The second side of a triangular deck is 3 feet longer than the shortest​ side, and the third side is 3 feet shorter than twice the length of the shortest side. If the perimeter of the deck is 72 feet, what are the lengths of the three​ sides?

Answer:

6

Step-by-step explanation:

f(2) = 10-4 = 6

Answer:

[tex] \sf \: d) \: 6[/tex]

Step-by-step explanation:

Given function,

→ f(x) = 5x - 4

We have to find,

→ The required value of f(2).

Now value of f(2) will be,

→ f(x) = 5x - 4

→ f(2) = 5(2) - 4

→ f(2) = 10 - 4

→ [ f(2) = 6 ]

Therefore, the answer is 6.

The transformation used are:

(a)

This is a translation of one unit to the left and one unit up.

(b)

- There is a vertical stretch of 2 units.

- This is a translation of four units down.

It is the movement of the shape in the left, right, up, and down directions.

The translated shape will have the same shape and shape.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

The graph from y = h(x) to y = h(-x)  + 1.

This is a translation of one unit to the left and one unit up.

The graph from y = g(x) to y = 2g(x)  - 4.

- There is a vertical stretch of 2 units.

- This is a translation of four units down.

Now,

The graph of y = h(-x)  + 1 is given below.

The graph of y = 2g(x)  - 4 is given below.

Thus,

(a)

This is a translation of one unit to the left and one unit up.

(b)

- There is a vertical stretch of 2 units.

- This is a translation of four units down.

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Answer:

Step-by-step explanation:

You want to order the accounts greatest to least by their value after 10 years.

The value of each account can be found using the compound interest formula:

  A = P(1 +r/n)^(nt)

Principal P earning rate r compounded n times per year for t years.

For the three accounts, the corresponding values are ...

The order, greatest to least, according to the account values is ...

__

Additional comment

The $700 account will overtake the $950 account after 11 years. It will take about 46 years for it to overtake the $800 account. Eventually, the higher interest rate with greater frequency of compounding wins out.

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Answer:

Angle P= Angle W=2(2x-6)

=4x-12

Answer:

Step-by-step explanation:

6

The value of the expression is -11/15

It is important to note that algebraic expressions are expressions having factors, constants, variables, coefficients and terms.

From the information given, we have that;

3 1/2x - 5 1/3x

turn into improper fractions

7x/2 - 16x/3

Now, let's determine the value by substituting the  value of x as 2/5 in the expression, we have;

7(2/5)/2 - 16(2/5)/3

Multiply the values

14/5/2 - 32/5 /3

Take inverse of the denominator

14/5 ×1/2 - 32/5 × 1/3

7/5 - 32/15

21 - 32/15

-11/5

Hence, the value is -11/15

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The value of x is 12. The solution has been obtained by using trigonometry.

What is trigonometry?

The primary objective of the branch of mathematics known as "trigonometry" is the study of the sides, angles, and connections of the right-angle triangle. The angles of 0, 30, 45, 60, and 90 degrees are the most typical trigonometric angles to be utilised in computations.

We are given a right - angled triangle with one angle equal to 24° and the length of the base is 11.

Using trigonometry,

We know that cos theta = adjacent side/hypotenuse

So,

⇒cos θ = 11/x

Here, θ = 24°

So,

⇒cos 24° = 11/x

⇒x = 11/cos 24°

⇒x ≈ 12.04

⇒x ≈ 12

Hence, the  value of x is 12.

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Answer: The formula for exponential decay is given by:

P(t) = P0 * e^(-rt)

where P(t) is the profit at time t, P0 is the initial profit, r is the rate of decrease in percentage, and t is the time elapsed in years.

In this case, P0 = $9500, r = 0.9%, and t = 5 (the time elapsed from 2014 to 2019).

First, we need to convert the rate of decrease from a percentage to a decimal:

r = 0.9% / 100 = 0.009

Now, we can plug in the values into the exponential decay formula:

P(5) = $9500 * e^(-0.009 * 5) = $9500 * e^(-0.0455)

We can calculate the value of e^(-0.0455) using a calculator or mathematical software. The result is approximately 0.955.

Therefore, the profit in 2019 is:

P(5) = $9500 * 0.955 = $9027.25

So, the profit in 2019 would be $9027.25.

Step-by-step explanation:

Answer:

18x+9

Step-by-step explanation:

Answer: 18x + 9

Step-by-step explanation:

1) Combine like terms 23x -5x to get a new equation of 18x + 9.

