Onna received a $80 gift card for a coffee store. She used it in buying some coffee that cost $8.09 per pound. After buying the
1 answer:
Answer:
She bought 5 pounds
Step-by-step explanation:
Original worth of gift card = $80
Balance on card after purchase = $39.55
Amount used for purchase = 80 - 39.55 = $40.45
Next let us determine how many pounds of coffee she bought as follows:
Price of coffee = $8.09 per pound
amount spent on coffee = $40.45
Lett the number of pounds of coffee she bought be x
$ 8.09 = 1 pound
$40.45 = x pounds
since $8.09 = 1 pound
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As z-values increase, areas to the left of z increase.
As the z-value increases to the right, areas to the left of z (shown shaded) will increase.
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As z-values increase, areas to the left of z increase.
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Find below the calculations of the two areas, each with two methods. The results are:
- Upper triangle:
- Lower triangle:
Explanation:
<u>A) Method 1</u>
When you are not given the height, but you are given two sides and the included angle between the two sides, you can use this formula:
Where, is the measure of the included angle.
1. <u>Upper triangle:</u>
2. <u>Lower triangle:</u>
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<u>B) Method 2</u>
You can find the height of the triangle using trigonometric properties, and then use the very well known formula:
Use it for both triangles.
3. <u>Upper triangle:</u>
The trigonometric ratio that you can use is:
Notice the height is the opposite leg to the angle of 60º, and the side that measures 100 units is the hypotenuse of that right triangle. Then:
3. <u>Lower triangle:</u>
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Answer:
The coordinates of point B are (-2, 2)
Step-by-step explanation:
We have two points: A and C.
The coordinates for A are (2, -8) and the coordinates for C are (-4, 7).
We have to find the coordinates of the point B, that satisfies the condition that the distance AB is 2 times the distance BC.
We also know that B is a point of the line AC.
We can calculate the line AC as a linear function y=mx+b.
The slope m is:
Then, the y-intercept b can be calculated using the coordinates of one of the points, in this case point A:
Then, we know that B is a point of the linear function y=-2.5x-3, within the range x ∈ (-4; 2).
To have a ratio AB to BC of 2 to 1, we can divide the length of the line AC in 3 parts, and the point B will be located in the end of the segment nearer to point C.
In the picture attached, you can see the division of the segment AC in three parts and the location of point B=(x, y).
Applying the Thales theorem, we can divide the segment in the y-axis in three and calculate y, and the same for the x-axis.
Then, the coordinate y for the point B is:
Then, the point B has coordinates (-2, 2).
We can verify the distances as:
