How do I solve for x in #34 and #35?

Answer:

the rationalized form of the denominator 1/(5^(1/2)-2) is (x+2)/((x-2)(x-1)(x+1)).

Step-by-step explanation:

Correctly me if im wrong. To rationalize the denominator of the fraction 1/(5^(1/2)-2), we can use the conjugate of the denominator. The conjugate of a+b is a-b, so the conjugate of 5^(1/2)-2 is 5^(1/2)+2. We can then multiply the numerator and denominator of the fraction by the conjugate to obtain:

1/(5^(1/2)-2) * (5^(1/2)+2)/(5^(1/2)+2)

= (1*(5^(1/2)+2)) / ((5^(1/2)-2)*(5^(1/2)+2))

= (5^(1/2)+2) / (5^2 - 2*5^(1/2) - 4)

Notice that we can further simplify this expression by substituting 5^(1/2) with x and expanding the denominator:

(5^(1/2)+2) / (5^2 - 2*5^(1/2) - 4)

= (x+2) / (x^2 - 2x - 4)

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

The denominator of this expression can be further simplified by factoring out x-2, which gives us:

(x+2) / (x-2)(x+2)

= (x+2) / (x-2)(x-2 + 4)

= (x+2) / (x-2)(x^2 - 2x + 4 - 4)

= (x+2) / (x-2)(x^2 - 2x)

= (x+2) / (x-2)((x-1)(x+1))
Finally, we can use the fact that x-1 and x+1 are factors of x^2-2x, which means that we can factor out x-1 and x+1 from the denominator to obtain the fully simplified expression:
(x+2) / (x-2)(x^2 - 2x)

= (x+2) / (x-2)(x-1)(x+1)

= (x+2) / ((x-2)(x-1)(x+1))

Therefore, the rationalized form of the denominator 1/(5^(1/2)-2) is (x+2)/((x-2)(x-1)(x+1)).

Answer: The y-intercept is 14

Step-by-step explanation:

The slope intercept is y=mx+b

since we already have the slope, we can write this as

y=-5x+b

substitute the points of (3,-1) into the equation and solve for b

-1=-5(3)+b

-1=-15+b

b=14

The y-intercept is 14

The y-intercept of the line is 14.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

Slope = -5

The line passes through the point (3, -1).

The equation of the line is y = mx + c.

y = -5x + c

(3, -1) = (x, y)

-1 = -5 x 3 + c

-1 = -15 + c

-1 + 15 = c

c = 14

Thus,

The y-intercept is 14.

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Answer: y=-1/2x+4

Step-by-step explanation:

find the slope of the line given which would be-2/4 which simlifys down to 1/2 then add your b (y intercept) and that wold be 4.  

A  conditional probability p(b | a) is equal to its marginal probability p(b) if A and B are independent.

The likelihood that any two events will occur is equal to the sum of the probabilities of each event separately, less the probability that the two occurrences will meet. However, if two occurrences are incompatible with one another, then there is a zero probability of the two events intersecting, therefore the likelihood that either one or the other will occur is equal to the sum of the two individual probabilities.

To calculate conditional probability, use the following formula:

p( b | a ) = p( a ∩ b )/ p(a)

It is known that if two events A and B are independent, then p(a ∩ b) = p (a) . p(b)

So, p(b | a) = [p (a) . p(b)]/p(a) = p(b)

Thus, it is concluded that a conditional probability p(b | a) is equal to its marginal probability p(b) if A and B are independent.

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The rate of interest for simple compounding if Louis is offered an interest rate of 6.35% for an investment with continuous compounding, is 0.0656 or 6.56%, so option D is correct.

When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.

Given:

Louis is offered an interest rate of 6.35% for an investment with continuous compounding,

Here, P will be the same, the amount will be the same and the time period will be the same then,

The amount in simple compounding = The amount in continuous compounding

[tex]P(1 + r)^t = Pe^{rt}[/tex]

Here, r is the rate of interest for simple compounding,

[tex]1 + r = e^{0.0635}[/tex]   (All same quantities get canceled)

r = 1.0656 - 1

r = 0.06556

r = 0.0656

r = 6.56%

Thus, the rate of interest for simple compounding is 6.56%.

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Answer: x ≥ 8

Step-by-step explanation:

      We know that our inequality must be greater than or equal to $112 because she needs at least $112 to buy the new dress. This is the first part of our inequality.

