A pole that is 3.1 m tall casts a shadow that is 1.65 m long. At the same time, a nearby building casts a shadow that is 44.75 m long. How tall is the building?
Round your answer to the nearest meter.

The domain restrictions of the expression q²−7q−8/q²+3q−4 are q ≠ -4 and q ≠ 1. (option c)

The denominator of the expression is q²+3q−4. To determine the values that would make the denominator equal to zero, we can set it equal to zero and solve for q:

q² + 3q - 4 = 0

Now, we can factorize the quadratic equation:

(q + 4)(q - 1) = 0

To find the values of q, we set each factor equal to zero and solve for q:

q + 4 = 0 or q - 1 = 0

Solving these equations, we get:

q = -4 or q = 1

So, the values of q that would make the denominator equal to zero are q = -4 and q = 1. These are the values we need to exclude from the domain of the expression to avoid division by zero.

Therefore, the correct answer is option c) q ≠ 1 and q ≠ -4.

To know more about domain here

https://brainly.com/question/28599653

#SPJ4

Complete Question:

What are the domain restrictions of q²−7q−8/q²+3q−4?

a) q≠1 and q≠−8

b) q≠−1 and q≠4

c) q≠1 and q≠−4

d) q≠−1 and q≠8

Answer:

\(x(t) = 54t\)  and \(y(t) = 134(t - 3)\)

Step-by-step explanation:

Represent the swimmers with A and B

For Swimmer A:

\(Rate = 54m/min\)

For Swimmer B:

\(Rate = 134m/min\)

Required:

Write a parametric equation

For Swimmer A:

If swimmer A covers 54 meters in 1 minutes, then the swimmer covers 54t in t minutes

So, the function is:

\(x(t) = 54t\)

For Swimmer B:

If swimmer A covers t minutes, swimmer B swims for (t - 3) minutes because swimmer B starts 3 minutes later.

If in 1 minutes, swimmer B covers 134 minutes; In (t - 3) minutes, the swimmer covers 134(t - 3)

So, the rate is:

\(y(t) = 134(t + 3)\)

Hence, the parametric functions are:

\(x(t) = 54t\) and

\(y(t) = 134(t - 3)\)

Answer:

A on Edge

Step-by-step explanation:

Answer:

118.7 inches squared.

Step-by-step explanation:

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.

The expression for solving the area of a circle is A = π × \(r^{2}\).

To solve for the semicircle above, we can divide the diameter into 2 to get the radius.

So, the radius of the upper semicircle is 6 inches.

If the radius of a circle is 6 inches, then you can substitute r for 6 into the formula.

This simplifies to A = 36π. If a semicircle if half the size of a normal circle, then it will be A = 18π, because 36 ÷ 2 = 18.

To solve for the lower semicircle, we can do the same this as we did above.

But wait, we don't know the radius or diameter!

No worries! To solve for the diameter of the circle, we can take the line that is parallel to the semicircle (the one that has a length of 12in) and subtract 6 from it. We subtract 6 from it because the semicircle takes up the remaining length of the line, not including the 6in.

To solve for the lower semicircle, we can divide the diameter by 2 to get the radius.

So, the radius of the circle is 3.

Now we can insert 3 into the expression.

This simplifies to A = 9π. If a semicircle if half the size of a normal circle, then it will be A = 4.5π because like above, 9 ÷ 2 = 4.5.

Adding the two semicircles together:

So, the area of both semicircles is approximately 70.6858 square inches.

To solve for the area of a rectangle we use the expression:

Inserting the dimensions of the rectangle:

So, the area of the rectangle is 48 square inches.

Adding the two areas together:

Therefore, the area of the entire figure, rounded to the nearest tenth is \(118.7\) \(in^{2}\).

The measure of angle DAB in the circle shown with the given arc length is: 2.23 radians.

Arc length = θ × r, where r is the radius of the circle, and θ is the central angle in radians.

