I need help with this!!

the zeroes of the function f (x) = 2 x² + 8 x - 3 are x = - 2 ± √ 11 / 2.

We are given a function:

f (x) = 2 x² + 8 x - 3

We need to use the completing the square method to find the zeroes.

f (x) = 2 x² + 8 x - 3

f (x) =  x² + 4 x - 3 / 2

f (x) =  ( x )² + 2 (2) (x) + (2)² - (2)² - 3 / 2

f (x) = ( x + 2 )² - 4 - 3 / 2

f (x) = ( x + 2 )² - 11 / 2

(x + 2)² = 11 / 2

x + 2 = ± √ 11 / 2

x = - 2 ± √ 11 / 2

Therefore, the zeroes of the function f (x) = 2 x² + 8 x - 3 are x = - 2 ± √ 11 / 2.

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The value of x in the equation is 5. 25

Algebraic expressions are defined as expressions comprising of terms, variables, coefficients, factors, and constants.

They are also made up of mathematical operations such as addition, multiplication, division, bracket, etc

Given the expression;

x - 9.8 / -2.2 = 9.7

Find the quotient

x - (-4. 45) = 9. 7

expand the bracket

x + 4. 45 = 9. 7

collect like terms

x  = 9. 7 - 4. 45

Subtract like terms

x = 5. 25

Thus, the value of x in the equation is 5. 25

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Hence, the complete the point-slope equation of the line through ( − 2 , 6 ) (−2,6) is y = 6 .

We have given two points ( − 2 , 6 )and  (−2,6) .

Using slope formula , we get

m = 6 - 6 / -2 -(-2)

m = 0

Putting m = 0 , x₁ = -2 and y₁ = 6 in equation (1) , we get

 y - 6 = 0

 y = 6

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Answer:

Step-by-step explanation:

Given

Answer:

[tex]r = 5[/tex]

Step-by-step explanation:

[tex]r^3 = 125 \text{ // Take the 3rd sqrt of both sides}\\\to \sqrt[3]{r^3} = \sqrt[3]{125}\\\to r = 5[/tex]

Answer:

Brainleast Answer

Step-by-step explanation:

r=5

hopebit helps

Population in the year 2000= 198.85million

From the question, we get to know that the population in 2009 was 191.5 million.

And we have to find the population of the year 2000 which is 3.7%more than the 2009 population.

So let us take the population of the year 2000 to be x.

From the above, we can form an equation:

(population of year 2000 * ( 100-3.7 /100) = (population of year 2009)

i.e., x * 100-3.7/ 100 = 191.5

x * 96.3 = 191.5

x = 198.85

So 198.85 is the population of 2000.

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Answer:

[tex]19^{z-y}[/tex]

Step-by-step explanation:

assuming you meant z > y

using the rule of exponents

[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{m-n}[/tex] ( m > n ) , then

[tex]\frac{19^{z} }{19^{y} }[/tex] = [tex]19^{z-y}[/tex]

According to the solving the line segment LM of line KM = 3.

A line segment is defined as the area between two different points on a line. A line segment is a section of a line that links two points. A line has no endpoints and stretches in both directions indefinitely, but a line segment includes two fixed or definite endpoints.

In general, if both end points of a line segment are vertices of such a polygon or polyhedron, the line segment has to be either the edge (of that polygon or polyhedron) if they are both adjacent vertices, or a diagonal. A chord is a line segment whose end points are both on a curve (such as a circle) (of that curve).

KL = 9

LM = x - 1

KM = -4 + 4x

So

KL + LM = KM

Substituting the value we get:

9 + x - 1 =  -4 + 4x

8 + x = -4 + 4x

8 + 4 = 4x - x

12 = 3x

x = 4

The value of x  = 4 putting the value in the (LM = x - 1):

We get:

LM = x - 1

LM = 4 - 1

     = 3

LM = 3

According to the solving the line segment LM of line KM = 3.

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The interest that 2560 earns in 17 months at a rate of 5 1/8% is $185.9.

In the fields of finance and economics, interest is the payment of a sum over and above the principal amount to a lender or depositor by a borrower or deposit-taking financial institution at a set rate. It is not the same as a fee that the borrower might pay to the lender or another entity.

Principal = $2560

Time = 17 months = 1.417 years

Rate = 5.125%

Therefore, the Interest will be:

= (Principal × Rate × Time) / 100

= (2560 × 1.417 × 5.125) / 100

= $185.9

Therefore, the interest that 2560 earns in 17 months at a rate of 5 1/8% is $185.9.

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Answer:x=0

Step-by-step explanation:hope it helps, brainliest? i could really use it

Potential energy required is 4,018 kg m² /s²

What is Potential Energy ?

Potential energy is the stored energy of the object which is generally based on the relative position of the various parts of the object. It is also known as gravitational energy. Potential energy always measures if we know the height of the object and the mass of the object on which energy is applied as well.

Formula of potential energy :

U = mgh

where, U = gravitational energy

           m = mass of object

           g = gravitational acceleration

           h = vertical height  of object

In the question given,

g= -9.8m/s² , h = 10 m , m = 41kg

as, U = mgh

        = (41 )(9.8)(10)

        = 4,018 kg m² /s²

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The reasons arranged in the order that correctly completes the two column table to prove that ‹2 and ‹3 are supplementary is as follows;

Supplementary angles are angles that have a sum of 180°.

The completed table is presented as follows;

Statements Reasons

1. ‹1 and ‹2 form a linear pair; Given(‹1 and ‹2 form a linear pair)

2. ‹1 and ‹2 are supplementary; Supplementary theorem

3. m‹1 and m‹2 = 180°; Definition of supplementary angles

4. ‹1 congruent ‹3;Given (‹1 and ‹3 are congruent)

5. m‹1 = m‹3; Definition of congruency

6. m‹3 + m‹2 = 180°; Substitution

7. ‹2 and ‹3 are supplementary; Definition of supplementary angles

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Answer:

[tex]A = x^2 + 12x + 36[/tex]

Step-by-step explanation:

The new square's side can be algebraically expressed as [tex]x + 6[/tex], as we know it's 6 units longer than the previous square with side length [tex]x[/tex].

Therefore, its area would be:

[tex]A = (x + 6)^2 \text{ // Remember: } (a + b)^2 = a^2 + 2ab + b^2\\\to A = x^2 + 12x + 36[/tex]

Answer:

A = arithmetic mean

n = number of values

a_i = data set values

Step-by-step explanation:

Hope it helps! =D

Solution of log 6-log 3 x = -2 is , x =200

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as [tex]log_{a}x[/tex] .

where, a is the base of function or equation

           x is the expression

Mathematically, if [tex]a^x = N[/tex] is an exponential function then, this can be converted to logarithmic function as  [tex]log_aN = x[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms :

According to given statement,

log 6-log 3 x= -2

using formula of log a - log b, we can write the eq. as

[tex]log \frac{6}{3x} = -2[/tex]

=> [tex]6 / 3x = 10^{ -2}[/tex]

=> [tex]3x = 600[/tex]

=> [tex]x =200[/tex]

Thus solution of log 6-log 3 x=-2 is , x =200

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Answer:

27.77

Step-by-step explanation:

To convert a decimal to a percentage, multiply by 100 (just move the decimal point 2 places to the right).

0.2777 × 100 = 27.77

log (5) - log (2x) = 1 => x = 0.2499, by properties of logarithm.

Now,

log(5) - (log (2x)) =1

=> log (5) - [log (2) + log (x)] = 1 (as log(ab) = log(a) + log (b))

=>log (5) - log (2) - log (x) = 1

=> log ([tex]\frac{5}{2}[/tex]) - log (x) = 1

=> 0.3979 - log (x) = 1

=> log (x) = 0.3979 - 1

Since, generally the base of log is 10, raising them to 10

=> [tex]10^{log_{10}x} = 10^{-0.6021}[/tex]

=> x = 0.2499

Hence, log (5) - log (2x) = 1 => x = 0.2499, by properties of logarithm.

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The decimal value the digital scale will show for 3¹/₂ lb of turkey is 3.5.

A decimal value is a fractional value.  Sometimes, a decimal contains a whole number and some fractions.

In a decimal number, the first digit after the decimal is in the tenth place. The next digit after the first decimal value represents the hundredth place.

Decimal values are obtained during the mathematical operation of divisions to show that there are remainders or uneven dividends.

Thus, the decimal value that the digital scale will show for 3¹/₂ lb of turkey is 3.5.

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The simplest form of the expression is determined by solving the fractional exponent.

If an exponent of the base (number) is expressed in a fraction, it is called a fractional exponent. In an expression say x^1/y, 1/y is the fractional exponent. Fractional exponent represents the power and root together.

In the given expression, the base term is -32y^15, while the exponent is 1/5.

Since, (ab)^m=a^mb^m

Hence, (-32y¹⁵)^¹/₅=(-32)^1/5*(y^15)^1/5

When a base number has a negative sign, and the power is an odd number, the negative sign is extracted.

(-32)^1/5*(y^15)^1/5=-(32)^1/5*(y^15)^1/5

Since, (a^m)^n=a^m*n

-(32)^1/5*(y^15)^1/5=-32^1/5y^15*1/5

As 32=2*2*2*2*2=2^5

The expression becomes.

-(2^5)^1/5*(y^15^)1/5

Multiplying the powers,

-(25)^1/5*(y^15)^1/5=-(2^5*1/5)(y^15*1/5)=-2y^3

The simplest form of expression is (-32y¹⁵)^¹/₅ is -2y^3.

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Answer:

4.5

Step-by-step explanation:

a^2+b^2=c^2

64+16=80=c^2

c=80^0.5

x^2+80=100

x^2=20

x=4.5

The distance is √116.

The distance formula to calculate the distance between two points (x1,y1) ( x 1 , y 1 ) , and (x2,y2) ( x 2 , y 2 ) is given as,

D=√(x2−x1)²+(y2−y1)²

Given:

(10,0) (0,4)

Using Distance formula

=√(x2 - x1)² + (y2 - y1)²

=√(0-10)² + ( 4-0)²

=√100 + 16

=√116

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Answer:

the correct ones are 30 , 120, 75

Let the two points be given by:

[tex]P(x_{1},y_{1}) \\ Q(x_{2},y_{2})[/tex]

[tex]rate = \frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]

  The proportion of the sample obtained from the survey is 0.055

 The percentage is a mathematical operation that is expressed with the symbol "%" is a relationship that allows us to know the portion of an initial value to represent a set.

  It could also be defined as a representation of an original value that lets us know a certain number of elements that we want from that original value or set.

 To solve this problem, we use a simple rule of three to find the percentage value of the sample.

289 -------- 100%

273 ---------  x

x = (273 * 100%) / 289

x = 94.46%

100% - 94.46% = 5.53%

The ratio in propotion with 3 decimals is

5.53/100  = 0.055

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Answer:

Step-by-step explanation:

Step 1: we write 23% in decimal form: 23%=0.23.Step 2: we find the multiplier. Since we're increasing by 23%, we add 0.23 to 1: 1+0.23=1.23.Step 3: we multiply 80 by the multiplier 1.23: 80×1.23=98.4

So that means your answer is 1.23

The solutions to the equation (3x - 5)²= 19 are: - [tex]\frac{\sqrt{19} + 5}{3}[/tex] and [tex]\frac{\sqrt{19} + 5}{3}[/tex] .

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

In this question we have been given an equation that is (3x - 5)²= 19

Now taking square root both sides

(3x - 5)² = 19

3x - 5 = ± [tex]\sqrt{19}[/tex]

Add 5 to both sides to make equation simpler

3x = ± [tex]\sqrt{19}[/tex]+ 5

Divide both sides by 3

x = ±[tex]\frac{\sqrt{19} + 5}{3}[/tex]

Now separating the solutions we get

x = [tex]\frac{\sqrt{19} + 5}{3}[/tex] .

x = - [tex]\frac{\sqrt{19} + 5}{3}[/tex] .

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The number of video games that Max will have left when he keeps one is 18 games.

It should be noted that the total amount that he has is $625.95.

Cost of each video game = $32.10

Therefore, the number of games that he can buy will be:

= Amount / Cost of game

= $625.95 / $32.10

= 19.5

= He can buy 19 games.

Therefore, if he keeps one, the number left will be:

= 19 - 1 = 18

He I'll have 18 left.

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It should be noted that 5 groups of 2 hundredths will be 3.2e-9.

It should be noted that the information is simply about finding 5 groups of 2 hundredths.

In this case, this will be illustrated as:

= 5 × 2 hundredths

It should be noted that 2 hundredths simply means 0.02. Therefore, the information is to calculate 0.02 in 5 places. This will be illustrated thus:

= 0.02 × 0.02 × 0.02 × 0.02 × 0.02

= 3.2e-9.

Therefore, it should be noted that 5 groups of 2 hundredths will be 3.2e-9.

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Answer:

38

Step-by-step explanation:

It is clear that the number of sweets that should be bought so that each child can get either 8 or 9 sweets should be divisible by both 8 and 9

This is called the LCM or least common multiple of 8 and 9
Since 8 and 9 have no divisors in common LCM of 8 and 9 is 72 so 72 is the minimum number of sweets to buy so that there are no leftovers if each child gets 8 or 9 sweets

Let's compute the number of sweets that were bought the first time. Let the number of children be X

Since each child got 8 sweets and 2 were left over, the total of sweets must be 8X + 2

If each child were to get 9 sweets each then there would be 2 sweets short

This can be written as 9X -2 for the total number of sweets

Since these have to be equal,
9X - 2 = 8X + 2

Add 2 to both sides:
9X - 2 + 2 = 8X +2 + 2
9X = 8X + 4

Subtract 8X from both sides
9X - 8X = 8X - 8X + 4
1X = 4
==> X = 4
So number of children is 4

Total number of sweets bought
= 8 x 4 + 2 = 34

or

= 9 x 4 - 2 = 34

Therefore number of extra sweets to be bought = 72 - 34 = 38

Hope that helps and if you don't understand and need more explanation, please post a comment