Solve for x and the missing angles in the diagram below: x = The missing angles are °, ° and °.

The perimeter of the rectangle with area 174.8m² and side-length 3.8m is equal to 99.6 meters.

Area of the rectangle is equal to 174.8 m².

Length of the rectangle is equal to 3.8 m

let us consider 'w' be the width of the rectangle.

area of the rectangle = length × width

⇒ 174.8 = 3.8 × w

⇒ w = 174.8 / 3.8

⇒ w = 46 m

Perimeter of the rectangle = 2 ( length + width )

⇒ Perimeter of the rectangle = 2 ( 3.8 + 46 )

⇒ Perimeter of the rectangle = 2 ( 49.8 )

⇒Perimeter of the rectangle = 99.6 meter.

Therefore, the perimeter of the rectangle with length 3.8m and width 46m is equal to 99.6m.

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Answer: A decline of 10% per year means that the number of landlines will be multiplied by 0.9 (100% - 10%) every year.

So, in 12 years the number of landlines will be multiplied by 0.9^12 = 0.531441

So, in 12 years there will be 86,652 * 0.531441 = 46,115.69 landlines.

Rounded to the nearest whole number there will be 46,116 landlines in 12 years.

Step-by-step explanation:

Answer: 24,473

Step-by-step explanation: This is the formula for exponential decay:

y=a(1–r)t

In this formula, a is the initial amount, r is the rate of decrease expressed as a decimal, t is the elapsed time, and y is the final amount.

solve

Plug in 86,652 landlines for the initial amount, 0.1 for the rate of decrease, and 12 years for the time elapsed.

y

= a(1–r)t

y

= 86,652(1–0.1)12 Plug in values

y

= 86,652(0.9)12 Subtract

y

= 86,652(0.28242…) Simplify

y

= 24,473.08419… Multiply

Round to the nearest whole number.

24,473.08419… → 24,473

To the nearest whole number, there will be 24,473 landlines.

So, there are 52 ways to draw two cards such that the first card is a spade and the second card is a queen.

In a standard 52-card deck, there are 13 cards of each suit: spades, hearts, diamonds, and clubs. Each suit has 4 face cards (Jack, Queen, King, and Ace) and 9 numbered cards (2 through 10).

To find the number of ways to draw two cards such that the first card is a spade and the second card is a queen, we first need to determine the number of spades in the deck, and then the number of queens.

There are 13 spades in a standard 52-card deck, so there are 13 ways to draw a spade as the first card.

There are 4 queens in a standard 52-card deck (one from each suit), so there are 4 ways to draw a queen as the second card.

To find the total number of ways to draw two cards such that the first card is a spade and the second card is a queen, we multiply the number of ways to draw each card: 13 * 4 = 52 ways.

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Answer:

False

Step-by-step explanation:

Answer come only two

Answer:  Timo is correct; the hypotenuse rounds to 11

Work Shown:

[tex]a^2+b^2 = c^2\\\\c = \sqrt{a^2+b^2}\\\\c = \sqrt{6^2+9^2}\\\\c = \sqrt{36+81}\\\\c = \sqrt{117}\\\\c \approx 10.81665\\\\c \approx 11\\\\[/tex]

This confirms Timo is correct.

It appears Lucy mistakenly added the side lengths 6 and 9 to get 6+9 = 15, which is not the correct way to get the hypotenuse.

Annie mentioning the 117 seems to suggest that she might have forgotten about the square root, since we got [tex]\sqrt{117}[/tex] earlier in the steps shown above.

If Annie said [tex]\text{The hypotenuse is } \sqrt{117} \text{ units long}[/tex], then she would be correct. Though it's probably better to go with the decimal form (rounding however you want) to get a better sense of how long the hypotenuse is.

Answer:

$709.58

Step-by-step explanation:

The total cost is 100% plus the tax rate of 8.5%, it will be 108.5%

To find the cost of the camera with the sales tax included, we take

$653.99 divided by 100, then times 108.5 = $709.58

So, the cost of the camera with sales tax is $709.58

Answer: 83000

Step-by-step explanation:

Answer: Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex: (3,−4)

Focus:  (3,−15/4)

Axis of Symmetry: x = 3

Directrix:  y = − 17/4

X   Y    

1    0

2   -3  

3   -4

4   -3

5    0

Step-by-step explanation:

Below is the answer

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This data's linear regression equation is y = mx + b, where y is the quantity of chicken feed, x is the number of months since March, m is the line's slope (or the rate at which y changes with respect to x), and b is the y-intercept (or the value of y at x = 0).

The pace at which the amount of chicken feed has been decreasing over time is seen by the slope of the line. The beginning quantity of chicken feed in the barn in March is represented by the y-intercept.

Based on the rate of reduction and beginning quantity for each month since March, the linear regression equation may be used to forecast the amount of chicken feed in the barn in the issue situation.

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The number of occupied rooms is 140 rooms

Percentage can be defined as a ratio or number that is expressed as a fraction of the number, 100.

