Does this equation have exactly one solution?

13b+7=9b−33+4b

onde esta a altenaativas

Answer:

A = 3

Step-by-step explanation:

8a-4=-10a+50

8a-4+4=-10a+50+4

8a=-10a+54

8a+10a=-10a+54+10a

18a=54

54 / 18 = 3

A = 3

Answer:

y= 1.5x

Step-by-step explanation:

The y-intercept is 0 so we don't put anything there. The slope is 1.5. You can find the slope by using rise and run.

Answer:

Answer 93

Step-by-step explanation:

Answer:

x=30 cm

y=24 cm

Step-by-step explanation:

y=24 cm

x=√(24²+18²)=√[6²(4²+3²)]=6√(16+9)=6√25=6×5=30 cm

Answer:

Step-by-step explanation:

P is the exterior point to the circle with centre O

Radius = 5cm

Length of the tangent = 12 cm

Distance between the point and centre of the circle = x cm

We know that

The angle between the radius of the circle and the tangent at the point of contact is 90°

By Pythagoras Theorem

Hypotenuse² = Side²+Side²

⇛OP² = OT1² +PT1²

⇛x² = 24²+18²

⇛x² = 576+324

⇛x² = 900

⇛x² = 30²

⇛x = √(30)²

⇛x = √(30*30)

We know that

The lengths of tangents drawn from the exterior point to the circle are equal.

PT1 = PT2

Answer: Hence, the value of x=30cm and y = 18cm.

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Answer:

D.  sin 18°

Step-by-step explanation:

sin 18 because 18 + 72 = 90

Answer:

x

Step-by-step explanation:

(log to the base 3) of 27^x can be re-written as

x*(log to the base 3) of 27, which is equivalent to:

x*(log to the base 3 of 3^3)  =  x

So the answer is simply " x "

Answer:

\( \frac{6}{x} = \frac{8}{24} \)

\(8x = 144\)

\(x = 18\)

\( \frac{8}{24} = \frac{y}{12} \)

\(24y = 96\)

\(y = 4\)

So x = 18 and y = 4.

Answer:

Hello good morning

Step-by-step explanation:

Answer:

2/8×5=10/8=5/4

Step-by-step explanation:

2+5+0-6=7-6=1

The reason for the required step using property of equality are as follow:

1.  Subtraction property of equality.

2. Subtraction property of equality.

3.  Addition property of equality.

As given in the question,

The reason for the required step using property of equality are as follow:

1. 3x + 3 = 5 + x

3x - x + 3 = 5

2x + 3 = 5

Here

Subtraction property of equality is applied.

If x, y, and z are real numbers and x = y

then

x - z = y - z

2. 2x + 3 = 5

2x = 5-3

2x = 2

Here Subtraction property of equality is applied.

If a, b, and c are real numbers and a = b, then

a - c = b - c

3. -x - 1 = 3

-x = 3 + 1

-x = 4

Here Addition property of equality is applied.

If x, y and z are real numbers and x = y, then

x + z = y + z

Therefore, the reason for the required step using property of equality are as follow:

1.  Subtraction property of equality.

2. Subtraction property of equality.

3.  Addition property of equality.

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For the given figure, a parallel to b and l  parallel to m

                                          x° = 95°

                                          y° = 95°

                                          z =  85°  

From figure,

                  a || b    and l || m

                      ∠RUT = ∠aRU (Alternate interior angle)

                       ∠RUT = 85°

Again,

               ∠RUT +  ∠UTS = 180° (Co-interior angle)

               85° + x° = 180°

                 x° = 180° - 85°

                  x°  = 95°

again from figure,

                              x° = y° (Vertical opposite angle)

                              y° =  95°

also,

               ∠UTS +  z° = 180°  (Linear Pair)

                x° + z° = 180°

                  z° = 180° - x°

                     = 180° - 95°

                    z° = 85°

So from above calculation,

                                           x° = 95°

                                          y° = 95°

                                          z =  85°  

Hence option B is correct

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To determine how well Luke must score on exam B in order to do equivalently well as he did on exam A, we need to first standardize his score on exam A using z-scores.

A z-score represents the number of standard deviations a given data point is away from the mean. The formula for calculating z-scores is:

z = (x - μ) / σ

where x is the data point, μ is the mean, and σ is the standard deviation.

