of 12 such cubes is

= 12V

= 12×384√6 cm³

= 4608√6 cm³

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Answer: what is the question?

Step-by-step explanation:

Substitution is generally better than elimination equations because it is typically faster and easier to solve.

Substitution is generally a better method than elimination when solving equations. This is because substitution is typically faster and easier to solve. With substitution, you simply substitute one of the variables in the equation with a known value in order to solve for the other variable. This is generally easier than elimination, which involves eliminating one of the variables by adding and subtracting equations. Elimination can be more tedious, especially when dealing with large equations. Additionally, it may be difficult to eliminate one variable when the equations are not balanced or when there are multiple variables. For these reasons, substitution is generally better than elimination.

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The simplified form of the expression 18x² + 4 - [6(x² -2) + 5] is 12x² + 11.

Mathematical statements are called expressions if they have at least two words that are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

The given expression is

18x² + 4 - [6(x² -2) + 5]

We can rewrite it as

= 18x² + 4 - [6x² - 12 + 5]

= 18x² + 4 - [6x² - 7]

= 18x² + 4 - 6x² + 7

= 12x² + 11

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The complete question is:

Simplify the expression: 18x² + 4 - [6(x² -2) + 5]

Answer:

-4/4 = -1

Step-by-step explanation:

Answer: -4/4

Step-by-step explanation:

m = slope

(x1, y1) = coordinates of first point in the line

(x2, y2) = coordinates of second point in the line

-3,-1   1,-5 are the corrdinates

(-5) - (-1) = -4

1 - (-3) = 4

The bicyclist’s acceleration is 2.7 m/s²

the correct answer is an option (C)

We know that the acceleration is nothing but the change in velocity over the change in time.

A = Δv / Δt

where, Δv = change in velocity

Δt = change in time

A = acceleration

Here, we have been given a  bicyclist starts from rest and accelerates along a straight path to a speed of 12.15 m/s in a time of 4.5 seconds.

So,  Δv = 12.15 m/s and  Δt = 4.5 seconds

Using above formula of the acceleration would be,

A = Δv / Δt

A = 12.15 / 4.5

A = 2.7 m/s²

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The amount of the constant k is known as the "constant of proportionality".

Given any position, we can calculate k by dividing the y-coordinate by the x-coordinate because k is constant (the same for every point). Where k is the constant of variation, y = kx.

We refer to a relationship between two variables as having a direct relationship when the equation for the relationship is of the form y = kx, where k is a constant. The "constant of proportionality" is the value of the constant k.

For some constant k, often known as the proportionality or variational constant, y=kx. (Some textbooks will refer to direct variation as "y varies as x," "y varies proportionally as x," or "y is directly proportional to x.

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Answer: y=1/6x−2/3

Step-by-step explanation:

-6y= x-4

/-6 .      /-6

y= 1/6x-2/3

*somethin like this*

The number of markers that Stella has would be = 27 markers

The number of markers owned by Jerry = U

The number markers owned by Stella = t +16

If U = 43

t = X

That is, 43= t + 16

Make t the subject of formula;

t = 43-16

t = 27

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Complete question;

Jerry and Stella are working on an art project together. Jerry has 16 more markers than Stella. The equation given below shows this relationship, where u represents the number of markers Jerry has, and t represents the number of markers Stella has. U = t + 16 If Jerry has 43 markers, how many markers does Stella have? Show your work

We can rewrite the quadratic to get the equivalent expression:

3*(x - 4)*(x + 2/3)

We want to find an expression equivalent to the quadratic equation:

3x^2 -10x -8

Remember that if the quadratic equation has the roots a and b, then we can rewrite the equation as:

3*(x - a)*(x - b)

So let's find the roots, using the quadratic formula we will get:

[tex]x = \frac{10 \pm \sqrt{(-10)^2 - 4*3*(-8)} }{2*3} \\\\x = \frac{10 \pm 14 }{6}[/tex]

So the two roots are:

x = (10 + 14)/6 = 4

x = (10 - 4)/6 = -4/6 = -2/3

Then the equivalent expression is:

3*(x - 4)*(x + 2/3)

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the constant of proportionality for this relationship is 3/4

the property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in the destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.

Given, A poster at the train station shows the number of miles to different stations and the time it takes for the train to travel there.

Time in Minutes(x)         Distance in Miles(y)

          24                                  18

          44                                  33

          76                                  57

          96                                  72

From the general formula of constant of proportionality

constant of proportionality = y/x

constant of proportionality (k) = 18/24

constant of proportionality (k) = 3/4

Therefore, 3/4 is the constant of proportionality for this relationship.

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In a shape or space, volume refers to the quantity that can be accommodated.

