Jennifer travels from Boston , Massachusetts, to Fairfield, Connecticut, a distance of 90 miles, at a speed of 45 miles per hour, and returns at a speed of 60 miles per hour. To the nearest half mile per hour, what is Jennifer's average rate for the whole trip?

A) 50 1/2
B) 51
C) 51 1/2
D) 52 1/2
E) 53 1/2

Answer:

π - irrational

0.04053.. - irrational

0.76 - rational

3.565565565 - irrational

-17 - rational

3.275 - rational

Step-by-step explanation:

rational = can express as fraction

irrational = cannot

Answer:

The height is 12 cm

Step-by-step explanation:

Hi there!

We are given a triangle with the 3 sides marked as 15, 20, and 25 and we want to find the height of it (marked as x in the problem).

This problem can seem a bit difficult, but let's see if the triangle is a right triangle first off.  

One way to figure out if it is a right triangle is to apply the converse of the Pythagorean theorem.

Let's label the sides, where a is the shortest side, b is the second shortest side, and c is the longest side:

a=15

b=20

c=25  

Now square a and b, then add the result together. If it's the same as c squared, then the triangle is a right triangle

15²+20²=25²

225+400=625

625=625

So we can safely say that the triangle is a right triangle

This makes the problem way easier, as there are 2 ways to find the area of a right triangle:

The first way is to multiply the legs (the sides that make up the right angle) together, then divide the result by 2

The other way is to multiply the height and the hypotenuse (the side OPPOSITE to the right angle) together, and then divide the result by 2

First, we need to figure out which sides are the legs, and which side is the hypotenuse

By the triangle inequality theorem, the hypotenuse of a right triangle is the longest side, which means that the 25 cm side is the hypotenuse, and that leaves 15 cm and the 20 cm sides as the legs

So let's find the area of the triangle using the legs

A=[tex]\frac{15*20}{2}[/tex]=[tex]\frac{300}{2}[/tex]=150

So the area of the triangle is 150 cm²

However, as mentioned above, we can also find the area of the triangle by multiplying the hypotenuse by the base, then dividing the result by 2

Which means that the area is also:

A=[tex]\frac{25x}{2}[/tex] cm²

As these both equal the area of the triangle, we can set them equal to each other. This is possible via a property known as transitivity (if a=b and b=c, then a=c)

[tex]\frac{25x}{2}=150[/tex]

Multiply both sides by 2

25x=300

Divide both sides by 25

x=12 cm

So the height of the triangle is 12 cm

Hope this helps!

Answer:

x=50

Step-by-step explanation:

Let's look at the red angle. if a flat line makes the angle 180, and the outer angle is 120, subtract 120 from 180. This will give you 60. Now every angle of a triangle added together will give you the sum of 180. So you already have 60 and 70, which make 130 all together. Subract 130 from 180 - (180-130) - and you'll get the result of 50.

The solution is :  the measure of the missing angle X is x=50.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

here, we have,

from the given diagram, we get,

Let's look at the red angle.

if a flat line makes the angle 180, and the outer angle is 120,

subtract 120 from 180.

This will give you 60.

Now every angle of a triangle added together will give you the sum of 180.

So you already have 60 and 70,

which make 130 all together.

Subtract 130 from 180

i.e. (180-130) = 50

and we get the result of 50.

Hence, The solution is :  the measure of the missing angle X is x=50.

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Answer:

12

Step-by-step explanation:

The first number they will both say = L.C.M of (6,4)

=> L.C.M of (6,4) is 12

The first number they will both say is 12

Answer:

Step-by-step explanation:

Remark

I have to assume that you know calculus. It is the only way the problem can be done that I know of. If you don't, I'm not sure how you will do this.

The curve is of y  = e^(-2x) + x^2 - 3

The curve crosses the y axis when x = 0. The y value is

y = e^0 + x^2 - 3

yint = 1 + 0 - 3

yint = -2

The slope at point (0,-2) is

y' = -2e^(-2x) +2x

y' = -2 at point A

Therefore the normal will have a slope

m1 * m2 = - 1

The slope of the curve C  at A = -2

The equation of the tangent line at A = -2x - 2

Call this m1

m2 = slope of the normal

-2 * m2 = -1

m2 = 1/2

Equation of the line (l) =

y = 1/2 x  - 2

The graph is shown below. Notice the two lines actually look like they are at a 90 degree angle.

Answer:

(-2,4] and [7,α)

Step-by-step explanation:

the domain is open at -2 but closed at 4 and also closed at 7 but open till infinity..

The domain of the given function is (-2,4] U [7, ∞), which is the correct option (B).

A piecewise-defined function (also known as a piecewise function or a hybrid function) is a function defined by multiple sub-functions, each of which applies to a different interval of the main function's domain (a sub-domain).

The graph is given in the question, as shown

f(x) = x²+1 if (-2,0]

This the sub-function define between the interval (-2,0].

f(x) = -1 if (0, 4]

This the sub-function define between the interval (0, 4].

f(x) = -(x-7)² if [7, ∞)

This the sub-function define between the interval [7, ∞).

Thus, the domain of the given function is (-2,4] U [7, ∞).

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Answer:

13/45

Step-by-step explanation:

x = .2888888888

100(x + .2888888)

100x + 28.8888

 10x + 2.88888

90x = 26

x = 26/90 = 13/45

Answer:

24units

Step-by-step explanation:

From the parallelogram given, we can see that the line FH bisects EG at V. Hence;

GE = 2GV.

Given that

GV = 12

GE = 2(12)

GE = 24

Hence the measure of the length GE is 24units

Answer:

12/20 = 60%

Step-by-step explanation:

The probability that the candy Roger selected was NOT a gummy worm;

P(Not a gummy worm) = 0.6

Miniature peanut butter cups = 5

Dark Chocolate bars = 7

Gummy worms = 8

Total number of candy bars = 5 + 7 + 8

Total number of candy bars = 20

Probability is found as; number of possible outcomes/number of events.

P(randomly selected is a gummy worm) = 8/20

P(randomly selected is a gummy worm) = 0.4

Probability that it was not a gummy worm = 0.6

Read more at; https://brainly.com/question/13160116

Step-by-step explanation:

> 2n³+4²+6n-6n-21

2n³+4n²-21

> -4n²-3n-8+2n+18

-4n²-3n-8+2n+18

-4n²-n-8+18

-4n²-n+10

Answer:

1. about 11.18

2. about 8.66

Step-by-step explanation:

1. 5^2 + 10^2= 125

square root of 125 equals about 11.18

2. 10^2-5^2=75

square root of 75 equals about 8.66

Answer:

14 yards shorter

Step-by-step explanation:

Use Pythagoras' Theorem

a²+b²=c²

16²+63²=4225

√4225= 65yd

The diagonal line (c) is 65 yards long

16 + 63 = 79 yd

It would be 14 yards shorter (79-65)

Answer:

right by 3 I think

Step-by-step explanation:

Answer: Right by 3 Units

Step-by-step explanation:

Right on edge 2021

Answer: 4. A base area of 16y^2 square units and height of y^2 + y + 3 units

Step-by-step explanation:

Using the distributive property; you can see that 16y^2(y^2+y+3)=

16y^4+16y^3+48y^2

Answer:

D. a base area of 16y2 square units and height of y^2 + y + 3 units

Step-by-step explanation:

Ed22

Answer:

surface area of a square = 2 ( lb + bh + hl )

given that,

length = 8cm

breadth = 10cm

height = 15 cm

surface area = 2 ( 8* 10 + 10*15 + 15*8 )

                     = 2 ( 80 + 150 + 120 )

                     = 2 * 350

                     = 700 [tex]cm^{2}[/tex]

hope this answer helps you!!

Answer:

could u take a picture of the angles please

Step-by-step explanation:

Answer:

RS, RT, ST

Step-by-step explanation:

We require the third angle in the triangle

∠ T = 180° - (92 + 71)° = 180° - 163° = 17°

The shortest side is opposite the smallest angle

∠ T = 17° → opposite side RS

The longest side is opposite the largest angle

∠ R = 92° → opposite side ST

Then sides from shortest to longest is

RS, RT, ST

Answer:

100% - 76% = 24%

24% = 0.24

0.24*50 = 12

You got 12 questions wrong.

Step-by-step explanation:

Please mark brainliest!

Number of questions that got wrong are 12 .

Given,

76% on a 50 question test.

Here,

Let total percentage value be 100%.

Then,

100% - 76% = 24%

24% questions got wrong.

Number of questions that got wrong out of 50 will be ,

24% of 50

= 0.24*50

= 12

Therefore 12 questions got wrong.

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Answer: 111.1 m

Step-by-step explanation:

(30*2)/60 = 1 km ( the tunnel length is 1 Km.)

1 Km = 1000 m.

1000/9 = 111.1 m.

A general cosine function (we could also use a sine function) is written as:

y = A*cos(k*x + p) + M

We will find that the function of the graph is:

f(x) = 2*cos(2*x + 2.09) - 2

Let's return to the general function:

y = A*cos(k*x + p) + M

A is the amplitude, it defines the distance between the value of a maximum and the value of the minimum, such that A is exactly half of that difference.

Here we can see that the maximum is 0, and the minimum is -4

The differene is: 0 - (-4) = 4

Then:

A = 4/2 = 2

f(x) = 2*cos(k*x + p) + M.

M is the midline, this is, the horizontal line that cuts the graph in two halves. Here we can see that the midline is x = -2, then:

M = -2

f(x) = 2*cos(k*x + p) - 2

p is the phase shift.

In the graph, we can see that f(0) = -3, so we have:

f(0) = 2*cos(0 + p) - 2 = -3

      cos(p) = -1/2

             p = Acos(-1/2) = 2.09

Then we have:

f(x) = 2*cos(k*x + 2.09) - 2

Finally, k is related to the frequency of the function.

