MATHEMATICS HIGH SCHOOL

Square root of 4+2 root 3

Answers

Answer 1
Answer: (a+b)^2=a^2+2ab+b^2\ \ \ (*)\n\n\n√(4+2\sqrt3)=√(3+2\sqrt3+1)=\sqrt{\underbrace{(\sqrt3)^2+2\cdot\sqrt3\cdot1+1^2}_((*))}\n\n=√((\sqrt3+1)^2)=|\sqrt3+1|=\sqrt3+1
Answer 2
Answer: (a+b)^2=a^2+2\cdot a\cdot b+b^2\n \n4+2 √(3)=1^2+2\cdot1\cdot √(3)+ √(3) ^2\ \ \ \Rightarrow\ \ \ a=1\ \ \ \wedge\ \ \ b= √(3) \n \n4+2 √(3) =(1+ √(3) )^2\n \n \sqrt{4+2 √(3)} = \sqrt{(1+ √(3) )^2} =|1+ √(3) |=1+ √(3)

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If the population of Centerville in 1910 was 4,200 and 5,000 in 1920, assuming exponential growth, what would the population be in 2020?​

Answers

The exponential equation is solved and the population in 2020 is given by the relation P ( A ) = 27,369

What is exponential growth factor?

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units

Given data ,

Let the initial population be P ( 0 ) = 4,200

Let the population in 10 years be P ( 1 ) = 5,000

Now , the population in 100 years is P ( 100 ) =

The exponential growth formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

r = ln(5,000/4,200) / 10 = 0.017

Now we can use this value of r to predict the population in 2020, which is 100 years after 1920:

P(100) = 5,000 × e^(0.017 × 100) = 27,369

Hence , the predicted population of Centerville in 2020, assuming exponential growth, is 27,369

To learn more about exponential growth factor click :

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Answer:

the real answer is 28588

Step-by-step explanation:

If f(x) = 2x + 3 and g(x) = x2-7, find (f+g)(x)

Answers

f(x) = 2x + 3
g(x) = x²-7

(f+g)(x) = f(x) + g(x) = 2x + 3 + x² - 7 = x² + 2x - 4

(f+g)(x)  =  x² + 2x - 4

Which is the equation of a line with the slope of -2 that passes through the point (-2,0)

Answers

y = -2x - 4

-2x is the slope and -4 is the y intercept.
The equation of a line is y = mx + b (m is the slope; b is the y-intercept)

We are given the slope of -2 so...

y = -2x + b

We must determine b. Since they give us a point, we can sub in the x and y coords (-2,0)

0 = -2(-2) + b
0 = 2 + b
[Subtract 2 from both sides]
0-2=2-2+b
-2=b

Now, go back to the original equation (before adding coordinates in) and input b.

y = -2x-2

Calculate the surface area of sphere with a radius of 5 inches. (4πr2)

Answers

4(3.14) (5) squared

4 (3.14 ) ( 25)

the answer is 314

the spoke of a wheel reaches from the center of the wheel to its rim. If the circumstances of the rim of the wheel is 42 inches, how long is each spoke?

Answers

The spoke of the wheel serves as the radius of the circle. 
To solve for the circumference of the circle, we use this formula:

C = 2πr
42 inches = 2 * 3.14 * r
42 inches = 6.28 * r
42 inches / 6.28 = r 
6.69 inches = r

The length of each spoke is 6.69 inches.

What additional information do you need to prove that ∆LMO ≅ ∆LNO by the HL Theorem? ∠NLO ≅ ∠MLO ∠MOL ≅ ∠NOL

Answers

The hypotenuse leg theorem states that any two right triangles that have a congruent hypotenuse and a corresponding, congruent leg are congruent triangles.
The triangles ΔLNO and ΔLMO have the same leg Lo, therefore you need the equality of hypotenuses LM=LN.

For a better understanding of the solution given here please find the diagram in the file attached.

We know from the Hypotenuse Leg Theorem (the HL theorem) that "if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent."

Thus, as can be seen from the diagram, Side LO (also called leg LO) is common to both the triangles LMO and LNO. Therefore, the additional information that will be required to prove the congruence is that the respective hypotenuses, MO and NO are equal.
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