If you are given a right triangle with length of side A= 18 feet and length of hypotenuse C= 24 feet, what is the length of side B?
The length of side B can be found by using Pythagorean's Theorem: A^2+B^2=C^2. Since A and C are both given, the equation can be rearranged to solve for B^2=C^2-A^2 Plugging in A^2= 324 ft and C^2= 576 ft, B^2= 252 ft. Taking the square root of 252, B = 15.87 ft ANSWER: length of side B= 15.87 feet
Find and correct the errors in the following paragraph. Jim is a tall skinny boy. He has black hair and blue eyes and likes to wear tee shirts and athletic shorts and running shoes. Jim likes to go swimming and Jim likes to play baseball. He is 13 years old and goes to school five days a week. One day, Jim saw his friend bill in the neighborhood and asked him, would you like to play baseball? Bill responds by saying, "I would love to play baseball." Together, the two of them play, but lose there ball over the fence. Eventually, they find the ball and go home. Was a fun day for Jim.
There is a total of 7 errors in this paragraph. 1. tall skinny boy is grammatically incorrect but could be fixed by saying (tall and skinny) or (tall, skinny). 2. He has black hair and blue eyes... is a run on sentence. it would sound much better by being broken up into two sentences. (He has black hair and blue eyes. He likes to wear tee shirts, athletic shorts, and running shoes.) 3. Jim likes to go swimming and Jim likes to play baseball is redundant and repetitive. This can be fixed by saying (Jim likes to go swimming and play baseball.) 4. Jim saw his friend bill is incorrect because (Bill) is a noun and needs to be capitalized. 5. Would you like to play baseball? has errors because it is a direct quote and needs to have quotations. ("Would you like to play baseball?") 6. lose there ball over the fence is wrong because it is the wrong spelling of the word there. Since it is being used in a possessive sense, the correct spelling should be (their). 7. Was a fun day for Jim is an incomplete sentence. This can be fixed by adding a subject, such as It., making a complete sentence. (It was a fun day for Jim.)
Solve for x: x^2+5x+6=0
The form of the equation that this problem is written in is ax^2+bx+c=0. This allows for x to be found by two different methods. 1. Factor Method.: *This method can only be used when values of x are whole numbers* The equation is currently in the expanded form and needs to be broken down into factored format. this gives (x+2)(x+3). setting each of the two factors equal to 0 will give a value for x. x+2=0 , x+3=0 when solved, x= -2, -3. you can check your work by expanding the factored equation using distribution and determining if you get the original equation. x^2+ 2x+3x+6=0. when simplified, this becomes x^2+5x+6=0, so the equation was factored correctly. 2. Quadratic Formula: *This method can be used to solve any type of quadratic problem* The equation for the quadratic formula: x= -b=+ or - (sq.rt(b^2-4(a)(c)/2a)) Given a= 1, b= 5, and c= 6, the equation can be solved using x=-b+ (sq.rt(b^2-4(a)(c)/2a)) plugging in the numbers, x= - 5+(sq.rt(25-4(1)(6)/2(1)))= -2 now, solving for x=-b-(sq.rt(b^2-4(a)(c)/2a)) by plugging in the same values as before for a,b, and c the answer should be x= -3 this gives answers of x= -3, -2 which is the same as method 1. ANSWER: x= -2, x= -3