How would you solve this problem?

The rule for any number raised to the power of 1 is that the number remains unchanged.

Mathematically, this can be written as: a^1 = a where "a" is the base number. The rule for a number raised to the power of 1, is also known as the exponent.

For example, if we take the number 2, and raise it to the power of 1, we would get:

Key points:

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Answer:

His secret is in generalizing two roots together instead of keeping them as separate values.

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The absolute value (Modulus) of a number is the distance of the number from zero.

Absolute value is always acting for in the modulus(|z|) and its value is always positive.

So, the absolute value of the complex number is Z = a + ib is |z| = √ (a2 + b2).

Now, the absolute value of the complex number is the positive square root of the sum of the square of the real part and the square of the unreal part, i.e.,

The complex number is defined as the number in the form a+ib, where a is the real part while ib is the unreal part of the complex number in which i is known as iota and b is a real number.

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There are 1.449 ×  10⁸ pet fish and pet reptiles all together in the United States.

Total number of pet fish in the United states = 1.4 ×  10⁸

Total number of pet reptiles in the United States = 4.9 × 10⁶

So the total number of pet fish and pet reptiles = (1.4 ×  10⁸) + (4.9 × 10⁶)

= 1.449 ×  10⁸

The final answer is in scientific notation. Scientific notation is the way of writing number that are too big or too small and inconvenient to write in decimal form. They are expressed in the multiple of 10 with a suitable power on 10.

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The first number in an ordered pair (x,y) is the x-coordinate, also called the "abscissa". It represents the horizontal position of the point on a coordinate plane. The second number in an ordered pair is the y-coordinate, also called the "ordinate". It represents the vertical position of the point on a coordinate plane.

Answer:

Dimensions are 12 , 6

Step-by-step explanation:

      Let the length be 'x' miles.

                   width = (x - 6) miles

 Area of a rectangle = length * width

       x *(x -6) = 72 square miles

       x*x - x *6 = 72

     x² - 6x -72 = 0

Sum = -6

Product = -72

Factors = -12 , 6   { -12 * 6 = -72  & -12 + 6 = -6}

x² - 12x + 6x - 72 = 0       {Rewrite the middle term using the factors}

x(x - 12) +6(x - 12)=0

(x -12)(x + 6) =0

x - 12 = 0 ;

    x = 12

{x + 6= 0 is ignored, as dimensions will not have negative value}

length = 12 miles

widht = 12 - 6 = 6 miles

This is because the sum of the measures of a pair of supplementary angles is always 180°. Therefore, the measure of the original angle is 93.4° and the measure of its supplementary angle is 180°.

Plagiarism is the practice of taking someone else's work or ideas and passing them off as one's own. Plagiarism can take many forms, including: copying word-for-word, copying ideas or facts without providing a citation or reference, or paraphrasing someone else's words or ideas without providing a citation or reference. It can be intentional or unintentional, and it is considered a form of academic dishonesty.

The measure of the original angle is 86.6° less than the measure of its supplementary angle. This means that the measure of the original angle is 180° - 86.6° = 93.4°. The measure of the supplementary angle is 180°.

This is because the sum of the measures of a pair of supplementary angles is always 180°. Therefore, the measure of the original angle is 93.4° and the measure of its supplementary angle is 180°.

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Answer: if one hiker walks faster than the other, their rate would be 9.68mph or 9.7mph if u round up and the rate of the other hiker that is walking slower is 4.4mph.

Step-by-step explanation:

For the hiker walking 2.2mph

I did: 22 x 2.2 = 48.4/5 = 9.68

Rate = 9.68mph

For the other hiker

I did: 22/5= 4.4

rate = 4.4mph

The area of the trapezium shown is 284.31 in²

An equation is an expression that shows the relationship between variables and numbers.

The area is calculated for a two dimensional shape. It shows the amount of space occupied for that shape.

The area of a trapezium is given by:

Area = (1/2)(sum of parallel sides) * height

For the trapezium shown, the parallel sides have a measure of 17 inches and 31 inches respectively. The height is 11.7 inches, hence:

Area = (1/2)(17 + 31.6)(11.7) = 284.31 in²

The area is 284.31 in²

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 y = 4x - 8 is linear equation .

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                    Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Linear equations with two variables, and so forth, are what the equation is known as if it has two variables. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, and x + y = 2. Another example is 3x - y + z = 3.

(0,-8) and (2,0)

 m = 0 - (-8)/2 - 0

      = 8/2 = 4

y - (-8) = 4 ( x - 0)

 y + 8 = 4x

  y = 4x - 8

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Answer: To find Janice's running speed, we need to determine how many miles she runs per hour.

We know that the track is 1/4 mile long and Janice can complete each lap in 1/10 of an hour. To find the total number of miles Janice runs in an hour, we can multiply the length of the track by the number of laps she completes in an hour.

Length of the track * number of laps = total miles

1/4 mile * (1/10 hour)^-1 = total miles

On the second equation, we are using the inverse of the time, to get the number of laps completed in an hour

The speed is distance over time, so we need to express the distance in miles and the time in hours.

So Janice's running speed is 4 miles/hour.

Step-by-step explanation:

The statement best describes where she should attach each triangle is perpendicular bisectors intersect.

When perpendicular bisectors overlap, the sentence best indicates where she should join each triangle. A triangle is a three-sided polygon that is sometimes (but not always) referred to as the trigon. Every triangle has three sides and three angles, which may or may not be the same. Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The total of the triangle's three angles equals 180 degrees.

Here,

When perpendicular bisectors overlap, the sentence best indicates where she should join each triangle.

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The number of cups of sugar that you will need to make lemonade would be = 2 cups of sugar.

A recipe is defined as the list of condiments that are used for the preparation of a food and it's guidelines.

In the recipe to make lemonade,

6 cups of water = 1/2 cup of sugar

24 cups of water = X cup of sugar.

Make X the subject of formula;

X cup of sugar = 24 × 1/2 ÷ 6

= 12/6 = 2 cups of sugar.

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The fraction of Miriam’s budget would be left for food/dining if Miriam follows these guidelines is 1/7.

The fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split.

From the information, 2/7 of the budget will be spent on lodging.

The amount spent on sightseeing will be twice as much as the amount spent on lodging. This will be:

= 2 × 2/7

= 4/7

The fraction of Miriam’s budget would be left for food/dining if Miriam follows these guidelines will be:

= 1 - (2/7 + 4/7)

= 1/7

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The third one will represent a linear relationship between x and y.

What is a linear relationship?

A linear relationship is any relationship between two variables that creates a line when graphed in the xy-plane.

Linear equations can be used to represent the relationship between two variables, most commonly x and y. To form the simplest linear relationship, we can make our two variables equal:

y=x

By plugging numbers into the equation, we can find some relative values of

x and y.

0        0

1         1

2        2

3        3

If we plot those points in the xy-plane, we create a line.

Now,

For the given graphs only the third one shows a straight line made from equations.

Hence, It represents the linear relationship between x and y.

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Therefore , the solution of the given problem of quadratic equation comes out to be the value of y = 12.

x2+ cx + z = 0 is a quadratic problem with one variable in quadratic algebra. a 0. According to the Underpinning Theorem of Algebra, this quadratic's second order ensures that it has at least one solution. The solutions could be simple or complex. Four variables make up a quadratic equation. This implies that at least one word should be squared. "ax2 + bx + c = 0" is one of the basic formulae for solving quadratic equations, where the numbers or integers a, b, and c stand in for the undefined variable "X".

Here,

Given :   A right angled triangle with dimension of y, y+3 and 9

To find the value of y :

We use pythagoras theorem :

So,

=> (y+3)² = y²+9²

=> y² + 9 + 6y = y²+ 81

=>  y² - y² + 6y = 81-9

=> 6y =72

=>y =72/6

=>y=12

Therefore , the solution of the given problem of quadratic equation  comes out to be the value of y = 12.

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The solution to the inequality is m ∈ (2, 9)

What is the Compound inequality?

A compound inequality is an inequality that contains two or more conditions that must be met simultaneously. It is formed by connecting two or more simple inequalities using the words "and" or "or". The word "and" indicates that all the conditions must be true at the same time, while the word "or" indicates that at least one of the conditions must be true.

The compound inequality "m - 3 < 6 and m + 2 > 4" can be read as "m is less than 6 and 3 less than m and m is greater than 4 and m is 2 more than 4".

To solve the inequality, we can start by isolating the variable on one side of the inequality sign.

m - 3 < 6 => m < 9

m + 2 > 4 => m > 2

The solution is the set of all m that satisfies both inequalities, which is the intersection of the solution sets of each inequality. In this case, it is the set of all real numbers m such that 2 < m < 9.

Hence, the solution to the inequality is m ∈ (2, 9)

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Consider that the denominator is not zero. The formula that results from simplifying will equal  -n-5/2n(1+3n).

A fraction is divided by multiplying its reciprocal:

6n²-23n+7/8n3-28n2.

2n²-10n/1-9n²

Factoring the phrase: 6n²-23n+7/4n²(2n-7). 2n(n-5)/1-9n²)

A2-b2=(a+b)(a-b) (3n-1) (2n-7)/4n² can be used to factor the expression (2n-7).

2n(n-5)/(1+3n)(1-3n)

By eliminating the most prevalent element, reduce the proportion to its lowest term. 3n-1/4n²

2n(n-5)/(1+3n)(1-3n)

Purge the expression of all except the lowest word Write 1/2n as a single fraction: -n-5/2n(1+3n)\s-n-5/2n(1+3n).

In general, a fraction with a zero denominator cannot have a single value given to it; therefore, the value is left undefined.

Any definitional attempt results in a contradiction, which is why the outcome of a division by zero is not defined. a=r*b. r*0=a. (1) However, r*0=0 for any r, hence unless a=0, there is no solution to the problem (1).

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·

Answer:

[tex]m\angle 1=67^{\circ}[/tex]

Step-by-step explanation:

By the inscribed angle theorem, [tex]m\angle 1=21^{\circ}+46^{\circ}=67^{\circ}[/tex].

In designing the waterskiing ramp using direct variation the vertical supports, y will be related to the horizontal distance, x by a constant k,  as in the relation

k = y/x

The ratio between two quantities that are directly proportional is the constant of proportionality.

When two quantities grow and shrink at the same rate, they are directly proportional.

When y and x are two values that are directly proportional to one another, the proportionality constant k is defined as k=y/x.

In the problem, the distances between the vertical supports is x while the height of the support is y. To have a direct proportionality this relationship between x and y must be a constant say k.

Hence we say k = y / x

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The probability of a random variable x being greater than 43 if it is normally distributed with a mean of 50 and a standard deviation of 7 is 0.22662735237686885.

The formula for the normal distribution is:

P(x) = 1/(sqrt(2*pi*o^2)) * e^(-(x-u)^2/(2*o^2))

where u is the mean and o is the standard deviation.

For the first part, we have u = 50 and o = 7.

So, P(x>43) = 1/(sqrt(2*pi*7^2)) * e^(-(43-50)^2/(2*7^2)) = 0.22662735237686885

For the second part, we have u = 81 and o = 4.

So, P(x<76) = 1/(sqrt(2*pi*4^2)) * e^(-(76-81)^2/(2*4^2)) = 0.8413447460685429

The probability of a random variable x being greater than 43 if it is normally distributed with a mean of 50 and a standard deviation of 7 is 0.22662735237686885. Similarly, the probability of a random variable x being less than 76 if it is normally distributed with a mean of 81 and a standard deviation of 4 is 0.8413447460685429. This can be calculated using the formula for the normal distribution, which is P(x) = 1/(sqrt(2*pi*o^2)) * e^(-(x-u)^2/(2*o^2)), where u is the mean and o is the standard deviation.

the complete question is : Assume the random variable x is normally distributed with mean u = 50 and standard deviation o = 7.

Find the indicated probability. P(x >43) P(x>43)=

Assume the random variable x is normally distributed with mean u = 81 and standard deviation = 4.

Find the indicated probability. P(x <76) P(x<76)= 0.8413447460685429

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In shown regular hexagon, all of the transformations that carry the hexagon onto itself are, 180° rotation counterclockwise and reflection in 'l'. So Options D,E,F are correct.

It is a type of  polygon, which has 6 equal sides and all the interior angles are 120°.

Given that,

We have one hexagon and axis of rotation l,

lets check the given options

A.  at 60° rotation clockwise it makes certain angle from the initial position, it will not onto itself

B.  at 60° rotation counter-clockwise it makes certain angle from the initial position, it will not onto itself

C.  at 90° rotation counter-clockwise and 180° rotation clockwise it makes 90° angle from initial position, it will not onto itself

D. 180° rotation counter-clockwise it will be in same plane of original position. So it will onto itself

E. Reflection in L  again it will be in same plane, So it will onto itself

F. Reflection in L and 180° rotation counter-clockwise gain it will be in same plane, So it will onto itself

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The equation is true when putting parentheses. The equation becomes:

(5 - 3)(-1 + 6)² = 50.

What is an 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 an 'equal' sign.

The given equation is 5 - 3 - 1 + 6² = 50.

Here we need two parentheses.

Since 50 can be written as 50 = 25 × 2 = 5² × 2

Now 2 can be written as (5-3) and 5 can be written as (-1+6).

Now put the parentheses:

(5 - 3)(- 1 + 6)²

= 50

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Answer:

One

Step-by-step explanation: Anything that has the exponent of 0 will always be 1

So on solving the provided question, we can say that inequality equation will be as follows r - 8 <= 7 r<=15 or r >= -15

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.

here the question, is

r - 8 <= 7

r<=15

or r >= -15

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Answer:

B. 0.25

Step-by-step explanation:

There are 8 total pieces.

2 of them are green.

that makes it a 2/8 chance it will land on green.

2/8 = 1/4

1/4 = 0.25

Answer:

B. 0.25

Step-by-step explanation:

There are 8 possible landing areas, all with equal size.

There are 2 green area.

p(event) = (number of desired outcomes)/(number of total outcomes)

The desired outcome is landing on green. There are 2 desired outcomes.

The total number of possible outcomes is 8.

p(green) = 2/8 = 1/4 = 0.25

Answer: B. 0.25

To get the simplified form of the algebraic expression x²+ y², we need to subtract -2xy from the expression x² +y²-2xy.

To subtract 2xy from the expression x² + y² - 2xy and get x² + y², you can simply remove the -2xy term. This is because subtracting 2xy is the same as adding -2xy, which is the same as negating 2xy and keeping it in the same position.

The reason for this is that subtracting a number is the same as adding its opposite. In this case, -2xy is the opposite of 2xy, so when you subtract 2xy, you are effectively adding -2xy.

Therefore, x² + y² - 2xy and x² + y² are equivalent expressions, since they both represent the same mathematical value.

In mathematical terms:

x² +y²-2xy = x²+ y² +2xy

In other words, the subtraction of 2xy is a commutative operation and the order of the terms does not matter. If you add or subtract the same value, it does not change the final result.

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The angles m∠GFH and m∠HFJ are complementary angles and the correct option for the measure of angle m∠GFH is equal to 61.9°.

In geometry, if two angles are said to be complementary, then the total of their sum is equal to 90°

From the question, we have that the complementary angle m∠HFJ = 28.1° so;

m∠GFH + m∠HFJ = 90°

m∠GFH + 28.1° = 90°

m∠GFH = 90° - 28.1°

m∠GFH = 61.9°

Therefore, the measure for the complementary angle m∠GFH is equal to 61.9°

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Answer: 28x^4y^7

Step-by-step explanation: Add exponents of common base

Answer:

28x⁴y⁷

Step-by-step explanation:

First multiply the numbers;

Then combine the exponents;

Then combine the exponents again;

Then you have the answer :)