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KATRIN_1 [288]
3 years ago
9

Given uv = su tu sv prove vt = st

Mathematics
1 answer:
Lady bird [3.3K]3 years ago
5 0

Answer:  see proof below

<u>Step-by-step explanation:</u>

\begin{array}{cl|cl}&\underline{\text{Statement}}&&\underline{\text{Reason}}\\1.&TU\perp SV&1.&\text{Given}\\2.&\angle TUV = 90^o&2.&\text{De finition of Perpendicular angles}\\&\angle TUS = 90^o&&\\3.&\angle TUV=\angle TUS&3.&\text{Transitive Property}\\4.&UV=US&4.&\text{Given}\\5.&TU=TU &5.&\text{Reflexive Property}\\6.&\triangle TUV = \triangle TUS&6.&\text{SAS Congruency Theorem}\\7.&VT=ST&7.&CPCTC\end{array}

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Step-by-step explanation:

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2 years ago
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Factor the difference of cubes. Select prime if the polynomial cannot be factored
tester [92]

Answer:

(m-(1/3))(m^2+(1/3)m+(1/9)

Step-by-step explanation:

Just use the difference of cubes

3 0
3 years ago
The graph of a quadratic function has a vertex located at (7,-3) and passes through points (5,5) and (9,5). Which equation best
Serga [27]

Answer:

B) f(x)=2(x-7)^2-3.

Step-by-step explanation:

The vertex form of the equation is given by f(x)=a(x-h)^2+k.

We plug in the vertex to obtain:

f(x)=a(x-7)^2-3.

Since the graph passes through (5,5) and (9,5), they must satisfy its equation.

5=a(9-7)^2-3.

5+3=4a.

8=4a

Divide both sides by 4.

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Therefore the equation is:

f(x)=2(x-7)^2-3.

4 0
3 years ago
Pre-Calc :
nikitadnepr [17]
The answer is 
x=2t and t=x/2, but we have <span>y = 3t -1
so </span><span>y = 3(x/2) -1
so y = 3x/2  - 1</span>
5 0
3 years ago
A cardboard box without a lid is to have a volume of 8,788 cm3. Find the dimensions that minimize the amount of cardboard used.
Montano1993 [528]

Answer:

  x = y = 26 cm; z = 13 cm

Step-by-step explanation:

The generic solution for the minimum material in an open-top box is that the box is square and half as high as it is wide. It is half a cube of twice the volume.

The dimensions of the square base are ...

  ∛(2·8788 cm³) = 26 cm

Then the height is half that, or 13 cm.

  x = y = 26 cm; z = 13 cm

_____

If you need to see the development, you can use the method of Lagrange multipliers to find the minimum area for the given volume;

  area = xy +2(xz +yz)

  volume = xyz = 8788

We require each of the partial derivatives of L with respect to x, y, z, and λ to be zero.

  L = xy +2(xz +yz) +λ(xyz -8788)

  partial with respect to x: 0 = y+2z +λyz

  partial with respect to y: 0 = x +2z +λxz

  partial with respect to z: 0 = 2x+2y +λxy

  partial with respect to λ: 0 = xyz -8788

From the first two equations, we have ...

  λ = (y +2z)/(yz) = 1/z +2/y

  λ = (x +2z)/(xz) = 1/z +2/x

Equating these expressions for λ, we find ...

  1/z +2/y = 1/z +2/x   ⇒   x = y

The third equation then tells us ...

  λ = (2x +2y)/(xy) = 2/y +2/x

Comparing this to either of the first two expressions for λ, we see ...

  1/z +2y = 2/x +2/y   ⇒   z = x/2

This is the result we started the answer with:

  x = y = 2z = ∛(2·8788 cm³)

7 0
2 years ago
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