4,-3 reflected over the x axis

The steps to convert the graph a quadratic equation in factored form is explained below.

Factored form in math is defined as the process of expressing a given number or algebraic expression as the product of its factors is called factoring.

Here we need to explain the process of graph a quadratic equation in factored form.

There are three ways are defined to convert them.

The very first way to When every term of the equation has GCD ≠ 0 then it can be factored by taking out GCD as a common factor.

the next way is to use the Identity that is a² - b² = (a + b) (a - b)

The last way is to use the Identity (x + a)(x + b)

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The introduction of harmful chemicals into the air is known as air pollution.

The chief causes of man-made air pollution include vehicle emissions, fuel oils and natural gas used to heat houses, byproducts of manufacturing and electricity generation, notably coal-fueled power plants, and odors from chemical manufacture.Industrial emissions, automobile emissions, and any other place where fossil fuels are burnt are all sources of atmospheric pollution, or air pollution. Another major contaminant that can cause ozone depletion is methane, which is released by landfills and cattle.

Air pollution can have long-term harmful consequences, such as acid rain, which pollutes the Earth’s bodies of water and ruins infrastructure.

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Answer:12

Step-by-step explanation:

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

12

Answer:

1/2x-10

Step-by-step explanation:

[tex]\frac{1}{5} x+\frac{1}{2} (\frac{3}{5}) +\frac{1}{2}(-20)\\\frac{1}{5} x+\frac{3}{10} x-10\\\frac{1}{2} x-10\\[/tex]

Hope this helped! :)

Hey there!

1/5x + 1/2(3/5x - 20)

DISTRIBUTE 1/2 within the PARENTHESES:
= 1/5x + 1/2(3/5x) + 1/2(-20)

= 1/5x + 3/10x - 10

COMBINE the TERMS

= (1/5x + 3/10x) - (10)

= 1/5x + 3/10x - 10

= 1/2x - 10

Therefore, your should be:

1/2x - 10

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The total distance cover by Sagar is, 15 km 385 m.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

To reach the Powai lake picnic spot from star apartments,

Sagar went 13 km 665m by bus ,1 km220 m by autorickshaw and 500 m by foot.

Now, Total distance cover by Sagar is,

⇒ 13 km 665 m + 1 km 220 m + 500 m

We know that;

1 km = 1000m

Hence, We get;

⇒ 13665 m + 1220 m + 500 m

⇒ 15,385 m

⇒ 15 km 385 m

Thus, The total distance cover by Sagar = 15 km 385 m.

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If the caffeine in the body drops by 15% each hour then the equation for this problem is [tex]f(t) = 150\times (0.85)^{t}[/tex]  and the equation represents a exponential decay problem .

the amount of caffeine present in the cup of coffee (a) = 150 mg  ;

the percent drop in caffeine in body each hour (r) = 15% = 0.15  ;

Since the percent of caffeine is dropping in the body , the exponential decay function will be used to represent this situation ;

the exponential decay equation is written as : [tex]f(t) = a\times (1-r)^{t}[/tex] ;

substituting the given values of "a" and "r" in the equation ,

we get ;

⇒ [tex]f(t) = 150\times (1-0.15)^{t}[/tex]

⇒ [tex]f(t) = 150\times (0.85)^{t}[/tex]

Therefore , the exponential decay equation is [tex]f(t) = 150\times (0.85)^{t}[/tex] .

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The expression is [(4^10)×2]/q.

Division is the process of splitting a number or an amount into equal parts.

Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

Here, we have,

given that,

raise 4 to the 10th power, double the result, then divide what you have by q

so. we get,

[(4^10)×2]/q

Hence, The expression is [(4^10)×2]/q.

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Answer: Although I am not 100% sure, I would think the domain 2<x<6  (x being the domain and the point must be on the line) although for these signs they would be "or equal" to. The range would be 6<y<18  (y being the range and once again the point must be on the line) with "or equal" to signs.

Step-by-step explanation:

This is because since there are no concrete points, other than the two ends of this (piecewise?) function, you would have to set the domain to be all x values that fall on this line, hence x being between 2 and 6. The same happens for y, in which, since there are no points plotted, the range is all the y values on the line. Once again, I am not absolutely sure about this, but it seems logical, at least to me.

The function that could be used to define and continue this function is f(n) = 1.25n -3

An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.

Thus, the nth term of arithmetic sequence is given by:

Tₙ  = a + (n-1)d         (for all positive integer values of n)

where a is the first term, n is the number of term and d is common difference

d is the constant difference between each subsequent terms. That is:

d = -0.5 - (-1.75) = 1.25

Tₙ  = -1.75 + (n - 1)1.25

Tₙ  = -1.75 + 1.25n - 1.25

Tₙ  = 1.25n - 3

If we take Tₙ = f(n) , then the function that gives the nth term is:

is f(n) = 1.25n + 3

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The solutions to the given quadratic equation are 1/4 and -1.

The correct options are Options E and F.

          [tex]x = \frac{-b + \sqrt{b^{2} -4ac} }{2a}[/tex]  and [tex]x = \frac{-b - \sqrt{b^{2} -4ac} }{2a}[/tex]

Given equation :

4x² + 3x -1 = 0

Here,a = 4, b = 3, and c = -1.

[tex]x = \frac{-b + \sqrt{b^{2} -4ac} }{2a}[/tex]

The roots of the equation are:

[tex]x = \frac{-3 + \sqrt{3^{2} -4(4)(-1)} }{2(4)}[/tex] and  [tex]x = \frac{-3 - \sqrt{3^{2} -4(4)(-1)} }{2(4)}[/tex]

[tex]x = \frac{-3 + \sqrt{25} }{2(4)}[/tex]  and  [tex]x = \frac{-3 - \sqrt{25} }{2(4)}[/tex]

[tex]x = \frac{2}{8} = \frac{1}{4}[/tex]   and  [tex]x = \frac{-8}{8} = -1[/tex]

Hence the roots of the equation are 1/4 and -1.

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Answer:

153 ft

Step-by-step explanation:

[tex]16 + 1 + 2 + 2 + 5 + 2 + 2 + 8 + 5 + 18 + 9 + 5 +3 + 9 + 3 + 2 + 6 + 6 + 6 + 6 + 6 + 3 + 5 + 23 = 153[/tex]

The polynomial 2x³ + x² -3x +14 must be added to (x³ + 3x -8) to obtain (3x³ + x² +6).

Quadratics are polynomial equations of the second degree, which means that they contain at least one squared term. Quadratic equations are another name for it. The general form of the quadratic equation is:  ax² + bx + c = 0,

where x is an unknown variable and a, b, c are numerical coefficients.

The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics.

Let a polynomial P must be added.

Therefore, according to the question,

P+ (x³ + 3x -8) = (3x³ + x² +6)

=> P= (3x³ + x² +6) - (x³ + 3x -8)

=> P= (3-1)x³ + x² -3x +(6-(-8) )

=> P= 2x³ + x² -3x +14

Thus, the polynomial 2x³ + x² -3x +14 must be added to (x³ + 3x -8) to obtain (3x³ + x² +6).

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Three cards are randomly selected from a standard deck of 52 cards. The probability that each card is a king (k) if the sampling is done without replacement is  1/5525

Probability measures the likelihood of the occurrence of an event. The probability is defined as:

p(A) = n(A) / n(S)

Where:

n(A) = number of possible ways an event A can happens

n(S) = number of possible outcomes.

In a standard deck, there are 4 kings. Hence,

1st draw, the probability it is a king = 4/52

Suppose, that the first card is a king, then the remaining kings are 3 and the remaining cards are 51.

Hence, at 2nd draw, the probability it is a king = 3/51.

Similarly, at 3rd draw, the probability it is a king = 2/50

The probability that each card is a king:

P (3 kings) = 4/52 x 3/51 x 2/50

                  = 24/13260

                  = 1/5525

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Answer:

4x²+4x+3

Step-by-step explanation:

g(f(x))= (2x+1)²+2

= 4x²+4x+1+2

=4x²+4x+3

The answer is: Yes, Yes, Yes, No.

The expression -8 + 5 shows the sum of two integers. This expression has a value of -3. Because -3 is also an integer, the set of integers appears to be closed under addition.

The expression 9 − (-11) shows the difference between two integers. This expression has a value of 20. Because 20 is also an integer, the set of integers appears to be closed under subtraction.

