Fill in the blanks

A=P e rt is known as the ______ formula.

Factorization of 25 yields 5×5. In index form, this is written as 5^2. Use the power rule (a^m)^n = a^mn

25=5^2

25^(3/2) = (5^2)^(3/2)

5^(2x3/2)= 5^3

5x5x5 = 125

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After simplification of m9m - 3 the answer is 3(3[tex]m^{2}[/tex] - 1).

Given that :

= m9m - 3

a. Reordering terms:

= 9mm - 3

b.Exponents combining:

= 9mm -3

= 9[tex]m^{2}[/tex] - 3

c.Common value factor:

= 9[tex]m^{2}[/tex] - 3

Take 3 has common

= 3(3[tex]m^{2}[/tex] - 1)

Therefore after simplification of m9m - 3 the answer is 3(3[tex]m^{2}[/tex] - 1).

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Answer: -8b -  24

Step-by-step explanation:

For distributive property, you multiply the number outside of the parenthesis (8) by the numbers/variables inside the parenthesis (b and 3)

-8 × b = -8b

-8 × 3 = -24

After solving the given equation  [tex]2 e^{x-2}=e^x+7[/tex], the value of [tex]x=\ln 7-\ln \left(2 e^{-2}-1\right)[/tex].

So,

Given equation: [tex]2 e^{x-2}=e^x+7[/tex]

Then,

[tex]2 e^{x-2}=e^x+7\\2 \frac{e^x}{e^2}=e^x+7\\2 \frac{e^x}{e^2}-e^x=7\\e^x\left(2 e^{-2}-1\right)=7\\e^x=\frac{7}{\left(2 e^{-2}-1\right)}\\x=\ln \left(\frac{7}{\left(2 e^{-2}-1\right)}\right)\\x=\ln 7-\ln \left(2 e^{-2}-1\right)[/tex]

Therefore, after solving the given equation  [tex]2 e^{x-2}=e^x+7[/tex], the value of [tex]x=\ln 7-\ln \left(2 e^{-2}-1\right)[/tex].

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Answer: 13.15

Step-by-step explanation:

50

-

36.85

Answer:

Step-by-step explanation:

13.50

The value of the expression log₃54 is 3.6.

Given that the expression is log₃54.

We are required to find the value of the expression by using the change of base formula.

The change of base formula is the formula that will give us the answer of a log with a different base by using only log calculations with a base of 10.

The expression is log₃54.

log₃54= log (54)/log (3)          

(We know that [tex]log_{a}b[/tex]=log b/ log a)

Now we have to use the values of logarithms in the above expression to find its value.

=1.73/0.48

=3.6

Hence the value of the expression log₃54 is 3.6.

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Answer: The fabrics that cost less than $8 per yard are cotton, flannel and fleece.

In order to determine the cost of a yard of each material, divide the total cost of 3/4 yards of that fabric by 3/4

cost of a yard = total cost ÷

Cost of a yard of cotton = 5.54 ÷  = 6.85

Cost of a yard of Flannel = 2.62 ÷ = 3.49

Cost per yard of Fleece = 4.27 ÷  =  5.69

Cost per yard of Terry Cloth = 6.52 ÷ = 8.69

Based on the above calculations, all but Terry cloth cost less than $8 per yard

Answer:

1. roots may be +/-1,2,3,6 and fractions

A root must be minus since if they were positive, the function would be >0.

-1 works by inspection, so (x+1) is a factor.

-1/1==6==11==6

1===5===6==0

the factors are (x-1)(x^2+5x+6)=(x+1)(x+2)(x+3)

Roots are -1, -2,-3

-

2.x^3-7x+6, Try+/-1,2,3,6

start with 1, and1-7+6=0; (x-1) is a factor

can divide

1/1=0==-7===6

1---1-- -6===0

The factors are (x+1)(x^2+x-6)=(x-1)(x+3)(x-2)

roots are 1,2,-3

-

3.x^3+x^2-12x

factor out an x

x(x^2+x-12)=x(x+4)(x-3)

roots are 0, -4, 3

-

4.9x^3-7x+2

roots can be +/-1, and +/-2 along with (1/3) (2/3),(1/9), (2/9)

-1

(x+1) is a factor.

-1/9===0== -7===2

9----- -9===2====0

(x+1)(9x^2-9x+2)

factor the last with +/- 1, 2.

second factors by noting x^2-9x+18 factors Into (x-6)(x-3)

divide the constant by 9 and put the denominator in front

(3x-2)(3x-1)

so the roots are -1, (2/3), and (1/3)

-

5x³+4x²-31x+6, note: I will assume 31 x.

Roots include (1/5)(2/5)(3/5)(6/5) along with

+/- 1,2,3,6, and 1, -1 do not work by inspection

2/5===4=== -31===6

5------14---- -3===0

so (x-2)(5x^2+14x-3)

or (x-2)(5x-1)(x+3) are the factors

roots are 2, (1/5), -3

hope this helps

The expression 25x^2 - 40xy + 16y^2 can be factored as (5x - 4y)(5x - 4y).

Factorization is defined as the process of breaking down a number or polynomial into factors that when multiplied will give the same value.

The expression 25x^2 - 40xy + 16y^2 resembles the form

ax^2 + bxy + cy^2 which has factors (mx + ny)(ox + py).

Factoring polynomial expression like 25x^2 - 40xy + 16y^2 can be done by grouping method shown earlier.

Find the two pairs of numbers whose products are 25 and 16.

Taking 5 and 5, and 4 and 4 as the pair of numbers.

(5x - 4y)(5x - 4y)

Checking the product of this factors:

(5x -4y)(5x - 4y)

25x^2 - 20xy - 20xy + 16y^2

25x^2 - 40xy + 16y^2

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The number of newspapers that each bundle have contained will be 23373 newspapers.

From the information, the printing press printed 934,920 newspapers, which were bound into 40 identical bundles for easy transportation.

Therefore, the number of newspapers that each bundle have contained will be:

= Total newspaper / Number of bundle

= 934920 / 40

= 23373

Therefore, the number of newspapers that each bundle have contained will be 23373 newspapers.

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Last month, a printing press printed 934,920 newspapers, which were bound into 40 identical bundles for easy transportation. How many newspapers could each bundle have contained

-2 is the extraneous solution of the equation.

The equation is:

[tex](x + 3)^{1/2}[/tex] - 1 = x

To find the extraneous solution of the expression first we need to find the value of x.

[tex](x + 3)^{1/2}[/tex] = x + 1

Squaring both sides we have,

[tex](x+ 3)^{}[/tex] = [tex](x + 1)^{2}[/tex]

x + 3 = [tex]x^{2}[/tex] + 2x + 1

[tex]x^{2}[/tex] + x - 2 = 0

[tex]x^{2}[/tex] + 2x - x - 2 = 0

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

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

x = -2, 1

Now we have to put the value of x in the equation:

x = -2

[tex](-2 +3)^{1/2}[/tex] - 1 = -2

1-1 =-2

0≠ -2

x = 1

[tex](1 + 3)^{1/2}[/tex] - 1= 1

2 - 1 = 1

1= 1

Therefore we get x = -2 is as extraneous solution of the equation and x= 1 is the solution of the equation.

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2 nickles, 6 dimes. Not 100% sure but I think it's right

a. the length of the rectangle is 11 units while the width of rectangle is 7 units

b. The rectangles dimensions written as ordered pair (l, w) are

c. the points on coordinate can be (0, 0), (0, 11), (7, 11), and (7, 0).

d. The points are on the first quadrant because I plotted the points starting from the origin and moved in anticlockwise direction

Given data

perimeter = 36 units

perimeter of inner rectangle = 16 units

From the inner rectangle as plotted: 5 units on the graph represents 5 units of the rectangle on the x axis and 3 units on the graph represents 3 units on the rectangle on the y axis.

let the length of the outer rectangle be 5x and the width be 3x such that, the perimeter is solved as:

2(5x + 3x) = 36

16x = 36

x = 2.25

For the length

= 5x

= 5 * 2.25

= 11.25

= 11  (as a possible whole number)

For the width

= 3x

= 3 * 2.25

= 6.75

= 7 (as a possible whole number)

Hence we can say that the length is 11 units and the width is 7 units

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The ratio of impressions to fans is a measure of fan acquisition.

Given is to find the ratio of impressions to fans.

The ratio of impressions to fans is a measure of fan acquisition. Social marketing campaigns begin with fan acquisition, which involves using any of a variety of means, from display ads to News Feed and page pop-ups, to attract people to your Web page.

Therefore, the ratio of impressions to fans is a measure of fan acquisition.

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In 5 weeks Joe's brother will have more money than Joe

Joe and his brother are collecting money for charity

Joe has collected $170 and he plans to earn $20 weekly

His brother has already collected $80 and he plans to earn $40 weekly

Let's start off with Joe and the amount he will be earning weekly

First week: 170 + 20 = 190

Second week: 190 + 20 = 210

Third week: 210 + 20 = 230

Fourth week: 230 + 20= 250

Fifth week: 250+20= 270

Next is to calculate Joe's brother earnings

First week: 80 + 40 = 120

Second week: 120 + 40 = 160

Third week: 160 + 40 = 200

Fourth week: 200 + 40= 240

Fifth week: 240 + 40 = 280

In five weeks Joe's brother will earn $280 while Joe will earn $270

Hence Joe bother will have more money that joe in 5 weeks

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The result of simplifying each number 10,000⁰.⁷⁵ using the properties of exponents is 1

To solve this exercise we have to resolve algebraic operations following the exponent properties.

(10,000⁰)⁷⁵

Using the zero exponent rule that indicates that: any base with an exponent of zero is equal to one, we have:

1⁷⁵

One multiplied by itself many time will be one

1

In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.

Example: 3² = 3*3 = 9

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Answer:

56°

Step-by-step explanation:

The angles are supplementary. They add up to 180°

So ∠AYZ + ∠AYX = 180

6x+4 + 3x - 4 = 180

9x = 180

x = 20

Measure of ∠AYX = 3x - 4 = 3 x 20 - 4 = 60 -4 = 56°

Answer:

add then simplify

Step-by-step explanation:

The transformations that take rectangle ABCD to rectangle A'B'C'D' are given as follows:

Transformations in the graph of a function involve operations such as multiplication/division or sum/subtraction, either in the domain of the function, involving values of x, or the range, involving values of y.

Examples of transformations are as follows:

For this problem, we have that:

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A scenario which Micah's graph could represent is: 2. Micah's plant is 2 inches tall and grows at a rate of 1 inch per week (where x is the number of weeks), for a total of y inches.

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

Mathematically, the average rate of change (slope) of any straight line can be calculated by using this formula;

[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Substituting the given points into the formula, we have;

Average rate of change = (6 - 2)/4 - 0)

Average rate of change = 4/4

Average rate of change = 1.

Therefore, Micah's plant is 2 inches tall and grows at a rate of 1 inch per week (where x is the number of weeks), for a total of y inches.

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Answer: b or Micah’s plant is 2 inches tall and grows at a rate of 1 inch per week (where x is the number of weeks), for a total of y inches.

Step-by-step explanation:

Answer:

15/50

Step-by-step explanation:

[tex]\frac{6}{20}[/tex] = [tex]\frac{x}{50}[/tex]  Cross multiply

20x = 6(50)

20x = 300   Divide both sides by 20

x = 15

The sum of numbers from 1 to 100 is 50 × 101.

Carl Friedrich Gauss is a renowned mathematician. He has contributed many theories to the fields of mathematics and physics.

The sum of the first hundred numbers is calculated by making pairs of two numbers. The sum of these pairs is 101.

And there is a total of 50 pairs.

So, the sum of all these numbers is,

101 ×50

= 5050

Therefore, the sum of numbers from 1 to 100 is 5050.

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Both Katie and Ismailia are both correct because 20 is a coefficient and factor of the expression 20xy.

A coefficient is a number multiplied by a variable.

In other word, a coefficient is a number or any symbol representing a constant value that is multiplied by the variable of a single term or the terms of a polynomial.

A factor is a number that divides another number, leaving no remainder.

Therefore, the coefficient of the expression 20xy is 20.

The factor of the expression 20xy is also 20.

Therefore, Both Katie and Ismailia are both correct.

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Answer:

there both right

Step-by-step explanation:

✔✔✔‍♂️‍♂️‍♀️

The inverse of the function y=2x³+10 is y = [tex]\sqrt[-2]{x-5}[/tex] .

So,

Then,

Therefore,  the inverse of the function y=2x³+10 is y = [tex]\sqrt[-2]{x-5}[/tex] .

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Answer:

having two side equal on triangle

Answer:

if the two side of triangle is same then we can say that the triangle is isosceles triangle

(a) The scientific notation of 26,000 is  2.6 ×  10⁴  .

(b) The scientific notation of 425,000 is 4.25 ×  10⁵ .

(c) The scientific notation of 630,000 is  6.3 ×  10⁵ .

(d) The scientific notation of 2,000,000 is 2.0 ×  10⁶ .

(e) The scientific notation of 21,000 is 2.1 ×  10⁴ .

(f) The scientific notation of 231,000 is 2.31 ×  10⁵

(g) The scientific notation of 43,000,000 is 4.3 ×  10⁷ .

(a) As 26000 has three zeroes which can be represented by 10³.

scientific notation is given by 26 ×  10³ which on simplification gives

2.6 ×  10⁴

Hence,  2.6 ×  10⁴  is that the scientific notation of the quantity.

(b)  As 425000 has three zeroes which can be represented by 10³.

scientific notation is given by 425 ×  10³ which on simplification gives

4.25 ×  10⁵

Hence,  4.25 ×  10⁵  is that the scientific notation of the quantity.

(c) As 630000 has four zeroes which can be represented by 10⁴.

scientific notation is given by 63 ×  10⁴ which on simplification gives

6.3 ×  10⁵

Hence,   6.3 ×  10⁵ is that the scientific notation of the quantity.

(d) As 2,000,000 has six zeroes which can be represented by 10⁶.

scientific notation is given by 2 ×  10⁶ which on simplification gives

2.0 ×  10⁶

Hence, 2.0 ×  10⁶ is that the scientific notation of the quantity.

(e)  As 21000 has three zeroes which can be represented by 10³.

scientific notation is given by 21 ×  10³ which on simplification gives

2.1 ×  10⁴

Hence,  2.1 ×  10⁴  is that the scientific notation of the quantity.

(f)   As 231000 has three zeroes which can be represented by 10³.

scientific notation is given by 231 ×  10³ which on simplification gives

2.31 ×  10⁵

Hence,  2.31 ×  10⁵  is that the scientific notation of the quantity.

(g) As 43,000,000 has six zeroes which can be represented by 10⁶.

scientific notation is given by 43 ×  10⁶ which on simplification gives

4.3 ×  10⁷

Hence, 4.3 ×  10⁷ is that the scientific notation of the quantity.

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Question: scientific notation for the following numbers (with a power of 10).... someone pleaaaase help me!!! thnx bestie

26,000

425,000

630,000

2,000,000

21,000

231,000

43,000,000

Answer: (a) The scientific notation of 26,000 is  2.6 ×  10⁴  .

(b) The scientific notation of 425,000 is 4.25 ×  10⁵ .

(c) The scientific notation of 630,000 is  6.3 ×  10⁵ .

(d) The scientific notation of 2,000,000 is 2.0 ×  10⁶ .

(e) The scientific notation of 21,000 is 2.1 ×  10⁴ .

(f) The scientific notation of 231,000 is 2.31 ×  10⁵

(g) The scientific notation of 43,000,000 is 4.3 ×  10⁷ .

The scientific notation helps US to represent the numbers that ar terribly Brobdingnagian or terribly small during a kind of multiplication of single-digit numbers and ten raised to the facility of the individual exponent.

The exponent is positive if the quantity is extremely giant and it's negative if the quantity is extremely tiny a × 10ᵇ ; 1 a < ten

(a) As 26000 has three zeroes which can be represented by 10³.

scientific notation is given by 26 ×  10³ which on simplification gives

2.6 ×  10⁴

Hence,  2.6 ×  10⁴  is that the scientific notation of the quantity.

(b)  As 425000 has three zeroes which can be represented by 10³.

scientific notation is given by 425 ×  10³ which on simplification gives

4.25 ×  10⁵

Hence,  4.25 ×  10⁵  is that the scientific notation of the quantity.

(c) As 630000 has four zeroes which can be represented by 10⁴.

6.3 ×  10⁵

(d) As 2,000,000 has six zeroes which can be represented by 10⁶.

2.0 ×  10⁶

(e)  As 21000 has three zeroes which can be represented by 10³.

2.1 ×  10⁴

(f)   As 231000 has three zeroes which can be represented by 10³.

2.31 ×  10⁵

(g) As 43,000,000 has six zeroes which can be represented by 10⁶.

4.3 ×  10⁷

Have an awesome night/day<3

Answer:

Rule: Multiplying ×5 in turn

50 { third term}

1,250 {fifth term}

Step-by-step explanation:

2 × 5 = 10 {second term}

10 × 5 = 50 { third term}

50 × 5 = 250 { fourth term}

250 × 5 = 1,250 {fifth term}