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Nuetrik [128]
3 years ago
9

HELP PLEASE What is the area of the regular trapezoid below?

Mathematics
1 answer:
Schach [20]3 years ago
8 0

Answer:

64 Centimeters squared

Step-by-step explanation:

Formula for the Area of a trapezoid:

A = a+b

----- h

2

a (base) = 6

b (base) = 10

h (height) = 8

6+10 = 16

16/2 = 8

8 times 8 = 64

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How many different 4 digit even numbers can be written using 0,5,6,3,8,7?
kherson [118]

Step-by-step explanation:

I assume the digits cannot be repeated in the numbers.

and that we don't want any numbers that start with 0, as that would be considered a 3- digit number, right ?

so, under these assumptions we have the question of in how many ways can we pull 4 digits out of 6.

if the sequence of the pulled digits would not matter, it would be combinations C(6, 4).

but because we are building actual numbers, the sequence does matter, and we use permutations P(6, 4).

P(6, 4) = 6!/(6-4)! = 6!/2! = 6×5×4×3 = 360

so, we can create 360 different numbers.

but not all of them are wanted.

we don't want the ones that start with 0. how many are those ?

since we are handling all digits in the same way and priority, there are an equal amount of numbers that start with a 0, or a 5, or a 6, or a 3, or a 8, or a 7.

so, 1/6 of the 360 numbers start with a 0, and we need to subtract them :

360 - 60 = 300 really 4-digit numbers

and from these 300 we only want even numbers. that means they can only end with 0, 6 or 8.

in the same way as for the first position, we have 1/6 of the more 300 numbers that end with one of these digits.

we allow 3 digits, so we have

3×1/6 × 300 = 1/2 × 300 = 150

that means we can write 150 different 4-digit even numbers out of these 6 digits.

6 0
2 years ago
The function h(x) = x2 + 14x + 41 represents a parabola.
defon
Part A:

h(x)= x^{2} +14x+41

The first step of completing the square is writing the expression x^{2} +14x as (x+7)^{2} which expands to x^{2} +14x+49.

We have the first two terms exactly the same with the function we start with: x^{2} and 14x but we need to add/subtract from the last term, 49, to obtain 41. 

So the second step is to subtract -8 from the expression x^{2} +14x+49

The function in completing the square form is
h(x)= (x+7)^{2}-8

Part B:

The vertex is obtained by equating the expression in the bracket from part A to zero

x+7=0
x=-7

It means the curve has a turning point at x = -7

This vertex is a minimum since the function will make a U-shape. 
A quadratic function a x^{2} +bx+c can either make U-shape or ∩-shape depends on the value of the constant a that goes with x^{2}. When a is (+), the curve is U-shape. When a (-), the curve is ∩-shape

Part C:

The symmetry line of the curve will pass through the vertex, hence the symmetry line is x=-7

This function is shown in the diagram below




3 0
4 years ago
Read 2 more answers
Find the height of a trapezoid if b1= 2x + 1 and b2 = x+4 and the area = 3x2 + 5x Show all your work for full credit.
Advocard [28]
A = 1/2 h (b1+b2)
so
h = 2A / (b1+b2)
h = [2(3x^2 + 5x)] / (2x + 1 + <span>x + 4)
h = (6x^2 + 10x)/(3x +5)
h = 2x(3x + 5)/(3x +5)
h = 2x

answer: </span><span>height of a trapezoid = 2x</span>
5 0
3 years ago
17<br><br> i already did the test
Dmitry [639]

Answer:

17

Step-by-step explanation:

I believe the answer is 17.

Simplify

17

=17

Now,

Consider point O at zero on the number line.

Mark a point A such at number 4 such that OA= 4

Draw a perpendicular AB at point A of unit length.

Join AB

Taking radius of length AB draw an arc to intersect the number line at C.

Finally,    OC=\sqrt{17}

Thus proving the answer is 17 or \sqrt{289} = 17

3 0
3 years ago
What is the area of a triangle whose vertices are J(−2, 1) , K(4, 3) , and L(−2, −5) ?
MArishka [77]
Hello,


J (-2,1), K (4,3), and L (-2,-5) 
<span>Area of triangle: 18.00
</span>

REMEMBER: <span>Notice that one side is vertical. Use that side as base. 
</span>

Once again, Your answer is 18.


Hope this helps
8 0
4 years ago
Read 2 more answers
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