How would the fraction 1/3+square root of 2 be rewritten if its denominator is rationalized using difference of squares? A. 3-square root of 2 B. 3-square root of 2/5 C. 3-square root of 2/7 D. - 3+square root of 2/7

it's x = 2 my dude it's really easy but glad u asked help

She ran the last 100 meters in 2:15 -1:25 = 0:50, so her average speed was

... (100 m)/(50 s) = 2.0 m/s

x^3−4x^2−3x+18=0

(x - 3)^2 (x + 2) = 0

Choice B

A

since x = 3 is a zero then (x - 3) is a factor

dividing x³ - 4x² - 3x + 18 by (x - 3) gives

x³ - 4x² - 3x + 18 = (x - 3)(x² - x - 6 ) = 0,

(x - 3)(x - 3 )(x + 2 ) = 0

(x + 2 )(x - 3)² = 0 → A

The statements that are true are:

The following information should be considered;

Learn more: https://brainly.com/question/1301963?referrer=searchResults

Answer: B & C

Step-by-step explanation:

on edge

The median is "B) 82". The word "median" means middle so you have to find the number in the middle. If you cross out the corner numbers and keep doing that until you have one number left, you get the answer.

Answer:

Step-by-step explanation:

A

My answer was: y=0.5x+16.5

Put the numbers where the corresponding variables are, then do the arithmetic.

... 20·3 + 25·4 -10 = 60 +100 -10 = 150

[tex]\frac{11}{24}[/tex]

combine the fractions of each type by adding them

[tex]\frac{3}{8}[/tex] + [tex]\frac{1}{12}[/tex]

Before we can add the fractions we require them to have the same denominator

To achieve this we require the lowest common multiple (LCM ) of 8 and 12

The LCM of 8 and 12 is 24

To change the denominators , multiply the numerator/ denominator by the appropriate value

[tex]\frac{3}{8}[/tex] = [tex]\frac{3(3)}{8(3)}[/tex] = [tex]\frac{9}{24}[/tex]

[tex]\frac{1}{12}[/tex] = [tex]\frac{1(2)}{12(2)}[/tex] = [tex]\frac{2}{24}[/tex]

Add the numerators leaving the denominator as it is

= [tex]\frac{9+2}{24}[/tex] = [tex]\frac{11}{24}[/tex]

Answer:111/24

Step-by-step explanation:

A(,-2,4)=b= -2

B,(5,2)= b=17

We need to find the triangle bounded by the y-axis the line [tex]f(x)=9-\frac{6}{7}x[/tex] and the line perpendicular to it that passes through the origin.

This triangle is illustrated in the First Figure bellow. The triangle has been dotted with black dots. So, let's identify each part of this graph:

        Therefore, this line is the blue one and is written as:

         [tex]f(x)=\frac{7}{6}x[/tex]

To find [tex]y(t)[/tex] we need to find the slope and y-intercept. So, taking two points:

[tex]P_{1}(15,150) \ and \ P_{2}(25,450) \\ \\m=\frac{450-150}{25-15}=30[/tex]

So:

[tex]Using \ P_{1}(15,150) \\\\y=30t+b\\\\150=30(15)+b \therefore b=-300 \\\\\boxed{y(t)=30t-300}[/tex]

The y-intercept is [tex]b=-300[/tex] and has been calculated above. This value represents the profit in thousands of dollars in 1980, that is, there is no any profit or there is a lost of $300.000.

The x-intercept can be found when y=0 (year 1980), that is:

[tex]y(t)=30t-300 \\\\0=30t-300 \therefore t=10[/tex]

This value shows that there is no any profit for the company at the year that represents t=10 (year 1990), because at this point the company starts earning money.

The slope of this function is [tex]m=30[/tex]

This value tells you that the profit increases $30.000 each year.

Hello,

Please, see the attached files.

Thanks.

B! 650 x 36 +400 = 23,800!

Answer:

$23800.

Step-by-step explanation:

Monthly payment of loan of a car = $650

His loan is for 36 months

So, Total payment of 36 months = [tex]36 \times 650[/tex]

                                                       = [tex]23400[/tex]

He paid the down payment of amount $400

So, Total cost of the car = [tex]23400+400[/tex]

                                       = [tex]23800[/tex]

Hence the total cost of the car for Jared is $23800.

So, Option B is correct.

Answer:

Step-by-step explanation:

Recall the definition for conditional probability.

We have P(A/D) = P(A and D)/P(D)

P(AD) = 2/17

P(A) = 8/17 and P(D) = 10/17

From the definition of conditional probability,

P(A/D) = P(AD)/P(D) = 2/17 divided by 10/17 = 1/5

But P(D/A) = P(AD)/P(A) = 2/17 divided by 8/17 = 1/4

Hence the two are not equal.

