Which of the following inequalities represents the number line below?

Answer: (c)

(√2-√3)(√2+√3)

Step-by-step explanation:

An irrational number is one that cannot be expressed as the ratio of two integers. In other words it cannot be expressed as [tex]\frac{x}{y}[/tex] where x and y are integers

[tex]\sqrt{2}[/tex] is irrational

[tex]\sqrt{3}[/tex] is irrational

In fact the square root of any prime number is irrational. So [tex]\sqrt{5}[/tex], [tex]\sqrt{7}[/tex] etc are irrational. But [tex]\sqrt{9}[/tex] is not irrational since it evaluates to 3 which can be expressed as [tex]\frac{3}{1}[/tex]

Any expression that contains the square root of a prime number is also irrational

Looking at the choices we see that choices (a), (b) and (d) all evaluate to expressions containing square roots of primes

(a)  (2-√3)2 = 4 - 2√3  . Hence irrational

(b) √2+√3)2 = 2√2+2√3. Hence irrational

(d) 27√7​ is irrational

Let's look at choice (c)

(√2-√3)(√2+√3)

An expression [tex](a+b)(a-b)[/tex]  can be evaluated as [tex]a^{2} - b^{2}[/tex]

Here a = √2, [tex]a^{2}[/tex] =[tex]a = \sqrt{2}\\ a^2 = (\sqrt{2} )^2 = 2\\\\b = \sqrt{3} \\b^2 = (\sqrt{3} )^2 = 3\\\\a^2 - b^2 = 2-3 = -1\\[/tex]

This is a whole number(integer) and all integers are rational numbers

Hence correct answer is (c)

The two missing numbers in the pattern are 10 and 1

The sequence is given as:

100 000 , 10 000 , 1000 , 100 , A , B

From the above sequence, the next term is the quotient of the current term and 10.

So, we have:

A = 100/10 = 10

B = A/10 = 10/10 = 1

Hence, the two missing numbers in the pattern are 10 and 1

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Answer:

Step-by-step explanation:

98-7=91

165-9=156

(91/156)/13=7/12

Answer = 13

It is divided by a positive integer a, which will equal the number 13.

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the data provided by the question,

The number are 98 and 165.

The remainders are 7 and 9.

So, the actual number is,

98 - 7 = 91 and,

165 - 9 = 156

They are divided by the number 13, so the value of a will be equal to 13.

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Answer:

4[tex]v^{7}[/tex]x³(7[tex]y^{6}[/tex] - 3v²[tex]x^{6}[/tex])

Step-by-step explanation:

28[tex]v^{7}[/tex]x³[tex]y^{6}[/tex] - 12[tex]v^{9}[/tex][tex]x^{9}[/tex] ← factor out 4[tex]v^{7}[/tex]x³ from each term

= 4[tex]v^{7}[/tex]x³(7[tex]y^{6}[/tex] - 3v²[tex]x^{6}[/tex])

simple interest= principal x time x rate/100

Step-by-step explanation:

we know from the laws of motion that in the equation

h = 20t - 1.86t²

the gravitational acceleration is in the factor of the t² term.

h = v0t + 1/2 × g × t²

v0 being the initial velocity (20 m/s).

and we can therefore see, that the gravitational acceleration "a" on Mars is 2×1.86 = 3.72 m/s²

(a)

the velocity v after 2 seconds is (first law of motion)

v = v0 + at = 20 - 3.72×2 = 12.56 m/s

gravity pulling down, so negative acceleration.

(b)

first we need the time when the rock is at 25 m.

25 = 20t - 1.86t²

0 = -1.86t² + 20t - 25

the solution to a quadratic equation is always

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = t

a = -1.86

b = 20

c = -25

t = (-20 ± sqrt(400 - 4×-1.86×-25))/(2×-1.86) =

= (-20 ± sqrt(214))/-3.72

t1 = (-20 + 14.62873884...)/-3.72 =

= 1.443887409... s ≈ 1.44 s

t2 = (-20 - 14.62873884...)/-3.72 =

= 9.308800763... s ≈ 9.31 s

that means, on its way up the rock reached 25m after

1.44 s.

on its way down the rock reached 25 m after

9.31 s.

velocity 0 (the rock came to a stop before falling back down) was after

0 = 20 - 3.72t

3.72t = 20

t = 20/3.72 = 5.376344086... s

that means the rock was falling after this point back to the ground and was gaining speed again.

that accelerating phase until the rock was again at 25 m was

9.308800763... - 5.376344086... = 3.932456677... s

long

the velocity at these points was

v-up = 20 - 3.72×1.443887409... = 14.62873884... m/s ≈

≈ 14.63 m/s

v-down = 0 + 3.72×3.932456677... = 14.62873884... m/s ≈

≈ 14.63 m/s

as expected : the rock did a perfectly symmetric flight path between the two 25 m marks.

so time and speed on both sides had to be identical.

but we have proven it.

Answer:

a)  12.56 m/s

b) up:  14.63 m/s (2 d.p.)

   down:  -14.63 m/s (2 d.p.)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{The Constant Acceleration Equations (SUVAT)}\\\\s = displacement in m (meters)\\u = initial velocity in m s$^{-1}$ (meters per second)\\v = final velocity in m s$^{-1}$ (meters per second)\\a = acceleration in m s$^{-2}$ (meters per second per second)\\t = time in s (seconds)\\\\When using SUVAT, assume the object is modeled\\ as a particle and that acceleration is constant.\end{minipage}}[/tex]

The average gravitational acceleration on Mars is 3.721 m/s² (about 38% of that of Earth).  The fact that the rock is thrown from the surface of Mars rather than the surface of Earth is of no consequence when using the equations of constant acceleration (SUVAT equations) as long as acceleration is not used in the calculations.

Given:

[tex]s=20t-1.86t^2, \quad u=20, \quad t=2[/tex]

[tex]\begin{aligned}\textsf{Using }\: s&=\dfrac{1}{2}(u+v)t\\\\\implies 20(2)-1.86(2)^2 & = \dfrac{1}{2}(20+v)(2)\\\\32.56 & = 20+v\\\\v & = 32.56-20\\\\v & = 12.56\:\: \sf m/s\end{aligned}[/tex]

Therefore, the velocity of the rock after 2 s is 12.56 m/s.

Find the time when the height of the rock is 25 m:

[tex]\begin{aligned}20t-1.86t^2 & = s\\\implies 20t-1.86t^2 & = 25\\1.86t^2-20t+25 & = 0\end{aligned}[/tex]

Quadratic Formula

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

Therefore:

[tex]a=1.86, \quad b=-20, \quad c=25[/tex]

[tex]\implies t=\dfrac{-(-20) \pm \sqrt{(-20)^2-4(1.86)(25)} }{2(1.86)}[/tex]

[tex]\implies t=\dfrac{20 \pm \sqrt{214}}{3.72}[/tex]

[tex]\implies t=9.308800763..., 1.443887409...[/tex]

Therefore, the height of the rock is 25 m when:

To find the velocity (v) of the rock at these times, substitute the found values of t into the equation, along with s = 25 and u 20 m/s:

[tex]\begin{aligned}\textsf{Using }\: s&=\dfrac{1}{2}(u+v)t\\\\\implies v & = \dfrac{2s}{t}-u\\\\v & = \dfrac{2(25)}{t}-20\\\\v & = \dfrac{50}{t}-20\\\\\end{aligned}[/tex]

When t = 1.443887409...s

[tex]\implies v=\dfrac{50}{1.443887409...}-20=14.63\:\: \sf m/s \: \:(2\:d.p.)[/tex]

When t = 9.308800763...s

[tex]\implies v=\dfrac{50}{9.308800763...}-20=-14.63\:\: \sf m/s \: \:(2\:d.p.)[/tex]

Therefore, the velocity of the rock when its height is 25 m is:

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The inequality suitable if 1 is greater than x is x<1.

Given that 1 is greater than x.

We are required to form an inequality which shows that 1 is greater than x.

Inequality is like an equation showing relationship between two or more variables.It is mostly not found in equal to form.

It shows the range of quantities.

When 1 is greater than x means the greater than sign will be used for 1 not x and the inequality will be as under:

x<1

We have not used equal to sign because 1 is greater than x not equal to x.

Hence the inequality suitable if 1 is greater than x is x<1.

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The domain of the function is x  ≠ 7

The function is given as:

y = 1/x - 7

Set the denominator not equal to 0

x - 7 ≠ 0

Add 7 to both sides

x  ≠ 7

Hence, the domain of the function is x  ≠ 7

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Answer: tan 1 radians = 1.557, tan 1 degrees = 0.017

The answer to the question is B. The test statistic is not between the critical values, so we reject the null hypothesis. There is sufficient evidence to support a claim of correlation between percentage of vote and income level.

This is the plot that shows the relationship between two different variables along a straight line. All of the points that are known to have a relationship between these variables would fall under this line. Other parts that fall outside the line are regarded as the outliers in the plot.

In this particular question, the outlier is seen to be outside of the critical values so we have to conclude that the solution is B. We fail to reject the null hypothesis.

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Answer:

4days atlases in the week

Quantity             day

  25------------------1

 1000---------------x

We solve

                  [tex]\boldsymbol{\sf{x=\dfrac{1000\times1}{25}=\dfrac{1000}{25}=40 }}[/tex]

Answer: To spend $1,000 it will take 40 days.

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Answer:

5.5 hours

Step-by-step explanation:

I am going to assume that a helmet is necessary prerequisite for renting the bike.

I also am assuming that the hourly rate can be turned into a sub hourly rate if the full hour isn’t used.

10+4.25h=33.38

4.25h=23.38

h=23.38/4.25

h=5.5

The probability that a randomly selected study's participant was less than 4 is 0.2266.

Given that:

mean = 5.8

standard deviation = 2.4

a) P(x < 4) = P[(x - mean ) /sd < (4 - 5.8) / 2.4]

= P(z < -0.75)

Using z table,

= 0.2266

b) P(4 < x < 6) = P[(4 - 5.8)/ 2.4) < (x - \m ) /sd < (6 - 5.8) / 2.4) ]

= P(-0.75 < z < 0.08)

= P(z < 0.08) - P(z < -0.75 )

Using z table,

= 0.5319 - 0.2266

= 0.3053

c) P(x > 8) = 1 - p( x< 8)

=1- p P[(x - \m ) / sd< (8 - 5.8) / 2.4]

=1- P(z < 0.92)

Using z table,

= 1 - 0.8212

= 0.1788

Lastly, there are no unusual events because all the probabilities are greater than 0.05.

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The Evaluating expression √6 +√6+√27-√12 become √3(2√2+ 1) after simplification.

According to the statement

We have given that one evaluating expression which is √6 +√6+√27-√12

And we have to simplify this expression by evaluating it.

So, Given expression is:

√6 +√6+√27-√12

√6 +√6+√(9*3)-√(4*3)

√6 +√6+3√(3)-2√(3)

√6 +√6+√3( 3-2)

After evaluating the expression it become

√6 +√6+√3(1)

√(3*2) +√(3*2) +(1)√3

Take common from above expression then

√3(√2 +√2 ) +√3

√3(2√2) +√3

√3(2√2+ 1)

Now the expression √6 +√6+√27-√12 become √3(2√2+ 1) after simplification.

So, The Evaluating expression √6 +√6+√27-√12 become √3(2√2+ 1) after simplification.

Disclaimer: This question was incomplete. Please find the full content below.

Question:

Which choice is equivalent to the expression below?

√6 +√6+√27-√12

A. √3(2√2+ 1)

B. 2√3-√21

C. 3√3+√6

D. 5√3

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Answer: 2/8, 3/8, 4/8, 5/8, 7/8

Step-by-step explanation:

     Since they all have a common denominator, we can list them based on their numerator without having to worry about the denominator.

2/8 < 3/8 < 4/8 < 5/8 < 7/8

Answer: [tex]x \leq 3[/tex]

Step-by-step explanation:

[tex]9-3x \geq 2(x-3)\\\\9-3x \geq 2x-6\\\\15-3x \geq 2x\\\\15 \geq 5x\\\\3 \geq x\\\\x \leq 3[/tex]

The value of the stock a year ago is $7778

The given parameters are:

Depreciation rate, r = 10%

Value of investment today, V(t) = $7000

The value of the stock a year ago is then calculated as:

Value of investment today = Value of investment last year * (1 - Depreciation rate)

Substitute the known values in the above equation

7000 = Last year * (1 - 10%)

Evaluate the difference of 1 and 10%

7000 = Last year * (90%)

Divide both sides by 90%

Last year = 7778

Hence, the value of the stock a year ago is $7778

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Answer:

Los números son 23 y 35.

Step-by-step explanation:

Q: The sum of two numbers is 58. If one of the numbers is 12 more than the other number, what are the numbers?

Set the numbers as x and y. Using the given information, we have two equations:

x+y=58

x=y+12

Solving using substitution, we have:

y+y+12=58 -> y=23

Substituting, x=23+12=35

The numbers are 23 and 35.

Hey there!

8!
= 8(7)(6)(5)(4)(3)(2)(1)

= 56(6)(5)(4)(3)(2)(1)

= 336(5)(4)(3)(2)(1)

= 1,680(4)(3)(2)(1)

= 6,720(3)(2)(1)

= 20,160(2)(1)

= 40,320(1)

= 40,320

Therefore, your answer should be:

40,320

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer: 5/36

Step-by-step explanation:

Answer:

144

Step-by-step explanation:

First find g(7) --

[tex]g(7)=2(7)-2\\=14-2\\=12[/tex]

Then plug 12 into f(x) --

[tex]f(12)=(12)^{2} \\=144[/tex]

Using the substitution method, the system of equation that is easily solved is:

c. y = 2x + 3

2x + y = 5

Using the substitution method to solve a system of equations is best when one of the equations have one isolated variable that we can simply plug its value into the second equation.

For example, given the system of equations:

y = 2x + 3 --> eqn. 1

2x + y = 5 --> eqn. 2

Substitute y = (2x + 3) into eqn. 2 and find x:

2x + y = 5 --> eqn. 2

2x + 2x + 3 = 5

4x + 3 = 5

4x = 5 - 3

4x = 2

x = 2/4

x = 1/2

Substitute x = 1/2 into eqn. 1 to find y

y = 2x + 3 --> eqn. 1

y = 2(1/2) + 3

y = 1 + 3

y = 4

From the above, we can see that the system of equations that is quite easy to solve using the substitution method is:

c. y = 2x + 3

2x + y = 5

The rest of the equations are quite different and not as straightforward as solving as this using the substitution method.

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Hello,

The triangle be right only if : 18² = 8² + 12²

We have : 18² = 18 × 18 = 324

and 8² + 12² = 8 × 8 + 12 × 12 = 208

324 ≠ 208 → the triangle can not be a right triangle

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

The given figure shows a vertical hyperbola with its centre at origin, and as we observe the figure, we can conclude that :

Length of transverse axis is :

[tex]\qquad \sf  \dashrightarrow \: 2b = 12[/tex]

[tex]\qquad \sf  \dashrightarrow \: b = 6[/tex]

length of conjugate axis is :

[tex]\qquad \sf  \dashrightarrow \: 2a = 8[/tex]

[tex]\qquad \sf  \dashrightarrow \: a = 4[/tex]

Equation of hyperbola ~

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {y}^{2} }{ {b}^{2} } - \cfrac{ {x}^{2} }{ {a}^{2} } = 1[/tex]

plug in the values ~

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {y}^{2} }{ {6}^{2} } - \cfrac{ {x}^{2} }{ {4}^{2} } = 1[/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {y}^{2} }{ {36}^{} } - \cfrac{ {x}^{2} }{ {16}^{} } = 1[/tex]

Answer:

[tex]\dfrac{y^2}{36}-\dfrac{x^2}{16}=1[/tex]

Step-by-step explanation:

Standard form equation of a vertical hyperbola

[tex]\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1[/tex]

where:

From inspection of the graph:

Substitute the found values into the formula:

[tex]\implies \dfrac{(y-0)^2}{6^2}-\dfrac{(x-0)^2}{4^2}=1[/tex]

[tex]\implies \dfrac{y^2}{36}-\dfrac{x^2}{16}=1[/tex]

Answer:

1/19

Step-by-step explanation:

The number in the set that are a multiple of both 4 and 6 is 12.

This is one number out of the 19 numbers in the set, so the probability is 1/19.

Answer:

  log(0.0003) = -3.5229

Step-by-step explanation:

The rules of logarithms tell you ...

  log(ab) = log(a) +log(b)

  log(0.0003) = log(3×10^-4) = log(3) +log(10^-4)

  = log(3) -4 = 0.4771 -4

  log(0.0003) = -3.5229

__

Additional comment

If you do much work with logarithms, you find that negative logarithms are generally expressed using a positive mantissa with a negative add-on. Often, that negative add-on is -9, so this would be ...

  5.4771-9

This helps when taking antilogs, as you look up 0.4771 in the table to see that the multiplier is 3.

If you were to look up 0.5229, you would find 3.333, meaning the multiplier is 1/3.333 and the antilog of -3.5229 is (10^-3)/3.333. This may not be a convenient value to work with.

Answer:

shown below

Step-by-step explanation:

Look at the white squares, count them. 1, 2, 3. the next will be 4 and 5. draw 4 white squares, then house it in black squares like the others. to know if u did it right, count the black squares, there should be 8, then 9.

Terminal point: (0, 1); sinФ = 1 ⇒ A

On a unit circle Ф = 90°

Using the second rule listed above

The terminal point is (0, 1)

sinФ = 1

Terminal point: (0, 1); sinФ = 1

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