find the roots of each expression with rational exponents.

1.27⅓

2.225½

3.49³/²


(please show solution
you can write in on paper)
simplify each expression ​

Answer:

4 times the difference of x and 2 is 4(x-2)

Answer:

x=-9

Step-by-step explanation:

-2x+5=23

-5 on both sides

-2x=18

/-2 on both sides

x=-9

The coordinates of the point that is one-half the distance between A(-1,-2) and B(6,12) is (2.5,5)

What is the midpoint?

The mid-point lies midway between the two ends. Its x value lies in the middle of the other two x values. Its y value lies in the middle of the other two y values.

Given, [tex]A(6,12) = (x_{1}, y_{1} )[/tex]

           [tex]B(6,12) = (x_{2}, y_{2} )[/tex]

Let M is a midpoint of AB, then

[tex]M(x,y)=(\frac{x_{1}+x_{2} }{2} ,\frac{y_{1} +y_{2}}{2} )= (\frac{-1+6}{2} ,\frac{-2+12}{2} )=(2.5,5)[/tex]

The midpoint of point AB is M(2.5,5)

Therefore, the coordinates of the point which is one-half the distance between A(-1,-2) and B(6,12) is M(2.5,5).

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Answer: 0.04536

Step-by-step explanation:

Answer:

B: [tex]3\frac{6}{8}[/tex]

Step-by-step explanation:

we multiply numerator by numerator and denominator by denominator

6/8x5/1

30/8

3 6/8

Hopes this helps please mark brainliest

The equation that could solve how many hours it will take for the second car to catch up to the first car is 55t = 120 + 40t.

An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question. An equation is the equality of expressions.

If the first car is going 40 mi/h, and has a 120 mile head start, then the distance it covers at time = t is,

d1 = 120 + 40t

If the second car is going 55 mi/h, you want to know the amount of time it will catch the first car, then, their distance must be equal.

d2 = 55t

d1 = d2

120 + 40t = 55t

Simplify the equation of t.

55t - 40t = 120

15t = 120

t = 8

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Answer:

The slope is 5.

Step-by-step explanation:

[tex]m = \frac{1 - 6}{ - 1 - 0} = \frac{ - 5}{ - 1} = 5[/tex]

The value needs to be added to x²+10x+6 to complete the square is 19.

Perfect square trinomials come in the form a² + 2ab + b², which is equal to (a + b)².

In the presented trinomial, we can immediately find that a = x, and b² = c,

We know that a = x, and , 2ab = 2bx.

Now, 2bx and 30x are corresponding terms, 2bx = 30x.

Take the coefficient of x = 10

Divide by 2

10/2 =5

Then Square it

5 x 5=25

Add this to make a perfect square trinomial;

x² + 10x + 25

In the given equation we need to add 19 to make the perfect square trinomial; x² + 10x + 25.

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The values satisfies the linear equation y = −47x−2 is (0, -2).

For the given question.

The linear equation is given as;

y = −47x −2

Check the result by putting the values from option.

For : −7 −6

Put x = -7

y = −47(-7) −2

y = 799 -2

y = 498 (incorrect)

For: 0 −2

Put x = 0

y = −47x −2

y = −47(0) −2

y = -2 (correct)

Thus, the values satisfies the linear equation y = −47x−2 is (0, -2).

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The standard error with "mean of 7 for some characteristic of interest and a standard deviation of 9.6 and a sample is drawn from this population of size 64" is 1.2.

Standard deviation of the theoretical distribution of a large population of such estimates is equal to the standard error, which is a measure of an estimate's statistical accuracy. The population mean's likelihood to differ from a sample mean is indicated by the standard error of the mean, or simply standard error. It reveals how much the sample mean would change if a study were to be repeated with fresh samples drawn from a single population.

Here,

Sample size=64

Standard deviation= 9.6

Error=Standard deviation/Sample size

=σ/√n

=9.6/√64

=9.6/8

=1.2

The sample is taken from this population of 64 people, with a mean of 7 for some relevant characteristics, a standard deviation of 9.6, and a standard error of 1.2.

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The probability of randomly drawing a value greater than 3.0 from a z-distribution is 0.0013

The Z-score, commonly referred to as the standard score, expresses how far away from the mean an object is.

An element that is below the mean is indicated by a z-score that is less than 0.

An element bigger than the mean is indicated by a z-score greater than 0.

An element that is equal to the mean is represented by a z-score of 0.

P(Z > a) = 1-P(Z<a)

Let's say we want to know, for instance, the likelihood that a z-score will be higher than 3.00.

