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3 years ago

13) mZFCD= x +41, mZBCF= x + 78, and mZBCD=95°. Find x. BO C D

Mathematics

1 answer:

Setler [38]3 years ago

4 0

Answer:

x = - 12

Step-by-step explanation:

∠ FCD + ∠ BCF = ∠ BCD , substitute values

x + 41 + x + 78 = 95 , that is

2x + 119 = 95 ( subtract 119 from both sides )

2x = - 24 ( divide both sides by 2 )

x = - 12

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A positive integer is twice another.the sum of the reciprocal of the two positive integer is 3/14. Find the integers

icang [17]

Answer:

$\huge\boxed{14\ \text{and}\ 7}$

Step-by-step explanation:

$n,\ m-\text{positive integer}\\\\n=2m-\text{a positive integer is twice another}\\\\\dfrac{1}{n}+\dfrac{1}{m}=\dfrac{3}{14}-\text{the sum of the reciprocal of the two positive integer is }\ \dfrac{3}{14}\\\\\text{We have the system of equations:}\\\\\left\{\begin{array}{ccc}n=2m&(1)\\\dfrac{1}{n}+\dfrac{1}{m}=\dfrac{3}{14}&(2)\end{array}\right$

$\text{Substitute (1) to (2):}\\\\\dfrac{1}{2m}+\dfrac{1}{m}=\dfrac{3}{14}\\\\\dfrac{1}{2m}+\dfrac{1\cdot2}{m\cdot2}=\dfrac{3}{14}\\\\\dfrac{1}{2m}+\dfrac{2}{2m}=\dfrac{3}{14}\\\\\dfrac{1+2}{2m}=\dfrac{3}{14}\\\\\dfrac{3}{2m}=\dfrac{3}{14}\Rightarrow2m=14\qquad\text{divide both sides by 2}\\\\\dfrac{2m}{2}=\dfrac{14}{2}\\\\\boxed{m=7}$

$\text{Substitute it to (1):}\\\\n=2\cdot7\\\\\boxed{n=14}$

8 0

3 years ago

The radioactive isotope radium has a half-life of 1,600 years. The mass of a 100-gram sample of radium will be______ grams after

Olenka [21]

To solve this we are going to use the half life equation $N(t)=N_{0} e^{( \frac{-0.693t}{t _{1/2} }) }$
Where:
$N_{0}$ is the initial sample
$t$ is the time in years
$t_{1/2}$ is the half life of the substance
$N(t)$ is the remainder quantity after $t$ years

From the problem we know that:
$N_{0} =100$
$t=200$
$t_{1/2} =1600$

Lets replace those values in our equation to find $N(t)$ :
$N(200) =100e^{( \frac{(-0.693)(200)}{1600}) }$
$N(200)=100e^{( \frac{-138.6}{1600} )}$
$N(200)=100e^{-0.086625}$
$N(200)=91.7$

We can conclude that after 1600 years of radioactive decay, the mass of the 100-gram sample will be 91.7 grams.

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3 years ago

business plans are aimed MAINLY at A.Government Regulators B.employees C.marketing firms D.potential investors

Talja [164]

Salutations!

Business plans are mainly aimed at ----

Business plans are mainly aimed at potential investors. You need plan your business so thoroughly to gain the attention of potential investors. Potential investors are people who give you cash (capital) to help invest you in other companies or business.

Thus, your answer is option D.

Hope I helped :D

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3 years ago

Read 2 more answers

Please help! acellus

ch4aika [34]

Answer:

The number that belongs in the green box is equal to 909.

General Formulas and Concepts:
Algebra I

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Trigonometry

[Right Triangles Only] Pythagorean Theorem:
$\displaystyle a^2 + b^2 = c^2$

a is a leg
b is another leg
c is the hypotenuse

Step-by-step explanation:

Step 1: Define

Identify given variables.

a = 30

b = 3

c = x

Step 2: Find x

Let's solve for the general equation that allows us to find the hypotenuse:

[Pythagorean Theorem] Square root both sides [Equality Property]:
$\displaystyle \begin{aligned}a^2 + b^2 = c^2 \rightarrow c = \sqrt{a^2 + b^2}\end{aligned}$

Now that we have the formula to solve for the hypotenuse, let's figure out what x is equal to:

[Equation] Substitute in variables:
$\displaystyle \begin{aligned}c & = \sqrt{a^2 + b^2} \\x & = \sqrt{30^2 + 3^2}\end{aligned}$
Evaluate:
$\displaystyle \begin{aligned}c & = \sqrt{a^2 + b^2} \\x & = \sqrt{30^2 + 3^2} \\& = \boxed{ \sqrt{909} } \\\end{aligned}$