Which expression is equivalent to 4sin²(x) - 8sin²(x/2)
4(cos(x) - cos²(x))
4(-cos(x) - cos²(x))
4(2-cos(x) - cos²(x))
4(2 + cos(x) - cos²(x))

Answer:

6(4u+3u)

Step-by-step explanation:

4u+3u= 7u

you add the 4u and the 3u because they're inside the parentheses

and then you get 6(7u)  

Step 1:

Write the regression line equation.

Step 2:

y represents the cost and x represent the number of years.

From 2005 till 2022

x = 17 years

Step 3:

Let find the cost to go on a safari in 2022.

Final answer

The cost to go on a safari in 2022 = $74

Answer:

Step-by-step explanation:

(3x−5)(3x+5)

Multiplication can be transformed into difference of squares using the rule: (a−b)(a+b)=a

2

−b

2

.

(3x)

2

−5

2

Expand (3x)

2

.

3

2

x

2

−5

2

Calculate 3 to the power of 2 and get 9.

9x

2

−5

2

Calculate 5 to the power of 2 and get 25.

9x

2

−25

The probability of either a dot or a dragon tile is 48/64

Number of dot tiles in Mahjong game = 36 tiles

Probability of a dot tile = 36/64

Number of wind tiles in Mahjong game = 16 tiles

Probability of a wind tile = 16/64

Number of dragon tiles in Mahjong game = 12 tiles

Probability of a dragon tile = 12/64

Total number of tiles in the Mahjong strategy game = 36+16+12 = 64 tiles

Probability of Grace's drawing a dot or a dragon tile:

(Number of dot tiles + Number of dragon tiles)/ Total number of tiles in the game

= (36+12)/64

= 48/64

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The distance between the peter's house and John's house is found as √116 units.

For the given question;

Let the coordinates of the John's house be (x₁, y₁).

Let the coordinates of Paul's house M be (x, y) = ( 3, -5).

Let the coordinates of Peter's house be (x₂, y₂) = (5, -4).

Then, by the formula of mid point.

x = (x₁ + x₂)/2

Put the values and simplifying.

x₁ = (2×3) - 5

x₁ = 1

Similarly for the y coordinates.

y = (y₁ + y₂)/2

Put the values and simplifying.

y₁ = (2×-5) - 4

y₁ = -14

Thus, the coordinates of the John's house is found as (1, -14).

Now, the distance between peter's house and john's house is;

d = √(x₁ - x₂)² + (y₁ - y₂)²

Put the values;

d = √(5-1)² + (-4+14)²

d = √(4)² + (10)²

On simplification,

d = √116 units.

Thus, the distance between the peter's house and John's house is found as √116 units.

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Answer:

17.75

Step-by-step explanation:

The expression of the given quadratic equation in factor form is (x - 3)(x - 6) = 0 with a solution of x = 3 or 6.

We are given the quadratic expression;

(x - 3)² = 3(x - 3)

By expansion of the brackets, we have;

x² - 6x + 9 = 3x - 9

x² - 6x + 9 - 3x + 9 = 0

x² - 6x - 3x + 18 = 0

By grouping into brackets we have;

(x² - 6x) - (3x - 18) = 0

By bringing out common factors, we have;

x(x - 6) - 3(x - 6) = 0

Thus, we can write it in factor form as;

(x - 3)(x - 6) = 0

x = 3 or 6

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The number 0.0000005478 written in scientific notation is  54.78 x 10⁻⁸.

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

It is given that,

the given number in its scientific notation is 0.0000005478.

Using scientific notation, one can express extremely big or extremely small values. When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation. For instance, 650,000,000 can be represented as  6.5 ✕ 10^8 in scientific notation.

The decimal point must be moved till it is to the left of the first non-zero number in order to be written in scientific notation. The exponent is the number of places the decimal point advances since each movement signifies a "power of 10".

Thus, the number 0.0000005478 written in scientific notation is  54.78 x 10⁻⁸.

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Answer: 3,52 x 10²

Step-by-step explanation:

Answer:

3.5 x [tex]10^{2}[/tex]

Step-by-step explanation:

Multiply the numeric values times each other and add the exponents:

(3.2 x 1.1) x ([tex]10^{-7}[/tex] x [tex]10^{9}[/tex])

3.52 x [tex]10^{2}[/tex]

To one significant figure: 3.5 x [tex]10^{2}[/tex]

Answer:

The correct equation is b, x = 4.

