Harry and Selma start driving from the same location. Harry drives 42 miles north and Selma drives 144 mies east. How far apart are Harry and Selma when they stop?

Answer:

8 inches on each side

Step-by-step explanation:

The value of x in the equation (m^5/6) (m^1/6)^7 = m^x is 2

The exponents of numbers are added when the numbers are multiplied, subtracted when the numbers are divided, and multiplied when raised by still another exponent: a^m×a^n = a^(m+n); a^m÷a^n = a^(m−n);

(am)ⁿ = a^mn.

Given an equation, (m^5/6) (m^1/6)^7 = m^x

Using the law of exponent, we get,

(m^5/6) (m^1/6)^7 = m^5/6*m^7/6

= m^(5/6+7/6)

= m^12/6

= m^2

Hence, the value of x in the equation (m^5/6) (m^1/6)^7 = m^x is 2

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Answer:

x= 12 6/17

Step-by-step explanation:

Answer:

[tex]\boxed {\boxed {\sf 102.1 \ meters}}[/tex]

Step-by-step explanation:

Let's assume the tree forms a right angle with the ground.

The distance from the tree to the man is 18 meters. The angle of elevation, which is 80 degrees, is the angle from where the man is to the top of the tree. We want to find the height of the tree, which we can call x.

Let's draw a diagram. (not to scale)

We can use sine (opposite/hypotenuse), cosine (adjacent/hypotenuse) or tangent (opposite/adjacent). We base the sides off of the elevation angle.

x is opposite the elevation angle and 18 is adjacent to the angle. So, we must use tangent.

[tex]tan(\theta)=opposite/adjacent[/tex]

The angle (θ) is 80. The opposite is x. The adjacent is 18.

[tex]tan(80)=x/18[/tex]

Now, solve for x by isolating it.

x is being divided by 18. The inverse of division is multiplication. Multiply both sides of the equation by 18.

[tex]18*tan(80)=x/18*18[/tex]

[tex]18*tan(80)=x[/tex]

[tex]18*5.67128182=x[/tex]

[tex]102.0830728=x[/tex]

Round to the nearest tenth. The 8 in the hundredth place tells us to round up.

[tex]102.1\approx x[/tex]

The height of the tree is about 102.1 meters.

**diagram is not to scale

Answer:

[tex]a^{2}[/tex]

Step-by-step explanation:

√a^4 is the same as:

√a × √a × √a × √a

group them as 2 pairs of

(√a × √a) × (√a × √a)

which makes

a × a

which is the same as [tex]a^{2}[/tex]

Answer: m=0

Step-by-step explanation: simplify each individual expression first. The left side of the equation is equal to -12m-6, and the right side is equal to 30m-6. Then together, it equals to -12m-6=30m-6. The -6 cancel each other out. M=0

The measure of the other 7 angles are;

m∠2 = m∠3 = 109°; m∠4 = m∠5 = m∠8  = 71°;  m∠6 = m∠7 = 109°

We are given;

m∠1 = 71°

Thus;

m∠1 and m∠2 are angles that form a straight line and as such they are supplementary angles and sum up to 180°

Thus; m∠1 + m∠2 = 180°

71 + m∠2 = 180°

m∠2 = 180 - 71

m∠2 = 109°

Now, m∠2 and m∠3 are alternate angles and as such;

m∠2 =  m∠3

Thus; m∠3 = 109°

Similarly,

m∠1 and m∠4 are alternate angles and as such;

m∠1 =  m∠4

Thus;

m∠4 = 71°

m∠1 and m∠5 are corresponding angles and as such;

m∠1 =  m∠5

Thus;

m∠5 = 71°

m∠2 and m∠6 are corresponding angles and as such;

m∠2 = m∠6

Thus;

m∠6 = 109°

Similar to how angles were gotten earlier, we can say that;

m∠5 = m∠8  = 71°

and m∠6 = m∠7 = 109°

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15 represent the car travled 15 miles / gallons.

Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.

We have been given that -

 y = 15 * x

Where y = the distance and

x = the number of gallons of gas to cover that distance.

A common unit of capacity in English-speaking countries, equal to four quarts, the U.S. standard gallon being equal to 231 cubic inches (3.7853 liters), and the British imperial gallon to 277.42 cubic inches (4.546 liters).

Consider the units:

y[miles] = 15[??] * x[gallons]

15[??] = y[miles] / x[gallons]

[??] = [miles] / [gallons]

So the units of the parameter 15 must be [miles / gallon] to convert the gallons to miles.

Therefore 15  represents the miles / gallon for the vehicle.

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Answer:

The height of the kite is approximately 278.6 feet

Step-by-step explanation:

The length of Jason's Kite string, l = 325 feet

The angle of elevation of the kite string, θ = 58°

The height of Jason's hand, h = 3 feet above the ground

Therefore, we have;

The height of the kite = The vertical component of the length of the kite string + The height of Jason's hand above the ground

The height of the kite = l × sin(θ) + h

Substituting the values, we get

The height of the kite = 325 × sin(58°) + 3 ≈ 278.6 (which is obtained by rounding the answer to the nearest tenth)

The height of the kite ≈ 278.6 feet.

hi

You have two points     A ( X;Y)  and B ( X ; Y)

slope is   :    ( Yb -Ya)   / (Xb -Xa )

A(2 ; 1)  and  B (17 ; - 17)  

so   :  (-17 - 1 )  / (17 -2) =  -18/ 15 =  - 6*3 / 5*3 =  -6/5

Answer:

For every hour the car is parked, the cost increases by $5.

Step-by-step explanation:

The cost, in dollars, of parking a car in a busy downtown area for h hours is $15 + $5h.

The fixed cost for the parking is $15. Here, $5 is extra. It increases as the number of hours increases. For every hour, the cost increases by $5.  Hence, the correct statement for the given problem is (C) "for every hour the car is parked, the cost increases by $5".

148+35=183

80+(-53)=27

(-125) x (-42)=5250

Answer:

Katherine will rent at least 64 movies and 20 games to make a profit

Step-by-step explanation:

The given parameters are;

The amount for which she rents games = 4

The amount for which she rents movies = 4

The number of games and movies she most rent to make profit = 84

The number of games she ≤ 20

Let x represent the number of games, let y represents the number movies, we have;

x + y ≥ 84

x ≤ 20

64 ≤ y ≤ 84

The graph of the inequality created with Microsoft Excel showing the feasible region is included

Answer:

There are 480 lockers in school.

Step-by-step explanation:

480

Step-by-step explanation:

180÷3=60

60x5=300

300+180=480

Answer:

This is an obtuse scalene triangle with the length of E measuring around 749 cm.

<D = 54.754° ≈ 55°

<E = 114°

<F = 11.246° ≈ 11°

Side D = 670 cm

Side E = 749.46937 cm ≈ 749 cm

Side F = 160 cm

Explanation:

When given two sides, and an angle, we can use trigonometry to find the missing angles, and sides.

Given the triangle ∆DEF with side D measuring 670 cm, side F measuring 160 cm, and angle E measuring 117°, we can apply the law of sines to identify the missing information. A & a chronologically refers to the first angle, and side. B & b chronologically refers to the second angle, and side. And C & c chronologically refers to the third angle, and side.

a / Sin (A) = b / Sin (B) = c / Sin (C)

[side 1]. [side 2]. [side 3].

↓ ↓ ↓

sideD/sin(<D) SideE/sin(<E) SideF/sin(<F)

______________________________

670cm / Sin(D) = E cm / Sin(114) = 160 / sin(F).

Since we are only given two sides with an angle measure, we can refer to the law of cosines to figure this one out.

It states that A = arccos(b²+c²-a²/2bc) → cos(A) = b²+c²-a²/2bc

B = arccos(a²+c²-b²/2ac) → cos(B) = a²+c²-b²/2ac

and C = arccos(a²+b²-c²/2ab) → cos(C) = a²+b²-c²/2ab

capital A, B, and C are angles A, B, and C.

lowercase a, b, and c are sides a, b, and c.

Therefore c² = a² + b² − 2ab cos(C),

b² = a² + c² - 2ac cos (B), and a² = b²+c² - 2bc.

SOH CAH TOA.

Since we know this, we can solve for pretty much everything as long as we are given at least 3 variables. Chronologically, because we are solving for side e, we must use b² = a² + c² - 2ac cos (B), because the rest are only variables we are given, making it easy to solve. So b² = 670² + 160² - 2(670 × 160) × cos(114°) = 561704.3362754.

Now take the square root of that to get b by itself, so √561704.3362754.... = 749.4693698046.... ≈ 749

Answer:749

Step-by-step explanation:

S.A.S law or Cosines

e=561704.33628= 749.469= 749

Answer:

121/12 is the answer your welcome

Answer:

$7.56

Step-by-step explanation:

$7(.08) = .56 in tax

$7 item cost + .56 in tax

Answer:

A. 1733 scooters

Step-by-step explanation:

To get x for minimum value of C bar, set derivative = 0

We Find our x.

