Solve the following quadratic equation, giving your answer accurate to 2 decimal places:


3x^2-16x+6=0

Answer:

Below

Step-by-step explanation:

The point-slope form of a line is:

y - y1 = m(x - x1)

Where m is the slope of the line and (x1, y1) is a point on the line.

Given that the line contains the point (-2, 1) we know that this point is on the line, so we can use it as (x1, y1) in the point-slope form.

By using the point (-2,1) we can write the point-slope form of the line as:

y - 1 = m(x + 2)

This means that the point-slope form of a line with slope that contains the point (-2, 1) is y - 1 = m(x + 2) where m is the slope of the line.

Answer:30:1

Step-by-step explanation:

60÷2

=30/1

=30:1

Total charge that Tom has to pay is $142.2, and the express function for the monthly charge is c(x) = 105 + (x -4) * 12

As per data given, monthly value given is $105 = free text + free call + 4gb  and extra gigabyte x $12. Tom that use 7.1 of data will be charge as follow:

Tom charge = normal use + extra use

To charge = 105 + extra gigabyte x12

Extra gigabyte = tom use - normal use

Extra gigabyte = 7.1 - 4

Extra gigabyte = 3.1

Tom charge = 105 + 3.1 x 12

Tom charge = 105 + 37.2

Tom charge = 142.2

The expression of monthly charge, since we have already define that value is $105 = free text + free call + 4gb and extra gigabyte x $12. We can see that text is not charge and call is not charge. So the formula will be:

Monthly charge = 105 + (extra gigabyte - 4) x 12

As per question said the variable for extra gigabyte is x and monthly charge is c(x) then

c(x) = 105 + (x - 4) * 12



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The data 36, 6); (18, 5); (0, 4); (-18, 3) is an example of a function.

A relation is a function if it has only One y-value for each x-value.

We have to check whether the data (36, 6); (18, 5); (0, 4); (-18, 3)

is an example of function.

The ordered pairs are thirty six comma six comma eighteen comma five comma zero comma four comma minus eighteen comma three.

As we observe there is only one y value for each x value.

and the x values are not repeated.

Hence, the data 36, 6); (18, 5); (0, 4); (-18, 3) is an example of a function.

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The relationship of the degree x - [[- b+v(b2 - 4ac)V2a] = 0 describes the relationship between a quadratic equation's factors and its solutions. A quadratic equation's general equation is f(x) = ax*+ bx +. function:

A function in mathematics from a set X to a set Y allocates 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 respectively.

expression: Terms (constants and variables) are separated by mathematical operators to form a mathematical expression. equation: Two expressions are equated using a mathematical equation. The quadratic equation f(x) = axe + bx + c is given.

The quadratic equation (ax2 + bx + c= 0) can be expressed as a product of its linear factors as (x - k)(x - h), where h, k are the quadratic equation's roots. This process is known as factoring a quadratic equation.

We may write [h] =- b + v(b2 - 4ac)y2a [K]=(-b- V(b2 - 4ac))/2a using the quadratic formula. The link between the elements of a quadratic equation and its solutions can be expressed as - x- [[-b+v(b- 4ac)y2a] =0

X=[(b' - 4AC)y2A] = 0.

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Sum in math the sum of the series is computed using the summation formulas.

The sum of the series is computed using the summation formulas. There are many different kinds of sequences, including arithmetic and geometric sequences, and consequently, there are many different kinds of summing formulas for those different kinds of sequences.

There are also summation formulas that determine the sum of natural numbers, sum of natural number squares, sum of natural number cubes, sum of natural number evens, sum of natural number odds, etc. The list of summation formulas is provided here. Each of these formulas will be covered in detail in the section that follows.

a₁ + a₂ + a₃ +.......aₙ = Σ a

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The height of the TV would be 61.27 inches.

What is Pythagoras theorem?

The hypotenuse's square length is equal to the sum of the squares of the lengths of the other two sides of the right-angled triangle, according to the Pythagorean theorem, commonly known as the Pythagoras theorem.

Here, The 75 inches represents the length of diagonal of the TV because the length of TV is always measured diagonally. So, the diagonal's length is 75 inches.

We've width as 43.25 inches.

Since TV is of the shape of rectangle, we can calculate the height by applying Pythagoras theorem.

