Triangle ABC has vertices A(5, 3) , B(3, 7) , and C(1, 4) . Triangle ABC is dilated, and the vertices of the image are A′(7.5, 4.5) , B′(4.5, 10.5) , and C′(1.5, 6) . The center of dilation is the origin.

What is the scale factor of the dilation?

Answer: what i did was put "change one of the tails, heads or heads, tails to add the data for the 3 pets" because you couldn't tell if it was heads tails or tails heads

Final answer:

To generate data for three pets in a simulation, expand the outcome possibilities to include all combinations of Heads and Tails for three entities, and then record the frequency of each outcome to analyze probabilities or patterns.

Explanation:

To determine how to change a simulation to generate data for three pets when you currently have data for two, you need to expand the number of possible outcomes to account for the additional pet. For the current two-pet scenario, there are four outcomes: Heads-Heads, Heads-Tails, Tails-Heads, and Tails-Tails. When adding a third pet, each of these outcomes would branch into two further outcomes, representing the two possibilities for the third pet (let's call it Pet C).

The possible outcomes would be:

For each outcome, you would simulate or record the frequency as you did with the two-pet scenario, totaling the number of trials to ensure you have complete data for analysis. You would then use this data to analyze the probabilities or patterns of outcomes involving three pets.

You can infer from this problem that the shape of the wooden plank is a rectangle based on the dimensions given. The length of a rectangle is usually the longest side of the rectangle so you can conclude that the length of the rectangle is 12.5 cm. Therefore, the width is 8.5 cm.

Answer:

f(x) = 2(x-11)^2 - 57

Step-by-step explanation:

To write f(x) = 2x^2 – 44x + 185, factor out from the first two terms.

Next, form a perfect square tri nomial keeping the value of the function equivalent: f(x) = 2(x^2 – 22x + 121) + 185 – 242

To get vertex form we factor x^2 -22x+121

product is 121 and sum is -22

-11*-11= 121 and sum -11+(-11)= -22

x^2 -22x+121

(x-11)(x-11)

f(x) = 2(x^2 – 22x + 121) + 185 – 242

f(x) = 2(x-11)(x-11)+ 185 – 242

f(x) = 2(x-11)^2 - 57

a. Using properties of exponents, the value of the expression is 10⁰

b. The equation has no solution

a. Properties of exponents are mathematical rules that allow us to simplify and manipulate expressions involving exponents. These properties help us perform operations such as multiplication, division, and raising to a power more efficiently.

In the given problem, we have to solve and simplify using properties of exponents.

Given that; [tex]\frac{10^-^3}{10^-^3}[/tex];

we can apply quotient rule when dividing exponents here;

[tex]\frac{10^-^3}{10^-^3} = 10^-^3 ^+^3 = 10^0[/tex]

The answer is 10⁰

b. To simply the equation, we just need to use basic mathematical operation to find the value of x.

3x - 2x + 4 = 5x - 4x - 8

Simplify;

x + 4 = x - 8

Collect like terms

x - x = -8 - 4

0 = -12

No solution

Learn more on properties of exponents here;

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Answer:

[tex]3,944ft^{2}[/tex] of marble is needed.

Step-by-step explanation:

The picture below represents the top of the Washington Monument, with 4 triangles, one on the base and the other 3 forming the monument.

First of all whe have to find the area of one pyramid:

[tex]A=\frac{height*width}{2}[/tex]

Replacing the values, we have:

[tex]A=\frac{58ft*34ft}{2}[/tex]

[tex]A=986ft^{2}[/tex]

As we have 4 triangles forming the top of the Monument, we have to multiply by 4 to find the quantity of marble to use:

Quantity of marble=Area of each triangle * quantity of triangles

Quantity of marble=[tex]986ft^{2}*4[/tex]

Quantity of marble=[tex]3,944ft^{2}[/tex]

To find the area of marble covering the Washington Monument's pyramid faces, calculate the area of one triangular face (985 square feet) and then multiply by 3, resulting in approximately 2955 square feet.

The Washington Monument's pyramid at the top has triangular faces that are covered with white marble. Each face is 58 feet tall and 34 feet wide. To find the total area covered by marble, we need to calculate the area of one triangular face and then multiply by the number of faces.

Therefore, approximately 2955 square feet of marble cover the faces of the pyramid.

Its C. 4

Correct on edge :D

A ratio compares two quantities and can form a proportion when two ratios are equivalent. A unit rate is a ratio with one quantity of one, while a unit scale compares actual object dimensions to a model or drawing. These concepts are used in various fields, including health sciences and when working with scale models or maps.

A ratio is a comparison between two different quantities. When we express ratios, we can use a fraction format, a colon, or the word 'to'. Examples include 2/3, 2:3, and '2 to 3'. In certain situations, this comparison can lead to the formation of a proportion, which occurs when two ratios are equivalent, like 1/2 = 3/6. Proportions are especially useful when we deal with scale distances or dimensions, such as in map reading or model building.

