Zoe says that 2³ · 4² can be rewritten as 8⁶. Juana says that it can be rewritten as 8⁵. Danladi says that it cannot be rewritten as either of these expressions. Who is correct? Explain.

Simplify the integrand.

[tex]\displaystyle \frac{x^3-x^2-1}{x^2-x-1} = x + \frac{x-1}{x^2-x-1}[/tex]

Expand into partial fractions, recalling that [tex]\phi[/tex] and [tex]-\frac1\phi[/tex] are roots to the quadratic in the denominator.

[tex]\dfrac{x-1}{(x - \phi) \left(x + \frac1\phi\right)} = \dfrac1{1+\phi^2} \left(\dfrac1{x-\phi} + \dfrac{\phi^2}{x + \dfrac1\phi}\right)[/tex]

Then the integral is

[tex]\displaystyle I = \int_0^1 \frac{x^3-x^2-1}{x^2-x-1} \, dx \\\\ ~~~~ = \int_0^1 x \, dx + \frac1{1+\phi^2} \int_0^1 \left(\frac1{x-\phi} + \frac{\phi^2}{x+\frac1\phi}\right) \, dx \\\\ ~~~~ = \frac12 + \frac{1}{1+\phi^2} \left(\ln|1-\phi| + \phi^2 \ln\left|1 + \frac1\phi\right| - \ln|-\phi| - \phi^2 \ln\left|\frac1\phi\right|\right)[/tex]

and this reduces significantly, when we recall that [tex]\phi = 1 + \frac1\phi[/tex], to

[tex]\displaystyle I = \boxed{\frac12 + \frac{2\phi}{1 + \phi^2} \ln(\phi)}[/tex]

Answer:

-2/6

Step-by-step explanation:

go down the y axis 2 times (-2) and over 6

y=-2/6x+4

The translation of the phrase into an algebraic expression which is the sum of 6 and b is 6+b.

It should be noted that an algebraic expression is used in Mathematics to show the relationship between the terms that are given. The concept of utilizing letters or alphabets to convey numbers without defining their exact values is known as algebraic expressions.

We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.

In this case, we want to translate the phrase into an algebraic expression. The phrase is the sum of 6 and b. This will simply be:

= 6 + b

Therefore, the expression is 6+b.

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The quotient of 581 and 14 has a value of 40.07

The quotient expression is given as

581/14

Next, we express 581 as the sum of a multiple of 14 and another number

Say 581 = 280 + 280 + 1

So, we have the following equation

581/14 = (280 + 280 + 1)/14

Expand the bracket

So, we have the following equation

581/14 = 280/14 + 280/14 + 1/14

Evaluate the quotients

581/14 = 20 + 20 + 0.07

Evaluate the sum

581/14 = 40.07

Hence, the value of the quotient expression is 40.07

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Answer: 20m/s

Step-by-step explanation:

Velocity final= Velocity initial+acceleration*time

Vf=0+4*5= 20m/s

after solving each compound given in the picture

there was a existing solution that is as follows -

a ) ( - ∞ , 1] U [12 , ∞ )

b) ( - ∞ , 8] U [4 , ∞)

inequality, When two integers or algebraic expressions are stated to be greater than, greater than or equal to, less than, or less than or equal to each other in order.

A mathematical statement known as an inequality in algebra uses the inequality symbol to show the relationship between two expressions.  It indicates that the expressions on the left and right should be bigger or less than one another, or vice versa. Literal inequalities occur when the relationship between two algebraic expressions is shown using the inequality symbol. An inequality in algebra is a mathematical statement that demonstrates the relationship between two expressions.  In other words, the expression on the left should be greater or smaller than the expression on the right.

a ) ( - ∞ , 1] U [12 , ∞ )

b) ( - ∞ , 8] U [4 , ∞)

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The answer for this is 7 4/9

Using simple multiplication, we concluded that Total coins equals 127 × 10 ⁷

Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The factors in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the product is the number 54.

People in the United States = 3.1 x 10⁸

each person has 4.1 x 10¹ coins

Total coins = ( 4.1 x 10¹ ) × ( 3.1 x 10⁸ )

Total coins = 12710000000

= 127 × 10 ⁷

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The value of the estimated standard error for the following set of D scores 4, 8, 4, 4 is 1.

The standard deviation of a statistic's sample distribution, or an approximation of that standard deviation, is the statistic's standard error. The term "standard error of the mean" is used when referring to a statistic that is the sample mean.

Consider the following set of D scores,

4, 8, 4, 4

We will calculate ∑D and ∑D² to find the SS for the D scores.

Therefore,

∑D = 4 + 8 + 4 + 4

∑D = 20

∑D² = 4² + 8² + 4² + 4²

∑D² = 16 + 64 + 16 + 16

∑D² = 112

Now, the formula for the standard score is given as:

[tex]SS=\sum D^2- \frac{(\sum)^2}{n}[/tex]

SS = 112 - [ (20)² /4 ]

SS = 112 - 100

SS = 12

Now,

[tex]S_{D}=\sqrt{\frac{SS}{n-1} }[/tex]

[tex]S_{D}=\sqrt{\frac{12}{4-1} }[/tex]

[tex]S_{D}=\sqrt{4}\\ S_{D}=2[/tex]

[tex]S_{\overline D}=\frac{S_{D}}{\sqrt{n} }[/tex]

[tex]S_{\overline D}=\frac{2}{\sqrt{4} }[/tex]

[tex]S_{\overline D}=\frac{2}{2}=1[/tex]

Hence, the standard error of the set of D scores is 1.

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The answer of (7 ×5) ×2 using associative property is 70.

What is associative property?

(a ×b) ×c = a ×(b ×c) and (a+b)+c = a+(b+c)

Addition and multiplication are supported by the associative property but not division and subtraction.

Using associative property ,

(7 ×5) ×2 = 7×(5 ×2)

(7 ×5) ×2  =  7×10

(7 ×5) ×2  =  70

Therefore, the answer of (7 ×5) ×2 using associative property is 70.

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If Gabriella has 3 more nickels than dimes and they have a combined value of 90 cents, The number of coin she have is; 4 nickels and 7 dimes.

x =  number of nickels that Gabriella has

x +3 =number of dimes that Gabriella

Hence,

0.05x  + 0.10 ( x + 3 ) = 0.9

Solving for x

Multiply both sides of the equation by 100 so as to eliminate two  decimal places

5x + 10x + 30 = 90

Collect like terms

15x  = 60

Divide both side by 15x

x = 60/15

x = 4 nickels

So,

x + 3 where x = 4

4 + 3 =7 dimes

Therefore she has 4 nickels and  7 dimes.

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Factor of trinomial 8x+2x-3 is 4x-3(binomial).

The breaking or decomposition of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring in mathematics. Complete factoring is a three-step process: If at all possible, factor a GCF from the expression. Try to factor a trinomial if you can. Factor as many times as you can using a Difference Between Two Squares. Factorizing is the practice of expressing a number or other mathematical object as the sum of a number of other, typically smaller or more basic items of the same kind.

Given Data

8x² + 2x -3

Factorizing,

8x² + 2x -3 =0

8x² - 6x + 4x - 3 = 0

2x(4x -3) +1(4x - 3) =0

(2x + 1) (4x-3) = 0

Binomials are (2x+1) and (4x-3)

Binomial is 4x-3.

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Answer: The answer is 234.7

Step-by-step explanation:

Answer:

B) The blue square on the right contains the yellow square + the green square on the left

Step-by-step explanation:

hope this helps ;)

Answer:

Rounds down to 7000.

Step-by-step explanation:

Answer:

Option 4

Step-by-step explanation:

[tex]x^2+10x=-81 \\ \\ x^2+10x+25=-56 \\ \\ (x+5)^2=-56 \\ \\ x+5= \pm \sqrt{-56}=\pm 2i \sqrt{14} \\ \\ x=-5 \pm 2i \sqrt{14}[/tex]

1 3/5 ÷ 3 1/5

Change the mixed fraction to improper fraction

8/5 ÷ 16/5

Change the division to multiplication, thereby inverting 16/5

8/5 x 5/16

= 8/16

= 1/2

Answer:

0.5

Step-by-step explanation:

Answer: 23+42=42+23

how the heak is this a colledge question*_* i learned this in 2nd grade lol

We have rewritten 23 + 42 = 65 as 23 + 42 = 65 using the Commutative Law of Addition.

A number system is defined as a system of writing to express numbers.

The Commutative Law of Addition states that changing the order of the addends does not change the sum.

a+b=b+a

Therefore, we can rewrite 23 + 42 as 42 + 23, and the equation becomes:

42 + 23 = 65

or 42+23=23+42

So, we have rewritten 23 + 42 = 65 using the Commutative Law of Addition.

Hence,  we have rewritten 23 + 42 = 65 as 23 + 42 = 65 using the Commutative Law of Addition.

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I believe the slope of the the line passing through the given points would be m = 1.

Hope this helps!

Answer:

  angle 1 = 108°

Step-by-step explanation:

You want the measure of angle 1, given the measure of angle 4 is 72° in the diagram.

Angles 1 and 4 are a linear pair, so are supplementary:

  angle 1 + angle 4 = 180°

  angle 1 + 72° = 180°

  angle 1 = 108° . . . . . . . subtract 72°

Which property is illustrated in Step 2 ? Option B. Commutative property

How is this explained?

Given:

Step 1 = 10+ 8x - 10 - 4x +4 = 0

Step 2 = 10 + (-10+ 8x) -4x + 4

Here , 8x - 10 = -10 + 8x

This is of the form , A+B = B+A

Commutative property of addition = A+B = B+A

What is the commutative property?

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Answer:

240%

Step-by-step explanation:

Times the two whole number by five, add the result to top number, divide by denominator.

The change in temperature between the two readings as measured by Miguel is 18.7°F  .

In the question ,

the temperature  readings on the Miguel is

Average low temperature = -8.5°F

Average high temperature = 10.2°F

the change in the temperature , is given by the difference between the two reading .

which means

Change in temperature = Average high temperature - Average low temperature .

Substituting the values of average high and average low reading of the temperature from above ,

we get ,

Change in temperature = 10.2 -(-8.5)

= 10.2 + 8.5

= 18.7

the temperature change is 18.7°F .

Therefore , the temperature change is 18.7°F .

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Answer:

The value of x is 3 cm

Step-by-step explanation:

x is 3 cm because we can take 3/2 and make it easier for us and turn it into 1 and 1/2. As you can see 6, is 1 and 1/2 of 4, so all we have to do is find out what x equals by finding out what is 1 and 1/2 of 2. 2 is already 1, so we take half of 2 and add it and we get our answer 3 cm.

∠a=90° as the rays of the angles meet at the right angle that is 90°.One of the angle is 21, The remaining would be 90-21=69°.

When two straight lines or rays intersect at a common endpoint, an angle is formed. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner."

A ray is a vector that extends from one point to another. A ray is typically defined in geometry as a half-infinite line (also known as a half-line) with one of the two points and taken to be at infinity.

The right angle is formed when two straight lines intersect at 90 degrees or are perpendicular to each other at the intersection. The symbol is used to represent a right angle.∠

Here, The total sum of angles is 90°.

one the value is 21°. The value of adjacent angle would be,

remaining angle=90-21

                          =69°

So the remaining value of adjacent angle is 69°.

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The baker can put all the 576 muffins in the box that contains exactly 9 muffins with none left over.

In order to determine if the baker can put all the 576 muffins in the box that contains exactly 9 muffins with none left over, divide 576 by 9. If 9 perfectly divides 576, then there would be no remainder.

Division is the process in mathematics that is used to group a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations. Other operations in mathematics are addition, subtraction and multiplication.

Number of boxes needed = number of muffins / capacity of each box

576 / 9 = 64

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The maximum height reached by the ball is 22 feet

The ball stayed in the air for 1 second

A function can be defined as a rule, law or expression that shows the relationship between two identifiable variables:

Given the function:

h(t) = -16t² + 32t + 6

Where;

To determine the maximum height in feet that the ball reached, we would be required to substitute the value of t as 1

We have:

h(1) = -16(1)² + 32(1) + 6

expand the bracket

h(1) = -16 + 32 + 6

Add the values

h(t) = 22 feet

To determine the time, we have;

-16t² + 32t + 6 = 22

-16t² +32t + 6 - 22 = 0

Add like terms

-16t² +32t - 16 = 0

Factorize further

-16t² + 16t + 16t - 16 = 0

Factorize in pairs

16t( t - 1) + 16 ( t - 1) = 0

Then,

t - 1 = 0

t = 1 second

Thus, the maximum height is 22 feet

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After solving some mathematical operations we can conclude that the cashier has 16 bills of $10 and 18 bills of $20.

So, the total value of money by 35 bills is $0, and $20 is $520.

Therefore, after solving some mathematical operations we can conclude that the cashier has 16 bills of $10 and 18 bills of $20.

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The points on the x-axis that are 12 units away from the point (3,-6) is       found to be  3 ±  [tex]6\sqrt{3}[/tex].

r² = (x - h)² + (y - k)²is the standard equation for a circle, where (h,k) are the coordinates of the circle's center and r is the radius.

We must locate all points on the x-axis that are 12 units away from the starting point (3,-6).

Let these points be (x,0)

All points 12 units away from the point (3,-6) form a circle with a radius of 12 and a center at (3,-6). The formula would be as follows:

r² = (x - h)² + (y - k)²

12² = (x-3)² + (0+6)²

144 = (x-3)² + 36

(x-3)² = 108

x-3 = ± [tex]\sqrt{108}[/tex]

x = ± [tex]\sqrt{108}+3[/tex]

x = 3 ± [tex]6\sqrt{3}[/tex]

Therefore, the points on the x-axis 12 units away from point (3,-6) is  calculated as  3 ± [tex]6\sqrt{3}[/tex].

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The quantity of the new sweaters at a price of $12 is gotten using the slope of 3 to be 36 sweaters

given data

Pa = $120

Qa = 40

Pb = $12

slope of the supply curve is m=3

The slope represents the relationship between the the input variable and the output variable.

The input variable is the price while the output variable is the quantity supplied.

The slope is the factor that multiplies the input to get the output, we therefore solves as follows

= Pb * slope

= $12 * 3

= 36

Therefore at the price of$15 the quantity supplied is 36 sweaters

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Answer:

4 sweaters

Step-by-step explanation:

Pa-Pb /Qa-Qb