(2)
Solve the inequality 2r - 5 ≤ 9 and present your answer in interval
notation.

The factors which would be considered while constructing a road for a steep slope are the terrain of the area, the estimated daily traffic, minimum and maximum sight distance, and the design speed.

Constructing roads on a steep slope is a challenge for every civil engineer. It is because such slopes which are possibly found in hilly areas have less access to main land from where the resources/ material for construction are to be transported and also need specific calculations to estimate maximum durability of the roads and also prevent accidents which might occur due to steep slopes.

Hence, an engineer has to keep in mind several factors which can help to reduce the accident cases, provide road safety and better connectivity with major areas.  It is essential that roadway engineers design roads that allow drivers to travel at the right speed. Topography determines the terrain, the different gradient and the construction cost. Every roadway should be built with illuminated raised pavement markings for facilitating safe travel during the night.

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To solve for x, start by expanding the expression in the parentheses:

x = 6+((4x-28)1/2)
x = 6 + 2√(4x-28)

Next, subtract 6 from both sides of the equation:

2√(4x-28) = x - 6

Next, square both sides of the equation:

(2√(4x-28))2 = (x - 6)2

Then, solve for x:

(4x-28) = (x - 6)2
4x-28 = x2 - 12x + 36
x2 - 16x + 64 = 0

Solve for x by factoring:

(x-8)(x-8) = 0

x = 8

Therefore, the solution to the equation x = 6+((4x-28)1/2) is x = 8.

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It will take 11 days to sell 3872 liters of fuel at the same rate as 1760 liters sold in 5 days.

We can use the following proportion to solve the problem:

1760 liters / 5 days = 3872 liters / x days

Where x is the number of days it will take to sell 3872 liters of fuel.

We can use the unitary method to solve this problem.

Let's start by finding out how much fuel is sold in one day. To do this, we need to divide the total amount of fuel sold (1760 liters) by the number of days it was sold for (5 days):

1760 liters ÷ 5 days = 352 liters per day

Now we can use this rate to find out how many days it will take to sell 3872 liters of fuel:

3872 liters ÷ 352 liters per day = 11 days (rounded to the nearest whole number)

Therefore, it will take 11 days to sell 3872 liters of fuel at the same rate as 1760 liters sold in 5 days.

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The symbols, in accordance with the provided assertion, are 27 ÷ 3 + 5 × 2 = 19

A object must imply a meaning that is distinct from its true definition in order to be referred to as a symbol; a symbol is a thing that transcends class or type. A emblem might signify several different things.

The triple bar, also known as the tribar, or, is a sign that denotes the equality of two distinct objects and has a variety of context-dependent meanings. Logic and arithmetic are its two primary applications. It looks like a third line attached to an equals symbol (=).

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The value of (f - g) (3) is 32.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given are two functions, f and g.

f(x) = 3x² and g(x) = x - 8

Subtraction of two functions is defined as,

(f - g) (x) = f(x) - g(x)

             = 3x² - (x - 8)

             = 3x² - x + 8

To find (f - g)(3), substitute 3 in place of x.

(f - g)(3) = 3(3)² - 3 + 8

             = 27 - 3 + 8

             = 32

Hence the value of the subtraction of functions is 32.

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Answer:

D

Step-by-step explanation:

The solutions to the given polynomial equation are x = (1 + √5)/(3) and x = (1 - √5)/(3).

To solve the given polynomial equation using the quadratic formula, we need to first identify the values of a, b, and c. In this case, a = -9, b = 6, and c = 4. The quadratic formula is given by:

x = (-b ± √(b^(2) - 4ac))/(2a)

Plugging in the values of a, b, and c into the formula, we get:

x = (-(6) ± √((6)^(2) - 4(-9)(4)))/(2(-9))

Simplifying the equation, we get:

x = (-6 ± √(36 + 144))/(-18)

x = (-6 ± √180)/(-18)

x = (-6 ± 6√5)/(-18)

x = (1 ± √5)/(3)

Therefore, the solutions to the given polynomial equation are x = (1 + √5)/(3) and x = (1 - √5)/(3).

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You need to buy 1 stamp that costs 12 cents, 3 stamps that cost 4 cents each, and 8 stamps that cost 1 cent each, to have a total of 40 stamps and spend exactly $1.