It's a formula: V = lwh. six-faced solid object in three dimensions. an indication of an object's length. an indicator of an object's width.

In a shape or space, volume refers to the quantity that can be accommodated. Remember that volume is equal to the number of cubes that can completely occupy a space. Area is the number of squares that can cover a space (in square units) (cubic units). For calculating volume, each 3D shape has a formula.

In a shape or space, volume refers to the quantity that can be accommodated.

The complete question is,

In 7th grade mathematics, what is volume?

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The equation of the parabola is y = 2 ( x + 1/4 )² - 49/8 and the vertex of the parabola is ( -1/4 , -49/8 )

A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line

The equation of the parabola is given by

( x - h )² = 4p ( y - k )

y = a ( x - h )² + k

where ( h , k ) is the vertex and ( h , k + p ) is the focus

y is the directrix and y = k – p

The equation of the parabola is also given by the equation

y = ax² + bx + c

where a , b , and c are the three coefficients and the parabola is uniquely identified

Given data ,

Let the equation be represented as A

Now , the value of A is

y = 2x² + x - 6   be equation (1)

On simplifying the equation , we get

On factorizing the x² coefficient , we get

y = 2 ( x² + ( 1/2 )x ) - 6

Adding and subtracting ( 1/16 ) inside the parentheses , we get

y = 2 ( x² + ( 1/2 )x + 1/16 - 1/16 ) - 6

On simplifying the equation , we get

y = 2 ( x² + ( 1/2 )x + 1/16 ) - 6 - 1/8

The trinomial inside the brackets is a perfect square

y = 2 ( x + 1/4 )² - 49/8

Now , the equation of the parabola is given by y = a ( x - h )² + k ,

where ( h , k ) is the vertex

So , y = 2 ( x + 1/4 )² - 49/8

Hence , the vertex of the parabola is ( -1/4 , -49/8 )

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y = 75x - 450 represents the number of customers served per hour where y is the number of customers served and x is the number of hours.

The point-slope form of a linear equation is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

To find the equation representing the number of customers served per hour, we can first find the slope of the line by using the information given. The slope of a line is the change in y over the change in x.

In 8 hours, the restaurant serves 600 customers and in 12 hours, 900 customers. Therefore, the change in y is 900 - 600 = 300 and the change in x is 12 - 8 = 4. The slope of the line is 300/4 = 75.

We also know that the restaurant serves 600 customers in 8 hours. This means that when x = 8, y = 600.

Using this information, we can write the equation in point-slope form:

y - 600 = 75(x - 8)

So the equation of the line representing the number of customers served per hour is:

y = 75x - 450

Where y is the number of customers served and x is the number of hours.

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A quadratic equation 9x² + 3kx + 4 = 0 has equal roots. Thus, the values of k are -4, and +4.

The equation of the second degree is a quadratic equation. This indicates that it contains a phrase that is squared, at least once. ax² + bx + c = 0, which uses constants or numerical coefficients for the variables a, b, and c, is one of the classic formulae for solving quadratic equations. Unknown variable 'x' is used here.

The given problem can be solved using the concepts of quadratic equations.  

1. The given quadratic equation is   9x² + 3kx + 4 = 0.

2. For an equation to have equal roots the value of the discriminant is 0,

=> The discriminant of a quadratic equation ax² + b x + c = 0 is given by the formula,

=> Discriminant ( D ) = [tex]\sqrt{b^2 - 4ac}[/tex]

=> For equal roots D = 0.

3. Substitute the values in the above formula:

⇒ [tex]\sqrt{(3k)^2 - 4*9*4}[/tex] = 0

⇒ [tex]{9k^2 - 144}[/tex] = 0

⇒9k² = 144

⇒ k² = 16

⇒ k = ± 4

Therefore, the values of k are -4, and +4.

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Shari has twelve cards, numbered from one to twelve. She randomly draws three cards with replacement. What is the probability that Shari draws an even card and then two odds.

a. 3/8

b. 1/16

c. 1/4

d. 1/8

I think the answer is 3/8.

In the 4th month, the height of the f(x) plant exceeds that of the g(x) plant. This can be solved using the concept of polynomials.

When exponents, constants, and variables are joined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable).

Month (x)

f(x) = 3x / g(x) = 5x + 12

⇒f(x)  × g(x) = 3X

⇒g(x) = 3X/ 5x + 12

At 4th month let x = 4

f(x) =g(x)

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The complete question is as follows:

Two different plants that grow each month at different rates are represented by the functions f(x) and g(x). In what month does the height of the f(x) plant exceed that of the g(x) plant?

Month (x) / f(x) = 3x / g(x) = 5x + 12

1 / 3 / 17

2 / 9 / 22

A) Month 3

B) Month 4

C) Month 5

D) Month 6