So, we've   hypotenuse² = (side 1)² + (side 2)²

It can be written as,

                   diagonal² = height² + width²

                   (75)² = height² + (43.25)²

                  height² =  (75)² -  (43.25)²

                               = 5625 - 1870.5625

                               = 3754.4375

                   height = √3754.4375 = 61.27 inches.

Hence, height will be 61.27 inches.

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A square yard of carpet that is selling for $8.95 per square foot would cost $80.55 per square yard.

What is the conversion factor?

A conversion factor is a number used to change one set of units to another, by multiplying or dividing. When a conversion is necessary, the appropriate conversion factor to an equal value must be used. For example, to convert inches to feet, the appropriate conversion value is 12 inches equals 1 foot.

A square yard of carpet is equivalent to 9 square feet because 1 yard = 3 feet and 1 square foot = 1 foot x 1 foot.

So, to find the cost of a square yard of carpet that is selling for $8.95 per square foot, we need to multiply the price per square foot by the conversion factor of 9 square feet per square yard.

$8.95/square foot * 9 square feet/square yard = $80.55/square yard

Hence, a square yard of carpet that is selling for $8.95 per square foot would cost $80.55 per square yard.

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The sum of the roots of the equation is

97/9

Generally, The roots of equation 3x^2 + 4x + 12 = 0 can be found by factoring or by using the quadratic formula.

By factoring: 3x^2 + 4x + 12 = 0 \Rightarrow (3x + 4)(x + 3) = 0$

Thus, the roots are

r = [tex]-\frac{4}{3}[/tex][tex]-\frac{4}{3}[/tex]

s = -3.

By using the quadratic formula:

[tex]r,s = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\ = \frac{-4 \pm \sqrt{4^2 - 4(3)(12)}}{2(3)} \\\\= \frac{-4 \pm \sqrt{-48}}{6}\\\\ = -\frac{2}{3} \pm \frac{\sqrt{-3}}{3}i[/tex]

The sum of squares of roots is

r^2+s^2 =[tex](-\frac{4}{3})^2 + (-3)^2[/tex]

[tex]= \frac{16}{9} + 9\\\\ = \frac{16+81}{9}[/tex]

= [tex]\boxed{\frac{97}{9}}[/tex]

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Answer:

Step-by-step explanation:

Liam went into a movie theater and bought 9 bags of popcorn and 8 drinks costing a total of $97.50. This will be:

9p + 8d = 97.50

Jacob went into the same movie theater and bought 5 bags of popcorn and 4 drinks, costing a total of $51.50. This will be:

5p + 4d = 51.50

where P = popcorn

d = drink

The equations will be:

9p + 8d = 97.50

5p + 4d = 51.50

Multiply equation i by 5

Multiply equation ii by 9

45p + 40d = 487.50

45p + 36d = 463.50

Subtract

4d = 24

Divide.

d = 24/4

d = 6

Since 9p + 8d = 97.50

9p + 8(6) = 97.50

9p + 48 = 97.50

9p = 97.50 - 48

p = $5.50

where P = popcorn and d = drink

Answer:

2 apples

Step-by-step explanation:

It is because she had 1 apple then she added another which made it 2.

If the number can be expressed in the form of the fraction [tex]\frac{p}{q}[/tex] , then the number is called as Rational Number otherwise it is called as irrational number .

The Rational Numbers are the type of numbers that can be expressed in the form of [tex]\frac{p}{q}[/tex] , where p and q both are integers , and the denominator q should not be equal to 0 .

For Example : the numbers 5 , 2/3 , 6 are rational numbers .

The Irrational Numbers are defined as the type of real numbers which cannot be represented as simple fractions. The Irrational number cannot be expressed as a ratio .

For Example : [tex]\sqrt{2}[/tex] , [tex]\sqrt{5}[/tex] cannot be expressed as a fraction of integers , so they are irrational .

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The y-value of the solution to the system of equations 3x + 5y = 1 and 7x + 4y = - 13 is 2.

In the given question, we have to solve the y-value of the solution to the system of equations.

3x + 5y = 1..................(1)

7x + 4y = -13...............(2)

Multiply equation 1 by 4 and equation 2 by 5, we get

12x + 20y = 4................(3)

35x + 20y = -65................(4)

Subtract equation 4 by 3, we get

23x = -69

Divide by 23 on both side, we get

x = -3

Now putting the value of x in the equation 1, we get

3(-3) + 5y = 1

-9 + 5y = 1

Add 9 on both side, we get

5y = 10

Divide by 5 on both side, we get

y = 2

Hence, the y-value of the solution to the system of equations 3x + 5y = 1 and 7x + 4y = - 13 is 2.

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The complete question is:

What is the y-value of the solution to the system of equations?

3x + 5y = 1; 7x + 4y = - 13

The general form for the absolute value equation to describe a graph is written as f(x) = a|x - h| + k  .

The Absolute Value Function is defined as a function in algebra where the variable is inside the absolute value bars.

The general form for absolute value function is f(x) = a |x - h| + k and  commonly used form of this function is f(x) = |x| .

Plot the graph of  function f(x) = |x| whose formula can also be expressed as f(x) = x, if x ≥ 0 and -x, if x < 0.

Consider different points for x = -1 , y is 1 ,

for x = 1 , y is 1 .

On plotting we get the graph as shown below .

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The other equation of the system of linear equation that has no solution is y = 2x - 2.

If a system of linear equations has no solution, it means that the equations are inconsistent, which means that the two lines represented by the equations will not intersect. Therefore, the lines are parallel with each other.

One way to find the equation of the other line that would make the system inconsistent is to find the equation of a line that is parallel to the given equation but has a different y-intercept.

The given equation is in slope-intercept form, y = mx + b, where m is the slope (in this case, m = 2) and b is the y-intercept (in this case, b = -1).

A line that is parallel to the given line will have the same slope (m = 2), but a different y-intercept. For example, a line with y-intercept of -2: y = 2x - 2.

So, one equation that could be the other equation of the system and make it inconsistent is y = 2x - 2.

The problem seems incomplete, it must have been...

"A system of linear equation has no solution. One of the equations of the system is shown. y = 2x − 1 Which equation could be the other equation of the system?"

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Answer:

Step-by-step explanation:

To prove that sinA/(1-cosA) = 1/cosA, we will start with the left-hand side and simplify it using trigonometric identities.

sinA/(1-cosA) = sinA/(1-cosA) * (sin^2A + cos^2A) / (sin^2A + cos^2A)

= (sinAsin^2A + sinAcos^2A) / (sin^2A + cos^2A - sin^2AcosA - cos^2AcosA)

= (sinAsinAcosA + sinAcosAcosA) / (sinAcosA - cosAcosA)

= sinA/cosA / (sinA/cosA - 1)

= 1/cosA

Therefore, sinA/(1-cosA) = 1/cosA, which is true.

Both Elena and Lin are right , in my opinion. According to Elena, length BC is 16.5 units. Lin estimates that BC is 17.1 units long.

The remainder of the query is included in the attachment. The figure shows that ED is parallel to A B and B C is parallel to A B. In light of the Pythagoras theorem,

[tex]$\mathrm{AC}^ 2=\mathrm{AB}^ 2+\mathrm{BC}^ 2$[/tex]

[tex]$\mathrm{BC}^ 2=196-36=160$[/tex]

[tex]$\mathrm{BC}=12.649$[/tex] or [tex]$12.65$[/tex]

Both Elena and Lin are right .A visual that conveys information rather than just representing it. particularly : a diagram demonstrating the relationships and arrangements (as between parts): a dotted line drawing used in science or math .

A diagram is a picture that shows how something works, how it's organised, or how it's related to something else. Even when they go by the names "map," "chart," or "graph," several diagram kinds are still considered to be diagrams. as flowcharts, organisational charts, and mind maps. An illustration that depicts an object's component elements and their relationships to one another is called a diagram.

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Answer:

x = -3, -1, 1, 3.

Step-by-step explanation:

x^4 - 10x^2 + 9 = 0

Step 1

Let t = x^2

So , we have the quadratic

t^2 - 10t + 9 = 0

Step 2

Factorise:

(t - 1)(t - 9) = 0

Step 3

So, t - 1 = 0 or t - 9 = 0

t = 1, 9.

But t = x^2

So, we have x^2 = 1 or x^2 = 9

So, x = ±1, ±3.

x = -3, -1, 1, 3.

Angel check out 12 library book and Inola check out 1/3 then Inola checks out 8 books.

What is algebraic equation ?

