The length of a rectangle is 3 inches longer than its width. If the perimeter of the rectangle is 62 inches , find its length and width

Final answer:

The reference angle of -150 degrees is found by first determining the positive angle in standard position by adding 180 degrees, resulting in 330 degrees. Since 330 degrees is in the fourth quadrant, we subtract it from 360 degrees to get the reference angle, which is 30 degrees.

Explanation:

To find the reference angle of -150 degrees, we must determine the smallest angle between the terminal side of the given angle and the x-axis. A reference angle is always positive and measured between 0 to 90 degrees. Since -150 degrees is in the third quadrant when considering standard position in a coordinate system, where angles are measured counterclockwise from the positive x-axis, you add 180 degrees to determine its corresponding positive angle in the second quadrant. Therefore, the reference angle of -150 degrees is:

180° - (-150°) = 180° + 150° = 330°

Since 330 degrees is in the fourth quadrant, to find the reference angle, we subtract it from 360 degrees:

360° - 330° = 30°

Thus, the reference angle for -150 degrees is 30 degrees.

[tex](4t-\dfrac{8}{5})-(3-\dfrac{4}{3}t)---------------\dfrac{16t}{3}-\dfrac{23}{5}[/tex]

[tex]5(2t+1)+(-7t+28)--------------3t+33[/tex]

[tex](\dfrac{-9}{2}t+3)+(\dfrac{7}{4}t+33)-----------------\dfrac{-11t}{4}+36[/tex]

[tex]3(3t-4)-(2t+10)-------------7t-22[/tex]

a)

[tex](4t-\dfrac{8}{5})-(3-\dfrac{4}{3}t)[/tex]

Firstly we will open the parentheses term and then on combining the like terms and then solving them.

[tex]=4t-\dfrac{8}{5}-3+\dfrac{4}{3}t\\\\i.e.\\\\=4t+\dfrac{4}{3}t-\dfrac{8}{5}-3\\\\=\dfrac{4t\times 3+4t}{3}+\dfrac{-8-3\times 5}{5}\\\\=\dfrac{16t}{3}-\dfrac{23}{5}[/tex]

b)

[tex]5(2t+1)+(-7t+28)\\\\=5\times 2t+5\times 1-7t+28\\\\=10t+5-7t+28\\\\=10t-7t+5+28\\\\=3t+33[/tex]

( Here we used distributive property for first bracket and open the parentheses term and them we combined the like terms and finally simplified our terms )

c)

[tex](\dfrac{-9}{2}t+3)+(\dfrac{7}{4}t+33)[/tex]

We firstly open our parentheses term but there will be no change in the terms since the sign before parentheses is positive.

and then we will combine the like terms and simplify them.

[tex]=\dfrac{-9}{2}t+3+\dfrac{7}{4}t+33\\\\\\=\dfrac{-9}{2}t+\dfrac{7}{4}t+3+33\\\\\\=\dfrac{-9t\times 2+7t}{4}+36\\\\\\=\dfrac{-11t}{4}+36[/tex]

d)

[tex]3(3t-4)-(2t+10)[/tex]

i.e. we use the distributive property for first bracket and open second parentheses term. since the sign before the second parentheses is negative hence the sign of the terms will get interchanged.

i.e.

[tex]=3\times 3t+3\times (-4)-2t-10\\\\i.e.\\\\=9t-12-2t-10\\\\=9t-2t-12-10\\\\=7t-22[/tex]

Answer:

Cone= [tex]\frac{1}{3} *pi*r^{2}*h[/tex]    Cylinder= [tex]pi*r^{2} * h[/tex]

Step-by-step explanation:

Cone volume= 1/3 × π × r²×h            Cylinder volume= π × r² × h

                        1/3 × π × 15²×7                                         π × 15² × 7

                        1/3 × π × 225×7                                       π × 225 × 7

                        525π                                                       1575π

Using the surface area of a sphere, it is found that the total surface area that will be painted is of 769.69 cm².