The expression 3 · (-4) shows the product of two integers. This expression has a value of -12. Because -12 is an integer, the set of integers appears to be closed under multiplication.

The expression, -1 ÷ 6, shows the quotient of two integers. This expression has a value of -1/6, Because -1/6 is not an integer, the set of integers is not closed under division.

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The value of P(1≤x≤3)  is 0.84

What is Probability ?

Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.

P(1≤x≤3) defined the probability that the result is between 1 and 3, included. You can answer this question in two ways:

1. Sum the probabilities of good events:

From the graph, we have

P ( x= 1 ) = 0.32

P ( x = 2 ) = 0.24

P ( x= 3 ) = 0.28

So,

P ( 1 <= X <= 3 ) = 0.32 + 0.24 + 0.28

= 0.84

2. Use complementary probabilities

Asking that the result is 1, 2 or 3 is the same as asking that the result is not 4. The probability that the result is 4 is 0.16, so the probability that the result is not 4 will be

P ( x not equal to 4 ) = 1 - P ( x = 4 )

= 1- 0.16

= 0.84

Therefore, The value of P(1≤x≤3)  is 0.84

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The length of the yard as calculated from the given data is found out to be as 5 yards long.

let the length of the yard be , 27 - 9x

and the width of the yard is x.

Given , the are of the yard = 360.

Therefore, we can say that

=>x(27 - 9x) = 360

=>27x - 9x² = 360

=> 3x - x²  = 40

=> x²  - 3x + 40 = 0

=>x²  + 5x - 8x + 40 = 0

=> x ( x - 5) -8 ( x - 5 )

Therefore, the value of x will be 5 or 8.

On putting these values in the equation we get that , the length being 5 is the correct answer.

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Answer: Probability that she attended class regularly given that she receives A grade is 0.9286.

Step-by-step explanation: i looked it up man ‍♀️

There are 1001 different committees can be chosen.

The problem is asking how many different committees can be chosen or the number of ways to select 4 students out of a group of 14 without regard to order. This is a combinatorics problem, and it can be solved using the combination formula:

nCr = n!/(r!(n-r)!)

Where n is the total number of items to choose from (14 students in this case) and r is the number of items to choose (4 students).

Plug in the values and solve.

14C4 = 14!/(4!(14-4)!)

14C4 = 14!/(4!10!)

14C4 = 1001

Therefore, the number of different committees that can be chosen is 1001.

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The solution to the system of equation 4y + x = 15 and x = 8y + 3 is (11, 1)

An equation shows the relationship between numbers and variables in an expression.

The standard form of a linear equation is:

Ax + By = C

Where A, B and C are constants

Given that:

4y + x = 15

multiply by 2:

8y + 2x = 30    (1)

Also:

x = 8y + 3

8y - x = -3     (2)

Subtract equation 2 from 1 to solve using elimination method:

3x = 33

x = 11

put x = 11 in equation 2:

8y - 11 = -3

y = 1

The solution is (11, 1)

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The area of triangle OPQ is 44 square units.

How to find the area of tringle?

There are different ways to find the area of a triangle, depending on the information given. Here are a few common methods:

There are different methods to find the area of a triangle, but one common method is to use the coordinates of its vertices and the distance formula. The distance formula is

d = √((x2-x1)^2 + (y2-y1)^2)

We can use the distance formula to find the lengths of the sides of the triangle OPQ, which are:

OP = √((8-3)^2 + (3-4)^2) = √((5)^2 + (-1)^2) = √(25+1) = √26

OQ = √((4-3)^2 + (8-4)^2) = √((1)^2 + (4)^2) = √(1+16) = √17

PQ = √((4-8)^2 + (8-3)^2) = √((-4)^2 + (5)^2) = √(16+25) = √41

Once we have the lengths of the sides of the triangle, we can use the Heron's formula to find its area:

s = (OP + OQ + PQ)/2

Area = √(s(s-OP)(s-OQ)(s-PQ))

s = (√26 + √17 + √41)/2 = (√44)/2 = 4√11

Area = √(4√11(4√11-√26)(4√11-√17)(4√11-√41))

Area = √(4√11 * √(44-26) * √(44-17) * √(44-41))

Area = √(4√11 * √18 * √27 * √3)

Area = √(4√11 * 3√2 * 3√3 * √3)

Area = 4*11 = 44 square units

Hence, the area of triangle OPQ is 44 square units.