It is denoted the the percent sign, "%"

Percentage is known as a dimensionless number. This means that is it has no unit of measurement.

They can also be represented in fraction or decimal forms, like 0.3%, 0.5%, etc

From the information given, we have that;

The number of occupied rooms is;

= 16/100 × 875

Find the fraction

=0. 16 × 875

multiply the values

= 140 rooms

Hence, the value is 140 rooms

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The number of copies that have been sold to date approximately is equal to 361,538 copies.

In Mathematics, a percentage simply refers to any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.

In order to determine the number of copies that have been sold to date, we would develop an expression to multiply the total number of copies (T) by the percentage of the number of copies sold in its first month of release as follows;

9.1/100 × T = 32,900

0.091T = 32,900

Dividing both sides of the equation by 0.091, we have the following:

Total number of copies (T) = 32,900/0.091

Total number of copies (T) = 361,538 copies.

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The exponential equation to represent the reduce rate of the insects as conducted in the new experiment with initial population of 2500 is given by y(n) = 2500 ( 1 - 0.14 ) ⁿ.

What is Exponential equation ?

Exponential equation can be defined as the equation in which it contains the exponent.

The exponential equation in the 'y' form to represent the reduce rate of the insects 14% as conducted in the new experiment with initial population of 2500 is given by y(n) = 2500 ( 1 - 0.14 ) ⁿ.

As given in the question,

Initial population scientist starts with is given by P₀ = 2500 insects

Rate by which number of insects reduce each week = 14%

                                                                                       = 0.14

Let time be 'n'

Final population of the insects represented by y(t)

Exponential equation to represents the reduce rate each week is given by :

y(n) = P₀( 1 - r ) ⁿ

⇒ y(n) = 2500 ( 1 - 0.14 ) ⁿ

Therefore, the exponential equation to represent the reduce rate of the insects as conducted in the new experiment with initial population of 2500 is given by y(n) = 2500 ( 1 - 0.14 ) ⁿ.

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Answer: 4.53

Step-by-step explanation:

10 times less than 45.3 means that you will be looking for an answer that is the solution to 45.3 / 10, which equals 4.53.

Answer:

Step-by-step explanation:

The formula of the area of a triangle is equal to Length multiply by Width[A = L * W]

Using the digits 7,8 and 9, the positive seven-digit integers can be made that are palindromes are 729.

When constructing a seven-digit palindrome out of the digits 7, 8, and 9, the first three digits must be the same as the last three digits in reverse order.

This means that each of the first three digits can be either a 7, 8, or 9. Therefore, the total number of combinations for the first three digits is 3 x 3 x 3 = 27.

Since the last three digits must match the first three, the total number of possible combinations of integers is 27 x 27 = 729.

Thus, the total number of positive seven-digit palindromes that can be created using the digits 7, 8 and 9 is 729.

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The mode of each data-set is given by the input that has the most dots in the dot plot.

After obtaining the mode, the difference is obtained subtracting the mode from the MAD of 1.4 for each data-set.

A dot plot shows the number of times that each observation appears in the data-set.

The mode of a data-set is the observation that appears the most times in the data-set, hence it will be given by the observation with the most dots in the dot plot.

The mean absolute deviation is of 1.4, then for each data-set the mode is subtracted by 1.4.

The problem is incomplete, hence the answer was given in general terms.

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The points for the inequality are plotted on the graph attached below.

What is inequality?

A linear inequality is one that, if the equals relation were used in place of the inequality, would provide a linear equation. When multiplying or dividing both sides by a negative number, the direction of the inequality is reversed when the problem is solved. The solution set for an inequality is the set of all solutions.

We are given an inequality as y ≤ 6x/5 - 6

Now, in order to plot the points, we need to find x and y

So, let y be 0, then

⇒0 ≤ 6x/5 - 6

⇒6 ≤ 6x/5

⇒6 ≤ 6x/5

⇒5 ≤ x

So, we get first point as (5,0).

Now, let x=0, then

⇒y ≤ 6(0)/5 - 6

⇒y ≤ -6

So, we get second point as (-6,0).

From these two points, the graph is plotted which is shown below.

Hence, the graph for the inequality is plotted.

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The value of x and y in the equation are 1 and 4 respectively

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 , 4x − 4y = 4.

7x-3y=-5 equation 1

3x+2y=11 equation 2

using elimination method, we multiply the coefficient of x by both equations

21x- 9y = -15 equation 3

21x +14y = 77 equation 4

subtract equation 3 from 4

23y = 92

y = 92/23

y = 4

substitute 4 for y in equation 1

7x -3(4) = -5

7x -12 = -5

7x = -5+12

7x = 7

x= 7/7= 1

therefore the value of x and y are 1 and 4 respectively

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x^-4/x^3 times x^-7 in equivalent expression is x⁻¹⁴

The index form of a number can be defined as the number that is written as an exponential expression.

It is also seen as the single number that is raised to another number.