The surface area of a sphere of radius r is given by:

[tex]S = 4\pi r^2[/tex]

In this problem, we have five spheres, with radius(half the diameter) r = 3.5 cm, hence the total surface area in square centimeters is given by:

[tex]S_t = 5 \times 4\pi \times 3.5^2 = 769.69[/tex]

The total surface area that will be painted is of 769.69 cm².

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Answer:  B) y = -4 sin(x - π/2)

Step-by-step explanation:

The graph of a sine function is the cosine function shifted π/2 units to the right.

Similarly, the graph of a cosine function is the sine function shifted π/2 units to the left.

Answer:

-20

Step-by-step explanation:

-2(3^2)+3-5

-2(9)+3-5

-18+3-5

-18-2

-20

Answer:

-20

Step-by-step explanation:

The guy before me said so

Answer:

y-axis The vertical number line in a coordinate graph. The line in the coordinate plane, usually vertical, or in space, containing those points whose first coordinates (and third, in space) are 0. y-coordinate The second coordinate of an ordered pair or ordered triple.

Step-by-step explanation:

Answer:

sqrt(61)

Step-by-step explanation:

The distance between two points is found by the following formula

d = sqrt (( x2-x1)^2 + (y2-y1)^2 )

   = sqrt( (-1--6)^2 + (1-7)^2)

  = sqrt( (-1+6)^2 + (1-7)^2)

= sqrt( (5)^2 + (6)^2)

= sqrt( 25 + 36)

= sqrt(61)

Answer:

The ratio between their surface areas = 49/9

Step-by-step explanation:

* Lets revise the similarity of to prism

- If two prisms are similar, then there is a ratio between their

 corresponding dimensions

- There is a ratio between their volumes and surface area

- The the ratio between their corresponding dimensions is a/b,

  then the ratio between their volumes is (a/b)³ and the ratio between

 their surface area is (a/b)²

* Lets solve the problem

∵ The two rectangular prisms are similar

∵ The ratio between their corresponding sides is 7/3

∴ The ratio between their surface areas = (7/3)² = 49/9

* Lets check our answer

∵ The surface area of the rectangular prism is :

  S.A = Perimeter of base × its height + 2 × area of its base

- Find the surface area of the large prism

∵ The base has dimensions 14 units and 21 units

∵ Its height = 7 units

∵ The base is a rectangle

∵ Perimeter the rectangle = 2L + 2W

∵ Area the rectangle = L × W

∴ S.A = (2×14 + 2×21) × 7 + 2(14 × 21) = 1078 unit²

- Find the surface area of the small prism

∵ The base has dimensions 6 units and 9 units

∵ Its height = 3 units

∴ S.A = (2×6 + 2×9) × 3 + 2(6 × 9) = 198 unit²

- Lets find the ratio between them

∴ The ratio between surface areas of them = 1078/198 = 49/9

- It is the same with the answer above so we are right

ANSWER

C [0,9]

EXPLANATION

The number of bottled water on the shelf is modeled by the function

[tex]4x + y = 36[/tex]

We make y the subject to obtain;

[tex]y = 36 - 4x[/tex]

When no water is sold, then x=0.

When all the bottles are sold, then

[tex]4x - 36 = 0[/tex]

[tex]4x = 36[/tex]

[tex]x = \frac{36}{4} = 9[/tex]

Therefore the store cannot sell more than 9 bottles.

The domain is [0,9]

Answer:

1. J=10

2. L<=7

3. h>32

4. O=15

5. q<=17

Step-by-step explanation:

J/10+4=5

subtract 4 from both sides

j/10=1

multiply 10 by both sides

j=10

-7L+5>=-49

subtract 5 from both sides

-7L>=-49

divide by -7 and change your symbol

L<=7

9+h/2>16

subtract 9 from both sides

h/2>16

multiply by 2 on both sides

h>32

O-5/2=5

multiply by 2 on each side

O-5=10

add 5 on each side

O=15

8q+2<=138

subtract 2 from both sides

8q<=136

divide by 8 on both sides

q<=17

Answer:

x= −6

Step-by-step explanation:

you are supposed to isolate the variable by dividing both sides by the factor that do not contain the variable

