A boat leaves a dock and goes 240 miles in a direction of 290 degrees. It then turns and goes 50 miles in a direction on 30 degrees. How far is the boat from the dock and in what direction?

The different values that could be be the greatest common divisor of the two integers are; 1, 2, 3, 4, 6

Let the numbers be a, b. Thus, the product of the GCD(a, b) and the LCM(a, b) will be ab.

Now, for us to get something to be a factor of the GCD we need to make it be a factor of both a, b. Thus, its' square must be a factor of 180.

Therefore, the only numbers whose square is a factor of 1800 are 1, 2, 3, 4, 6 and as such they are the only GCDs possible.

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[tex]\bullet\:{\boxed{\tt{\red{{Given :}}}}}[/tex]

• Length of the wooden box [tex](l)[/tex] = 80cm.

• Breadth of the wooden box [tex](b)[/tex] = 40cm.

• Height of the wooden box [tex](h)[/tex] = 20cm.

• Side of the square sheet paper = 40cm.

[tex]\bullet\:{\boxed{\tt{\red{{To : Find :}}}}}[/tex]

The number of sheets required.

[tex] \bullet\:{\boxed{\tt{\red{{Formula \: \: used :}}}}}[/tex]

[tex] \star{\underline{\boxed{{\sf{{{TSA}} = \underline{\underline{{\purple\sf 2(lb+bh+hl)}}}}}}}} \star[/tex]

[tex]\star{\underline{\boxed{{\sf{{{Area \: of \: square}} = \underline{\underline{{\purple{\sf side \times side }}}}}}}}}\star[/tex]

[tex]\star{\underline{\boxed{{\sf{{{Number \: of \: sheets \: required} = {{{\purple{\sf \dfrac{TSA}{area \: of \: one \: sheet}}}}}}}}}}} \star[/tex]

[tex] \bullet\:{\boxed{\tt{\red{{Concept :}}}}}[/tex]

As Quayleen wants to place the tree on a wooden block covered with coloured paper with picture of Santa Claus on it. So for knowing the number of sheets required, we need two things one the TSA and Area of one sheet. Once, we will get the values we will divide them to get the answer. Let's Start !!

[tex] \bullet\:{\boxed{\tt{\red{{Solution :}}}}}[/tex]

As we know that ::

Total surface area of cuboid [tex]\large[ \sf 2(lb+bh + hl)][/tex]

Here,

✧ Length [tex](l)[/tex] = 80cm

✧ Breadth [tex](b)[/tex] = 40cm

✧ Height [tex](h)[/tex] = 20cm

Now, by putting the values we get :

[tex] \longrightarrow 2 \bigg[ (80 \times 40) + (40 \times 20) + (20 \times 80) \bigg]\sf {cm}^{2}[/tex]

[tex]\longrightarrow 2 \bigg[ (3200) + (800) + (1600) \bigg] \sf {cm}^{2} [/tex]

[tex] \longrightarrow 2 \bigg[ 5600 \bigg] \sf {cm}^{2} [/tex]

[tex] \longrightarrow 11200 \: \sf {cm}^{2}[/tex]

Hence, the total surface area of the wooden box is 11200 cm²

Now,

The area of each sheet of paper will be :

[tex] \sf \longrightarrow side \times side[/tex]

[tex]\sf \longrightarrow (40 \times 40) \: {cm}^{2} [/tex]

[tex]\longrightarrow \sf (1600) \: {cm}^{2} [/tex]

Hence, the area of each sheet of paper is 1600 cm²

Now,

For finding the number of sheets required

[tex] \longrightarrow \tt \dfrac{total \: surface \: area \: of \: box}{ area \: of \: one \: sheet} [/tex]

[tex]\longrightarrow \sf\dfrac{ \cancel{11200}_{7}}{\cancel{1600}_{1}}[/tex]

[tex] \longrightarrow \purple{ \sf 7}[/tex]

Therefore, Quayleen requires 7 sheets.

[tex]\rule{280pt}{2pt}[/tex]

The number of boys signed up to play basketball this year is 560.

Given that, the number of boys who played basketball last year = 320.

We need to find the number of boys signed up to play basketball this year.

In mathematics, a percentage is a number or ratio expressed as a fraction of 100.

Now, the number of boys signed up to play basketball this year = 175 per cent of what it was last year.

So, the number of boys signed up to play basketball this year = 175% of 320

[tex]=\frac{175}{10} \times 320=1.75 \times 320=560[/tex]

Therefore, the number of boys signed up to play basketball this year is 560.

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Answer:

a₃ = 1.25

Step-by-step explanation:

the sum to infinity is calculated as

S ∞ = [tex]\frac{a_{1} }{1-r}[/tex]

a₁ is the first term and r the common ratio

given a₁ = 5 and S∞ = 10 , then

10 = [tex]\frac{5}{1-r}[/tex] ( multiply both sides by (1 - r)

10(1 - r) = 5

10 - 10r = 5 ( subtract 10 from both sides )

- 10r = - 5 ( divide both sides by - 10 )

r = 0.5

then

a₂ = a₁ × r = 5 × 0.5 = 2.5

a₃ = a₂ × r = 2.5 × 0.5 = 1.25

Answer:

Mark will use 1.25 pounds of pork.