C(x) = 600+ 0.05x + 0.0002x^2

We need average cos per unit

So divide by x both sides

C(x) / x = 600/x + 0.05x + 0.0002x

c(x)/c = Ç(x)

Therefore, Ç(x) = 600/x + 0.05x + 0.0002x

Now differentiate both side with x

dÇ(x)/dx = 600/x^2 + 0 + 0.0002

To find x for minimum Ç(x)

Set dÇ(x)/dx = 0 => -600/x^2 + 0.0002 = 0

=> x^2 = 600/0.0002

x^2 =3000000

x = √3000000

x = 1732.05

x = 1733

Answer:

12

Step-by-step explanation:

[tex]a_{n-1}=12\\\\

Plug\: n = n + 1\\\\

a_{n+1-1}=12\\\\

\huge \red {\boxed {a_{n}=12}} \\\\[/tex]

Answer:

x2+ 16k+ 64= not factorable with rational numbers

x2+ 7x+ 10= (x+2)(x+5)

These are what I got from your picture, so don't quote me on this the picture wasn't the best.

Answer:

B

Supplementary means they add to make 180 deg, so solve (4x-8)+(2x+2)=180

Answer:

angle a + angle b=180

4x-8+(2x+2)=180

6x-6=180

6x=180+6

x=186/6

{x=31°}

Answer:

Answer is D. 2 & -2

Answer:D

I THINK

Step-by-step explanation:

Hopefully this is the right one

Answer:

w=v/lh

Step-by-step explanation:

Answer:

[tex]L=2l[/tex] where [tex]l,L[/tex] denote arc lengths of two circles

Step-by-step explanation:

Let [tex]l,L[/tex] denote arc lengths of two circles, [tex]r,R[/tex] denote corresponding radii and

[tex]\alpha _1\,,\alpha _2[/tex] denote the corresponding central angles.

So,

[tex]l=r\alpha _1[/tex] and [tex]L=R\alpha _2[/tex]

This implies [tex]\alpha _1=\frac{l}{r}[/tex] and [tex]\alpha _2=\frac{L}{R}[/tex]

As each circle has an arc where the measures of the corresponding central angles are the same, [tex]\alpha _1=\alpha _2[/tex]

[tex]\frac{l}{r}=\frac{L}{R}[/tex]

As radius of one circle is twice the radius of the other circle,

[tex]R=2r[/tex]

[tex]\frac{l}{r}=\frac{L}{2r}\\\frac{l}{1} =\frac{L}{2}\\L=2l[/tex]

Answer:

a) 0.8

b) 0.075

c) 0.04

d) 3.3125

Step-by-step explanation:

To find the decimal of a fraction, just divide.

And if it's a mixed number, first turn it into an improper fraction. For 3 5/16 multiply 3 by 16 then add the product to 5. It would be 53/16

Answer:

Cosine

Step-by-step explanation:

I took the test

In order to solve for x , we use the trigonometric function cosine

What are trigonometric relations?

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the triangle be ΔABC , where ∠B = 90°

Let the side AB be x

So , the adjacent side = x

The angle of the triangle ∠A is = 72°

So , θ = 72°

The hypotenuse AC = 8

And , by trigonometric relations , we get

cos θ = adjacent / hypotenuse

Substituting the values in the equations , we get

cos 72° = x / 8

Multiply by 8 on both sides , we get

x = cos 72° × 8

Now , cos 72° = 0.30901

Substituting the value of cos 72° , we get

x = 0.30901 × 8

x = 2.472

Hence , the value of x is determined by cosine function

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Answer:

The correct option is;

A vertical line can be represented using a table but not a function because the slope is undefined

Step-by-step explanation:

A function, f(x), representing a linear relationship can be presented as follows;

f(x) = m·x + c

Where;

m = The slope = Δy/Δx = (y₂ - y₁)/(x₂ - x₁)

c = The y-intercept

Whereby the line is a vertical line, x₂ = x₁ and x₂ - x₁ =

Therefore;

The slope of a vertical function, m =  (y₂ - y₁)/(x₂ - x₁) = (y₂ - y₁)/0 = ∞ from which we have;

f(x) = ∞·x + c = ∞ which is undefined and the vertical line can only be represented using a table but not a function because the slope is undefined

Answer:

There's no options but it will get closed

Step-by-step explanation:

Answer:

Step-by-step explanation:

-75.5

Answer:

13.4

27.1

8.8

Step-by-step explanation:

hope that helps