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a_sh-v [17]
3 years ago
15

Please answer this question as fast as u can

Mathematics
1 answer:
Sidana [21]3 years ago
4 0
Ok.graph the 2.3 and the 6.8 as regular decimals, draw a line, annd I dont know how to do the last part. :(
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Does the function f(x) = 2x^2− 6x + 9 have a minimum or a maximum? Identify its value.
exis [7]

Answer:

minimum value of function is   \frac{45}{8} .

Step-by-step explanation:

Given function represents a parabola.

Now, here coefficient of x^{2} is positive , so the parabola will be facing upwards and thus the function will be having a minimum.

Now, as we know that minimum value of a parabolic function occurs at

x = \frac{-b}{4a} .

Where , b represents the coefficient of x and a represents the coefficient of x^{2} .

here, a = 2 , b = -6

Thus \frac{-b}{4a} = \frac{6}{8}

                                            =  \frac{3}{4}

So, at x =  \frac{3}{4}  minimum value will occur and which equals

y = 2×\frac{9}{16} - \frac{18}{4} + 9 =  \frac{45}{8} .

Thus , minimum value of function is   \frac{45}{8} .

4 0
3 years ago
Verify that the points are the vertices of a parallelogram and find its area. (2,-1,1), (5, 1,4), (0,1,1), (3,3,4)
Gelneren [198K]

Answer:

Area = 13.15 square units

Step-by-step explanation:

Let the given vertices be represented as follows:

A(2, -1, 1) = 2i - j + k

B(5, 1, 4) = 5i + j + 4k

C(0, 1, 1) = 0i + j + k

D(3, 3, 4) = 3i + 3j + 4k

(i) Let's calculate the vectors of all the sides:

\\AB = B - A =  (5i + j + 4k) - (2i - j + k)

AB = 5i + j + 4k - 2i + j - k                 [Collect like terms]

AB = 3i + 2j + 3k

BC = C - B =  (0i + j + k) - (5i + j + 4k)

BC = 0i + j + k - 5i - j - 4k                 [Collect like terms]

BC = -5i + 0j - 3k

CD = D - C =  (3i + 3j + 4k) - (0i + j + k)

CD = 3i + 3j + 4k - 0i - j - k                [Collect like terms]

CD = 3i + 2j + 3k

DA = A - D =  (2i - j + k) - (3i + 3j + 4k)

DA = 2i - j + k - 3i - 3j - 4k                [Collect like terms]

DA = -i - 4j - 3k

AC = C - A =  (0i + j + k) - (2i - j + k)

AC = 0i + j + k - 2i + j - k                [Collect like terms]

AC = -2i + 2j

BD = D - B = (3i + 3j + 4k) - (5i + j + 4k)

BD = 3i + 3j + 4k - 5i - j - 4k                [Collect like terms]

BD = -2i + 2j

(ii) From the results in (i) above, we can deduce that;

AB = CD This implies that AB || CD  [AB is parallel to CD]

AC = BD This implies that AC || BD  [AC is parallel to BD]

(iii) Therefore, ABDC is a parallelogram since opposite sides (AB and CD) are parallel. Hence, the points are vertices of a parallelogram

<u>Now let's calculate the area</u>

To find the area of the parallelogram, we find the magnitude of the cross product of any two adjacent sides.

In this case, we'll choose AB and AC

Area = |AB X AC|

Where;

AB X AC = \left[\begin{array}{ccc}i&j&k\\3&2&3\\-2&2&0\end{array}\right]

<u></u>

AB X AC = i(0 - 6) - j(0 + 6) + k(6 + 4)

AB X AC = - 6i - 6j + 10k

|AB X AC| = \sqrt{(-6)^2 + (-6)^2 + (10)^2}

|AB X AC| = \sqrt{172}

|AB X AC| = 13.15

Area = 13.15 square units.

<u></u>

<u></u>

<u>PS: </u> ACBD is also a parallelogram. The diagram has also been attached to this response.

6 0
3 years ago
Find the value of the trigonometric ratio.<br> Answer has to be a reduced ratio.<br> PLS HELP!!
zloy xaker [14]

Answer:

3/5

Step-by-step explanation:

I'm not completely sure but from what I see it says 'sin <em>C </em>' and both 12 , 20 are on C.

so i simply just did 12/20

reduced once - 6/10

reduced twice - 3/5

4 0
3 years ago
Ed intends to roll a six-sided number cube 100 times. What probability model can he use to predict whether or not each roll will
Stells [14]
The answer is Each roll has a 0.333 probability of being composite.

<em>(I just took the test, B was the answer)</em>

8 0
3 years ago
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A marathon runner ran 15 miles in 120 minutes. What is the ratio of minutes per mile?
yawa3891 [41]

Answer:

Step-by-step explanation:

5 0
3 years ago
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