Find the arc length intercepted by a central angle of radians in a circle whose radius is 18.4 inches. 13.8π 15.2π 24.5π

Answer:

  (x, y) = (4, 0)

Step-by-step explanation:

It is convenient to first put the equations into standard form by eliminating common factors. The first equation has a factor of 2 that can be removed; the second equation has a factor of 3 that can be removed. Then you have ...

Subtracting the second equation from the first eliminates the x variable. That gives you ...

  (x +2y) -(x -y) = (4) -(4)

  3y = 0 . . . . . . simplify

  y = 0 . . . . . . . divide by 3

Substituting this value into either equation above, you get ...

  x + 0 = 4

  x = 4

The solution is (x, y) = (4, 0).

Answer:

The probability that the dart lands inside the triangle is 0.25

Step-by-step explanation:

* Lets explain how to find the probability of an event

- The probability of an Event = Number of favorable outcomes ÷ Total

  number of possible outcomes

- P(A) = n(E) ÷ n(S) , where

# P(A) means finding the probability of an event A

# n(E) means the number of favorable outcomes of an event

# n(S) means set of all possible outcomes of an event

- P(A) < 1

* Lets solve the problem

- A rectangular dartboard has an area of 648 cm²

- The triangular part of the dartboard has an area of 162 cm²

- A dart is randomly thrown at the dartboard

- The dart lands in the rectangle

∴ The area of the rectangle is the set of all possible outcomes n(S)

- The probability P(A) that the dart lands inside the triangle

∴ The area of the triangle is set of favorable outcomes of an

   event n(E)

∵ P(A) = n(E) ÷ n(S)

∴ P(T) = area of the triangle ÷ area of the rectangle

∵ Area of the rectangle is 648 cm²

∴ n(S) = 648

∵ The area of the triangle is 162 cm²

∴ n(E) = 162

∴ P(T) = 162 ÷ 648 = 1/4 = 0.25

* The probability that the dart lands inside the triangle is 0.25

The hole which was initially 8 feet deep and then extended by 3 more feet got partially filled by 4 feet of dirt by a tractor, resulting in a total remaining depth of 7 feet.

Your question is a simplifying numerical values scenario. First, you dug a hole that was 8 feet deep. Next, you dug an additional 3 feet, so you would add these two values together to get a total depth of 11 feet (8 + 3). Finally, a tractor accidentally filled 4 feet of the hole with dirt. Subtracting this from the total depth of the hole means your hole is now 7 feet deep (11 - 4).

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Answer: Option d

They are opposites and parallel.

Step-by-step explanation:

Although they have the same magnitude, one can not say that a and b are equal because they have opposite directions.

If we know that both vectors have opposite directions then necessarily a and b must be parallel.

So what we know about a and b is that they are parallel and opposite.

The correct answer is the option d

Answer:

guy above is right

Step-by-step explanation:

Answer:

Answer: 23, 67, 90

Step-by-step explanation: The measures of the three angles are 23, 67, 90

I know you don’t care how I got the answer so enjoy it!

Answer:

x = 16

Step-by-step explanation:

From the first statement, we can say that:

Angle A is equal to angle D,

Angle B is equal to and E.

Since measure of Angle B and E are given and they are equal, we equate them and solve for x.

[tex]B=E\\x+15=6x-65\\15+65=6x-x\\80=5x\\x=\frac{80}{5}\\x=16[/tex]

Hence x = 16

Answer:

f(6) = 82

Step-by-step explanation:

f(x) = 2x^2+5 sqrt(x-2)

Let x =6

f(6) = 2(6)^2+5 sqrt(6-2)

    = 2 * 36 + 5 sqrt(4)

    = 72+5*2

    = 72+10

    =82

f(6) = 82

Answer:

x=6.6 cm

Step-by-step explanation:

The angle force at the point where the tangent touches the circle is 90° hence the  triangle is a right angle triangle . We can apply the Pythagorean relationship in this case