In this case, Luke's score on exam A has a z-score of:

z = (850 - 750) / 50 = 2

This means that his score on exam A is 2 standard deviations above the mean.

To do equivalently well on exam B, Luke needs to achieve a score that has the same z-score of 2. We can use the formula for z-scores again to determine what score he needs to achieve:

2 = (x - 38) / 5

Solving for x, we get:

x = 48

Therefore, Luke needs to score 48 on exam B in order to do equivalently well as he did on exam A.

It's important to note that we're assuming that the distributions of the two exams are both normal distributions. If this assumption is not valid, then our answer may not be accurate.

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Answer:

Collect Like terms...Then Take the LCM

1/4x -1/3x +3 - 2

-1/12x + 1

Or

1 - 1/12x .

Option D.

Answer:

the function rule is y=2x-2

The number of subscribers with land-line phones for any year after 2000, taking into account the 27% annual decline rate.

According to the given information, land-line phones are decreasing at a rate of 27% each year since 2000. This means that each year, the number of subscribers with land-line phones is reduced to 73% (100% - 27%) of the previous year's value.

To create a formula that models this scenario, we start with the initial number of subscribers in the year 2000, which is given as 10,000. We can express this as y(0) = 10,000, where y(0) represents the number of subscribers in the starting year (t = 0).

Based on the decline rate of 27% per year, we can express the relationship between the number of subscribers in a given year (y) and the number of subscribers in the previous year (y-1) as follows:

y = 0.73 * y(t-1)

Here, 0.73 represents the probability of retaining a land-line phone subscription from one year to the next, given the 27% annual decline rate. Multiplying this probability by the number of subscribers in the previous year gives us the estimated number of subscribers in the current year.

By iterating this formula year after year, we can estimate the number of subscribers with land-line phones for any given year after 2000.

For example, let's calculate the number of subscribers in the year 2023, which is 23 years after 2000 (t = 23). Using the formula, we can substitute t = 23 into the equation:

y(23) = 0.73 * y(22)

To find y(22), we substitute t = 22 into the equation:

y(22) = 0.73 * y(21)

We continue this process until we reach the starting year, y(0) = 10,000.

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Complete Question:

With the growing popularity of cell phones, a local phone company had a sharp decline in the number of customers with land-line phones in their homes. Suppose land-line phones are decreasing at a rate of 27% each year since 2000. Assume that there were 10,000 subscribers with land-line phones in the year 2000.

For convenience let t = the number of years after 2000 and y = number of subscribers with land-line phones.

A formula that models this scenario is

The remainder of the polynomial using the remainder theorem and factor theorem is 6.

Apply the remainder theorem,

When we divide a polynomial

f(x) by (x − c)

f(x) = (x − c)q(x) + r

f(c) = 0 + r

Here,

f(x)=(x−c)q(x)+rf(c)=0+r

and (x−c) is (x−(−2))

Therefore,

f(−2) = \((-2)^{4} - (-2)^3 - 3(-2)^2 + 4(-2) + 2\)

= 16 + 8 − 12 − 8 + 2

= 6

Hence, the remainder of the polynomial using the remainder theorem is 6.

Whereas using the factor theorem and doing synthetic division, we get,  

x = -2 is a zero of f(x), and x+2 is a factor of f(x). To factor f(x), we divide

the coefficients of the polynomial as follows -

         -2   |   1  -1    -3     4      2

                      -2   6    -6      4

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

                    1   -3   3    -2     6

Hence, we get that 6 is the remainder when (\(x^4-x^3-3x^2+4x+2\)) ÷ (x+2), using the factor theorem.

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The complete question is -

Find the remainder using the Remainder Theorem and Factor Theorem using the synthetic division of the given polynomial, \(x^4-x^3-3x^2+4x+2\) ÷ (x+2)

The correct option is that in science, a theory encompasses many hypotheses.

In science, a theory is a well-established explanation that is supported by scientific evidence and is extensively tested through experimentation and observation.

It's a big idea that includes several connected hypothese that have been thoroughly investigated and found to be true. A theory that hasn't been put to the test is called a hypothesis.

A hypothesis is a proposed explanation that is subject to further testing. It's an untested hypothesis that hasn't yet undergone experimental validation. Theories are the result of a drawn-out and labor-intensive process of experimentation and observation.

They can never be established as an absolute answer to a scientific problem. Instead, they lay the groundwork for additional investigation and experimentation in that field of study.

