Which expression is undefined?
A. 0➗7
B. 9/(-6+6)
C.(5-5)/8
D.(0-10/-5

\(\begin{array}{llll} \textit{Logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array}~\hfill~ \begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \stackrel{ \textit{we'll use this one} }{a^{log_a (x)}=x} \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log(3)+\log(x)=3\implies \log(3\cdot x)=3\implies \log(3x)=3 \implies \log_{10}(3x)=3 \\\\\\ 10^{\log_{10}(3x)}=10^3\implies 3x=10^3\implies x=\cfrac{10^3}{3}\implies x=\cfrac{1000}{3}\)

Answer:

50

Step-by-step explanation:

Parentheses first, but division before subtraction

9 -      28/7

9 -     4

9 - 4 = 5

30/3(5)

Now go left to right

10 x 5

50

Answer:

42

Step-by-step explanation:

60% is 3/5 of the total, and the total is 70. 70/5 is 14, and 14 x 3 is 42.

hope this helped!

To solve the exercise, we can use the formula for the frequency of simple harmonic motion in terms of the mass and spring constant.

The formula for the frequency of simple harmonic motion is given by:

f = 1 / (2π) * sqrt(k / m),

where f is the frequency, k is the spring constant, and m is the mass.

In the first part of the exercise, we are given that the frequency is 2/1 cycles/s and the mass is 20 kg. We need to find the value of the spring constant k.

We can rearrange the formula as follows:

k = (2πf)^2 * m.

Substituting the given values, we have:

k = (2π * (2/1))^2 * 20 = (4π)^2 * 20 = 16π^2 * 20 ≈ 1005.31 N/m.

Therefore, the value of the spring constant k is approximately 1005.31 N/m.

In the second part of the exercise, we are asked to find the frequency of simple harmonic motion if the mass is replaced with 80 kg. We can use the same formula, but with the new mass value.

f = 1 / (2π) * sqrt(k / m) = 1 / (2π) * sqrt(1005.31 / 80) ≈ 0.199 cycles/s.

Therefore, the frequency of simple harmonic motion with the mass of 80 kg is approximately 0.199 cycles/s.

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Answer:

7=x

Step-by-step explanation:

multiply 5 and 2x by 2, you'll then have (10+4x)=-4+6x. Then add 4 to both sides and you have (14+4x)=6x. Subtract 4x from both sides and that'll get you 14=2x and you divide 2 from each side to get x by itself so 7 is your answer.

Answer:

x = 10

Step-by-step explanation:

Answer:

No, but x = 4

Step-by-step explanation:

3(7) + 8 - 7 = 5(7) - 4

21 + 8 - 7 = 22

22 = 35 - 4

22 = 31

It is not

How this equation may work is by subtracting the numbers by each side

3x + 8 - x = 2x + 8

2x + 8 = 5x - 4

     -8          -8

2x = 5x - 12

-5x  -5x

-3x = -12

x = 4

Answer:

k=1

Step-by-step explanation:

so FG and FE are equal meaning same magnitude

formula for magnitude is √{x2-x1}+{y2-y1}

(the square root is for all of it)

so use line FG since you have both points

you get √7 as magnitude

then apply it to FE

√7=√(4-0)+(4-k)

you can square both sides to remove the root and you get k=1

(when calculating magnitude the value is always absolute no regard to signs)

Answer:

c

Step-by-step explanation:

Answer: C

Step-by-step explanation: Im not positive of this answer

Answer:

a = 1.5

b = 1.75

Step-by-step explanation:

First, we need to solve \((x+a)^2\) and replace the result in the initial equation as:

\(x^2+3x+4=(x+a)^2+b\\x^2+3x+4=x^2+2ax+a^2+b\)

Then, this equality apply only if the coefficient of \(x\) is equal in both sides and the constant is equal in both sides.

