5x² - 20x + k = 0 has exactly one real solution, show that k=20​

Over the course of three weeks, she practiced for 609 minutes to become ready. The constant of proportionality is k=203.

Given that,

Rochelle planned out additional practice because she was getting ready for a big swim meet.

Over the course of three weeks, she practiced for 609 minutes to become ready. Every week she practiced for the same amount of time.

We have to find the constant of proportionality (k) between Rochelle's weekly practice time (w) and the number of minutes she practiced each week (m).

3 week =609 minutes

3w=609m

1w=609m/3

1w=203m

For 1 week she practiced 203 minutes.

Now,

Constant of proportionality is

m=kw

203=k(1)

k=203

Therefore, the constant of proportionality is k=203.

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The standard deviation of the portfolio return is 3.14%

What is Sharpe ratio?

Sharpe ratio measures the by extent to which the risk of an investment portfolio is compensated as it indicates the return per unit of risk inherent in the portfolio whereas the standard deviation measures the risk of expected return of the portfolio.

It should be noted that the Sharpe ratio can be determined as the expected return of the portfolio minus the risk-free rate of return divided by the standard deviation of the portfolio.

Sharpe ratio=(expected return-risk-free rate)/standard deviation

Sharpe=2.99

expected return=12.9%

risk-free rate=3.5%

standard deviation=unknown(assume it is x)

2.99=(12.9%-3.5%)/x

2.99*x=9.40%

x=9.40%/2.99

x=3.14%

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The product of 2√5 and √2 is 2√10.

And, The result is an irrational number.

Here,

We have to find the product of 2√5 and √2.

And, also determine the result is a rational or irrational number.

What is Irrational number?

A number which cannot be written in the form of fraction p/q, is called an Irrational number.

Now,

The product of 2√5 and √2 is;

⇒ 2√5 * √2 = 2√5*2 = 2√10

Hence, The product of 2√5 and √2 = 2√10.

Since, √10 is an irrational number because it cannot be written in the form of fraction.

Hence, 2√10 is an irrational number.

Therefore, The product of 2√5 and √2 is 2√10.

And, The result is an irrational number.

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The correct question is this;

Find the product of 2√5 and √2 in simplest form. Also, determine whether the result is irrational or rational and explain

Answer:

82% or 23/28

Step-by-step explanation:

2+3+18=23

2+3+18+6=28

23/28=

Answer:

The number is 5.

Step-by-step explanation:

Given: If 6 is added to the square of a positive number, the sum is 31. Find the number.​

Step-by-step solution:

Step 1: Formula

We know that the square of a positive number plus 6 is equal to 31. In a formula, it would look like [tex]\sqrt{x}[/tex] + 6 = 31 where x replaces the positive number.

Step 2: Subtract 6

We need to get x by itself to find the number. Subtract 6 on both sides to cancel it out and move it to the left

so, [tex]\sqrt{x}[/tex] + 6 -6 = 31 -6 = [tex]\sqrt{x}[/tex] = 25

Step 3: Square Root of 25

The Square Root of 25 is 5. We know this because 5*5 = 25.

Therefore, the number is 5.

Answer:

send the image of the exercise

the answer is 8

Step-by-step explanation:

just minus 11by 3

0.61166117... is not an rational number as it has no regularly repeating digit or group of digits.

A rational number is one that can be stated mathematically as the ratio or fraction p/q of two integers, p and q, which must both be non-zero. Every integer, including 3/7 (3 = 5/1) and 7 is a rational number.

Boldface Q is typically used to represent the field of rationals, also known as the field of rational numbers, the set of all rational numbers, or "the rationals."

Real numbers are those that make sense. The rational real numbers are those whose decimal expansion either ends after a finite number of digits (for example, 3/4 = 0.75), or eventually starts to repeatedly repeat the same finite sequence of digits (for instance, 9/44 = 0.20454545).

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Answer:

Yes, 14 × 216 = 3024

Step-by-step explanation:

The acceleration during this time will be 0.5 m/s².

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Han's younger sister is moving straight ahead on her tricycle. Her speed is 0.5 m/s after 3 seconds. Her speed is 1.5 m/s after 5 seconds.

We know that the first equation of motion is given as,

v = u + at

The information is given below.

v = 1.5 m/s, u = 0.5 m/s, and t = 2 s. Then the value of the acceleration will be

v = u + at

1.5 = 0.5 + 2a

2a = 1

a = 1/2

a = 0.5 m/s²

The acceleration during this time will be 0.5 m/s².

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Answer:

If you're just looking for the area of the square, then it's 49m. If you want the surface area of the whole pyramid, it's 189.

Step-by-step explanation:

For just the square, it's easy: Multiply the side lengths. 7x7 is 49.

For the surface area, find the area of the square (49) and the four triangles. To find the areas of the triangles, multiply the base (bottom, here it's the side length of the square) by the height (in this case 10m) and divide by 2. 7x10=70 and 70/2=35. Now since there are 4 triangles, multiply that by 4. 35x4=140, and now add the area of the square; 140+49=189. I don't think you wanted the surface area though, but I hope this helps!

3/4*1/4 = 3/16

3/7*1/2 = 6/7

The system of inequalities that represents the graph are:

y−6≤−11x

y+3x≥−4

−2x+3y>15

Option B

This is further explained below.

Generally, The term "set of simultaneous equations" refers to a finite collection of equations in the subject of mathematics, all of which are looking for the same solution.

A system of equations or an equation system is a name that is sometimes used to refer to this kind of collection of equations.

In conclusion,

y−6≤−11x

y+3x≥−4

−2x+3y>15

represents the graph

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The solution set to the inequality m-7>-2(m+0.5) is all real numbers greater than -0.75.

Real numbers are the set of all rational and irrational numbers, which includes all positive and negative numbers, fractions, decimals, and integers. They are represented on the number line and are composed of an infinite amount of numbers between any two given numbers.

This can be represented graphically on a number line by selecting a ray starting at -0.75 and extending infinitely in the positive direction. The point on the ray at -0.75 represents the boundary between the solution set and the numbers not included in the solution set.

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From the calculation below, the probability that a tourist will spend more than $250 on the 2 legs of the trip is 2/3.

From the question, the number of possible options available and their total amount is as follows:

Airplane and Van = $350 + $60 = $410

Airplane and Cab = $350 + $40 = $390

Bus and Van = $150 + $60 = $210

Bus and Cab = $150 + $40 = $190

Train and Van = $225 + $60 = $285

Train and Cab = $225 + $40 = $265

From the above, it can be observed that we have a total number of 6 different options available and 4 of the options are more than $250.

Therefore, we have:

Probability of spending more than $250 = Number of options that are more than $250 / Total number of different options = 4/6 = 2/3

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By using multiplication, we get that the number of pounds of rice will be 19.8 pounds.

We are given that:

1 kg of rice = 2.2 pounds of rice.

We need to find the number of pounds of rice in 9 kg of rice.

So, we will use the operation of multiplication to covert the units from kg into pounds.

So, we get that:

9 kg of rice = 2.2 × 9 pounds of rice

9 kg of rice = 19.8 pounds of rice.

Therefore, by using multiplication, we get that the number of pounds of rice will be 19.8 pounds.

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From the given equation 6.8x+8.8y+9.8=0 the value of x-intercept is -98/68 and value of y-intercept is -98 /88.

As given in the question,

Given equation :

6.8 x +8.8 y +9.8= 0

To get x -intercept substitute y =0 in the equation :

6.8 x+ 8.8 (0) + 9.8=0

⇒6.8x= -9.8

⇒x= 98 /68

To get y -intercept substitute x =0 in the equation :

6.8 (0)+ 8.8y + 9.8 =0

⇒8.8y= -9.8

⇒ y= 98 /68

Therefore, from the given equation 6.8x+8.8y+9.8=0 the value of

x-intercept is -98/68 and value of y-intercept is -98 /88.

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Using the relation between acceleration, velocity and distance, it is found that:

a) The differential equation for the velocity is: [tex]\frac{dV}{dt} = 0.5[/tex]

b) The formula for the velocity is given by: V(t) = 0.5t + 6.

c) The initial value problem to find the position is: [tex]\frac{dS}{dt} = 0.5t + 6, S(0) = 0[/tex]

d) The formula for the position of the car is S(t) = 0.25t² + 6t.

e) The car is at a velocity of 21 m/s after 30 seconds.

We have that:

For item a, we have that the acceleration is constant of 0.5 m/s², hence the differential equation for the velocity is:

[tex]\frac{dV}{dt} = 0.5[/tex]

For item b, we apply separation of variables, and find the velocity as follows:

[tex]\frac{dV}{dt} = 0.5[/tex]

[tex]\int dV = \int 0.5 dt[/tex]

V(t) = 0.5t + v(0).

v(0) is the initial velocity and is the constant of integration, hence:

The formula for the velocity is given by: V(t) = 0.5t + 6.

For item c, we have that the position is the integral of the velocity, hence:

The initial value problem to find the position is: [tex]\frac{dS}{dt} = 0.5t + 6, S(0) = 0[/tex]

For item d, applying separation of variables, we have that:

[tex]\frac{dS}{dt} = 0.5t + 6[/tex]

[tex]\int dS = \int (0.5t + 6) dt[/tex]

S(t) = 0.25t² + 6t + s(0).

Since s(0) = 0, we have that:

The formula for the position of the car is S(t) = 0.25t² + 6t.

The velocity after 30 seconds is of:

v(30) = 6 + 0.5(30) = 21.

The car is at a velocity of 21 m/s after 30 seconds.

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Answer:

In those questions you asked, we can use equation to find the answer but the 1st question's x did not get an exact value so you can do no solution. Thank you

At the end of 4.5 hours, Nell and Kristin will be at a distance of 9 miles apart.

