All categories

2 years ago

Rectangle ABCD has m∠BAC=4x+5and m∠ACD=5x−4. Find m∠CAD m∠CAD =

Mathematics

1 answer:

Natalija [7]2 years ago

6 0

Answer:

m∠CAD = 49degrees

Step-by-step explanation:

For a rectangle ABCD if m∠BAC=4x+5and m∠ACD=5x−4, then;

m∠BAC = m∠ACD (alternate angles)

4x+5 = 5x - 4

4x-5x = -4-5

-x = -9

x = 9

Also

m∠BAC+m∠CAD = 90

4x+5+m∠CAD = 90

4(9)+5+m∠CAD = 90

36+5+m∠CAD = 90

41+m∠CAD = 90

m∠CAD = 90-41

m∠CAD = 49degrees

You might be interested in

A circular mirror measures 24 cm in diameter.

Basile [38]

Answer:

The perimeter or circumference of a half mirror = 37.68 cm

Step-by-step explanation:

The diameter of circular measure = 24 cm

We know that the perimeter of a circular shape is called the 'circumference', with the formula

Circumference of a circle = C = 2πr

When the mirror is cut into half, the diameter gets half as well.

Thus, the diameter of a half mirror = 24/2 = 12 cm

We know that radius = r = diameter / 2 = 12/2 = 6 cm

Thus, the perimeter of half of the mirror = C = 2πr

= 2(3.14)6

= 37.68 cm

Therefore, the perimeter or circumference of a half mirror = 37.68 cm

4 0

2 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

1 year ago

Suppose a basketball player typically makes one-third of his foul shots. Which simulation could be used to generate frequencies

Nat2105 [25]

Answer:

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Find the value of u in paralellogram

Serggg [28]

Answer:

Step-by-step explanation:

2u=u+34

2u-u=34

u=34

6 0

2 years ago

Read 2 more answers

Which choice is the simple formula for the nth term of the following arithmetic sequence?

Murrr4er [49]

-4(1)+10=6
-4(2)+10=2
-4(3)+10=-2
-4(4)+10=-6
-4(5)+10=-10
So d is the answer

5 0

2 years ago