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kotegsom [21]
3 years ago
6

When a number is decreased by 4.5%, the result is 90. What is the original number to

Mathematics
1 answer:
Contact [7]3 years ago
3 0

Answer:

x = 94.2

Step-by-step explanation:

Let x represent the number

x - 4.5%x = 90

x - 4.5/100x = 90

x - 0.045x = 90

0.955x = 90

Divide both sides by 0.955(the coefficient of )

x = 90/0.955

x = 94.2

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Find the area of the shaded triangle, if the side of each square is 1 unit long.
Vedmedyk [2.9K]

Answer:

10 units²

Step-by-step explanation:

The shape is a triangle.

The area can be found by multiplying the base (in units) with height (in units) divided by 2.

base = 4 units

height = 5 units

\frac{4 \times 5}{2}

\frac{20}{2}  =10

8 0
4 years ago
Find the minimum and maximum of f(x,y,z)=x^2+y^2+z^2 subject to two constraints, x+2y+z=4 and x-y=8.
Alika [10]
The Lagrangian for this function and the given constraints is

L(x,y,z,\lambda_1,\lambda_2)=x^2+y^2+z^2+\lambda_1(x+2y+z-4)+\lambda_2(x-y-8)

which has partial derivatives (set equal to 0) satisfying

\begin{cases}L_x=2x+\lambda_1+\lambda_2=0\\L_y=2y+2\lambda_1-\lambda_2=0\\L_z=2z+\lambda_1=0\\L_{\lambda_1}=x+2y+z-4=0\\L_{\lambda_2}=x-y-8=0\end{cases}

This is a fairly standard linear system. Solving yields Lagrange multipliers of \lambda_1=-\dfrac{32}{11} and \lambda_2=-\dfrac{104}{11}, and at the same time we find only one critical point at (x,y,z)=\left(\dfrac{68}{11},-\dfrac{20}{11},\dfrac{16}{11}\right).

Check the Hessian for f(x,y,z), given by

\mathbf H(x,y,z)=\begin{bmatrix}f_{xx}&f_{xy}&f_{xz}\\f_{yx}&f_{yy}&f_{yz}\\f_{zx}&f_{zy}&f_{zz}\end{bmatrix}=\begin{bmatrix}=\begin{bmatrix}2&0&0\\0&2&0\\0&0&2\end{bmatrix}

\mathbf H is positive definite, since \mathbf v^\top\mathbf{Hv}>0 for any vector \mathbf v=\begin{bmatrix}x&y&z\end{bmatrix}^\top, which means f(x,y,z)=x^2+y^2+z^2 attains a minimum value of \dfrac{480}{11} at \left(\dfrac{68}{11},-\dfrac{20}{11},\dfrac{16}{11}\right). There is no maximum over the given constraints.
7 0
4 years ago
Y=2x-5<br> 4x-y=7 what is the value of x
amid [387]

Answer:

x=1 and y=-3

Step-by-step explanation:

hope this helped :)

7 0
3 years ago
Evaluate without a calculator:
noname [10]

Answer:

240

Step-by-step explanation:

4 x -5 = -20

-20 x -12 = 240

240 is your answer

hope this helps!

4 0
2 years ago
Which point is on the line 4y-2x=0?
hoa [83]
To figure this out, we just need to plug in the points.

4(-1) - 2(-2) = 0
-4 - (-4) = 0
-4 + 4 = 0
0 = 0 
True

The correct answer is a. (-2, -1).
5 0
3 years ago
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