To get to the park from her house, Rachel walked 4 kilometers due north and then 3 kilometers due west. On the way back, she cut across a field, taking the shortest
possible route home,
How far did Rachel walk on the round-trip?

Answer:

0.9

Step-by-step explanation:

This is a sine triangle. We have the hypotenuse (7) and an angle opposite of x (6). The formula for sine is opposite/hypotenuse; 6/7 = 0.8571428571428571. This, rounded to the nearest tenth, is 0.9.

Answer:

59 degrees

Step-by-step explanation:

Sin = opposite / hypotenuse

In this case sin is 6/7

To find the angle of this we need to use the arcsin, or sin^-1 function

Arcsin(6/7) = 58.9972809 degrees

This gets rounded to 59 degrees

Answer:

A.{7}^{15}

[tex]4.7475615 {}^{12}[/tex]

Step-by-step explanation:

[tex]( {7}^{5} ) {}^{3} = {7}^{5} =(16807) {}^{3}=4.7475615 {}^{12} [/tex]

Hope this helps ;) ❤❤❤

Answer:

The correct option is;

a. 1

Step-by-step explanation:

Given that the origin (0, 0) is the corner of the square

The equation of one of the sides = 3·X + 4·Y + 5 = 0

Therefore, we have;

Y = -3/4·X - 5/4

Which gives the slope as -3/4 and the y-intercept as (0, -5/4)

The sloe of the perpendicular side from the origin to the given line is therefore = -(1/(3/4)) = 4/3

The y-intercept of the current particular perpendicular side = 0

The equation is therefore;

y = 4/3·x + 0

The coordinate of the point of intersection of the two sides of the square above is found by equating the two lines to each other as follows;

4/3·x = -3/4·X - 5/4

4/3·x + 3/4·X = -5/4

25/12·X = -5/4

X = -5/4×12/25 = -3/5

Y = 4/3·x = 4/3× (-3/5) =-4/5

The length of a side = √((-3, 5) - 0)² + ((-4, 5) - 0)² = √1 = 1

The area of a square = (Length of side) × (Length of side)

∴ The area of the square = 1 × 1 = 1

The area of the square  = 1.

Answer:

30, 85, 95, 150

Step-by-step explanation:

The angles of a quadrilateral add to 360

Let x be the smallest angle

x+55

x+65

x+120 are the other three angles

Add the 4 angles together and they sum to 360

x+x+55 x+65+ x+120 = 360

Combine like terms

4x+240 = 360

Subtract 240 from each side

4x+240-240 = 360 -240

4x = 120

Divide by 4

4x/4 = 120/4

x = 30

x+55= 30+55 = 85

x+65 = 30+65 = 95

x+120 = 30+120 = 150

Answer:   simplified algebraic expression  : x

Step-by-step explanation:

The given phrase : 100 % of x

We can write 100 as 1 because 100% means complete or entire part.

Also, replace 'of' by '×' (Multiply sign).

So, the given phrase will become

1 × x   [Algebraic expression]

= x         [Simplified]

hence, the simplified algebraic expression is 'x'.

Answer:

slope = 1/4

Step-by-step explanation:

If a equation is in form of y = mx + c

them m is the slope of line.

____________________________________________

Let Y(d) be the distance ran by Alexandria on dth day

Y(0) = 2

she adds 1/4 miles each day then

Y(1) = 2 + 1/4

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

Y(3) = 2 + 1/4 +1/4 +1/4= 2 +1/4(3)

.

.

.

.

similarly

in d days she can run 2 miles + 1/4*d miles

thus, we have

Y(d) = 2 + 1/4(d)

it can be also solved

Thus we see that it is a linear relationship y = 2 + 1/4(d)

which is in the form of y = mx + c

comparing mx to 1/4 d

we have m = 1/4

thus,

slope of this linear relationship is 1/4

Answer:

Colin has 8 sheets left for his third class.

