Solve for x in the triangle. Round your answer to the nearest tenth.

Answer:

To find the difference between the elevations of City A and City B, we need to subtract the elevation of City A from the elevation of City B. Since City A is located 15 meters below sea level, and City B is located 43 meters above sea level, the difference between their elevations is $43 - (-15) = 43 + 15 = 58 meters. Therefore, the difference between the elevations of City A and City B is 58 meters.

Answer:

f - 36

-3f - 23

are your prime polynomials.

63 degrees is the angle.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The given triangle is a right angle triangle.

The opposite side length is 85 and the adjacent side is 38.

Opposite side=85

Adjacent side=38.

Calculate Opposite/Adjacent

= 85/38= 2.236

Which is tanθ=2.236

Now tan inverse on both the sides

θ=tan⁻¹2.236

θ=tan⁻¹2

θ=63 degrees.

Hence, the angle is 63 degrees.

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Answer:

  (c)  x = -1/11(y -3)²

Step-by-step explanation:

You want an equation of the parabola with directrix x = 11/4 and vertex (0, 3).

The directrix is a vertical line to the right of the vertex. This means the parabola opens to the left.

The vertex form of the equation is ...

  x = 1/(4p)(y -k)² +h . . . . . . . . where (h, k) is the vertex, and p is the distance from the directrix to the vertex (also, the distance from the vertex to the focus)

Here, we have ...

  p = 0 -11/4 = -11/4 . . . . negative because the vertex is left of the directrix

and

  (h, k) = (0, 3)

so the equation is ...

  x = 1/(4(-11/4))(y -3)² +0

  x = -1/11(y -3)²

After 81 minutes of driving the distance to destination is 32.8 miles.

Th function that has two variables with first order term is called linear function.  While plotting on the XY coordinate system we get a straight line.

Why do we use linear equation in this problem?

as per question, distance to destination is a linear function of total driving time so we use the equation of straight-line having slope m and y intercept b for determining unknown values.

given, distance to destination in miles is a linear function of total driving time in minutes.

y=mx+b

in the equation, y denotes the distance to destination in miles

                 x is the total driving time in minutes

         m is the slope of linear equation

      b is the y intercept

Milan has 68 miles to his destination after 37 minutes of driving

68 = mx37+b

he has 45.6 miles to destination after 65 minutes of driving

45.6=mX65+b

solving the two equations by addition method

slope, m= -0.8

from the above two equation

we get b=97.6

now, after 81 minutes of driving the distance to destination, y=mx+b

                                               y= -0.8x81+97.6

                               distance = 32.8 miles

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Answer:

x- intercept = - 8 , y- intercept = 6

Step-by-step explanation:

to find the x- intercept let y = 0 in the equation and solve for x

3x - 4(0) = - 24

3x = - 24 ( divide both sides by 3 )

x = - 8 ← x- intercept

to find the y- intercept let x = 0 in the equation and solve for y

3(0) - 4y = - 24

- 4y = - 24 ( divide both sides by - 4 )

y = 6 ← y- intercept

The solution is D = 200 feet

The diameter of the circular store is = 200 feet

What is a Circle?

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The perimeter of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle

Given data ,

Let the diameter of the circle be represented as = D

Let the radius of the circular store be = r

D = 2r

Now , the area of the circular store be = A

The value of A = 31,415 feet²

The area of the circular store is given by the formula

Area of the circle = πr²

Substituting the values in the equation , we get

31415 = 3.1415 x r²

Divide by 3.1415 on both sides of the equation , we get

r² = 10000

Taking square roots on both sides of the equation , we get

r = 100 feet

Now , the diameter of the store = 2 x radius of the store

Diameter of the store D = 2 x 100 feet

Therefore , diameter of the store D = 200 feet

Hence , The diameter of the circular store is = 200 feet

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Answer:

  2x² +5

Step-by-step explanation:

You want the width of a rectangle with a length of x+3 and an area of A(x) = 2x³ +6x² +5x +15.

The area is the product of length and width, so the width will be ...

  A = LW

  W = A/L = (2x³ +6x² +5x +15)/(x +3)

The cubic expression can be factored by grouping, so we have ...

  Area = (2x³ +6x²) +(5x +15)

  = 2x²(x +3) +5(x +3)

  = (2x² +5)(x +3)

Then the width is ...

  [tex]\text{width}=\dfrac{(x+3)(2x^2+5)}{x+3}=\boxed{2x^2+5}[/tex]

The width of the rectangle is 2x² +5.

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All the real numbers except 1 make the two expressions equal. Then the correct option is A.

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expressions are given below.

[(x - 1)(x - 6)] / [4(x - 1)] and (x - 6) / 4

Simplify the expression [(x - 1)(x - 6)] / [4(x - 1)], then we have

⇒ [(x - 1)(x - 6)] / [4(x - 1)]

⇒ (x - 6) / 4

But at x = 1, the expression [(x - 1)(x - 6)] / [4(x - 1)] is not defined.

All the real numbers except 1 make the two expressions equal. Then the correct option is A.

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x(7 - x) > 8

First solve x(7 - x)  = 8

x^2 - 7x + 8 = 0

x = 5.56, 1.44

If we plug in these values into the original equation we can see that solution is

1.44 < x < 5.56

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The complete answer: A domain is a set of input data in a relationship.

The collection of all conceivable independent values that a function or relation may take is known as its domain.

An input value and an output value are matched in a relation.

A relation is a function where each input value yields one and only one output value.

Graphs, tables, and ordered pairs can all be used to represent functions. The domain is the set of input values,

while the range is the set of output values.

The domain of a function or relation is the set of all possible independent values that it can have.

Therefore,  a domain is a set of input data in a relationship.

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44 seconds will pass before the planes are at the same altitude.

What do you mean by algebraic expression?

An algebraic expression in mathematics is an expression that consists of variables and constants and algebraic operations (addition, subtraction, etc.). Expressions are made up of concepts.

There are three main types of algebraic expressions:

Monomial Expression

Binomial Expression

Polynomial Expression

An algebraic expression with only one term is called a monomial.

It is given that plane A is at an altitude of 3500 feet and plane B is at an altitude of 2609 feet. Plane A is gaining altitude at 45.5 feet per second and plane B is gaining 65.75 feet per second.

Let x seconds will pass before the planes are at the same altitude.

Plane A, 3500 + 45.5x

Plane B, 2609 + 65.75x

x is number of seconds of time

When altitudes equal

3500 + 45.5x = 2609 + 65.75x

3500 - 2609 = 65.75x - 45.5x

891 = 20.25x

891/20.25 = x

44 = x

Therefore, 44 seconds will pass before the planes are at the same altitude.

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There are 21 days for there to be 150 frogs in the pond.

There are 37 days for there to be 1400 frogs in the pond.

What is exponential growth?

Quantity increases over time through a process called exponential growth. When a quantity's instantaneous rate of change with respect to time is proportional to the quantity itself, it happens.

Given:

There are currently 25 frogs in a (large) pond. The frog population grows exponentially, tripling every 10 days.

The exponential equation for the given problem is,

[tex]A(t) = Ar^t^/^1^0[/tex]

To find the number of days for there to be 150 frogs in the pond.

Here,

A(t) = 250, A = 25, r = 3

⇒

[tex]250 = 25(3)^t^/^1^0\\10 = 3^t^/^1^0\\t = 20.97[/tex]

t ≈ 21

Hence, there are 21 days for there to be 150 frogs in the pond.

Now to find how long for there to be 1400 frogs in the pond, we solve:

[tex]1400 = 25(3)^t^/^1^0\\56 = (3)^t^/^1^0\\t = 36.64[/tex]

t ≈ 37

Hence, there are 37 days for there to be 1400 frogs in the pond.

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Answer:

[tex]2x^2+7x+C[/tex]

Step-by-step explanation:

Find the antiderivative of f'(x)=4x+7

[tex]\frac{4x^{1+1} }{1+1}+7x+C\\\frac{4x^2}{2}+7x+C\\ 2x^2+7x+C\\[/tex]

Conditional problems are problems that involve one or more conditions that must be met in order for a certain action to be taken or a certain result to be obtained. The temperature of the solution in degrees Fahrenheit after x hours, is y = 1.5x - 100.

The required details for Conditional problems in given paragraph

This function models the temperature of the solution as it decreases at a constant rate of 1.5 °F per hour. The initial temperature of the solution is 100 °F, and the temperature decreases by 1.5 °F for each hour that passes. Therefore, the temperature of the solution after x hours can be found by subtracting 1.5x degrees from the initial temperature of 100 degrees.

For example, if we plug in x = 2 into the function, we get y = 1.5 * 2 - 100 = 3 - 100 = -97, which means that the temperature of the solution after 2 hours is -97 °F.

The other options listed are not correct because they do not correctly model the temperature of the solution as it decreases at a constant rate of 1.5 °F per hour. Option A is incorrect because it adds 1.5x degrees to the initial temperature, rather than subtracting it. Option B is incorrect because it adds 100 degrees to the temperature, rather than subtracting it. Option C is incorrect because it multiplies the initial temperature by 1.5x, rather than subtracting 1.5x degrees from it. Option D is incorrect because it adds 1.5 to the temperature, rather than subtracting 1.5x degrees from it.

what are conditional problems?

Conditional problems are often expressed using words like "if," "then," or "when." For example, a conditional problem might involve finding the value of a variable x if it satisfies a certain condition, such as "If x is greater than 5, then x is even." In this case, the problem specifies that x must be greater than 5 in order for it to be even.

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A number has the same digit in its hundreds place and in its hundreds place. 10,000

Generally, Given that a number's hundreds place and its hundredths place both have the same digit, we may assume that the number is perfect.

Let's say that the digit is a 1.

Therefore, the value of the hundreds position in a number is equal to 100.

The value of the hundredth position in a number is equal to 0.01%.

The following formula may be used to determine the number of instances in which the value of the digit in the hundreds place is higher than the value of the digit in the hundredths place:

As a result, the difference between the value of the digit in the hundreds place and the value of the digit in the hundredth place is 10,000 times bigger.

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CQ

A number has the same digit in its hundreds place and its hundredths place. How many times greater is is the value of the digit in the hundreds place than the value of the digit in the hundredths place?

A. 100,00

B. 100

C. 1,000

D. 10,000

Answer:

Step-by-step explanation:

Given a total of 244 sodas and hot dogs sold, with sodas numbering 42 more than hot dogs, you want to know the number of each that were sold.

Let s represent the number of sodas sold. Then s-42 is the number of hot dogs sold, and the total sold is ...

  s +(s -42) = 244

Add 42 and simplify

  2s = 286

  s = 143 . . . . . divide by 2

  hot dogs = 143 -42 = 101 . . . . . figure the number of hot dogs

143 sodas and 101 hot dogs were sold.

The dimensions of the rectangular box with largest volume if the total surface area is given as 100 cm2: x = y = z = 2.449 cm.

Given that:

Total surface area of the rectangular box or cuboid = 100 cm²

A rectangular box with largest volume is a cube.

The total surface area of a cube = 6 times square of one edge length.

Let the edge length = given dimensions; x, y, z

So,

x = y = z

6x^2 = 100

x^2 = 100 / 6

x = √ 100 / 6

x = 10 / √ 6 cm

x = 2.449 cm

Hence, dimensions of the rectangular box with largest volume if the total surface area is given as 100 cm2: x = y = z = 2.449 cm.

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Answer: 2 complete games

Step-by-step explanation:

add shoes and game charge

$10.00 + 2.75 = 12.75 <— that’s 1 complete game

subtract it from $30.00

$30.00 - 12.75 = 17.25.

A complete game costs 12.75. so, Kim had enough money for one more game.

17.25 - 12.75 = $4.50 remaining after 2 complete games

Answer: 7 games

Step-by-step explanation: if it charges 10 for shoes, then you already subtract 10 from 30. 30-10=20. then, to find out how many games she can play, divide 2.75 from 20. 20/2.75=7.272727.... Since you can't pay for half of a game, it would be 7 games.

There is no property named 'left' for the circle. So the answer is 'c'.

Circle is a two dimensional figure which has a round shape. It is formed by joining all the points which are at an equal distance from a fixed point called the center of the circle.

The line formed by joining the center to any point on the boundary of the circle is called radius. Diameter is double of the radius.

Rotate angle is the term defining the angle of rotation of the circle. Angle of rotation of a complete circle is 2π.

Width is another term for diameter of the circle, although it is not commonly used.

Left is the only term which does not have any role in the properties of circles.

Hence, the term 'left' is not a valid property of circles.

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The required equation of the line which contains the points (−7,2) and (2,−2) is y = -4/9x - 8/9.

A straight line's general equation is y = MX + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept.

The equation of the line's general form is:

y = MX + c

Where, m = slope, c = y-intercept and slope = ( y₂ - y₁ ) / ( x₂ - x₁ ).

