From the top of a cliff 90 m high, the angle of depression of a boat on the sea is 26.2°. Calculate how far the boat is
a from the foot of the cliff,
b from the top of the cliff.​

The radius will be equal to 7.55 centimeters.

The arc length is the curved length on the circumference of a circle suspended by a small angle.

The radius will be calculated as follows:-

r = [tex]\dfrac{Arc}{Angle}[/tex]

r = [tex]\dfrac{\dfrac{26\pi}{9}}{\dfrac{69\times \pi}{180}}[/tex]

r = [tex]\dfrac{9.07}{1.20}[/tex]

r = 7.55 centimeters

Therefore the radius will be equal to 7.55 centimeters.

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[tex] \sf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve for z and x ~

[tex]\qquad \sf  \dashrightarrow \: 82 + z = 180[/tex]

[ they form co-interior angle pair ]

[tex]\qquad \sf  \dashrightarrow \: z = 180 - 82[/tex]

[tex]\qquad \sf  \dashrightarrow \: z = 98 \degree[/tex]

and

[tex]\qquad \sf  \dashrightarrow \: z = (5x - 82)[/tex]

[ by Alternate interior angle pair ]

[tex]\qquad \sf  \dashrightarrow \: 98 = 5x - 82[/tex]

[tex]\qquad \sf  \dashrightarrow \: 5x = 98 + 82[/tex]

[tex]\qquad \sf  \dashrightarrow \: 5x = 180[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 180 \div 5[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 36 \degree[/tex]

Answer:

z = 98

x= 36

Step-by-step explanation:

z + 82 = 180 -> due to same side interior angles adding up to 180

z = 180 - 82

z = 98

z = 5x - 82 due to opposite interior angles being equal

98 = 5x - 82

98+82 = 5x - 82+82

180 = 5x

180/5 = 5x/5

36 = x

To check:

z = 5x - 82

(98) = 5(36) - 82

98 = 180 - 82

Answer:

The values x = 7 and y = 3 make the equation true.

Step-by-step explanation:

hope this helps

The area of the square is 16 square inches and its perimeter is 16 inches.

What is Area of square ?

A square is a two-dimensional geometric shape with four equal sides and four right angles. The area of a square is the measure of the region enclosed by the square. The area is expressed in square units, such as square inches, square meters, or square feet.

The area of a square is given by the formula:

A = s²

where A is the area and s is the length of a side.

If the side length of the square is 4 inches, the area can be calculated as:

A = 4² = 16 square inches.

The perimeter of a square is given by the formula:

P = 4s

where P is the perimeter and s is the length of a side.

If the side length of the square is 4 inches, the perimeter can be calculated as:

P = 4 x 4 = 16 inches.

Therefore, the area of the square is 16 square inches and its perimeter is 16 inches.

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Answer:

1317 is the additive inverse of x = -1317.

Step-by-step explanation:

Additive inverse of a number which when added to the original number gives zero as the result.

Additive inverse of x = -1317

-1317 + 1317 = 0

1317 is the additive inverse of x = -1317.

Verification of -(-x) = x

L. H. S

-(-x) = -{-(-1317)}

= - 1317

R. H. S

x = -1317

Thus, L.H.S. = R.H.S

-(-x) = x

Verified

Answer:

11

Step-by-step explanation:

The value of x will be 4 ,  Option A is the answer.

A triangle that has one angle as 90 degree is called a Right angled Triangle.

In a right angled triangle

the length of the sides can be determined using Pythagoras Theorem

The length of the side is given in the image attached as

x-2 , x , √20

Hypotenuse ² = Perpendicular² + Base²

(√20)² = x² + (x-2)²

20 = x² + x² +4 -4x

2x²-4x -16 = 0

x² -2x -8 = 0

x² - 4x +2x -8 = 0

x (x-4) +2(x-4) = 0

(x+2)(x-4) = 0

x = -2 , 4

The value of x will be 4 .

Therefore Option A is the answer.

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Step-by-step explanation:

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The graph is plotted and attached in the attachment. The given equation is a linear equation with the intercept 0.

A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation one variable is present then the equation is known as the linear equation in one variable.

If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as y = mx + c.

Given equation;

y + 2 = (x+2)

Rearrange the equation;

y + 2 = x+ 2

y=x

The standard equation for the straight line is;

y = mx + c

Where c is the intercept and m is the slope

After comparing the given equation with the standard equation we get;

m = 1

c =0

Hence,the graph is plotted and attached in the attachment.

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Step-by-step explanation:

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The solution of the given expression is [tex][p^{2}(p-y)^{y-1} (p-y)^{y-2} -2p(p-y)^{y} (p-y)^{y-2} +7(p-y)^{y} (p-y)^{y-1}]/ (p-y)^{y} (p-y)^{y-1}(p-y)^{y-2}[/tex]

Given [tex]p^{2} /(p-y)^{y} -2p/(p-y)^{y-1} +7/(p-y)^{y-2}[/tex]

We have to solve the above expression.