Step-by-step explanation:

Let b represent the number of pounds of pork and p represent the number of pounds of beef. Since the ratio of beef to pork is 3 to 1, we have b/p = 3/1, which then becomes b = 3p. From this:

[tex]3p + p = 7[/tex]

[tex]4p = 7[/tex]

[tex]p = 1.75[/tex]

[tex]b = 3 \times 1.75 = 5.25[/tex]

Answer:

Maths is the subject which deals with numbers, calculations, areas, geometry etc

Various topics in maths are

trigonometry

geometry

airthmatic

etc

Answer:

the answer is f(x)=2x+192

Answer:

The answer is F(x)=2x+192

SECOND ONE

Step-by-step explanation:

Trust me

The second box plot represents the data 8.5, 8.3, 8.2, 8.9, 8.4, 8.2, 8.7, 8.5, 8.3, 8.5, 8.4 option second is correct.

A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.

We have a box plot shown in the picture.

The data:

8.5, 8.3, 8.2, 8.9, 8.4, 8.2, 8.7, 8.5, 8.3, 8.5, 8.4

From the data given:

The minimum value = 8.2

The maximum value = 8.9

Q1 = 8.3

Q2 = 8.4

Q3 = 8.5

As we can see in the second box plot this data is represented.

Thus, the second box plot represents the data 8.5, 8.3, 8.2, 8.9, 8.4, 8.2, 8.7, 8.5, 8.3, 8.5, 8.4 option second is correct.

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Answer:

c: -7

Step-by-step explanation:

the slope of a perpendicular line is the negative reciprocal of the original line

a way to find this is to flip the numerator and the denominator of a slope and make it negative

1/7 --> 7 --> -7

that would be your slope

The total tax rate and the sales tax will be given below.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Total selling price (TSP), State tax rate (STR), City tax rate (CTR), Total tax rate (TTR) and Sales tax (ST).

The table complete table is given below.

Item                            TSP            STR        CTR           TTR              ST

Clothing                     $81.39            3%        0%            3%            $2.44

Cell phone               $159.95           5%        0%            5%            $7.99

MP3 player               $195.55          4%         2%            6%           $11.73

Computer                $1599.75      4.88%     1.50%       6.38%      $102.06

Take-out                   $49.85         8.13%    2.50%      10.63%        $5.29

Pickup truck          $38,526.42    6.50%    1.25%        7.75%     $2985.79

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Answer:

Closer to 30.

Step-by-step explanation:

To answer this first find 40% of 90.

90*0.4=36

0.4 is the same as 40%

Hope this helps!

If not, I am sorry.

The velocity of the wind will be 50 km per hour.

The quantity which has magnitude, direction and follows the law of vector addition is called a vector.

A motorcyclist riding North along a straight road at 50 km per hour observes that the wind appeared to have a velocity of 50 km per hour from the direction North 60 degrees West.

Then the velocity of the wind will be

Let x be the speed of the wind. Then we have

x² = 50² + 50² - 2 x 50 x 50 x cos 60°

x² = 2500 + 2500 - 2500

x² = 2500

x = 50 km per hour

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Answer:

y=-4 is a function

Step-by-step explanation:

It passes the vertical line test, and each x has only one y, so it is a function.

x = -4 is NOT a function because one x has multiple y values. It does not pass the vertical line test.

Answer: Yes

Step-by-step explanation:

[tex]\frac{123}{2}=\frac{246}{4}=\frac{369}{6}=\frac{492}{8}=61.5[/tex].

Since the ratio of distance in miles and the time in hours is constant, the relationship is proportional.

Answer:

(-2,-9)

(-1,8)

(0,-5)

(1,0)

(2,7)

Step-by-step explanation:

Answer:

[tex]-75x^{7}y^{9}[/tex]

Step-by-step explanation:

Triangle JKL is mapped to Triangle MNQ by two rigid transformations. Vertex L to vertex Q translation is the first. a rotation about point L is the second transformation. Option A is correct.

A triangle is a three-sided polygon. It is one of the most fundamental geometric forms.

Two rigid transformations are used to map Triangle JKL to Triangle MNQ. The first is a translation of vertex L to vertex Q.

The second transformation is a rotation about point L.

Hence option A is correct.

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Answer: Option 3 or C. a rotation about point L

Step-by-step explanation:

I took the quiz and got 100% correct on Edge 2022. Trust me if you are working on Edge the answer is correct. The proof is down below. I hope someone finds this helpful. Good luck everyone!  :)

Answer:

x = 58°

z = 60°

y = 29( 58°)

Step-by-step explanation:

The arrows on the lines are trying to tell you that these lines are parallel to each other, whenever you see parallel lines think of *FUN* method

2y = 58° (alternate angles)

y = 29

x = 58° (alternate angles)

62° + 58° + z = 180° (sum of angles on a triangle)

120° + z = 180°

z = 60°

The other name for angle 2 is ∠DBC

The correct option is (D)

A figure which is formed by two rays or lines that shares a common endpoint is called an angle.