An algebraic equation is a mathematical statement that uses mathematical symbols (such as numbers, variables and mathematical operations) to express the equality of two expressions. It is used to represent mathematical relationships and to find solutions to problems. The most common operations used in algebraic equations are addition, subtraction, multiplication, and division.

Let x be the number of books that Inola check out

We know that:

Angel checks out 12 books

Inola checks out 1/3 less than Angel

We can set up the equation:

x = 12 - (1/3*12)

x = 12 - 4

x = 8

So, Angel check out 12 library book and Inola check out 1/3 then Inola checks out 8 books.

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Angel checks out 12 books

Inola checks out 1/3 less than Angel

We can set up the equation:

x = 12 - (1/3*12)

x = 12 - 4

x = 8

5([tex]x^{2}[/tex] + 10/2[tex]x[/tex]) + 2

The number in the brackets is b/2a.

So:

5(x + 10/2(5))^2

5(x + 10/10)^2

5(x + 1)^2

Expand the double brackets for (x + 1)^2:

[tex]x^{2}[/tex] + [tex]x[/tex] + [tex]x[/tex] + 1

This simplifies to:

[tex]x^2[/tex] + 2[tex]x[/tex] + 1

5([tex]x^2[/tex] + 2[tex]x[/tex] + 1)

5x^2 + 10x + 5

2 - 5 = -3

5(x + 1)^2 - 3

Answer:

5(x + 1)^2 - 3

The shrink-wrapped carton of 64 juice boxes contained 2 gallons of juice.

To find out how many gallons of juice were in the shrink-wrapped carton, we first need to convert the number of juice boxes to cups and then convert that amount to gallons.

Each juice box contains 1/2 cup of juice, so 64 boxes contain 64 * (1/2) = 32 cups.

There are 16 cups in 1 gallon, so to convert 32 cups to gallons, we divide 32 cups by 16 cups/gallon.

32 cups / 16 cups/gallon = 2 gallons

So, the shrink-wrapped carton of 64 juice boxes contained 2 gallons of juice.

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The distance between the pair of points (- 5, 7) and (- 1, 3) is 5.7 units.

We know that the distance formula.

The distance between points (x₁, y₁) and (x₂, y₂) is given by,

[tex]d = \sqrt{[(x_2 - x_1)^2 + (y_2 - y_1)^2]}[/tex]

Here we have been given a pair of points (- 5, 7) and (- 1, 3)

Let us assume that  (x₁, y₁) = (-5, 7)

and (x₂, y₂) = (-1, 3)

Using above distance formula,

[tex]d = \sqrt{[(x_2 - x_1)^2 + (y_2 - y_1)^2]} \\\\ d = \sqrt{[(-1 - (-5))^2 + (3 - 7)^2]}\\\\d = \sqrt{[(-1+5)^2 + (-4)^2]}\\\\d = \sqrt{[(4)^2 + (-4)^2]}\\\\d = \sqrt{(16+16)}\\\\d = \sqrt{32}\\\\d = 5.7~ units[/tex]

So, the distance is 5.7 units.

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The complete question is:

What is the distance between the pair of points (- 5, 7) and (- 1, 3)?.

Answer:f=56 I hope this helps

Step-by-step explanation:

f divide (-7) =-8

Dividing a positive and a negative equals a negative: (+) divided sign (-) =( -) and then

Write the division as a fraction

-1/7f=-8

Multiply both sides of the equation by -7

f=56

Answer:

f = 56

Step-by-step explanation:

Given statement,

→ f divided by -7 is -8.

Forming the equation,

→ f/-7 = -8

Now the value of f will be,

→ f/-7 = -8

→ f = -8 × -7

→ f = 8 × 7

→ [ f = 56 ]

Hence, the value of f is 56.

The value of exponential growth  after 327 minutes is 1870.

Exponential growth is the process by which quantity increases over time. It occurs when a quantity's instantaneous rate of change with respect to time is proportional to the quantity itself.

An exponential function depicts the relationship between an input and an output by using repeated multiplication on an initial value to obtain the output for any given input.

We are aware that

The exponential growth equation is equal to

y = a(1 + r)ˣ

where

an is the starting point.

r denotes the growth rate.

x represents the time in hours.

y is the quantity's value.