Given the hypotenuse as x+ 8.45  and the base as x and height as 13.5 then;

a²+b²=c²  .................where a=x  , b= 13.5 and c x+8.45

x² +13.5²= (x+8.45)²

x²+182.25=x²+8.45x+8.45x+71.4025

x²+182.25=x²+16.90x+71.4025-----------------collect like terms

x²-x²+ 182.25-71.4025=16.90x

110.8475=16.90x-------------------divide by 16.90 to remain with x

110.8475/16.90 = x

x=6.5590

x= 6.6 cm

Answer:

  C.  postulate; theorem

Step-by-step explanation:

While a "given" is taken as true without proof, and a "problem" sometimes involves an assertion that can be proven, the answer choices involving these terms are not correct here.

The dictionary definitions of "postulate" and "theorem" apply. It is useful to learn the meaning of these terms so you can understand problems and descriptions that use them.

The answer is:

The correct option is:

D. 40 feet.

To solve the problem and calculate the width of the river, we need to assume that the distance from A to B and the angle formed between that distance and the distance from A to the other point (C) is equal to 90°, meaning that we are working with a right triangle, also, we need to use the given angle which is equal to 34°. So, to solve the problem we can use the following trigonometric relation:

[tex]Tan\alpha =\frac{Opposite}{Adjacent}[/tex]

Where,

alpha is the given angle, 34°

Adjacent is the distance from A to B, which is equal to 60 feet.

Opposite is the distance from A to C which is also equal to the width of the river.

So, substituting and calculating we have:

[tex]Tan(34\°) =\frac{Width}{60ft}[/tex]

[tex]Width=60ft*Tan(34\°)=60ft*0.67=40.2ft=40ft[/tex]

Hence, we have that the correct option is:

D. 40 feet.

Have a nice day!

Answer: OPTION D

Step-by-tep explanation:

Observe the figure attached.

You can notice that the the width of the river is represented with "x".

To calculate it you need to use this identity:

[tex]tan\alpha=\frac{opposite}{adjacent}[/tex]

In this case:

[tex]\alpha=34\°\\opposite=x\\adjacent=60[/tex]

Now you must substitute values:

 [tex]tan(34\°)=\frac{x}{60}[/tex]

And solve for "x":

[tex]60*tan(34\°)=x\\\\x=40.4ft[/tex]

[tex]x[/tex]≈[tex]40ft[/tex]

Answer: Graph D

Step-by-step explanation:

in slope intercept form, the equation is y</= 1/2x-6

Since it's </=, the line is solid instead of dashed

The graph that matches the inequality is:

                         Graph D

We are given a inequality as:

[tex]y+4\leq \dfrac{1}{2}x-2[/tex]

i.e. it could also be represented in the form:

[tex]y\leq \dfrac{1}{2}x-2-4\\\\i.e.\\\\y\leq \dfrac{1}{2}x-6[/tex]

The graph of this inequality is a straight solid line ( since the inequality is not strict i.e. it is a inequality with a equality sign) that passes through (0,-6) and (12,0) .It also passes through (4,-4) and the shaded region is away from the origin.

Hence, the graph which satisfies all the above property is:

                           Graph D

Answer:

8 inches

Step-by-step explanation:

Area (A) of a triangle = [tex]\frac{1}{2}[/tex] × base (b) × height (h)

72 square inches = [tex]\frac{1}{2}[/tex] × 18 × h

9h = 72

h = 8 inches

Follow below steps:

The area of a triangle: A = 1/2 * base * height. Given area = 72 sq in and base = 18 in, we can calculate the height:

72 = 1/2 * 18 * height

height = 8 inches

Answer:

  C.  1.8 m × 1.1 m

Step-by-step explanation:

Actual dimensions will be 18 times those shown:

The approximate window dimensions are 1.8 m × 1.1 m.

Answer:

Step-by-step explanation:

A cross section is the intersection of a cut plane with the object of interest. In a classroom setting, we often try to do the cross sectioning mentally or with diagrams, rather than physically cutting anything. Sometimes, there is no substitute for actually performing the cut to see what the cross section looks like.

For certain samples that don't take kindly to cutting, we sometimes encase them in a block of material that helps them hold their shape during the process. Sometimes the "cutting" is performed by grinding away the portion of the material on one side of the cut plane.

Answer: Place 3 points on 2 or 3 edges or faces.

Connect the points to form a triangle.

Extend the triangle to form a plane.

Determine where the plane intersects the edges of the solid.

Step-by-step explanation:

Answer: OPTION D.

Step-by-step explanation:

Rectangles have four right angles (angles of 90 degrees).

The point of intersection of the diagonals divides each one of them into two equal parts.

Knowing this, we can conclude that:

[tex]m\angle c=m\angle b=55\°[/tex]

(Observe the figure)

Therefore, since the sum of the interior angles of a triangle is 180 degrees, we can find the value of "x":

[tex]x+m\angle c+m\angle b=180\°\\x=180\°-55\°-55\°\\x=70\°[/tex]

Answer:

70 degrees

Step-by-step explanation:

55*2= 110

180-110=70

Answer: Option 'c' is correct.

Step-by-step explanation:

Since we have given that

If a transversal intersects two parallel lines, then _____ angles are supplementary.

Since the sum of interior angle on the same side is supplementary.

Supplementary angles are those angles whose sum is 180°.

Hence, Option 'c' is correct.

If a transversal intersects two parallel lines, then alternate interior angles are supplementary.

When a transversal intersects two parallel lines, alternate interior angles are formed. Alternate interior angles are pairs of nonadjacent interior angles located on opposite sides of the transversal and between parallel lines.

These angles have equal measures and are supplementary, meaning they add up to 180 degrees. This property holds true for any pair of parallel lines intersected by a transversal, providing a relationship between the angles that helps in solving geometric problems and proofs.

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Answer:

A

Step-by-step explanation:

it has to do with the people's ethnics or standard or values.

The statement is not ambiguous so it has no language barrier

Answer:

  C.  use of language

Step-by-step explanation:

The descriptor "childish" will likely influence results. Most Grade 9 students prefer not to be thought of as "childish."

Answer:

24 hours.

Step-by-step explanation:

This is one of those problems where the easiest way to do is just to reason it out without trying to devise a formula.

Call the water in the basement = w

Therefore w/2 = 4*x where x is the rate of the pump. The statement means that 1/2 the water in the basement is pumped out by x in 4 hours.

Now x and y work together. They (together ) pump out the rest of the water which is also w/2

w/2 = 3x + 3y              Now you can equate the two values for w/2

4x = 3x + 3y                Subtract 3x from both sides.

4x-3x = 3x-3x + 3y

x = 3y

Now you have to be very careful in interpreting what you found. It takes pump y three times as long to do anything as it does x.

So here's the reasoning part.

x by itself will empty the basement in 8 hours. It takes x four hours to get 1/2 the water out.

It will take pump y 3 times as long to pump out that basement. 3*8 = 24 hours

Answer:

  one solution: (x, y) = (1, 0)

Step-by-step explanation:

See below for a graph with the one solution identified.

Answer:

The system has one solution at (1,0).

Step-by-step explanation:

Consider the provided system of equations

y=-6x+6

Substitute x = 0 in above equation.

y=-6(0)+6

y=6

The coordinate is (0,6)

Now substitute y=0 in the above equation.

0=-6x+6

-6=-6x

x=1

The coordinate is (1,0)

Now use the coordinates (0,6) and (1,0) in order to draw the graph.

The graph of y= -6x + 6 is shown in figure 1.

Similarly, consider the second equation y= 3x - 3

Substitute x = 0 in above equation.

y=3(0)-3

y=-3

The coordinate is (0,-3)

Now substitute y=0 in the above equation.

