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swat32
3 years ago
11

Find the measure of the side of the right triangle whose length is designated by a lowercase letter. (see attachment)

Mathematics
1 answer:
PilotLPTM [1.2K]3 years ago
8 0

Answer:

a≈18 cm

Step-by-step explanation:

     we have given:

an angle,

the adjacent side and

     we need to find:

the opposite side

     

we know that the definition of

tan of an angle = opp. side/ adj. side

              tan 61° = a/ 10

multiply both sides by 10

        10 * tan61° = a

   18.04047755 = a

                      18 ≈ a

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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
2 years ago
Which equation is true for x = 5? A) 2x + 5 = 25 Eliminate B) 3x + 5 = 17 C) 5x − 18 = 7 D) 6x − 10 = 26
xxTIMURxx [149]

Answer:

C) 5x - 18 = 7

Step-by-step explanation:

Plug in 5 for x.

5x - 18 = 7

5(5) - 18 = 7

Simplify. First, multiply, then subtract.

25 - 18 = 7

7 = 7 (True)

~

7 0
3 years ago
Read 2 more answers
Find f(-1)<br><br> please help, not good at math.
bagirrra123 [75]
This means that X in the equation equals -1
7 0
2 years ago
What is half of the fraction 3/4
schepotkina [342]
The half of 3/4 is 0.375, or 3/8. All you have to do is multiply 3/4 times 1/2. 
5 0
3 years ago
Examine the following graph, where the function P(x) is mapped to I(x) by a translation.
Murrr4er [49]

f(x) = p(x) + 4 shows the correct transformation.

<h3>Define transformations.</h3>

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location. The most typical varieties are listed below: When a figure is translated, it is moved in any direction. Flipping a figure over a line is called reflection. Rotation is the process of turning a figure a specific amount around a point.

Given,

Function

f(x) = p(x) + 4

shows the correct transformation.

To learn more about transformation, visit:

brainly.com/question/11709244

#SPJ9

6 0
1 year ago
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