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3 years ago

If ABCD is a rectangle, find the length of each diagonal. AC=3c/9 and BD=4-c

1 answer:

4 0

So we know that the diagonals of a rectangle are equal than

3c/9 = 4 - c

c/3 = 4-c

c = 3(4-c)

c = 12 -3c

4c = 12

c = 12/4

c = 3

so in this case the length of AC = 3*3/9 = 9/9 = 1 and the length of
BD = 4 - 3 = 1

hope this will help you

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There is a sales tax of $14 on an item that costs $147before tax. A second item costs$84 before tax. What is the sales tax on th

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4 years ago

Cade covered the outside of a box shaped like a rectangular prism with paper. The box is 3.5 feet long, 2.2 feet wide, and 4.1 f

Orlov [11]

Answer:

The total surface area of this box is 62.14 square feet

Step-by-step explanation:

Given:

Length = 3.5 feet

Width = 2.2 feet

Height = 4.1 feet

To Find:

The Surface area of the prism = ?

Solution:

The box is the shape of rectangular prism

Then the surface area of the prism = 2(lh +hw +wl)

Where

l is the length

w is the width

h is the height

Substituting the values

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8 0

4 years ago

Solve for x and y in the given the 45° - 45° - 90° triangle shown above. When applicable, simplify all radicals and show your wo

vazorg [7]

Answer:

Therefore,

$x=y= 4\sqrt{2}=5.6568\ units$

Step-by-step explanation:

Given:

Consider In Right Angle Triangle ABC

∠B = 90°

∠C = ∠A = 45°

AB = y

BC = x = adjacent side

AC = 8 = hypotenuse

To Find:

x = ?

y = ?

Solution:

In Right Angle Triangle ABC by Cosine Identity we have

$\cos C = \dfrac{\textrm{side adjacent to angle C}}{Hypotenuse}\\$

substituting the above given values we get

$\cos 45 = \dfrac{BC}{AC}=\dfrac{x}{8}$

$\dfrac{1}{\sqrt{2} } =\dfrac{x}{8}\\\therefore x=\dfrac{8}{\sqrt{2} } \\Rationalizing\ we\ get\\\therefore x=\dfrac{8}{\sqrt{2}}\times \dfrac{\sqrt{2} }{\sqrt{2}}}\\\therefore x=4\sqrt{2}=4\times 1.4142=5.6568\ units$