Step-by-step explanation:

Given that:

Total Number of pieces of papers = [tex]x[/tex]

Number of pieces of papers used for 1st class = 5 fewer than half of the pieces in the pad

Writing the equation:

[tex]\text{Number of pieces of papers used for 1st class =} \dfrac{x}{2} -5 ...... (1)[/tex]

Also, Given that number of pieces of papers used for the 2nd class are 2 more than that of papers used in the 1st class.

[tex]\text{Number of pieces of papers used for 2nd class =} \dfrac{x}{2} -5+2 = \dfrac{x}2 -3 ...... (2)[/tex]

Now, number of pieces of papers left for the third class = Total number of pieces of papers in the pad - Number of pieces of papers used in the first class - Number of pieces of papers used in the first class

[tex]\text{number of pieces of papers left for the third class = }x-(\dfrac{x}{2}-5)-(\dfrac{x}{2}-3)\\\Rightarrow x-\dfrac{x}2-\dfrac{x}2+5+3\\\Rightarrow x-x+5+3\\\Rightarrow 8[/tex]

So, the answer is:

Colin has 8 sheets left for his third class.

Answer:

{-0.5, 0.1}

Step-by-step explanation:

[tex]x = \frac{8 \pm \sqrt{(-8)^2 - 4 \cdot -20 \cdot 1}}{-40} = \frac{8 \pm 12}{-40}[/tex]

so x is 20/-40 = -0.5 or x = -4/-40 = 0.1

Answer:

B

Step-by-step explanation:

Just reduce your x's and y's. The x^-1 cancels with the x^5, and the y^-9 and y^-3 get simplified. After some basic simplifying, you get answer B.

Answer:

The steps include:

1. y = –3/4x + 9

2. x = –3/4y + 9

3. x – 9 = –3/4y

4. –4/3(x – 9) = y

5. y = –4/3x + 12

6. f¯¹(x) = –4/3x + 12

Step-by-step explanation:

f(x) = –3/4x + 9

The inverse, f¯¹(x) of the above expression can be obtained as follow:

f(x) = –3/4x + 9

Let y = f(x)

y = –3/4x + 9

Interchange x and y

x = –3/4y + 9

Making y the subject of the expression, we have:

x = –3/4y + 9

Rearrange

x – 9 = –3/4y

Cross multiply

4(x – 9) = –3y

Divide both side by –3

–4/3(x – 9) = y

Clear bracket

y = –4/3x + 12

Replace y with f¯¹(x)

f¯¹(x) = –4/3x + 12

Therefore, the steps include:

1. y = –3/4x + 9

2. x = –3/4y + 9

3. x – 9 = –3/4y

4. –4/3(x – 9) = y

5. y = –4/3x + 12

6. f¯¹(x) = –4/3x + 12

Answer:

1. y = –3/4x + 9

2. x = –3/4y + 9

3. x – 9 = –3/4y

4. –4/3(x – 9) = y

5. y = –4/3x + 12

6. f¯¹(x) = –4/3x + 12

Step-by-step explanation:

f(x) = –3/4x + 9

The inverse, f¯¹(x) of the above expression can be obtained as follow:

f(x) = –3/4x + 9

Let y = f(x)

y = –3/4x + 9

Interchange x and y

x = –3/4y + 9

Making y the subject of the expression, we have:

x = –3/4y + 9

Rearrange

x – 9 = –3/4y

Cross multiply

4(x – 9) = –3y

Divide both side by –3

–4/3(x – 9) = y

Clear bracket

y = –4/3x + 12

Replace y with f¯¹(x)

f¯¹(x) = –4/3x + 12

Therefore, the steps include:

1. y = –3/4x + 9

2. x = –3/4y + 9

3. x – 9 = –3/4y

4. –4/3(x – 9) = y

5. y = –4/3x + 12

6. f¯¹(x) = –4/3x + 12

Step-by-step explanation:

Answer:

B gains 100 yards every minute. So, after 10 minutes, B has lapped A once.

C gains 100 yards on B every minute, so after 10 minutes C has lapped B.

Thus, after 10 minutes, A has gone 7 laps, B has gone 8 laps, C has gone 9 laps, and all are even again.

Answer:6 a p e x

Step-by-step explanation:

Answer:

initial investment in the account is 5500.

Step by step Explanation:

exponential growth model provide details of what happens when the same number is multiplied over and over again, it's applications can be found in economics and science generally.

Exponential models gives situations when the rate of change of a particular thing is directly proportional to how much of that thing is.

the given equation becomes A = 5500 * e^(0.065* T)

But an exponential growth equation can be expressed in this form F = P * e^(RT)

Where F = the future value

P = the present or initial value

R = interest rate per time period

T = number of time periods

From the given equation in the question, we can see that

F = A which is the future value

P = 5500 which is the present or initial value.

R = 0.065 which is interest rate per time period

Therefore, your initial investment in the account is 5500.

Answer:

42°

Step-by-step explanation:

AD bisects ∠CAB, which means it splits ∠CAB into two equal parts. ∠CAB equals 84°. 84° ÷ 2 = 42°.

Answer:

StartFraction 24 Over 65 EndFraction

Step-by-step explanation:

Total number of students = 26

Number of boys = 10

Number of girls = 26-10

=16

Eduardo has to pull two names out of the hat without replacing them.

First name

Probability= Favourable outcome/Total outcome

Probability of girls=16

Total probability=26

Eduardo has to pull two names out of the hat without replacing them.

Probability= Favourable outcome/Total outcome

=16/26

=8/13

For the second name:

Without replacement of the first hat

Probability of girls=16-1=15

Total probability=26-1=25

Probability= Favourable outcome/Total outcome

=15/25

=3/5

Probability of both of Eduardo's partner for the group project will be girls=8/13*3/5

=24/65

StartFraction 24 Over 65 EndFraction

Answer:

B.) 24/65

Step-by-step explanation:

Took the test

Answer:

ﾠﾠﾠﾠﾠﾠﾠﾠ

Step-by-step explanation:

ﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠﾠ

Answer:

9/16

Step-by-step explanation:

Answer:

a = 55° and b = 60°

Step-by-step explanation:

→ Remember 2 key points about angles

→ Angle a is alternate to 55° so using the 2nd point,

a = 55°

→ Remember the fact that angle in a triangle add up to 180°

55°  + 65° + b = 180°

→ Collect the whole numbers

120° + b = 180°

→ Minus 120° from both sides to isolate b

b = 60°

The solution is : the measures of angles A and B are:

A = 55° and B = 60°

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,

We know that 55+ b+ other angle = 180 since they make a straight line

The other angle = 65 since they are alternate interior angles

55+ B+ 65 = 180

Combine like terms

120 + B = 180

B = 60

A + B + 65 = 180

interior angles of a triangle must equal 180 degrees

A +60+ 65 =180  

Combine like terms

A +125 = 180

A = 55

Hence, The solution is : the measures of angles A and B are:

A = 55° and B = 60°

To learn more on angle click:

brainly.com/question/28451077

#SPJ3

Answer:

∠ GDH = 67.5°

Step-by-step explanation:

The measure of the chord- chord angle GDH is half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

∠ GDH = [tex]\frac{1}{2}[/tex](GH + EF) = [tex]\frac{1}{2}[/tex] (90 + 45)° = 0.5 × 135° = 67.5°

Answer:

Step-by-step explanation:

tan∅ = opposite / adjacent

From the question

AC is the adjacent

BC is the opposite

So we have

tan (a) = BC / AC

tan (a) = 24/7

Hope this helps you

Answer:

x = 2

Step-by-step explanation:

3(2x+1) = 15

6x +3 = 15

6x = 12

x - 2

Answer:

67 - p = 52

Step-by-step explanation:

the train starts with 47 people:      47

it picks up 20 more:      47 + 20 = 67

p people get off:                            67 - p

52 people are left on train:           67 - p = 52

Answer:

x = E/(p - y)

Step-by-step explanation:

p - y = e/x

x(p-y) = e

x = e/(p-y)

Answer:

Hey there!

p=e/x+y

p-y=e/x

x(p-y)=e

x=e/(p-y)

Hope this helps :)

Answer:

[tex]c = \frac{2}{5} t[/tex], if the number of texts is 4, then the cost is $1.60.

