Answer:
The SAS rule states that two triangles are similar if the ratio of their corresponding two sides is equal and also, the angle formed by the two sides is equal. Side-Side-Side (SSS) rule: Two triangles are similar if all the corresponding three sides of the given triangles are in the same proportion.
Step-by-step explanation:
Answer:
3. r = -8
4. x = -5
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
Step-by-step explanation:
<u>Step 1: Define equation</u>
2(-5r + 2) = 84
<u>Step 2: Solve for </u><em><u>r</u></em>
- Divide 2 on both sides: -5r + 2 = 42
- Subtract 2 on both sides: -5r = 40
- Divide -5 on both sides: r = -8
<u>Step 3: Check</u>
<em>Plug in r into the original equation to verify it's a solution.</em>
- Substitute in <em>r</em>: 2(-5(-8) + 2) = 84
- Multiply: 2(40 + 2) = 84
- Add: 2(42) = 84
- Multiply: 84 = 84
Here we see that 84 does indeed equal 84.
∴ r = -8 is a solution of the equation.
<u>Step 4: Define equation</u>
264 = -8(-8 + 5x)
<u>Step 5: Solve for </u><em><u>x</u></em>
- Divide both sides by -8: -33 = -8 + 5x
- Add 8 to both sides: -25 = 5x
- Divide 5 on both sides: -5 = x
- Rewrite: x = -5
<u>Step 6: Check</u>
<em>Plug in x into the original equation to verify it's a solution.</em>
- Substitute in<em> x</em>: 264 = -8(-8 + 5(-5))
- Multiply: 264 = -8(-8 - 25)
- Subtract: 264 = -8(-33)
- Multiply: 264 = 264
Here we see that 264 does indeed equal 264.
∴ x = -5 is a solution of the equation.
Answer:
third option
Step-by-step explanation:
Given
3 ![\left[\begin{array}{ccc}-2&5\\1&0\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%265%5C%5C1%260%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Multiply each element in the matrix by 3
= ![\left[\begin{array}{ccc}3(-2)&3(5)\\3(1)&3(0)\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%28-2%29%263%285%29%5C%5C3%281%29%263%280%29%5C%5C%5Cend%7Barray%7D%5Cright%5D)
= ![\left[\begin{array}{ccc}-6&15\\3&0\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-6%2615%5C%5C3%260%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Answer:
B, A
Step-by-step explanation:
In the first equation, if an unknown number plus 17 equals 66, then what step would you take?
For example, if an unknown number plus 2 equaled 3, then you would know that number is 1, right? What steps did you take to get that? You subtracted 2 from both sides.
In this example, if x + 17 = 66, then subtracting 17 from both sides gets us x = 49.
The same applies for the second example. If x minus 54 equals 125, then you would add 54 to get x = 179.
24,610. All you have to do is multiply 5 and 4,852 and add 150.
