All categories

2 years ago

In quadrilateral ABCD, AC = x +5 and BD = 2x-12 For what value of x is ABCD a rectangle?

Mathematics

1 answer:

Triss [41]2 years ago

8 0

Answer:

x = 17

Step-by-step explanation:

The diagonals of a rectangle are congruent, thus

BD = AC, that is

2x - 12 = x + 5 ( subtract x from both sides )

x - 12 = 5 ( add 12 to both sides )

x = 17

You might be interested in

Factor completely: 3x^2 + 12x + 7

Goshia [24]

Answer:

6x+12

Step-by-step explanation:

7 0

3 years ago

On the grid, draw a rotation of triangle ABC, a translation of triangle ABC, and a reflection of triangle ABC. Describe clearly

Ulleksa [173]

Answer:

Step-by-step explanation:

6 0

3 years ago

Find a potential function for the vector field

alexdok [17]

(a) We want to find a scalar function $f(x,y,z)$ such that $\mathbf F = \nabla f$ . This means

$\dfrac{\partial f}{\partial x} = 2xy + 24$

$\dfrac{\partial f}{\partial y} = x^2 + 16$

Looking at the first equation, integrating both sides with respect to $x$ gives

$f(x,y) = x^2y + 24x + g(y)$

Differentiating both sides of this with respect to $y$ gives

$\dfrac{\partial f}{\partial y} = x^2 + 16 = x^2 + \dfrac{dg}{dy} \implies \dfrac{dg}{dy} = 16 \implies g(y) = 16y + C$

Then the potential function is

$f(x,y) = \boxed{x^2y + 24x + 16y + C}$

(b) By the FTCoLI, we have

$\displaystyle \int_{(1,1)}^{(-1,2)} \mathbf F \cdot d\mathbf r = f(-1,2) - f(1,1) = 10-41 = \boxed{-31}$

$\displaystyle \int_{(-1,2)}^{(0,4)} \mathbf F \cdot d\mathbf r = f(0,4) - f(-1,2) = 64 - 41 = \boxed{23}$

$\displaystyle \int_{(0,4)}^{(2,3)} \mathbf F \cdot d\mathbf r = f(2,3) - f(0,4) = 108 - 64 = \boxed{44}$

7 0

2 years ago

Standard form for y-5=6(x+1)

olga_2 [115]

Y−5x6=−1y-5x6=-1 AA must be positive, so multiply both sides of the equation by −1-1 .−1⋅(y−5x6)=−1⋅−1-1⋅(y-5x6)=-1⋅-1 Simplify the left side of the equation.Tap for more steps...Multiply −1-1 by y−5x6y-5x6 to get −1(y−5x6)-1(y-5x6) .−1(y−5x6)=−1⋅−1-1(y-5x6)=-1⋅-1 Apply the distributive property.−1y−1(−5x6)=−1⋅−1-1y-1(-5x6)=-1⋅-1 Rewrite −1y-1y as −y-y .−y−1(−5x6)=−1⋅−1-y-1(-5x6)=-1⋅-1 Simplify −1(−5x6)-1(-5x6) .Tap for more steps...Multiply −1-1 by −1-1 to get 11 .−y+1(5x6)=−1⋅−1-y+1(5x6)=-1⋅-1 Multiply 5x65x6 by 11 to get 5x65x6 .−y+5x6=−1⋅−1-y+5x6=-1⋅-1 −y+5x6=−1⋅−1-y+5x6=-1⋅-1 Reorder −y-y and 5x65x6 .5x6−y=−1⋅−15x6-y=-1⋅-1 5x6−y=−1⋅−15x6-y=-1⋅-1 Multiply −1-1 by −1-1 to get 11 .5x6−y=15x6-y=1

4 0

3 years ago

Read 2 more answers

The cost, c(x), for a taxi ride is given by c(x)=2x+3.00 , where x is the number of minutes. What does th slope mean for this si

Masja [62]

The rate of change of the cost of the taxi ride is $2.00 per minute.

4 0

3 years ago

Read 2 more answers