By solving a quadratic equation we will find two solutions, one is good and that is x = 0.62, and the other is extraneous and is x = -1.62

Here we have the following equation:

ln(x + 2) + ln(2x - 1) = 0

To solve this we need to know two things, first:

ln(a)+ ln(b) = ln(a*b)

ln(1) = 0

Using the first property, we can rewrite:

ln(x + 2) + ln(2x - 1) = ln( (x + 2)*(2x - 1)) = 0

And that can only be equal to zero if:

(x + 2)*(2x - 1) = 1

So we have a quadratic equation:

(x + 2)*(2x - 1) = 1

2x² - x + 4x - 2 = 1

2x² + 3x - 3 = 0

The solutions are:

[tex]x = \frac{-3 \pm \sqrt{3^2 - 4*3*(-3)} }{2*3} \\\\x = \frac{-3 \pm 6.7 }{6}[/tex]

So we have:

x = (-3 + 6.7)/6 = 0.62

x = (-3 - 6.7)/6 = -1.62

The second solution when evaluated in the second term of the equation gives:

ln(2*(-1.62) - 1) = ln(-4.24)

And this is not defined, so x = -1.62 is an extraneous solution.

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The linear equation that passes through the anchor points (-3, -38) and (8, 61) is:

y = 9*x - 11

The general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

We know that for a line that passes through two points (x₁, y₁) and (x₂, y₂) can be written as:

a = (y₂ - y₁)/(x₂ - x₁)

Now, in this case we know that our line passes through the points (-3, -38) and (8, 61), then the slope will be:

a = (61 + 38)/(8 + 3) = 9

Replacing that we get:

y = 9*x + b

Now, using one of the points we can find the y-intercept, I will use (8, 61), replacing the values we get:

61 = 9*8 + b

61 = 72 + b

61 - 72 = b

-11 = b

The linear equation is:

y = 9*x - 11

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The given side lengths of AC, BC, and EF, of the similar triangles, using the ratio of similarity between segments of similar figures, gives;

The measure of side DF as 15 centimeters

When two figures are similar, the corresponding side pairs have the same ratio of one to the other.

The given information on the two triangles are;

Triangle ∆ABC is similar to triangle ∆DEF

Triangle ∆ABC and triangle ∆DEF are right triangles

The length of segment AC = 9 centimeter

Length of segment BC = 15 centimeters

In triangle ∆DEF, we have;

Length of segment EF = 25 centimeters

Required;

The length of segment DF

Solution;

By comparison, the corresponding sides of the two triangles are;

AC corresponds to DF

BC corresponds to EF

In similar triangles, the ratio of the corresponding sides are the same, which gives;

[tex] \displaystyle{ \frac{AC}{DF} = \frac{BC}{EF} }[/tex]

[tex] \displaystyle{ \frac{9}{DF} = \frac{15}{25} }[/tex]

[tex] \displaystyle{ DF = \frac{9 \times 25}{15} = 15 }[/tex]

The measure of side DF is 15 centimeters

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The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Expressions that add up to one another make form an equation. A formula is an equation containing two or more variables that shows how the variables relate to one another. A line with the equation y=mx+b, where m denotes the slope and b the y-intercept, is an example of a linear equation.

Given that we've done it

h(t)=-16t²+305

Here, h stands for the penny's height.

The time is expressed as t in seconds.

Now, t equals 4 seconds.

The distance the penny must travel before it touches the earth is explained by

h(4)=- 16(4)² + 305

h(4)=- 16 x 16+ 305

h(4)= 256 - + 305

h(4)= 49 feet

Hence, penny need to travel 49 feet before it hits the ground

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Solving a linear equation that comes from the relation:

TV = TU + UV

We will see that the value of x is 1.

I'm answering the question you wrote.

We know that point U is on the line segment TV, then we can write:

TV = TU + UV

This says that the total length of TV is equal to the sum of the two segments in it.

It says:

"the length of segment TV is equal to the sum between the lengths of segments TU and UV"

Here we know that:

TU = 4

UV = 5x

TV = 3x + 6

Then we can write the linear equation:

3x + 6 = 4 + 5x

And solve this for x.

