Write an equation of the line that passes through (-3, 5) and is perpendicular to the line y=-3r-1.
y =

The nature of the roots of the quadratic equation 9x2 12x + 4 is that it has one root, which is equal to -4.

The nature of the roots of a quadratic equation is determined by its discriminant (b2 – 4ac). The discriminant of the given equation 9x2 12x + 4 is (12)2 – 4(9)(4) = 144 – 144 = 0.

Since the discriminant is equal to zero, the equation has two equal (or identical) roots. This indicates that the equation has one root since its roots are equal. We may apply the quadratic formula to get the equation's root.

The quadratic formula states that the roots of a quadratic equation can be found by solving the equation:

x = (-b ± √(b2 – 4ac))/2a

When we apply the formula to the given equation, we get:

x= (-12 ± √(0))/2(9)

Since the discriminant is equal to zero, the equation has one root. The root of the equation is x = -4.

Therefore, the nature of the roots of the quadratic equation 9x2 12x + 4 is that it has one root, which is equal to -4.

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Miles per hour and meters per second are formally known as mph and m/s, respectively.

Kilometers per hour 28 km/h

Miles per hour 62.6342  

Let's first review the metric conversions for a mile and an hour. Speed is the distance traveled in a given amount of time.

Miles per hour and meters per second are formally known as mph and m/s, respectively. If so, converting mph to m/s will be simple. We are cognizant of:

A mile is equal to 1.60934 kilometers or 1609.34 meters.

3600 seconds make up 1 hour, which is equal to 60 minutes, 60 minutes, and 60 seconds.

With the help of these conversions, let's create the mph to m/s formula.

mph to m/s Formula

1 mph = 1 mile per hour

=1 mile / 1 hour

=1609.34 meters/3600 seconds

0.447 meter / seconds

=0.447 m/s

So, multiplying by 0.447 is required to change mph to m/s.

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The product of 4 x 5 is 20.

The term product in math is defined as product of two numbers is the result you get when you multiply them together.

Here we need to identify the product of 4 x 5.

As per the definition we all know that the product also known as multiplication is the process of multiplying it by another number.

Here we all know that the multiplication table is used for this onw,

So, here we have to write the multiplication table, that is

=> 4 x 1 = 4

=> 4 x 2 = 8

=> 4 x 3 = 12

=> 4 x 4 = 16

And then the value of

=> 4 x 5 = 20.

Complete Question:

What is the product of 4 x 5?

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The graph transformations are discussed below.

Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph.

Given is the transformation of a graph.

A function transformation either "moves" or "resizes" or "reflects" the graph of the parent function. There are mainly three types of function transformations:

Transformation                Function                  Changes in Position/Size

Translation                 moves the curve                     Change in position

Dilation                Stretches or shrinks the curve     Change in the size

Reflection                   Flips the curve                      Change in position

                           and produces the mirror image.

Therefore, the graph transformations are discussed above.

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(5a - 6)(5a + 6)

The correct answer is D

The total problems assigned over the weekend are 15.

In mathematics, a fraction is used to denote a portion or component of the total. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, while the denominator is the number at the bottom. The denominator specifies the total number of equal parts in the whole, whereas the numerator specifies the number of equal parts that were taken.

Let us suppose the total number of problems assigned = x.

Given that the problems solved on Saturday is 3/5 of her total questions. This is represented as:

(3/5) x

The remaining problems are:

1 - (3/5) x = (2/5) x

On, Sunday the problems solved are 1/3 of the remaining. This is represented as:

(1/3) (2/5) x

(2/15) x

The remaining problems are:

(1 - 1/3)(2/5 x) = (2/3) * (2/5) x = 4/15 x

Given that the final number of problems remaining are 4, that is:

(4/15) x = 4

x = 4 (15/4)

x = 15

Hence, the total problems assigned over the weekend are 15.

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Answer:   [tex]11\text{x}^{3}\text{y}^{4}[/tex]

=====================================

Work Shown:

[tex]\left(121\text{x}^6\text{y}^8\right)^{1/2}\\\\\left(121\right)^{1/2}*\left(\text{x}^6\right)^{1/2}*\left(\text{y}^8\right)^{1/2}\\\\\sqrt{121}\text{x}^{6*(1/2)}\text{y}^{8*(1/2)}\\\\11\text{x}^{3}\text{y}^{4}\\\\[/tex]

Therefore,

[tex]\left(121\text{x}^6\text{y}^8\right)^{1/2}=11\text{x}^{3}\text{y}^{4}\\\\[/tex]

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

Explanation:

The exponent of 1/2 represents a square root. This is how [tex](121)^{1/2}[/tex] turned into [tex]\sqrt{121}[/tex] which then simplified to 11.

As for the variable terms, we multiply that outer exponent 1/2 with each exponent inside the parenthesis. Think of it like the distribution rule. It's not really distribution, but similar.

Recall that [tex](a^b)^c = a^{bc}[/tex]

Answer:

y=-2x+5

Step-by-step explanation:

The types of solutions for an equation depend on the type of equation, but in general, the most common types of solutions are: single solution, no solution and infinite solutions.

In mathematics, particularly in algebra, a solution of an equation is a value or a set of values that, when substituted into the equation, makes it a true statement.

Single solution: An equation has a single solution when it has exactly one value that satisfies the equation. This solution is unique and it can be found by solving the equation for the variable.

No solution: An equation has no solution when it is impossible to find a value that satisfies the equation. This happens when the equation is contradictory or inconsistent. For example, the equation "2x = 5x + 1" has no solution because no value of x can make the equation true.

Infinite solutions: An equation has infinite solutions when any value of the variable satisfies the equation. This happens when the equation is an identity, meaning it is true for all values of the variable. For example, the equation "2x + 0 = 2x" has infinite solutions because any value of x will make the equation true.

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Step-by-step explanation:

(f○g)(x) = f(g(x))

it simply means that we put the expression of g(x) into ask places of x in f(x).

(f○g)(x) = g(x)² + 3

therefore,

g(x)² + 3 = 9x² - 12x + 7

g(x)² = 9x² - 12x + 4 = (a + b)² = a² + 2ab + b²

9x² = a² tells us that a = ±3x

4 = b² tells us that b = ±2

which signs of a and b do we need ?

-12x = 2ab gives us the answer

-6x = ab

that means the signs need to be opposite and we have 2 possible solutions

g(x) = 3x - 2

or

g(x) = -3x + 2

Factor the radicand: If the radicand is not already in the form of a perfect square, you can factor it into its prime factors and pull out any perfect squares from the radicand.

For example, √(36) can be simplified to √(49) = √4 * √9 = 23.

Simplify the exponent: If the radical has an exponent (such as cube root), divide the exponent by the index of the radical. Example ∛64 = ∛(4^3) = ∛4 * ∛4 * ∛4 = 4 *4 *4 =4

Combine like factors: If there are any factors in the radicand that match the exponent, you can combine them and simplify the radical further. For example, √(2235) = √(2^235) = 2√(35) = 2√15 = 2*3 = 6.

It is important to note that not all radicals can be simplified to a whole number or a fraction. In some cases, the radical will be in its simplest form when it is left as an irrational number.

For Example, √2 cannot be simplified further.

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The round plate in the problem has a surface area of 63.754 square inches.

The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.

Given, A circular plate has a circumference of 28.3 inches.

Since circumference of a circle = 2*3.14 * r

Where r is the radius

Thus,

circumference  = 28.3

6.28 * r = 28.3

r = 4.506

Radius of circle = 4.506

Since the area of the circle = 3.14 * r * r

Thus,

Area of given circle = 3.14 * 4.506 * 4.506

Therefore, the Area of the given Circular plate is 63.754 square inches.

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Grams per cubic centimeter to kilograms per cubic meter is 1000.

1 g/cm³ = 1000 1 kg/m³

The conversion value:

Find the conversion from grams per cubic centimeter to kilograms per cubic meter!

Multiply the number with the each conversion value!

See that the cubic centimeter is as a denominator. So, we reverse the fractional value.

1 g/cm³

= 1 × 1/1000 × 1000000/1 kg/m³

= 1000 kg/m³

Hence, the conversion value from grams per cubic centimeter to kilograms per cubic meter is 1000.

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The width that is left on each side of the mirror is 13 1/4 inches.

Mirrors, due to their size, weight, and combination of robustness and fragility present a challenge for drywall and plaster walls.