We learn from the table, that

P(Z < 3.00) = 0.9987.

Therefore,

P(Z > 3.00) = 1 - P(Z < 3.00)

= 1 - 0.9987

= 0.0013.

Therefore, the probability of randomly drawing a value greater than 3.0 from a z-distribution is 0.0013

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The solution of the linear equation:

(2x + 6)/5 = 4x - 3

is x = 7/6

Here we have the following equation:

(2x + 6)/5 = 4x - 3

To solve this, we need to isolate x in one of the sides of the equation, we can start by multiplying both sides by 5.

2x + 6 = 5*(4x - 3)

Expanding the right side we get:

2x + 6 = 20x - 15

Now you can see that this is a simple linear equation, now we need to group like terms:

6 + 15 = 20x - 2x

21 = 18x

Now we can divide both sides by 18 to get:

21/18 = x

Finally, if we divide both numerator and denominator of the fraction by 3, we get:

21/3 = 7

18/3 = 6

Then 21/18 = 7/6

Finally, we conclude that the solution is:

x = 7/6

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The factor of the polynomial f(x) graphed on the coordinate plane is

(x - 1).

What is factor of the polynomial?

A polynomial with coefficients in a certain field or in integers is expressed as the product of irreducible factors with coefficients in the same domain in mathematics and computer algebra, which is known as polynomial factorization.

A polynomial can be factored by expressing it as the product of two or more components; this is somewhat the opposite of multiplying.

From the given graph we can see that, graph crosses x - axis at points

x = 1 and x = 8.

That means x = 1, 8 are the zero of the polynomial.

Since, if x = a is a zero of the polynomial, then (x - a) is the factor of the polynomial.

As x = 1, 8 are zero of the polynomial so (x - 1) and (x - 8) are the factors of the polynomial.

Hence, from the given options (x - 1) is factor of the polynomial.

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The solution of x when solving x/2 + 1 = √3 is :

x is 2√3 - 2 .

Here in the question given equation ,

x/2 + 1 = √3

To find solution,

we have to subtract 1 from LHS and RHS of equation,

⇒ x/2 + 1 - 1 = √3 - 1

⇒ x/2 = √3 - 1

Next multiply both sides  by 2

2( x/2) = 2(√3 -1)

By simplifying both sides we get,

x = 2√3 - 2

So the value of x = 2√3 -2.

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Answer:

Maximum height of 32 feet after 1.25s

Step-by-step explanation:

Answer:

[tex]g(x) + h(x) = x^3 + 6x + 5[/tex]

Step-by-step explanation:

We are told that:

[tex]g(x) = x^3 + 5x[/tex]

[tex]h(x) = x + 5[/tex],

and we are asked to find an expression for [tex]g(x) + h(x)[/tex].

In order to find the expression for  [tex]g(x) + h(x)[/tex], we have to simply add the expressions of [tex]g(x)[/tex] and [tex]h(x)[/tex] together:

[tex]g(x) + h(x)[/tex]

= [tex]x^3 + 5x + x + 5[/tex]

= [tex]x^3 + 6x + 5[/tex]

A midwife delivers 10 babies, with 50% chance of delivering a boy and 50% of delivering a girl. The probability that 6 out of 10 babies will be boys is 20.5%

The problem can be solved using binomial distribution, that is the probability of 2 possible outcomes in a number of trials.

The formula is given by:

P(x) = ⁿCx . P^x . (1 - P)^(n-x)

x = total number of event A

n = number of trials

P = probability of A in a single trial

Parameters given in the problem:

n = 10

x = 6

P = 50% = 0.5

Plug these parameters into the formula:

P(6 boys) = ¹⁰C₆ . (0.5)⁶ .  (0.5)⁴

                = 0.205 = 20.5%

Hence, the probability that 6 out of 10 babies will be boys is 20.5%

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Answer:

Step-by-step explanation:

We start by developing an equation for Line 1, and then use that to find the equation for Line 2.  We'll use the form of an equation for a straight line:

 y = mx + b,

where m is the slope and b the y-intercept (the value of y when x=0).

Line 1

Determine the slope, m, by calculating the "Rise/Run" between the two points (-3,-7) and (5,3).

Line up the two points from left to right (based on x) and then calculate:

  Rise:  (3 - (-7)) = 10

   Run:  (5 -(-3) = 8

The slope, m, is Rise/Run or (10/8)

The equation becomes y = (5/4)x + b

We could calculate b, the y-intercept, by entering one of the two given points and solving for b, but the only thing we need from this line is it's slope, m.  Slope is (5/4), which we'll use in the next step:  Line 2.