The inverse of the given function is f(x) = 2x/(1 - x)

What is a function?

A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two varying quantities.

Given function is

f(x) = x/(2+x)

Assume that y = f(x) = x/(2+x)

Solve y = x/(2+x) for x:

y = x/(2+x)

Multiply (2+x) on both sides:

y(2+x) = x

2y + xy = x

Subtract xy from both sides:

2y = x - xy

2y = x(1 - y)

x = 2y/ (1 - y)

Now replace x with y and y with x:

y = 2x/(1 - x)

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Answer:

Step-by-step explanation:

What is the least number and greatest number of shells he would need

To find the weight of 4.3 cubic feet of water, we need to first find the number of gallons of water that 4.3 cubic feet holds and then multiply that by the weight of 1 gallon of water.

1 cubic foot holds 7.48 gallons of water, so 4.3 cubic feet holds 4.3 x 7.48 = 31.964 gallons.

1 gallon of water weighs 8.33 pounds, so 31.964 gallons of water weigh 31.964 x 8.33 = 265.9012 pounds.

Therefore, 4.3 cubic feet of water weigh 265.9012 pounds.

To find the weight in tons, we need to divide the weight in pounds by 2000:

265.9012 pounds ÷ 2000 = 0.13295 tons

So 4.3 cubic feet of water weigh 0.13295 tons.

Answer:

0.13314 tons.

Step-by-step explanation:

We can start the calculation by first converting the cubic feet of water to gallons and then converting the gallons to pounds.

Conversion from cubic feet to gallons:

4.3 cubic feet = 4.3 cubic feet * 7.48 gallons/cubic foot = 32.084 gallons

Conversion from gallons to pounds:

32.084 gallons = 32.084 gallons * 8.33 pounds/gallon = 266.279 pounds

Conversion from pounds to tons:

266.279 pounds = 266.279 pounds / 2000 pounds/ton = 0.13314 tons

So, 4.3 cubic feet of water weigh 266.279 pounds or 0.13314 tons.

The length of the dotted line would be 7.922 ft.

A circle's diameter is measured from the center of the circle outward. It is equivalent to twice the radius, or the distance a circle's radius is measured from its center to any other point on the circle.

The mathematical formula for a circle's diameter is d = 2r if d is the circumference and r is the radius.

When we subtract the circle's thickness from its outer diameter to determine the provided circle's inner diameter, we obtain q = 17.708 - 4.893 - 4.893.

We can solve this for q = 7.922

The dotted line would be 7.922 feet long as a result.

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The ratio that is equivalent to the greatest fraction is B. 8:4.

A ratio is a relative size or value contained in another quantity.  It is computed as the quotient of the smaller and larger values.

Ratios are fractional values, which we can depict as fractions, decimals, or percentages.

Ratios are also depicted using the ratio symbol (:), describing the numerical relationship between two or more values or variables.

The sum of ratios = 8

5/8 = 0.625

The sum of ratios = 12

8/12 = 0.67

The sum of ratios = 9

2/9 = 0.22

The sum of ratios = 14

9/14 = 0.64

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The Main Street is 1/12 of a mile longer than the Oak Street

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

Difference = Main Street - Oak Street

substitute the known values in the above equation, so, we have the following representation

Difference = 1/3 - 1/4

Evaluate the difference

Difference = 1/12

Hence, the difference is 1/12 of a mile

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Answer:

Step-by-step explanation:

Range: the difference between the highest and lowest values

Heights:

130

142

142

143

144

145

147

147

149

150

151

153

154

154

158

161

162

Formula to find the range

R= H-L

R = range

H = highest value

L = lowest value

    R = 160 - 130.

The range is 30.

Answer:

$2160

Step-by-step explanation:

Area of a rectangle = Length * Width

A = L * W

Divide both sides by width

W/(A = L * W)/w

[tex]\frac{A}{W} = L[/tex]

Plug in values

[tex]\frac{384}{24} =16[/tex]

Multiply Length and width to find perimeter

2W + 2L = P

plug in values

2(24) + 2(16) =  80

Multiply perimeter by cost per foot

1yd = 3ft

80yd * 3ft = 240ft

240ft * $9 = $2160

The trait would be MOST useful for these farmers is to be considered as the fast growth rate.

The main goal of science that should create knowledge and understanding.

Since the plan for using the breeding to produce a new type for the wheat for farmers that lived in the northern areas.

The growth rate of a value (GDP, turnover, wages, etc.) measures its change from one period to another (month, quarter, year). It is very generally expressed as a percentage.

The annual average rate of change of the gross domestic product (GDP) at market prices based on constant local currency, for a given national economy, during a specified period of time.

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Faith earned £96 in interest at the end of the 3 years.

Using the  simple interest formula:

I = P x r x t

where

I is the interest earned,

P is the principal or initial amount invested,

r is the interest rate as a decimal, and t is the time period in years.

In this case, Faith invested £800 for 3 years at a simple interest rate of 0.4% per year, or 0.04 as a decimal. Plugging in the values:

I = £800 x 0.04 x 3

= £96

Therefore, Faith earned £96 in interest at the end of the 3 years.

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Step-by-step explanation:

Same as the triangles. Find the area of the large rectangle and the small rectangle, then subtract.

A = L x W

For the large rectangle

A = 30 x 25 = 750

For the small rectangle

A = 26 x 21 = 546

Now to subtract these two

750 - 546 = 240

The exponential regression equation that best fits the data in the table is given as follows:

C. f(t) = 11.9(1.12)^t.

The standard definition of an exponential function is given as follows:

y = a(b)^x.

In which:

For this problem, we have that the parameters are estimated as follows:

This means that the correct option is given by option C.

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1) The length of the missing side of the right triangle is 34.

2) The values of the six trigonometric functions of θ are:

sin θ = sin A = 8/17

cos θ = cos A = 15/17

tan θ = tan A = 8/15

csc θ = csc A = 17/8

sec θ = sec A = 17/15

cot θ = cot A = 15/8

What is Pythagorean Theorem?

Pythagoras Theorem is a method for calculating the missing length of a right-angled triangle. The triangle has three sides: the hypotenuse (which is usually the longest), the opposite (which does not touch the hypotenuse), and the adjacent (which is always the shortest) (which is between the opposite and the hypotenuse).

Part 1

To find the length of the missing side (c) of the right triangle, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, we have:

a² + b² = c²

Substituting the given values, we get:

16² + 30² = c²

Simplifying, we get:

256 + 900 = c²

1156 = c²

Taking the square root of both sides, we get:

c = sqrt(1156) = 34

Therefore, the length of the missing side of the right triangle is 34.

Part 2

To find the values of the six trigonometric functions of θ, we need to know one of the acute angles of the triangle. Let's call the acute angle opposite side a as angle A. Using the given values, we can find the sine, cosine, tangent, cosecant, secant, and cotangent of angle A as follows:

sin A = a/c = 16/34 = 8/17

cos A = b/c = 30/34 = 15/17

tan A = a/b = 16/30 = 8/15

csc A = 1/sin A = 17/8

sec A = 1/cos A = 17/15

cot A = 1/tan A = 15/8

Therefore, the values of the six trigonometric functions of θ are:

sin θ = sin A = 8/17

cos θ = cos A = 15/17

tan θ = tan A = 8/15

csc θ = csc A = 17/8

sec θ = sec A = 17/15

cot θ = cot A = 15/8

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Answer:

a.  2p + 2d + 1c + 1p + 1c + 2p + 1d

b. 5p + 3d + 2c

c. In an algebraic expression each term can only be combined with another like term. For example x terms can be combined only with x terms, y terms can be combined only with y terms etc.

This is similar to the above example in which pizza(p) can only be combined with pizza(p), drinks (d) can only be combined with drinks(d) and cone(c) can only be combined with cone(c)

Step-by-step explanation:

a.
From the cute diagram we see that the family bought

2 pizzas + 2 drinks + 1 cone + 1 pizza + 1 cone + 2 pizzas + 1 drink

Using the variables provided, this becomes

2p + 2d + 1c + 1p + 1c + 2p + 1d

b.
Combining like terms the total purchase is:
(2p + 1p + 2p) + (2d + 1d) + (1c + 1c)

Adding the coefficients of each grouped term we get

(5p) + (3d) + (2c)

Opening the brackets, this becomes
5p + 3d + 2c

c.
In an algebraic expression each term can only be combined with another like term. For example x terms can be combined only with x terms, y terms can be combined only with y terms etc.

This is similar to the above example in which pizza(p) can only be combined with pizza(p), drinks (d) can only be combined with drinks(d) and cone(c) can only be combined with cone(c)

The area of the kite is 0.08 metres squared.

A kite is a quadrilateral. Therefore, the window has the shape of a kite. The square metres of glass that will be used to construct the kite can be calculated as follows:

The area of a kite is half the products of the diagonals of the kite.

Therefore,

area of the kite = 1 / 2 pq

where

Therefore,

p = 20 + 20 = 40 cm

q = 25 + 15 = 40 cm

Hence,

area of the kite = 1 / 2 × 40 × 40

area of the kite = 1600  /2

area of the kite = 800 cm²

area of the kite = 0.08 m²

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Answer:

Step-by-step explanation:

x/sin90=17.3/sin53

sin90=1

x=17.3/sin53

x=13.8

Answer: y > 8

Step-by-step explanation:

6 - 5y < -34

-5y < -40

y > 8

[tex]6-5y < -34[/tex]

Simplify:

[tex]-5y+6 < -34[/tex]

Subtract 6 from both sides:

[tex]-5y+6-6 < -34-6[/tex]

[tex]-5y < -40[/tex]

Since we are dividing by a negative number, the sign will reverse.

Divide both sides by -5:

[tex]\dfrac{-5y}{-5} > \dfrac{-40}{-5}[/tex]

[tex]\boxed{y > 8}[/tex]

We obtain the sum of the expressions as 5z + 1. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

Four fundamental mathematical operations which can be used to express any real number are known as arithmetic operations. The four  operations are addition, subtraction, multiplication and division.

We are given two expressions as 3z - 4 and 2z + 5.

In order to add the expressions, we will add the like terms.

On adding the like terms, we get

⇒(3z - 4) + (2z + 5)

⇒3z + 2z - 4 + 5

⇒5z + 1

Hence, we get the expression as 5z + 1.

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a)The standard deviation is given by σ = sqrt(np(1-p)) = sqrt(24 × 0.75 × 0.25) = 2.12 . b)Significantly low: μ - 2σ = 18 - 2 × 2.12 ≈ 13.76 ,Significantly high: μ + 2σ = 18 + 2 × 2.12 ≈ 22.24 ,c)z = (x - μ) / σ = (3 - 18) / 2.12 ≈ -7.08.

A group of 24 peas with green pods has a binomial distribution with n = 24 and p = 0.75. The mean is calculated as = np = 24 0.75 = 18, and the standard deviation is calculated as = sqrt(np(1-p)) = sqrt(24 0.75 0.25) = 2.12 (rounded to two decimal places).

b) The range rule of thumb states that results that deviate from the mean by more than two standard deviations are considered significantly low or significantly high. In this case, the values separating significantly low and significantly high results are:

Significantly reduced: - 2 = 18 - 2 2.12 13.76

Significantly greater: + 2 = 18 + 2 2.12 22.24

c) To see if a result of three peas with green pods is significantly low, we must calculate its z-score, which is given by:

z = (x - μ) / σ = (3 - 18) / 2.12 ≈ -7.08

Because the z-score is much lower than -2, the cutoff for significantly low results, we can conclude that a result of 3 peas with green pods is significantly low.

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Answer: a) Calculate the probability of getting both contracts:

The probability of getting both contracts is given by P(Contract 1 and Contract 2) = P(Contract 1) * P(Contract 2|Contract 1) = 0.4 * 0.3 = 0.12

b) Calculate the probability of getting either contract:

The probability of getting either contract is given by P(Contract 1 or Contract 2) = P(Contract 1) + P(Contract 2) - P(Contract 1 and Contract 2) = 0.4 + 0.5 - 0.12 = 0.78

c) Calculate the probability of not getting either contract:

The probability of not getting either contract is given by P(Neither Contract) = 1 - P(Contract 1 or Contract 2) = 1 - 0.78 = 0.22.

So, there is a 22% chance that the construction firm will not get either contract.

Step-by-step explanation:

Using the fact that the figures are similar, we will find that MN = 12.4

We know that both figures are similar, then there is a scale factor that relates them.

We know the length of two correspondent sides, these are:

HI and LM

HI = 3

LM = 18.6

if k is the scale factor, then we can wite:

3*k = 18.6

k = 18.6/3 = 6.2

Now the length of MN will be 6.2 times the length of the correspondent side on the smaller figure:

MN = 6.2*2 = 12.4

That is the lenght.

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