We can see that the function does a complete cycle at x = pi

This means that:

f(x) = f(x + pi)

Knowing that the period of a cosine function is 2*pi, then:

k*(x + pi) = k*x + 2*pi

k = 2

Then the equation of the graph is:

f(x) = 2*cos(2*x + 2.09) - 2

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Answer(s):

[tex]\displaystyle y = 2sin\:(2x + 1\frac{1}{4}\pi) - 2 \\ y = 2cos\:(2x - 1\frac{1}{4}\pi) - 2[/tex]

Step-by-step explanation:

[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow -2 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{5}{8}\pi} \hookrightarrow \frac{-1\frac{1}{4}\pi}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 2[/tex]

OR

[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow -2 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\frac{5}{8}\pi} \hookrightarrow \frac{1\frac{1}{4}\pi}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 2[/tex]

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then by all means, go for it, but be careful and follow what is explained here. Now, as you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 2sin\:(2x - 1\frac{1}{4}\pi) - 2,[/tex] in which you need to replase “cosine” with “sine”, then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{4}\:unit[/tex] to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD [tex]\displaystyle \frac{\pi}{4}\:unit,[/tex] which means the C-term will be negative. Now, BEFORE we go any further, we must remember that this particular cosine graph [thank goodness it is a cosine graph we are working with] ALREADY has a horisontal shift and does not have a single crest oscıllαtıng about any endpoint on the y-axis. So, in this case we need to figure out how far the FIRST oscıllαtıng crest is from the origin, and that obviously would be [tex]\displaystyle \frac{5}{8}\pi\:units.[/tex] Though, sinse we want the sine equation of this graph, it must be “negative”; so, by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{5}{8}\pi} = \frac{-1\frac{1}{4}\pi}{2},[/tex] in which the value of C is [tex]\displaystyle -1\frac{1}{4}\pi.[/tex] So, the sine equation of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 2sin\:(2x + 1\frac{1}{4}\pi) - 2.[/tex] Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits [tex]\displaystyle [\frac{7}{8}\pi, -2],[/tex] from there to [tex]\displaystyle [-\frac{\pi}{8}, -2],[/tex] they are obviously [tex]\displaystyle \pi\:units[/tex] apart, telling you that the period of the graph is [tex]\displaystyle \pi.[/tex] Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = -2,[/tex] in which each crest is extended two units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

**As you can see, this is one of those moments where you will really need to be careful because if you notised, both equations have OPPOCITE horisontal shifts and C-values. Now, the ONLY TIME this occurs is when all crests in a SINUSOIDAL graph cycle half-way in between endpoints. Your best bet is to jot this down for when you see graphs like these in the future.

I am delighted to assist you at any time.

Answer:

$17.5

Step-by-step explanation:

original price of shirt=$25

discount on shirt=30%

discount on shirt in $=$25*30%

discount on shirt=$7.5

cost of shirt after discount=origanl price-discount

=$25-$7.5

=$17.5

Answer:

x + 3

Step-by-step explanation:

Image below

Answer:

5^3

Step-by-step explanation:

5^1 x 5^2

indices rules when multiplying you add the powers to 1+2=3

5^3

Answer:

Step-by-step explanation:

θ=l/r

θ=6/11 radians

≈0.555... radians

Answer:

always

Step-by-step explanation:

Zero is always greater than any negative integer.

Answer:

10

Step-by-step explanation:

2000/ 2x = 10

Multiply each side by 2x

2000/ 2x = 10 *2x

2000 = 20x

Divide by 20

2000/20 = 20x/20

100 = x

Take the square root of each side

sqrt(100) = sqrt(x)

10 = sqrt(x)

Answer:

10/3

Step-by-step explanation:

rate of change = gradient

(17-7)/(6-3) = 10/3

basically difference of y values / difference of x values

Answer: 2, acute equilateral

Step-by-step explanation:

the image shows a triangle with all 3 sides congruent and 3 acute angles

Answer:

45 hours

Step-by-step explanation:

1 mile * 1609 meters  *     1 s           = 160900 sec

               1 mile               .01 meters

160900 sec / 60 /60 = 44.7 = 45 hours

Step-by-step explanation:

This is a cute question lol.

So this lil snail is trying to go 1609 meters, at a speed of 0.01 m/s (meters per second). Lets see how long that takes.

The way I like to do conversion problems is by starting with the value that doesn't have something on the bottom (1609 m) then multiplying to get rid of that variable.

I'll show you what I mean:

[tex]\frac{1609 m}{1} *\frac{1 s}{0.01 m} *\frac{1 min}{60s} *\frac{1 hr}{60 min}[/tex]

Then, we just multiply everything.

[tex]\frac{1609 *1*1}{1*0.01*60*60}hr[/tex]

Simplify.

[tex]\frac{1609}{36}hr[/tex]

Divide.

[tex]44.694444444...hr[/tex]

Round to the nearest whole hour.

[tex]45 hr[/tex]

Answer:

45 hours