What is the sum of the first 14 terms of the sequence -11+(-18)+(-25)+(-32)...-791
-483
-102
-714
Answers
the difference between -18 and -25 is -7
the difference between -25 and -32 is -7
therefore we can say that the difference between all of the terms will be -7.
the first term is -11 -> call this a
the difference is -7 -> call this d
the number of terms is 14 -> call this n
use the equation (sum of)
(sum of)
= -7(-22 + (13 x -7))
= -7(-22 + -91)
= -7(-111)
= 777
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Clarise has $290 in her checking account. She writes checks for $102 and $75 and then makes a deposit of $170. Find the amount left in her account.
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9/20
11/20
1/2
3/5
Answers
Answer:
option 2=11/20 is the answer.
Step-by-step explanation:
given that there are 20 cards numbers 1,2... 20.
A card is randomly drawn.
We have to find the probability of drawing either 1 or even card.
P(drawing even card) = no of even cards/total cards = 10/20= 0.5
P(drawing one) = no of 1's/total cards = 1/20 = 0.05
P(drawing both one and even card) = 0 (since impossible)
Hence P(drawing even or one) =0.5+0.05-0
=0.55
= 11/20
Hence option 2 is the answer.
Answer : 11/20
There are 20 cards labeled from 1 to 20 in a bag. A card is randomly selected from the bag.
Total number of outcomes = 20
outcomes of an even number ={2,4,6,8,10,12,14,16,18,20}
So number of outcomes of even number = 10
outcomes of a 1 ={1}
So number of outcomes of a 1 = 1
Number of outcomes of even number and a 1 = 10+1 = 11
Probability ( any event) =number of favorable outcomes divide by total number of outcomes
Probability (getting an even number or a 1) =
Answers
m=slope
paralell has same slope
point (8,-2)
x=8 and y=-2 is a solution
sub those for x and y
-2=5(8)+b
-2=40+b
minus 40 both sides
-42=b
the value is -42
3x –y = 7
Answers
Let's write both equations in the standard form of [ y = mx + b ],
and then see what we can tell about their graphs.
First equation: x + 3y = 9
Subtract 'x' from each side: 3y = -x + 9
Divide each side by 3: y = -1/3 x + 3
This line crosses the y-axis at y=3, and it has a slope of -1/3 .
Second equation: 3x - y = 7
Subtract 3x from each side: -y = -3x + 7
Multiply each side by -1 : y = 3x - 7
This line crosses the y-axis at y=-7, and it has a slope of 3 .
-- The two lines have different slopes, so they're not parallel.
They must intersect somewhere.
-- They're not the same line, so they can't 'intersect' everywhere.
-- They have slopes of -1/3 and 3 . Their slopes are negative reciprocals,
so the lines are perpendicular.
All of this says that the two equations can't have no solution, and they can't have
infinitely many solutions. They must have one and only one solution.
I guess that means that it's our job to find it now.
============================================
For each equation, the "mx + b" form is equal to 'y' . Since these two things are
equal to the same thing, they must be equal to each other, and we can write:
-1/3 x + 3 = 3x - 7
Multiply each side by 3 : -x + 9 = 9x - 21
Add 'x' to each side: 9 = 10x - 21
Add 21 to each side: 30 = 10x
Divide each side by 10 : 3 = x
The intersection/solution is some place where x=3 .
Let's put that back into the first equation:
x + 3y = 9
3 + 3y = 9
Subtract 3 from each side: 3y = 6
Divide each side by 3 : y = 2
And there's your solution: x = 3
y = 2
On the graph, the two lines intersect at the point (3, 2) .
We used the first equation to get part of the solution, so we can't use
the same equation to check the solution. We'll put our solution into the
second equation, and see whether it checks there:
3x - y = 7
3(3) - (2) = 7
9 - 2 = 7
7 = 7 yay !
The two equations have one and only one solution,
and it is definitely x = 3, y = 2 .
Substitution or Elimination
im using substitution
1. solve for variable for one of the equation
x + 3y = 9
x = 9 - 3y
2. Substitute the variable into one of the equation
3 (9-3y) - y = 7
27 - 9y - y = 7
27 - 10y = 7
-10y = 7 - 27
-10y = -20
y = 2
3. sub y = 2 into any equation to find x
3x - 2 = 7
3x = 7 -2
3x = 5
x = 5/3
X+3(2) = 9
x + 6 = 9
x = 9-6
x= 3
therefore there are two solutions x = 3 and x= 5/3
Answers
Disadvantages: Mishandling of account and exceeded expenses can cause a refund check and bad credit
Answers
-4 - -3 = -1
-4 - -1 = -3
The nth term is -n - 3
b.(a + bi) × 0 = 0
c.(a + bi) × (c + di) = (c + di) × (a + bi)
d.(a + bi) × 1 = (a + bi)
Answers
The identity property of multiplication states that the product of 1 and any number is that given number.
We have then, for example:
Where,
a: real number
Applying the definition, we have that the expression that models the identity property is given by:
Where,
a: real part
bi: imaginary part Answer:
d.(a + bi) × 1 = (a + bi)
Equation shows identity property of multiplication is (a + bi) × 1 = (a + bi)
The correct option is (d)
What is Identity property of multiplication?
The identity property of multiplication says that the product of 1 and any number is that number.
We know, Identity property of multiplication states that
"the product of 1 and any number is that given number".
We know that every complex number have two parts one is real and other is imaginary.
If a is real number and b is imaginary part then by definition
(a + bi) × 1 = (a + bi).
1. Uses Distributive Property of Multiplication.
2. Zero product property.
3. Commutative property of multiplication
4. Identity property of multiplication.
Hence, equation shows identity property of multiplication is (a + bi) × 1 = (a + bi)
Learn more identity property of multiplication here:
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