A hiker starts at an elevation of 12 feet above sea level. She descends 43 feet into an
underground cave to explore. While exploring, she slips and slides 17 feet further down
into the cave. Write an expression that can be used to model this situation and evaluate
it to determine her location below sea level.

Answer 5-5.190 =-945 -2=-947 2-2=0+3 =3+7=-935

Step-by-step explanation:

[tex]\qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a=7.2\\ b=6.7\\ c=4.5\\ s=\frac{7.2+6.7+4.5}{2}\\[0.5em] \qquad 9.2 \end{cases} \\\\\\ A\sqrt{9.2(9.2-7.2)(9.2-6.7)(9.2-4.5)}\implies A=\sqrt{9.2(2)(2.5)(4.7)} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill A\approx 14.704~\hfill[/tex]

Answer:

The answer is C. 14.704

Step-by-step explanation: I just took the test

The circle that passes through the vertices of triangle ΔABC (A, B, C) is the

circumscribing circle of triangle ΔABC.

The area of the circle that passes through vertices A, B, and C, is (C) 26·π

Reasons:

The given parameters are;

Side length of isosceles triangle ΔABC; [tex]\overline{AB}[/tex] = [tex]\overline{AC}[/tex] = 3·√6

Radius of circle tangent to [tex]\overline{AB}[/tex] at B and [tex]\overline{AC}[/tex] at C = 5·√2

Required:

Area of the circle that passes through vertices A, B, and C

Solution:

Angle ∠BAO is given as follows;

[tex]\angle BAO = arctan\left(\dfrac{5 \cdot \sqrt{2} }{3 \cdot \sqrt{6}} \right) = \mathbf{arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)}[/tex]

Therefore;

[tex]\angle BOA = 90^{\circ} - arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)[/tex]

[tex]\overline{BC} = 2 \times 5 \cdot \sqrt{2} \times sin\left(90^{\circ} - arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)\right) = 15\cdot \sqrt{\dfrac{6}{13} }[/tex]

∠ABO' = ∠BAO' (Base angles of isosceles triangle ΔABO')

[tex]\angle BAO' = \angle BAO = \mathbf{arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)}[/tex]

Therefore;

[tex]\angle BO'A = 180^{\circ} - 2 \times arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)[/tex]

From sine rule, we have;

[tex]\dfrac{\overline{AB}}{sin \left(\angle BO'A \right)} = \mathbf{\dfrac{\overline{BO'}}{sin \left(\angle BAO' \right) \right)}}[/tex]

Which gives;

[tex]\mathbf{\dfrac{3 \cdot \sqrt{6} }{sin \left( 180^{\circ} - 2 \times arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)\right)}} = \dfrac{\overline{BO'}}{sin \left(arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right) \right)}[/tex]

Using a graphing calculator, we get;

[tex]\overline{BO'} = \dfrac{3 \cdot \sqrt{6} }{sin \left( 180^{\circ} - 2 \times arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)\right)} \times sin \left(arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right) \right) = \sqrt{26}[/tex]

The radius of the circumscribing circle [tex]\overline{BO'}[/tex] = √(26)

Therefore, area of the circumscribing circle, [tex]A_{O'}[/tex] = π·(√(26))² = 26·π

The area of the circle that passes through vertices A, B, and C, is (C) 26·π

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The possible question options obtained from a similar question online are;

(A) 24·π (B) 25·π (C) 26·π (D) 27·π (E) 28·π

Answer:

Step-by-step explanation:

Assuming we're rolling a cube die with 6 sides.

Odds for rolling any of 1, 4, 3, or 5 has four possible successes

4/6 = 2/3

Odds for NOT rolling any of 1, 4, 3, or 5 has two possible successes, 2 and 6

2/6 = 1/3

Answer:

x<5   or  x<3/2

Step-by-step explanation:

2[tex]x^{2}[/tex]-13x+15<0

2[tex]x^{2}[/tex]-10x-3x+15<0

2x(x-5)-3(x-5)<0

(x-5)(2x-3)<0

x-5<0  or 2x-3<0

x<5  or  x<3/2

Answer:

Domain: -10 < x < 10

Range: -2 < y < 8

Step-by-step explanation:

Hope this helps!