The rules of index forms are;

From the information given, we have that;

x⁻⁴/x³ × x⁷

Since the denominators are of the same base, add the powers

x⁻⁴/x³⁺⁷

Add the values

x⁻⁴/x¹⁰

Now, subtract the powers

x⁻¹⁴

Hence, the value is x⁻¹⁴

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The part containing the sum of two terms in the given expression can be found to be as (3 + 4) and (6 + 8) respectively.

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

here, we have,

The given expression is 2(3 + 4).

It can be rewritten as follows,

2(3 + 4)

=2 × 3 + 2 × 4

=6 + 8

or, 2 × 7

Thus, in order to find the expression for sum of two terms in the given expression, there can be two possible ways, the first is (3 + 4) and the other is (6 + 8).

Hence, the sum of two terms in the given expression is found to be as (3 + 4) and (6 + 8) respectively.

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7/6 = 28/x

To solve for x, you can cross-multiply:

7 * x = 6 * 28

Simplifying:

x = 6*28/7

x = 24

So, you would need 24 cups of milk.

Answer:

28 cups of sugar / 7 parts of sugar = 4 cups

If 4 cups is 1 part, 6 parts of milk would be 4 x 6

4 x 6

= 24

You would need 24 cups of milk.

The equation in slope-intercept form as required is; y = 240x + 500

This is when the value of the dependent variable depends partly on the value of the independent variable and partly on an initial value that is not 0

According to the statements in the task content;

One employee sells 5 cars and makes $1,700 that week.

A second employee sells 6 cars and makes $1,940 that week.

Hence, it follows from partial variation that;

1700 = 5a + b

1940 = 6a + b

Hence, by solving simultaneously, it follows that;

a = 240

b = 500

Hence, the equation in slope-intercept form as required is; y = 240x + 500

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If Katy wants to wrap a present that is 15cm wide, 18cm deep and 4cm high , then amount of wrapping paper that she need to use is 804 cm² .

Katy is wrapping a gift ,

the dimensions of the box that needs to be wrapped is ⇒

length(l) is = 15cm , width(w) is = 18cm and height(h) is = 4cm .

the present is in shape of cuboid ,

we know that Total Surface Area of cuboid is = 2(lw + wh + hl) ;

substituting values of length , width and height ,

we get ;

Area is = 2(15×18 + 18×4 + 4×15)

= 2( 270 + 72 + 60)

= 2( 402 )

= 804 cm² .

Therefore , Katy will need 804 cm² of wrapping paper to wrap the gift .

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In the exponential function the initial amount a = 14 and the growth fact b = 2.

One of the key mathematical operations is the exponential function (though it would have to admit that the linear function ranks even higher in importance). We allow the exponent to be the independent variable to create an exponential function.

The simplest kinds of dynamical systems have solutions in the form of exponential functions.

Growth or decay can both be described by an exponential function.

g(x)=14x2^x

It is an exponential function.

g(x)=axb^x

where, a is initial amount and b is growth/decay factor.

Now we will compare the  function with this one.

a = 14

b = 2

Hence, The initial amount a=14 and factor b=2

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If her average rate was 20 miles per hour faster on the trip home, Amy live 480 miles far from the mountains

Suppose Amy lives x miles from the mountains.

Fill in x as both distances and the times

going and coming 12 hours and 8 hours.  

Distance         |  speed | time

To mountains |    x        |   8

Coming home  |    x      |   5

Use: speed =distance/ time

to fill in the two rate boxes:

                         Distance | Speed | time

To mountains |          x     |  x/12  |  8

Coming home  |    x         |  x/8  |  5

The equation comes from this sentence:

Her average rate was 20 miles per hour faster on the trip home

Her speed coming home late = Her speed going to the mountains + 20 miles per hour

x/8 = x/12+20

20 = x/8-x/12

20 = x/24

x = 24×20

x = 480

So Amy lives 480 miles from the mountains.

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Note that the answer to the expression {96 ÷ [36÷3-(18 x 2 - 30)]} ÷ (31-16+1) Is: one (1). This problem is solved using PEMDAS.

PEMDAS is the acronym for parenthesis, exponents, multiplication, division, addition, and subtraction. These operators must be solved exactly in the order given above. Thus:

{96 ÷ [36÷3-(18 x 2 - 30)]} ÷ (31-16+1)

⇒ {96 ÷ [36÷3-(6)]} ÷ (31-16+1)

⇒ {96 ÷ [12-6]} ÷ (31-16+1)

⇒ {96 ÷ 6} ÷ (31-16+1)

⇒ 16 ÷ 16

⇒ 1

Thus, it is correct to state that the answer to the mathematical expression  {96 ÷ [36÷3-(18 x 2 - 30)]} ÷ (31-16+1) is 1 or

{96 ÷ [36÷3-(18 x 2 - 30)]} ÷ (31-16+1) = 1

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The train travels an average 12 miles/hr

We always need to be working in the same units, so lets convert the trains speed to minutes since the time traveled is in minutes.

12 miles / 60 min = 0.2 miles/min

Answer:

Answer is in attached photo.

Step-by-step explanation:

Solution is in attached photo, this question is testing on function substitution. (Substituting an input to get an output.)