3x + 6 = 4 + 5x

6 - 4 = 5x - 3x

2 = 2x

2/2 = x

1 = x

The value of x is 1.

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The probability that the dial stops on a yellow or blue slice is 50%.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the event's impossibility and 1 indicates certainty.

An event's likelihood of occurring increases with its probability. The flip of a fair (unbiased) coin serves as a straightforward illustration. Since there are no other possible outcomes and the coin is fair, the probability of both the outcomes, "heads" and "tails," is half.

The total no. of outcomes in the events = 10

Outcomes favourable to yellow and blue = 3 + 2  

                                                                     = 5

Probability = outcomes favourable/total no. of outcome

                  =  5/10

                  = 1/2

                  = 1/2 × 100%

                  = 50%

Thus, The probability that the dial stops on a yellow or blue slice is 50%.

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Answer:

[tex]y - 3 = -\dfrac{1}{4}(x - 4)[/tex]

Step-by-step explanation:

This can be solved without too much calculation

First note that the lope of the graph is negative. If you look at the graph, as x increases, y decreases so that indicates a negative slope

We can safely eliminate the last two options because the coefficient of x in both is +1/4 indicating a positive slope

That leaves the first two for consideration

We can plug in the x, y  values for the given point (4, 3) which lies on the  line and see which of the equations is consistent, i.e whether the LHS and RHS of the equation match

Putting y = 3 and x = 4 in the first equation y - 4 = -1/4(x - 3) gives us
3 - 4 = -1/4(4-3) ??

-1 = -1/4(1) ?

-1 = -1/4? NO

So the correct choice is the second option and we can verify that by plugging in (4, 3) into y - 3 = -1/4(x - 4)

y - 3 = 3 - 3 = 0

x - 4 = 4 - 4 = 0

So 0 = -1/4(0) = 0

which is consistent

Answer: the volume of cube is 64 x6 + 144x4 + 108x2 + 27.

Step-by-step explanation: As given in the problem statement the volume

V = s3----- (1)

And

s = 4x2 + 3--------(2)

Hence,

the volume is obtained by substituting (2) in (1).

We get,

V = (4x2 + 3)3

= 64 x6 + 144x4 + 108x2 + 27

Therefore,

the volume of cube is 64 x6 + 144x4 + 108x2 + 27.

Answer:

Step-by-step explanation:

The side length, s, of a cube is 4x2 + 3. If V = s3, what is the volume of the cube?

Volume = s³

s = 4×2+3

so

(4 × 2  + 3)² =                 (remember PEMDAS)

(8 + 3)² =

11² =

121 units²

Answer: A≈1922.46

Step-by-step explanation: A=6a^2=6·17.92≈1922.46

The percentage of tip that Kylie left is 20%  

Finding percentage:

To find the percentage of the number in a given whole number divide the number by the whole number and multiply by 100. To find the percentage of the tip we will calculate the percentage of tips in the total cost.

Here we have,

To find the total plus tip, Kylie multiplied the cost of the meal by 1.2  

Let $ x be the cost of the meal

Then total cost plus including tip = x × 1.2 = 1.2x

From the above calculations,

The amount of tip paid by Kylie = 1.2x - x = 0.2x

There percentage of tip = (0.2x)/x × (100) = 20%      

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Answer: 13.56 kg

Step-by-step explanation:

We can make two equations:

1) A = B + 2.5

2) C = B - 4.86

Replace C with 6.2.

(6.2) = B - 4.86 can be rewritten as 6.2 + 4.86 = B.

B = 11.06

Add 2.5 to 11.06 and you get 13.56 kg.

Answer:

135

Step-by-step explanation:

If 3x = 5, x = 5/3

3^4 = 81

3^4 x = 81x = 81 x 5/3 = 135

Answer:

Last choice:

  3/10 · 2/9

Step-by-step explanation:

The total number of marbles and the number of red marbles is not provided but only one answer fits the problem solution

3/10 x 2/9 which is the last choice

It can be deduced that there are 10 marbles totally and 3 of them are red

The probability of a red marble on first draw = 3/10

After the first draw given a red marble was drawn, there are 2 red marbles and total of  marbles so the probability of a second red marble = 2/9

The combined probability is 3/10 x 2/9

Answer:

Length of segment PQ = 5

Step-by-step explanation:

Coordinates of P (-2, 4) and coordinates of Q are (3,4)

y coordinates are the same so the segment PQ is a horizontal line

The length is simply the difference between the x coordinates = 3 -(-2) = 3 + 2 = 5

Answer:

[tex]36\frac{5}{9}[/tex]

Step-by-step explanation:

Given expression:

[tex]329 \div 9[/tex]

Solve using long division:

[tex]\large \begin{array}{r}36\phantom{)}\\9{\overline{\smash{\big)}\,329\phantom{)}}}\\{-~\phantom{(}\underline{0\phantom{)).)}}\\ {32\phantom{...}}\\{-~\phantom{(}\underline{27\phantom{...}}\\59\phantom{)}\\-~\phantom{()}\underline{54\phantom{)}}\\5\phantom{)}\\\end{array}[/tex]

Therefore, the solution to the given expression is:  

If a milk truck delivers 486 dozen gallons of milk to stores in 1 day, then equation to calculate "g",  the number of gallons of milk the milk truck delivers in 1 day, can be written as [g = (486 * 12)]

As per the question statement, a milk truck delivers 486 dozen gallons of milk to stores in 1 day.

We are required to determine the equation that can best express "g", the number of gallons of milk the milk truck delivers in 1 day.

To solve this question, first we need to know what an equation is.

Here, We know that (1 dozen = a set of 12),

Then, [486 Dozen Gallons = (486 * 12)] gallons, which is the total number of gallons of milk the milk truck delivers in 1 day.

On the other hand, the variable "g" can also be used to determine the number of gallons of milk the milk truck delivers in 1 day.

Therefore, our required equation is [g = (486 * 12)].

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We need to know to solve equations by elimination method to solve the problem. The solution for the given pair of equations is g=0 and h=7.

When we solve a given pair of equations by elimination method, we need to express one of the variables in terms of the other variable and then substitute this value in the other equation to find the value of one of the variables. We use the value of this variable to find the value of the other variable. In this question we have a pair of equations and we need to solve for the variables g and h.

5g+2h=14..(i)

3g-4h=-28..(ii)

From equation (i)

2h=14-5g⇒h=7-5g/2

Substitute this in equation (ii)

3g-4(7-5g/2)=-28

3g-28+10g=-28

13g=0

g=0

Using value of g to find out h

h=7-5g/2=7

Therefore the solution of the given pair of equations is g=0 and h=7.

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Answer:

There are 20 long tables and 5 round tables y.

Step-by-step explanation:

Given:

long tables x + round tables y = total of 25 tables

8seats ·x +6seats ·y = 190 seats

Find x and y:

x+y= 25 so x= 25-y

8x+6y = 190, we substitute x for 25-y to find y

8(25-y) +6y = 190, we distribute 8 in parenthesis

200 -8y+6y = 190, combine like terms

200 -2y = 190, subtract 200 from both sides

-2y = 190-200, combine like terms

-2y = -10, divide both sides by -2

y = 5

x+y = 25, substitute y for 5

x+5 = 25, subtract 5 from both sides

x= 20

Conclusion:

There are 20 long tables and 5 round tables y.

Check :

20·8+5·6 = 160+30 = 190 seats

The slope of line segment XZ in triangle XYZ is: -1/3.

Given a line segment on a coordinate plane, we can find the slope of the line by using two points on the line to find the ratio of change in y / change in x = (y2 - y1)/(x2 - x1).

The coordinates of the two points of line segment XZ in triangle XYZ are:

Plug the values into the formula used for finding the slope of a line:

Slope of line segment XZ = change in y / change in x = (5 - 3)/(1 - 7)

Slope of line segment XZ = 2/-6

Slope of line segment XZ = -1/3

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The area of rectangle A is (A) 256 cm².

So, the area of rectangle A:

Therefore, the area of rectangle A is (A) 256 cm².

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Answer:

128 cm^2

Step-by-step explanation:

The area of rectangle B is 512 cm2. Since the dimensions of rectangle B are two times larger than the dimensions of rectangle A, the scale factor is 2.

To find the area of rectangle A, first square the scale factor, 2.

2^2 = 4

Next, divide the area of rectangle B by 4.

512 cm^2 ÷ 4 = 128 cm^2