A whale is swimming due north at a speed of 40 kilometers per hour. Just 6 kilometers away,
a whale-watching tour boat is traveling south, directly toward the whale, at a speed of 83
kilometers per hour. How long will it be before they meet?

A total of 3 five ounces glass are needed so have the same alcohol as that of a 12 ounce glass.

In order to find the number of glass of capacity five ounces that will have the same capacity as that of the twelve ounce glass can be calculated as followed,

Let us say that n number of five ounces glasses are required to equate 12 ounce glass.

Now, we can write the relation,

using simple algebra,

n(Five ounces glasses) = 1 Ounce alcohol content

n = 12/5

n = 2.4

But, we have to answer an integral value, so, we will say that the required number of the glasses is 3.

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The solution indicates 40 positive three-digit integers of this kind are available.

The numbers used for counting as well as organizing are known as natural numbers in mathematics. Cardinal numbers and ordinal numbers are two different types of numbers that are used for counting and ordering, respectively.

Left of zero on the number line, a negative number is an integer. It is not zero, though.

Any solution x will mod 23 will also have x+23n as a solution, for some integer n.

Since;

900/23 = 39 3/23,

we know:

There are 39 or 40 three-digit integers of this form.

As it happens,

100 is the smallest 3-digit solution. So, there are 40 three-digit numbers that are of the form 100 +23n,

hence 40 solutions to the equation.

The equation reduces, mod 23, to

10x = 11

Its solutions are x = 23n +8.

This shows There are 40 three-digit positive integers of this form.

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Answer:

Mean: 10.8

Median: 12

Mode: 13

Step-by-step explanation:

I hope this is what you were looking for! If you have and questions ask in the comments :D

If the equation that relates the Runner 2’s distance (in miles) with time (in minutes) is [tex]t=8.5d[/tex]  then the slope/rate of change of Runner 2 is 8.5 minutes for 1 mile  .

The three runners are training for the marathon ,

The equation that relates the Runner 2’s distance (in miles) with time (in minutes) is ⇒ [tex]t=8.5d[/tex] ,

to cover the distance of 2 miles Runner2 will take [tex]t= 8.5 \times 2[/tex] minutes ;

So , [tex]t=17[/tex] minutes ;

the first point will be (2,17) .

and to cover the distance of 4 miles the runner 2 will take [tex]t= 8.5 \times 4[/tex]

So , [tex]t=34[/tex] minutes ;

the second point will be (4,34) .

we have to find the rate of change/slope of runner 2  ,

that can be written as : [tex]Slope = \frac{34-17}{4-2}[/tex]

On simplifying ,

we get ;

[tex]Slope = \frac{17}{2}[/tex] ;

So , [tex]Slope = 8.5[/tex].

Therefore , the rate of change of Runner 2 is 8.5 .

The given question is incomplete , the complete question is

Three runners are training for a marathon. One day, they all run about ten miles, each at their own constant speed. The equation that relates the Runner 2’s distance (in miles) with time (in minutes) is "t = 8.5d". Find the slope/rate of change of Runner 2 ?

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The length of the median = 6[tex]\sqrt{3}[/tex]

If we call the longer base "a" and the shorter base "b", then we know that:

a:b = 2:1

Since the ratio of the four sides is 1:1:1:1, we know that the height, median and the longer base are all equal.

We can use that information to determine the area of the trapezoid. The formula for the area of a trapezoid is:

Area = (a + b) * h / 2

We know that the area is  27[tex]\sqrt{3}[/tex] and the height and median are equal, so we can set up the equation:

(a + b) * h / 2 = 27[tex]\sqrt{3}[/tex]

We also know that a:b = 2:1, so we can substitute that in:

(2b + b) * b / 2 = 27[tex]\sqrt{3}[/tex]

Simplifying, we get:

3b^2 = 54 * [tex]\sqrt{3}[/tex]

So the length of the median (h) is b

= [tex]\sqrt{(54 * \sqrt{3} / 3) }[/tex]

= 6[tex]\sqrt{3}[/tex]

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Answer:

10 feet, option D

Step-by-step explanation:

Got it right on my test.

The equation of a line is given by y = mx + b, where m is the slope and b is the y-intercept. Given that the slope is 3 and the y-intercept is 5, the equation of the line is y = 3x + 5.

The equation of a line is a mathematical expression of the form y = mx + b, where m is the slope and b is the y-intercept. This equation can be used to describe the relationship between the x-coordinate and y-coordinate of points on a line. In this specific equation, the slope is 3 and the y-intercept is 5, which means that the line passes through the point (0, 5) and has a slope of 3. Substituting 3 for m and 5 for b in the equation, we get y = 3x + 5, which is the equation of the line with a slope of 3 and a y-intercept of 5. We can use this equation to determine the y-coordinate of any given point on the line, provided we know the x-coordinate of the point. It is important to note that this equation is only applicable to straight lines, and not curves.

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Answer:

down there with the work :)

Step-by-step explanation:

formula: a^2+b^2=c^2

Page 1:

1)

6^2+8^2=c^2

36+64=c^2

100=c^2

take the square root of both sides

c=10

2)

8^2+b^2=12^2

64+b^2=144

80=b^2

b=[tex]4\sqrt{5}[/tex]

3)

14^2+b^2=48^2

196+b^2=2304

b^2=2108

b=[tex]2\sqrt{527}[/tex]

Page 2:

1)

5^2+11^2=13^2

25+121=169

no this is not true so this is not a right triangle

2)

10^2+24^2=26^2

100+576=676

this is true so this IS a right triangle

hope this helps!

Answer:

i think it's a quadrilateral it's a rhombus.

Step-by-step explanation:

hope this helps

The growth in x years for the gym will be represented as [tex]y = 840(1.25)^x[/tex].

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

City Fitness, a popular gym currently has 840 members. Based on its membership statistics since opening a few years ago, City Fitness expects to grow its membership by a factor of 1/4.

The expression can be written as,

[tex]y = 840(1.25)^x[/tex].

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Answer:

80/89 (I messed it up with sine sorry :)

Answer:

cos ∅ = 80/89

Step-by-step explanation:

As required from the question the picture below represent a triangle UVW . The angle W = 90°. The sides WV = 39 , VU = 89 and UW = 80. The triangle forms a right angle triangle .

Such triangle one can establish trigonometric relationship using the SOHCAHTOA principle.

The question requested us to find the ratio that represent the cosine of  ∠U.

The ∠U is represented as ∅ .

Therefore,

cos ∅ = adjacent/hypotenuse

adjacent = 80. The adjacent side is the non hypotenuse side that is next to the given angle.

hypotenuse = 89 . Hypotenuse is the longest side of a right angle triangle and it opposite the right angle.  

cos ∅ = adjacent/hypotenuse

cos ∅ = 80/89

The number of hats that Leah had on Monday, given that half the hats were destroyed and four hats were bought, was, A. 22 hats.

If half the hats that Leah owns were destroyed on Wednesday such that only 13 hats were left, then it means that the total hats before the destruction, was :

= 13 hats x 2

= 26 hats

Seeing as Leah bought four hats on Tuesday, this means that the hats she had on Monday were :

= Total hats - Hats purchased on Tuesday

= 26 - 4

= 22 hats

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On solving the provided question, we can say that since it it is right angled triangle so the relation that be formed is  [tex]m^2 = p^2 + z^2[/tex]

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

since it it is right angled triangle

so the relation that be formed is

[tex]m^2 = p^2 + z^2[/tex]

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√6/3 is the value after rationalization of √2/√3

An expression is combination of variables, numbers and operators.

The given expression is √2/√3

Square root two divided by square root three.

We need to rationalize the denominator

To rationalize multiply numerator and denominator by √3

√2/√3×√3/√3

√2×3/3

√6/3

Hence, √6/3 is the value after rationalization of √2/√3

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Answer:

a) 3

b) 16 Celsius

Answer:

A. -4°C

B. 16°C

Step-by-step explanation:

A. (-7°C)-(-3°C)= -4°C

Therefore Paris is -4°C colder than Malé.

B. 23+(-7°C)=16°C

Therefore the temperature in Rome is 16°C

Hope it helps you

PLS RATE AS BRAINLIEST ANSWER

Yes the explanation satisfy the questions stated.

From the question, distance is said to be a function of time and the constant rate of change is 64.

y = 64x + 22

The above is in the form of a Linear equation:

y = mx + c

Where y = dependent variable (distance)

x = unrelated variable (time)

m = slope = time/distance

22 for c = constant.

m = constant rate of change = 64

If x (time) = 4

y (distance) = 278 miles

y = 64(4) + 22

y = 256 + 22

y = 256 + 22

y = 278 miles

Therefore the value of y is 278 miles.

The complete question is : Distance is a function of time. The constant rate of change is 64. Write

the equation Y=64x + 22. Substitute 4 in for x to get 278 miles,

Compare your response to the sample response above. Did your explanation

include that distance is a function of time?

include that the constant rate of change, or slope, is 64?

include the equation y = 64x + 22?

say to substitute 4 in for x to get 278 miles?

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Answer:

176

Step-by-step explanation:

2+62+77= 141

62/141

400 x 62/141 = 175.8

=176

so hmmm we look at hmm x³ + x² - 8x - 6 so how do squeak out a factor out of it, well, using the rational root test and using our p/q checking for factors, we find that likely factors can be ± 6/1 and ±(3, 2, 1) / 1, anyhow so we check some of those and hopefully without boring you to death we find that -3 works, we can always use the remainder theorem to check if that's true, by simply plugin in f(-3) and if it's indeed a factor, that'd give us 0, well, f(-3) = -27 + 9 +24 +6 = 0, holly smokes!! is a factor.

well, all that jazz means that -3 is a factor, namely the factor is really x = -3 or x + 3 = 0 so the factor is (x+3) and for our synthetic division we'll use the -3 version, Check the picture below.

so we end up with the factors of (x+3)(x²-2x-2), now for the 2nd factor what we can do to break it up is use the quadratic formula

[tex]~~~~~~~~~~~~\textit{quadratic formula} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{-2}x\stackrel{\stackrel{c}{\downarrow }}{-2} \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}[/tex]

[tex]x= \cfrac{ - (-2) \pm \sqrt { (-2)^2 -4(1)(-2)}}{2(1)} \implies x = \cfrac{ 2 \pm \sqrt { 4 +8}}{ 2 } \\\\\\ x= \cfrac{ 2 \pm \sqrt { 12 }}{ 2 }\implies x=\cfrac{2\pm\sqrt{2^2\cdot 3}}{2}\implies x=\cfrac{2\pm 2\sqrt{3}}{2}\implies x=1\pm\sqrt{3} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} (x+3)(x-1+\sqrt{3})(x-1-\sqrt{3}) \end{array}}~\hfill[/tex]

now, just to clarify, all those are real roots, and the last two come from simply setting x = 1 ± √3 to 0 to get the factors.

Answer:

No

Step-by-step explanation:

4 5/8 = 4.625 because 458=4+(5÷8)=4+0.625=4.625

4.65>4.625 so she has less

The first ferry's speed is 18.5 mph and the second ferry, which is slower, travels at 13.5 mph.

Let x represent the first ferry's speed.

The second, slower ferry's speed is then x-5 (since 5 miles per hour slower)

First ferry time equals distance/speed equals

50/x

Time spent on the second ferry:

50 / x - 5

The difference in times is 1 hour because the second ferry departs an hour earlier.

50 / x - 5 - 50/x = 1

50x - 50(x - 5) = x (x - 5 )

250 = x² - 5x

x² - 5x - 250 = 0

(x - 10 )(x + 5) = 0

x = 18.5 - 13.5

Speed can never be detrimental.

Therefore, the first ferry's speed is 18.5 mph.

and the second ferry, which is slower, travels at 13.5 mph.

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Answer:

hairy ball sack

Step-by-step explanation:

In any function y = f(x) , set of all possible values of x define the domain of f(x), in the graph The curve in terms of x-axis(in 1st & 3rd quadrant) goes from -4 to -2(doesnt include -2).

So domain = [-4, -2)

Similarly, in 2nd and 4th quadrant, for x-axis

It goes from 2 to 5 (doesnt include 2 & 5)

So domain = (2, 5)

Hence,

Domain of the f(x) is [-4, -2) U (2, 5).

Range tells the possible values of y, for this function it goes from -5 to +3(doesnt include 3).

Range is [-5, 3)

Answer:

170.52 in

Step-by-step explanation:

The distance between two points A and B is 5 units.

Answer:

False.

Step-by-step explanation:

It says Jacob walked to the store to get milk. The use of the word walked means it was past tense. He had already walked to the store.

When reflected in the y-axis, the image of the point (2/3) is (-2/3).

The sign of the x coordinate changes when a point is mirrored on the y-axis.

When a figure is built around a single point known as the point of reflection or the figure's centre, a reflection point results. There is an exact opposite point on the other side of each point in the figure. The shape and dimensions of the figure remain unchanged underneath the point of reflection.

The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the y-axis as (-x, y).

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Answer:

  135.5 m

Step-by-step explanation:

Given a triangle with angles A=46°, B=103°, and side c=97 m, you want to find the length of side 'a'.

Given one side and two angles we can solve the triangle using the Law of Sines:

  a/sin(A) = b/sin(B) = c/sin(C)

In order to do that, we need to have a (side, angle) pair, so we need to find the measure of angle C.

  A + B + C = 180°

  46° +103° +C = 180° . . . use the given measures

  C = 31° . . . . . . . . . . . . . subtract 149°

Now, we can find 'a' from ...

  a/sin(A) = c/sin(C)

  a = c·sin(A)/sin(C) = (97 m)·sin(46°)/sin(31°) ≈ 135.477286 m

The distance from B to the tree at C is about 135.5 meters.

Answer:

alpha=cos^-1(0.6)

alpha=53°

sin(37+53)

=1

Answer:

Step-by-step explanation:

Since both sin θ and cos α have same value of 3/5 and both angles are in the I quadrant, the angles θ and α are complementary.

It means:

Answer:

a₄ = - 2

Step-by-step explanation:

to calculate a term in the sequence subtract 5 from the previous term

give first term a₁  = 13 , then

a₂ = a₁ - 5 = 13 - 5 = 8

a₃ = a₂ - 5 = 8 - 5 = 3

a₄ = a₃ - 5 = 3 - 5 = - 2