This is because there is a difference in the denominators

P(A|D) and P(D|A) from the table are not equal because the total number of A and D are not equal

From the table, we have the following parameters:

P(A|D) and P(D|A) are both conditional probabilities, and they are calculated using:

[tex]P(A|D) = \frac{n(A\ and\ D)}{n(D)}[/tex]

[tex]P(D|A) = \frac{n(A\ and\ D)}{n(A)}[/tex]

So, we have:

[tex]P(A|D) = \frac{2}{10}[/tex]

[tex]P(A|D) = 0.2[/tex]

[tex]P(D|A) = \frac{2}{8}[/tex]

[tex]P(D|A) = 0.25[/tex]

From the above computations, we have:

[tex]P(D|A) \ne P(A|D)[/tex]

This is so, because:

The total number of A and D are not equal

Read more about probabilities at:

https://brainly.com/question/15246027

y = - 2x + 12

the equation of a line in slope- intercept form is

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

y = - 2x + 7 is in this form with slope m = - 2

Parallel lines have equal slopes, thus

y = - 2x + c is the partial equation.

To find c, substitute (3, 6 ) into the partial equation

6 = - 6 + c ⇒ c = 6 + 6 = 12

y = - 2x + 12 ← equation of parallel line

Any arithmetic operation on polynomials except division* will result in a polynomial. Appropriate choices are ...

A. (x^2+2) (x-1)

C. (x+1) plus (X^2-3X -2)

D. (X +5)-(3X +6)

E. (4/8)x . . . . . but not if you mean 4/(8x)

_____

* For division, the result may be a polynomial. In the specific example given here for B, it is not.

The term closure in mathematics refers to the property of a set, in this case, polynomials, where doing certain operations (addition, subtraction, multiplication) with any numbers from the set always yields a number within the set. The options demonstrating closure in a polynomial are A, C, D, E, all but option B, which implies division.

The term 'closure' in mathematics refers to the property of a set under an operation where the operation performed on any numbers in the set always produces a number that is also in that set. In the case of polynomials, the operations could be addition, subtraction, or multiplication.

The expressions that demonstrate closure in a polynomial for addition, subtraction, and multiplication are all but option B. Option B, '(x^2+2) over (X -1)', isn't representative of closure in a polynomial as it implies a division operation. Polynomial closure doesn't include division because it can produce numbers outside the original set.

So, the correct answers are A.(x^2+2) (x-1), C.(x+1) plus (X^2-3X -2), D.(X +5)-(3X +6) and E.4/8x as they illustrate closure by either multiplication of two polynomials, addition of two polynomials, or subtraction of two polynomials.

https://brainly.com/question/3205290

#SPJ2

Answer:

[tex]x=[tex]\frac{1}{2}[/tex][/tex]

Step-by-step explanation:

Solving the equation mean finding the value of x

Equation given is:

[tex]-3x+1+10x=x+4[/tex]

Now what we need to do is take the values with x in it to the left side of the equation and the other numbers to the right side of the equation.

[tex]-3x+10x-x=4-1[/tex]

Now simplify values with x and the numbers.

[tex]6x=3[/tex]

[tex]x=[tex]\frac{1}{2}[/tex][/tex]

Therefore [tex]x=[tex]\frac{1}{2}[/tex][/tex]

x = [tex]\frac{1}{2}[/tex]

simplify the left side by collecting like terms

7x + 1 = x + 4 ( subtract x from both sides )

6x + 1 = 4 ( subtract 1 from both sides )

6x = 3 ( divide both sides by 6 )

x = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]

Often, variability is most usefully expressed in the same units as the original data. That's what standard deviation (square root of variance) does. In situations where that is the case, the variance is useful only for getting to the value of standard deviation.

Kiran is correct. (I agree with Kiran.)

_____

Suppose the length and width are L and W. The Pythagorean theorem says the diagonal distance is ...

... d = √(L² +W²)

If the dimensions are doubled, the the diagonal distance becomes ...

... D = √((2L)² +(2W)²) = √(4(L² +W²)) = 2√(L² +W²)

... D = 2d

Answer:

Kiran's statement is correct.

Step-by-step explanation:

Kiran says that if the field were twice as long and twice as wide, then it would be twice the distance to the far corner.

Let the original length be = l

Let the original width be = w

Let the original diagonal be = d1

As per Pythagoras theorem,

[tex]d1^{2} =l^{2} +w^{2}[/tex]

When the dimensions are twice the original;

Length = 2l

Width = 2w

Diagonal = d2

We get the formula :

[tex]d2^{2} =2l^{2} +2w^{2}[/tex]

[tex]d2^{2} =2(l^{2} +w^{2})[/tex]

Or [tex]d2^{2} =2d1^{2}[/tex]

So, we can say that Kiran is correct.