[Note:  Out of curiosity, here is the calculation for b:  Use point (5,3) in y = (5/4)x + b and solve for b.   3 = (5/4)*5 + b.  3 = (25/4) + b  b = -13/4.  This means that Line 1 is y = (5/4)x -(13/4)]

Line 2

The slope of a line perpendicular to the first is the "negative inverse" of the first line.  In this case, line 1's slope of (13/8) would become a slope of -(8/13) for line 2.

    Line 2:  y = -(8/13)x + b

We'll calculate b for this line by enetering the single point provided,  (-4,-2), and solving for b:

          y = -(8/13)x + b

        -2 = -(8/13)*(-4) + b

          -2 = (32/13) + b

          -2 - (32/13) =  b

b = -(26/13) - (32/13)

b = -(58/13)

The new line perpendicular to Line 1 and passing through (-4,-2) is:

          y = -(8/13)x -(58/13)

See attached graph.

Step-by-step explanation:

E=29

G = 180-29-107= 44

F = 180-29-29 = 122

H = 180-29-29 = 122

S = 180-107 = 73

M = 107

C = 73

D = 107

T = 73

B = 107

N = 73

K = 44

A = 360-44-44-107 = 165

O = 180-44 = 136

P = 44

J= 136

Answer:

y = - 2x + 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

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

with (x₁, y₁ ) = (- 5, 11) and (x₂, y₂ ) = (6, - 11) ← 2 points on the line

m = [tex]\frac{-11-11}{6-(-5)}[/tex] = [tex]\frac{-22}{6+5}[/tex] = [tex]\frac{-22}{11}[/tex] = - 2

the line crosses the y- axis at (0, 1 ) ⇒ c = 1

y = - 2x + 1 ← equation of line

The amounts are given as follows, using proportions:

i) Amount spent on entertainment: $240.

c) Monthly salary: $840.

A proportion is a fraction of an amount, and this fraction is combined with the unit rates in the context of a problem along with basic arithmetic operations such as multiplication or division to find the desired amounts.

The ratio of food : travelling : entertainment = 4 : 2 : 3 means that:

The amount spent on food $160 more than travelling, the total amount is obtained as follows:

(4/9 - 2/9)x = 160

2/9x = 160

2x = 160 x 9

x = 80 x 9

x = 720.

Then the amount invested in entertainment was of:

3/9 x 720 = 1/3 x 720 = $240.

He invests 6/7 of his monthly salary, as 1/7 is deposited, hence:

6x/7 = 720

6x = 720 x 7

x = 120 x 7 (simplifying both sides of the equality by 6)

x = $840.

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Answer:

2 3/16

Step-by-step explanation:

It's simple math :D

NOVEMBER QUOTE!

Ooo! It's fall and thanksgiving time! I gotta get prepared for Thanksgiving and so my friends will come over! Fun! - Ash the Fox

(sorry that ones so long- ;-;)

The chief of police use sample statistical study  to estimate the number of people above the age of 18 who are using illegal substances in town.

In the given question,

The chief of police in statville wanted to estimate the number of people above the age of 18 who are using illegal substances in town.

He obtained 200 random names of statville residents from a computer database and sent his officers to survey these people about substance abuse.

Once the results came in, he calculated the margin of error and got an estimate of the percentage of residents who use illegal substances.

We have to explain what type of statistical study the chief of police use.

In the given question chief of police wants to check number of people who using illegal substances in town above the age of 18. So he take  200 random names from a computer database. That means he take the sample of 200 random people.

As we know that a sample is a selection from a larger population of individuals, things, or things that are used for measurement. To enable us to extrapolate the research sample's findings to the entire population, the sample must be representative of the population.

So we can say that the chief of police use sample statistical study  to estimate the number of people above the age of 18 who are using illegal substances in town.

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Answer: Sample Study

No because there’s a great risk of obtaining biased answers.

Answer:

-4/5

Step-by-step explanation:

do -3/2to get your answer

Step-by-step explanation:

You find the image of triangle by translation

Answer:

d+12/3

Step-by-step explanation:

*= multiply /= fraction ALL OVER= fraction over fraction

find the common denominator-

d/3+4

d/3+3*4/3

combine fractions with the common denominator

d/3+3*4/3 ALL OVER d+3*4/3

multiply

d+3*4/3 ALL OVER d+12/3