Triangle ABC has vertices at (2,2), (4,3), and (6,1).
Using triangle ABC as the pre-image and origin as the center of dilation, what are the coordinates of a dilation of these vertices that uses a scale factor of 0.5?

A. (10,10)(20,15)(30,5)
B. (-1,-1)(-2,-15)(-3,-0.5)
C. (1,1)(1.5,2)(0.5,3)
D. (1,1)(2,1.5)(3,0.5)

Answer:

Step 1: a = 1, b = -4

Step 2: x = 2, f(2) = -9

Step 4: (5,0) and (-1,0)

Step 6: f(0) = -5

On the graph the points plotted are (-1,0) , (0,-5) , (2,-9) , and (5,0)

By assuming that x = 2 and substituting this into the original equation x^2 + x = 4, we arrive at a contradiction because 4 + 2 ≠ 4. Thus, we conclude through indirect proof that x cannot equal 2.

To give an indirect proof of the statement If x2 + x = 4, then x ≠ 2, we start by assuming the opposite of what we want to prove, which is that x = 2. Our goal is to show that this assumption leads to a contradiction.

Assume that x = 2. Substituting 2 for x in the original equation gives us (2)2 + 2 = 4 + 2 = 6, which is clearly not equal to 4. This contradicts the original equation x2 + x = 4. Since our assumption that x = 2 leads to a false statement, it follows that x cannot be 2, thereby proving the original statement by contradiction.

The method of assuming the negation and arriving at a contradiction shows that the original statement must be true according to the logical principle of indirect proof. Hence, if x2 + x = 4, then indeed x ≠ 2.

Answer:

Step-by-step explanation:

Alright, lets get started.

We are asked to find arithmetic mean of two terms given.

For finding arithmetic mean, we add up the values and divide the sum by the number of values.

Here we have given two numbers , below

[tex]a_{n-1}=3.9[/tex]

[tex]a_{n+1}=7.1[/tex]

So, mean of these two numbers will be = [tex]\frac{3.9+7.1}{2}[/tex]

So, mean of these two numbers will be = [tex]\frac{11}{2}=5.5[/tex]

So, arithmetic mean for given two numbers are 5.5  :  Answer (b)

Hope it will help :)

b.  5.5

FOR LEARNING ONLY.. not necessary to read, but I hope it helps!

you start with:

[tex]a_{n-1}=3.9\\a_{n-1}=7.1[/tex]

arithmetic questions like this are like finding an average.

so you add the values while dividing by the total of values there are.

in this case:

[tex]\frac{7.1+3.9}{2}[/tex]

which is simplified to:

[tex]\frac{11}{2}[/tex]

then decimal:

[tex]5.5[/tex]

Answer:

The initial value of the graph is 2. Third option is correct.

Step-by-step explanation:

It is given that A coordinate grid is shown with x and y axes labeled from 0 to 7 at increments of 1.

The line is passing through the points (0,2) and (7,5).

The point (0,2) is the y-intercept and graph labeled from 0 to 7, therefore 2 is the initial value.

Slope of line is

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{5-2}{7-0}=\frac{3}{7}[/tex]

The equation of line is

[tex]y=mx+b[/tex]

Where, m is slope and b is y-intercept. So the equation of given line is

[tex]y=\frac{3}{7}x+2[/tex]

At initial condition the value of x is 0. So, put x=0.

[tex]y=\frac{3}{7}(0)+2=2[/tex]

Therefore the initial value of the graph is 2. Option 3 is correct.

Answer:

Option 3 rd is correct

Initial value = 2

Step-by-step explanation:

A equation of line is given by:

[tex]y =mx+b[/tex]          ....[1]

where

m is the slope of the line and b is the y-intercept or the initial value

As per the statement:

A coordinate grid is shown with x and y axes labeled from 0 to 7 at increments of 1.

It is also given that:

A straight line joins the ordered pair (0, 2) with the ordered pair (7, 5)

Calculate slope:

using formula:

[tex]\text{Slope (m)} = \frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the given ordered pairs we have;

[tex]\text{Slope (m)} = \frac{5-2}{7-0}=\frac{3}{7}[/tex]

y-intercept states that the graph which cut y-axis.