We know that expression is a combination of numbers, symbols, variables and coefficients, indeterminants. Expression shows relationship between variables. LCM is the smallest number that is divisible by both the numbers whose LCM has been taken. Coefficients are present in the beginning of variables. Symbols are arithmetic signs like addition, subtraction, multiplication and division, etc.

We have to take LCM of the expression and solve accordingly so that the expression can be solved =

[tex]p^{2} /(p-y)^{y} -2p/(p-y)^{y-1} +7/(p-y)^{y-2}[/tex]=  [tex][p^{2}(p-y)^{y-1} (p-y)^{y-2} -2p(p-y)^{y} (p-y)^{y-2} +7(p-y)^{y} (p-y)^{y-1}]/ (p-y)^{y} (p-y)^{y-1}(p-y)^{y-2}[/tex]

Hence the expression  [tex]p^{2} /(p-y)^{y} -2p/(p-y)^{y-1} +7/(p-y)^{y-2}[/tex] is equal to = [tex][p^{2}(p-y)^{y-1} (p-y)^{y-2} -2p(p-y)^{y} (p-y)^{y-2} +7(p-y)^{y} (p-y)^{y-1}]/ (p-y)^{y} (p-y)^{y-1}(p-y)^{y-2}[/tex]

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Based on the information provided, the table that best matches the data in the scatter plot is shown below.

A scatter plot is a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.

Based on the information provided, the table that best matches the data in the scatter plot is given by:

Data                       1    2    4    5.5    6.3

Height (cm)            1    2    3     4       5

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Area of the rectangle is 96.05 sq.units , The ratio of the areas is 2/3 , Area of rectangle ABEF is 64.03 sq.units.

The complete question is

In the figure, the ratio of the area of rectangle ABEF to the area of rectangle ACDF is(a)_____ . If the coordinates of point A are (0,6), the area of rectangle ABEF is(b)____ square units, and the area of rectangle ACDF is(c)____ square units.  The perimeter of rectangle BCDE is(d)____ units.

A rectangle is a polygon with four sides and for angles and four vertices , Its opposite sides are parallel and equal.

The  area of rectangle ACDF is square units. = ?

The perimeter of rectangle BCDE is units. = ?

[tex]\rm d = \sqrt{ (y_2 -y_1 )^2 + (x_2 -x_1)^2}\\\\\rm d = \sqrt{ (2 - 6 )^2 + (5 - 0)^2}[/tex]

d = 9.605

the length of  [tex]\rm EF[/tex]

[tex]\rm FE[/tex] = 10 units.

and [tex]\rm FD[/tex] = 15 units

Area of a Rectangle [tex]\rm ACDF[/tex] is given by

Length x width

10 * 9.605

Area of the rectangle is 96.05 sq.units

Perimeter of a rectangle is = 2( length + breadth)

ED = FD-FE = 15- 10 = 5 units

Therefore

Perimeter = 2 ( 5 +  √41 )

Perimeter = 22.81 units

Area of rectangle ABEF is 64.03 sq.units

The ratio of the areas

= 64.03/96.05

= 0.666667

= 2/3

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Answer:

D. None of the Above

Step-by-step explanation:

They don't relate whatsoever

You buy 3 shirts and 1 pair of pants for $32. Your friend buys 2 shirts and 3 pairs of pants for $40. How much did each item cost?

First let’s define a shirt as X and pants as Y!

In the first scenario, the equation will be 3X + Y =$32

In the second scenario, the equation will be 2X + 3Y = $40  

Now because we have two different variables (X & Y) let’s solve for one of them (Ex: Y) to simplify the equations!

3X + Y= $32—> subtract 3X on both sides of the equation  

-3X.        - 3X

Net result: Y= 32- 3X

Now we can insert this into the second equation 2X + 3Y = $40 in order to solve for X variable  

2X + 3(32-3X) = $40

2X + 96 - 9X = $40 —> simplify the equation  

-7X + 96 = $40 —> substrate 96 from both sides  

-7X = -56 —> divide both sides by -7  

X= 8  

Now reinsert 8= X into 3X + Y = $32

3(8) + Y = $32

24+ Y = $32 —> substract 24 from both sides

y = 8

ANSWER: X= 8, Y= 8

Answer:

oranges

Step-by-step explanation:

Answer: The oranges.

Step-by-step explanation: I'll set up my work below.

Mangoes: $[tex]49/7=7[/tex] =$7 per mango

Apples: $[tex]24/4=6[/tex]=$6 per apple

Oranges: $[tex]15/3=5[/tex]=$5 per orange

Given this, the cheapest fruit is the orange.

I hope this helps!! Pls mark brainliest :)

One meter is 100 cm so Tanya should plant the saplings 20 centimetres apart.

Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.

As we know;-

1 meter is 100 cm so 0.2 meters will be calculated as:-

1 meter = 100 cm

0.2 meter = 0.2 x 100 = 20 centimeters.

Therefore One meter is 100 cm so Tanya should plant the saplings 20 centimetres apart.

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Answer:

-8x²-3x+5

Step-by-step explanation:

First, add like terms.

3-6x-2x²+3x-6x²+2=

= 5-3x-8x²

Put it in standard form. To put in standard form, put the exponent from greatest to least.

-8x²-3x+5.

Hope this helps!

If not, I am sorry.

Answer:

[tex]\huge\boxed{\sf 20z\³ + 24z\² - 5z - 6}[/tex]

Step-by-step explanation:

= (5z + 6)(2z + 1)(2x - 1)

= (5z + 6)[(2z)² - (1)²]

= (5z + 6)(4z² - 1)

Distributing

= 5z (4z² - 1) + 6(4z² - 1)

= 20z³ - 5z + 24z² - 6

Arrange

= 20z³ + 24z² - 5z - 6

[tex]\rule[225]{225}{2}[/tex]

The probability that the number's units digit will be less than 5 is 0.5 that it is equal to 1/2.

Probability is a branch of mathematics concerned with numerical descriptions of how likely an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.

There are 10 possible digits, 0, 1, 2, ... 9 that make up the 5-digit number made up of integral values.

There are 5 digits that are less than 5 which are 0, 1, 2, 3, and 4 so the probability will be found by taking only those nubers which have unit's place less than 5,

By probability formula , Probability= no. of favourable outcomes/total no. of outcomes

So probability will be found that will be equal to 5/10, or 1/2

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Answer:

3.5 and 3½

Step-by-step explanation:

Half of 7 is positive 3.5 aka 3½. It can't be -7/2 or -3.5 because they result in a negative number. It also can't be 7.2 because that's too big of a number.

the initial statement is y ∝ x

to convert to an equation multiply by k the constant of variation

[tex]y = kx[/tex]

to find k use the given condition

[tex]y = 27 \\ \\ when \\ \\ x = 3[/tex]

[tex]y = kx \\ \\ k = \frac{y}{x} = \frac{27}{3} = 9[/tex]

equation is y = 9x

when x = 4 then

[tex]y = 9 \times 4 = 36.[/tex]

Answer:

y = 36

Step-by-step explanation:

given y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation

to find k use the condition y = 27 when x = 3 , then

27 = 3k ( divide both sides by 3 )

9 = k

y = 9x ← equation of variation

when x = 4 , then

y = 9 × 4 = 36

Answer:

ytyt

Step-by-step explanation:

tyt5667

Answer:

Largest total : [tex]\mathsf {\frac{69}{20}}[/tex]

Smallest total : [tex]\mathsf {\frac{121}{40} }[/tex]

Step-by-step explanation:

Finding the largest total :

Finding the smallest total :

Answer:

Largest Totals : 69/20

Smallest Totals : 121/40

Step-by-step explanation:

Given:

Charlie adds together two of his four number cards. Find the largest and smallest totals that Charlie can make. Give your answers as improper fractions in their simplest form.  

Solve:

First let change all to improper fractions:
7/4      {already a improper fractions}

1 3/8  = 11/8

1 7/10 = 17/10

33/20       {already a improper fractions}

Thus we have:

7/4

11/8

17/10

33/20

According to the solving above ,

⇒ 70/40 , 55/40, 68/40, 66/40

⇒ 70/40 > 68/40 > 66/40 > 55/40

⇒ 7/4 > 1 7/10 > 33/20 > 1 3/8

⇒ Largest Totals : 7/4 + 1 7/10 = 69/20 = 3 9/20

⇒ Smallest Totals : 33/20 + 1 3/8 = 121/40 = 3 1/40

Since, it says given your answers as improper fractions in their simplest form:

Thus,

Largest Totals : 69/20

Smallest Totals : 121/40

RevyBreeze

Answer:

B

Step-by-step explanation:

Similar to the one you asked earlier.

Given from the table

1 Gallon of gas = $2.15

15 gallons of gas = $2.15 x 15

= $32.25 (B)

Answer:

A

Step-by-step explanation:

these two triangles are similar

therefore corresping sides are proportionate

12/8=9/x

12x=72

x=72/12=6

Answer:

the answer is 6

Step-by-step explanation:

i hope this is helpful

Answer:

4

Step-by-step explanation:

5

The exponential function is used. Use x as your variable common ratio.

This is pretty obviously

If it wasn't obvious we can find the common ratio r by dividing successive values:

5/1=5

25/5=5

125/25=5

625/125=5

The common ratio is the number you multiply or divide by at each stage of the sequence. You can find it by dividing two consecutive pairs of terms.

That's the common ratio.  We multiply by the first term, but the first term is one, so that has no effect.

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