Haley read three less than twice as many books as her brother did last summer. haley read five books.which equation could you use to find how many books her brother read (b)?

Lines that are not in the same plane are called skew lines.

"A line is a one-dimensional figure, which has length but no width. A line is made of a set of points which is extended in opposite directions infinitely."

Given, two lines are not in the same plane.

Here, perpendicular lines, transversal lines, and parallel lines should be in the same plane.

Two lines are called skew lines are two lines if they do not intersect and are not parallel.

Therefore, skew lines are not in the same plane.

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The requried both A and B refer to the same calculation, which is finding the inverse tangent of -√3. The result is -60 degrees or -π/3 radians.

A. The expression "arctan(-√3)" represents the inverse tangent function of the value -√3. The inverse tangent function returns an angle whose tangent is equal to the given value.

To evaluate arctan(-√3), we can use a calculator or reference table that provides trigonometric function values. In this case, the value is approximately -60 degrees or -π/3 radians.

B. The expression "Arctan(-√3)" is the same as "arctan(-√3)" and represents the inverse tangent function of -√3. The uppercase "Arctan" notation is commonly used in mathematical literature and calculators to represent the inverse tangent function.

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The dimensions of the rectangle are width = 4 yds and length = 7 yds.

The area of a rectangle is defined as the product of the length and width.

The area of a rectangle = L × W

Where W is the width of the rectangle  and L is the length of the rectangle

We have been given that the length of a rectangle is 5 yds less than three times the width,

The area of the rectangle is 28 yds square.

Let the width of the rectangle is x

So the length of the rectangle = 3x - 5

The area of a rectangle = x × (3x - 5)

28 = 3x² - 5x

3x² - 5x - 28 = 0

(3x + 7)(x - 4) = 0

3x + 7 = 0 and and x - 4 = 0

x = -7/3 and x = 4

Take x = 4 as the width

So the length of the rectangle = 3(4) - 5 = 12 - 5 = 7

Therefore, the dimensions of the rectangle are width = 4 yds and length = 7 yds.

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Answer:

Nick's car can travel 384 miles using a full tank of gas.

Step-by-step explanation:

Answer:

$800,000 because she will need to save for 20 years times $40,000

Step-by-step explanation:

Silvia wants to retire at 65 and live on $40,000 a year.

She wants to live till 85 and retire at 65 years.

So, number of years to save = [tex]85 -65= 20[/tex]

And she needs to save [tex]40000\times20=800000[/tex]

Hence, she must save 800,000.

The value of x in the equation given is 8

Using the equations given for our Calculation;

Take the L.C.M of 8 and x ; which is 8x

(7x - 8) / 8x = 3/4

Now we cross multiply;

4(7x - 8) = 3 * 8x

open the bracket

28x - 32 = 24x

28x - 24x = 32

4x = 32

x = 8

Hence, the value of x = 8

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Answer:

1.)- B. 5/12

2)- A. 7/9

Step-by-step explanation:

Answer: The Work done to move the object is  [tex]=23.15 \text { foot pounds }[/tex]

Step-by-step explanation:

Given;

Force F=3 [tex]l b s[/tex]

Vectors of F= (3,-1)

Moves object to a distance=9 [tex]f t s[/tex]

Let A and B be the displacements Vectors

A= (0,-5)

B= (6,-2)

To Find:

Work done in foot-pounds

Solution:

Work done [tex]W=F \times D[/tex]

Direction of force vector= (3,-1)  (i, j)  

                                        =3i-j

Unit of force vector [tex]=\sqrt{3^{2}+\left(-1^{2}\right)}[/tex]

                                 [tex]=\sqrt{9+1}[/tex]

Force vector=(Force/Unit Vector)Direction of  force vectors

                   F=[tex]3 / \sqrt{10} \times(3 i-j)[/tex]

Direction of motion vector= (B-A)  

                                          = (6,-2)-(0,-5) x i,j)

                                          =(6-0),(-2-5) x (i, j)

                                          =(6,-7) x (i, j)

                                          =6i-7j

Unit of motion vector [tex]=\sqrt{6^{2}+\left(-7^{2}\right)}[/tex]

                                   [tex]=\sqrt{36+49}[/tex]

                                   [tex]=\sqrt{85}[/tex]

Motion Vector= (Distance moved by the object/Unit motion vector) × (Direction of motion vectors)

                        [tex]D=9 / \sqrt{85} \times(6 i-7 j)[/tex]

Workdone [tex]W=F \times D[/tex]

                  [tex]= [3/ \sqrt{10} \times (3i-j)] \times [9/ \sqrt{85} \times (6i-7j)][/tex]

                  [tex]= [3/ \sqrt{10} \times 9/ \sqrt{85}] \times [(3i-j)  \times(6i-7j)][/tex]

                  [tex]= [3/3.1623 \times 9/9.2195] \times [(3\times6) + ((-1) \times (-7))][/tex]

                  [tex]= [0.94867 \times 0.97619] \times [18+7][/tex]

                  [tex]=23.15 \text { foot pounds }[/tex]

Result:

   Work done to move an object [tex]=23.15 \text { foot pounds }[/tex]

Answer:

[tex]W = 25.617\,lbf\cdot ft[/tex]

Step-by-step explanation:

The work done to move the object is:

[tex]W = F \cdot s \cdot \cos \alpha[/tex]

The angle of the force with respect to change in the position vector is:

[tex]\alpha = \tan^{-1}\left(-\frac{7}{6} \right) - \tan^{-1}\left(-\frac{1}{3} \right)[/tex]

[tex]\alpha \approx 18.415^{\textdegree}[/tex]

The magnitude of the work done is:

[tex]W = (3\,lbf)\cdot (9\,ft)\cdot \cos 18.415^{\textdegree}[/tex]

[tex]W = 25.617\,lbf\cdot ft[/tex]

Using the combination formula, 21 different 5-person committees can be chosen from a group of 7 students.

To determine how many different 5-person committees can be chosen from a group of 7 students, we use the concept of combinations, specifically the combination formula which is defined as:

C(n, k) = n! / [k! * (n - k)!]

where n is the total number of items to choose from, k is the number of items to choose, and the exclamation point represents a factorial, which is the product of all positive integers up to that number.

Applying this to the given problem, we have:

C(7, 5) = 7! / [5! * (7 - 5)!]

This simplifies to:

C(7, 5) = (7 * 6) / (2 * 1)

Therefore, C(7, 5) = 21.

There are 21 different 5-person committees that can be formed from 7 students.

Answer:

  1 13/20

Step-by-step explanation:

You want the total of distances walked to be the length of the hike:

  2 1/10 + 1 1/4 + (left to walk) = 5

Then the amount left to walk is the difference ...

  left to walk = 5 - 2 1/10 - 1 1/4

___

You are expected to know how to do arithmetic with mixed numbers, and/or to be able to use a calculator for the purpose.

  5 - 2 1/10 - 1 1/4

  = (5 -2 -1/10) - 1 1/4

  = 2 9/10 - 1 1/4

  = (2 -1) + (9/10 -1/4)

  = 1 + (9/10 -1/4)

  = 1 + (18/20 - 5/20)

  = 1 13/20 . . . miles left to walk

___

Using a calculator:

  5 -2.1 -1.25 = 1.65 = 1 65/100 = 1 13/20

Since, it is given that the pentagon ABCDE is congruent to pentagon FGHIJ.

By being congruent, the corresponding angles and sides are equal.

Therefore, [tex]\angle A = \angle F[/tex], [tex]\angle B = \angle G[/tex], [tex]\angle C = \angle H[/tex], [tex]\angle D= \angle I[/tex], [tex]\angle E = \angle J[/tex].

By using [tex]\angle A = \angle F[/tex]

So, [tex]100^\circ = \angle 1[/tex]

Therefore, the measure of angle 1 is 100 degrees.

So, Option B is the correct answer.