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2 years ago

How to divide 43.75 and 3.5

Mathematics

1 answer:

Alona [7]2 years ago

4 0

$\dfrac{43.75}{3.5} = 12.5.$ <span>
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in parallelogram ABCD, AC is diagonal, the measure <ABC is 40°, and the measure of <ACD IS 57°. what is the measure of &lt

Nutka1998 [239]

Answer: $\angle CAD = 83^\circ$ Option D

Step-by-step explanation:

In this question we use properties of parallelogram and angle sum property of a triangle.

In parallelogram ABCD

$\angle ABC=40^\circ$

As, we know that opposite angles of parallelogram are equal

Therefore,

$\angle ABC =\angle ADC =40^\circ$

Now, in triangle ADC

We know that sum of all the angles of a triangle is $=180^\circ$

$\angle ACD +\angle ADC +\angle DAC =180^\circ$

$57^\circ +40^\circ +\angle DAC =180^\circ$

$97^\circ + \angle DAC = 180^\circ$

Subtracting 97 from both sides we get

$\angle DAC = 180^\circ - 97^\circ$

$\angle DAC = 83^\circ$

Measure of $\angle CAD = 83^\circ$

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2 years ago

The function A=A_oe^{-0.01155x} A = A o e − 0.01155 x models the amount in pounds of a particular radioactive material stored in

vivado [14]

They are essentially asking us to solve:

$357=900e^{-0.01155x} \implies\\ \frac{357}{900}=e^{-0.01155x} \implies\\ \ln{\frac{357}{900}}=-0.01155x \implies \\ x\approx 80.1$

Solving this equation for x tells us that it will take around 80.1 years for the materials in the vault to reduce to 357 pounds.

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3 years ago

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What is the Volume of the square pyramid? (Round to the nearest tenth as needed)

goldenfox [79]

Answer:

5229 mm³

Step-by-step explanation:

Volume of square pyramid

$\sf \boxed{Volume \ of \ the \ square \ pyramid = \dfrac{1}{3}*b^2*H}$

b = base length = 25 mm

H = height

We have to find 'H' using Pythagorean theorem,

slant height (hypotenuse) = 28 mm

leg₁ = base length ÷ 2 = 25÷2 = 12.5

leg₂ = H

H² + (12.5)² = 28²

H² = 784 - 156.25

= 627.75

$\sf H = \sqrt{627.75}$

H = 25.01 mm

$\sf \text{Volume of square pyramid =$\dfrac{1}{3}*25*25*25.1$ }$

= 5229 mm³

$\sf \boxed{\text{Volume of square pyramid = \dfrac{1}{3}*25*25*28}}$

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