The mounting gear for most new mirrors is already included, but it is important to take great consideration when choosing the anchors, screws, and bolts that will connect the mirror to the wall.

Use the following guidance on how to hang a heavy mirror safely so you may update your space while safeguarding your walls and decor after deciding what kind of wall you have and selecting the appropriate materials.

25 - 12 3/4 = 13 1/4

5 1/8 inches broad on each side of the mirror when 13 1/4 are split by two.

5 1/8 + 5 1/8 + 14 3/4 = 25.

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The cab ride will cost you $14.

Cost is the quantity of money spent by a business or work to produce or create goods or services. It excludes the profit margin markup. Cost is the sum of money spent on making a good or product, as seen from the seller's perspective.

as stated in the inquiry, Meena I'm using an online taxi service to order a taxi.

The cab bills $3.50 for the pickup alone, plus an extra $1.75 for each subsequent mile driven.

The original taxi fare plus the number of kilometres multiplied by the 1.75-cent-per-kilometer cost of the additional drive equals 3.50 + 6 (1.75), which equals $14.

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The construction site area is 2025 square meters, calculated by finding the area of a square with side length 45m.

What is square ?

A square is a two-dimensional geometric shape that has four equal sides and four right angles. It is a type of rectangle where all sides are equal in length and opposite sides are parallel. It can also be defined as a polygon with four sides and four angles, all of which are right angles.

The construction site is in the shape of a square and the wooden wall surrounding it is 2m high and has a length of 45m.

Since the wall encloses a square, the length of one side of the square is equal to the length of the wall (45m).

Therefore, the area of the construction site can be calculated by finding the area of a square with side length 45m.

The formula for the area of a square is side length squared (s^2).

area = 45m x 45m = 2025 square meters.

So , The construction site area is 2025 square meters, calculated by finding the area of a square with side length 45m.

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Three points can define the two distinct vectors AB and AC (A, B, and C). The two vectors' cross product, which they both lie on, may be utilized as the plane's normal.

It is logical to assume that this is the case since a plane contains precisely two linearly independent vectors since it has a dimension of two. If the three points were collinear, there wouldn't be two linearly independent vectors; instead, the origin and tips of the two vectors are the three points.

The three points that make up a plane in a three-dimensional space can be used to define it as long as they are not on the same line. On a plane, there exist at least three non-collinear points. A line that connects any two locations in a plane is also considered to be a part of the plane. A line is created at the place of intersection when two planes clash.

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The area of the front side of the fifty-cent piece is 48.06 mm².

The circumference of a circle is the distance around the circle which is 2πr.

The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.

Given, The front side of a circular area fifty-cent piece has a diameter of 30.61 mm.

We know, Radius is half of the diameter which is, (30.61/2) mm.

= 15.305 mm.

We also know the area of a circle is πr².

Therefore, The area of the front side of the fifty-cent piece is,

= π(15.305)² mm².

= 48.0577 mm².

= 48.06 mm².

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99.9% of the population is within 4 standard deviations of the mean.

In information, the standard deviation is a degree of the quantity of variation or dispersion of a fixed of values. A low standard deviation indicates that the values tend to be near the implied (additionally called the predicted price) of the set, whilst an excessive preferred deviation suggests that the values are spread out over a wider variety.

Popular deviation can be abbreviated SD, and is maximum commonly represented in mathematical texts and equations by means of the decrease case Greek letter σ (sigma), for the population standard deviation, or the Latin letter s, for the sample general deviation.

The standard deviation of a random variable, pattern, statistical population, statistics set, or possibility distribution is the square root of its variance. it's miles algebraically easier, even though in exercise less sturdy, than the common absolute deviation.

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To find the radius of the circular area, the organizers must divide 50,000 by pi and then multiply by 5. The result of this calculation is the amount of area needed, which can then be divided by pi to find the radius of the circular region, rounding to the nearest foot.

To find the radius of the circular area, the organizers should first calculate the amount of area needed to accommodate each person in the field. This is done by dividing the total number of people (50,000) by pi and then multiplying by 5, which represents the 5 square feet of space allotted to each person. The result of this calculation is the amount of area needed to fit all 50,000 people. Next, the organizers should divide this area by pi to calculate the radius of the circular region. Finally, they should round the result to the nearest foot. This will give them the radius of the circular area that is needed to fit all 50,000 people in the field.

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The distance between the building and the base of the ladder is 4 feet.

The trigonometric functions are functions that can be applied to determined the side or measure of internal angle of a given triangle. Given that some required properties are given.

Given that the ladder is 8 feet long, let the distance between the building and the base of ladder be represented by t.

So that;

Cos θ = adjacent/ hypotenuse

Cos 60 = x/ 8

x = 8*Cos 60

  = 8*0.5

x = 4

Thus, the building is 4 feet far to the base of the ladder.

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The hip breadth of 95% of all male is 16.2 inches, which is greater than the mean of 14.8 inches with a standard deviation of 0.9 inches.

1. Calculate the Z-score for 95th percentile:

Z = (P95 - mean)/standard deviation

= (16.2 - 14.8)/0.9

= 2.44

2. Look up the Z-score in a Z-table to find the corresponding percentile:

95th percentile = 2.44

The hip breadth of 95% of all male can be calculated using the normal distribution. First, we must find the Z-score for the 95th percentile, which is calculated by subtracting the mean (14.8 inches) from the desired percentile (16.2 inches) and dividing by the standard deviation (0.9 inches). This gives us a Z-score of 2.44. We can then look this up in a Z-table to find the corresponding percentile, which is 95th percentile. Therefore, the hip breadth of 95% of all male is 16.2 inches.

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The polynomial function is obtained to be h(x) = -2 (x - 4)(x - 1)²(x + 2), with the values a = -2, b = -4, c = -1 and d = 2.

What is a polynomial?

An algebraic expression known as a polynomial requires that all of its exponents be whole numbers. Any polynomial must have variable exponents that are non-negative integers. Although a polynomial contains variables and constants, we are unable to divide a polynomial by a variable.

The characteristics of the polynomial are -

The zeros are located at 4, 1 (multiplicity of 2) and-2

The end behavior is as follows -

As x reaches negative infinity, f(x) reaches negative infinity.

As x reaches infinity, f(x) reaches negative infinity.

The y-intercept of the function is (0, 16)

The equation of h(x) can be written as -

h(x) = a(x+b)(x+c)²(x+d)

The zeroes of the polynomial can be written as -

x = 4 ⇒ (x - 4)

x = 1 ⇒ (x - 1)

x = 1 ⇒ (x - 1)....Since the multiplicity is 2 so write it two times.

x = -2 ⇒ (x + 2)

So, the equation will be -

y = a (x - 4)(x - 1)(x - 1)(x + 2)

The y-intercept is given as (0,16).

So, substitute the values of x and y with 0 and 16 respectively.

y = a (x - 4)(x - 1)(x - 1)(x + 2)

16 = a (0 - 4)(0 - 1)(0 - 1)(0 + 2)

16 = 2a(-4)(-1)(-1)

16 = 2a × -4

16 = -8a

a = -2

Hence, the equation becomes y = -2 (x - 4)(x - 1)(x - 1)(x + 2).

On graphing the equation it can be seen that -

As x → -∞, f(x) x → -∞

As x x → ∞, f(x) x → -∞

Therefore, the polynomial equation is h(x) = -2 (x - 4)(x - 1)²(x + 2).

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First, solve the equation for one of the variables in the pair of equations to be solved using substitution method x = 2/13, y = 52

The substitution method is one algebraic approach to solving a linear system. By substituting one y-value for another, the substitution method works. We will illustrate this with an example. Since y = y, we can use y in the first equation instead of the second one.

                                      4x+2y=10⋅2x=26+2y

Take the first equation, for example. For a result of 20, multiply 10 by 2.

                                     4x+2y=20x

20 x both sides should be subtracted.

                                    4x+2y−20x=0

Get 16x by combining 4x and 20x.

                                  −16x+2y=0

The second equation is an example. For a result of 20, multiply 10 by 2.

                                      20x=26+2y

From both sides, subtract 2y.

                                          20x−2y=26

First, solve the equation for one of the variables in the pair of equations to be solved using substitution. Replacing that variable in the other equation with the result follows.

                                       −16x+2y=0,   20x−2y=26

By placing x on the left side of the equal sign, isolate x from one of the equations and solve it for x.

                                                −16x+2y=0

In the equation, deduct 2y from both sides.

                                     −16x=−2y

Subtract 16 from both sides.

