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1 year ago

Describe each as below sea level, at sea level, or above sea level.

Mathematics

1 answer:

sukhopar [10]1 year ago

3 0

Step-by-step explanation:

A negative altitude is below sea level.

A positive altitude is above sea level.

An elevation of zero is at sea level.

Death Valley sits at an elevation of –282 feet. negative: below sea level

The elevation of Mount Whitney is 14,494 feet. positive: above sea level

The elevation of the Singapore Strait is 0 feet. zero: at sea level

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Solve the simultaneous equation y-2x+1=0 and 4x^2+3y^2-2xy=7

Lapatulllka [165]

The first equation is $y-2x+1=0$

$y=2x-1$ (Equation 1)

The second equation is $4x^{2}+3y^{2}-2xy=7$ (Equation 2)

Putting the value of x from equation 1 in equation 2.

we get,

$4x^{2}+3(2x-1)^{2}-2x(2x-1)=7$

$4x^{2}+3(4x^{2}+1-4x)-4x^{2}+2x=7$

by simplifying the given equation,

$12x^{2}-10x-4=0$

$6x^{2}-5x-2=0$

Using discriminant formula,

$D=b^{2}-4ac$

$D=25-4 \times 6 \times -2 = 73$

Now the formula for solution 'x' of quadratic equation is given by:

$x=\frac{-b+\sqrt{D}}{2a} and x=\frac{-b-\sqrt{D}}{2a}$

$x=\frac{5+\sqrt{73}}{12} and x=\frac{5-\sqrt{73}}{12}$

Hence, these are the required solutions.

8 0

2 years ago

Please help with #12 im confused<br> that is the key but i dont get it

Svetllana [295]

Given Equation

$\boxed{ \tt \: (8 \sqrt{3} - 2 \sqrt{2} )(8 \sqrt{3} + 2 \sqrt{2})}$

Step by step expansion:

$\dashrightarrow \sf \: (8 \sqrt{3} - 2 \sqrt{2} )(8 \sqrt{3} + 2 \sqrt{2})$

$\\ \\$

$\dashrightarrow \sf \: (8 \sqrt{3})^{2} - (2 \sqrt{2} {)}^{2}$

Reason:

(a + b)(a - b) = a²- b²

$\\ \\$

$\dashrightarrow \sf \: (8 {}^{2} \times { \sqrt{3} }^{2} )- (2 \sqrt{2} {)}^{2}$

$\\ \\$

$\dashrightarrow \sf \: (64 \times 3 ) - (2 \sqrt{2} {)}^{2}$

$\\ \\$

$\dashrightarrow \sf \: (64 \times 3 ) - (2 {}^{2} \times \sqrt{2} {}^{2} {)}$

$\\ \\$

$\dashrightarrow \sf \: 192- 8$

$\\ \\$

$\dashrightarrow \sf \: 184$

$\\ \\$

~BrainlyVIP ♡

4 0

1 year ago

Read 2 more answers

Can someone explain to me in words how to do this problem 3x+122=22x-11

inn [45]

When you have this type of problem, you need to combine the like-terms and isolate the variable.

3x + 122 = 22x - 11

Add 11 to both sides to get rid of it

3x + 122 + 11 = 22x - 11 + 11 (-11 + 11=0)

3x + 133 = 22x

Then you would bring the 3x to the other side, so subtract 3x from both sides

3x + 133 = 22x

-3x -3x

133 = 22x - 3x

133 = 19x

Then divide both sides by 19 to isolate x

133/19 = 19x/19

133/19 = 7, so x = 7

Hope this helps!!

8 0

2 years ago

Find the area of each regular polygon. Round your answer to the nearest tenth if necessary.

tatuchka [14]

*I am assuming that the hexagons in all questions are regular and the triangle in (24) is equilateral*

(21)

Area of a Regular Hexagon: $\frac{3\sqrt{3}}{2}(side)^{2} = \frac{3\sqrt{3}}{2}*(\frac{20\sqrt{3} }{3} )^{2} =200\sqrt{3}$ square units

(22)

Similar to (21)

Area = $216\sqrt{3}$ square units

(23)

For this case, we will have to consider the relation between the side and inradius of the hexagon. Since, a hexagon is basically a combination of six equilateral triangles, the inradius of the hexagon is basically the altitude of one of the six equilateral triangles. The relation between altitude of an equilateral triangle and its side is given by:

$altitude=\frac{\sqrt{3}}{2}*side$

$side = \frac{36}{\sqrt{3}}$

Hence, area of the hexagon will be: $648\sqrt{3}$ square units

(24)

Given is the inradius of an equilateral triangle.

$Inradius = \frac{\sqrt{3}}{6}*side$

Substituting the value of inradius and calculating the length of the side of the equilateral triangle:

Side = 16 units

Area of equilateral triangle = $\frac{\sqrt{3}}{4}*(side)^{2} = \frac{\sqrt{3}}{4}*256 = 64\sqrt{3}$ square units

4 0

2 years ago

4^(4x-1)=32 <br><br> How do I solve this problem? Do I do 4 to the fourth power first?

yKpoI14uk [10]

Answer:

$\large\boxed{x=\dfrac{7}{8}}$

Step-by-step explanation:

$4^{(4x-1)}=32\\\\(2^2)^{4x-1}=2^5\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{2(4x-1)}=2^5\iff2(4x-1)=5\ \ \text{use the distributive property}\ a(b+c)=ab+ac\\\\(2)(4x)+(2)(-1)=5\\\\8x-2=5\qquad\text{add 2 to both sides}\\\\8x=7\qquad\text{divide both sides by 8}\\\\x=\dfrac{7}{8}$

7 0

2 years ago

Read 2 more answers