Numerical expression for the difference between 72 and 16

5 and 6

√25 = 5 and √36 = 6

5 < √29 < 6

Answer:

The number of ducks were sold be 48

Step-by-step explanation:

Let the number of chicken be 3x and the number of ducks on a farm be 8x.

From the given conditions, it is states that there were 40 more ducks than chicken, i.e

8x+40=3x

or [tex]8x-3x=40[/tex]

or 5x=40

Simplify:

[tex]x=8[/tex]

Then, the number of chicken be [tex]3x=3\cdot 8=24[/tex]

and the number of ducks be, [tex]8x=8\cdot 8=64[/tex].

Since it is given that half the chicken and some of the ducks were sold ; then the ratio of the number of chicken to the number of ducks became 3:4

Let the number of ducks that were sold be y.

now by above condition, we have

[tex]\frac{12}{64-y}= \frac{3}{4}[/tex]

then,

[tex]12\cdot 4= 3\cdot (64-y)[/tex]

Simplify:

[tex]48=192-3y[/tex] or

[tex]3y=192-48[/tex] or

[tex]3y=144[/tex]

On simplify we get,

y=48.

Therefore, the number of ducks were sold be, 48.

Final answer:

By setting up simultaneous equations based on the given ratios and the additional information, we can determine that initially there were 120 chickens and 160 ducks. After selling half the chickens and some ducks, 80 ducks were sold to maintain the new ratio of 3:4.

Explanation:

Let's denote the number of chickens as c and the number of ducks as d. According to the problem, the initial ratio of chickens to ducks is 3:8, so we can write the relation as 3d = 8c. Since there are 40 more ducks than chickens, we have the equation d = c + 40.

Now we'll solve these two equations simultaneously. Multiplying both sides of the first equation by c to eliminate fractions, we get 3d = 8c, or 3(c + 40) = 8c. Simplifying this, we find that c = 120 (the number of chickens) and d = 160 (the number of ducks).

After selling half of the chickens and some ducks, the ratio becomes 3:4. The new number of chickens is 120/2 = 60. Let's call the new number of ducks d'. Then, we have 3d' = 4x60. Solving for d', we get d' = 80. Since initially there were 160 ducks and now there are 80, 80 ducks were sold.

Final answer:

The expression 5ac+10ab-2c²-4bc is factored by first taking out the common factor of 2, and then grouping terms to extract 'a' from the first two and 'c' from the last two terms to get 2(a(5c + 5b) - c(c + 2b)).

Explanation:

To factor the expression 5ac+10ab-2c²-4bc, we look for common factors in each term. Observing the coefficients, we see that each term is divisible by 2. Also, we can factor out variable 'a' from the first two terms and variable 'c' from the last two terms. The factored expression is:

2a(5c + 5b) - 2c(c + 2b).

We can then extract the common factor 2 from both parts to get:

2(a(5c + 5b) - c(c + 2b)).

This is the fully factored form of the given expression.

the answer for this question is D

The 11th term in the given sequence is 11/59049 according to the expressed pattern which is n/(3^(n-1)).

The given sequence is a mathematical sequence, where each term appears to be the result of dividing an ascending integer numerator by the ascending powers of 3 in the denominator. Essentially, the pattern of the sequence can be expressed as n/(3^(n-1)) for the nth term. By this pattern, the 11th term in this sequence would fall into the pattern by substituting n = 11, which gives us 11/(3^10).

To simplify the term, you can leave it as 11/59049 as it’s the simplest form.

Therefore, the 11th term of this sequence is 11/59049.

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Answer: C

Step-by-step explanation:

"Commute" means travel so commutative property is when one of the terms or parentheses move elsewhere in the expression: 72 + (28 + 93) = (28 + 93) + 72  

"Associate" is partner so associative property is when the parentheses switch partners but the order of the terms remains the same: 72 + (28 + 93) = (72 + 28) + 93

The operation between the terms is addition.

Answer:

B

Step-by-step explanation:

Hole

Ok so logically it would be the blue which is consistently low and unlike the others doesn't get any spikes of interst so BLUE.

A: Amount of hours (h) you spend landscaping

B: Earnings ($20)

C: h(20)= 20^h  

After translating the statement into an inequality and simplifying, we find that the solution to 'The sum of a number and twenty is greater than four times the number decreased by one' lies in the set of numbers that is less than 7.

The question asks us to solve an inequality. Let's take the given statement: 'The sum of a number and twenty is greater than four times the number decreased by one'. We can translate that into an inequality as follows: x + 20 > 4x - 1, where x stands for the unknown number.

Now, let's simplify the inequality: we subtract x from both sides to get 20 > 3x - 1, and then add 1 to both sides, yielding 21 > 3x. Lastly, divide each side by 3 for the final inequality x < 7.

So the solution to the inequality means any number less than 7, when added to 20, is greater than four times the number minus one.

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The answer for x is 9. Hope this helps. See work below.

i think the answer is 9 hope this helps

The measure of the third angle in the triangular sail, given that the largest angle is 90° and the smallest angle is x°, is found by subtracting the known angles from 180°, giving the expression 90° - x°.

In a triangular sail, the sum of all the angles totals to 180°. Given that the largest angle measures 90° and the smallest angle measures x°. We find the measure of the third angle by using the fact that the sum of angles in a triangle equals 180 degrees. Therefore, if we subtract the two known angles from 180, we can locate the measure of the third angle. So the expression to determine the third angle in degrees would be 180° - 90° - x°, simplifying the expression to 90° - x°.

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3. AB ~= CE

4. CE ~= AC

5. Definition of isosceles triangle

6. Transitive Property of Congruence

The method would be the best to ensure they select the "most talented" soccer players is They watch the players during tryouts and then put them on a list in order from the most skilled to the least skilled and then select the top six from the list.

The correct option is (A).

A. This method involves observing the players during tryouts and then ranking them from the most skilled to the least skilled. By selecting the top six players from this ranked list, the team is more likely to pick the most talented individuals based on their performance and skills demonstrated during the tryouts.

Option B (selecting the first six that show up) may not necessarily guarantee selecting the most talented players as eagerness to show up early does not always correlate with soccer skills.

Option C (selecting randomly from a hat) is not ideal because it does not take into account the players' actual skills and performance during tryouts. It relies solely on chance.

Option D (selecting the top three and bottom three) may overlook potentially talented players who fall in the middle range. Additionally, selecting the bottom three solely based on being the least skilled may not be fair or accurate.

Therefore, option A is the most suitable method for ensuring the selection of the "most talented" soccer players.

complete question given below:

A local club team is holding tryouts for six spots on the soccer team. Since there is not much time before a very important tournament they need to select the best players. Which method would be the best to ensure they select the "most talented" soccer players?

A. They watch the players during tryouts and then put them on a list in order from the most skilled to the least skilled and then select the top six from the list.

B. The first day of tryouts they select the first six that show up as they figure those are the most eager for a spot.

C. They place all of the names of the people trying out in a hat and theselect six out of the hat. Those are the ones that are chosen.

D. They watch the players during tryouts and then put them on a list in order from the most skilled to the least skilled and then select the top three and the bottom three from the list.

Utilize open tryouts, structured evaluations, scouting, fitness assessments, game simulations, background checks, objective evaluation, expert consultation, feedback, and review.

To ensure the selection of the most talented soccer players for the local club team, the following method can be adopted:

1. **Open Tryouts**: Organize open tryouts where any interested player can participate. This allows for a wide pool of talent to be assessed.

2. **Structured Evaluation**: Develop a structured evaluation system that includes various aspects of soccer skills such as dribbling, passing, shooting, defending, and game intelligence. Each player should be assessed on these criteria.

3. **Scouting**: Utilize scouts who have a keen eye for talent to observe players in local leagues, school teams, or other relevant competitions. They can provide insights into players who may not have attended the tryouts.

4. **Physical Fitness Assessment**: Soccer requires a good level of physical fitness. Conduct physical fitness assessments to gauge players' endurance, speed, agility, and strength.

5. **Game Simulations**: Organize scrimmages or small-sided games during tryouts to see how players perform in real-game situations. This can reveal their decision-making abilities, teamwork skills, and adaptability.

6. **Background Checks**: Consider players' past performances, achievements, and behavioral aspects. Look for players who demonstrate dedication, discipline, and a positive attitude.

7. **Objective Evaluation**: Ensure that the selection process is fair and transparent, with scores and assessments being recorded objectively. Avoid biases based on personal preferences or relationships.

8. **Consult Coaches and Experts**: Involve experienced coaches or soccer experts in the selection process. They can provide valuable insights and perspectives on players' potential and suitability for the team.

9. **Feedback and Review**: Provide feedback to players after the tryouts, highlighting areas of improvement and offering guidance for future development. Additionally, periodically review the selected players' performance to ensure they continue to meet the team's standards.

By combining these methods, the local club team can maximize the chances of selecting the most talented soccer players for their upcoming tournament.

Given

In an acute angled triangle ABC .

sin 2(A+B-C) = 1

tan(B + C -A) =√3

To proof

As given in the question

In an acute angled triangle ABC .

first solving the equation

sin 2(A+B-C) = 1

[tex]2 ( A + B - C ) = sin^{-1} (1)[/tex]

As we know

1 = sin90°

put this in the above equation

we get

[tex]2 ( A + B - C ) = sin^{-1} (sin90^{\circ})[/tex]

2A + 2B - 2C = 90

A+B -C =45      ( first equation )

now solving the equation

we get

tan(B + C -A) =√3

[tex]B + C -A =tan^{-1} \sqrt{3}[/tex]

[tex]B + C -A =tan^{-1}(tan60^{\circ})[/tex]

B + C -A = 60   ( second equation )

As given  acute angled triangle ABC

thus

∠A + ∠ B +∠ C = 180°   ( Angle sum property of a triangle )

than  the third equation becomes

A + B + C = 180  ( third equation)

Now solve the equation

A+B -C =45

and  B + C -A = 60

Now  subtract  B + C -A = 60 from A+B -C =45

we get

(A+B -C) - (B + C -A) = 45-60

2A -2C = -15

Put this value in the  equation 2A + 2B - 2C = 90

-15 + 2B = 90

2B = 90 + 15

B = 52.5

now subtracted -A +B +C = 60 from A + B + C =180

A + B + C +A - B - C =180 - 60

2A = 120

A  = 60

Put the value of A , B  in the equation A + B + C =180

60 + 52.5 + C = 180

C = 180 - 112.5

C = 67.5

Thus  ΔABC is an acute angle triangle

therefore

∠A = 60°

∠B = 52.5°

∠C = 67.5°

Hence proved

Final answer:

The value of an expression will be negative when the sum of the two numbers subtracted from a given first number is greater than the initial number itself, resulting in a negative outcome after applying the appropriate rules for addition and subtraction.

Explanation:

The value of an expression involving the subtraction of two numbers from a given first number will be negative under specific conditions. When the combination of the two numbers to be subtracted is larger than the first number, the result will be negative. To understand this, let's consider the basic rules of addition and subtraction with positive and negative numbers:

In subtraction, we change the sign of the number being subtracted and then apply the rules of addition:

Therefore, to have a negative result, the magnitude of the sum of the two numbers being subtracted should exceed the first number and, reflecting the sign rules, should result in a negative value. For instance, if the first number is 1 and the two numbers to subtract are 3 and 5, the expression would be 1 - (3 + 5) = 1 - 8 = -7, resulting in a negative value.

Answer: D

Step-by-step explanation:

Let x represent the score on her next test

[tex]\frac{78 + 92 + 88 + 89 + x}{5} = 90[/tex]

[tex](5)\frac{78 + 92 + 88 + 89 + x}{5} = (5)90[/tex]

78 + 92 + 88 + 89 + x = 5(90)

                      347 + x = 450

                    -347         -347

                                x = 103

8.75 feet

trust me i got it right on my test ;;

Answer:

1: 3; Enlargement

2: 1/2

3. 8.75 feet

4: 560 millimeters

Step-by-step explanation:

I got 4/4. Hope this helps!

A. 8 would be your answer. add all the numbers up, and divide by how many numbers there are.

Answer:

'Transitive postulate of equality'

Step-by-step explanation:

To find : The postulate of equality or inequality that is illustrated.  

Solution :

Given illustration is  

[tex]\frac{1}{4}+\frac{1}{4}=\frac{2}{4}[/tex] and  [tex]\frac{2}{4}=\frac{1}{2}[/tex]        

Then, [tex]\frac{1}{4}+\frac{1}{4}=\frac{1}{2}[/tex]  

Now, We let  [tex]\frac{1}{4}+\frac{1}{4}=a,\frac{2}{4}=b,\frac{1}{2}=c[/tex]

According to this, [tex]a=b\text{ and }b=c\text{ then }a=c[/tex]

Which is 'Transitive postulate of equality'.

So, The required postulate of equality is transitive.

The equation 'One Fourth (1/4) + One Fourth (1/4) = One Half (1/2)' illustrates the Transitive Property of Equality. This mathematical property states that if 'a' equals 'b' and 'b' equals 'c', then 'a' must also equal 'c'. In this case, 'a' is '1/4 + 1/4', 'b' is '2/4', and 'c' is '1/2'.

The mathematical postulate illustrated by the equation One Fourth (1/4) + One Fourth (1/4) = One Half (1/2) is the Transitive Property of Equality. In mathematics, the transitive property states that if a = b and b = c, then a = c. In this case, 'a' is One Fourth (1/4) + One Fourth (1/4), 'b' is Two Fourths (2/4), and 'c' is One Half (1/2). Because it has been established that 'a' equals 'b' (1/4 + 1/4 = 2/4) and 'b' equals 'c' (2/4 = 1/2), the Transitive Property of Equality allows us to conclude that 'a' equals 'c' (1/4 + 1/4 = 1/2).

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[tex]4(k+5)=2(9k-4)\qquad|\text{use distributive property}\\\\(4)(k)+(4)(5)=(2)(9k)+(2)(-4)\\\\4k+20=18k-8\qquad|\text{subtract 20 from both sides}\\\\4k=18k-28\qquad|\text{subtract 18k from both sides}\\\\-14k=-28\qquad|\text{divide both sides by -14}\\\\\boxed{k=2}\to\boxed{d.}[/tex]

Answer: The statement H(R)=4H means the height of ball is 4H meter at a horizontal distance of R meters from Kaori.

Explanation:

It is given that Kaori is taking a free-throw. H(d) models the basketball's height (in meters) at a horizontal distance of d meters from Kaori.

The given statement is H(R) = 4H.

Here we have H(R) instead of H(d) and it shows the height of basketball. So it clear that the height of basketball's is 4H because H(R)=4H at d = R

Since d represents the horizontal distance from Kaori, therefore the horizontal distance from Kaori is R.

Thus, Answer: The statement H(R)=4H means the height of ball is 4H meter at a horizontal distance of R meters from Kaori.

Answer:

At a horizontal distance of RRR meters from Kaori, the ball's height was equal to 444 meters.

Step-by-step explanation:

Answer:

an=27*(1/3)^(n-1)

Step-by-step explanation:APEX

The correct option is B.

A geometric progression is a sequence in which every next term of the sequence is found out by multiplying the previous term by a fixed ratio.

Any nth term of the sequence is found out the formula,

[tex]a_n = a_1 \times r^{n-1}[/tex],

where,

[tex]a_n[/tex] is the nth term,

[tex]a_1[/tex] is the first term,

r is the fixed common ratio.

Sequence, 27, 9, 3, 1.

the first term, [tex]a_1[/tex]= 27,

As we can see from the series 27, 9, 3, 1. the series is a geometric series,

And can be written as [tex]3^3,\ 3^2,\ 3^1\ ,3^0[/tex].

therefore, will follow the formula of a geometric series.

[tex]a_n = a_1 \times r^{n-1}[/tex],

we know the value of r can be found out using the formula,

[tex]r = \dfrac{a_{n}}{a_{n-1}}}[/tex]

taking n =2,

[tex]r = \dfrac{a_{2}}{a_{2-1}}} = \dfrac{a_{2}}{a_{1}}}= \dfrac{9}{27} = \dfrac{1}{3}[/tex]

Substituting the values in the formula of geometric progression we get,

[tex]a_n = a_1 \times r^{n-1}\\a_n = 27\times {\dfrac{1}{3}}^{n-1}\\a_n = (27)\times ({\dfrac{1}{3}})^{n-1}[/tex]

Therefore, the correct option is B.

Learn more about Substituting Geometric Progression:

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Answer:

B.Triangle ACD is congruent to triangle ABD

Step-by-step-explanation:

We are given that AC is congruent to segment AB

We have to prove that angle ABD is congruent to angle ACD

When triangle ACD is congruent to triangle ABD

Then ,Angle ACD is congruent to angle ABD

Angle ADC is congruent to angle ADB

Angle CAD is congruent to angle DAB

Segment CD congruent to segment BD

Because when two triangles are congruent then sides and length of a triangle congruent to its corresponding sides and angles of other triangle .

Therefore,Triangle ACD is congruent to triangle triangle ABD is used to prove that angle ABD is congruent to angle ACD.

Hence, option B is true.

[tex]4w-2(1-w)=-38\qquad|\text{use distributive property}\\\\4w+(-2)(1)+(-2)(-w)=-38\\\\4w-2+2w=-38\qquad|\text{add 2 to both sides}\\\\4w+2w=-36\\\\6w=-36\qquad|\text{divide both sides by 6}\\\\\boxed{w=-6}[/tex]