      Next, we see that she already has $40 and will earn $9 an hour babysitting, if x is the number of hours. $9 an hour can become 9x, then we will add the $40 she already has for 9x + 40 as the second part of our inequality.

      This complete inequality is:

9x + 40 ≥ 112

      Now, we can solve by isolating the variable x with inverse operations.

9x + 40 ≥ 112

9x ≥ 72

x ≥ 8

      Matilda needs to babysit at least 8 hours to afford the new dress.

After solving the equation, the value of A will be equal to 16 and the value of B will be equal to 28.

What is an arithmetic operation?

The four fundamental operations of arithmetic are addition, subtract, multiply, and division of two or more numbers. Included in them is the study of integers, especially the order of operations, which is important for all other aspects of mathematics, notably algebra, information management, and geometry.

As per the provided data in the question,

The given equation is,

A + B = 44

Given ratio A:B = 4:7

Let the value of A = 4x and value of B = 7x

4x + 7x = 44

11x = 44

x = 4

A = 4x

A = 4(4) = 16

B = 7x

B = 7(4) = 28.

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Answer: x=2

Step-by-step explanation:

1/2(40x-16)=32

20x - 8 = 32

Add 8 on both sides

20x = 40

Divided both sides by 20

x = 2

Step-by-step explanation:

To Find : size of angle x

Solution:

Area of ΔABC = (1/2) * BC * AC

=> (1/2) * BC * AC = 42

=> (1/2) * 6 * AC = 42

=> AC = 14 cm

BD = BC + CD

=> 22 = 6 + CD

=> CD = 16 cm

Tan x = AC /CD

=> Tan x = 14/16

=> Tanx = 7/8

=> x = Tan⁻¹(7/8)

=> x = 41.186°

The size of the angle is - 41. 186°

    area of triangle ABC = 1/2 * BC * AC

    or, 1/2 *BC * AC = 42

     or, 1/2 * 6 * AC = 42

     or, 3 * AC = 42

divide both sides by 3,

        AC = 14 cm

     BD = BC + CD

or, 22 = 6 + CD

or, CD = 16 cm

   tan x = [tex]\frac{AC}{CD}[/tex]

or, tan x = [tex]\frac{14}{16}[/tex]

or, tan x = [tex]\frac{7}{8}[/tex]

or , x =  41. 186°

∴ The size of the angle is - 41. 186°.

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The point-slope form with a slope of 5/2 and a point of (4,-7) is 5x-2y=34.

What is line equation?

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10. Linear equations are classified into three types: point-slope, standard, and slope-intercept.

Here,

The slope of line perpendicular to the line y +6=-2/5(x-1)

m1=5/2

point=(4,-7)

y-y1=m(x-x1)

y+7=5/2(x-4)

2y+14=5x-20

5x-2y=34

The point-slope form for slope given as 5/2 and point as (4,-7) will be 5x-2y=34.

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Answer:

-6

Step-by-step explanation:

2+(-8)=-6

equation will be the number of shirts ordered in each size. division equation with that model the theory 45 ÷ 5 = 9

The Harbor Lighthouse gift shop ordered a shipment of 45 shirts with a special whale print. This means that we need to divide 45 by 5, in order to find out how many shirts were ordered in each size. To do this, we can use a division equation.

In this equation, 45 represents the total number of shirts and 5 represents the number of sizes. The answer to this equation will be the number of shirts ordered in each size. When we divide 45 by 5, we get 9 as our answer. Therefore, the store ordered 9 shirts in each size.

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The vertical angles are congruent, then the two lines cut by a transversal are parallel is False.

Option B is the correct answer.

The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

Corresponding angles are equal.

We have,

Vertical angles are congruent.

Vertical angles are pairs of opposite angles made by intersecting lines.

Thus,

For vertical lines to be congruent, we do not need two parallel lines.

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Answer:

11/50

Step-by-step explanation:

=5x2+1= 11/5

=1/10×11×5

=11/50

The length of the mid-segment of the given trapezoid will be 8.5.

A quadrilateral is a geometrical 2d shape in which there are four sides and each side is connected and makes a close polygon.

In other meaning, a quadrilateral is a kind of polygon in which four sides for example rectangle, square, and parallelogram are quadrilateral.

As per the given vertices,

I(-3, -5), J(8, -5), K(3, -9), and L(-3, -9)

The trapezoid has been plotted below.

