What is the area, in square feet, of an isosceles triangle whose vertex angle is $120^{\circ}$ and whose base is $20$ feet long

The simplified form of the given expression is, [tex]\frac{81x^5}{125y^1^8}[/tex].

What is simplifying an expression?

To simplify an expression, create an equivalent expression without any terms that are similar. The expression will then be rewritten using the fewest terms possible.

Solving a math problem is the same thing as simplifying an expression. You basically try to write an expression as simply as you can when you simplify it. At the conclusion, there shouldn't be any more multiplying, dividing, adding, or removing to do.

Consider, the given expression:

[tex](\frac{3x^3y^0}{x^-2} )^4*(\frac{y^2x^-^4}{5xy^-^8} )^3[/tex]

Using the rule:  [tex](\frac{a}{b} )^m = \frac{a^m}{b^m}[/tex]

⇒  [tex](\frac{3x^3y^0}{x^-2} )^4*(\frac{y^2x^-^4}{5xy^-^8} )^3 = (\frac{81x^1^2y^0}{x^-^8})(\frac{y^6x^-^1^2}{125x^3y^2^4} ) = \frac{81y^6}{125x^-^5y^2^4} = \frac{81y^-^1^8}{125x^-^5}= \frac{81x^5}{125y^1^8}[/tex]

Hence, the simplified form of the given expression is, [tex]\frac{81x^5}{125y^1^8}[/tex].

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a) The maximum Height of Projectile is 843.75 m

b) The projectile reach its maximum at t= 12.5 sec.

A quadratic equation is a second-order polynomial equation in a single variable x ax²+bx+c=0. with a ≠ 0 .

It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem.

Given:

h(t) = -5t² +120t + 125

a) For the maximum height, h= 0

-5t² +120t + 125 = 0

t²  - 24 t - 25 = 0

t²  - 25t + t - 25 = 0

t( t- 25) + 1(t-25)= 0

(t-25)(t+1)=0

t= 25, -1

So, Max height is reached after half the total flight time, t= 25/2

So, h(25/2 )= -5(25/2)² +120(25/2) + 125

= -5 x 156.25 + 1500+ 125

= 843.75 m

b) The projectile reach its maximum at t= 12.5 sec.

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The number of the books owed by Tara which she has not read would be = 152 books.

Percentage is defined as the part of the value that can be expressed as per 100 of the whole given value. This can be represented with a symbol such as %..

The number of books owned by Tara = 160 books

The percentage of books read by Tara = 95%

Therefore, 95% of her books = 95/100 × 160

= 15200/100

= 152 books.

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(a) The 6 a.m. temperature in montreal was 84 Fahrenheit lower than in atlanta.

(b) by noon, the temperature in milwaukee was 3 Fahrenheit.

In mathematics, it deals with numbers of operations according to the statements.

The process in mathematics to operate and interpret the function to make the function simple or more understandable is called simplifying and the process is called simplification.

Given that,

    City                Temperature table (°F)

   Montreal                -16

   Atlanta                   68

   Dayton                   36

  milwaukee               -5

   Juneau                   -31

Part A- Temperature difference in Atlanta and Juneau

= (-16) - 68

= -84 F

Part B- temperature in milwaukee raise by 8 F at noon

Temperature in noon = - 5 + 8 = +3 F

Thus,

(a) The 6 a.m. temperature in montreal was 84 Fahrenheit lower than in atlanta.

(b) by noon, the temperature in milwaukee was 3 Fahrenheit.

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The slope-intercept form of the given equation is y = -3/5x - 5

From the question, we are to write the given equation in the slope-intercept form

From the given information,

The given equation is

3x + 5y = -25  

The general form for the slope-intercept form of the equation of a line is

y = mx + b

Where m is the slope

and b is the y-intercept

Writing the equation in the slope-intercept form of a line

3x + 5y = -25

5y = -3x - 25

Divide through by 5

5y/5 = -3/5x - 25/5  

y = -3/5x - 5

The equation is y = -3/5x - 5

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1 kilograms is equal to 2.205 pounds, which leads to the conversion factor of 2.205. The conversion factor is based on both the Avoirdupois system of measurement, which is used in the United States and the United Kingdom to measure weight or mass, and the International System of Units (SI).

  The basis for the Avoirdupois system is the pound, which is equal to 0.45359237 kilos. Consequently, 0.45359237 kilograms equal one pound.

  Finding the weight in pounds of 1 kilograms is necessary to convert kilograms to pounds. We can divide 1 kilograms by 0.45359237 kilograms/pound to get this equivalent weight.

1 kg / 0.45359237 kg/lb = 2.20462262 lb

 This is the kilograms to pound conversion factor. The value is rounded to the widely regarded and employed value of 2.205.

 Therefore, to convert kilograms to pounds, we multiply the weight in kilograms by 2.205.

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By solving a linear equation we will see that there are 20 games left.

We know that there is a total of 100 games, and the ratio of wins to loses for the rockets is:

3:2

The ratio for the rangers is:

7:13

We know that if the rockets loses all the remaining games, and the rangers win all the remaining games then both teams will win the same number of games.

Let's define X as the number of games left, the number of games won by the rockets is:

(100 - X)*(3/5)

The number of games won by the rangers is:

(100 - X)*(7/20)

We know that if the rangers win the X games left, they will have the same number of wins than the rockets (if the rockets don't win any more game)

Then we can write the linear equation:

(100 - X)*(7/20) + X = (100 - X)*(3/5)

we can solve this for X.

X = (100 - X)*(3/5) - (100 - X)*(7/20)

X = (100 - X)*(3/5 - 7/20)

X = (100 - X)*(12/20 - 7/20)

X = (100 - X)*(5/20)

(20/5)*X = 100 - X

4*X = 100 - X

4*X + X = 100

5*X = 100

X = 100/5

X = 20

There are 20 games left for the rockets.

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Answer:Volume of Pipe Formula. The pipe volume formula is: Volume = pi x radius² x length. To do piping size calculation, follow these steps: Find the inner diameter and length of the pipe, in inches or millimeters. Calculate the inner diameter of the pipe by measuring

Step-by-step explanation:

A polynomials is a mathematical statement made up of real number coefficients and a sum of power in one or so more parameters (indeterminates) having non-negative integer exponents.

SOLUTION:

Three terms with non-negative integers exponents (x2, x1) make up Option "polynomial, "'s which has real numbers (x3, -2x3, and 3) as coefficients.

Option "c" x+1/x is a rational function; it is not a polynomials because of the fraction in it. It consist of one polynomials divided by another polynomial. 1/x

Option "d" is a polynomial that has real numbers (5, -3, and 2) as coefficients and terms with non-negative integers exponents (x2, x1) as its exponents.

Consequently, option "b" 3x3/2-5x2-1/2x-1 is not a polynomial due to the fraction and non-integer exponent (3/2).

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Option "b" 3x3/2-5x2-1/2x-1 is not a polynomial due to the fraction and non-integer exponent (3/2). A polynomials is a mathematical statement made up of real number coefficients and a sum of power in one or so more parameters (indeterminates) having non-negative integer exponents.

Three terms with non-negative integers exponents (x2, x1) make up Option "polynomial, "'s which has real numbers (x3, -2x3, and 3) as coefficients.

Option "c" x+1/x is a rational function; it is not a polynomials because of the fraction in it. It consist of one polynomials divided by another polynomial. 1/x

Option "d" is a polynomial that has real numbers (5, -3, and 2) as coefficients and terms with non-negative integers exponents (x2, x1) as its exponents.

Consequently, option "b" 3x3/2-5x2-1/2x-1 is not a polynomial due to the fraction and non-integer exponent (3/2).

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(a)- The study was experimental.

(b)- No, the researchers would not be justified in doing so.

(c)- Such a method leads to an incorrect conclusions for justifiable reasons.

This problem involves minute statistical knowledge and assesses the student's ability to differentiate between an experiment and an observation and also his/her potential to make justifiable logics as to draw conclusions for a scientific research. The explainations are-

Part - (a)

The study was not an observation, it was an experiment because the treatments involving D-Cycloserine or placebo were imposed by the researchers on the people with acrophobia.

Part (b) -No, the experiment was designed to compare the D-Cycloserine group with a control group that received a placebo . The researchers can conclude that the D-Cycloserine and two therapy sessions show significantly more improvement than a placebo and two therapy sessions. However, there is no basis for comparison with the other group of people with acrophobia who received eight therapy sessions and no pill.

Part (c)-

We can cite an example that if the therapists were allowed to choose who received a placebo and who received D-Cycloserine, they might assign the people with more severe acrophobia with the other group. Thus, the improvement after only two therapy sessions can be related to the initial severity of the acrophobia rather than to the effects of D-Cycloserine.

Therefore, the answers are -

(a)- The study was experimental.

(b)- No, the researchers would not be justified in doing so.

(c)- Such a method leads to an incorrect conclusions for justifiable reasons.

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The inequality describing how much she can withdraw is x < 3550

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

Inequalities are used in expression for non equal comparison of variables.

Let x represent the amount of money that can be withdrawn.

Tabitha’s account balance is $3,800. Of this, $750 is for rent. Hence:

Money remaining = 3800 - 750 = 3050

Tabitha wants to keep a balance greater than $500. Hence:

3050 - x > 500

x < 3550

The inequality is x < 3550

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0.1 is probability  in distribution table.

What are examples and probability?

The quantity of success-producing options. the total number of outcomes that could occur.

                             For instance, the chance of flipping a coin and obtaining heads is 1 in 2, as there is only one way to acquire a head and there are a total of 2 possible outcomes (a head or tail). We specify P(heads) = 12.

Here X is a random variable. P(X) is its probabilities corresponding to the different values of X.

now according to the properties of probability theory we know that sum of probabilities is 1.

so here to find the value of the probability of X coresponding to the value 53 we should use the following steps:

sum of given probabilities =(0.2+0.4+0.3) = 0.9

required probability = 1 - sum of given probabilities = 1 - 0.9 = 0.1

hence the complete probability table is

X P(X)

20 0.2

49 0.4

53 0.1

80 0.3

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Answer:

Step-by-step explanation:

The constant of proportionality from the number of bottles of juice bought to the total cost is 1.15 dollars and cents.

Answer: The answer is 4

Step-by-step explanation: Firstly you want to convert the whole number into a fraction, the fraction will be 24/1. Then you multiply 1/6 by 24/1 or 1x24/6x1 which equals 26/6. This fractio can be simplified, by finding the greatest common factor. The GCF of 24 and 6 is 6.

24/6 = 4

6/6 = 1

So our full answer is 4/1 which simplifies to 4

Answer:

4

Step-by-step explanation:

take 24 divided by 6 you'll get

The length of the side overline(FH) when Triangle FGH is formed by connecting the midpoints of the side of triangle CDE is 5.

This problem can be solved using the Median Line theorem. The Median Theorem states that the medians of a triangle intersect at a point called the centroid which is two-thirds of the distance from the vertices to the midpoint of the opposite sides. This is what we will use to solve the given problem.

From the problem, we can conclude that points H and F are the midpoints of the sides CE and CD respectively. Hence, line HF is the median line of the triangle CDE. So, the length of the line HF/FH is going to be -

= (1/2)*ED

= 5

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Answer:

4 and 7

Step-by-step explanation:

7-4=3

4x7=28

Significant figures are in this measurement 1.090

In a number, to determine the number of significant figures following three rules are used:  

The digits which are non-zero are always significant.

Any zeros between two digits which are non-zero are significant.

In the decimal portion, trailing zeros are significant.  

Significant figures = Numbers that carry meaning in the measurements of a number.

The number is 1.090, it has two non-zero digits, 1 zero in between two non-zero digit and one trailing zero thus, all of them are significant figures.

Therefore, it has 4 significant figures : 1.090

Significant figures are in this measurement 1.090

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The slope of the line that passes through (-4, 7) and (-6, 5) is 1.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).

The given coordinate points are (-4, 7) and (-6, 5).

Now, slope m=(5-7)/(-6+4)

m=-2/(-2)

m=1

Substitute m=1 and (x, y)=(-4, 7) in y=mx+c, we get

7=1(-4)+c

c=11

Substitute m=1 and c=11 in y=mx+c, we get

y=x+11

Therefore, the slope of the line that passes through (-4, 7) and (-6, 5) is 1.

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Answer:

54 cm^2

Step-by-step explanation:

calculate the area of each of the 2 rectangles and add them .

area of rectangle = l × w

so let the area of the big rectangle be A1 and the area of the small one A2 :

A1 = l × w = 11 × 4 = 44 cm^2

A2 = l × w = 5 × 2 = 10 cm^2

then , the area of the shape is = A1 + A2 = 44 + 10 = 54 cm^2

If Sarah has a 20% discount, her total cost after the discount in dollars and cents be 31.40.

Therefore the answer is $31.40

Sarah has a 20% discount, so the percentage of the cost she needs to pay is

100 - 20 = 80%.

To calculate the total cost after the discount, we need to multiply the original total cost by the percentage of the cost Sarah needs to pay:

= $39.25 x 0.8

= $31.40

So, after the discount, Sarah would pay $31.40 before tax.

To round it to the nearest cent we have $31.40 so the answer is 31.40

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The slope of a line f(x) exceeds the slope of a line g. (x). As a result, option A is the right response.

A line's slope or gradient is a number that defines both its direction and its steepness. The slope may be calculated using the following formula: slope = (y2-y1)/ (x2-x1). The coordinate points on the equation of line g(x) are (0, 2), (5, 4) and (10, 6) while the coordinate points on the equation of line f(x) are (3, 1) and (0, -1).

The slope of the line g(x) is now (4-2)/(5-0) =2/5.

The slope of a line f(x) is (-1)/. (0-3)

=2/3

The slope of a line f(x) exceeds the slope of a line g. (x). As a result, option A is the right response.

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The drone has flown a total distance of 4 units, as it has travelled the same distance as the two cars (2 units each).