[tex]x = - \frac{2 \sqrt{3} + 12 }{11} [/tex]

hope it helps

see the attachment for explanation

[tex] \: [/tex]

Answer:

3/2 x -1/9= -1/6

-5/4 divided by 1 3/7=-7/8

Step-by-step explanation:

Answer:

As 1 feet = 12 inches

Therefore, 4 feet = 48/12

= 4

Answer = 4 feet

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

The solution to the differential equation will be expressed as [tex]y_c=Ce^{2x}[/tex]

Given the differential equation;

[tex]\frac{d^2y}{dx^2}+2y \frac{dy}{dx} =0[/tex]

Since the right-hand side of the homogenous equation is zero, the differential equation is a homogenous equation

Let [tex]D=\frac{dy}{dx}[/tex]

The differential equation becomes;

[tex]D^2y-2Dy=0\\(D^2-2D)y=0[/tex]

Factorizing the auxiliary equation m² - 2m = 0

m² = 2m

m = 2

Since the auxiliary solution is real and distinct, the solution to the differential equation will be expressed as  [tex]y_c=C_1e^{m_1x} + C_1e^{m_2x} \\[/tex]

Given that m =2, the solution will be expressed as [tex]y_c=Ce^{2x}[/tex]

b) Most linear differential equations have a constant coefficient because they are mostly solved using the quadratic method which is also called the method of quadrature. This means that the solution maybe expressed in integral form.

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Answer:

Step-by-step explanation:

Answer:

ratio of long-sleeved shirts to short-sleeved shirts is 1:2 this is my answer that I thought of if you don't feel comfortable believing me just wait for another person to answer and see what they say.

Step-by-step explanation:

Answer:

3. (X-6)(X-6)

Given polynomial:

(4x²-3x+7) - (x²+8x-5)

⇛ 4x²-3x+7-x²-8x+5

⇛ (4x²-x²) +(-3x-8x)+(7+5)

⇛ (4-1)x²+(-3-8)x+12

⇛ 3x²+(-11)x+12

⇛ 3x²-11x+12

Note:-

When subtracting two polynomials,change the symbols of the each term in the second polynomial which is subtracted from the first polynomial.

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Answer:

[tex]3x^2-11x+12[/tex]

Step-by-step explanation:

First, distribute the negative:

[tex]4x^2-3x+7-x^2-8x+5[/tex]

Then combine like terms:

[tex]3x^2-11x+12[/tex]

Answer:

8

Step-by-step explanation:

Answer:

Sum of the interior angles = 1260°.

Step-by-step explanation:

Sum of the interior angles =  (n - 2)180° where n= number of sides

Sum of the interior angles = (9-2)180

Sum of the interior angles = 1260°

Answer:

D. -3

Step-by-step explanation:

g(x) moved 3 units to the right

Answer:

y = 9/2 - 5/2(x)

Step-by-step explanation:

I think this is right

Answer:

the quotient, fixed as a percentage

Step-by-step explanation:

Answer:

Fixed Percentage means, the quotient, expressed as a percentage, obtained by dividing the unexpended and not withdrawn amount of the Allocated Amount, at the time a Net Profits Interest is assigned by the total of (i) the unexpended and not withdrawn amount of the Allocated Amount and (ii) the unexpended and not.

Answer:

2/3 ​sandwich.

Step-by-step explanation:

No Explanation

Answer:7777

Step-by-step explanation:

[tex] \: \: \: [/tex]

[tex]f(x) = 4[/tex]

[tex]x = R[/tex]

[tex] \: \: \: [/tex]

Answer:

800

Step-by-step explanation:

800+799=1599

Answer: They are all divisible by 2.

Step-by-step explanation: They all have 2 in common. If you divide them by 2, they all work. Also, if you simplify all to the lowest number, they equal 2 except 2 itself which equals 1.

Answer:

divisible by 2 luv

Step-by-step explanation:

Answer:

  20.1°

Step-by-step explanation:

Put the given numbers into the given formula and do the arithmetic.

  ∆L = 1050/(60·cos(29.5°)) ≈ 20.1°

The change in longitude is about 20.1 degrees.

__

Additional comments

A degree is 60 minutes: 1° = 60', so 30' = 0.5°.

This formula is accurate when the distance units are nautical miles.

Step-by-step explanation:

1. Not all rational numbers are whole numbers.  Whole numbers can be rational numbers, if expressed in fraction form.  For example, 1 can be expressed as [tex]\frac{1}{1}[/tex].  A set of rational numbers consists of a set of numbers written as a quotient of two integers, a and b, in the form [tex]\frac{a}{b}[/tex] , where b ≠ 0.  The reason why b ≠ 0 because division by zero is an undefined mathematical operation.

2. Irrational numbers differ from rational numbers in terms of its representation: while the rational numbers can be expressed as a ratio or in fraction form, irrational numbers cannot be expressed in fraction form.

Irrational numbers are a set of numbers for which its decimal representations is neither terminating, nor repeating.  A couple examples of irrational numbers are:  π and [tex]\sqrt{2}[/tex], as their decimal representations do not come to an end and doesn't have a block of repeating digits.

3. All real numbers are rational numbers. Real numbers comprise of natural numbers, whole numbers, integers, rational numbers, and irrational numbers.

Answer:

Step-by-step explanation:

Squares have equal length and widths

2t - 9 = 1 + t

2t - t - 9 + 9 = 1 + 9 + t - t

t = 10 s