We know that while naming the angle we have to consider the point where the angle is made should be at center.

Hence, the angle 2 can also be written as ∠DCB.

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Answer:

D. 4

Explanation:

Linear relationship refers to relationships which give straight lines when graphed. All the segments, except segment 4, show straight-line, linear relationships.

As section 4 is curved, it show nonlinear relationship.

Answer:

x = 70 and the labeled angles are 110 and 70

Step-by-step explanation:

This is a trapezoid, the bases are parallel.

Since the bases are parallel, given two angles are supplementary and their sum is equal to 180:

x + 40 + x = 180 add like terms

2x + 40 = 180 subtract 40 from both sides

2x = 140 divide both sides by 2

x = 70 and the labeled angles are 110 and 70

Answer:

fraction:4/10 or 2/5

decimal: 0.4

percent: 40%

Step-by-step explanation:

The rectangle is divided into 10 parts, this is a total number that goes on the bottom of a fraction. 4 parts are shaded, that number goes on the top of the fraction.

4/10 is shown in the image. But 4/10 can be reduced. You should always simplify a fraction when it is possible.

4/10 = 2/5

As for the decimal, 4/10 spoken, "four tenths" tells you the decimal 0.4 (we all say "point four", but this is properly called "four-tenths" also) You can divide, because a fraction bar is a division symbol:

4÷10 OR 2÷5 and you will get the decimal 0.4

To change the decimal to a percent, multiply by 100.

0.4 × 100 is 40

0.4 is 40%

fraction:: 4/10 or 2/5 (simplified)

decimal: 0.04

percentage: 4%

Answer:

x = 4

Step-by-step explanation:

The figure in the picture is a parallelogram. In parallelograms diagonals bisect each other. That means that they divide each other in half. That means that 6x + 1 is the same as 4x + 9.

6x + 1 = 4x + 9

2x + 1 = 9

2x = 8

x = 4

Answer:

in a rectangle, opposite sides are equal in length

Step-by-step explanation:

now in this question, Pythagoras theorem is being used to find the length

we know both sides by using Pythagoras theorem find third side and get the sum to find ac+bd

Step-by-step explanation:

So it tells you that AB = 21 and AD = 28
and you to find what BD + AC is and since BD is the same length as AC
you only need to find one of them, then double it
There is a formula you use called the Pythagorean theorem
The Pythagorean theorem is A²+B²=C²  
In this problem A = 21    B = 28  and C = the length of BD
so it'll look like  21²+28²=Length of BD²  or BD²=21²+28²  now you find BD
first do 21²+28² --> 441+784 --> 1225   Now you know that 21²+28²=1225
so BD²=1225  Then to find BD, you find √1225(square root of 1225)
Which is 35     So BD=35 and you want to know what BD+AC is
so 35+35=70        

The values of the trigonometry ratios are:

1: sin α = -12/13 and tan α > 0, find cos α and cot α

Because tan α > 0, then it means that cos α and sin α are negative

So, we have:

sin²α + cos²α = 1

Substitute sin α = -12/13

(-12/13)² + cos²α = 1

This gives

cos²α = 1 - (-12/13)²

Evaluate the squares

cos²α = 1 - 144/169

Evaluate the difference

cos²α = 25/169

Take the square root of both sides

cos α = - 5/13

The cotangent ratio is represented as:

cot α = cos α/sin α

This gives

cot α = (-5/13)/(-12/13)

Evaluate

cot α = 5/12

Hence, cos α = - 5/13 and cot α = 5/12

2: tan α = -12/5 for α in quadrant IV, find sec α and cot α

Because α is in quadrant IV, then it means that sec α is positive

cot α = 1/tan α

This gives

cot α = 1/(-12/5)

Evaluate

cot α = -5/12

Also, we have:

sec²α = 1 + tan²α

Substitute tan α = -12/5

sec²α = 1 + (-12/5)²

Evaluate the squares

sec²α = 1 + 144/25

Evaluate the sum

sec²α = 169/25

Take the square root of both sides

sec α = 13/5

Hence, cot α = -5/12 and sec α = 13/5

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Answer:

10√7

Step-by-step explanation:

you can simplify the second radical and break it up into

√4 * √7 which then simplifies to 2√7 which you then multiply by 3. 4√7 + 3(2√7) which becomes 4√7 + 6√7 and then you just add the numbers Infront to get 10√7

The area of the deck that surrounds the hot tub is 17.93 m²

The area is the amount of space within the perimeter of a 2D shape.

radius = 3/2 = 1.5 m

Area of deck,

=Area of square - area of circle

= side side- πr²

=5*5 - 3.14* 1.5*1.5

= 25- 7.065

=  17.93 m²

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Answer:

8

Step-by-step explanation:

To one decimal place:

[tex]2 \sqrt{10} = 6.3[/tex]

[tex]10 \sqrt{2} = 14.1[/tex]

So there are eight integers between 2√10 and 10√2: 7, 8, 9, 10, 11, 12, 13, and 14.