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The solution for the system of equations is x = -6 and y = 8.

When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."

There are both one-variable and two-variable linear equations.

Given the equations,

-2x + 5y = 52

x + 4y = 26

solving by elimination method,

multiply by 2 in equation x + 4y = 26

= 2x + 8y = 52

now add both equations,

-2x + 5y + 2x + 8y = 52 + 52

13y = 104

y = 104/13

y = 8

substitute the value of y in equation x + 4y = 26

x + 4(8) = 26

x = 26 - 32

x = -6

Hence the solution of an equation is at x = -6 and y = 8.

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The value on simplifying the fraction expression 5/6 - 7/12 is obtained as 1/4.

What is a fraction?

In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.

The fraction expression is given as 5/6 - 7/12.

5/6 - 7/12

First take the LCM of the denominator -

LCM = 12

Now, multiply 2 by 5 in first fraction numerator, as 6 multiplied by 2 is 12 (LCM) -

10/12 - 7/12

Now, use the arithmetic operation of subtraction -

(10 - 7)/12

3/12

Divide numerator and denominator by 3 -

1/4

Therefore, the final value as a fraction is obtained as 1/4.

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It is been proved that c(a+b) = ab.

Prove:-

c(a+b) = ab.

it is given that ∠ ABD = ∠ XYD = ∠ CDB = 90°

So, Lines AB, XY, and CD are parallel to Each other.

→ AB || XY || CD

Now In ΔABD, we have,

→ AB || XY

So,

→ DY/BD = c/a

→ DY = (c/a)*BD ----------------------- Equation (1)

In Δ BDC we have

→ CD || XY

So,

→ BY/BD = c/b

→ BY = (c/b)*BD ----------------------- Equation (2)

______________________

Adding Equation(1) and Equation(2) now, we get

→ DY + BY = (c/a)*BD + (c/b)*BD

taking (c * BD) common From LHS, we get,

→ BD = c * BD(1/a + 1/b)

BD will be canceled from both sides,

→ 1/c = 1/a + 1/b

→ 1/c = (a+b)/ab

→ c(a+b) = ab

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The Question is incomplete although I've found a similar question of it.

: Picture attached:

The rule of the functions for the ordered pairs will be f(x) = (2/3)².

An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values written in parentheses in a specific order. In order to understand a point visually, it can be helpful to locate it on the Cartesian plane. An ordered pair's numerical values may be fractions or integers.

Given that the ordered pairs are (1,2/3), (2,4/9),(3,8/27),(4,16/81) (5,32/243).

x          y

1        2/3        = (2/3)^1

2        4/9        = (2/3)^2

3        8/27      = (2/3)^3

4        16/81    = (2/3)^4

5        32/243  = (2/3)^5

Function rule is f(x) = (2/3)²

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The length of each leg, just divide the hypotenuse, 12 , by the square root of 2. Then to remove the radical from the denominator, multiply both numerator and denominator by square root of 2.

Find the length of each leg?

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The total of all the angles created on a transverse that are inside either of the two parallel lines is always 180 degrees.

Lines that are parallel to one another on a plane do not intersect or meet at any point. They are always equidistant from one another and parallel. Non-intersecting lines are parallel lines. Parallel lines can also be said to meet at infinity.

When a transversal intersects two parallel lines, the angles that are created inside are equal to the alternate pairings of that transversal. Alternate interior angles are what they are termed.

When a transversal intersects two parallel lines, co-interior angles result between the lines. On the same side of the transversal, the two angles always sum to 180 degrees.

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Answer:

2790 ft²

Step-by-step explanation:

Area of rectangle with length L and width W:

area = LW

area = 45 ft × 62 ft

area = 2790 ft²

The algebraic expression to represent how much time he has left to drive as function is given as f(g) = g - 21.

Given is that Greg will travel on his trip across the country to attend his cousin's wedding. The first day he travels 8 hours. The second day he travels 9 hours. The third day he had mechanical problems and only drove 4 hours.

We can write an algebraic expression to represent how much time he has left to drive as function f(g). We can write -

f(g) = g - (8 + 9 + 4)

f(g) = g - 21

Therefore, the algebraic expression to represent how much time he has left to drive as function is given as f(g) = g - 21.

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