A prince has arrived to rescue a princess standing in a tower balcony 18 meters up across a
moat 12 meters wide. He knew the princess was high up and there was a moat, so he
brought the longest ladder in the kingdom, a 20-meter monster. Is the ladder long enough?

Usando el concepto de seno, hay que la escalera debe formar un angulo de 41.8º con el suelo.

El seno de un angulo viene dada por el cambio vertical dividido por el cambio diagonal.

En este problema:

Por eso:

[tex]\sin{\alpha} = \frac{8}{12}[/tex]

[tex]\alpha = \sin^{-1}{\left(\frac{8}{12}\right)}[/tex]

[tex]\alpha = 41.8^\circ[/tex]

La escalera debe formar un angulo de 41.8º con el suelo.

Puede-se aprender más a cerca de el concepto de seno en https://brainly.com/question/24766917

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Answer:

Part A:

B. rhombus

Part B:

C. Opposite sides are parallel and congruent

Given Equation :

[tex]\\ {\longrightarrow \pmb{\sf {\qquad {x}^{2} + 9x - 22 = 0 \:}}} \\ \\[/tex]

To Find :

Solution :

[tex]\\ {\longrightarrow \pmb{\sf {\qquad {x}^{2} + 9x - 22 = 0 \:}}} \\ \\[/tex]

We are to find two numbers such that,

[tex]\\ {\longrightarrow \pmb{\sf {\qquad p + q = 9 \:}}} \\ \\[/tex]

[tex]{\longrightarrow \pmb{\sf {\qquad p \times q = 22 \:}}} \\ \\[/tex]

The two numbers are 2 and 11, so

[tex]\\ {\longrightarrow \pmb{\sf {\qquad {x}^{2} + ( - 2x) + 11x - 22 = 0 \:}}} \\ \\[/tex]

Finding common factors :

[tex]{\longrightarrow \pmb{\sf {\qquad {x} (x - 2) + 11(x - 2) = 0 \:}}} \\ \\[/tex]

[tex]{\longrightarrow \pmb{\sf {\qquad (x - 2)(x + 11) = 0 \:}}} \\ \\[/tex]

Whether, the value of x is :

[tex] \\ {\longrightarrow \pmb{\sf {\qquad (x - 2) = 0 \:}}} \\ \\[/tex]

[tex]{\longrightarrow \pmb{\sf {\qquad x = 2 \:}}} \\ \\[/tex]

Or, Whether the value of x is :

[tex] \\ {\longrightarrow \pmb{\sf {\qquad (x + 11) = 0 \:}}} \\ \\[/tex]

[tex]{\longrightarrow \pmb{\sf {\qquad x = - \: 11 \:}}} \\ \\[/tex]

So,

Answer:

A) –11

D) 2

Step-by-step explanation:

Got it right on edge!

Answer:

Missing angle is 55°

Step-by-step explanation:

Given :-

To find:-

Solution:-

We know that the sum of all angles in a triangle is 180°

and let the unknown angle be x

So ,

90°+35°+x = 180°

x = 180° - 125°

x = 55°

Answer:

0 ≤ y ≤ 7

Step-by-step explanation:

Hey there! :)

Please see an explanation for better understanding, and let me know if you have any questions!

Range in Function means set of all y-values. We know by the graph that y-value is a vertical value while x-value is horizontal value. From the graph, we have y-axis which is vertical line and x-axis which is horizontal line.

For this question, I would like you to focus on y-value instead, at best, only. That is because we are finding the range, as said above that range is the set of all y-values.

To find the range in graph, first, you must understand that range starts from minimum point/value to maximum point/value. Therefore, we will have to find y-values for both points and combine the interval.

From the graph, we see that there are two points given which are (-6,0) and (9,7). Since (-6,0) is the minimum point because below y = 0, there exists no values. On the other hand, (9,7) is our maximum point because above y = 7, there exists no values.

Focus only y-values, for both points, we have y = 0 and y = 7. Since range is minimum < y < maximum - for opened dots of both points or minimum ≤ y ≤ maximum - for closed dots for both points.

In case if you don’t know what opened dots and closed dots are. Opened dots are white dots while closed dots are colored dots, usually dark ones.

Thus, from the y-values of both point, our range is 0 ≤ y ≤ 7

Answer:

27 cm²

Step-by-step explanation:

Refer to the attachment for visual reference.

First, divide into each rectangles or squares.

Then find the areas individually.

After that, combine all areas and that is the area of figure.

Area of Rectangle

A = width * length (Keep in mind that width is always less than length.)

Area of Square

A = side * side

Unit for area is cm² because we are finding area which is two dimensional.

Answer:

$ 80.73

Step-by-step explanation:

You can find the complete solution in the given attachment

Answer:

3

Step-by-step explanation:

Answer:

the one where it say it takes height

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

I got 100%

B.)

Step-by-step explanation:

area of a 10 inch pizza: A=pi * r^2 = 25 pi

area of a 14 inch pizza : A= 49 pi

the change : 49pi - 25pi = 24 pi or about 75.39822

Answer:Let's start b writing down coordinates of all points:A(0,0,0)B(0,5,0)C(3,5,0)D(3,0,0)E(3,0,4)F(0,0,4)G(0,5,4)H(3,5,4)a.) When we reflect over xz plane x and z coordinates stay same, y coordinate  changes to same numerical value but opposite sign. Moving front-back is moving over x-axis, moving left-right is moving over y-axis, moving up-down is moving over z-axis.A(0,0,0)ReflectingA(0,0,0)B(0,5,0)ReflectingB(0,-5,0)C(3,5,0)ReflectingC(3,-5,0)D(3,0,0)ReflectingD(3,0,0)b.)A(0,0,0)MovingA(-2,-3,1)B(0,-5,0)MovingB(-2,-8,1)C(3,-5,0)MovingC(1,-8,1)D(3,0,0)MovingD(1,-3,1)

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer:

[tex]\displaystyle \large{-5^{-3}}[/tex]

Step-by-step explanation:

Given:

[tex]\displaystyle \large{-\dfrac{1}{125}}[/tex]

Convert to exponent using the laws of exponent:

[tex]\displaystyle \large{\dfrac{1}{a^n} = a^{-n}}[/tex]

That means we must find the base and exponent for 125, which is [tex]\displaystyle \large{5^3}[/tex]:

[tex]\displaystyle \large{-\dfrac{1}{125} = -\dfrac{1}{5^3}}[/tex]

From the law of exponent:

[tex]\displaystyle \large{-\dfrac{1}{5^3} = -5^{-3}}[/tex]

Therefore, the solution is [tex]\displaystyle \large{-5^{-3}}[/tex]

Answer:

Step-by-step explanation:

Answer:

66°

Step-by-step explanation:

mJK = ( 6x - 45 )°

mJH = ( x + 20 )°

mJK = mJH

6x - 45 = x + 20

5x = 65

x = 13

mHK = ( x + 20 )° + ( 6x - 45 )°

mHK = 2 × 33° = 66 °

Answer:

slope of perpendicular: [tex]\sf \bold{\frac{1}{5} }}[/tex]

slope of parallel: -5

rewrite in slope intercept form:                           [ y = mx + b ]

comparing with y = mx + b       [ where m is slope, b is y-intercept ]

Parallel slope is same

formula: m₁ = m₂

slope of parallel: -5

Perpendicular slope is negatively reciprocal

formula: m₁ = -(m₂)⁻¹

slope of perpendicular: 1/5

Answer:

Slope of the line that is parallel: -5

Slope of the line that is perpendicular: [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

For the parallel line:

Rewrite your equation to slope-intercept form: y = mx + b

y = mx + b

-5x - y = 1 <== add 5x to both sides

+5x      +5x

-y = 5x + 1 <== divide both sides by -1

/-1      /-1

y = -5x - 1

The slope of the line that is parallel to this line is -5.

For the perpendicular line:

*Perpendicular lines have negative reciprocals*

Steps:

1. Take your original slope (-5)

2. Flip it (-1/5)

3. Change the sign (1/5)

For a slope of -5, the reciprocal would be: [tex]\frac{1}{5}[/tex]

Hope this helps!

Step-by-step explanation:

Insribed angle is half the measure of intercepted arc.

Since O is the center COB is the diameter of this circle.

The diameter splits the circle into two equal arcs. As the full circle is 360°,  each semicircle is 180°.

So

And the angle measure is

Proved

Answer:

[tex]\overline{\sf COB}[/tex] is the diameter of circle O.

The angle on a straight line is 180°  ⇒  ∠COB = 180°

The angle at the center of a circle is twice the angle at the circumference:

⇒ ∠CAB = 1/2 of ∠COB = 1/2 x 180°

⇒ ∠CAB = 90°

Answer:

The bench mark values might be 10/120 - 30/80

Step-by-step explanation

Answer:

the answer is 4,500kgm/s2

Step-by-step explanation:

force= mass × acceleration

[tex]f = 1500 \times 3 \\ = 4500kgm {s}^{ - 2} [/tex]

Answer:

[A] 20%

[B] 400%

Step-by-step explanation:

Part A:

To Find: Percentage

= Price in 1985/price in 2003

Thus,

$62000×100%=6200000÷310000=20%

Part B:

To FInd: Percentage increase

= (Price in 2003-price in 1985)/price in 1985

Thus,

$248000×100=$24800000÷62000=400%

[RevyBreeze]

Answer:

whats rhe question itdoesntsay

Answer:

arc AB = 70°

arc BC = 110°

arc ABC = 180°

arc CDB = 250°

Step-by-step explanation:

Since these angles are not inscribed, but are at the center point of the circle, the angles and arcs will be the same measure.

Solve for arc AB:

Angle AFB = 70°, so arc AB = 70°

Solve for arc BC:

Angle AFC is a straight angle so it is 180°. To find angle BFC, subtract angle AFB from 180°.

180 - 70 = 110°

Since angle BFC = 110°, arc BC = 110°

Solve for arc ABC:

Add arc AB and arc BC together.

70° + 110° = 180°

arc ABC = 180°

Solve for arc CDB:

There are 360° in a cirlce. To find arc CDB, subtract arc BC from 360°.

360° - 110° = 250°

arc CDB = 250°

The radius of the balloon given the information in the question is 8.98cm.

The first step is to determine the volum of the balloon.

Volume = 81π cm^3 x 12 = 972π cm^3

Now, determine the radius using this formula:

∛[Volume / (4/3π )]

∛[972π cm^3/ (4/3π )] = 8.98cm

Here is the complete question:

Andy is blowing up a spherically shaped balloon. If he is able to blow 81π cm^3 of air with every breath, it takes him 12 breaths to fully inflate the balloon. What is the radius of the balloon?

To learn more about the volume of a sphere, please check: https://brainly.com/question/13705125

Answer:

16

Step-by-step explanation:

no image, but 6 + 2 + 2 + 6 = 16

Answer:

$240

Step-by-step explanation:

200% x 80 = 160

80 + 160 = $240

Answer:

3

Step-by-step explanation:

the absolute value function always returns a positive value , that is

| - a | = | a | = a

given

- 10 - | 5 - 12 | + 3 + | 5 + 12 |

= - 10 - | - 7 | + 3 + | 17 |

= - 10 - 7 + 3 + 17

= 3

From the calculations;

The equations of motion are used in kinematics to obtain the various variables that has to do with motion.

In this case;

distance covered = 30 ft

initial velocity = 40 ft/second

Final velocity = 0 m/s at the maximum height

Hence;

v^2 = u^2 - 2gh

since v = 0

u^2 = 2gh

h = u^2/2g

h = (40)^2/2(9.8)

h = 82 feet

highest point above the ground = 82 feet + 30 feet = 112 feet

Now;

v = u - gt

since v = 0

u = gt

t = u/g

t = 40/9.8

t = 4 seconds

Time taken to hit the ground = 2(4 seconds) = 8 seconds

Learn more about kinematics:https://brainly.com/question/27126557

Answer:

2

5

YES

trinomial

Step-by-step explanation:

Given expression:  [tex]5x^2+3x+6[/tex]

The degree of the polynomial is the highest exponent = 2

The leading coefficient, is the coefficient (value) before the [tex]x^2[/tex] = 5

The constant in the polynomial is the value without a variable, i.e. 6 = YES

This expression can be called a trinomial expression since it is a polynomial with exactly three terms.

Expression given:-

So