The sum of two numbers is -18. If the first number is 10, which equation represents this situation, and what is the second numbe
1 answer:
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The image of the triangle is missing, so i have attached it.
Also, the options are;
A) The apothem can be found using the Pythagorean theorem.
B) The apothem can be found using the tangent ratio.
C) The perimeter of the equilateral triangle is 15 cm.
D) The length of the apothem is approximately 2.5 cm.
E) The area of the equilateral triangle is approximately 65 cm².
Answer:
Options A, B & D are true
Step-by-step explanation:
A) We are told that the triangle is an equilateral triangle.
Thus, the 3 sides equal 8.7 cm.
Now from the image, b is half of one of the sides.
Thus, b = 8.7/2 = 4.35 cm
Now, we want to find the apothem "a".
Using Pythagoras theorem, we have;
a² + 4.35² = 5²
a² = 25 - 18.9225
a² = 6.0775
a = √6.0775
a ≈ 2.5 cm.
Thus, option A is true as pythagoras theorem was able to calculate the apothem "a"
B) since the main triangle is equilateral, it means each angle is 60°.
Now,the radius line from one corner point to the centre will divide the 60° angle into 2 equal parts.
Thus, the angle made by the radius line with the base of the triangle is 60/2 = 30°
Now,from tangent ratios, we know that;
Opposite/Adjacent = tan θ
In the small triangle, opposite is apothem "a" while adjacent is b = 4.35 cm
Thus;
a/4.35 = tan 30
a = 4.35 tan 30
a ≈ 2.5 cm.
Thus, option B is correct as Tangent ratio can be used to find the apothem
C) The perimeter of equilateral triangle = 3x
Where x is length of one side.
One side is 8.7 cm
Thus, perimeter = 3 × 8.7 = 26.1 cm
Thus option C is not correct.
D) From calculations above, we saw that in both options A & B, the apothem is approximately 2.5 cm.
Thus, option D is true.
E) Area of triangle is;
A = ½ × base × height
Base = 8.7 cm
To get height, we will use trigonometric ratio. Thus;
h/8.7 = sin 60°
h = 8.7 sin 60°
Thus;
A = ½ × 8.7 × 8.7 sin 60°
A = 32.77 cm²
Thus is not equal to 65 cm². Thus, option E is not correct.
The square feet of grass that will cover the entire land is equal to the area of the rectangular field.
Remember that area of a rectangle
Remember that area of a rectangle
9514 1404 393
Answer:
- x = -4
- y = 7
Step-by-step explanation:
It looks like your interactive graphing tool needs you to plot some points on each of the lines. For these lines, it is convenient to use the x- and y-intercepts. Each intercept can be found by dividing the constant by the coefficient of the variable.
<u>-7x -2y = 14</u>
The x-intercept is 14/-7 = -2. Plot (-2, 0) on the x-axis.
The y-intercept is 14/-2 = -7. Plot (0, -7) on the y-axis.
<u>6x +6y = 18</u>
The x-intercept is 18/6 = 3. Plot (3, 0) on the x-axis.
The y-intercept is 18/6 = 3. Plot (0, 3) on the y-axis.
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The point of intersection of the two lines is the solution: (x, y) = (-4, 7).
