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deff fn [24]
3 years ago
11

What is the perimeter of triangleABC

Mathematics
2 answers:
QveST [7]3 years ago
8 0

The triangle is the question

Sunny_sXe [5.5K]3 years ago
7 0

The triangle in the question

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Jamie ordered 200 business cards and paid $23. She ordered 500 business cards a few months later and paid $35. Write and solve a
Gnesinka [82]

Answer:

To purchase 700 business cards, Jamie needs to pay $43.

Step-by-step explanation:

We are given that Jamie ordered 200 business cards and paid $23 in total.

We are also given that Jamie ordered 500 business cards and paid $35.

We can use the rate of change formula to find the average change.

\displaystyle \bullet \ \ \ \frac{\triangle y}{\triangle x}

This can also be represented with:

\displaystyle \bullet \ \ \ \frac{y_2-y_1}{x_2-x_1}

Therefore, we need to identify our variables.

In every relationship, there is a <u>dependent variable</u> and an <u>independent variable</u>.

  • The independent variable is the variable that an experimenter adjusts in order to receive an altered effect from an output.
  • The dependent variable is the variable that adjusts based on the changes made to the independent variable.

We change the amount of business cards that are purchased, which in turn, changes the price.

The y-variable is assigned to the dependent variable and the x-variable is assigned to the dependent variable.

Therefore, if we use the coordinate system:

  • (200, 23)
  • (500, 35)

Now, we can name our coordinates. We use this system:

  • (x₁, y₁)
  • (x₂, y₂)

This means that we can name our points:

  • x₁ = 200
  • y₁ = 23
  • x₂ = 500
  • y₂ = 35

Revisiting the rate of change formula, we can insert these values.

\displaystyle \frac{y_2-y_1}{x_2-x_1}

\displaystyle \frac{35 - 23}{500-200}\\\\\frac{12}{300}=\frac{1}{25}

Next, we need to find the y-intercept of our line. We can do this by using one coordinate pair from above and our slope.

The slope-intercept equation is:

\bullet \ \ \ y = mx + b

We already know m:

\displaystyle \bullet \ \ \ \frac{1}{25}

We also know x and y (we take them from of the coordinate pairs):

\bullet \ \ \ x = 200

\bullet \ \ \ y = 23

Now, we can substitute these values into the equation and solve for b.

\displaystyle [y = mx + b]\\\\23 = \frac{1}{25}(200) + b\\\\23 = 8 + b\\\\23 - 8 = 8 - 8 + b\\\\15 = b\\\\b = 15

Now, we can set up our linear equation.

\displaystyle y = \frac{1}{25}x + 15

Therefore, in order to find the price of 700 business cards, we make x in the equation equal 700 and then solve.

\displaystyle y = \frac{1}{25}(700)+15\\\\y = 28 + 15\\\\y = 43

Therefore, the price of 700 business cards is equal to $43.

3 0
3 years ago
Given g(x) = :-2 +4, solve for a when g(x) = 0.
evablogger [386]

Answer:

-7/4

Step-by-step explanation:

You are looking for the composite g(f(2)). The simplest way to solve this is to evaluate f(2) and enter the solution in to your g function.

g(f(2))=g(-(2)^2-2(2)+4)=g(-4-4+4)=g(-4)

g(-4)=4/(-4(-4)-2)=4/(16-2)=4/14=2/7

Therfor, g(f(2))=2/7  **I'm assuming the -4x-2 is all in the denominator of the g(x) function. If -2 is not in the denominator you would have

g(f(2))=4/(-4(-4)) -2=4/16 -2=1/4 -2=1/4-8/4= -7/4

8 0
3 years ago
Using the given points and line, determine the slope of the line. (1, 2) and (2, 1) slope = 2 slope = 1 slope = -1
Bas_tet [7]

Answer:

-1

Step-by-step explanation:

Slope formula: (y₂ - y₁) / (x₂ - x₁)

= (2 - 1) / (1 - 2)

= -1

8 0
3 years ago
Question: A box of chocolates contains square chocolates, which weigh 10 g each, and round chocolates, which weigh 8 g each. The
Viktor [21]

Answer: the box contained 9 square chocolates and 15 round chocolates.

Step-by-step explanation:

Let x represent the number of square chocolates contained in the box.

Let y represent the number of round chocolates contained in the box.

The box of chocolates contains square chocolates, which weigh 10g each and round chocolates which weigh 8g each. The combined weight of all the chocolates is 210g. It means that

10x + 8y = 210- - - - - - - - - - -1

The number of round chocolates is 3 less than twice the number of square chocolates. It means that

y = 2x - 3

Substituting y = 2x - 3 into equation 1, it becomes

10x + 8(2x - 3) = 210

10x + 16x - 24 = 210

26x = 210 + 24

26x = 234

x = 234/26

x = 9

y = 2x - 3 = 2 × 9 - 3

y = 18 - 3

y = 15

3 0
3 years ago
What is the value of (-14^0)^-2?
Ainat [17]

Answer:

-6

Step-by-step explanation:

3 0
3 years ago
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