Answer:
x = 4, ∠I = 33°
Step-by-step explanation:
<u>Question 1</u>
Converse to Base Angles Theorem: 28 = 9x - 8,
28 = 9x - 8 (add 8 to both sides)
9x = 36 (divide both sides by 9)
x = 4
<u>Question 2</u>
Since the triangles are congruent, ∠A ≅ ∠G:
∠A = 55 = ∠G
If we consider triangle ALX we have ∠L = 180-55-92 = 33°
And since ∠L ≅ ∠I, ∠I = 33° respectively
Answer:
see explanation
Step-by-step explanation:
To find the y-intercept let x = 0, in the equation
6x - 3y = 15 → (1)
x = 0 : - 3y = 15 ⇒ y = - 5 ⇒ (0, - 5) ← y- intercept
x + 3y = - 8 → (2)
x = 0 : 3y = - 8 ⇒ y = -
⇒ (0, -
) ← y- intercept
Answer:
The tree is 20.6 ft tall.
Step-by-step explanation:
Please check the attached graph.
From the diagram, it is clear that John is 5 ft tall is standing 20 feet away from a tree, making an angle of elevation to be 38⁰.
The diagram makes a right-angled triangle.
- Given the angle = Ф = 38⁰
- Hypotenuse = Tree length = c ?
Pythagorean Theorem:
For a right-angled triangle, with sides 'a' and 'b', the hypotenuse 'c' is defined as:
![\:c=\sqrt{a^2+b^2}](https://tex.z-dn.net/?f=%5C%3Ac%3D%5Csqrt%7Ba%5E2%2Bb%5E2%7D)
substituting a=5, b=20
![c=\sqrt{5^2+20^2}](https://tex.z-dn.net/?f=c%3D%5Csqrt%7B5%5E2%2B20%5E2%7D)
![c=5\sqrt{17}](https://tex.z-dn.net/?f=c%3D5%5Csqrt%7B17%7D)
ft
Thus, the tree is 20.6 ft tall.
The triangles are ACD and XYZ
Congruent segments means that they have the same length.
Then CD = XY, AC = ZX and AD = ZY
This is the option B. from the list.
Answer :<span>B.CD=XY,DA=YZ,AC=ZX</span>
Answer:
![\displaystyle m=\frac{-2}{5}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%3D%5Cfrac%7B-2%7D%7B5%7D)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS<u>
</u>
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Coordinates (x, y)
- Slope Formula:
![\displaystyle m=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Step-by-step explanation:
<u>Step 1: Define</u>
Point (2, 5)
Point (-3, 7)
<u>Step 2: Identify</u>
x₁ = 2, y₁ = 5
x₂ = -3, y₂ = 7
<u>Step 3: Find slope </u><em><u>m</u></em>
Simply plug in the 2 coordinates into the slope formula to find slope<em> m</em>
- Substitute in points [Slope Formula]:
![\displaystyle m=\frac{7-5}{-3-2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%3D%5Cfrac%7B7-5%7D%7B-3-2%7D)
- [Slope] [Fraction] Subtract:
![\displaystyle m=\frac{2}{-5}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%3D%5Cfrac%7B2%7D%7B-5%7D)
- [Slope] [Fraction] Rewrite:
![\displaystyle m=\frac{-2}{5}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%3D%5Cfrac%7B-2%7D%7B5%7D)