Determine the line's slope:

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( -2-2) / (2+7 )

Slope= -4/9

The y-intercept is determined as follows:

y = MX + c

2 = -4/9x 2+c

c = -8/9

The lines' equation:

y = MX + c

y = -4/9x - 8/9

Therefore, the required equation of the line which contains the points (−7,2) and (2,−2) is y = -4/9x - 8/9.

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The probability that the first success occurs on trial number n = 3 is 0.032

Given:

probability of success on a single trial p = 0.80

trial number, n = 3

Recall the formula for the Geometric Probability Distribution

P(n) = p(1 - p)ⁿ⁻¹

where n is the number of the binomial trial on which the first success occurs and p is the probability of success on each trial

P(n) = p(1 - p)ⁿ⁻¹

P(3) = 0.8(1-0.8)³⁻¹

P(3) = 0.8(0.2)²

P(3) = 0.032

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The following statements are true are more than 40% of the students at the school are freshmen or sophomores who plan to attend college.

Given :

emily surveyed all the students at her school to find out if they plan to attend college. the results are shown in the two-way frequency table. emily knows that the student body at her high school is distributed as follows: freshmen: 28 % sophomores: 26 % juniors: 24 % seniors: 22 %  .

Freshmen = 0.85

sophomores = 0.80

it is clearly visible that the freshmen or sophomores is greater than the 40 % .

Hence , more than 40% of the students at the school are freshmen or sophomores who plan to attend college.

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The number of djembe drums you sold is 8

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

Total = 12 sets of maracas, 6 sets of claves, and x djembe drums.

Earning = $326

Also, we have:

The maracas costs $14 per set, the claves costs $5 per set, and the drum cost $16.

So, we have

12 * 14 + 6 * 5 + x * 16 = 326

Evaluate the products

198 + 16x = 326

Evaluate the iike terms

16x = 128

So, we have

x = 8

Hence, the number of djembe drums is 8

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Complete question

You sell instruments at a Caribbean music festival. You earn $326 by selling 12 sets of maracas, 6 sets of claves, and x djembe drums.

The maracas costs $14 per set, the claves costs $5 per set, and the drum cost $16.

Find the number of djembe drums you sold.

After the markup in the price, the new cost of goldfish will be equal to $4.45.

The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.

As per the given information in the question,

Cost of goldfish = $3.45

Markup = 29%

So, the price increase will be,

(3.45 × 29)/100

= 100.05/100

= 1.0005

So, the new price is,

$3.45 + $1.0005

= $4.4505 ≈ $4.45

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The factor of the expression 8w - 16 will be 8 and (w - 2).

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

A frequency table displays a sequence of scores in either increasing or decreasing order together with their occurrences as a way to compactly organize raw data.

The expression is given below.

⇒ 8w - 16

The factor of each term in the expression, then we have

8w = 8 x w

16 = 8 x 2

Then the expression is written as,

⇒ 8w - 16

⇒ 8 × w - 8 × 2

⇒ 8 × (w - 2)

⇒ 8(w - 2)

The component of the articulation 8w - 16 will be 8 and (w - 2).

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The amount of money for selling 450 baked goods will be

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

At a bake sale, the Math Club raised $225 by selling 300 baked goods.

And, The amount raised varies directly with the baked goods sold.

Now,

Let the amount of money for selling 450 baked goods = x

Since, At a bake sale, the Math Club raised $225 by selling 300 baked goods.

And, The amount raised varies directly with the baked goods sold.

Hence, By definition of proportion we get;

⇒ $225/300 = x / 450

⇒ x = 225 × 450 / 300

⇒ x = $337.5

Thus, The amount of money for selling 450 baked goods = $337.5

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The maximum area of the tile to contain both grounds is 12x²y²

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

Area of ground A = 12x^2y sq. units

Area of ground B = 6xy^2sq units

Rewrite these areas properly

So, we have the following representation

Area of ground A = 12x²y sq. units

Area of ground B = 6xy² sq units

Express the areas as the products of their prime factors

This gives

Area of ground A = 2 * 2 * 3 * x * x * y

Area of ground B = 2 * 3 * x * y * y

From the above products, we have

Least common multiple = 2 * 2 * 3 * x * x *y * y

Evaluate the products

Least common multiple = 12x²y²

This represents the greatest area

Hence, the greatest area is 12x²y²

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