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Answer:

P=1538.461

Step-by-step explanation:

do it by the formula of

I=PRT, I=750 R=3.25% T=15

The graph C shows the proportional relationship between x and y.

A proportional relationship is defined as "y varies proportionally with x" or "y is directly proportional to x."

For the given question;

The graph of the proportional relationship are given.

For the graph C, the relation tween x and y is said to be proportional because when the value of x increases the value of y decreases and also this line passes from the origin.

Thus, the graph C shows the proportional relationship between x and y.

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Answer:

a = -3

Step-by-step explanation:

Step 1:  Since we're told that 5 to the power of a = 1/125, we can use the following equation to solve for a:

5^a = 1/125

Step 2:  Take the log of both sides

log(5^a) = log(1/125)

Step 3:  According to the power rule of logs, we can bring a down and multiply it by log(5):

a * log(5) = log (1/125)

Step 4:  Divide both sides by log(5) to solve for a:

(a * log(5) = log(1/125)) / log(5)

a = -3

Optional 5:  We can check our answer by plugging in -3 for a and seeing if we get 1/125 when completing the operation:

5^-3 = 1/125

1/(5^3) = 1/125 (rule of exponents states that a negative exponent creates a fraction with 1 as the numerator and the base (5) and exponent (-3 becoming 3) as the denominator

1/125 = 1/125

Answer:

A. Quadratic, degree 2

Step-by-step explanation:

The degree is found by simply finding the term with the power of, that is the highest. Which would be 2x^2. It is raised to the 2nd power, so the degree is 2.

Answer:

the number less than -1.5 would be 0-1 so it would be A)

The probability that a box of 40 light bulbs will last for 5 years is very low, due to the short mean lifetime of 2 months and the relatively high standard deviation of 0.25 months.

The mean lifetime of a particular type of light bulb is given as 2 months, and the standard deviation is given as 0.25 months. The mean lifetime represents the average time that the light bulbs will last, while the standard deviation represents how much the lifetimes of the bulbs vary from the mean.

To determine the probability that a box of 40 light bulbs will last for 5 years, we need to convert the given information into a format that we can work with. 5 years is equal to 60 months, and since we have 40 light bulbs, we can assume that the lifetimes of the bulbs are independent and identically distributed. This means that the probability of one bulb lasting for 60 months is the same as the probability of any other bulb lasting for 60 months.

Next, we need to calculate the standard deviation of the sample mean. The standard deviation of the sample mean represents how much the means of different samples of size 40 would vary from the population mean. The formula for the standard deviation of the sample mean is given by the following equation:

standard deviation of the sample mean = standard deviation of the population / square root of the sample size

In this case, the standard deviation of the population is given as 0.25 months, and the sample size is 40. Therefore, the standard deviation of the sample mean is:

0.25 / sqrt(40) = 0.0395

Now that we have the mean lifetime and the standard deviation of the sample mean, we can use the normal distribution to determine the probability that a box of 40 light bulbs will last for 5 years. We can assume that the lifetimes of the bulbs follow a normal distribution with a mean of 2 months and a standard deviation of 0.0395 months (which is the standard deviation of the sample mean).

To find the probability that a bulb will last for 60 months, we can use the following equation:

z = (x - μ) / σ

where z is the standard score, x is the value we want to find the probability for (60 months in this case), μ is the mean, and σ is the standard deviation.

Plugging in the values, we get:

z = (60 - 2) / 0.0395 = 1509.49

To find the probability corresponding to this standard score, we can use a standard normal distribution table or a calculator. The probability is extremely small (close to zero), which means that it is highly unlikely that all 40 light bulbs will last for 5 years.

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Answer:

105cm

Step-by-step explanation:

first convert 1.5 metres to cm;

1m = 100cm

1.5 =?

1.5×100= 150cm

we then subtract:

255-150=105cm

Answer:

Step-by-step explanation:

d = 4 cm   ⇒  r = 2 cm

so:

\(V=\frac13\pi r^2\cdot H=\frac13\pi\cdot 2^2\cdot8\approx\frac13\cdot3.1415926...\cdot32=33.51032...\approx33.5\ cm^3\)

Answer:

47/53 or 0.88 or 88%

Step-by-step explanation:

Answer:

2.48

Step-by-step explanation:

Answer: is there a graph

Step-by-step explanation: