Hello, I need some assistance with this homework question please for precalculusHW Q10

a) the coordinates of the dilated trapezoid is F'(-3, 2), G'(-2, 3), H'(-1, 3), I'(0, 2)

b) Dilation is reduction.

In this question, we have been given a trapezoid has coordinates F (−9, 6), G (−6, 9), H (−3, 9), and I (0, 6).

a. We need to dilate the trapezoid by a scale factor of 1/3 with a center of dilation at the origin.

The scale factor is 1/3

so, the coordinates of the image would be,

F' = 1/3 (-9, 6)

   = (-3, 2),

G' = 1/3(-6, 9)

    = (-2, 3),

H' = 1/3 (−3, 9)

    = (-1, 3),

and I' = 1/3 (0, 6)

         = (0, 2)

b. We know that a dilation is a geometric transformation that either enlarges or reduces a figure in size.

As we know, if the scale factor is between 0 to 1 then the image is reduction and if the scale factor is greater than 1 then the image is enlargement.

Here, scale factor is 1/3 which is 0 < 1/3 < 1

So, in this case the dilation is reduction.

Therefore, a) the coordinates of the dilated trapezoid is F'(-3, 2), G'(-2, 3), H'(-1, 3), I'(0, 2)

b) Dilation is reduction.

Learn more about the dilation here:

https://brainly.com/question/10855880

#SPJ1

• Given:

You need to find this probability:

The Binomial Distribution Formula is:

Where "n" is the number of trials, "x" is the number of successes desired, and "p" is the probability of getting a success in one trial.

In this case you know that:

Therefore, by substituting values into the formula and evaluating, you get:

• Given that:

You need to find:

In this case:

Therefore, using the same formula, you get:

• Given:

You need to find:

This is:

Therefore, using the formula, set up:

Then, you get:

Hence, the answers are:

A list of all the three-element subsets of the given set include the following:

In order to determine the three-element subsets from the given set {1, 2, 3, 4, 5}, we would have to calculate the number of ways to choose the three (3) elements by applying a mathematical model referred to as combination.

Mathematically, combination is given by this mathematical equation:

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

Where:

Substituting the given parameters into the formula, we have;

Number of ways = ⁵C₃

Number of ways = 5!/(3! × (5 - 3)!)

Number of ways = 5!/(3! × 2!)

Number of ways = [5 × 4 × 3 × 2 × 1]/[3 × 2 × 2 × 1]

Number of ways = 120/12

Number of ways = 10 ways.

Therefore, there are 10 three-element subsets of this set.

Read more on combination here: https://brainly.com/question/9449874

#SPJ1

Complete Question:

List all the three-element subsets of the set {1, 2, 3, 4, 5}

Answer:

9*x³ or 9x³

Step-by-step explanation:

a number = x

cubed = to the power of 3

not really much to explain here

Answer:

z=16

Step-by-step explanation:

1/4 *16=4

and 4 +8=12

Answer:

is that a z or 2?

Based on the calculations using the given points, the slope in this situation is equal to 5.

A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.

Mathematically, the slope of any straight line can be calculated by using this formula;

[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Substituting the given points into the formula, we have;

Slope = (30 - 10)/6 - 2)

Slope = 20/4

Slope = 5.

In conclusion, the slope of the line that passes through the given points is equal to 5.

Read more on slope here: brainly.com/question/3493733

#SPJ1

The difference between each annual wage figure and the poverty threshold is as shown in the attached completed table.

Annual Income is a term in economics that is calculated by multiplying the Hourly wage by 4,000 hours.

Now, the Difference between annual wage and the federal poverty line is calculated by subtracting the 2019 Poverty threshold of $13,011 from the Annual Income.

The Difference between annual wage and median household income is calculated by deducting the 2019 Median household income of $68,703 from the Annual income. Negative balances are highlighted.

The attached table shows us the completed annual income table

Read more about Annual Income at; https://brainly.com/question/25745683

#SPJ1

Answer:

5

Step-by-step explanation:

use math-way

Answer:

  987

Step-by-step explanation:

You want to determine a three-digit combination based on clues about which digits are right and/or correctly placed.

This tells you one of digits 1, 2, or 7 is correct and correctly placed.

Clue 2 tells you that digit is not 1. Clue 4 tells you that digit is not 2.

  7 is correctly placed as the 3rd digit

We already know that 1 is not the correct digit. This means 3 must be the first digit, or 8 must be the first or second digit.

We already know that 7 is a correct digit, properly placed as the 3rd digit. Since 1 is not a correct digit, 9 must be a correct digit, properly placed as the 1st digit.

  9 is correctly placed as the 1st digit

Combining this fact with Clue 2 means ...

  8 is correctly placed as the 2nd digit

The combination is 987.

__

Check

Clues 4 and 5 are consistent with this combination.

Answer:420

Step-by-step explanation: multiply 300 times 4% =12. Then multiply 12 times 10=120. Then add 300 and 120=420

Length of the side, x = 11/2

radical form, x = √5.5

The longest side of a right-angled triangle which is the side opposite to the right angle is called hypotenuse. The hypotenuse can be easily found using the Pythagorean theorem. It states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

As given in question, ∅ = 60°,

Using, Cos ∅ = adjacent/hypotenuse :

Cos 60°= x/11

As we know cos 60° = 1/2

1/2 = x/11

x, length of the side = 11/2= 5.5

radical form = 5.5

To know more about hypotenuse, refer

https://brainly.com/question/2217700

#SPJ13

ANSWER

STEP-BY-STEP EXPLANATION:

Given information

Find g(5x)?

Step 1: make x = 5x

Answer: 11

Step-by-step explanation: 8/4.40 = x/6.05

8 times 6.05

Divide by 4.40 is 11

The total ratio of the drive is 9.58:1.

Given ratios of the three separate stages of a gear reduction drive are 3:1,2.38:1 and 4.2:1.

To find the total ratio of the drive we have to add the respective ratios.

When the denominator of the ratios are same, as in this case we just have to add the numerators to obtain the result.

Total ratio of the drive = 3:1 + 2.38:1 + 4.2:1 = 9.58:1

So, the total ratio of the drive is 9.58:1.

To learn more about ratios visit:

https://brainly.com/question/24199409

#SPJ9

Answer:

Range is called a set of possible outputs..in an realtion or function.

Every relation is not function but all function is relation

Actually some specified relations are called function.

Thanks

Here Range= {5}

Answer: 35

Step-by-step explanation:

1) Substitute the x's and y's

(2)9+(12−(-5))

2) Simplify the numbers inside the equation

18+(12-(-5)

= 18+(17)

= 35

3) Solved.

35

[tex]\sin^2 x=1-\cos^2 x \\ \\ \cos^2 x=1-\sin^2 x[/tex]

Equation is 5y = 3x + 8.

Slope is the inclination of a line with respect to the horizontal is measured numerically. The slope of any line, ray, or line segment in analytical geometry is defined as the ratio of the vertical to the horizontal distance between any two points on the line, ray, or segment. The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope.

Given Data

line that passes through the point (1, -1) &

is parallel to the graph of y = 3/5x + 2

y = mx + c

y = [tex]\frac{3}{5}[/tex]x + 2

m = [tex]\frac{3}{5}[/tex]

Equating points,

-1 = [tex]\frac{3}{5}[/tex](1) + c

-1 = [tex]\frac{3}{5}[/tex] + c

-1 - [tex]\frac{3}{5}[/tex] = c

[tex]\frac{-5-3}{5}[/tex] = c

[tex]\frac{-8}{5}[/tex]

Equation-

y = [tex]\frac{3}{5}[/tex]x + [tex]\frac{8}{5}[/tex]

5y = 3x + 8

Equation is 5y = 3x + 8.

To learn more about slope, visit:

https://brainly.com/question/3605446

#SPJ9

Answer: for the first one, there is no picture i need a picture to solve it that's also for the second one.

Step-by-step explanation:

hope that helps

Answer:

9812.29

Step-by-step explanation:

Using the compound interest formula,

[tex]8500 \left(1+\frac{0.024}{4} \right)^{(6)(4)} \approx 9812.29[/tex]

Given:

The expression is,

Simplify the expression,

Answer:

Probability of randomly selecting two members who currently hold positions of chairman and ranking member and reassigning them to their current positions from a committee of 14 members is (1 /182).

As given,

Total members in the committee=14

Number of members serve as chairman and ranking member=2

Total number of ways to assigned new position

=¹⁴P₂

=(14!) / (14-2)!

=(14 × 13 × 12!) / 12!

=14 ×13

=182

Each member is equally likely to serve in any of positions.

Each position there is only one way to reassign position.

Probability of randomly selecting two members = 1 /182

Therefore, probability of randomly selecting two members who currently hold positions of chairman and ranking member and reassigning them to their current positions from a committee of 14 members is (1 /182).

Learn more about probability here

brainly.com/question/11234923

#SPJ1

Answer: y=1

Step-by-step explanation:

1. Subtract 4y from both sides to get y + 4 = 5.

2. Then subtract 4 from both sides to get y = 1.

Therefore, you get your answer, y = 1. Hope this helps!

The fraction of the man's income left is 3/20.

Let's assume the monthly income of the man is x.

Income spend on children's school fees =  [tex]\frac{1}{4} x[/tex]

Income spend on home affairs =  [tex]\frac{3}{5} x[/tex]

The fraction of his income left with the man is,

Total income - Total expenditure

=  [tex]x-(\frac{1}{4} x + \frac{3}{5} x)[/tex]

=  [tex]x-(\frac{5x+12x}{20})[/tex]

=  [tex]x - \frac{17x}{20}[/tex]

=  [tex]\frac{3}{20}x[/tex]

So the man has 3/20 of his income left with him.

To learn more about fractions visit:

https://brainly.com/question/3516373

#SPJ9

The first four terms of the binomial series are  1, x, - x²/2 and - 1/32x³ respectively.

The binomial provided to us is [tex](1+2x)^{1/2}[/tex]

To find out the first four terms of the binomial, we shall first extend the standard binomial (1+x)^n.

(1+x)^n = 1 + nx + [n(n - 1)/2!] x² +  [n(n - 1)(n - 2)/3!] x³ +...

As we can see here,

The value of x = 2x,

The value of n = 1/2.

We get,

(1+2x)^1/2 = 1 + 1/2(2x) + [1/2(1/2-1)/2!]x² + [1/2(1/2-1)(1/2-2)/3!]x³ +

(1+2x)^1/2 = 1 + x  - x²/2 - 9/4x³ + .....

From the expansion, we can see,

First term = 1

Second term = x

Third term = -x²/2

Fourth term = -1/32x³.

To know more about Binomial series, visit,

https://brainly.com/question/14004514

#SPJ1

optionsWe want to obtain an expression equivalent to 8 using these symbols and numbers.

The option that exactly matches this is,

That is because,

7 divided by 7 is 1.

1 squared is still one, and;

1 added to 7 is 8.

So one answer is option D.

We also have another answer.

Which is;

That's because 7 squared is 49, and 7 + 49 is 56.

56 divided by 7 is 8.

So our answers are option C and option D

The graph of the solution to this inequality is: C. number line with an open circle plotted at negative eight and arrow pointing left.

A number line simply refers to a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.

Next, we would solve the given inequality as follows:

−0.4b + 2.4 < 5.6

Subtracting 2.4 from both sides, we have:

−0.4b + 2.4 - 2.4 < 5.6 - 2.4

−0.4b < 5.6 - 2.4

−0.4b < 3.2

Dividing both sides by -0.4, we have:

b < -3.2/0.4

b < -8

In conclusion, the circle on a number line should be open and would point to the left when the inequality symbol is <.

Read more on inequality here: brainly.com/question/3061666

#SPJ1

In the given triangle we have :

Base line with angle A, and the Hypotenuse of angle A

Since the ratio of Base to the hypotenuse is the Cosine trignometric ratio:

Answer : Cosine

The given graph shown in the image is a function, Option b is correct.

Given that,
A graph is shown, and we have to determine whether the graph shown is a function or not.

The function which is in format f(x) =a^x  where a is constant and x is variable,  the domain of this exponential function lies   (-∞, ∞).

here,
The graph shows of a curve representing an exponential function,

There is why the graph shown is a function, and also the graph is continuous and as well as differentiable.

Thus, the given graph shown in the image is a function, Option b is correct.

learn more about exponential function here:

brainly.com/question/15352175

#SPJ5

Answer:

1.45

Step-by-step explanation:

1200-800=400

400/275=1.4545454545...

the answer $1.45