Here, we are given that Nell and Kristin start from the same point and skate in the same direction.

Speed of Nell = 8 miles per hour

Time for which he skates = 4.5 hours

Thus, the distance travelled by Nell will be-

Distance = Speed × time

= 8 × 4.5

= 36 miles

Similarly, Speed of Kristin = 10 miles per hour

Time for which he skates = 4.5 hours

Thus, the distance travelled by Kristin will be-

= 10 × 4.5

= 45 miles

Thus, the distance between them will be-

45 - 36 = 9 miles.

Thus, at the end of 4.5 hours, Nell and Kristin will be at a distance of 9 miles apart.

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Nell and Kristin, two inline skaters, begin at the same location and move in the same direction. While Kristin skates at 10 miles per hour, Nell skates at 8 miles per hour. 5 miles apart will they be at the conclusion of the 4.5 hours if they maintain their current rate.

Distance =Rate x time ....... d=rt

The difference in the distances traveled will be how far apart they are 12(2.5)-10(2.5)=2(2.5)=5 miles apart

Note that you can find their individual distances and subtract those to get the same answer:

Nell: distance =10(2.5)=25 miles

Kristin: distance =12(2.5)=30$ miles

30-25=5 miles apart

Distance is the sum of an object's movements, regardless of direction. Distance may be defined as the amount of space an item has covered, regardless of its beginning or finishing position.

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The "additional wages" that the company will have to pay out next year at the inflation-adjusted rate of 7.5% (in $) is $494,208.

The inflation-adjusted pay rate is the rate after adjusting for inflation.

The number of fast-food restaurants = 16

The number of workers per restaurant = 55

Average weekly hours per worker = 20 hours

The number of weeks per year = 52

The current federal minimum wage per hour = $7.25

The total hours worked by the workers = 915,200 hours (16 x 55 x 20 x 52)

Total current wages = $6,635,200 (915,200 x $7.25)

Inflation rate = 7.5%

Inflation-adjusted wage rate = $7.79 ($7.25 x 1.075)

Total wages for next year = $7,129,408 ($7.79 x 915,200)

Additional wages next year = $494,208 ($7,129,408 - $6,635,200)

Thus, the "additional wages" that the company will have to pay out next year at the inflation-adjusted rate of 7.5% (in $) is $494,208.

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Error: They failed to account for when x-5 is negative.

Solution:

[tex]|x-5|<20 \\ \\ -20<x-5<20 \\ \\ \boxed{-15<x<25}[/tex]

Answer:

Step-by-step explanation:

You want the next number in the sequence 31, 27, 23, 19, 15, ... such that it follows the same pattern.

It is often useful to look at the differences between successive terms of a sequence. This can quickly reveal a pattern if the sequence is polynomial or exponential.

Here, the differences are ...

  27 -31 = -4

  23 -27 = -4

  19 -23 = -4

  15 -19 = -4

It appears reasonable to assume that the pattern is that each term is 4 less than the previous one.

The number that is 4 less than 15 is ...

  15 -4 = 11

The next number in the pattern is 11.

The algebraic expression from the given statement is 8+x/4=x

Given the statement is the "eight more than the quotient of a number and 4 is equal to 2."

In mathematics, an expression is defined as a set of numbers, variables, and operations that are formed according to context-dependent rules.

Lat us assume the number be x.

In the given statement the quotient of a number and 4 means x/4.

And eight more than the quotient of a number and 4 means 8 is the sum of quotient of a number and 4 and it can be written as

8+x/4      ......(1)

As given in the statement eight more than the quotient of a number and 4 is equal to 2 means we want to equate equation (1) with 2 and written as

8+x/4=2

Hence, the algebraic expression from the given statement "eight more than the quotient of a number and 4 is equal to 2" is 8+x/4=2.

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Answer: 1/7

Step-by-step explanation:

The total amount of cars that had AC problems is 30+20=50. The total amount of cars is 30+20+200+100=350. 50/350 = 1/7

Answer:

x = -26

Step-by-step explanation:

[tex](f-g)(x)=\frac{4}{x-3}-\frac{3}{x+5}=\frac{3}{x^2 +2x-15} \\ \\ \frac{4(x+5)-3(x-3)}{x^2 +2x-15} \\ \\ =\frac{4x+20-3x+9}{x^2 +2x-15}=\frac{3}{x^2 +2x-15} \\ \\ \frac{x+29}{x^2 +2x-15}=\frac{3}{x^2+2x-15} \\ \\ x+29=3 \\ \\ x=-26[/tex]

This is in the domain of the equation, and is thus a solution.

Answer:

B. Irrational

Step-by-step explanation:

The √14 = 3.74 recurring. This isn't an integer and therefore can't be written as a fraction. Therefore it's an irrational number.

Whereas, if it was √16 which equals 4, the answer would be rational as it is an integer which can be written as a fraction such as 4/1 or 8/2 etc.