It means that we have two equations:

\(3x=2ax\\4=a^2+b\)

So, using the first equation and solving for a, we get:

\(3x=2ax\\3=2a\\a=\frac{3}{2}=1.5\)

Finally, replacing the value of a in the second equation and solving for b, we get:

\(4=a^2+b\\4=1.5^2+b\\b=4-1.5^2\\b=4-2.25\\b=1.75\)

Answer:

x²+15x+26

Step-by-step explanation:

zeros are x=-13, x=-2

x=-13 then x+13=0

x=-2 then x+2=0

(x+13) (x+2)

x²+15x+26

y=ax²+bx+c

The solution to the given quadratic equation by using the quadratic formula is x = -4 + i, -4 - i.

The quadratic formula can be used to solve any quadratic equation. It is represented by the formula;

\(x = (-b \± \sqrt{b^2 - 4ac)} / (2a)\)

where x is the variable that we want to solve for, and a, b, and c are coefficients of the quadratic equation. The quadratic equation in this case is;

x² + 8x + 17

Therefore, a is 1, b is 8, and c is 17.

Substituting these values into the quadratic formula, we have;

\(x = (-8 \± \sqrt{8^2 - 4(1)(17))} / (2(1))\)

This simplifies to;

\(x = (-8 \± \sqrt{(64 - 68))} / 2\)

This further simplifies to;

\(x = (-8 \± \sqrt{(-4))} / 2\)

Therefore, the answer is x = (-8 + 2i) / 2, (-8 - 2i) / 2.

Simplifying this equation by factoring 2 in the numerator, we get;

x = -4 + i, -4 - i.

This concludes the solution to the given quadratic equation by using the quadratic formula.

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The experimental probability of rolling a 1 or a 2 is 0.2.

Hence, Option A is correct.

We know that,

The experimental probability of an event is defined as the number of times the event occurred divided by the total number of trials.

In this case,

The event is rolling a 1 or a 3,

Which occurred ⇒  3 + 1

                           = 4 times.

Given that there are total number of trials = 20.

Therefore,

The experimental probability of rolling a 1 or a 3 = 4/20,

                                                                                = 1/5

                                                                                 = 0.2

Hence, the required probability is 0.2.

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The complete question is:

Sarah is playing a game in which she rolls a number cube 20 times. The results are recorded in the chart below. What is the experimental probability of rolling a 1 or a 3?

Number on cube:1,2,3,4,5,6

Number of times event occurs:3,6,1,5,3,2

A.0.2

B.0.3

C.0.6

D.0.83

Answer:

1) 5x - 4 ≥ 12

5x ≥ 12 + 4

5x ≥ 16

x ≥ 16/5

2) 12x + 5 ≤ -4

12x ≤ -4 - 5

12x ≤ -9

x ≤ -9/12

Step-by-step explanation:

The fixed cost for suit is $125 and for every additional day, the cost can be calculated as 30*x.

Therefore, the total cost is the sum of the fixed cost ($125) and the additional cost per additional day ($30x). So, the total cost y is:

y = 125 + 30x

To calculate the total cost after 3 days, we need to replace x by 3 on the initial equation as:

y = 125 + 30*3

y = 125 + 90

y = 215

Answers: 21. y = 125 + 30x

22. $215

Number of clients who do not play either the piano or the guitar is 22

To find the number of clients who do not play either instrument, we need to subtract the number of clients who play either the piano or the guitar or both from the total number of clients.

Let A be the set of clients who play the piano, and B be the set of clients who play the guitar. Then, we can use the formula A union B

|A ∪ B| = |A| + |B| - |A ∩ B|

where |A ∪ B| is the number of clients who play either the piano or the guitar or both, |A| is the number of clients who play the piano, |B| is the number of clients who play the guitar, and |A ∩ B| is the number of clients who play both instruments

Substituting the given values, we get

|A ∪ B| = 46 + 58 - 17

|A ∪ B| = 87

Therefore, the number of clients who do not play either instrument is:

109 - 87 = 22

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For every pound a company spends on advertising, it spends £0.45 on its website. Express the amount spent on advertising to the amount spent on its website as a ratio in its simplest form

Step-by-step explanation:

COMPANY HAS EARNED (IF) = 1 POUND

SPENDS ON WEBSITE = 0.45 POUND

THEN RATIO = 1-0.45÷ 0.45

                        = 0.55/0.45

                        =11/9

Answer:

22% of the two classes were elected to the student committee

Step-by-step explanation:

Given

class 9 : class 10 = 3:2 = 60% : 40%

Total fraction = 60% * 30% + 40% * 10% = 18% + 4% = 22%

The values in the table 2 and table 3 represents linear functions and table 1 represent nonlinear function.

A linear function is a function that represents a straight line on the coordinate plane. The standard form of a linear function is y = mx + b.

Here, 'm' is the slope of the line, 'b' is the y-intercept of the line, 'x' is the independent variable and 'y' (or f(x)) is the dependent variable.

From table 1:

(-2.5, 2) and (-1.5, 3)

Here, m =(3-2)/(-1.5+2.5)

m=1

Substitute m=1 and (x, y)=(-2.5, 2), we get

2=1(-2.5)+c

c=4.5

y=x+4.5

Verification: Put (x, y)=(0.5, 6)

6=0.5+4.5

6≠5

It is nonlinear function.

From table 2:

(-1, 0.8) and (1, 2.8)

Here, m =(2.8-0.8)/(1+1)

m=1

Substitute m=1 and (x, y)=(-1, 0.8), we get

0.8=1(-1)+c

c=1.8

y=x+1.8

Verification: Put (x, y)=(2, 3.8)

3.8=2+1.8

It is linear function.

From table 3:

(-3, 12) and (-2, 10)

Here, m =(10-12)/(-2+3)

m=-2

Substitute m=-2 and (x, y)=(-3, 12), we get

12= -2(-3)+c

c=6

y= -2x+6

Verification: Put (x, y)=(0, 6)

6=6

Put (x, y)=(-1, 8)

8= -2(-1)+6

8=8

It is linear function.

Therefore, the values in the table 2 and table 3 represents linear functions and table 1 represent nonlinear function.

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Answer: b. four fifths plus two fourths

Step-by-step explanation: Change the fractions to their equivalents in 20ths-- like finding the common denominator.

Divide the original denominator into 20, then multiply the result by the original numerator to get the new numerator.

4/5  20/5 = 4    4×4 = 16   so 4/5 is equivalent to 16/20

2/4   20/4 = 5    5×2 = 10   so  2/4 is equivalent to 10/20  

Add:    16/20 + 10/20 = 26/20

===========================================================

Explanation:

Water leaks out at a rate of 3 gallons for every 2 days. The unit rate is 3/2 = 1.5 gallons per day that's leaked out.

Let x be the number of days. After x days, the container leaks a total of 1.5x gallons of water. Set this equal to 75 and solve for x. We'll divide both sides by 1.5

1.5x = 75

x = 75/(1.5)

x = 50

It takes 50 days for the container to empty.

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

Here's another way to solve:

(3 gallons leaked)/(2 days) = (75 gallons leaked)/(x days)

3/2 = 75/x

3x = 2*75 .... cross multiply

3x = 150

x = 150/3

x = 50 days

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

Yet another way to solve:

3 gallons : 2 days

25*(3 gallons) : 25*(2 days) ..... multiply both parts by 25

75 gallons : 50 days

We multiplied by 25 to get that "3 gallons" to "75 gallons". You can use trial and error, or note that 75/3 = 25.

This equation x + (x + 1) + (x + 2) = negative 21 will be used.

Let the first Number is x.

We have to take 3 consecutive integers.

second Number is x+1

third Number is x+2.

Sum of these 3 consecutive integers is x+(x+1)+(x+2).

Sum of these 3 consecutive integers is given as negative21.

so we can write  x+(x+1)+(x+2)=negative 21.

by using above equation we can find the value of 3 numbers.

So the final equation will be x + (x + 1) + (x + 2) = negative 21.

Given Question is incomplete, Complete Question here:

Three consecutive integers have a sum of –21. Which equation can be used to find the value of the three numbers? x + x + x = negative 21 x + 2 x + 3 x = negative 21 x + (x + 1) + (x + 2) = negative 21 x + (x + 2) + (x + 4) = negative 21

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Answer:

0.7

Step-by-step explanation:

-4 - x1

3 - y1

2- x2

-1- y2

-1 - 3

2 - -4

-4

6

-4/6 = 0.7

Answer:

-4/6

Step-by-step explanation:

-1-3/2-(-4)=-4/6

The right-hand side of the given equation is rational and can be expressed as a ratio of two integers. Specifically, it can be expressed as the ratio of the integer 2 and the integer 1 raised to the power of\(2^n\).

To determine if the right hand-side of the given equation is rational, we need to evaluate the expression on the right-hand side and see if it can be expressed as a ratio of two integers.

Using the formula given on the left-hand side, we can simplify the right-hand side as follows:

\(1 - (1/2^n+1) / 1 - (1/2)\\= [(1 - 1/2^(n+1)) * 2] / [2 - 1]\\= (2 - 1/2^(n)) / 1\\= 2 - 1/2^n\)

Since 2 and\(1/2^n\) are both rational numbers (2 can be expressed as 2/1 and \(1/2^n as 1/(2^n/1))\), their difference \(2 - 1/2^n\) is also a rational number.

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Answer:

3.7

Step-by-step explanation:

.

Answer:

x−(−16)=−28+12

x−(−16)=−28+12

x+16=−28+12

x+16=(−28+12)

x+16=−16

x+16=−16

x+16−16=−16−16

x=−32

Irrational numbers are real numbers that can't be expressed as a fraction, p/q, where p and q are integers.

Thus, √13 is irrational number.

Thus, 4 1/3 and 8 are rational number.

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Answer:

1st one

Step-by-step explanation:

340 x 0.03 = 10.2 (in state)

84 x 0.11 = 9.24 (out of state)

10.2 + 9.24 + 11.25

= $30.69 monthly charge

hope it helps :)

The total monthly charge for a customer is given as $30.69.

Simplifying allows us to test each process and strategy to determine which is the most efficient and best suited for its specific goal.

here,

A phone provider costs each customer $11.25 per month. Furthermore, it charges $0.03 per minute for in-state calls and $0.11 for out-of-state calls.

Charge within the boundary  of state for 340 minutes = 340 x 0.03 = 10.2

Charge beyond the boundary  of state for 84 minutes  = 84 x 0.11 = 9.24

Total monthly charge = 10.2 + 9.24 + 11.25

                                = $30.69 monthly charge

Thus, A customer's total monthly price is shown as $30.69.

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as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.

\(\stackrel{f(x)}{y}~~ = ~~2x^2+4x\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~2y^2+4y} \\\\\\ x=2(y^2+2y)\implies \cfrac{x}{2}=y^2+2y\impliedby \begin{array}{llll} \textit{now let's complete the square}\\ \textit{to make it a perfect square trinomial}\\ \textit{by using our good friend, Mr "0"} \end{array} \\\\\\ \cfrac{x}{2}=y^2+2y(+1^2-1^2)\implies \cfrac{x}{2}=y^2+2y+1-1\implies \cfrac{x}{2}=(y^2+2y+1)-1\)

\(\cfrac{x}{2}+1=(y^2+2y+1^2)\implies \cfrac{x}{2}+1=(y+1)^2\implies \sqrt{\cfrac{x}{2}+1}=y+1 \\\\\\ \sqrt{\cfrac{x+2}{2}}=y+1\implies \sqrt{\cfrac{x+2}{2}}-1=y~~ = ~~f^{-1}(x)\)