What is the solution to the system of equations? (5, 0) (0, 5) (0, –5) (–5, 0)

The answer is -[tex]\frac{(a + 4) ( a +5) }{(a +2)( a - 5)}[/tex]

Simplify is making something simple. In mathematics, simplification means reducing the expression/ fraction/problem in a simpler form by using different operations.  

In the process of simplification, some basic rules are needed to be used. The principle of BODMAS (B= Bracket, O = Of, D = Division, M = Multiplication, A = Addition, S = Subtraction)must be followed for solving the questions.

The equation is :

[tex]\frac{a^{2} - 16 }{ a^{2} - 25 }[/tex]   ÷   [tex]\frac{a^{2} - 2a - 8}{a^{2} + 10a + 25}[/tex]

=[tex]\frac{a^{2} - 4^{2} }{a^{2} - 5^{2} }[/tex]  ÷   [tex]\frac{a^{2} - 2a - 8}{a^{2} + 10a + 25}[/tex]

= [tex]\frac{ (a +4 ) ( a - 4 )}{ (a + 5) ( a - 5 )}[/tex]    ÷   [tex]\frac{a^{2} - 4a + 2a - 8}{a^{2} + 5a + 5a + 25}[/tex] ( by applying middle term factor method)

(using [tex]a^{2} - b^{2}[/tex] formula )

=  [tex]\frac{ (a+4) ( a-4 )}{(a +5 ) (a - 5)}[/tex]     ÷      [tex]\frac{a(a -4) + 2 (a - 4)}{a (a + 5) + a (a + 5)}[/tex] ( by applying middle term factor method)

=[tex]\frac{( a + 4) ( a - 4)}{( a + 5) ( a - 5)}[/tex]     ÷  [tex]\frac{(a + 2) ( a -4)}{( a +5) (a+5)}[/tex]

= [tex]\frac{( a +4)(a-4)}{(a + 5)(a - 5)\\}[/tex]  *   [tex]\frac{(a + 5) ( a + 5)}{(a + 2) ( a - 4)}[/tex]

=[tex]\frac{( a + 4) ( a + 5)}{(a + 2) ( a - 5)}[/tex]

so, the answer is - [tex]\frac{( a + 4 ) ( a +5) }{( a + 2) ( a - 5)}[/tex]

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Step-by-step explanation:

3.1×10⁵ ÷ 5.4×10⁵

= (3.1/5.4) × 10^5-5

=0.5741 × 10⁰

= 5.7 × 10^-1

Answer:

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

For each tree you need 3 + 12 = 15 feet space.

On one side of the street you can plant:

Same number is applicable for the opposite side, so the total number is:

The matching choice is D.

Eggs are generally sold in batches of 12 (or dozens). The image shows the 3 different ways that 12 eggs can be packaged into arrays. Note that the array 3 by 4 is taken to be equivalent to the array 4 by 3 and therefore is not included. If it was decided that eggs should be sold in batches of 24, then these 24 eggs could be packaged into a total of 4

different arrays.

The arrangement is checked by writing out the factors of 24

24 = 1, 2, 3, 4, 6, 8, 12, 24

grouping them in pairs

1 * 24

2 * 12

3 * 8

4 * 6

this gave a total of 4 arrays

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The monthly payment will be $84.375 to the bank.

What is simple interest?

S.I = Pnr / 100

where P = prinicipal

n= number of years

r = rate of interest

= 45000 * 2 * 8 / 100

= 810000 /100

= $8100

where, the divide by number of months

Balance= 8100 / 96

= $84.375

Hence, the monthly payment will be $84.375 to the bank.

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The total value of the sales today is £1581 and the total value of the sales for each salesperson today is:

Mo = £330 +  £247 = £577,

Daz = £180 + £259 = £439,

Colin = £300 + £265 = £565,

What are arithmetic operations?

Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.

We have,

The value of sales each salesperson made this morning from the bar chart:

Mo = £330,  Daz = £180,  Colin = £300,

The value of sales each salesperson made this afternoon from the table given:

Mo = £247,  Daz = £259,  Colin = £265,

so, the total value of the sales today is :

= £330 + £180 + £300 + £247 + £259 + £265

= £1581.

also the total value of the sales for each salesperson today is:

Mo = £330 +  £247 = £577,

Daz = £180 + £259 = £439,

Colin = £300 + £265 = £565,

Hence, the total value of the sales today is £1581 and the total value of the sales for each salesperson today is:

Mo = £330 +  £247 = £577,

Daz = £180 + £259 = £439,

Colin = £300 + £265 = £565,

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Answer:

14 volleyballs  and 7 handballs

Step-by-step explanation:

sum the parts of the ratio , 2 + 1 = 3 parts , then

21 ÷ 3 = 7 ← value of 1 part of the ratio , so

volleyballs = 2 × 7 = 14

handballs = 1 × 7 = 7

Answer:

Hey

volleyball = 14

Handball = 7

Step-by-step explanation:

21 pieces = 2:1n

step 1

Add the ratios together

21 = 3n

Step 2

divide both sides by 3

n = 21/3 = 7

where n = number of balls

volley ball = n × 2 = 7 × 2 = 14

handballs = n × 1 = 7 × 1 = 7

total = 21

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Answer:

t= 2.52 hours

Step-by-step explanation:

it is given that for first 30 km, the speed of bicyclist is v km/hour

time taken to cover first 30 km is given by

          ( )

for next 17 km the speed of bicyclist is 2 km/hour greater than his original speed

so the speed to cover next 17 km = v+2

time taken to cover next 17 km is given by

now total time t spent by the bicyclist to cover entire trip is given by

now if v=18 , we have

now to add fractions we make the denominator same

Hence we will find the LCM of 18 and 20

LCM of 18 and 20 = 180

now we need to make both the denominator equal to 180

hours (approx)

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The coefficient of determination if the total sum of squares is 23.29 and the sum of squares due to regression is 10.03 is 0.43

How to calculate regression?

The standard formula for simple linear regression is Y = mX + b, where Y is the response (dependent) variable, X is the predictor (independent) variable, m is the estimated slope, and b is the estimated intercept.

Here we need to find the coefficient determination if the total sum of squares (sst) is 23.29 and the sum of squares due to regression (ssr) is 10.03.

Here we know that the value of the following are given,

Sum of square = 23.29

Sum of regression = 10.03

Then the coefficient determination is calculated as,

The coefficient of determination r2 = SSR/SST.

When we apply the value, then we get,

=> 10.03/23.29

=> 0.43

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No, it is not appropriate to estimate the probability using an approximately normal model because the population is not normal and the sample size is small.

The details given are,

Sample size = 9

mean = 43 sec

Standard deviation = 8.99

Therefore we conclude that is it not  appropriate to calculate the likelihood of the sample mean being less than 30 seconds using an approximately normal model.

Mean is also know as the average of a given data . We calculate the mean by the formula :   ∑xifi / ∑fi.

Normal Distribution is the probability density function ( pdf)  for a continuous random variable in a system .

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Answer: 11 16 21 26 31

Step-by-step explanation: the shows the sequence.

The conditions are not met by the extreme outliers, hence we are unable to draw inferences based on the statistical output presented above. So, option e is correct.

What is meant by null hypothesis?

The null hypothesis, often known as H₀, is the assertion that there is no difference between two sets of data or variables under analysis, or that there is no relationship between them. Because there is no underlying causative relationship, the null hypothesis holds that any experimentally detected difference is merely the result of chance; therefore, the name "null."

We can create a z-test hypothesis by assuming that the amount of rain produced by thunderheads follows a distribution that is nearly normal:

300 acre feet is the null hypothesis for the average quantity of rain that thunderheads produce on their own without fertilizing the clouds.

Alternative Hypothesis: The amount of rain that thunderheads often produce by seeding the clouds is greater than 300 acre feet.

This test has a right tail.

So, The conditions are not met by the extreme outliers, hence we are unable to draw inferences based on the statistical output presented above.

So, option e is correct.

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Total price paid by Michael for the basket of mangoes is $4.48.

For the calculation of total price, price of sales tax will be added with selling price. Forming the equation -

Total price = 4 + 12%×4

Calculating the percentage of sales tax on Right Hand Side of the equation

Total price = 4 + 12×4/100

Solving the percentage part on Right Hand Side of the equation

Total price = 4 + 0.48

Performing addition on Right Hand Side of the equation

Total price = $4.48

Hence, Michael has to pay $4.48 after addition of sales tax for the basket of mangoes.

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Learn more

By SAS congruence, the triangles LMO and LNO are concurrent.

Here given,

LM ≅ ON

∠ M ≅ ∠ N

From the figure it is clear that, the side LO is shared by both triangles.

So, in the concurrency SAS, two sides of a triangle are equal, and an angle is equal.

As a result, the triangles LMO and LNO are congruent by SAS congruence if LM ≅ ON, ∠ M ≅ ∠ N .

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Answer:

find the size of unknown angle in the following figure

Step-by-step explanation:

the solve by putting the given valu

A complete model that shows the system's whole data flow is a physical data model.

A thorough model that depicts the general flow of data through a system is a physical data model.

A physical data model is a thorough representation of the overall organizational data structure that is not dependent on a database management system or any other implementation factors.

A physical data model is a database-specific model that depicts relational data objects and their associations (such as tables, columns, primary keys, and foreign keys).

DDL statements can be produced from a physical data model and then delivered to a database server.

Examples of physical models include bridges, cell models, human organs, crash test dummies, landform models, building models, and chemical compound models.

Therefore, a complete model that shows the system's whole data flow is a physical data model.

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When we divide the 464 by 60 we get the following remainder in our answer that is 44.

The Remainder is the name for the value that is left behind after division. If an amount (reward) cannot be divided completely with another number, we are left with only a meaning (divisor). The remaining is the name for this amount. For instance, 10 is not precisely divisible by 3. We can calculate 3 x 3 = 9 because that is the closest value.

7.733333333333333

=7 44/60 ⇔ 7 R 44

464 divided by 60

=7 with a remainder of 44

Here, we provide you the outcome of the dividing with remainder, often known as the Euclidean division, along with a brief explanation of the following terms:

464 divide by 60 yields a quotient and residual of 7 R 44.

464 is the dividend & 60 is the divisor; the division (numeric division) of 464/60 is 7; the remainder ("left over") is 44.

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Given the circumstances of the question, it is feasible that the two friends would feel that they overreacted during the argument, and as a result, they decide to see a movie together to make up for it.

Regression toward the mean is a statistical condition that involves events that the outcomes produce based solely on chance rather than on real facts. Therefore, it is impossible to forecast with precision what will happen in a regression towards the mean.

Example

Two military units are brought back, one with 20% casualties and the other with 50%. He compliments the first while criticizing the second. The two units return with the opposite outcomes the following time. He "learns" from this experience that praise reduces performance and berating strengthens it.

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6 games are played by Xochitl and 3 rides went on by Xochitl

Two or more expressions with an Equal sign is called as Equation.

Given that the Xochitl is going to a carnival that has games and rides

The cost of each game is $2.50 and cost of each ride is  $5.

Xochitl spent $30 altogether on 9 games

Let x represents the number of games and y represents the number of rides.

By the given information we form two equations.

x+y=9...(1)

2.5x+5y=30...(2)

From equation (1)

x=9-y

Now plug in x value in (2)

2.5(9-y)+5y=30

22.5-2.5y=30

Subtract 22.5 on both sides

-2.5y=30-22.5

-2.5y=7.5

Divide both sides by 2.5

y=3

x+y=9

x+3=9

x=6

Hence, the number of games Xochitl played is 6 and the number of rides Xochitl went on is 3.

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Answer:

1/1000000 One gram is one millionth of a ton

Step-by-step explanation:

1 ton is 1000 kg = 1 million grams

1 gram = 1/1000000 ton

Hope this helps

Answer:

  Zach is correct

Step-by-step explanation:

You want to know if reflection across the two axes and translation right will achieve the same effect if the transformations are done in any order.

Translation right adds a value to the x-coordinate.

Reflection over the y-axis changes the sign of the x-coordinate.

If the order of these two transformations is changed, the result will change.

Example

Consider point (0,0) and the translation right 1 unit.

  Reflection, then translation: (0, 0) ⇒ (0, 0) ⇒ (1, 0)

  Translation, then reflection: (0, 0) ⇒ (1, 0) ⇒ (-1, 0)

Zach is correct that the transformations ...

cannot be done in any order.

Answer:

Zach

Step-by-step explanation:

The equations log₂ (0.25) = -2, 5² = 25, log₂ 32 = 5 and 25⁻¹ = 0.04 are equivalent to the equations 2⁻² = 0.25, log₅ 25 = 2, 2⁵ = 32, log₂₅ 0.04 = -1 respectively.

Logarithms are another way, which is the opposite of writing exponents. A number raised to some power will give some other values in case of exponentiation process. This power is called the logarithmic value.

We can write it as,

logₐ x = n ⇔ aⁿ = x

We have the equations on the left equivalent to the equations on the right using the definition of logarithms as,

log₂ (0.25) = -2 ⇔ 2⁻² = 0.25

5² = 25 ⇔ log₅ 25 = 2

log₂ 32 = 5 ⇔ 2⁵ = 32

25⁻¹ = 0.04 ⇔ log₂₅ 0.04 = -1

Hence the equations on the lefts log₂ (0.25) = -2, 5² = 25, log₂ 32 = 5 and 25⁻¹ = 0.04 are equivalent to the equations on the rights 2⁻² = 0.25, log₅ 25 = 2, 2⁵ = 32, log₂₅ 0.04 = -1 respectively.

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Answer:

Get math teacher

Step-by-step explanation:

go talk to them.

Answer:

Step-by-step explanation:

We need to graph all the given constraints(inequalities). The intersection of the of all the graphed system of inequalities gives the vertices of the feasible region.

The first inequality is .  

This is very simple to graph. It is the region bounded by the horizontal lines,

and .

The next constraint or inequality is

To graph this inequality, we need to graph the corresponding linear equation .  

We plot the intercepts  and .

We then draw a solid line through the points.

Next, we test the origin to determine which half plane to shade.

This statement is true so we shade the lower half plane.

We now graph the inequality,

To graph this inequality, we need to graph the corresponding linear equation .  

We plot the intercepts  and .

We then draw a solid line through the points.

Next, we test the origin to determine which half plane to shade.

This statement is true so we shade the lower half plane.

The feasible region is shown in the above diagram.

The vertices of the feasible region are;

We substitute the vertices into the objective function to obtain;

Therefore the maximum value is  and it occurs at .

The minimum value is  and it occurs a

ANSWER TO QUESTIONS 14 We need to graph all the - 1

By applying the fraction concept, it can be calculated that Mrs. Stewart sold 300 cakes.

How does the concept of fractions apply in real life?

In real life, the concept of a fraction is often used when we want to talk about a part of a whole, a part of something, a part of a group of people, etc.

In this case, it is stated that Mrs. Stewart made several pies, some of which were sold and given to food banks, and some were left over.

If we know that 1/4 of the unsold pies were given to the food bank, then the unsold pies that were not given to the food bank = 1 - 1/4 = 3/4 part.

Additionally, we also know that the number of unsold pies that were not given to the food bank (leftover pies) was 150.

If x is the number of unsold cakes, then the two statements above can be written in mathematical notation:

3/4 x = 150

      x = 150 : 3/4

         = 150 x 4/3

         = 200 pies

If pies made are y, then pies not sold = pies made - pies sold

x = y - 3/5y

  = 2/5y

if we put the value of x into this equation it becomes:

200 = 2/5y

    y = 200 : 2/5

       = 200 x 5/2

       = 500 pies

Then the pies were sold = 3/5y

                                         = 3/5 x 500

                                         = 300 pies

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The first and the second terms of the recursive sequence are given as follows:

a) u(1) = -25.

b) u(2) = -15623.

The definition of the recursive sequence is presented as follows:

u(n + 1) = u(n)³ + 2.

The initial term is needed to solve the sequence, hence it is given as follows:

u(0) = -3.

Thus the term with index 1 is given as follows:

u(1) = u(0)³ + 2.

u(1) = -3³ + 2

u(1) = -27 + 2

u(1) = -25.

Considering the term with index 1, the term with index 2 is obtained as follows:

u(2) = u(1)³ + 2

u(2) = (-25)³ + 2

u(2) = -15623.

And then the same rule is obtained if needed to obtain the 3th, 4th terms, and so on, considering the previous term and the definition.

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Answer:

PART A

x-intercept: (-7,0)

y-intercept: (0,9)

PART B

Answer is A (Top Left One)

Step-by-step explanation:

I left a desmos explanation on my previous answer