The length of LK = 3 - (-3) = 6 units.

Length IJ = 8 - (-3) = 11 units

The length of midsegment x = (11 + 6)/2 = 17/2 = 8.5

Hence "The supplied trapezoid's mid-segment will be 8.5 inches long.".

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Ms. Jones washed most of the laundry and the remaining laundry need to be washed is 7/20.

Converting the fraction to decimal to easily compare the amount of laundry washed.

Laundry washed by Ms. Jones = 2/5

Performing division

Laundry washed by Ms. Jones = 0.4

Laundry washed by her son = 1/4

Performing division

Laundry washed by her son = 0.25

0.4 is greater than 0.25, hence, Ms. Jones washed more laundry.

They washed the laundry in fractions. So, the total laundry can be taken as 1.

Total laundry washed = 0.4 + 0.25

Total laundry washed = 0.65

Remaining laundry = 1 - 0.65

Performing subtraction

Remaining laundry = 0.35

Converting into fraction = 35/100

Remaining laundry in fraction = 7/20

Thus, Ms. Jones washed more laundry and 7/20 is remaining.

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The complete question is -

Ms. Jones washed 2/5 of her laundry. Her son washed 1/4 of it. How much of the laundry still needs to be washed?

Answer:

The x-axis interval of 39 to 65 has the smallest rate of change.

Step-by-step explanation:

See the attached worksheet.  The interval of x that results in the least change in y can be visually seen by plotting the points and drawing a curve.  The curve begins to flatten as x increases.  So the smallest rate of change is between the last two points, x = 39 to 65.

This can also be calculated by finding the change in y per a change in x.  The table in the graph confirms the earlier observation.  Dx and Dy represent the "delta," or difference, D,  between the x (Dx) and y(Dy) values.  The rate of change is calculated as Dy/Dx, or the change in y divided by the change in x.  The results confirm that the 39 to 65 segment is the smallest, at 0.15.

The answer as a mixed number in simplest form will be 1 3/4.

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

Given that;

The expression is,

⇒ 1/4 - (- 1 1/2)

Now,

Since, The expression is,

⇒ 1/4 - (- 1 1/2)

Hence, Solve the expression as;

⇒ 1/4 - (- 1 1/2) = 1/4 + 3/2

                      = 1/4 + 6/4

                      = 7/4

                      = 1 3/4

Thus, The answer as a mixed number in simplest form will be 1 3/4.

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Answer:

It would take Sam 29 minutes and 30 seconds

Answer:

-38x - 14y

Step-by-step explanation:

2[x+2y - 24x - 12y + 4x + 3y]

2 [ -19x -7y]

- 38x - 14y

The common denominator of the fractions 2/3 and 1/6 will be 6.

The lowest common multiple is the smallest multiple which is common between any two numbers.

It means we can divide both numbers by that and that is the smallest number by which both dived.

As per the given fractions 2/3 and 1/6.

Multiply 2 in numerator and denominator in 2/3.

2/3 x 2/2 = 4/6

Now denominator is the same thus common denominator is 6.

Hence "6 will be the common denominator for the fractions 2/3 and 1/6".

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Answer:

Below

Step-by-step explanation:

10 % OFF means you pay 90% of price

x = original price

Store A :   5% off    means   price is .95x

                    then another 10% off would mean  .9 * (.95x)

                        then another 10% off would mean  .9 * ( .9 *(.95x)

                               this equals .7695 x

Store B 25% off means you pay 75%  

  price is then .75x

price of      .75x at store B is < than .7695 x at store A  

    so B has greater discount

Answer:

Step-by-step explanation: To compare the discounts offered by Store A and Store B, we need to calculate the final price of the item after all discounts have been applied.

For Store A, the successive discounts of 5%, 10%, and 10% can be applied as follows:

The initial price of the item is reduced by 5%, resulting in a price of 0.95 * Price.

The price from step 1 is reduced by an additional 10%, resulting in a price of 0.9 * (0.95 * Price) = 0.855 * Price.

The price from step 2 is reduced by an additional 10%, resulting in a price of 0.9 * (0.855 * Price) = 0.7695 * Price.

For Store B, the single discount of 25% can be applied as follows:

The initial price of the item is reduced by 25%, resulting in a price of 0.75 * Price.

