Answer:
The values of given function are shown in the below table.
Step-by-step explanation:
The given function is
Simplify the given function.
Cancel out the common factor.
Substitute x=5.5 in the above equation.
Similarly find the value for all values of x.
The values of given function are shown in the below table.
Answer:
The probability that the card will be a heart or a face card is P=0.4231.
Step-by-step explanation:
We have a standard deck of 52 cards.
In this deck, we have 13 cards that are a heart.
We also have a total of 12 face cards (4 per each suit). So there are 3 face cards that are also a heart.
To calculate the probability that a card be a heart or a face card, we sum the probability of a card being a heart and the probability of it being a face card, and substract the probability of being a heart AND a face card.
We can express that as:
x
=
−
8
,
−
2
Explanation:
Given:
x
2
+
10
x
+
16
=
0
To complete the square put the two
x
terms on the left and the constant on the right of the equation:
x
2
+
10
x
=
−
16
Complete the square by multiplying the
x
-term by
1
2
:
1
2
⋅
10
=
5
and adding the square of this number to the right side of the equation:
5
2
=
25
(
x
+
5
)
2
=
−
16
+
25
UNDERSTANDING CHECK:
(
x
+
5
)
2
=
x
2
+
10
x
+
25
.
The
+
25
was not in the original equation. If we add
+
25
to one side of the equation, we must add the same amount to the other side of the equation to keep it balanced.
(
x
+
5
)
2
=
9
To solve, square root both sides of the equation:
√
(
x
+
5
)
2
=
±
√
9
x
+
5
=
±
3
x
=
−
5
±
3
x
=
−
5
+
3
=
−
2
,
x
=
−
5
−
3
=
−
8
x
=
−
8
,
−
2
The cost of one taco is $3.75.
We are given cost of salad, the sales tax and tip along with total expenditure. We already know, that sales tax is calculated on the cost of items. Hence, forming the equation accordingly. Let us assumed the cost of one taco be $x. So, the cost of two tacos will be $2x.
The equation will be -
2x + 2.50 + (2x + 2.50)×(6÷100) + 3 = 13.60
2x + 2.50 + (2x + 2.50)×0.06 + 3 = 13.60
Now, solving this equation to find the value of x and hence the cost of one taco.
2x + 2.50 + 0.12x + 0.15 + 3 = 13.60
Performing addition on Left Hand Side
2.12x + 5.65 = 13.60
Shifting 0.18 to Right Hand Side and performing subtraction
2.12x = 13.60 - 5.65
2.12x = 7.95
x = 7.95÷2.12
Performing division
x = 3.75
Thus, the cost of one taco is $3.75.
Learn more about sales tax calculation -
brainly.com/question/9437038
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