ANSWER

C 6

EXPLANATION

The given equation is

[tex] - \frac{1}{2} (3x - 4) = 11[/tex]

Multiply through by -2 to get:

[tex] - \frac{1}{2} \times - 2(3x - 4) = 11 \times - 2[/tex]

[tex]3x - 4 = - 22[/tex]

Add 4 to both sides of the equation:

[tex]3x = - 22 + 4[/tex]

[tex]3x = - 18[/tex]

Divide both sides by 3.

[tex]x= - \frac{18}{3} [/tex]

This simplifies to

[tex]x = - 6[/tex]

The correct answer is C

Answer:

Area = 40

Step-by-step explanation:

The area of a rhombus is

Area = a*b/2

Where a and b are the lengths of the diagonals.

Area = 8 * 10/2

Area = 40

Answer:

40

Step-by-step explanation:

In a rhombus the two diagonals intersect perpendicularly. So you can see a rhombus as the union of two triangles whose base is one of the diagonals of the rhombus and whose height is the half of the other diagonal.

Therfor you can calculate the area of the rhombus calculating the area of the two triangles that are the same.

In this case the area of each triangle must be  [tex]\frac{4\times 10}{2}= 20[/tex] (if you take the 10-lenght-side as the basis of the triangles).

Hence the area of the rhombus is 40 because is the double of the area of each triangle.

Hey There!

To find how many seats are needed to be added, you need to subtract 15,340 by 13,451. You need to find the difference between the seats you need and the seats you have. So...

15,340-13,451= 1,889

You need to add 1,889 more seats.

Hope This helped!

Godspeed,

SongBird

Answer:

The required equation is 13451 + x = 15340,

1,889 seats are needed.

Step-by-step explanation:

Given,

Original number of seats = 13,451,

Also, the number of people who needed to be seated = 15,340,

Let x seats were added,

So, the new number of seats = 13451 + x

Thus, 15,340 will get the seat,

If total seats = 15340

⇒ 13451 + x = 15340

Which is the required equation,

Subtract 13451 on both sides,

We get,

x = 1889

Hence, 1889 seats are needed to accommodate all the people.

[tex]b=a+5[/tex]

Hope this helps.

Answer:

b=a+5

Step-by-step explanation:

6-1=5

7-2=5

8-3=5

9-4=5

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Answer: 48

96/2 = 48 cm

Answer:

ab = 48 cm

Step-by-step explanation:

Supposing ABC is a right angled triangle where m∠B = 90°, ac = 96 cm and c = 30°, we are to find the length of the side ab in cm.

For this, we will use the trignometric ratios to find ab.

[tex] sin B = \frac { a b } { a c } [/tex]

[tex] sin 30 = \frac { a b } { 9 6 } [/tex]

[tex]\frac{1}{2} =\frac{ab}{96}[/tex]

[tex]96=2ab[/tex]

[tex]ab=\frac{96}{2}[/tex]

ab = 48 cm

Answer:

a) Ellipse

b) Sphere

c) Great circle

d) Triangle

e) Circle

Step-by-step explanation:

A) Diagonal cross section of cylinder

Ellipse

B) Shape created when a semi circle is rotated about y axis

Sphere

C) Diagonal cross section through the widest part of sphere

Great Circle

D) Perpendicular cross section of cone

Triangle

E) Cross section parallel to the base of cone

Circle.

Answer:

880

Step-by-step explanation:

First we have to convert 1 mile into inches.

1 mi * 5280 ft/mi * 12 in/ft = 63,360 inches

Each rotation covers 72 inches, so the number of rotations is:

63,360 in / (72 in / rotation) = 880 rotations

Answer:

880

Step-by-step explanation:

I got it right on my test.

Answer:

x = -4.5

Step-by-step explanation:

We shall be using the following property of logarithms;

[tex]lna+lnb=ln(a*b)[/tex]

Therefore, In -x + In 8 can be re-written as;

[tex]ln-x+ln8=ln(-8x)\\\\ln(-8x)=ln36\\\\-8x=36\\\\x=-4.5[/tex]

Answer:

The answer is D.The arrangement of words and phrases suggests a thought process that flits from thought to thought.

Step-by-step explanation:

The best description of the syntax in the given text indicates that the arrangement of words and phrases suggests a thought process that moves erratically from one thought to another, reflecting the text's stream-of-consciousness style and mixed sentence constructions.

The question involves analyzing an excerpt for the syntax used, which refers to the manner by which words are organized into sentences. Among the given choices, the best description that matches the details provided about the text would be D) The arrangement of words and phrases suggests a thought process that flits from thought to thought. This is supported by the description of the text which includes mixed sentence constructions, lack of consistency in grammatical paths, and an attempt by the author to meet or challenge conventional expectations in rhetorically effective ways. The text also mentions the replication of a child's growing awareness and a stream-of-consciousness style which implies a thought process that is not linear but more erratic and intuitive, which is characteristic of syntax that flits from thought to thought.

6 ft person casts 18 ft shadow

x ft tree casts 20 ft shadow

6*20 = 18x

120 =18x

x=120/18

×≈6.67

The height of the tree is 6.67 feet.

The term proportionality describes any relationship that is always in the same ratio.

Given that, a tree casts a 20-foot shadow at the same time the person who is 6 feet tall casts a shadow 18 ft, we need to find the height of the tree.

Here, using the concept of proportionality, since, the phenomena is happening at the same time, therefore, the ratio of the height and length if the shadow will be equal for all.

Let the height of the tree be x,

20 / x = 18 / 6

120 = 18x

x = 6.67

Hence, the height of the tree is 6.67 feet.

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We have the function [tex]y = \frac{2}{3} x -3[/tex] and we want to find a function that has the same y-intercept than the previous function.

First, let's find the y-intercept by subtituting 0 for 'x'.

[tex]y = \frac{2}{3} (0) -3 = -3[/tex]

Now that we found that y-intercept =-3, any lineal function of the type: [tex]y = ax - 3[/tex] will have the same y-intercept. Where 'a' can take all the real values.

Also, any quadratic function of the type: [tex]y=ax^{2} + bx - 3[/tex] will have the same y-intercept. Where 'a' and 'b' can take all the real values.

Answer:

C

Step-by-step explanation:

We know a straight angle is 180 degrees ( a straight line).

Looking at the figure, we can say that A + F + E = 180 (since it creates a straight line).

We know A = 45, E = 85, plugging these into the equation, we can solve for F:

A + F + E = 180

45 + F + 85 = 180

130 + F = 180

F = 180 - 130

F = 50

Answer choice C is right.

Answer:

12.00, 37.70

Step-by-step explanation:

Area of a circle is:

A = πr²

We know A = 113.1 ft², so:

113.1 = πr²

r² = 36.00

r = 6.00

The diameter is double the radius, so:

d = 2r

d = 12.00

The diameter is 12 feet.

The circumference is:

C = 2πr

We found that r = 6 ft, so:

C = 2π (6)

C = 37.70

The circumference is 37.70 ft.

Answer:

see explanation

Step-by-step explanation:

The common difference d of an arithmetic sequence is

d = [tex]a_{2}[/tex] - [tex]a_{1}[/tex] = [tex]a_{3}[/tex] - [tex]a_{2}[/tex]

Substitute in values and solve for k, that is

5k - 1 - 2k = 6k + 2 - (5k - 1)

3k - 1 = 6k + 2 - 5k + 1

3k - 1 = k + 3 ( subtract k from both sides )

2k - 1 = 3 ( add 1 to both sides )

2k = 4 ⇒ k = 2

--------------------------------------------------------

The n th term of an arithmetic sequence is

[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n - 1)d

[tex]a_{1}[/tex] = 2k = 2 × 2 = 4 and

d = 5k - 1 - 2k = 3k - 1 = (3 × 2) - 1 = 5

Hence

[tex]a_{8}[/tex] = 4 + (7 × 5) = 4 + 35 = 39

Answer:

C)The rays extend infinitely, and the angle is made by rays which have a common endpoint

Step-by-step explanation:

A ray is a line segment having one end point while extending in the other/opposite direction

An angle is made by two lines(rays) with common end point (vertex)

So when an angle is formed by the pair of intersecting rays the following options are ruled out  

A) rays cannot have two end points

B) As rays extends infinitely in one direction, so having number of points is wrong

D)angles do not have lines

the following is best explanation is C

The rays extend infinitely, and the angle is made by rays which have a common endpoint !

Answer:

I'm pretty sure that the answer is C. The rays extend infinitely, and the angle is made by rays which have a common endpoint! It seems like the most correct answer of them all!

since this a 45 45 90 right triangle to get the side lengths you divide 2 times the square root of 2 and you get 2, since this has two congruent angles which makes it an Isosceles triangle. your a and b value are 2.

Answer:4/3

Step-by-step explanation:BY PHYTHAGORAS THEOREM

OPP=X,ADJ=3,HYP=5

5^2=3^2+X^2

25=9=X^2

25-9=X^2

16=X^2

4=X

BY TRIGONOMERTRY

SOHCAHTOA

TAN=OPP/ADJ

=4/3

The answer is:

[tex]Tan(\beta)=Tan(53.13)=1.33\°[/tex]

or

[tex]Tan(\beta)=\frac{4}{3}[/tex]

To find the answer, we first need to find the value of the given angle, we can calculate it since we already know the cosine of that angle.

So, solving we have:

[tex]Cosine(\beta)=\frac{3}{5} \\\\Cosine((\beta)^{-1}=Arccos(\frac{3}{5})\\\\\beta =53.13\°[/tex]

Now, that we know that the angle is equal to 53.13°, we can calculate the value of the tangent, so:

[tex]Tan(\beta)=Tan(53.13)=1.33\°[/tex]

Also, we can find it using the Pythagorean Theorem and the trigonometric identities:

We have that:

[tex]Cosine=\frac{Adjacent}{Hypothenuse}[/tex]

So, using the given information we have:

[tex]Cosine=\frac{3}{5}[/tex]

Where,

Hypothenuse, is equal to 5.

Adjacent, side is equal to 3.

So, we are looking for the opposite side.

Then, substituting it into the Pythagorean Theorem formula, we have:

[tex]Hypothenuse^{2}=Adjacent^{2}+Opposite^{2}\\\\5^{2}=3^{2}+Opposite^{2}\\\\Opposite^{2}=25-9=16\\\\Opposite=\sqrt{16}=4[/tex]

Now that we already know the opposite side, we can find the value of the tangent that will be:

[tex]Tan(\beta)=\frac{Opposite}{Adjacent}=\frac{4}{3}[/tex]

Have a nice day!

Hey there! :)

Equation 1 : -5x + 3y = 2

Equation 2 : -5x - 5y = -30

Because both equations contain a like term (which in this case is 5x), we can easily subtract these equations from one another.

Subtract equation 1 from equation 2 :

-5x - (-5x) = 0

3y - (-5y) = 3y + 5y --> 8y

2 - (-30) = 2 + 30 --> 32

This leaves us with 8y = 32. Simplify this to get y by dividing both sides by 8.

8y ÷ 8 = 32 ÷ 8

Simplify.

y = 4

Now, plug in 4 for y in our first equation.

-5x + 3(4) = 2

Simplify.

-5x + 12 = 2

Subtract 12 from both sides.

-5x = 2 - 12

Simplify.

-5x = -10

Divide both sides by -5.

-5x ÷ -5 = -10 ÷ -5

Simplify.

x = 2

Therefore, our answer is :

(2, 4) where x = 2, y = 4

~Hope I helped!~

Answer:

None of the above

Step-by-step explanation:

2 r + ( t + r )

2 r + t + r

3 r + t