Answer:
the answer would be 1/8
7/8-3/4
7/8-6/8
1/8
The quadratic value function is y = -x² - 4x + 16
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
Let the function passes through the given points. (-1,-11) (2,-26) (-3,-31)
And , using the point (-1,-11) , we get
-11 = a(-1)² + b(-1) + c
-11 = a - b + c
Using the point (2,-26) , we get
-26 = a(2)² + b(2) + c
-26 = 4a + 2b + c
Using the point (-3,-31) , we get
-31 = a(-3)² + b(-3) + c
-31 = 9a - 3b + c
And , the three set of equations are
-11 = a - b + c
-26 = 4a + 2b + c
-31 = 9a - 3b + c
From the first equation, we can solve for c:
c = 11 - a + b
Substituting this expression for c into the other two equations, we get:
-26 = 4a + 2b + 11 - a + b
-31 = 9a - 3b + 11 - a + b
Simplifying these equations, we get:
-15 = 3a + 3b
-21 = 8a - 2b
Solving the first equation for b in terms of a, we get:
b = -5 - a
Substituting this expression for b into the second equation, we get:
-21 = 8a - 2(-5 - a)
Simplifying and solving for a, we get:
a = -1
Substituting this value of a into the equation for b that we found earlier, we get:
b = -5 - (-1) = -4
Finally, substituting these values of a and b into the equation for c that we found earlier, we get:
c = 11 - (-1) - (-4) = 16
Hence , the quadratic function that passes through the given points is given by y = -x² - 4x + 16
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Options
Answer:
Step-by-step explanation:
In probability theory
Let the event that the show had animals in it = A
P(A)=0.7
Let the event that the show aired more than 10 times =B
P(B)=0.4
P(A and B)= 0.2
Therefore, the equation which shows the correct use of the addition rule to determine the probability that a randomly selected show had animals in it or aired more than 10 times is:
The correct option is E.
Answer:
(32, 31) (33,30) (34, 29) (35, 28) (36,27) (37, 26)
Step-by-step explanation:
The pairs of whole numbers that add to 63 and have a difference less than 10 are (27, 36), (28, 35), (29, 34), (30, 33), and (31, 32).
This problem is based in the domain of basic algebra. Essentially, you are being asked to find pairs of whole numbers that, added together, equal 63, with the condition that the difference between these two numbers is less than 10.
Starting from the number 32 (as any larger number plus any number greater than 0 would exceed 63), you can begin to list pairs, subtracting one number from the total of 63 while simultaneously adding that same amount to the other half of the pair. This will ensure that the sum always equals 63.
Here are the pairs satisfying the given conditions: (27, 36), (28, 35), (29, 34), (30, 33), (31, 32). For these pairs, the difference between the two numbers in each pair is less than 10.
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2. Regular pentagon PENTA has side lengths that are 9 meters long. To the nearest square meter, find the area of the pentagon.
Area of pentagon PENTA = _____square centimeter
1) Trapezoid BEAR with bases 11.5 and 6.5 and height 8.5, all in cm.
2) Regular pentagon PENTA with side lengths 9 m
The area of each figure, rounded to the nearest integer
1) The area of a trapezoid is given by
... A = (1/2)(b1 +b2)h
... A = (1/2)(11.5 +6.5)·(8.5) = 76.5 ≈ 77
The area of BEAR is about 77 cm².
2) The conventional formula for the area of a regular polygon makes use of its perimeter and the length of the apothem. For an n-sided polygon with side length s, the perimeter is p = n·s. The length of the apothem is found using trigonometry to be a = (s/2)/tan(180°/n). Then the area is ...
... A = (1/2)ap
... A = (1/2)(s/(2tan(180°/n)))(ns)
... A = (n/4)s²/tan(180°/n)
We have a polygon with s=9 and n=5, so its area is
... A = (5/4)·9²/tan(36°) ≈ 139.36
The area of PENTA is about 139 m².
Answer:139 cm squared
The area of a trapezoid is given by
... A = (1/2)(b1 +b2)h
... A = (1/2)(11.5 +6.5)·(8.5) = 76.5 ≈ 77
The area of BEAR is about 77 cm².
The conventional formula for the area of a regular polygon makes use of its perimeter and the length of the apothem. For an n-sided polygon with side length s, the perimeter is p = n·s. The length of the apothem is found using trigonometry to be a = (s/2)/tan(180°/n). Then the area is ...
... A = (1/2)ap
... A = (1/2)(s/(2tan(180°/n)))(ns)
... A = (n/4)s²/tan(180°/n)
We have a polygon with s=9 and n=5, so its area is
... A = (5/4)·9²/tan(36°) ≈ 139.36
The area of PENTA is about 139 m².
Answer:
0.4949
=
49 this is a fraction
99
Step-by-step explanation:
Let
XXX
x
=
0.49
¯¯¯¯
49
then
XXX
100
x
=
49.49
¯¯¯¯
49
and
XXX
99
x
=
100
x
−
x
=
49
XXX
x
=
49
99
12.8 km per hour
51.2 km in 4 hours