We now have

a = 1800

r = 0.7%

 = 0.7/100

 = 0.007

By substituting,

y = 1800(1 + 0.007)ˣ

x = 5.45 hr

y = 1800(1.007)^5.45

y = 1869.748182

y = 1870

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The answer will be 76, using a gradient.

What is the gradient of the slope?

To find the gradient of the given data, horizontal as well as the vertical distance between two points in parallel is necessary to find.

532/7=76

Hence the answer is 76

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The length of the base of the rectangle is B = 11 yards

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the rectangle be represented as A

Now , the value of A is

Let the base of the rectangle be represented as B

Area of rectangle A = 209 yards²

The length of the rectangle L = 19 yards

And , Area of Rectangle = Length x Width

Substituting the values in the equation , we get

Area of Rectangle = 19 x B

209 = 19 B

Divide by 19 on both sides of the equation , we get

B = 209 / 19

B = 11 yards

Hence , the length of the base of rectangle is 11 yards

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Yes, the function f(x)=2x-3 is a one-to-one function.

The Inverse of a Function:

The inverse of a function can be computed if the function can be proven to be one-to-one. Take the one-to-one function and compute its inverse by interchanging x and y in the expression and solving for y.

Graphically, then, the graphs of the function and its inverse are the reflections of each other about the line y=x.

Use the definition to test the one-to-one of f.

Let x and x be the elements in the domain off and assume f(x₁)=f(x₂)

2x₁-3=2x₂-3

2x₁=2x₂

x₁=x₂

since f(x₁)=f(x₂) implied x the function f is one-to-one.

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Yes, I would like to purchase a ticket for the movie. The discounted sale price would be $8.37 after factoring in the 20percentage student discount and the 5.75% tax rate.

Original Price: $10.90

Student Discount: 20% of 10.90 = 2.18

Subtotal: 10.90 - 2.18 = 8.72

Tax Rate: 5.75% of 8.72 = 0.50

Final Sale Price: 8.72 + 0.50 = 8.37

Yes, I would like to purchase a ticket for the movie. The original price of the ticket is $10.90. As a student, I am eligible for a 20% discount, which when applied to the original price brings it down to $8.72. To calculate the final sale price, I then need to factor in the 5.75% tax rate. This is done by multiplying the subtotal of $8.72 by 0.0575, which gives me a tax amount of $0.50. When this amount is added to the subtotal, the final sale price becomes $8.37.

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Carrie average has a head full of 16 curlers, with 4 of them being pink, 8 of them being green, and the remaining 12 being can curlers.

1. There are 16 total curlers on Carrie's head

2. One-fourth of the curlers are pink, so that is 16 ÷ 4 = 4 pink curlers

3. There are twice as many green curlers as pink ones, so that is 4 x 2 = 8 green curlers

4. The remaining 12 curlers are can curlers, so there are 12 can curlers on Carrie's head

Carrie has a head full of 16 curlers in total. One-fourth of the curlers are pink, so we can divide 16 by 4 to get 4 pink curlers. There are twice as many green curlers as pink ones, so we can multiply 4 by 2 to get 8 green curlers. This leaves 12 curlers, which must be can curlers. Therefore, there are 12 can curlers on Carrie's head. We can use basic mathematics to break down the problem into smaller pieces and calculate the number of each type of curler on her head.

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Their taxable income  $9,250.

Single-tax-return filing status with the IRS. For unmarried individuals who are not eligible to file as the head of household, single is the default filing status.

When submitting your tax return, you must choose the single filing status if you were not married on the last day of the tax year and you are not eligible to utilize any other filing status.

The amounts for the 2022 standard deduction are as follows: Married Jointly Filing or Qualifying Widow(er) - $25,900 (an increase of $800) $19,400 (an rise of $600) for the head of the household Married Filing Separately or Single: $12,950 (an increase of $400).

An individual making $50,000 will pay $9,250, according to the exhibit that is attached.

People who make $50,000 fall into the $42,001-$100,000 category and pay $7,250 plus 25% of any amount over $42,000.

The tax burden is as follows:

= 7,250 + ( 25% x (50,000 - 42,000))

= 7,250 + (25% x 8,000)

= $9,250.

The complete question is,

Using Exhibit 11-4 as a guide, calculate the tax due on a person with a $50,000 taxable income.

$9,250 \s$10,110 \sO $15,000 \sO $12,500.

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