A unit rate is a type of ratio in which one of the quantities is one. An example would be 55 miles per hour or 55 miles/1 hour. This is often used when discussing speed or cost per unit.

Similar to a unit rate is a unit scale, which compares the actual dimensions of an object to the dimensions of a model or drawing of the object. An example of a unit scale is 1 inch = 100 feet, which can be written as a ratio of 1 inch/100 ft.

In sectors like the health sciences, ratios are used to describe solutions and are given in terms of proportions, for example, 1:1000. In making comparisons or constructing models, we might set ratios equal to the unit scale to form proportions for various dimensions like length and width.

Four different situations accurately describe ratios.

Certainly! Let's evaluate each situation to see if it accurately describes a ratio.

Sally found five green fruit loops in her cereal bowl, out of every thirteen pieces.
This situation does describe a ratio: 5 green fruit loops to 13 total pieces. The ratio is 5:13.

Tobias picked five daisies and eight roses.
This situation does describe a ratio: 5 daisies to 8 roses. The ratio is 5:8.

Aly painted eight trees for every three birds.
This situation does describe a ratio: 8 trees to 3 birds. The ratio is 8:3.

For every eight shots, Micah made five baskets.
This situation also describes a ratio: 5 baskets to 8 shots. The ratio is 5:8.

So, all four situations accurately describe ratios.

The complete question is:

Which situations accurately describe a ratio of? Select all that apply.

Sally found five green fruit loops in her cereal bowl, out of every thirteen pieces.

Tobias picked five daisies and eight roses.

Aly painted eight trees for every three birds.

For every eight shots, Micah made five baskets.

To graph a line with a given slope passing through a point, use the point-slope form of a linear equation. Convert the equation to slope-intercept form, [tex]y = mx+b[/tex]. Plot the line on a graph using the y-intercept and the slope to find additional points.

To graph a line with a given slope and passing through a point, we can use the point-slope form of a linear equation, y - y1 = m(x - x1). In this case, the point-slope form would be y - 1 = (-2/3)(x - 2). We can simplify this equation into slope-intercept form, y = mx + b, by distributing the slope and rearranging the terms. After simplifying, the equation becomes y = (-2/3)x + 7/3. Finally, we can plot the line on a graph using the slope-intercept form equation by identifying the y-intercept at (0, 7/3) and using the slope to find additional points on the line.

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Answer:

3 x's

Step-by-step explanation:

Final answer:

To find two consecutive odd integers such that 36 more than the lesser is three times the greater, set up an equation and solve for the variable x. The two consecutive odd integers are 15 and 17.

Explanation:

To find two consecutive odd integers such that 36 more than the lesser is three times the greater, we can set up an equation:

x + 36 = 3(x + 2)

Simplifying this equation, we get:

x + 36 = 3x + 6

Subtracting x from both sides, we get:

36 = 2x + 6

Subtracting 6 from both sides, we get:

30 = 2x

Dividing both sides by 2, we get:

15 = x

Therefore, the two consecutive odd integers are 15 and 17.

a2 + b2 = c2

102 + 152 = c2

100 + 225 = c2

√325 = c

5√13 = c

The diagonal measures 5√13 cm.

Let's assume

number of chairs =x

number of tables =y

we are given

Gavin builds furniture for a living. he Sells chairs for $45 and tables for $70 each

So, we can find objective function as

[tex] Z=45x+70y [/tex]

now, we can find inequalities

A table requires 10 hours and $15 worth of supplies to make

so, total hours to make table =10y

amount spent on table =15y

It takes Gavin 4 hours and $10 worth of supplies to build each chair

so, total hours to make chair =4x

amount spent on chair =10x

total number of hours to make chair and table =4x+10y

Gavin wants to work for no more than 40 hours per week

so, we get

[tex] 4x+10y\leq 40 [/tex]

spend no more than $80 on materials

so, we get

[tex] 10x+15y\leq 80 [/tex]

so,

objective function:

[tex] Z=45x+70y [/tex]

Constraints:

[tex] 4x+10y\leq 40 [/tex]

[tex] 10x+15y\leq 80 [/tex]

Answer:

The solution set is given by {a, -b}.

Step-by-step explanation:

We have the equation,

[tex](x - a)(x + b) = 0[/tex]

Equating the factors to 0 gives,

[tex](x - a)=0[/tex] and [tex](x + b)=0[/tex]

i.e. x = a and x = -b

So, the solutions of the equation [tex](x - a)(x + b) = 0[/tex] are x= a and x= -b.

Thus, the solution set is given by {a, -b}.

Answer:

A) all the golf balls produced by the Acme Company

Step-by-step explanation: