|5x|=3
this is absolute value of five x equals three

Answer:

Step-by-step explanation:

Substitute the √2 with a letter a to expand the expression. Multiply individual components of the first bracket with the second bracket. Apply the index power rule to simplify raised numbers.

(1-2√2)(1+2√2) = (1-2a)(1+2a)

1(1+2a)-2a(1+2a) = 1+2a-2a-2a2a = 1+2a-2a-4a^2

a = √2,

1+2√2 -2√2 -4(√2 )^2 = 1-4( 2^1/2x2)

1-4(2) = 1-8

= -7

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Converting the radicals into exponent numbers, √3 (⁴√3) = ⁴√27

To work with radical numbers or roots, it is easier to express them in exponent:

[tex]\sqrt[n]{a^{b}}=a^{\frac{b}{n}[/tex]

Recall the rules of exponent operations:

Note that the first 3 rules use the same base. If there are more than 1 base number, then group the exponent that have the same base first.

Example:

[tex](2^{3}.3^{-2}) : (2^{-3}.3^{2})=( 2^{3}:2^{-3}).(3^{-2}:.3^{2})[/tex]

Tips: To simplify exponent numbers, sometimes it is useful to modify the base whenever possible.

Example:

8².2⁻⁵ = (2³)². 2⁻⁵ = 2⁶. 2⁻⁵ = 2⁶⁻⁵ = 2¹ = 2

The given problem:

Simplify  √3 (⁴√3)

[tex]\sqrt{3}=3^{1/2}[/tex]

[tex]\sqrt[4]{3} =3^{1/4}[/tex]

Hence,

[tex]\sqrt{3}.\sqrt[4]{3} =3^{1/2}.3^{1/4}\\ =3^{1/2+1/4}=3^{3/4}\\ =\sqrt[4]{3^{3}}= \sqrt[4]{27}[/tex]

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Answer:[tex]\sqrt 7,2.8,\pi ,\sqrt{17, 4.6[/tex]

Step-by-step explanation:

=========================================================

Explanation:

Let's evaluate what i^97 would be

First let's list out a few powers of i. Recall that [tex]i = \sqrt{-1}[/tex]

[tex]i^0 = 1\\\\i^1 = i\\\\i^2 = (\sqrt{-1})^2 = -1\\\\i^3 = i*i^2 = i*(-1) = -i\\\\i^4 = i*i^3 = i*(-i) = -i^2 = -(-1) = 1\\\\[/tex]

In short,

[tex]i^0 = 1\\\\i^1 = i\\\\i^2 = -1\\\\i^3 = -i\\\\i^4 = 1\\\\[/tex]

The sequence is: 1, i, -1, -i, 1, ...

The process repeats once we get to the fourth item. In other words, the process repeats every 4 terms.

So to quickly compute i^97, we'll divide the exponent by 4 to look at the remainder.

97/4 = 24 remainder 1

The remainder 1 means i^97 = i^1 = i

If we got a remainder 2, then it would be equal to i^2

Remainder 3 means it's equal to i^3, and so on.

-------------------

Here's another way to see why i^97 = i

i^97 = i^(96+1)

i^97 = i^96*i^1

i^97 = i^(24*4)*i

i^97 = (i^4)^24*i

i^97 = 1^24*i

i^97 = 1*i

i^97 = i

This helps verify the previous section. Though I recommend using the remainder trick as it's faster.

----------------------

So because i^97 = i, this means:

i^97 - i = i - i = 0

This is why 0 is the final answer (choice B).

Answer:

± 40

Step-by-step explanation:

± [tex]\sqrt{1600}[/tex]

= ± [tex]\sqrt{16(100)}[/tex]

= ± ( [tex]\sqrt{16}[/tex] × [tex]\sqrt{100}[/tex] )

= ± (4 × 10)

= ± 40

Answer:

True I think yes goodluck

The exponential function that has a y-intercept of (0, 3) and passes through the point (2, 48) is y = 3 · 1.386ˣ.

Herein we are asked to derive the exponential formula of the form y = a · bˣ that has a y-intercept of (0, 3) and passes through the point (2, 48). By using logarithm properties, the expression can be modify into this linear-like expression:

㏑ y = ㏑ a · bˣ

㏑ y = ㏑ a + x · ㏑ b

By substituting x and y, we find the following system of equations:

㏑ 3 = ㏑ a                              (1)

㏑ 48 = ㏑ a + 2 · ㏑ b           (2)

By (1):

a = 3

(1) in (2):

㏑ 48 = ㏑ 3 + 2 · ln b

㏑ b = (1 / 2) · ㏑ (48 / 3)

b ≈ 1.386

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Answer:

option D for you I have brainly plus and that's the answer I got.

Answer: Shade 10 of the pieces.

Step-by-step explanation: To figure this out, divide 15 by 3(5) and then multiple 5 by two and you will get 10!

Answer: You need to shade 10 of the pieces.

Take 15/3 and get 5

Then take 5 * 2 and get 10

Step-by-step explanation:

a)The acceleration, in km/h², in the first 15 mins = 200  km/h².

b) The distance between the two cities = 125 km.

c) The average speed during 20 the journey =  62.5  km/hr.

For the given question;

Every horizontal block is 1/8 hour = 7.5 minutes long.

Each vertical block has a speed of 10 km/hr:

The table drawn as per the data given in the table:

Time                    Velocity  km/hr

0 Min  ( 0 hr)   --->         0

15 Min (1/4 hr)   -->       50

45 Min (3/4 hr)  -->      50

60 MIn  ( 1 hr)      -->    100

90 Min  ( 3/2 hr)   --->  100

120 Min ( 2hr)     --->    0

The formula for acceleration:

Part a: Acceleration = final velocity - initial velocity / final time - initial time

Acceleration in the first 15 minutes:  (1/4 hr)  =  (50 - 0)/(1/4 - 0)  

= 50/(1/4)

=200

Thus, acceleration in the first 15 minutes is 200 kmph.

Part b: Distance among two cities:

= (1/2)(0 + 50)(1/4 - 0)  + 50 * (3/4 - 1/4)  + (1/2)(50 + 100)(1 - 3/4)  + 100 * (3/2 - 1) + (1/2)(100 + 0)(2 - 3/2)

=  25/4  + 25 + 75/4   + 50 + 25

= 125

The difference distance for two cities is 125 kilometers.

Part c: Average speed = distance/2

Average Travel Speed = 125/2 = 62.5 km/hr

Therefore,

a: Acceleration in the first 15 minutes = 200  km/h²

b: The distance between two cities is 125 kilometers.

c: The average speed of the journey is 62 miles per hour.

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Greg will pay $25.99 for one ink cartridge after the rebate.

As stated in the question, rebate is the refund that customer receives. It is part of the amount paid. So, it can be easily deducted from the total amount. To find the payment amount, we will simply subtract rebate amount from ink cartridge cost.

Keep the values in mentioned relation to find the payment amount to be given by Greg for one ink cartridge.

Payment = 35.99 - 10

Performing subtraction to find the payment amount to be given by Greg

Payment = 25.99

Hence, the payment of $25.99 will be done by Greg for one ink cartridge after the rebate.

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The logarithm expression can written as log₆ 24 - log₆ 4 = 1

There are 7 properties of logarithms: Product Rule, Quotient Rule, Power Rule, Zero Rule, Identity Rule, Inverse Property of Logarithm, Inverse Property of Exponent, Change of base formula.

In this question, we use the Quotient Rule of logarithms.

Quotient rule of logarithms states that the logarithm of a quotient is equal to a difference of logarithms.

Example: logₐ (x/y) = logₐ x - logₐ y

So, we get that:

log₆ 24 - log₆ 4

= log₆ (24 / 4)

= log₆ 6

which will also be equal to

= 1

Therefore, in the equation log₆ 24 - log₆ 4 = 1 and the property of the quotient rule of logarithms is used.

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Using factorization, the factors of 2 x²+x-28 are x = - 4 and x = 7/2

The factorization approach simplifies any algebraic or quadratic equation by using the fundamental factorization formula, which represents the equations as the product of factors rather than extending the brackets. Any equation may have an integer, a variable, or the algebraic expression itself as a component.

Given equation is -

2 x²+x-28

we will use the method of factorization.

⇒ 2x² + 8x -7x -28

⇒ 2x(x+4) - 7(x+4)

⇒ (x+4) (2x - 7)

⇒ x = -4 and x = 7/2

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total utensils = 3915

it is given that Mrs. Meester is purchasing supplies for her art class.

The arts are a very wide range of human practices of creative expression, storytelling and cultural participation. They encompass multiple diverse and plural modes of thinking, doing and being, in an extremely broad range of media. Both highly dynamic and a characteristically constant feature of human life, they have developed into innovative, stylized and sometimes intricate forms. This is often achieved through sustained and deliberate study, training and/or theorizing within a particular tradition, across generations and even between civilizations. The arts are a vehicle through which human beings cultivate distinct social, cultural and individual identities, while transmitting values, impressions, judgments, ideas, visions, spiritual meanings, patterns of life and experiences across time and space.

Mrs. Meester purchase some utensils for their scholars.

number of different types of utensils for each scholar are:-

total number of utensils for 1 scholar= 64+25+36+10

                                                            = 135

   64

   25

   36

+   10

   135

total number of utensils for 29 scholars=135*29

                                                                  =3915

hence, number of utensils Mrs. Meester buy= 3915

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(−∞,2)

Im just writting this bc the app said the answer was to short :)

The unit rate at which Darrell walks is 1.5 meters per second.

Unit rate is defined as per unit time. Unit rate can be anything from speed, acceleration or any other measurement.

The quantity that is achieved in a single unit of time is called the unit rate.

The unit rate is calculated by dividing the total amount by total time that is taken to complete the total amount.

Here Darrell walks 90 meters in 60 seconds.

The unit time to be considered here is 1 second.

so Darrell walks a certain amount of distance in 60 seconds.

Therefore the unit rate in which he walks = total distance covered ÷ total time taken

∴ unit rate = 90 ÷ 60 meters per second = 1.5 meters per second.

Disclaimer : The complete question is : In 60 seconds, Darrell walks 90 meters. Find the unit rate at which Darrell walks.

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The average rate of change of fuel efficiency = -3 gallon per hour

Fuel efficiency of the cooper when driving at a speed of 75 mph = 29 miles per gallon

Fuel efficiency of the cooper when driving at a speed of 60 mph = 34 miles per gallon

Let y₁ = 75 mph, y₂ = 60 mph

and x₁ = 29 miles/gallon , x₂ = 34 miles /gallon

Then the average rate of change of fuel efficiency = (y₂-y₁)/(x₂-x₁)

                                                        = (60 - 75)/(34-29)

                                                        = -3 gallon per hour

This means that the fuel efficiency dropped as the speed dropped from 75 mph tp 60 mph.

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Based on the fact that Sierra wants to purchase a M dozen muffins and B boxes of cinnamon, the inequality to show how many items Sierra can buy is 3.50M + 4.25B ≤ 25

The amount that Sierra can spend at most is $25 which means that the boxes of cinnamon buns and the muffins should not exceed this $25.

The cost of the muffins is $3.50 each so the representation is:

= 3.50M

The cost of the cinnamon buns is 4.25B which can be represented as:

= 4.25B

The inequality is therefore:

3.50M + 4.25B ≤ 25

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Answer:

1/36

Step-by-step explanation:

To find the probability of rolling a 2 AND a 3, you must multiply the probabilities of each individual outcome.

The probability of rolling a 2 on a 6 sided cube is 1/6.

The probability of rolling a 3 on a 6 sided cube is also 1/6.

So, to get the probability of both of those things happening:

(1/6) x (1/6) = 1/36

The quotient of 30 × 10⁻²⁴/5 × 10⁻²⁴ in scientific notation is equal to: C. 6 x 10^0.

Quotient can be defined as a mathematical expression that is simply used to represent the division of a number by another number.

In Mathematics, laws of indices can be defined as the standard principles and rules that are used for simplifying a mathematical equation or expression that involves powers of the same base.

By applying the laws of indices, the quotient is given by:

Quotient = 30 × 10⁻²⁴/5 × 10⁻²⁴

Quotient = 30/5 × 10⁽⁻²⁴ ⁺ ²⁴)

Quotient = 6 × 10⁰

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Answer:

The width, x, is in the interval (0, 7), or 0 < x < 7.

Step-by-step explanation:

width = x

length = 7x + 7

area = x(7x + 7)

x(7x + 7) < 392

7x² + 7x - 392 < 0

x² + x - 56 < 0

(x - 7)(x + 8) < 0

We have two points of interest on the number line:

-8 and 7

That makes three intervals of interest:

(-∞, -8), (-8, 7), (7, ∞)

Now we test a number from each interval.

Try -10:

(x - 7)(x + 8) < 0

(-10 - 7)(-10 + 8) < 0

(-17)(-2) < 0

34 < 0 False

Interval (-∞, -8) does not work.

Try 0:

(x - 7)(x + 8) < 0

(0 - 7)(0 + 8) < 0

(-7)(8) < 0

-56 < 0 True

Interval (-8, 7) works.

Try 10:

(x - 7)(x + 8) < 0

(10 - 7)(10 + 8) < 0

(3)(18) < 0

54 < 0 False

Interval (7, ∞) does not work.

Since we are dealing with a rectangle, the length and width must be positive numbers.

The interval (-8, 7) works mathematically for the width, but it must be limited to positive numbers, so the width must be in the interval

(0, 7)

The angles which form a linear pair are 40° and 140°.

Linear pair is defined as the pair of angles which add up to 180 degrees.

When two straight lines intersect with one another then 4 angles are formed. Any two adjacent angles thus formed are a linear pair.

Let us consider one angle be x . Now another angle is 3.5 times this angle.

Therefore measure of second angle = 3.5x

Now if these two angles are a linear pair then their sum will be equal to 180°.

Therefore we can form a linear equation in x and solve to get the values of the angles.

∴3.5x + x = 180°

or, 4.5x = 180°

or, x = 180 ÷ 4.5

or, x = 40°

Measure of the second angle = 3.5 × 40° = 140°

Hence the two angles which form a linear pair are  40° and 140° .

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Answer:

see below

Step-by-step explanation:

solve for y

y-4/x = a

Add 4x to each side

y-4/x+4/x = a+4x

y =  a+4x

If the equation is

(y-4)/x = a

Multiply each side by x

(y-4)/x *x = a*x

y-4 = ax

Add 4 to each side

y = ax+4

Answer:

y = a + 4/x

Step-by-step explanation:

-add 4/x to both sides: y - 4/x + 4/x = a + 4/x

- simplify: y = a + 4/x

The total number of 3/4 bags of pecans that Lisa can make will be B. 16.

From the information, Lisa gathered and shelled 12 lbs of pecans from her backyard and she is going to make 3/4 Ib bags of pecans for gifts.

Therefore, the total number of 3/4 bags of pecans that Lisa can make will be:

= 12 ÷ 3/4

= 12 × 4/3

= 16

She can make 16 bags.

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The characteristics of the parallelogram and star gives;

Parallelogram;

Rotational symmetry: Yes

Point symmetry: Yes

Star:

Rotational symmetry: Yes

Point symmetry: Yes

Rotational symmetry is one in which a shape assumes its original appearance after a rotation.

Point symmetry are the property of two points that are equidistant from and on opposite sides of the coordinate axis

The parallelogram has rotational symmetry of 180°

The parallelogram has point symmetry

Therefore;

Parallelogram:

Rotational symmetry; Yes

Point symmetry; Yes

The star has rotational symmetry of 360°/5 = 60°

Given that points on the star when rotated about its center can be made to match up with opposite side, it is said to have point symmetry.

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The graph for the function h(x) = x² + 2x is given by the graph -

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input.

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Answer: See attached.

Step-by-step explanation:

        This function will be a parabola (shaped like a "U")because it is a quadratic function. A quadratic function is in the form of y = ax² + bx + c. Our a value is 1, our b value  is 2, and we do not have a c value.

How would we graph this?

        Since a = 1, our quadratic function has a "slope" of 1. This means that we will count up one and right one, and up one and left one from the vertex and plot those points.

        Next, our b value is 2. This means we move the graph left 2 points from the parent function (y = x²).

        Lastly, we do not have a c value, so the graph is not transformed ("moved") up or down.

Answer:

3

Step-by-step explanation:

3

Answer:

4

Step-by-step explanation:

7.185629 x 102985 =   740,012.002565 which has 4 zeros