Substitute x =0 and solve for x:

we have given with the ordered pair (0, 2)

⇒y-intercept(b) = 2

Substitute the given values of m and b in [1]

[tex]y = \frac{3}{7}x+2[/tex]

The equation of straight line  joins the ordered pair (0, 2) with the ordered pair (7, 5) is:

[tex]y = \frac{3}{7}x+2[/tex]

The initial value of the function represented by the given graph as shown below is: 2

Final answer:

The sales tax rate is 4%.

Explanation:

To calculate the sales tax rate for the cinnamon-scented pencils, you first need to determine the amount of sales tax paid and then relate that to the original price of the pencils.

The total cost is given as $5.20, and the original price is $5.00.

The difference between these two amounts is the sales tax paid.

Subtract the original price from the total cost to find the sales tax amount:

$5.20 - $5.00 = $0.20.

Next, to find the sales tax rate, divide the sales tax amount by the original price and multiply by 100 to get a percentage:

Sales Tax Rate = ($0.20 / $5.00) x 100 = 4%

Therefore, the sales tax rate is 4%.

Answer:

$70

Step-by-step explanation:

Let's define the expenses first

Fixed expenses are those expenses that remain constant in all months like mortage payments, rents etc

Flexible expenses also called variable expense are expenses that are used for comfortable living like car maintenance o groceries.

Discretionary expenses are the expenses spent on non essential items like movie tickets, outings etc.

Savings are the expenses that are stored for future plans.

Hence, from the given pie chart the money going for optional expenses is $70 ..

Answer:

It is greater than −3 because 0.44 × 5 3/4 is less than 1/2 × 6

Step-by-step explanation:

i guessed it and it was right so ye.

To find the percentage of students who prefer walking, divide the number of students who prefer walking by the total number of students and multiply by 100. In this case, 65 students prefer walking out of a total of 300 students.

To find the percentage of students who prefer walking, you divide the number of students who prefer walking by the total number of students and then multiply by 100. In this case, 65 students prefer walking out of a total of 300 students.

So, you divide 65 by 300 and multiply by 100 to get the percentage.

Percentage of students who prefer walking = (65/300) * 100 = 21.67%

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Final answer:

A sine function with an amplitude of 4, period of 12, midline of y = 1, and y-intercept of (0, 1) would oscillate between 5 and -3, with a wave repeating every 12 units along the x-axis and starting upward from the y-intercept.

Explanation:

The graph of the sine function with the given properties will have the following characteristics:

The amplitude is 4, which means the function will oscillate 4 units above and below the midline.

The period is 12, indicating that it takes 12 units along the x-axis for the function to repeat its pattern.

The midline is y = 1, so the center of oscillation is not at the x-axis but is shifted upwards by 1 unit.

The y-intercept is (0, 1), which means the function starts at the midline.

Since the function is not a reflection over the x-axis, it means that it starts off going upwards from the midline.

Mapping these points, we can sketch the sine graph starting from the point (0, 1), curving up to a maximum of 5 (midline + amplitude), then down through the midline, reaching a minimum of -3 (midline - amplitude), and back to the midline at (12, 1), completing one full cycle.

Answer:

a and c

Step-by-step explanation:

The value of x so that lines c and d are parallel lines cut by transversal p is 18.

Transversal lines are lines that passes intersects the two lines on a plane in two different points.

Given are two parallel lines c and d.

p is the transversal line passing through c and d.

The angle at the exterior side of angle 81° is 180° - 81° = 99°

When two parallel lines are intersected by a transversal line, then the angles formed at the corresponding corners of the transversal with each of the parallel line is called corresponding angles.

(3x + 45)° and 99° are corresponding angles.

Corresponding angles are always equal.

(3x + 45)° = 99°

3x = 99 - 45

3x = 54

x = 54 / 3

x = 18

Hence the value of x is 18.

Learn more about Corresponding Angles here :

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Final answer:

To find the principal amount that would earn $500 in simple interest over 3 years at an 8% annual rate, divide the interest by the product of the rate and period. The principal amount is $2083.33.

Explanation:

Calculating the Principal Amount from Simple Interest

To calculate the principal amount that earns $500 in simple interest over 3 years at a rate of 8% per annum, we can utilize the simple interest formula:
Interest = Principal × rate × time. Plugging in the known values, we get $500 = Principal × 0.08 × 3. This yields the equation $500 = Principal  × 0.24.

To find the Principal, we divide $500 by 0.24, which gives us approximately $2083.33. Therefore, the initial principal amount is $2083.33.