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pshichka [43]
3 years ago
14

The area of a trapezium is 384cm². Its parallel sides are in the ratio3 : 5 and the perpendicular distance between them is 12 cm

. Find the length of each of the parallel sides. *
Mathematics
1 answer:
Pani-rosa [81]3 years ago
5 0
Area of trapezium=384 square cm
Ratio of parallel sides=
Distance between parallel sides=h=12 cm
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In a mixture of​ concrete, there are five lb of cement mix for each pound of gravel. if the mixture contains a total of 198 lb o
arsen [322]
There are 39.6 lbs. of gravel.
7 0
3 years ago
Which statement describes the inverse of m(x) = x2 – 17x?
stealth61 [152]

Answer:

The correct option is;

The \ domain \ restriction \ x \geq \dfrac{17}{2} \ results \ in \ m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }}

Step-by-step explanation:

The given information is that m(x) = x² - 17·x

The above equation can be written in the form;

y = x² - 17·x

Therefore;

0 = x² - 17·x - y

From the general solution of a quadratic equation, 0 = a·x² + b·x + c we have;

x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}

By comparison to the equation,0 = x² - 17·x - y, we have;

a = 1, b = -17, and c = -y

Substituting the values of a, b and c into the formula for the general solution of a quadratic equation, we have;

x = \dfrac{-(-17)\pm \sqrt{(-17)^{2}-4\times (1) \times (-y)}}{2\times (1)} = \dfrac{17\pm \sqrt{289+4\cdot y}}{2}

Which can be simplified as follows;

x =  \dfrac{17\pm \sqrt{289+4\cdot y}}{2}= \dfrac{17}{2} \pm \dfrac{1}{2}  \times \sqrt{289+4\cdot y}} = \dfrac{17}{2} \pm \sqrt{\dfrac{289}{4} +\dfrac{4\cdot y}{4} }}

And further simplified as follows;

x = \dfrac{17}{2} \pm \sqrt{\dfrac{289}{4} +y }} = \dfrac{17}{2} \pm \sqrt{y + \dfrac{289}{4} }}

Interchanging x and y in the function of the inverse, m⁻¹(x), we have;

m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }}

We note that the maximum or minimum point of the function, m(x) = x² - 17·x found by differentiating the function and equating the result to zero, gives;

m'(x) = 2·x - 17 = 0

x = 17/2

Similarly, the second derivative is taken to determine if the given point is a maximum or minimum point as follows;

m''(x) = 2 > 0, therefore, the point is a minimum point on the graph

Therefore, as x increases past the minimum point of 17/2, m⁻¹(x) increases to give;

The \ domain \ restriction \ x \geq \dfrac{17}{2} \ results \ in \ m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }} to increase m⁻¹(x) above the minimum.

8 0
3 years ago
Determine the equation of the parabola whose graph is given below. Write your answer in General Form. A parabola on a coordinate
dimaraw [331]

The equation of parabola becomes y = -2/25(x-3)^2 + 4.

According to the statement

we have given a graph and from this graph we have to find the equation of parabola in the general form.

So,

we know that the equation of parabola in general form is

y = a(x-h)^2 +k - (1)

From the graph we have:

a point on the graph is (x,y) = (-2,2)

the vertex of the graph is (h,k) = (3,4)

Now, substitute these values in the equation number (1)

Then

y = a(x-h)^2 +k

2 = a(-2-3)^2 +4

2 = a(-5)^2 +4

2 = a(25) +4

25a = -2

a = -2/25.

Now put a = -2/25 and (h,k) = (3,4) in the equation(1).

Then

the equation of parabola becomes y = -2/25(x-3)^2 + 4

So, The equation of parabola becomes y = -2/25(x-3)^2 + 4.

Learn more about equation of parabola here brainly.com/question/4061870

#SPJ4

6 0
2 years ago
Please help, I've been doing math since the time I woke up, with no breaks. I'm brain dead rn. It's all timed.
Yuki888 [10]
The correct answer is A and D
8 0
3 years ago
Evaluate the expression when m=-6.<br> 2<br> m + 5m - 4
Brums [2.3K]

Answer:

2

Step-by-step explanation:

m^2 + 5m - 4

Let m = -6

( -6) ^2 + 5(-6) -4

Exponents first

36 + 5(-6) -4

Then multiply

36 -30 -4

Then subtract

6 -4

2

5 0
3 years ago
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