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3 years ago

ABCD is a parallelogram. Segment AC = 4x + 10. Find the value of x and y.

Mathematics

1 answer:

valkas [14]3 years ago

5 0

Answer:

The values of x and y in the diagonals of the parallelogram are x=0 and y=5

Step-by-step explanation:

Given that ABCD is a parallelogram

And segment AC=4x+10

From the figure we have the diagonals AC=3x+y and BD=2x+y

By the property of parallelogram the diagonals are congruent

∴ we can equate the diagonals AC=BD

That is 3x+y=2x+y

3x+y-(2x+y)=2x+y-(2x+y)

3x+y-2x-y=2x+y-2x-y

x+0=0 ( by adding the like terms )

∴ x=0

Given that segment AC=4x+10

Substitute x=0 we have AC=4(0)+10

=0+10

=10

∴ AC=10

Now (3x+y)+(2x+y)=10

5x+2y=10

Substitute x=0, 5(0)+2y=10

2y=10

$y=\frac{10}{2}$

∴ y=5

∴ the values of x and y are x=0 and y=5

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2 years ago

Suppose T is a transformation from ℝ2 to ℝ2. Find the matrix A that induces T if T is reflection over the line y=1/2x

trapecia [35]

Answer:

$A = \left[\begin{array}{cc}1&\frac{4}{5}\\\frac{4}{3}&-\frac{3}{5}\end{array}\right]$

Step-by-step explanation:

We have to see how the canonical vectors are transformed throught T. Lets first define T in any basis.

Since T is a reflection, then any element of the line y = x/2 if fixed by T. Therefore T(2,1) = (2,1).

On the other hand, any vector perpendicular to the line direction should be sent to its opposite value. We can take, for example, (-1,2) (note that the scalar product (2,1) * (-1,2) = -2+2 = 0). As a consecuence T(-1,2) = (1,-2). We have

T(2,1) = (2,1)
T(-1,2) = (1,-2)

By summing the first vector with the double of the second one we get, using linearity

T(0,5) = T( (2,1) + 2(-1,2)) = T(2,1) + 2T(-1,2) = (2,1) + 2(1,-2) = (4,-3)

Hence, T(0,1) = (4/5,-3/5)

Now, we take the second vector and substract it the double of the first one (to kill the second variable)

T(-3,0) = T( (-1,2) - 2*(2,1) ) = T(-1,2) -2T(2,1) = (1,-2)-2(2,1) = (-3,-4)

Therefore, T(1,0) = (1,4/3)

The matrix A induced by T has in its first column T(1,0) and in its second column T(0,1). We conclude that

$A = \left[\begin{array}{cc}1&\frac{4}{5}\\\frac{4}{3}&-\frac{3}{5}\end{array}\right]$

3 0

3 years ago

Y varies directly with x. If y=25 when x=5, find y when x =-4<br><br>y =

alina1380 [7]

Answer:

y = -20

Step-by-step explanation:

Given that y varies directly with x it means changing x will also cause change in y

Mathematically it can be written as:

y∝x

Removing the proportionality symbol

y = kx

Given y=25 when x=5 Putting the values

$25 = k(5)\\k = \frac{25}{5}\\k = 5$

Now

$y = 5x$

We have to find the value of y when x = -4

Putting x=-4

$y = 5(-4)\\y = -20$

Hence,,

y = -20

7 0

3 years ago

Do i use SIN, COS, or TAN to find the missing lengths?

BaLLatris [955]

Answer:

Step-by-step explanation:

+ Because of a right triangle, so we can find them- the missing lengths:

+ sin(40)= GH/GF

so GH = GF * sin(40) = 88* sin (40) = 56.565= GH

+ cos( 40) = FH/GF

so FH= GF *cos(40)= 88* cos(40) = 67.412= FH

Have a good day

3 0

3 years ago