Step-by-step explanation:

If 2 texts costs $5, then each text costs $[tex]\frac{2}{5}[/tex].

So, we can setup the equation to  [tex]c = \frac{2}{5} t[/tex].

If the number of texts is 4, we can substitute that into our equation.

[tex]c = \frac{2}{5} \cdot 4[/tex]

[tex]c = \frac{8}{5}[/tex]

[tex]c = 1.60[/tex]

Hope this helped!

Answer:

The two equivalent expressions are 6(x − y) and 6x − 6y.

Step-by-step explanation:

The first expression shows subtracting the number of packages of cherry snacks from the number of packages of strawberry snacks in each box and then multiplying the difference by the number of boxes. That's the same as finding the total number of cherry snacks and subtracting it from the total number of strawberry snacks, as shown in the second expression.

Have a good day!<3

The two equivalent expressions means in terms of the situation are 6(x − y) and 6x − 6y.

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.

The first expression shows subtracting the number of packages of cherry snacks from the number of packages of strawberry snacks in each box and then multiplying the difference by the number of boxes then it will be as;

6(x-y)

Now, the total number of cherry snacks and subtracting it from the total number of strawberry snacks, as shown in the second expression will be;

6x - 6y

The two equivalent expressions means in terms of the situation are 6(x − y) and 6x − 6y.

Learn more about expression here;

https://brainly.com/question/14083225

#SPJ2

Answer:

16 and 24 ft

Step-by-step explanation:

If we call the length of one piece x, the length of the other piece is x + 8, therefore, we can write the following equation:

x + x + 8 = 40

2x + 8 = 40

2x = 32

x = 16 so x + 8 = 16 + 8 = 24.

Answer:

24 and 16

Step-by-step explanation:

x + x+8=40

2x+8=40

2x=32

x=16

16 and 24

Answer:

sqrt(68) is the length.

Step-by-step explanation:

For this you will use the distance formula, sqrt((x2-x1)^2+(y2-y1)^2)

So for this it is sqrt((5+3)^2+(-2+4)^2)

sqrt(64+4)

sqrt(68)

8.246

Answer:

The p-value is 0.025

Step-by-step explanation:

Given that:

30% of the people in Washington state want cell phone use banned in cafes

sample size N = 1450

X = 474 people have the same opinion.

The objective is to calculate the p-value.

Let's assume the level of significance = 5% = 0.05

From the information given ; the null and alternative hypothesis can be computed as:

[tex]\mathbf{H_o: p = 0.30 } \\ \\ \mathbf{H_a: p \neq 0.30}}[/tex]

USING MINITAB; the simulation on what we compute on our MINITAB can be written as:

Test for p = 0.3  vs p not  = 0.3

Sample  X       N         Sample p    95 C.I                            Z-value     P-value

1             474   1450   0.326897    (0.302752, 0.351041)   2.23            0.025

From what we have in our MINITAB Output;

Z - value = 2.23

P-Value = 0.025

Answer:

see below

Step-by-step explanation:

-3.55 g≤ -28.4

Divide each side by -3.55, remembering to flip the inequality

-3.55 g/-3.55≥ -28.4/-3.55

g≥8

Closed circle at 8 and the line goes to the right

Answer:

24

Step-by-step explanation:

30/100=x/80

cross multiply:

100x=2400

divide by 100:

x=24

Not quite sure how you want me to explain the other way step by step... Hope this helps!

80*.3=24

Answer:

Step-by-step explanation:

This problem is based on unit conversion from miles per hour to  meter per second.'

From tables 1 mph= 0.44704 m/s

Given 248 mph to be converted to meters per second.

hence we have

1 mph= 0.44704 m/s

248 mph= x

cross multiplying we have

x= 110.86592 m/s

to the nearest hundreth we have