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Vesnalui [34]
3 years ago
8

Evaluate 5c +cd when c = 1/5 and d= 15

Mathematics
2 answers:
Kitty [74]3 years ago
8 0
4 is the answer because you multiply
nirvana33 [79]3 years ago
4 0
The answer would be 4, here are the steps. :)

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The boundary of the lawn in front of a building is represented by the parabola . The parabola is represented on the coordinate p
Colt1911 [192]
The boundary of the lawn in front of a building is represented by the parabola

y = (x^2) /16 + x - 2

And you have three questions which require to find the focus, the vertex and the directrix of the parabola.

Note that it is a regular parabola (its symmetry axis is paralell to the y-axis).

1) Focus:

It is a point on the symmetry axis => x = the x-component of the vertex) at a distance equal to the distance between the directrix and the vertex).

In a regular parabola, the y - coordinate of the focus is p units from the y-coordinate of the focus, and p is equal to 1/(4a), where a is the coefficient that appears in this form of the parabola's equation: y = a(x - h)^2 + k (this is called the vertex form)

Then we will rearrange the standard form, (x^2)/16 + x - 2 fo find the vertex form y = a(x-h)^2 + k

What we need is to complete a square. You can follow these steps.

1) Extract common factor 1/16 => (1/16) [ (x^2) + 16x - 32]

2) Add (and subtract) the square of the half value of the coefficent ot the term on x =>

16/2 = 8 => add and subtract 8^2 => (1/16) [ (x^2) + 16 x + 8^2 - 32 - 8^2]

3) The three first terms inside the square brackets are a perfect square trinomial: =>

(1/16) [ (x+8)^2 - 32 - 64] = (1/16) [ (x+8)^2  - 96] =>

(1/16) [(x+8)^2 ] - 96/16 =>

(1/16) (x +8)^2 -  6

Which is now in the form a(x - h)^2 + k,
where:

a = 1/16 , h = - 8, and k = -6

(h,k) is the vertex: h is the x-coordinate of the vertex, and k is the y-coordinate of the vertex.

=> a = 1/16 => p =1/4a = 16/4 = 4
 
y-componente of the focus = -6 + 4 = -2

x-component of the focus = h = - 8

=> focus = (-8, -2)

2) Vertex

We found it above, vertex = (h,k) = (-8,-6)


3) Directrix

It is the line y = p units below the vertex = > y = -6 - 4 = -10

y = -10   

 


4 0
3 years ago
How fair is 50% of 140 yards? <br><br> 60yards <br> 50yards<br> 70yards<br> 80yards
r-ruslan [8.4K]

Answer:

70 yards.

Step-by-step explanation:

50% is also 1/2, so you put 140/2, and get 70.

6 0
3 years ago
Read 2 more answers
Solve for x: <br> 3x+2y=7
iVinArrow [24]
3x+2y=7\ \ \ |subract\ 2y\ from\ both\ sides\\\\3x=7-2y\ \ \ |divide\ both\ sides\ by\ 3\\\\\boxed{x=\dfrac{7-2y}{3}}
8 0
3 years ago
If TV ≅ WV and UV ≅ XV, then which congruency theorem shows that ΔTUV ≅ ΔWXV ?
VashaNatasha [74]

Answer:

Option (2).

Step-by-step explanation:

In the figure attached,

Given : TV ≅ WV and UV ≅ XV

To prove: ΔTUV ≅ ΔWXV

                Statements                  Reasons

1). TV ≅ WV                              1). Given

2). UV ≅ XV                             2). Given

3). ∠XVW ≅ ∠TVU                  3). Reflexive property

4). ΔTUV ≅ ΔWXV                  4). SAS (Side - angle - side) property of                                                             congruence

Therefore, Option (2) will be the answer.

5 0
3 years ago
Indica el valor del 3 en cada uno de los siguientes números 35.097 _ 753.978 _ 7.543 _ 312.501
lara31 [8.8K]
Free points pls and thank you
5 0
3 years ago
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