MATHEMATICS HIGH SCHOOL

How do I factor out a constant before factoring out a quadratic? 
Factor completely: 3w^2-3w-90

Answers

Answer 1
Answer: 3w^2-3w-90 =0 \ \ \:3 \n \nw^2- w-30 =0 \n \na=1 , \ b= -1 , c= -30 \n \n\Delta =b^2-4ac = (-1)^2 -4\cdot1\cdot (-30) =1+120=121 \n \nw_(1)=(-b-√(\Delta) )/(2a)=(1-√(121))/(2 )=( 1-11)/(2)=(-10)/(2)=-5

w_(2)=(-b+√(\Delta) )/(2a)=(1+√(121))/(2 )=( 1+11)/(2)=(12)/(2)=6 \n \n Answer:\n \n w^2- w-30 =(x+5)(x-6)
 

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What are the angles of a triangle

Answers

The angles inside a triangle are called interior angles. The diagram below shows the interior and exterior angles of a triangle. The three interior angles in a triangle will always add up to 180°. At each corner the exterior and interior angles are on a straight line, so at each corner these two angles add up to 180°.

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The (interior) angles of a triangle always add up to 180 degrees. To find the exterior angles of a triangle, subtract the interior triangle from 360 degrees.

The total degrees of any polygon is (n-2)×180 (n is the number of angles). 3-2 is 1 and 1 times 180 is 180. Therefore, the angles of a triangle always add up to 180 degrees.

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If f(x)=x-1/3and g(x)=3x+1, what is (f o g)(x)?
3x + 1
x – 3
3x
x

Answers

(f o g) means f(g(x))
f(g(x)) means put g(x) for x in f(x)
f(g(x))=(3x+1)-1/3
simplified
f(g(x))=3x+2 and 2/3

At Elisa's printing company llc there are two kinds of printing presses: model a which can print 70 books per day and model b which witch can print 55 books per day. Company owns 14 total Printing Presse sand this allows 905 books per day. How many of each type of press do they have..

Answers

a  (70 books/day)    A=number of model  A
b (55 books/day)      B =number of  B  ,   A=number of a then 
A+B =14    ........ A=14-B
aA+bB =905
70(14-B) +55B =905
980-70B+55B=905
-15B=-75
B=-75/-15 =5
A=14-B=14-5=9

Elisa's Printing Company has 9 Model A printing pressesand 5 Model B printing presses.

Given that Elisha's printing company have two kinds of printing presses,

Model A = 70 books per day

Model B = 55 books per day

In total they have printing presses, which allows 905 books per day.

We need to find number of each of press,

Let's assume Elisa's Printing Company has x Model A printing presses and y Model B printing presses.

According to the given information, the total number of Model A printing presses (x) can print 70x books per day, and the total number of Model B printing presses (y) can print 55y books per day. Since the company owns 14 total printing presses, we can create the following equation:

x + y = 14 (Equation 1)

The total number of books printed per day is given as 905. So, we can set up another equation based on the printing capacities of each model:

70x + 55y = 905 (Equation 2)

Now, we can solve these equations simultaneously to find the values of x and y.

Multiplying Equation 1 by 70, we get:

70x + 70y = 980 (Equation 3)

Subtracting Equation 2 from Equation 3:

(70x + 70y) - (70x + 55y) = 980 - 905

Simplifying:

15y = 75

Dividing both sides by 15:

y = 5

Substituting the value of y in Equation 1:

x + 5 = 14

x = 14 - 5

x = 9

Therefore, Elisa's Printing Company has 9 Model A printing pressesand 5 Model B printing presses.

Learn more about equation click;

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You just went on a blind date and wanted to impress the girl by adding an 18% tip to the total cost of the meal. Two dinners came to a total of $35.90. Desserts cost $7.50 and beverages cost $6.60. What is the 18% tip going to cost?

Answers

so find total
35+7.5+6.6=49.1

18% of 49.1=0.18 times 49.1=8.838 round
tip=$8.84

Answer:

the answer is 9.00

Step-by-step explanation:

Add all the courses to get the total cost of the meal:

Total cost = $35.90 + $7.50 + $6.60 = $50.00

Get 18% of the total, to compute the tip to be paid:

$50(18%) = $50(.18) = $9.00

Factor completely 12t ^8-75t^4

Answers

12t^8-75t^4=3t^4\cdot4t^4-3t^4\cdot25=3t^4(4t^4-25)\n\n=3t^4[(2t^2)^2-5^2]\n\nuse\ a^2-b^2=(a-b)(a+b)\n\n=3t^4(2t^2-5)(2t^2+5)=3t^4[(t\sqrt2)^2-(\sqrt5)^2](2t^2+5)\n\n=3t^4(t\sqrt2-\sqrt5)(t\sqrt2+\sqrt5)(2t^2+5)

Evaluate the summation of 2 n plus 5, from n equals 1 to 12..

Answers

Given:
2n + 5

n = 1 to n = 12

2(1) + 5 = 2 + 5 = 7
2(2) + 5 = 4 + 5 = 9
2(3) + 5 = 6 + 5 = 11
2(4) + 5 = 8 + 5 = 13
2(5) + 5 = 10 + 5 = 15
2(6) + 5 = 12 + 5 = 17
2(7) + 5 = 14 + 5 = 19
2(8) + 5 = 16 + 5 = 21
2(9) + 5 = 18 + 5 = 23
2(10) + 5 = 20 + 5 = 25
2(11) + 5 = 22 + 5 = 27
2(12) + 5 = 24 + 5 = 29

Sum: 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 + 27 + 29 = 216
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