Given the following:

Length of arc = 6.47 cm

Radius (r) = 2.9 cm

θ = m∠DAB

Plug in the values into the arc length formula:

6.47 = θ × 2.9

6.47/2.9 = θ

θ = 2.23 radians

m∠DAB = 2.23 radians

Learn more about length of arc on:

https://brainly.com/question/2005046

#SPJ1

Answer:

DAB = 2.23 radians

Hope this helps!

Step-by-step explanation:

Rolling a total of 8 when two dice are rolled is more likely than rolling a total of 8 when three dice are rolled.

This is because there are more combinations of two dice that can add up to 8 (four combinations; 1-7, 2-6, 3-5, 4-4) than there are combinations of three dice (three combinations; 1-3-4, 2-2-4, 3-3-2).

Therefore, the probability of rolling a total of 8 with two dice is greater than the probability of rolling a total of 8 with three dice.

Additionally, the odds of rolling a total of 8 with two dice can be calculated using the formula (Number of favourable outcomes/Total number of outcomes) x 100%.

In this case, the formula would be (4/36) x 100%, which equals 11.11%. The odds of rolling a total of 8 with three dice is calculated using the same formula, which would be (3/216) x 100%, which equals 1.39%.

This shows that the odds of rolling a total of 8 with two dice is much greater than the odds of rolling a total of 8 with three dice.

To learn more about combinations visit:

https://brainly.com/question/28065038

#SPJ4

The temperature of the room we get by using Newton’s Law of Cooling is 75 degrees.

Given that the temperature of the soup was initially 120 degrees. Its temperature was 105 degrees after 10 minutes. It reached a temperature of 95 degrees after an additional ten minutes.

We need to estimate the temperature of the room.

According to the Newton's law of cooling temperature T(t) after time t is given by:

\(\mathrm{T(t) = T_s + (T_0 - T_s)e^{kt}}\)

Where,

\(\mathrm{T_0}\) = initial temperature [120 degree]

\(\mathrm{T_s}\) = surrounding temperature

k = constant

Plugging the values;

\(105 = \mathrm{T_s + (120 - T_s)e^{10k}}}\)

\(\mathrm{e^{10k}} = \mathrm{\frac{105 - T_s}{120 - T_s} }\)

Similarly,

\(95 = \mathrm{T_s + (105 - T_s)e^{10k}}}\)

\(\mathrm{e^{10k}} = \mathrm{\frac{95 - T_s}{105 - T_s} }\)

Equating the equations,

\(\mathrm{\frac{95 - T_s}{105 - T_s} } = \mathrm{\frac{105 - T_s}{120 - T_s} }\)

Solving the equations,

\(\mathrm{\frac{225-2T_s}{-15} } = \mathrm{\frac{200-2T_s}{-10} }\)

Multiplying by -30,

\(\mathrm{2(225-2T_s)} = \mathrm{2(200-2T_s)}\)

\(\mathrm{2T_s = 150}\)

\(\mathrm{T_s = 75}\)

Hence the temperature of the room was 75 degrees.

Learn more about Newton’s Law of Cooling click;

https://brainly.com/question/30591664

#SPJ12

===================================================

Explanation:

Any triangle prism is composed of 2 parallel triangular faces (base faces), along with 3 rectangular lateral faces.

The bottom triangle face has a base of 10 cm and a height of 4 cm. The area is 0.5*base*height = 0.5*10*4 = 20 square cm. Two of these triangles combine to an area of 2*20 = 40 square cm. We'll use this later.

The lateral surface area of any prism can be found by multiplying the perimeter of the base by the height of the prism. The base triangle has side lengths 5, 8 and 10. The perimeter is 5+8+10 = 23. So the lateral surface area is (perimeter)*(height) = 23*9 = 207

Add this to the total base area we got earlier and the answer is 40+207 = 247. The units are in square cm, which we can write as cm^2.

Answer:

19.5

Step-by-step explanation:

2 x 19.5 = 39 - 29 = 10 :D

Answer:

The equation of the line that passes through the points (1,6) and (3,2) is y = -2x + 8.

Step-by-step explanation:

To find the equation of the line, we can use the point-slope form of the equation of a line, which is:

y - y1 = m(x - x1)

(x1, y1) = (1,6) and we can find the slope of the line using the following formula:

m = (y2 - y1) / (x2 - x1)

(x2, y2) = (3,2).

m = (2 - 6) / (3 - 1) = -4 / 2 = -2

point-slope form of the equation of a line to get:

y - 6 = -2(x - 1)

y = -2x + 8

This is the equation of the line that passes through the points (1,6) and (3,2).

Learn more about Straight Lines.

https://brainly.com/question/32655977

#SPJ11

Answer:

The Slope Equation = y2 -y1 over X2 - X1

Step-by-step explanation:

1.) Pick every graph

2.) Pick any 2 point in the graph

3.) do the slope equation

4.) the answers must be equal  

The highest score for the given distribution is 25.

This is because the distribution is divided into ranges, with the first range being 20-25, the second range being 15-19, the third range being 10-14, and the fourth range being 5-9.

The highest score in each range is the number on the right side of the dash.

Therefore, the highest score in the first range is 25, the highest score in the second range is 19, the highest score in the third range is 14, and the highest score in the fourth range is 9.

Since 25 is the highest score among all of the ranges, it is the highest score for the entire distribution.

The correct answer is c) 25.

Read more about distribution ranges at:

https://brainly.com/question/16237757

#SPJ11

Answer:

10(5+3) is the correct answer

The main answer for the first argument is that we cannot prove that the band could play rock music based on the given premises and rules of inference.

1. Let's assign the following propositions:

  - P: The band could play rock music.

  - Q: The refreshments were delivered on time.

  - R: The New Year's party was canceled.

  - S: Alicia was angry.

  - T: Refunds were made.

2. The given premises can be expressed as:

  (¬P ∨ ¬Q) → (R ∧ S)

  R → T

3. To prove that the band could play rock music (P), we need to derive it using valid rules of inference.

4. Using the premises, we can apply the rule of modus tollens to the second premise:

  R → T        (Premise)

  Therefore, ¬R.

5. Next, we can use disjunctive syllogism on the first premise:

  (¬P ∨ ¬Q) → (R ∧ S)     (Premise)

  ¬R                    (From step 4)

  Therefore, ¬(¬P ∨ ¬Q).

6. Applying De Morgan's law to step 5, we get:

  ¬(¬P ∨ ¬Q)  ≡  (P ∧ Q)

7. Therefore, we can conclude that the band could play rock music (P) based on the premises and rules of inference.

Learn more about De Morgan's law here: brainly.com/question/29073742

#SPJ11

Answer:

63

Step-by-step explanation:

the first one is 9x bigger then the second one

so 7x9 is 63

Answer:

yes

Step-by-step explanation:

In linear equation, the total number of possible hamburgers is 768.

What are a definition and an example of a linear equation?

Total number of possible hamburgers is 768

Given,

The number of condiments = 8

Total number of combinations with 8 condiments = 2⁸ = 256

A customer can choose one, two or three meat patties

Total number of possible hamburgers = 256×3= 768

Hence, the total number of possible hamburgers is 768

Learn more about linear equation

brainly.com/question/11897796

#SPJ4

Answer:

I don't know????????....................

Answer:

C

Step-by-step explanation:

Step by step explanation:

Answer:

369.15

Step-by-step explanation:

Answer:

To make students question their existence

Step-by-step explanation:

Answer:

y=2x-7

Step-by-step explanation:

y=mx+b

Slope (m)= \(\frac{9-3}{8-5} =\frac{6}{3} =2\)

Y-Intercept (b)= \(y=2x+b\\3=10+b\\b=-7\)

Answer:

64 degrees

Step-by-step explanation:

Combining the 90 degrees, x degrees, and 26 degrees creates a flat angle or 180 degrees

so first, combine 90 and 26 degrees

90+26= 116

then subtract 116 from 180

180-116= 64 degrees

The distance between tower A and the fire, x, is approximately 3.992 km, and the distance between tower B and the fire, y, is approximately 14.898 km.

To solve this problem, we can use the law of sines and trigonometric ratios to set up a system of equations that can be solved to find the distances from each tower to the fire.

We know that the distance between the two towers, AB, is 20.3 km, and that the bearing from tower A to tower B is N70°E. From this, we can infer that the bearing from tower B to tower A is S70°W, which is the opposite direction.

We can draw a triangle with vertices at A, B, and the fire. Let x be the distance from tower A to the fire, and y be the distance from tower B to the fire. We can use the law of sines to write:

sin(70°)/y = sin(25°)/x

sin(70°)/x = sin(15°)/y

We can then solve this system of equations to find x and y. Multiplying both sides of both equations by xy, we get:

x*sin(70°) = y*sin(25°)

y*sin(70°) = x*sin(15°)

We can then isolate y in the first equation and substitute into the second equation:

y = x*sin(15°)/sin(70°)

y*sin(70°) = x*sin(15°)

Solving for x, we get:

x = (y*sin(70°))/sin(15°)

Substituting the expression for y, we get:

x = (x*sin(70°)*sin(15°))/sin(70°)

x = sin(15°)*y

We can then solve for y using the first equation:

sin(70°)/y = sin(25°)/(sin(15°)*y)

y = (sin(15°)*sin(70°))/sin(25°)

Substituting y into the earlier expression for x, we get:

x = (sin(15°)*sin(70°))/sin(25°)

For such more questions on distance

https://brainly.com/question/26046491

#SPJ8

The concept is the Vertical Lines. The Vertical Lines are a pair of opposing, congruent angles created by intersecting lines. It is option A.

An upward line is a line on the direction plane where every one of the focuses on the line have a similar x-coordinate. Because they are perpendicular to the ground and extend toward the sky, vertical lines frequently convey a sense of height.

At the point when two straight lines cross each other vertical points are shaped. Every vertical angle is equal and congruent.

By super-imposing the two pairs of non-adjacent angles created by intersecting two lines, vertical angles are congruent.

Every vertical angle has the same length. We call angles congruent when their measurements are the same.

To know more about Vertical Lines,

brainly.com/question/30281262

#SPJ4

Question:

Which of coming up next is best depicted as a couple of inverse points shaped by crossing lines?

A. Vertical angles

B. Supplementary angles

C. Complementary angles

D. Linear pair

Step-by-step explanation:

FX=3+5+4+3+5+4

=24

N=6

mean (x)=?

Now,

x=FX÷N

=24÷6

=4

The probability that a family with 4 children has no more than 3 boys is 15/16.

To find the probability that a family with 4 children has no more than 3 boys, we can use the binomial distribution.

The binomial distribution is used to calculate the probability of obtaining a certain number of successes (boys in this case) in a fixed number of trials (children in this case), where each trial has only two possible outcomes (boy or girl) and the trials are independent.

Let X be the number of boys in the family. We want to find P(X ≤ 3), which is the probability of having no more than 3 boys. Since the probability of having a boy is 1/2 and the trials are independent, we can use the binomial distribution formula:

P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= (1/2)⁴ + 4(1/2)⁴ + 6(1/2)⁴ + 4(1/2)⁴

= 15/16

To learn more about probability click on,

https://brainly.com/question/29973811

#SPJ4

The student's final moment of inertia is 18.18 kgm².

The moment of inertia of an objecr is the property of an object which shows its ability to rotate.

Since a student is standing with her arms outstretched, on a platform that is rotating at 1.6 rev/s. She pulls her arms in and the platform now rotates at 2.2 rev/s. Her original moment of inertia (I0) is 25 kgm². To find the r final moment of inertia, we use the law of conservation of angular momentum.

The law of conservation of angular momentum states that for any rotation, angular momnetum is constant.

So, Iω = constant where

So, Iω = I'ω' where

Making I' subject of the formula, we have that

I' = Iω/ω'

So, substituting the values of the variables into the equation, we have that

I' = Iω/ω'

I' = 25 kgm² × 1.6 rev/s ÷ 2.2 rev/s

= 40 kgm²rev/s ÷ 2.2 rev/s

= 18.18 kgm²

So, the final moment of inertia is 18.18 kgm².

Learn more about moment of inertia here:

https://brainly.com/question/29471030

#SPJ1