i need help with 23-26 help please​

Answer:

x = -2

Step-by-step explanation:

I am not sure you typed this correctly.

the way you wrote this, it says

f(x) = (3/2)x - 3

but I suspect you mean

f(x) = 3/(2x) - 3

our even

f(x) = 3/(2x - 3)

I assume the last one.

3/(2x - 3) = 5x + 4

that is what is meant by f(x)=g(x) : find out the value(s) of x for which the y/result values of both functions are the same.

so, then we can transform

3 = (5x + 4)×(2x - 3)

3 = 10x² -15x + 8x - 12

10x² - 7x - 15 = 0

and this can be solved by the solution squared equations :

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case here

a = 10

b = -7

c = -15

so,

x = (7 ± sqrt(49 - 4×10×-15))/20 = (7 ± sqrt(49+600))/20 =

≈ (7 ± 25.48)/20

x1 = -18.48/20

x2 = 32.48/20

these are really not nice numbers for a homework or such.

so, let's try the next interpretation of what you wrote.

f(x) = 3/(2x) - 3

3/(2x) - 3 = 5x + 4

3/(2x) = 5x + 7

3 = 10x² + 14x

10x² + 14x - 3 = 0

a = 10

b = 14

c = -3

x = (-14 ± sqrt(196 - 4×10×-3))/20 =

= (-14 ± sqrt(196 + 120))/20 = (-14 ± 17.78)/20

that did not give any good numbers either.

so, next attempt :

f(x) = (3/2)x - 3 = 3x/2 - 3

3x/2 - 3 = 5x + 4

3x/2 = 5x + 7

3x = 10x + 14

7x = -14

x = -2

ok, so it seems the first, original interpretation was correct. sorry.

but just in case, please use the other 2 approaches if and as needed.

Answer:

  x = 90°

Step-by-step explanation:

We assume that angle x° is measured to a tangent to the circle.

__

The angle between a radius and the tangent to a circle is always 90°.

  x = 90°

Using the normal distribituion, it is found that 2.28% of of scores were less than 40.

In a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

In this problem, the mean and the standard deviation are given by, respectively:

\(\mu = 52, \sigma = 6\).

The proportion of scores that were less than 40​ is the p-value of Z when X = 40, hence:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{40 - 52}{6}\)

\(Z = -2\)

\(Z = -2\) has a p-value of 0.0228.

2.28% of of scores were less than 40.

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Answer:

\(a_n=-301 +37(n-1)\)

Step-by-step explanation:

arithmetic sequence formula:  \(a_n=a +(n-1)d\)

where \(a\) is the first term and \(d\) is the common difference

Given:

  \(a_{10}=32\)

⇒ \(a +(10-1)d=32\)

⇒ \(a+9d=32\)

Given:

    \(a_{12}=106\)

⇒ \(a +(12-1)d=106\)

⇒ \(a+11d=106\)

Rearrange the first equation to make \(a\) the subject:

a = 32 - 9d

Now substitute into the second equation and solve for \(d\)

    (32 - 9d) + 11d = 106

⇒ 32 + 2d = 106

⇒ 2d = 106 - 32 = 74

⇒ d = 74 ÷ 2 = 37

Substitute found value of \(d\) into the first equation and solve for \(a\):

a + (9 x 37) = 32

a + 333 = 32

a = 32 - 333 = -301

Therefore, the equation is: \(a_n=-301 +37(n-1)\)

Answer:

36:56

Step-by-step explanation:

Answer: C 34:55

Step-by-step explanation:

start with 6:8 that’s the first one multiply by 9 on each side you get 54:72 so that’s the same and then 6:8 divide by 2 and you get 3:4 but for 36:56 you’d have to multiply by 6 and that would give you 36:48 not 36:56

Answer:

\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)

Step-by-step explanation:

Use Quotient Rule to find f'(x)

\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)

Find f'(1) using f'(x)

\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)

Answer:

\(f'(1)=-\dfrac{9}{e^{3}}\)

Step-by-step explanation:

Given rational function:

\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)

To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)

\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)

\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)

Therefore:

\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)

\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)

\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)

To find f'(1), substitute x = 1 into f'(x):

\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)

\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)

\(f'(1)=-\dfrac{9}{e^{3}}\)

Answer:

Step-by-step explanation:

In order to write the equation of the line in point-slope form that goes through those points, we need to know the slope of that line. Therefore,

\(m=\frac{-7-5}{4-10}=\frac{-12}{-6}=2\) So the slope is 2. Now we'll pick a point and use it to write an equation in point-slope form. I'll use the first point given to see if that's the one used in any of the answers : (10, 5)

y - 5 = 2(x - 10). That's choice B. Let's see, just in case there are 2 answers to this, what the equation would be using the other point (4, -7):

y - (-7) = 2(x - 4) and simplified:

y + 7 = 2(x - 4) is the other equation. Since that's not a choice, the only answer is B

The following elements were included in the response: labeling x-axis as age, labeling y-axis as texting speed, plotting points according to age and texting speed, and identifying a relationship between texting speed and age.

In the response, the following elements were included:

1. Labeling the x-axis as the input variable, age: This is important to indicate the independent variable being plotted.

2. Labeling the y-axis as the output variable, texting speed: This is crucial to indicate the dependent variable being represented.

3  Plotting the points according to age and texting speed: This involves placing the ordered pairs (age, texting speed) on the coordinate plane, with age values on the x-axis and texting speed values on the y-axis.

4. Identifying a relationship between the change in texting speed as age increases: By analyzing the plotted points and examining the pattern or trend, one can determine if there is a relationship between age and texting speed. For example, if the texting speed generally increases as age increases or if there is a linear or nonlinear relationship between the two variables.

Including all of these elements allows for a comprehensive analysis of the relationship between age and texting speed, providing a visual representation and enabling the identification of any patterns or trends.

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In summary, the difference between these two regression equations is mainly in the notation used to represent the regression coefficients, with lowercase letters used in simple linear regression models and uppercase letters used in multiple linear regression models.

In mathematics, an equation is a statement that asserts that two mathematical expressions are equal to each other. It usually contains one or more variables, which are placeholders for values that can vary. Equations are used to describe mathematical relationships and to solve problems. They can take many forms, such as linear equations, quadratic equations, polynomial equations, exponential equations, and so on. The specific form of an equation depends on the type of problem being solved and the mathematical relationships involved.

Here,

Both the regression equations ^y = b0 + b1x and Y = B0 + B1x are used to model the relationship between a dependent variable (y or Y) and an independent variable (x). However, the key difference between these two equations lies in the notation used to represent the regression coefficients.

In the first equation ^y = b0 + b1x, the regression coefficients are represented with lowercase letters (b0 and b1). This notation is typically used in simple linear regression models where there is only one independent variable. The hat symbol (^) over the y indicates that this is an estimated value of y based on the model.

In the second equation Y = B0 + B1x, the regression coefficients are represented with uppercase letters (B0 and B1). This notation is typically used in multiple linear regression models where there are two or more independent variables. The capitalization of the letters helps to distinguish them from the coefficients in the simple linear regression model.

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Answer:

x=21

Step-by-step explanation:

45+x+the last angle=180

x+159=180

180-159=21

21+45= 66

180-66=114

so i think x would be 21 degrees but im not entirely sure do not quote me on this sorry

Answer:

-10 is the second term

Step-by-step explanation:

After the first term each term is obtained from the previous one by adding 10.

c(1) = -20

so c(2) = -20 + 10

= -10.

Answer: 2 because The second term: c(2) = 30. Step-by-step explanation: c(n) = c(n - 1) + 10​. c(1) =20. c(2) = c(1) + 10 = 20 + 10 = 30.

Step-by-step explanation:

I SMART AT MATH  (>‿◠)✌

The Emily soccer team has the higher ratio of wins to losses.

Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.

The ratio of a and b is denoted as a : b.

Given that,

Ratio of win to loss of Emily soccer team = 9 : 12

Ratio of win to loss of Grant soccer team = 10 : 15

9 : 12 = 9 / 12 = (9 × 5) / (12 × 5) = 45 / 60

10 : 15 = 10 / 15 = (10 × 4) / (15 × 4) = 40 / 60

If 60 games are losses, then 45 games are wins for Emily soccer team.

If 60 games are losses, then 40 games are wins for Grant soccer team.

Higher ratio is for Emily soccer team.

Hence higher ratio of wins to losses is for Emily soccer team.  

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Answer:

f = -6

Step-by-step explanation:

Answer:

\(105.13ft^2\)

Step-by-step explanation:

Rectangle

\(A=lw\\=10*8\\=80ft^2\\\)

Semicircle

\(A=\frac{1}{2} \pi r^2\\=\frac{1}{2}* \pi *4^2\\=25.13ft^2\)

Add both values together

\(80+25.13\\=105.13ft^2\)

Answer: 105.13

Step-by-step explanation:

Answer:.

Step-by-step explanation:

...

The average number of touchdown passes that the quarterback throws per game is 3 and this can be determined by using the unitary method.

Given :

An NFL quarterback throws 48 touchdown passes in 16 games.

The following steps can be used in order to determine the average number of touchdown passes that the quarterback throws per game:

Step 1 - The unitary method can be used in order to determine the average number of touchdown passes that the quarterback throws per game.

Step 2 - According to the given data, the NFL quarterback throws 48 touchdown passes in 16 games.

Step 3 - So, the total number of touchdown passes thrown in 1 game is:

\(=\dfrac{48}{16}\times 1\)

= 3 touchdown passes

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Answer:

40hsbdkankahjwdjbdifbcud

The money Jena will have after buying a set of markers in algebra expression is y = 15 - x.

Arithmetic operations like subtraction, addition, division, multiplication, and exponentiation are used to combine variables and integers to produce any algebraic expression. A variable, a number, or a variable and number with an exponent as a product can all be used as the phrase.

Cost is the amount of money spent by a business to produce or create goods or services.

The cost of one set of markers is x dollars.

Now Jen has a total of $15.

Then, the amount of money "y" Jena will have after buying one set of markers will be:

y = 15 - x

Hence, the algebraic expression after buying one set of markers is y = 15 - x.

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With a 12% housekeeping gratuity, the hotel bill for 4 nights comes to $891.52.

"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."

We always count the unit or amount value first and then calculate the more or less amount value.

For this reason, this procedure is called a unified procedure.

Many set values ​​are found by multiplying the set value by the number of sets.

A set value is obtained by dividing many set values ​​by the number of sets.

According to our question-

Total cost = Bill before tip + Tip

Total cost = $796 + $95.52

Total cost = $891.52

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The range of the equation f(x) = 3ˣ ⁻ ¹ - 2 is  y > -2

From the question, we have the following parameters that can be used in our computation:

f(x) = 3ˣ ⁻ ¹ - 2

The above equation is an exponential function

The rule of an exponential function is that

In this case, it is -2

So, the range is y > -2

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Answer:

The triangles are similar.

Explanation:

Similar triangles have 3 pairs of congruent angles. In this diagram, we can see that the triangles WXP and WYZ share angle W, which is congruent to itself; therefore, they have at least 1 pair of congruent angles. We are given that angle X is congruent to angle Y, so that is a second pair of congruent angles. Finally, we know that angle P is congruent to angle Z because if two pairs of corresponding angles are congruent, then the third pair must also be congruent because the measures of the interior angles of both triangles have to add to 180°.

Answer:

Option A is the right answer mate...

The correct statement regarding Isaiah is that A. His gross pay is $3,000 and net pay is $2,500

Before taxes, benefits, and other payroll deductions are taken out of an employee's paycheck, that amount is known as their gross pay. Net pay, often known as take-home pay, is the amount that is left after all withholdings have been taken into account. Determining the number of pay periods you have throughout the year is the first step in calculating the gross compensation for a salaried employee.

The time range for which you pay your employee is known as a pay period. You must first determine your employee's gross compensation before you can determine their net pay. This is where you should start. The next thing you need to know is what payroll deductions your employee receives.

Since the take-home pay is $2,500, this is the net pay.

In conclusion, the correct option is A.

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Isaiah works at a technology company in the summer and earns

$3000. After federal, state, and Social Security/Medicare taxes are

deducted, his take-home pay is $2,500. Which of the statements

below is CORRECT? *

His gross pay is $3,000 and net pay is $2,500

His gross and net pay are $3,000

His gross and net pay are $2,500

His gross pay is $2,500 and net pay is $3,000

Answer:

Option 3

Step-by-step explanation:

Each value of x maps onto one value of y and vice versa.

Answer:

Step-by-step explanation:

The way that the definitions of the absolute value of a number, connect is that the absolute value of a number is the positive representation of the number's distance from zero.

The absolute value of a number is the numerical value of a real number without regard to its sign. In other words, the absolute value of a number is the number's distance from zero on the number line. The absolute value of a number is always positive or zero, and is written as the number inside of absolute value notation, which is two vertical lines on either side of the number, like so: |number|. For example, the absolute value of -5 is 5, and the absolute value of 5 is also 5.

The distance from zero is the same as the magnitude of a number, and the absolute value of a number is a non-negative representation of its magnitude. So, in other words, the absolute value of a number is its distance from zero on the number line. The two definitions are connected because the absolute value of a number is a positive representation of its distance from zero.

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Hence the minimum value of x is 18 cm

a minimal requirement of coverage that is applicable to employment-based health plans. You cannot receive a premium tax credit if you purchase a Marketplace insurance plan if your employer's plan satisfies this criterion and is deemed "affordable."

given,

Within 10 cm of the A, a laser beam will pierce the water.

Snell's law permits us to state:

\(n_{1}sin\alpha ^{2} = n_{2}sin\beta^{2}\)

Where,

is equal to 1, which is air's refractive index.

a measure of water's refractive index is \(n_{2}\) = 1.33

At the interface, we can formulate a formula using Sell's law.

θ\(_{2}\) = 38.7°

x= 18 cm

hence the minimum value of x is 18 cm.

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Answer:

a) 0.1992 = 19.92% probability of finding fewer than two potholes in a quarter-mile stretch of the highway.

b) 0.8008 = 80.08% probability of finding more than one pothole in a quarter-mile stretch of the highway.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

\(P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}\)

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\(\mu\) is the mean in the given interval.

a. Find the probability of finding fewer than two potholes in a quarter-mile stretch of the highway.

Mean of 12 potholes per mile, which means that in a quarter-mile stretch, the mean is \(\mu = \frac{12}{4} = 3\)

This probability is:

\(P(X < 2) = P(X = 0) + P(X = 1)\)

In which

\(P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}\)

\(P(X = 0) = \frac{e^{-3}*(3)^{0}}{(0)!} = 0.0498\)

\(P(X = 1) = \frac{e^{-3}*(3)^{1}}{(1)!} = 0.1494\)

\(P(X < 2) = P(X = 0) + P(X = 1) = 0.0498 + 0.1494 = 0.1992\)

0.1992 = 19.92% probability of finding fewer than two potholes in a quarter-mile stretch of the highway.

b. Find the probability of finding more than one pothole in a quarter-mile stretch of the highway.

This is

\(P(X > 1) = 1 - P(X < 2)\)

We have that \(P(X < 2) = 0.1992\)

So

\(P(X > 1) = 1 - P(X < 2) = 1 - 0.1992 = 0.8008\)

0.8008 = 80.08% probability of finding more than one pothole in a quarter-mile stretch of the highway.

Answer:

x= 1325 ft (nearest foot)

Step-by-step explanation:

Please see the attached pictures for the full solution.