The reasoning is as follows:

If you were to buy only 1 cent stamps, you would need to purchase 100 of them to spend $1, which would exceed the required 40 stamps. On the other hand, if you were to buy only 12 cent stamps, you would only be able to purchase 8 stamps, which would fall short of the required 40 stamps. Therefore, a combination of all three types of stamps is necessary.

Starting with the most expensive stamp, one 12 cent stamp leaves you with 88 cents. Then, 3 stamps of 4 cents each will cost you 12 cents, leaving you with 76 cents. Finally, 8 stamps of 1 cent each will cost you 8 cents, which adds up to $1 and gives you a total of 40 stamps.

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The domain of a function is the set of all possible input values (x) for which the function is defined.

The range of a function is the set of all possible output values (f(x)) that the function can produce.

For the given function f(x) = 2^(x+1), the domain includes all real numbers because we can substitute any real number for x and obtain a valid output.

To find the range, we can examine the behavior of the function as x approaches positive and negative infinity. As x approaches negative infinity, the exponent (x+1) becomes very large negative number, and 2^(x+1) approaches zero. As x approaches positive infinity, the exponent (x+1) becomes very large positive number, and 2^(x+1) approaches infinity. Therefore, the range of the function is (0, infinity).

So, the domain is (-infinity, infinity) and the range is (0, infinity).

Answer:

  x = 1 or 5

Step-by-step explanation:

You want the value(s) of x that make 3x^2-x+1 and 2x^2+5x-4 have the same value.

Equating their values, we have ...

  3x² -x +1 = 2x² +5x -4

  x² -6x +5 = 0 . . . . . . . . . subtract (2x²+5x-4)

  (x -5)(x -1) = 0 . . . . . . . factor

  x = 1 or x = 5 . . . . . . values of x that make the factors zero

The two trinomials will have the same value for x=1 and for x=5.

__

Additional comment

The attached graph shows the points where the trinomials have the same value.

The value of p(3) is p(3)=12.

Here, we have,

Synthetic division :

It is a shorthand method of dividing polynomials for the special case of dividing by a linear factor whose leading coefficient is 1.

The given function is,

p(z)=8z⁴-17z³-20z²-4z+15                  

We have to find  p(3)  

Substitute z= 3 in above function.

p(3)=8×3⁴-17×3³-20×3²-4×3+15                

     =12      

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The mode of the set {2, 5, 6, 8, 9, 11, 15} is the number that appears most frequently in the set. In this case, all of the numbers appear only once, so there is no mode.

The mode of a set of numbers is the value that appears most frequently in the set. To find the mode of the set {2, 5, 6, 8, 9, 11, 15}, we need to count how many times each number appears and then determine which number appears most frequently.

From the set, we can see that no number appears more than once. Therefore, there is no single number that appears most frequently and we cannot determine a mode for this set.

In some cases, a set of numbers may have multiple modes if two or more numbers appear with the same frequency. For example, the set {1, 2, 2, 3, 3, 3, 4, 5, 5} has two modes, 2 and 3, since both of these numbers appear three times in the set.

However, in the case of the set {2, 5, 6, 8, 9, 11, 15}, there are no repeating numbers, so there is no mode.

In conclusion, the mode of the set {2, 5, 6, 8, 9, 11, 15} is undefined as there are no repeating numbers in the set.

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Answer:-15

Step-by-step explanation:

Answer:

y = -  125/18

Step-by-step explanation:

okay so here what i got when i was doing the equation

5 ( y + 25) = - 13y

5 y + 125 = - 13y

then you subtract 125 from both sides

subtract the numbers

and my solution was y = - 125 / 18 trust me!

Hope that helped

For the given square, m∠OKL=45° and m∠MOL=90°.

A square is a regular quadrilateral in Euclidean mathematics because it has four equal sides and four equal angles (right angles, 90-degree angles). It can also be explained as a rectangle with two adjacent sides that are of identical length. It is the only regular polygon whose diagonals are all the same length and whose internal, central, and exterior angles are all equal (90°).

In mathematics, an angle bisector is a line that divides an angle into two equal angles. The term "bisector" refers to a device that divides an object or a shape into two equal sections. An angle bisector is a beam that divides an angle into two identical segments of the same length.

Angle bisector points are equally spaced from both angle lines.

Any angle, including acute, obtuse, and right angles, can have an angle bisector traced to it.

In the given square,

The diagonals NL and KM are angle bisectors of ∠K, ∠L, ∠M and ∠N.

Therefore, ∠OKL= 90/2

                  ∠OKL=45°

We know that, in a square, diagonals are equal and bisect each other at right angles.

Therefore, ∠MOL=90°

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The measure of width of the computer is 75.89 inches.

Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.

The ratio of a and b is denoted as a : b.

Given that,

Ratio of diagonal to length of a rectangular computer = 13 : 7

This means that,

If diagonal = 13k and length = 7k for some constant k.

Given Actual length = 18 inches.

3k = 18

k = 18/3 = 6

So Diagonal length = 13 × 6 = 78 inches

We know that, the length, width and diagonal of a rectangle form a right angled triangle.

Let width of the rectangular computer be x.

Using Pythagorean Theorem,

(Length)² + (Width)² = (Diagonal)²

18² + x² = 78²

x² = 78² - 18²

x² = 5760

x = 75.89 inches.

Hence the measure of width is 75.89 inches.

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Answer:

410=50x+10

Step-by-step explanation:

your total is 410 so to get there you have to know the number of nights which is x. the 10 is a one time fee so you only need that once and not per night.

The correct statement regarding the domain and the range of the quadratic function are given as follows:

D. The domain is all real numbers, the range is y ≥ -4.

Hence, on a graph, the values are given as follows:

Meaning that option D is correct.

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The graph of the function y=3x+1 is shown.

All the points (and only those points) which lie on the graph of the function satisfy its equation.

Thus, if a point lies on the graph of a function, then it must also satisfy the function.

We are given that;

The function is y=3x+1

Now,

When x = 0, y = 3(0) + 1 = 1, so one point on the function is (0, 1).

When x = 1, y = 3(1) + 1 = 4, so another point on the function is (1, 4).

When x = -1, y = 3(-1) + 1 = -2, so a third point on the function is (-1, -2).

Therefore, the graph will be given the attachment

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When the wet-bulb reading is 66°F, the relative humidity is 100%.

Based on the given information, the dry-bulb temperature and wet-bulb temperature are the same, which means the air is fully saturated with water vapor, and the relative humidity is 100%.

Relative humidity is the ratio of the amount of moisture in the air compared to the amount of moisture that the air can hold at a particular temperature. The wet-bulb temperature measures the lowest temperature that can be achieved by evaporating water into the air until it is fully saturated, while the dry-bulb temperature measures the actual temperature of the air.

When the wet-bulb and dry-bulb temperatures are the same, it means that the air is fully saturated and cannot hold any more moisture, resulting in a relative humidity of 100%.

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The simplified expression is  [tex]8x^4y^4[/tex].

Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do. For example, take this expression: 4 + 6 + 5.

Here the given expression is

=> [tex](4x^3y^3)(2x.2y)[/tex]

=> [tex]4\times x^3\times y^3\times2x\times2y[/tex]

=> [tex]4\times2\times2\times x^3\times x \times y^3\times y[/tex]

=> 8[tex]\times x^{3+1}\times y^{3+1}[/tex]

=> [tex]8x^4y^4[/tex]

Hence the simplified expression is  [tex]8x^4y^4[/tex].

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Answer:

Trust me I guarantee you it's correct.

Step-by-step explanation:

D. 8x^5y^4

To find the altitude of the spherical segment, we need to use the formula for the total surface area of a spherical segment, which is given by:
A = 2πR(r + h), where R is the radius of the spherical surface, r is the radius of the base, and h is the height of the segment.

We are given that the total surface area of the spherical segment is 7 times greater than the surface area of the sphere inscribed in it, which means that:
7(4πR^2) = 2πR(r + h)
Simplifying this equation gives us:
14R = r + h

We are also given that the radius of the spherical surface is equal to R, which means that r = R. Substituting this into the equation gives us:
14R = R + h
Solving for h, we get:
h = 14R - R
h = 13R
Therefore, the altitude of the spherical segment is 13R.

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Answer:

E(2,-4), F(8,0), and G(5,3).

Step-by-step explanation:

Reflection in the y-axis means the signs of the x-coordinates should be flipped.

Answer:

Answer A

Step-by-step explanation:

I know that you already have the answer, but I wanted to show you a picture.

The given function, f(x)=-3x^(2)+4, has three types of symmetry: 1. Symmetry with respect to the y-axis (even symmetry).
2. Symmetry with respect to the x-axis (odd symmetry). 3. Symmetry with respect to the origin (rotational symmetry)

To check for symmetry with respect to the y-axis, we can substitute (-x) for x in the function and see if it is equal to the original function.

f(-x)=-3(-x)^(2)+4=-3x^(2)+4

Since f(-x)=f(x), the function is symmetric with respect to the y-axis.

To check for symmetry with respect to the x-axis, we can substitute (-y) for y in the function and see if it is equal to the original function.
-3x^(2)+4=-y
y=-3x^(2)-4

Since this is not equal to the original function, the function is not symmetric with respect to the x-axis.

To check for symmetry with respect to the origin, we can substitute (-x) for x and (-y) for y in the function and see if it is equal to the original function.
-3(-x)^(2)+4=-y
y=-3x^(2)-4

Since this is not equal to the original function, the function is not symmetric with respect to the origin.

Therefore, the given function f(x)=-3x^(2)+4 has symmetry with respect to the y-axis, but does not have symmetry with respect to the x-axis or the origin.

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The equation with a solution of -7 is x^2 = 49

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

The list of options and x = -7

To check which equation has a solution of x = -7, we can simply substitute -7 for x in each equation and see which one is true.

Hence, the equation x^2 = 49 has x = -7 as a solution.

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Answer:

x = 16

AB = 25

BC = 15

AC = 20

Step-by-step explanation:

I have marked the vertices to explain

There are three right triangles that can be seen in the picture

Δ ABC with legs BC and AC and hypotenuse AB

ΔACD with legs AD and CD and hypotenuse AC

ΔBCD with legs CD and BD and hypotenuse BC

We will using the Pythagorean formula in all three triangles:
hypotenuse² = sum of squares of legs

------------------------------------------------------------------------------------------

(1) Let's first find missing side BC

In right triangle ΔBCD ,
BC² = CD² + BD²

We have CD = 12, BD = 9
BC² = 12² + 9²
= 144 + 81

= 225

BC = √225 = 15

--------------------------------------------------------------------------------------------------
(2) Now let's focus on ΔABC

AB is the hypotenuse
AC and BC are the legs

AB² = AC² + BC²

or

AC² = AB² - BC²

Since AB = AD + BD = x + 9 and BC = 15

AC² = (x + 9)² - 15²

(x + 9)² = x² + 2 · 9 · x + 9² = x² + 18x + 81

15² = 225

AC² =  x² + 18x + 81 -225

AC² =  x² + 18x - 144                  (1)

-----------------------------------------------------------------------------------------------

(3) Now let's turn our attention to ΔACD with legs AD and CD  and hypotenuse AC

AC² = AD² + CD²

With AD = x and CD = 12,

AC² = x² + 12²

AC² = x² + 144                               (2)

------------------------------------------------------------------------------------------------

Equations (1) and (2) have the same left side, AC²
So the expressions on the right side must be equal

Therefore:

x² + 18x - 144     =  x² + 144

x² terms cancel out from left and right sides giving

18x - 144 =  144

Add 144 on both sides:
18x - 144 + 144 = 144 + 144

18x = 288

x = 288/18 = 16

Plugging this into equation (2) AC² = x² + 144 gives
AC² = 16² + 144

AC² = 256 + 144

AC² = 400

AC = √400

or

AC = 20

Since AB is the third unknown side and AB = x + 9 we get
AB = 16 + 9 = 25

The length of the rectangular box will be 2.03 cm. Then the correct option is C.

Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as,

V = L x W x H

The volume of a rectangular box is 109.86 cubic centimeters. The prism's breadth is 13.2 cm. The prism stands 4.1 cm tall.

The length of the rectangular prism is given as,

109.86 = L x 13.2 x 4.1

109.86 = 54.12L

L = 109.86 / 54.12

L = 2.03 cm

The length of the rectangular box will be 2.03 cm. Then the correct option is C.

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Answer:

y = -43x - 175

Step-by-step explanation:

Slope-intercept form is y = mx + b

m = -43

x = -4

y = -3

-3 = -43(-4) + b

b + 172 = -3

b = -3 - 172 = -175

=> y = -43x - 175

Answer: why do u need help again? this is easy boy

Step-by-step explanation: