Solve the radical equation. Please explain each step in detail.

The polynomial f(x) of degree 5 that has the following zeros is

f(x) = (x+2) (x-3) (x-7)(x-0) (x-4).

Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an expression made up of variables, constants, and exponents. In many branches of mathematics and science, polynomials are used. For instance, they are used to define polynomial functions, which show up in settings ranging from basic chemistry and physics to economics and social science. They are also used in calculus and numerical analysis to approximate other functions. Polynomial equations are used to form these functions.

The function's zeros are expressed as follows:

f(x) = (x-a)(x-b)..... where the a, b  are the zeros

f(x) = (x-(-2)) (x-3) (x -7)(x-0) ( x-4)

f(x) = (x+2) (x-3) (x-7)(x-0) (x-4)

Therefore, the polynomial f(x) of degree 5 that has the following zeros is

f(x) = (x+2) (x-3) (x-7)(x-0) (x-4)

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11/24 many minutes did it take for the winner of the race to finish.

A fraction represents a part of a whole.

Given,

Kyla finished a 100 meter race in one and three-eighths minutes.

Kylas time is [tex]1\frac{3}{8}[/tex] minutes.

Convert mixed fraction to improper fraction.

11/8 minutes.

The winner of the raced finished in one-third of Kyla's time.

Which means 1/3 of 11/8

1/3×11/8

11/24

Hence, 11/24 many minutes did it take for the winner of the race to finish.

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Answer:

Step-by-step explanation:

so first you need to find the slope

you can draw the line on a graph and use a protractor

final answer=46 degrees

Answer:-5/-19

the answer is -5/-19 and can not be simplify

Answer:

Step-by-step explanation:

the answer is a 28.27

Answer:

a) 28.27

Step-by-step explanation:

Formula we use,

→ πr²

Now the required area will be,

→ 3.14 × 3²

→ 3.14 × 9

→ 28.27 in²

Hence, the area is 28.27 in².

The system of equation is consistent and independent because it has one unique solution.

If a system has at least one solution, it is said to be consistent . If a consistent system has exactly one solution, it is independent.

Therefore, let's solve the equation,

y = -3x + 12

y = -6x + 2

Using substitution,

-6x + 2 = -3x + 12

-6x + 3x  = 12 - 2

-3x = 10

x = - 10 / 3

y = -6(-10 / 3) + 2

y = 60 / 3 + 2

y = 20 + 2

y = 2

Therefore, the system of equation is consistent and independent.

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Answer: Choose 15 and 20

Step-by-step explanation:

Both 15 and 20 will work because if you subtract 8 from both, you will get 7 and 12 and both numbers are still greater than 5.

Answer:

the answer is 0.5

Step-by-step explanation:

Answer:

18n

Step-by-step explanation:

Product : Multiplication result

number : n

18 : 18

of a number and 18 : n*18

The product of a number and 18 is n*18, or 18n.

Answer:

2⁶×2⁵

Step-by-step explanation:

64×32

= 2⁶×2⁵ ans

thank you for questioning ....

The value of the expression to the nearest tans is -8.4

Adjusting a number's digits so that it produces an approximation of a result is known as rounding

The given expression is -8 (5/12).

Rewrite the expression:

-8 (5/12)

= - 101/12

= - 8.4

Hence, the value of the expression to the nearest tans is -8.4

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Answer:

20:9

Step-by-step explanation:

Here we will simplify the ratio to 40:18 for you and show you how we did it.

To simplify the ratio 40:18, we find the greatest common divisor of 40 and 18, and then we divide 40 and 18 by the greatest common divisor.

The greatest common divisor that you can use to simplify 40:18 is 2. This means the answer to ratio 40:18 simplified is:

20:9

Answer:

  4

Step-by-step explanation:

You are given a table of function values in which x increases by 2, and you want to know the factor by which f(x) increases when x increases by 1.

Let k represent the factor by which f(x) increases when x increases by 1. This means ...

  f(2) = k·f(1)

  f(3) = k·f(2) = k·(k·f(1)) = k²·f(1)

  64 = k²·4

  k² = 64/4 = 16

  k = √16 = 4

The output value increases by a factor of 4 as the input value increases by 1.

__

Additional comment

The table values would also be obtained if the factor of increase were -4. That is, f(x) = -(-4)^x would give the same table. In that case, f(x) would not be a continuous function.

Answer: 50

Step-by-step explanation:

10+15+6+4+6+11= 50

Edit=

We can see that the length of one side is 10, and the width of one is 15. For the other side of the width, we can subtract 4 from 15 to get 11. For the other length, we can subtract 6 from 10 to get four. We also have to add in the 6 and 4 because they are parts of the border. (10+15+11+4+6+4)

These are the possible combination of winning players:

{P1, P2}( weight :32)                       {P1, P2, P4} (weight: 31)

{P1, P2, P3} (weight: 45)                 {P1, P2, P3, P4} (weight: 46)

{P1, P3, P4} (weight: 31)                   {P1, P3} (weight: 30)    

What is the distribution?

The mathematical expression known as a distribution function expresses the likelihood that a system would adopt a certain value or range of values. The traditional examples include games of chance.

The voting system tells us that the quota is 30, that Player 1 has 17 votes (or equivalently, has a weight of 17), Player 2 has 15 votes, Player 3 has 13 votes, and Player 4 has 1 votes.

A coalition is any group of one or more players. What we're looking for is winning coalitions - coalitions whose combined votes (weights) add to up to the quota or more. So the coalition  {P3, P4}  is not a winning coalition because the combined weight is  13 + 1 = 14, which is below the quota.

So we look at each possible combination of players and identify the winning ones:

{P1, P2}( weight :32)                       {P1, P2, P4} (weight: 31)

{P1, P2, P3} (weight: 45)                 {P1, P2, P3, P4} (weight: 46)

{P1, P3, P4} (weight: 31)                   {P1, P3} (weight: 30)            

Hence, these are the possible combination of winning players.

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The value of x is 6 degree that makes m || n.

What is parallel lines?

Parallel lines are coplanar, straight lines in geometry that don't cross at any point. When two planes in the same three-dimensional space are parallel, they never cross. Curves that maintain a set minimum distance from one another and do not touch or intersect are said to be parallel curves.

(8) Given: m || n

We have to find the value of x that makes m || n.

The lines m and n are divides by the line l of angle 90 degree.

⇒ 16x - 6 = 90

Add 6 on both sides,

16x - 6 = 90 + 6

16x = 96

Divide both sides by 16

16x/16 = 96/16

x = 6

Hence, the value of x is 6 degree that makes m || n.

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The equation in slope-intercept form to find the height is y = 0.75x + 5 and the number of years it will take the tree to reach 20 feet is 24

The given parameters in the question are

Growth = 9 inches per year

Length of the tree after 4 years = 5 feet

Convert inches to feet

So, we have

Growth = 0.75 feet per year

A linear equation of this scenario is represented as

Length = Growth * Number of years + Initial length

So, we have

y = Growth * x + Initial length

This gives

5 = 0.75 * 4 + Initial length

Evaluate

Initial length = 2

So, the equation is

y = 0.75x + 2

This means that

y = 20

Recall that

y = 0.75x + 2

So, we have

0.75x + 2 = 20

Evaluate

0.75x = 18

Divide by 0.75

x = 24

Hence, the number of years is 24

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Answer:

C. y = 45.6 in

Step-by-step explanation:

Given equation:

[tex]y=\dfrac{2}{5}x-60[/tex]

where:

If a guest lands 36 inches from the wall, then x = 36.

Substitute x = 36 into the equation:

[tex]\implies y=\dfrac{2}{5}(36)-60[/tex]

[tex]\implies y=\dfrac{2 \cdot 36}{5}-60[/tex]

[tex]\implies y=\dfrac{72}{5}-60[/tex]

[tex]\implies y=14.4-60[/tex]

[tex]\implies y=-45.6[/tex]

Therefore, the depth of the water is 45.6 inches (since -45.6 inches means it is that distance below the surface).

The maximum number of hours that he can hire the cleaning service would be 5.

An equation is an expression that shows the relationship between two or more numbers and variables.

Consider that the number of hours for which the total cost would be the same be x

The first inequality is;

$15x > $75

Now equate equations

$15x - $75 = 0

15x = 75

x = 5

Hence, the maximum number of hours that he can hire the cleaning service would be 5.

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The inequlity according to the given statement will be equal to 280 + 92(x) ≥ 1,108.

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare the two values. Less than (or less than and equal to), larger than (or greater or equal to), or not similar to signs are used in place of the equal sign in between.

As per the given information in the question,

Rate of production per hour by the factory = 92 per hour

The factory has to produce at least 1,108 units.

Number of units produced today = 280

Assume x is the number of production hours,

Then, the equation will be,

280 + 92(x) ≥ 1,108 units.

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The time  did Stanley run, swim, and bike yesterday if the total distance he covered was 64 miles is 1.5 hrs, 1 hrs, 3 hrs. The distance is 13.5 miles, 2.5 miles , 48 miles.

Let t represent the  time he ran

Let t -.5 represent  time he swam

Let 2t represent the  biking time

Hence,

9t + 2.5(t-.5) + 16(2t) = 64

9t + 2.5t - 1.25 + 32t = 64

Collect like terms

43.5t = 64 + 1.25

Divide both side by 43.5t

t = 65.25/43.5

t = 1.5 hrs (Time he ran)

So,

Time he swam

t -.5 where t is 1.5 hrs

1.5-.5 = 1 hr (Time he swam)

Biking time

2t where t is 1.5 hrs

2(1.5) = 3 hrs (biking time)

Distance of each

1.5(9) = 13.5 miles  (running)

1(2.5) = 2.5 miles   (swimming)

3(16) = 48 miles  (biking)

Total distance = 13.5 miles + 2.5 miles + 48 miles

Total distance = 64 miles

Therefore the time  is 1.5 hrs, 1 hrs, 3 hrs and the distance is 13.5 miles, 2.5 miles , 48 miles.

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Answer:

here you go !!

hope his helps

Answer:

Step-by-step explanation:

you do the math

Answer:

16

Step-by-step explanation:

I'm solving this question according to PEMDAS.

3x2-5(-2)

3x2+10

6+10

16

Could you please give me brainliest for this? Thanks!

The negative and zero exponents of the given exponents will be 3 x¹⁵y²⁰ × x⁻³y⁻⁵z⁰.

Index (indices) in Maths is the power or exponent which is raised to a number or a variable.

The mathematics of power or exponent of any number is called indices.

For example 5³ = 5²5 here we break 5³ into 5² and 5 so it is called the law of indices.

Another example could be 7² = 7³/7 here we divide to obtain power 2.

As per the given,

36 x¹⁵y²⁰/ 12 x³y⁵ = [(36/12) (x¹⁵y²⁰)/(x³y⁵)]

36 x¹⁵y²⁰/ 12 x³y⁵ = 3x¹⁵y²⁰ × x⁻³y⁻⁵z⁰

Hence "The negative and zero exponents of the given exponents will be 3 x¹⁵y²⁰ × x⁻³y⁻⁵z⁰".

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Answer:

37.5%

Step-by-step explanation:

2 hours = 120 mins

(Units need to be the same in order to work with them)

45/120 = x/100

45 * 100 = 120x

x= 37.5%

Answer: 100 ft sq.

Step-by-step explanation:

The equation for surface area is S = 2lw + 2lh + 2wh.

l=2, h=7, w=4.

S = 2(2)(4) + 2(2)(7) + 2(4)(7)

S = 16 + 28 + 56

S = 100

Answer:

[tex]-\frac{19}{50}[/tex]

Step-by-step explanation:

[tex]-\frac{\frac{38}{25} }{4}[/tex]

[tex]-\frac{38}{25 * 4}[/tex]

[tex]-\frac{19}{50}[/tex]

Answer:

y=-3x+12

Step-by-step explanation:

Plug in (5, -3) for x in the slope-intercept form. This gives -3 = 5*-3 + b, or -3 = -15 + b. We want to solve for b, so add 15 to both sides, giving b = 12.

Answer:3/2

Step-by-step explanation: so you have the number of cups of Chex Mix in the bag is 3x = 3*9 = 27 cups and the number of cups of chocolate chips is 2x = 2*9 = 18 cups. Indeed, we see that 27 + 18 = 45 and 27/18 = 3/2 as required.