                                          x= − 16/ 1(−2)y

16 divided by 2y is the answer.

                                         x= 8  / 1 y

The second equation, 20x2y=26, should now read 8 y instead of x.

                                  20×( 8 /1  )y−2y=26

multiply 20 times 8 y.

                          2  / 5 ​ y−2y=26

Boost 2y by 2.5 years.

                                 2 /1  y=26

2 times both sides will give you y=52.

In the formula x = 81y, change y to 52. You can solve for x directly because the resulting equation only has one variable.

                                        x= 8 /1  ×52

52 x 8 /1 is the multiplication.

                                   x= 2 /13

The system has now been resolved substitution equation are

x = 2/13, y=52

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The inequality form of the statement is: |4x - 2| ≤ 2. And the lowest value of x that makes this inequality true is x = -1.

To solve for the lowest value of x that makes this inequality true, we need to consider two cases:

If 4x - 2 ≥ 0, then |4x - 2| = 4x - 2, so the equation becomes:

4x - 2 ≤ 2

Adding 2 to both sides, we get:

4x ≤ 4

Dividing both sides by 4, we get:

x ≤ 1

If 4x - 2 < 0, then |4x - 2| = -(4x - 2), so the equation becomes:

-(4x - 2) ≤ 2

Adding 2 to both sides, we get:

-4x + 4 ≤ 4

Dividing both sides by -4, we get:

x ≥ -1

So, the solution to the inequality is -1 ≤ x ≤ 1. This means that any value of x that lies between -1 and 1, inclusive, satisfies the inequality.

So, the lowest value of x that makes this inequality true is x = -1.

"

Complete question

The absolute value of the difference between 4x and 2 is less than or equal to 2.

Write the statement as an inequality, then solve for the lowest value of  x that makes this inequality true. Lowest  value _____

"

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Answer: 3x^4*sqrt(3x) is the answer

Step-by-step explanation:

Factor 27 into its prime factors

          27 = 33

To simplify a square root, You take the square factors, or factors that are raised to an even exponent.

Factors which will be taken are:

          9 = 32

Factors which will remain inside the root are:

          3 = 3

To finish this we take the square root of the factors that were taken out. This can be done by dividing their exponents by 2 :

          3 = 3

I hope this helps!

Yes, thirty-six is a rational number. It is represented as a fraction of integers, so it is called an integer and a whole number.

A rational number is defined as the number that can be expressed as a fraction, P/Q and assuming that the denominator of the fraction is not zero, i.e., Q ≠0, and that both the numerator and denominator are integers. In case of an irrational numbers, they cannot be expressed as a fraction. We can identify a number is rational or irrational :

Now, we have a number say, x = 36 and we have to check it is rational or irrational number. Number 36 can be written as 36/1 = P/Q and 1 ≠0 like Q ≠ 0. So, x is a rational number because it can be expressed as the quotient of two integers.

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Complete question:

Is 36 is a rational or irrational?

[tex](4x+1)(2x^2 -2) \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{llll} 2x^2-2\\ \times ~~ 4x\\\cline{1-1} 8x^3-8x \end{array}~~ + ~~ \begin{array}{llll} 2x^2-2\\ \times ~~ 1\\\cline{1-1} 2x^2-2 \end{array}\qquad \implies \boxed{8x^3+2x^2-8x-2}[/tex]

Answer:

5%

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I = Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given:

Substitute the given values into the simple interest formula and solve for r:

[tex]\implies 500=5000 \cdot r \cdot 2[/tex]

[tex]\implies 500=10000r[/tex]

[tex]\implies r=\dfrac{500}{10000}[/tex]

[tex]\implies r=0.05[/tex]

[tex]\implies r=5\%[/tex]

Therefore, the interest rate is 5%.

Answer:

Interest rate = 5% (or) 0.05

Step-by-step explanation:

Now we have to,

→ find the required interest rate.

Formula we use,

→ I = P × R × T

→ PRT = I

→ R = I/PT

Then the interest rate will be,

→ R = I/PT

→ R = $500 ÷ ($5000 × 2 years)

→ R = 500/(5000 × 2)

→ R = 500/10000

→ R = 0.05 × (100)

→ [ R = 5% ]

Hence, the interest rate is 5%.

One must first divide a compound inequality into two other inequalities before solving it.

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