All categories

2 years ago

The base of an isosceles right triangle is 30 cm. What is its area?

Mathematics

1 answer:

dlinn [17]2 years ago

7 0

Answer:

A = 450 cm²

Step-by-step explanation:

Since the right triangle is isosceles then the 2 logs are congruent , both 30 cm and at right angles to each other.

The area (A ) of the triangle is calculated as

A = $\frac{1}{2}$ bh ( b is the base and h the perpendicular height )

Here b = h = 30 , then

A = $\frac{1}{2}$ × 30 × 30 = $\frac{1}{2}$ × 900 = 450 cm²

You might be interested in

Quantity of Jackets Price (in whole dollars) Total Revenue Marginal Revenue Total Cost Marginal Cost Profit (or loss) 0 20 1 20

KonstantinChe [14]

Answer:

18 dollars

Step-by-step explanation:

Marginal cost can be defined as the additional cost to produce every additional unit of a certain good. In mathematical terms;

Marginal cost = change in cost / change in quantity

For seven jackets, we have to find the difference between the cost of seven jackets and the cost of six jackets as follows

$101 - $83 = $18

Since the change in quantity is one, our marginal cost comes to $18.

3 0

3 years ago

Andrea needs a box that has a volume of 90 cubic inches what might the measures of her box be

Eduardwww [97]

Volume is Length x width x height. So what are three numbers that multiply to 90?
30x30x30=90

8 0

3 years ago

Read 2 more answers

What is the solution to the equation below? riund your answer to two decimal places. (24) log(3x) = 60

Amanda [17]

The answer is: " x = 105.41 " .

_____________________________________________

Explanation:

_____________________________________________

Given: " 24 log (3x) = 60 " ; Solve for "x" .

The default is to assume "base 10" for the "logarithm".

_____________________________________________

Start by dividing each side of the equation by "24" ;

→ [ 24 log(3x) ] / 24 = 60 / 24 ;

to get:

_____________________________________________

log (3x) = 2.5 ;

_____________________________________________

Rewrite as: log₁₀ (3x) = 2.5 ;

_____________________________________________

Using the property of logarithms:

⇔ 10⁽²·⁵⁾ = 3x ;

↔ 3x = 10⁽²·⁵⁾ ;

→ 10^ (2.5) = 316.2277660168379332 ;

→ 3x = 316.227766016837933 ;

Divide each side of the equation by "3" ;

to isolate "x" on one side of the equation;

and to solve for "x" ;

→ 3x / 3 = 316.2277660168379332 / 3 ;

to get:

→ x = 105.4092553389459777333 ;

→ round to 2 (two) decimal places;

_____________________________________________

→ " x = 105.41 " .

_____________________________________________

Hope this helps!

Best wishes to you!

_____________________________________________

8 0

3 years ago

Find e^cos(2+3i) as a complex number expressed in Cartesian form.

ozzi

Answer:

The complex number $e^{\cos(2+31)} = \exp(\cos(2+3i))$ has Cartesian form

$\exp\left(\cosh 3\cos 2\right)\cos(\sinh 3\sin 2)-i\exp\left(\cosh 3\cos 2\right)\sin(\sinh 3\sin 2)$ .

Step-by-step explanation:

First, we need to recall the definition of $\cos z$ when $z$ is a complex number:

$\cos z = \cos(x+iy) = \frac{e^{iz}+e^{-iz}}{2}$ .

Then,

$\cos(2+3i) = \frac{e^{i(2+31)} + e^{-i(2+31)}}{2} = \frac{e^{2i-3}+e^{-2i+3}}{2}$ . (I)

Now, recall the definition of the complex exponential:

$e^{z}=e^{x+iy} = e^x(\cos y +i\sin y)$ .

So,

$e^{2i-3} = e^{-3}(\cos 2+i\sin 2)$

$e^{-2i+3} = e^{3}(\cos 2-i\sin 2)$ (we use that $\sin(-y)=-\sin y)$ .

Thus,

$e^{2i-3}+e^{-2i+3} = e^{-3}\cos 2+ie^{-3}\sin 2 + e^{3}\cos 2-ie^{3}\sin 2)$

Now we group conveniently in the above expression:

$e^{2i-3}+e^{-2i+3} = (e^{-3}+e^{3})\cos 2 + i(e^{-3}-e^{3})\sin 2$ .

Now, substituting this equality in (I) we get

$\cos(2+3i) = \frac{e^{-3}+e^{3}}{2}\cos 2 -i\frac{e^{3}-e^{-3}}{2}\sin 2 = \cosh 3\cos 2-i\sinh 3\sin 2$ .

Thus,

$\exp\left(\cos(2+3i)\right) = \exp\left(\cosh 3\cos 2-i\sinh 3\sin 2\right)$

$\exp\left(\cos(2+3i)\right) = \exp\left(\cosh 3\cos 2\right)\left[ \cos(\sinh 3\sin 2)-i\sin(\sinh 3\sin 2)\right]$ .

5 0

3 years ago

What is the value of x ?? If u cant see numbers let me know

Hoochie [10]

Answer:

X = 58°

Step-by-step explanation:

105° = (2x -11)°

105° + 11° = 2x

116°= 2x

Divide both sides by 2

X = 58°.

4 0

2 years ago

Read 2 more answers