Solve each quadratic equation by factoring and using the zero product property.10x + 6 = -2x^2 -2
Answers
Answer:
x = -4 x=-1
Step-by-step explanation:
10x + 6 = -2x^2 -2
Add 2x^2 to each side
+2x^2 +10x + 6 =2x^2 -2x^2 -2
2x^2 +10x + 6 = -2
Add 2 to each side
2x^2 +10x + 6+2 = -2+2
2x^2 +10x + 8 = 0
Divide each side by 2
2/2x^2 +10/2x + 8/2 = 0/2
x^2 +5x+4 = 0
What 2 numbers multiply to 4 and add to 5
4*1 = 4
4+1 =5
(x+4) (x+1) = 0
Using the zero product property
x+4 = 0 x+1 =0
x+4-4 = 0-4 x+1-1 =0-1
x = -4 x=-1
Answer:
x = -4 or x = -1
Step-by-step explanation:
Given equation is :
10x+6 = -2x²-2
Adding 2x² and 2 to both sides of above equation , we get
2x²+2 +10x+6 = -2x²-2 +2x²+2
Adding like terms , we get
2x²+10x+8 = 0
As we have noticed that there are multiples of 2.
Taking 2 as common,we get
2(x²+5x+4) = 0
Multiplying by 1/2 to both sides of above equation , we get
1/2.2(x²+5x+4) = 1/2.0
x²+5x+4 = 0
Split the middle term of above equation so that the sum of two term should be 5 and their product be 4.
x²+4x+x+4 = 0
Making two groups ,we get
x(x+4)+1(x+4)
Taking (x+4) common,we get
(x+4)(x+1) = 0
Applying Zero-Product Property to above equation, we get
x+4 = 0 or x+1 = 0
Firstly, solve x+4 = 0
Adding -4 to both sides of above equation,we get
x+4-4 = 0-4
x +0 = -4
x = -4
Secondly, solve x+1 = 0
Adding -1 to both sides of above equation,we get
x+1-1 = 0-1
x = -1
Hence, the solution of 10x+6 = -2x²-2 is {-4,-1}.
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On a recent trip to the convenience store, you picked up 4 gallons of milk, 6 bottles of water and 5 snack size bags of chips. You total bill before tax was $ 27.2. If a bottle of water costs twice as much as a bag of chips, and a gallon of milk costs $1.80 more than a bottle of water, how much does each item costHow much does a snack size bag of chips cost? How much does a bottle of water cost? How much does a gallon of milk cost?
Margo’s wires measure 6 inches, 8 inches, and 14 inches.
Sonji’s wires measure 12 inches, 8 inches, and 17 inches.
Liam’s wires measure 16 inches, 8 inches, and 27 inches.
Which student chose pieces that can be used to construct a triangle?
Don
Margo
Sonji
Liam
Answers
Answer:
Sonji
Step-by-step explanation:
Given :
We will use the third important property of triangles is the triangle inequality rule, which states: the length of a side of a triangle is less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides.
So, applying this property in each case:
Case 1. Don’s wires measure 3 inches, 5 inches, and 12 inches.
Now using property
since sum of two sides = 3+5 =8
But third side 12 is not less than 8
So, Don’s wire cannot be used .
Case 2. Margo’s wires measure 6 inches, 8 inches, and 14 inches.
Now using property
since sum of two side :8+6=14
But third side 14 is not less than 14
So, Margo’s wire cannot be used .
Case 3. Sonji’s wires measure 12 inches, 8 inches, and 17 inches.
Now using property
since sum of two side :12+8=20
third side 17 is less than 20
Now , difference of two sides : 12-8=4
third side 17 is greater than 4
So, Sonji’s wire can be used .
Case 4. Liam’s wires measure 16 inches, 8 inches, and 27 inches.
Now using property
since sum of two side :16+8 =24
But third side 27 is not less than 24
So, Liam’s wire cannot be used .
Hence sonji's wire can be used to construct a triangle
The third important property of triangles is the triangle inequality rule, which states: the length of a side of a triangle is less than the sum of the lengths of the other twosides and greater than the difference of the lengths of the other two sides.
Answers
"6 to the 2nd power ÷ 2(3) + 4"
Rewriting the expression in algebraic form we have:
Rewriting the numerator we have:
Rewriting the denominator we have:
Dividing both numbers we have:
Answer:
The result of the given expression is:
So,
6² ÷ 2 ( 3 ) + 4
=36/2(3)+4
=(18)(3)+4
=54+4
=58
Answers
Answers
next, you multiply p and r to get 105=35t
after that, you divide the 105 by 35 to get the final answer of t=3
Answers
498 + 246 = 744 . . . total of cartons and bottles
Answers
3/4 = 0.75
that is the solution as decimal, they are equivalent
To convert fraction to decimal divide the numerator by denominator.
3 ÷ 4 = 0.75
0.75 is decimal