0=3x-3

3=3x

x=1

The coordinate is (1,0)

The graph of y= 3x - 3 is shown in figure 2.

Now draw the graph of both equation as shown in figure 3.

By observing the graph it can be concluded that the system has one solution at (1,0)

Hence, the system has one solution at (1,0).

Answer:4

Step-by-step explanation: 6 times 6 divide by 9

Multiply the denominators across and Multiply the numerators across

x/6= 6/9

9x= 36

x= 4

Check answer by using substitution method

x/6= 6/9

4/6= 6/9

Divide by 2 for 4/6

Divide by 3 for 6/9

2/3= 2/3

Answer is x= 4

For this case we have by definition that the volume of a cylinder is given by:

[tex]V = \pi * r ^ 2 * h[/tex]

Where:

r: It's the radio

h: It's the height

We have as data that:

[tex]V = 324 \pi\\r = 12[/tex]

Substituting:

[tex]324 \pi = \pi * (12) ^ 2 * h[/tex]

We cleared h:

[tex]324 \pi = \pi * 144 * h\\324 = 144 * h\\h = \frac {324} {144}\\h = 2.25[/tex]

Thus, the height of the cylinder is 2.25 inches.

Answer:

[tex]h = 2.25[/tex]

Answer:

the anser is d

Step-by-step explanation:

Answer:

(1/2, 0)

Step-by-step explanation:

The solution to a system of equations graphically is where they intersect on the graph.  In a coordinate, the x is first and the y is second.  Where our lines cross is ON the x-axis.  This means that y = 0 here.  Because we are to the right of the origin, we are in positive x values.  Because we are between x = 0 and x = 1, the best estimate from our choices is x = 1/2.  The coordinate for the solution is best represented by (1/2, 0)

Answer:

15

Step-by-step explanation:

The mean of the first graph comes to be the point at which the graph reaches its highest point.

The mean of the blue graph is: μ = 30

The mean of the blue graph is: μ = 45

The difference of the means of the distributions is: 45 - 30 = 15

Answer:

15

Step-by-step explanation:

Answer:

98.5 degrees

Step-by-step explanation:

To find the angle measurement between two vectors use: cos(theta)=(u dot v)/(|u|*|v|)

The vectors are u=sqrt(5)i-8j and v=sqrt(5)i+1j .

So find the dot product of u and v.  u dot v=sqrt5*sqrt(5)+(-8)*(1)=5-8=-3.

Second step: Find the magnitude of both vectors.  So to find the magnitude of a vector, let's call it t when t=ai+bj, you just do |t|=sqrt(a^2+b^2).

|u|=sqrt(5+64)=sqrt(69) and |v|=sqrt(5+1)=sqrt(6)

Now multiply your magnitudes of your vectors: sqrt(69)*sqrt(6)=sqrt(414).

So now we have:

cos(theta)=-3/sqrt(414)

Now arccos( ) or cos^(-1) to find the angle theta.

theta=cos^(-1)[-3/sqrt(414)] which is approximately 98.5 degrees.

Answer:

Ans 1) The correct option is B) 98.5

Ans 2) The correct option is C) [tex]\sqrt{5}[/tex]

Step-by-step explanation:

The angle measurement between two vectors by:

[tex]cos(\theta)=\frac{(u.v)}{(|u|\times |v|)}[/tex]

Magnitude of vector t=ai+bj, calculated by:

[tex]|t|=\sqrt{a^{2}+b^{2}}[/tex]

The given vectors are [tex]u=\sqrt{5}i-8j[/tex] and [tex]v=\sqrt{5}i+1j[/tex]

First find the dot product of u and v;

[tex]u.v=(\sqrt{5}i-8j)(\sqrt{5}i+1j) = 5-8= - 3[/tex]

Now,  Find the magnitude of both vectors u and v.  