Comparing the final prices of the item at Store A and Store B, we can see that Store B offers a greater discount. The final price of the item at Store A is 0.7695 * Price, while the final price at Store B is 0.75 * Price. Since 0.75 is less than 0.7695, the final price at Store B is lower.

Therefore, Store B offers a greater discount on the item.

similar triangles have a ratio and in this case the ratio is 1:2 i hope you understand

Option D is correct the answer. The average rate of change over the interval 1 < x < 5 is greater than the average rate of change over the same interval for the function g(x) = 1. 8x2 is k(x) = 2x^2

The average rate of change:

Given a function y, the average rate of change S of y=f(x)  in an interval (xs,xf) will be given by the following equation:

[tex]S=\frac{f(xf)-f(xo)}{xf-xo}[/tex]

In this problem, we have that:

Interval (1,5), so xf=5,xo=1

Then

[tex]S=\frac{f(5)-f(1)}{4}[/tex]

All options are compared to g(x).

[tex]g(x)=1.8x^{2}[/tex]

g(5) = 1.8*(5)^2 = 45

g(1) = 1.8*(1)^2 = 1.8

[tex]S=\frac{45-1.8}{4} =10.8[/tex]

A.=f(x) = x^2

f(5) = 5^2 = 25

f(1) = 1^2 = 1

[tex]S=\frac{25-1}{4} =6.25[/tex]

Smaller than 10.8, so this is not the answer.

B.=g(x) = 1.2x^2

g(5) = 1.2*(5)^2 = 30

g(1) = 1.2*(1)^2 = 1.2

[tex]S=\frac{30-1.2}{4} =7.2[/tex]

Smaller than 10.8, so this is not the answer.

C.=h(x) = 1.5x^2

h(5) = 1.5*(5)^2 = 37.5

h(1) = 1.5*(1)^2 = 1.5

[tex]S=\frac{37.5-1.5}{4}= 9[/tex]

Smaller than 10.8, so this is not the answer.

D.=k(x) = 2x^2

k(5) = 2*(5)^2 = 50

k(1) = 2*(1)^2 = 2

[tex]S=\frac{50-2}{4} =12[/tex]

Greater than 10.8, this is the answer.

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if f(x) +[tex]x^{2}[/tex]  [tex][ f(x) ]^{5}[/tex]  = 34 and f(1) = 2, then f '(1) = - [tex]\frac{64}{81}[/tex]

f ′(x )'s indicates that it is derived from f (x). The second notation is dydx. The instantaneous rate at which y changes in relation to x is shown by this notation.

f(x) + [tex]x^{2}[/tex]  [tex][ f(x) ]^{5}[/tex]  =  34

differentiate with respect to x :

f' (x) + [tex]x^{2}[/tex] . 5 [tex][ f(x) ]^{4}[/tex] f'(x) +  [tex][ f(x) ]^{5}[/tex]  2x = 0

putting x = 1

f' (1) + [tex]1^{2}[/tex] . 5  [tex]f(1)^{4}[/tex] f'(1) + [tex]f(1)^{5}[/tex] 2(1) = 0

f' (1) + 1.5 [tex](2)^{4}[/tex] f'(1) + [tex](2)^{5}[/tex] . 2 = 0

f' (1) + 80 f' (1) = - 64

81 f' (1) = - 64

f' (1) = - [tex]\frac{64}{81}[/tex]                    

thus , the f ' (1) is found.

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The domain and range for the following graph, is written below:

Domain (interval notation) : [-4,4)

Range (interval notation): [1,4)

Domain (inequality notation): -4 ≤ x < 4

Range (inequality notation): 1 ≤ x < 4

The collection of values that can be put into a function's domain are called its parameters. The x values for a function like f(x) are contained in this collection (x). The collection of values that a function can take on is known as its range. Following the putting of the x value, the function outputs this sequence of values.

Utilizing graphs is a useful tool for determining the scope and range of functions. A graph's domain is the entire set of input values shown on the x-axis since the term "domain" refers to the set of potential input values. The various output values are displayed on the y-axis and make up the range.

Domain (interval notation) : [-4,4)

Range (interval notation): [1,4)

Domain (inequality notation): -4 ≤ x < 4

Range (inequality notation): 1 ≤ x < 4

As we know,

Domain is the x-values of a function

Range is the y values of a function

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Answer:

No solution

Step-by-step explanation:

There is no real value of [tex]x[/tex] you can substitute into this equation to make it true.