How would I solve questions a through e?

The coordinates of the point shown after the transformation f(-2x) are given as follows:

(-4,-1).

The original coordinates of the the point in this problem are given as follows:

(2,-1).

Hence:

The transformation is given as follows:

f(-2x).

Meaning that the x-coordinate is multiplied by -2, hence the coordinates of the point shown after the transformation f(-2x) are given as follows:

(-4,-1).

(as 2 x -2 = -4).

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Answer:

40:60:80

Step-by-step explanation:

1. add the ratio first 2+3+4 =9, then divide the amount by the total number of parts

2. multiply the quotient by each part (20×2, 20×3 and 20×4)

30 * x⁵y⁸ will be the volume of the given rectangular prism.

Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface. The cubic meter (m3), a derived unit, is the SI unit of volume. Volume is another word for capacity.

Given a rectangular prism whose sides are mentioned in the problem.

From the general formula of the Volume of Cuboid:

Volume of cuboid = length *width*height

In our case,

Length = 3x²y²

Width = 5x²y⁴

Height = 2xy²

Thus,

volume of rectangular prism = 3x²y²* 5x²y⁴ * 2xy²

volume of rectangular prism = 30 * x⁵y⁸

therefore, the volume of the given rectangular prism will be 30 * x⁵y⁸.

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For a ΔABC when rotated 90° clockwise and dilated with a factor of 2 the new vertices becomes option C: A'(0,4), B'(6,-4) and C'(-2,-2).

What is dilation?

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial shape should be stretched or contracted during a dilatation.

The vertices of triangle ABC are - A(-2,0), B(2,3) and C(1,-1).

When an object is rotated at an angle of 90° clockwise the formula for the vertices becomes (x,y) → (y,-x)

So, the new vertices are -

A(-2,0) → [(0),-(-2)] → a(0,2)

B(2,3) → [(3),-(2)] → b(3,-2)

C(1,-1) → [(-1),-(1)] → c(-1,-1)

When an object is dilated by a factor of 2 the formula for the vertices becomes (x,y) → (2x,2y)

So, the new vertices are -

a(0,2) → [2(0),2(2)] → A'(0,4)

b(3,-2) → [2(3),2(-2)] → B'(6,-4)

c(-1,-1) → [2(-1),2(-1)] → C'(-2,-2)

Therefore, the new vertices are A'(0,4), B'(6,-4) and C'(-2,-2).

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Answer:

d. $6

Step-by-step explanation:

On the left side of the expression, the first term is cos(x y)sin(y) and the second term is sin(x y)cos( y ).cos(x y)sin(y) sin(x y)cos(y) = cos(x y)sin(y) − sin(x y)cos(y)

We can use the trigonometric identity sin(A)cos(B) - cos(A)sin(B) to simplify the expression.

On the left side of the expression, the first term is cos(x y)sin(y) and the second term is sin(x y)cos( y ).

We can rearrange the terms and apply the identity, which gives us:

On the left side of the expression, the first term is cos(x y)sin(y) and the second term is sin(x y)cos( y ).

cos(x y)sin(y) − sin(x y)cos(y)

the complete question is :

What is the result of cos(x y)sin(y) - sin(x y)cosy?

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The maximum profit that the florist will earn from selling celebration bouquets is $675.

The florist will break even after 20 one-dollar increases.

The interval of the number of one-dollar increases for which the florist makes a profit from celebration bouquets is [tex](0,20)[/tex].

Answer: He bought 16 books

Step-by-step explanation: $133-$5=$128 (taking away shipping)

$128/8=16 (separating non-shipping price into groups of $8 to compensate for the cost of books)

A: 8b+5=133

B: 8b-133=5

b=16

The percentage of American women that have shoe sizes that are at least 11.1 is; 0.0015

Empirical Rule

We are given;

Mean; x' = 8.04

Standard deviation; σ = 1.53

Using the empirical rule, we can have the data either 1, 2, or 3 standard deviations from the mean.

Thus;

At 1 standard deviation from the mean, we have;

8.04 ± 1(1.53)

⇒ (6.52, 8.56)

At 2 standard deviations from the mean, we have;

8.04 ± 2(1.53)

⇒ (5, 11.08)

At 3 standard deviations from the mean, we have;

8.04 ± 3(1.52)

⇒ (3.48, 12.6)

We can see that the one with at least 12,6 is 3 standard deviations from the mean which from the empirical rule is 99.7%

Thus;

percentage of American women have shoe sizes that are at least 12.6 = 100% - 99.7% - 0.15%

P(x ≥ 12.6) = 0.15% = 0.0015

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The interval notation for the set {x ∈ Z : −1 ≤ x < 43} is [-1, 43).

An "interval" in mathematics refers to a set of numbers between two given endpoints, where the endpoints can be included or excluded from the set, depending on the specific interval notation being used.

In the case of the set {x ∈ Z : −1 ≤ x < 43}, we are looking at all integers (x ∈ Z) that satisfy the inequality −1 ≤ x < 43.

This means that we are looking at all integers greater than or equal to −1 and less than 43.

Here we need to express this set in interval notation, we have to decide whether or not to include the endpoints −1 and 43.

Since the inequality symbol used is "<" for 43, we will exclude 43 from the set and use a parenthesis around 43 in the interval notation to indicate that it is not included in the set.

Therefore it can be written as, [-1, 43).

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Answer:

Each drink costs $1.50

Step-by-step explanation:

Let d = the cost of a drink

6(4.50) + 2d = 5(4.5) + 5d  Distribute the 6 and 5

27 + 2d = 22.50 + 5d  Subtract 2d from both sides

27 + 2d - 2d = 22.50 + 5d - 2d

27 = 22.50 + 3d  Subtract 22.50 from both sides

4.5 = 3d  Divide both sides by 3

1.50 = d                    

Answer:

Below

Step-by-step explanation:

1) The derivative of (2x³-5x²+6x-3)/x² is (6x²-10x+6-3x)/x³

2) The derivative of sin^-1(x)+cos^-1(x)-Inx is (1/(√(1-x²))*dx + (-1/(√(1-x²))*dx )- (1/x)*dx

3) The derivative of 5^x - 6cosec1/2(x) + 3/7(cos5x) - 2 is (ln(5) * 5^x) - (6*(-csc(x)cot(x))dx) + (3/7(-5sin(5x))*dx)

The ratio of Mary's share to Katherine's share to Alex's share is 5:4:1, which means Mary pays 5/10 of the bill, Katherine pays 4/10 of the bill, and Alex pays 1/10 of the bill.

To find the ratio, we can write their contribution as a fraction of the total parts and then solve the fractions then they'll have the same denominator.

So, Mary's share is 5/10, Katherine's share is 4/10, and Alex's share is 1/10.

To convert this as a ratio, we write 5:4:1, where each number represents the number of parts each person pays, and the colon separates each person's contribution.

Therefore, the ratio of Mary's share to Katherine's share to Alex's share is 5:4:1

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Answer:

50,000

Step-by-step explanation:

Answer:

Step-by-step explanation:

c is the correct answer

Answer: c

Step-by-step explanation:

The total number of different combinations Sam can make is 120.

The number of different ways that Sam can order the parts is given by the product of the number of choices he has for each part:

Chips: 2 options

Hard Drive: 4 options

Memory: 3 options

Accessory Bundle: 5 options

Therefore, the total number of different combinations Sam can make is 2 x 4 x 3 x 5 = 120.

This is about a person named Sam who is assembling a computer and has a choice of parts from different brands and stores. The problem is to calculate the number of different combinations of parts he can choose from. The solution involves finding the number of options he has for each part (chips, hard drive, memory, and accessory bundle) and then multiplying these numbers to get the total number of combinations.

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The simplified form of the expression is  [tex]2^{-3}[/tex].

What is expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

Here the given expression is,

=> [tex]\frac{2^5\times 2^2}{2^7 \times 2^3}[/tex]

We know that [tex]a^x\times a^y = a^{x+y}[/tex] then

=> [tex]\frac{2^{5+2}}{2^{7+3}}[/tex]

=> [tex]\frac{2^7}{2^{10}}[/tex]

Now [tex]\frac{a^x}{a^y}=a^{x-y}[/tex] then

=> [tex]2^{7-10}[/tex]

=> [tex]2^{-3}[/tex]

Hence the simplified form of the expression is  [tex]2^{-3}[/tex].

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There are 720  different slates of candidates possible.

Permutation:

The permutation is a statistical method that determines the number of possible arrangements. In permutation, the order of selection is important and replacements are not allowed.

Permutation can be divided into three different types:

The general formula of Permutations:

[tex]^nP_r=\frac{n!}{(n-r)!}[/tex]

n= total number of members.

r=number of members selected.

Here n=10 and r= 3

Now substitute the values in the above formula:

[tex]^nP_r=\frac{10!}{(10-3)!} \\\\^nP_r=\frac{10!}{7!}\\\\^nP_r= \frac{10*9*8*7!}{7!} \\\\^nP_r=10*9*8\\\\^nP_r=720[/tex]

Therefore, there are 720 different slates of candidates possible.

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The value of a and b are 1 and 6 respectively.

The equation of the line is y = 1 / 3 x + 1.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, let's find the value of a and b using the line.

Hence, using (3, 2) and (12, 5)

slope = 5 - 2 / 12 - 3

slope = 3 / 9

slope = 1  /3

Therefore, let's find the y-intercept using (3, 2)

y = 1 / 3 x + b

2 = 1  /3 (3) + b

2 - 1 = b

b = 1

Therefore, the equation is y = 1 / 3 x + 1.

Let's find a and b

a is the y-intercept. Therefore, a = 1

using (b, 3)

y = 1 / 3 x + 1

3 = 1 / 3 (b) + 1

3 - 1 = b / 3

b = 2 × 3

b = 6

Therefore,

a = 1 and b = 6

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The solution to the inequality equation given above would be = X ≥ 3

An Inequality equation is defined as the type of equation that is used to show the relationship between two variables that are not equal using the following symbols such as < or >.

The equation given are as follows:

= 8x−14≤10

Bring the like terms together;

= 8x ≤ 10+14

= 8x ≤ 24

= X ≥ 24/8

= X ≥ 3

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The solution to the inequality equation is expressed as; x ≤ 3

Equations and inequalities are considered to be both mathematical sentences that are formed by relating two expressions to each other. In an equation, the two expressions are considered as equal which is shown by the symbol =. Meanwhile in an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

The equation we are to solve is; 8x − 14 ≤ 10

Add 14 to both sides to get;

8x ≤ 24

Divide both sides by 8 to get;

x ≤ 3

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Answer: 325000

Step-by-step explanation:

In 2000 the population was 250,000 and it would grow 3 percent a year which is 7500 so that means we add 75000 since 7500 X 10 = 75000 so we add it which gives us 325000 in 2010.

Answer:

Step-by-step explanation:

THE CONSTANT RATE WILL BE 2.5 so that would =75%

Answer:

n = - 5

Step-by-step explanation:

- 2(8n - 3) = 43(n + 7) ← distribute parenthesis on both sides

- 16n + 6 = 43n + 301 ( subtract 43n from both sides )

- 59n + 6 = 301 ( subtract 6 from both sides )

- 59n = 295 ( divide both sides by - 59 )

n = - 5

Answer:

n=7.14

Step-by-step explanation:

-2(8n-3)=43(n+7)

distribute

-16n+6=43n+301

add 16n on both sides

6=43n-301

add 301 on both sides

307=43n

divide both sides by 43

n=7.1395

Answer:

Any angles that share a common vertex and side are adjacent angles.

Answer:

x = 7.5

y = 166º

Step-by-step explanation:

4 ------ 6

5 ------ x

4x = 30

x = 7.5

116 + 61 + 90 + (y - 73) = 360

y - 73 = 360 - 267

y = 93 + 73

y = 166

Answer:

The other answer shows how to get it but for points just showing his answers are right.

Step-by-step explanation:

The age of Lisa and Myra now is 35 years old and 5 years old, respectively.

To determine how old each person now, use algebraic expression and equation.

Let x = current age of Lisa

y = current age of Myra

If the sum of Lisa's age and Myra's age is 40, then we can express it as:

x + y = 40

x = 40 - y

If in 10 years, Lisa will be 3 times as old as Myra, then we can express it as:

x + 10 = 3(y + 10)

x + 10 = 3y + 30

x - 3y = 20

Substitute the equation for x into the 2nd equation and solve for y.

x - 3y = 20

(40 - y) - 3y = 20

40 - 4y = 20

4y = 20

y = 5

Substitute the value of y into the equation for x and solve.

x = 40 - y

x = 40 - 5

x = 35

Therefore, Lisa is 35 years old while Myra is 5 years old.

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The value of x in the triangle is 14.4 units.

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, let's find the length of x in the right triangle as follows;

Using similar triangle ratios,

x / 18 = 24 / 30

cross multiply

30x = 24 × 18

30x = 432

divide both sides of the equation by 30

x = 432 / 30

x = 14.4

Hence,

x = 14.4 units

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Our legs range in length from 15 to 36. (A & B). A hypotenuse is 39.

We must apply Pythagorean Theorem in order to solve for this.

In order to find the hypotenuse (C), or the side that is opposite the 90-degree angle, we add the squares of the legs (A & B). This is known as the Pythagorean Theorem.

A² + B²  = C²  is the Pythagorean Theorem's formula.

We have two different leg lengths: 15 and 36. (A & B).

Square 15 and 36.

15²  = 225

36²  = 1,296

Let's add the side lengths now that we have them.

225 + 1,296 = 1,521.

We now need to square root our sum in order to find C.

39 is the square root of 1,521.

39 is your hypotenuse.

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An orthogonal matrix has determinant and real eigenvalues of either 1 or -1, depending on the orientation and reflection properties of the matrix.

An orthogonal matrix is a special type of square matrix where the transpose of the matrix is equal to its inverse.

The determinant of an orthogonal matrix is either 1 or -1. This is because the determinant of a matrix represents the scaling factor of the matrix and an orthogonal matrix can only scale the space by a factor of 1 or -1.

The determinant of 1 indicates that the matrix preserves orientation, while a determinant of -1 indicates that the matrix reflects the space.

The real eigenvalues of an orthogonal matrix are either 1 or -1. This is because an orthogonal matrix preserves the magnitude of vectors, and therefore, the eigenvalues must be either 1 or -1.

The number of eigenvalues equal to 1 is equal to the number of dimensions preserved by the matrix, and the number of eigenvalues equal to -1 is equal to the number of dimensions reflected by the matrix.

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Answer:

[tex]x=\frac{1}{27}[/tex]

Step-by-step explanation:

Solve for x.

We need to use the quotient property of logarithms.

Quotient Property of Logarithms: [tex]\log _{b} (x)-\log _{b} (y)=\log _{b} (\frac{x}{y} )[/tex]

Apply the property to our equation.

[tex]\log(\frac{3}{x})=2\log(9)[/tex]

Simplify the right side by moving the 2 inside the logarithm.

[tex]\log(\frac{3}{x})=\log(9^2)[/tex]

For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.

[tex]\frac{3}{x}=9^2[/tex]

Evaluate [tex]9^2[/tex].

[tex]\frac{3}{x}=81[/tex]

Multiply both sides of the equation by x.

[tex]\frac{3}{x}x=81x[/tex]

Cancel the common factor of x on the left side.

[tex]3=81x[/tex]

Divide both sides by 81.

[tex]\frac{3}{81} =\frac{81x}{81}[/tex]

[tex]\frac{3}{81} =x[/tex]

Simplify the fraction.

[tex]x=\frac{1}{27}[/tex]