Perimeter is the total length of a two-dimensional shape's boundary. It is the sum of all the sides of a shape. Perimeter is used in many areas such as geometry, architecture, landscaping, and more. Perimeter is a measure of the distance around a shape and is often used to measure the size of a space or area.

As the cars have completed a full circuit of the square $abcd$, the drone has also completed a full circuit of the square. The perimeter of the square is 2, so the drone has flown a total distance of 4 units.

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The drone has flown a total distance of 4 units, as it has travelled the same distance as the two cars (2 units each). This can be solved by applying the concept of perimeter.

Perimeter is the total length of a two-dimensional shape's boundary. It is the sum of all the sides of a shape. Perimeter is used in many areas such as geometry, architecture, landscaping, and more. Perimeter is a measure of the distance around a shape and is often used to measure the size of a space or area.

As the cars have completed a full circuit of the square abcd, the drone has also completed a full circuit of the square. The perimeter of the square is 2, so the drone has flown a total distance of 4 units.

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The monthly payment is $130.50. Therefore, option C is the correct answer.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

Simple interest is calculated with the following formula: S.I. = (P × R × T)/100, where P = Principal, R = Rate of Interest in % per annum, and T = Time.

Given that, principal =$2700, rate of interest =8% and time =2 years

Here, SI=(2700×8×2)/100

= 43200/100

= $432

Amount =Principal+Interest

= 2700+432

= $3132

We know that 2 years =24 months

Now, the monthly payment = 3132/24

= $130.50

Therefore, option C is the correct answer.

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As per the remainder that the greatest possible value of 17

The term remainder in math defined as if a number is not completely divisible by another number  then we are left with a value once the division is done

Here we have if x is a positive integer, then r is the remainder when x is divided by 4 and r is the remainder when x is divided by 9.

As we all know that the remainder is always smaller than the divisor.

Here we have also know that it will be 0 if the dividend is evenly divisible or a positive integer less than the divisor.

So, when we divided by 4 then the largest remainder will be 3 and then here we have to  divided by 9, then the largest remainder will be written as

=> r² + R = 32 + 8

=> 9 + 8 = 17

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Answer:

You can use the second equation to substitute the value of x in the first equation and solve for y.

x = y - 4

-10(y - 4) + 3y = 5

-10y + 40 + 3y = 5

-7y = 35

y = 5

Now that you have the value of y, you can use the second equation to find the value of x.

x = y - 4

x = 5 - 4

x = 1

So the solution of the system of equations is x = 1 and y = 5

Step-by-step explanation:

Answer: To graph an inequality, treat the <, ≤, >, or ≥ sign as an = sign, and graph the equation. If the inequality is < or >, graph the equation as a dotted line. If the inequality is ≤ or ≥, graph the equation as a solid line.

Step-by-step explanation:

An integral in calculus is a mathematical concept that can be used to represent an area or an expanded version of an area. The basic components of calculus are integrals and derivatives is[tex]-1/2*(t^2/2+18ln(t)-81/(2t^2))+C\\[/tex].

The terms antiderivative and primal are additional terms for integral. Something that is essential is crucial or required. If you are an essential member of the team, it signifies that you are necessary for the team to work. To complete the whole, an essential component is required. The term "essential" is almost a synonym in this context.

The set of functions (the antiderivative) whose derivative is the integrand is represented by the integral, which is referred to as an indefinite integral. Calculus' fundamental theorem connects the assessment of definite integrals to that of indefinite integrals.

From 1 to 3:

[tex]sqrt(x^2+9)=t+x\\x=(9-t^2)/(2*t)\\anddx=-(t^2+9)/(2t^2)dt\\= 1/2int (t^2+9)^2/t^3dt\\= -1/2int (t+18/t+81/t^3)dt\\= -1/2*(t^2/2+18ln(t)-81/(2t^2))+C\\[/tex]

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Applying proportions, the amount of money Bob saved is $18.

Proportions can also be used to express a relationship between two or more values in the form of a ratio, such as a:b, where a and b are values being compared.

We can start the problem by using the proportion of saving to earning, which is 9/16.

If for every $16 he earns babysitting, he saves $9, then for $32 that he earned babysitting, he saved:

$9 / (16/32) = $9 * 2 = $18

So Rob saved $18 from the money he earned babysitting on Saturday

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Profit made by each girl Sarah, Lilly and Paula respectivly are R 200 , R 400 and R 600

A ratio displays the multiplicity of two numbers. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.

An ordered pair of integers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you might express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. Indicators of proportions include "::" and "=".

The amount of investment done by each girl Sarah, Lily and Paula respectivly is x, 2x and 3x

So, the profit will be

x + 2x + 3x = 1200

⇒6x  =1200

⇒ x = 200

Profit made by each girl respectivly are x = R 200 , 2x = R 400 and 3x = R 600.

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