If f(x)=−7ex, find f(2) rounded to the nearest tenth.

Answer:

The integers are 20 and 22

Step-by-step explanation:

Let the first even integer be x . Then the next consecutive even integer
= x  + 2
The relationship between these two integers is the difference of the squares = 84

This means
(x + 2)² - x² = 84

Use the relationship a² - b² = (a + b) (a -b)

Here a = x + 2 and b = x

So

a + b = (x + 2 ) + x = x + 2 + x = x + x + 2 = 2x + 2
a  - b = (x + 2) - x = x + 2 - x = x -x + 2 = 2

Therefore

(a + b)(a - b) in terms of x is
(2x + 2) x 2 = 4x + 4

We know this is 84

So 4x + 4 = 84

Subtract 4 on both sides:
4x = 84 -4

4x = 80

x = 20

So the next consecutive even integer = 22

The integers are 20 and 22

Answer:       5.1 x 10⁻¹ kg

To find the mass of water in the bottle, we can multiply the mass of one molecule by the number of molecules.

By using dimensional analysis, or by cancelling out units, we can figure out what to multiply or divide. Dimensional analysis uses fractions written with units. Dividing the same unit cancels out units we don't need.

To solve:

We are looking for the mass of H₂O in the bottle.

The units we need in the answer are:      [tex]\displaystyle{ \frac{kg}{bottle} }[/tex]

The question tells us:

Our equation puts the fractions in an equation, making them multiply to get the units we need.

[tex]\displaystyle{ \frac{(3 * 10^{-29}\ kg)}{1\ H_{2}O} \ *\ \frac{(1.7*10^{28}\ H_{2}O)}{1\ bottle}}\ =\ \frac{kg}{bottle}[/tex]

Why is this equation correct?

Remember that dividing the same unit will cancel them out. In the equation, we have H₂O in a numerator and H₂O in a denominator. So, H₂O will cancel out. In the end, we will only have kg in the numerator and bottle in the denominator.

Take the equation we wrote. Now that we know our equation gives us the right units, we only need the front part.

[tex]\displaystyle{ \frac{(3 * 10^{-29}\ kg)}{1\ H_{2}O} \ *\ \frac{(1.7*10^{28}\ H_{2}O)}{1\ bottle}}[/tex]

Cancel out H₂O:

[tex]=\displaystyle{ \frac{(3 * 10^{-29}\ kg)}{1} \ *\ \frac{(1.7*10^{28})}{1\ bottle}}[/tex]

Simplify the equation:

[tex]=\displaystyle{ \frac{(3 * 10^{-29})*(1.7*10^{28})\ kg}{1\ bottle}[/tex]

[tex]=\displaystyle{ \frac{3 * 10^{-29}*1.7*10^{28}\ kg}{1\ bottle}[/tex]

Use exponent rules to multiply 10⁻²⁹ with 10²⁸:

[tex]=\displaystyle{ \frac{3 *1.7*10^{28-29}\ kg}{1\ bottle}[/tex]

[tex]=\displaystyle{ \frac{3*1.7*10^{-1}\ kg}{1\ bottle}[/tex]

Multiply within the numerator to simplify:

[tex]=\displaystyle{ \frac{5.1*10^{-1}\ kg}{1\ bottle}[/tex]

∴ The mass of water in the bottle is 5.1 x 10⁻¹ kg.

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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.

3/4*1/4 = 3/16

3/7*1/2 = 6/7

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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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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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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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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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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The least degree polynomial function with integral coefficients and the given zeros, -1, 3+3i is f(x) = x³ + x².

So, given zeroes are -1, 3+3i.

Similarly,

So, the polynomial has the function: (x+1)x²

Therefore, the least degree polynomial function with integral coefficients and the given zeros, -1, 3+3i is f(x) = x³ + x².

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Answer:

send the image of the exercise

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

Negative powers of 10 helpful when writing and comparing small numbers.

Small numbers (numbers between 0 and 1) are written with a negative power of ten. The specific power of 10 indicates just how big or how small the number is. You can compare two numbers written in scientific notation by looking at their powers of 10. The number with the greater power of 10 will be the greater number.

When comparing small numbers, write these numbers in scientific notation (only one non-xero digit must be before point) and then

For example- 0.00003450000

                      3.45 x 10 -5

                      3.450000 x 10 -5

                       0.345 x 10 -4

                      0.3450000 x 10 -4

Hence it is prooved that negative powers of 10 helpful when writing and comparing small numbers.

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the answer is 8

Step-by-step explanation:

just minus 11by 3

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.

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:

f=-5

Step-by-step explanation:

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!

The option yes, d = -2 is correct

The arithmetic sequence or progression is a sequence of numbers such that the difference between the consecutive terms is constant.

The formula of an arithmetic sequence is

           [tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n-1)d

Here the sequence is 18, 16, 14, 12, 10...... which is in arithmetic sequence as there is a common difference between them.

Now we have to find the common difference between the two consecutive terms of the series,

common difference (d) = 16- 18 = 14 - 16 = -2

Therefore the series is an arithmetic sequence and the common difference between them is -2.

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Answer:

82% or 23/28

Step-by-step explanation:

2+3+18=23

2+3+18+6=28

23/28=

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

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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Answer:√16 and 6.39 are rational numbers because they can be expressed as a ratio and a fraction.

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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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

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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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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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.