[tex]|u|=\sqrt{(\sqrt{5})^{2}+8^{2}}[/tex]

[tex]|u|=\sqrt{5+64}[/tex]

[tex]|u|=\sqrt{69}[/tex]

and

[tex]|v|=\sqrt{(\sqrt{5})^{2}+1^{2}}[/tex]

[tex]|v|=\sqrt{5+1}[/tex]

[tex]|v|=\sqrt{6}[/tex]

Now, put the all values in  [tex]cos(\theta)=\frac{(u.v)}{(|u|\times |v|)}[/tex]

[tex]cos(\theta)=\frac{-3}{\sqrt{69} \times \sqrt{6}}[/tex]

[tex]=\frac{-3}{414}[/tex]

take arc cos both the sides,

[tex]\theta=cos^{-1} \frac{-3}{\414}[/tex]

[tex]\theta=98.5 \degree[/tex]   (approx)

Therefore, the correct option is B) 98.5

Ans 2)  calculate IvI by

If t= ai +bj then magnitute is [tex]\sqrt{a^{2}+b^{2}}[/tex]

Given : v = (-2,-1)

it means v = -2i -1 j

[tex]|v| =\sqrt{(-2)^{2}+(-1)^{2}}[/tex]

[tex]|v| =\sqrt{4+1}[/tex]

[tex]|v| =\sqrt{5}[/tex]

Therefore, the correct option is C) [tex]\sqrt{5}[/tex]

Answer and Step-by-step explanation:

Since we have given that

Time                Average age of a marriage

0                                  10

10                                 11.2

20                                13.9

30                                17.2

40                                29

We need to show that the above data indicated a non linear model.

For this it is enough to show that slope is different:

So, we consider the slope for first 2 points:

(0,10) and (10,11.2)

So, slope becomes

[tex]m_1=\dfrac{y_2y_1}{x_2-x_1}=\dfrac{11.2-10}{10-0}=\dfrac{1.2}{10}=0.12[/tex]

and similarly, (10,11.2) and (20,13.9)

[tex]m_2=\dfrac{y_2-y_}{x_2-x_1}\\m_2=\dfra{13.9-11.2}{20-10}=\dfrac{2.7}{10}=0.27[/tex]

so, [tex]m_1\neq m_2[/tex]

So, it becomes non linear model.

Answer:

  7 days

Step-by-step explanation:

We assume that "by day 4" means "at the end of day 3." Since Curtis had run 9 miles in 3 days, his average rate is 9/3 = 3 miles per day.

It will take Curtis ...

  (21 mi)/(3 mi/day) = 7 days

to run 21 miles at that rate.

_____

Comment on the question

There is nothing in the problem statement to suggest that the number of miles run each day is the same. A different assumption than the one we have made will give a different answer.

Answer:

It will take 8 hours to drive 400 miles

Step-by-step explanation:

The millers drive 50 miles an hour. So we can write the proportion 1/50 = x/400. Then we solve for x and get 8 hours.

Answer:

The answer is 8!

Step-by-step explanation:

It will take 8 hours to drive 400 miles

The millers drive 50 miles an hour. So we can write the proportion 1/50 = x/400. Then we solve for x and get 8 hours.

Answer:

It's B.

Step-by-step explanation:

It might be a square because  a rhombus is defined as a parallelogram with 4 equal sides. A square is a rhombus with each angle = 90 degrees and has 4 equal sides.

Answer:

  about 26 min

Step-by-step explanation:

Let x represent the time spent rowing distance d upstream. Then the time spent rowing downstream is ...

  time = distance/speed . . . . speed × time = distance

  downstream time = (4.5 km/h)(x)/(5.5 km/h)

So, the total time in both directions is ...

  x + 4.5/5.5x = 48 min

  x(1 + 9/11) = 48 min

  x = (48 min)/(20/11) = 26.4 min

Rounded to the nearest minute, Toni spent about 26 minutes rowing upstream.