Answer:

the unit cost per item

Step-by-step explanation:

The description of the graph tells you what the slope means. The slope is the (change in) y-value (cost) per (change in) x-value (item), thus is cost per item.

The slope of the line from the origin to a point is the average cost for that number of items. The slope of a tangent line at a point on the curve is the marginal cost for that number of items.

When the curve is linear and goes through the origin, the slope is the same everywhere and is the cost per item. (It is also the average cost and the marginal cost, where that is of interest.)

The slope of the graph, which represents the rate of change between the number of identical items purchased and the total cost, means the unit cost per item.

In the given context of a graph where the x-axis represents the number of identical items purchased and the y-axis represents the total cost in dollars, the slope of the graph represents the unit cost per item. This is because the slope of a line is a measure that describes the rate of change between the independent and dependent variables. It tells us how the dependent variable (in this case, total cost, represented by 'y') changes for every one-unit increase in the independent variable (in this case, number of items purchased, represented by 'x'), on average.  

Therefore, when you buy more items (increase in 'x'), the total cost ('y') increases. Hence, the rate at which 'y' is increasing per unit 'x' is actually the cost per item. This concept is fundamental in understanding how variations in quantity purchased impact the total cost, applicable in contexts from shopping to major business transactions.

https://brainly.com/question/28418462

#SPJ6

The quadrilaterals are two congruent isosceles trap ezoids and a kite.

In the smaller triangle, the corresponding side is 3 times the base length. Since these triangles are similar, the same ratio holds.

... n = 3×5

... n = 15

under a rotation about the origin of 180°

a point (x, y ) → (- x, - y )

hence D is correct, both the x and y coordinates of the points on ΔA'B'C' have opposite signs from the corresponding points on ΔABC

Answer:

Its D

Step-by-step explanation:

Both coordinates  have opposite signs.

2^8 = 256. I hope I satisfied your query!

The attachment shows the requested evaluations.

-a^n ≠ (-a)^n . . . . except when n is an odd integer

Answer:    [tex]g(f(a))=1.07a+50[/tex]

Step-by-step explanation:

The given functions are:   [tex]f(a)=1.07a[/tex] and [tex]g(b)= b+50[/tex]

[tex]g(f(a))[/tex] means [tex]f(a)[/tex] is the input of the function [tex]g[/tex].

Thus,  [tex]g(f(a))= g(1.07a)[/tex]

Now replacing  [tex]b[/tex] as [tex]1.07a[/tex]  into the given function of  [tex]g(b)[/tex], we will get......

[tex]g(1.07a)= 1.07a+50[/tex]

So, [tex]g(f(a))=1.07a+50[/tex]

You can eliminate parentheses and combine like terms.

(2x^2 +4x-9) +(3x^2-2x+10)

= 2x^2 +4x-9 +3x^2-2x+10 . . . . . nothing needs to be distributed, so we can simply drop the parentheses

= x^2(2 +3) +x(4 -2) +(-9 +10) . . . group like terms

= 5x^2 +2x +1

(c)

given the inequality | P | > a then the solution is always of the form

P < - a or P > a

for | P | > 3 , then

P < - 3 or P > 3

x = - 1

given [tex]\sqrt{(1-3x)}[/tex] = x + 3

square both sides

1 - 3x = (x + 3 )² ( expand right side using FOIL )

1 - 3x = x² + 6x + 9 ( subtract 1 - 3x from both sides )

0 = x² + 9x + 8

0 = ( x + 1)(x + 8)

equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = -1

x + 8 = 0 ⇒ x = - 8

As a check

substitute these values into the equation and if both sides are equal then they are the solutions

x = - 1 : [tex]\sqrt{1+3 }[/tex] = 2 and - 1 + 3 = 2 ← true

x = - 8 : [tex]\sqrt{1+24}[/tex] = 5 and - 8 + 3 = -5 ← false

thus the only solution is x = - 1

Hey there!!!

Given equation :

... - 3 ( 2x - y ) + 2y + 2 ( x + y )

... -6x + 3y + 2y + 2x + 2y

... -6x + 5y + 2x + 2y

... -4x + 7y

( or )

... 7y - 4x

Hope helps!

3/5 = 6/10 = 6×(1/10)

The piece will be divided into 6 sections of 1/10 yard each.

Answer:

3/5 = 6/10 = 6×(1/10)

The piece will be divided into 6 sections of 1/10 yard each.

Step-by-step explanation: