Find the measure of angle x.

Answer:

9 7/8

Step-by-step explanation:

1. 4 3/8 can be converted into the improper fraction 35/8, and 5 1/2 can be converted into 11/2.

2. Now that we have 35/8 + 11/2, we have to find a common denominator. Since 2 goes into 8 four times, we can turn 11/2 into 44/8 by multiplying the numerator and denominator (the top and the bottom numbers) by 4.

3. Now we have 35/8 + 44/8. At this point, the all we have to do is add the numerators (the top numbers). 35+44=79, so our answer is 79/8, which we can simplify to 9 7/8.

Answer:

A

Step-by-step explanation:

With function transformation, added/subtracted numbers outside of the x always mean the function is being translated up/down. In this case, since the 2 is being replaced with a 4, the new function is 2 units higher than the previous function.

Answer:

0.00907

Step-by-step explanation:

Answer:

0.00907

Step-by-step explanation:

Answer:

\(\displaystyle a = \frac{-11}{3}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

\(\displaystyle 9 = (\frac{1}{27})^{a + 3}\)

Step 2: Solve for a

Answer:

%88.88... and on and on

Formula Nonsense: percentage = b/l then *100 add % sign

so P= 32/36 so 0.888....*100= 88.88... so she made 88%

Answer:

Step-by-step explanation:

speed = 50 km / hr.

distance = 20 km

time = distance / speed.

time = ( / 50) hr.

speed =  2 km/hrs

Given, (9x - 4)(9x + 4) = ax² - b

From algebraic identities:

We know, (a + b)(a - b) = a² - b²

Now, 81x² + 36x - 36x - 16 = ax² - b

81x² - 16 = axis² - b

So ax² = 81x²

a = 81

-b = -16

b = 16

Solution

Therefore, the value of a is 81.

Answer:

The value of a is 81

Step-by-step explanation:

The solution is in the image

If a triangle has one side length of 9cm and another side of .12cm . The 3 possible answers for the third side​ are:  17, 20, and 21.

To determine the possible lengths for the third side of the triangle, we can use the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side.

Using this theorem, the possible lengths for the third side can be found by checking which of the following inequalities hold:

   9 + 12 > x

   9 + x > 12

   12 + x > 9

Simplifying these inequalities, we get:

   x > -3 (always true)

   x > -9 (always true)

   x > -3 (always true)

Therefore, the possible lengths for the third side of the triangle must satisfy x > -9, which eliminates the answer 3 (which is less than 9 - 12 = -3).

The possible lengths for the third side are:

   9 + 12 > x, so x < 21

   9 + x > 12, so x > -3

   12 + x > 9, so x > -3

Therefore, the possible lengths for the third side of the triangle are:

   17 (9 + 12 = 21, which is greater than 17)

   20 (9 + 12 = 21, which is greater than 20)

   21 (9 + 12 = 21, which is equal to 21)

So, the three possible lengths for the third side of the triangle are 17, 20, and 21.

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The complete question is:

A triangle has one side length of 9

centimeters (cm) and another side length of 12

cm.

Which answers are possible lengths for the third side?

Select three that apply

17

22

9

21

20

3

Let's look at some logarithm properties,

We will use this properties to simplify and write the expression as a single logarithm.

The steps are shown below:

The expression, as a single logarithm, is,

From the answer choices, the correct answer is D.

Answer

D

Answer:

Step-by-step explanation:

4x – 1.9 = 22.2 4x – 22.2 = 1.9 4x + 1.9 = 22.2 4x + 22.2 = –1.9 22.2 – 4x = 1.9

Answer: c and E

Step-by-step explanation:

Answer:

0.0005123

Step-by-step explanation:

The scientific notation 5.123e-4 is same as 5.123×10^-4 or 5.123×10-4. Thus, to get the answer to 5.123e-4 as a decimal, we multiply 5.123 by 10 to the power of -4.

= 5.123e-4

= 5.123 × 10-4

= 0.0005123

Answer:

\(^{}\)nk to the answer:

ly/3fcEdSx

bit.\(^{}\)

Step-by-step explanation:

Answer:

answer is B

hope it helps. tell me if its wrong pls ! stay safe :D

Answer:

f(2) = 1

x = 0

Step-by-step explanation:

f(2) = 1 since y=1 when x=2.

f(0) = -3 since x=0 when y=-3

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

Explanation:

Both AB and XY are the first two letters of ABC and XYZ respectively. So we have one fraction of AB/XY = 2/7.

AC and XZ are the first and last letters of ABC and XYZ respectively. We can form another fraction AC/XZ. I'm dividing in the same order of small over large to keep things consistent. As you can probably guess, the order of the letters ABC and XYZ are important so we see how the angles match up and how the proportional sides match up.

Because the triangles are similar, the two fractions formed earlier are equal to one another.

The equation we need to solve is AB/XY = AC/XZ

-----

AB/XY = AC/XZ

2/7 = 3/N ... plug in given values

2N = 7*3 .... cross multiply

2N = 21

N = 21/2 .... divide both sides by 2

N = 10.5

ZX is 10.5 units long.

Answer:

16,800 people

Step-by-step explanation:

105 * 250 = 26,250

p = 26250ft² * (16 people / 25ft²)

p = 16,800 people

Answer:

16800

Step-by-step explanation:

105 x 250 = 26250 and then divide it by 25 which is 1050 then multiply by 16 which is 16800

Hope this helps!

The amount of Duane's first payment that goes to interest is approximately $26.47.

To determine the amount of Duane's first payment that goes to interest, we need to use the amortization formula for a loan.

The formula to calculate the interest portion of a loan payment is:

Interest = Remaining Balance * Monthly Interest Rate.

Let's calculate the interest for the first payment using the given information:

Loan Amount = $5,000.00

Monthly Payment = $118.57

First, we need to calculate the monthly interest rate:

Monthly Interest Rate = Annual Interest Rate / 12

= 6.5% / 12

= 0.00542

Next, we need to calculate the remaining balance after the first payment:

Remaining Balance = Loan Amount - Principal Paid

= $5,000.00 - $118.57

= $4,881.43

Finally, we can calculate the interest portion of the first payment:

Interest = Remaining Balance * Monthly Interest Rate

= $4,881.43 * 0.00542

= $26.47

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Answer:

1)  The functions are not inverses.

\(\textsf{2)} \quad g^{-1}(n)=&\dfrac{3}{8}n-\dfrac{7}{8}\)

\(\textsf{3)} \quad g^{-1}(x)&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}\)

Step-by-step explanation:

The inverse composition rule states that if two functions are inverses of each other, then their compositions result in the identity function.

Given functions:

\(g(x) = 4 + \dfrac{7}{2}x \qquad \qquad f(x) = 5 - \dfrac{4}{5}x\)

Find g(f(x)) and f(g(x)):

\(\begin{aligned} g(f(x))&=4+\dfrac{7}{2}f(x)\\\\&=4+\dfrac{7}{2}\left(5 - \dfrac{4}{5}x\right)\\\\&=4+\dfrac{35}{2}-\dfrac{14}{5}x\\\\&=\dfrac{43}{2}-\dfrac{14}{5}x\\\\\end{aligned}\)                 \(\begin{aligned} f(g(x))&=5 - \dfrac{4}{5}g(x)\\\\&=5 - \dfrac{4}{5}\left(4 + \dfrac{7}{2}x \right)\\\\&=5-\dfrac{16}{5}-\dfrac{14}{5}x\\\\&=\dfrac{9}{5}-\dfrac{14}{5}x\end{aligned}\)

As g(f(x)) or f(g(x)) is not equal to x, then f and g cannot be inverses.

\(\hrulefill\)

To find the inverse of a function, swap the dependent and independent variables, and solve for the new dependent variable.

Calculate the inverse of g(n):

\(\begin{aligned}y &= \dfrac{8}{3}n + \dfrac{7}{3}\\\\n &= \dfrac{8}{3}y + \dfrac{7}{3}\\\\3n &= 8y + 7\\\\3n-7 &= 8y\\\\y&=\dfrac{3}{8}n-\dfrac{7}{8}\\\\g^{-1}(n)&=\dfrac{3}{8}n-\dfrac{7}{8}\end{aligned}\)

Calculate the inverse of g(x):

\(\begin{aligned}y &= 1-2x^3\\\\x &= 1-2y^3\\\\x -1&=-2y^3\\\\2y^3&=1-x\\\\y^3&=\dfrac{1}{2}-\dfrac{1}{2}x\\\\y&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}\\\\g^{-1}(x)&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}\\\\\end{aligned}\)

Answer:

1.

If the composition of two functions is the identity function, then the two functions are inverses. In other words, if f(g(x)) = x and g(f(x)) = x, then f and g are inverses.

For\(\bold{g(x) = 4 + \frac{7}{2}x\: and \:f(x) = 5 -\frac{4}{5}x}\), we have:

\(f(g(x)) = 5 - \frac{4}{5}(4 + \frac{7}{2}x)\\ =5 - \frac{4}{5}(\frac{8+7x}{2})\\=5 - \frac{2}{5}(8+7x)\\=\frac{25-16-14x}{5}\\=\frac{9-14x}{5}\)

\(g(f(x)) = 4 + (\frac{7}{5})(5 - \frac{4}{5}x) \\=4 + (\frac{7}{5})(\frac{25-4x}{5})\\=4+ \frac{175-28x}{25}\\=\frac{100+175-28x}{25}\\=\frac{175-28x}{25}\)

As you can see, f(g(x)) does not equal x, and g(f(x)) does not equal x. Therefore, g(x) and f(x) are not inverses.

Sure, here are the inverses of the functions you provided:

2. g(n) = (8/3)n + 7/3

we can swap the roles of x and y and solve for y to find the inverse of g(n). In other words, we can write the equation as y = (8/3)n + 7/3 and solve for n.

y = (8/3)n + 7/3

n =3/8*( y-7/3)

Therefore, the inverse of g(n) is:

\(g^{-1}(n) = \frac{3}{8}(n - \frac{7}{3})=\frac{3}{8}*\frac{3n-7}{3}=\boxed{\frac{3n-7}{8}}\)

3. g(x) = 1 - 2x^3

We can use the method of substitution to find the inverse of g(x). We can substitute y for g(x) and solve for x.

\(y = 1 - 2x^3\\2x^3 = 1 - y\\x = \sqrt[3]{\frac{1 - y}{2}}\)

Therefore, the inverse of g(x) is:

\(g^{-1}(x) =\boxed{ \sqrt[3]{\frac{1 - x}{2}}}\)

The limit of the function as x approaches -2 is 20.To find the limit of the function (if it exists), we can substitute the given value into the function and simplify. Given function: f(x) = 4x² + 5x - 6x + 2

To find the limit as x approaches -2, we substitute -2 into the function:

f(-2) = 4(-2)² + 5(-2) - 6(-2) + 2
      = 4(4) - 10 + 12 + 2
      = 16 - 10 + 12 + 2
      = 20

Therefore, the limit of the function as x approaches -2 is 20.

To write a simpler function that agrees with the given function at all but one point, we can use a graphing utility. By plotting the given function and observing its behavior, we can create a simpler function that matches the original function except at one point.

However, without further information about the specific behavior of the given function, it is not possible to provide a more detailed explanation or a graph of the simpler function.

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Length of bike route A is 12(65)=780 and length of bike route B is 65.

Two or more expressions with an Equal sign is called as Equation.

Given that the Bike route A is 12 times as long as bike route B.

Let x be the length of the bike route B.

12x be the  length of the bike route B.

The total length of the bike trails is 845 miles

12x+x=845

13x=845

Divide both sides by 13

x=65

Length of bike route A is 12(65)=780 and length of bike route B is 65.

Hence, Length of bike route A is 12(65)=780 and length of bike route B is 65.

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Answer:

The answer would be 98.

Step-by-step explanation:

You divide 700 by 50. Then multiply by 7.

Answer:

238

Step-by-step explanation:

Complete Question

The complete question is shown on the first uploaded image

Answer:

a

\(33.55 <  \mu < 35.5\)

b

\(34.03 <  \mu < 34.969 \)

c

Generally the width at  n =  49 is mathematically represented as

   \(w =  2 *  E\)

    \(w =  2 *  0.952 \)

     \(w =  1.904 \)

Generally the width at  n =  196 is mathematically represented as

   \(w =  2 *  E\)

    \(w =  2 *  0.4687 \)

     \(w =  0.9374  \)

d

The correct option is E

Step-by-step explanation:

From the question we are told  that

   The sample mean is  \(\= x  =  34.5\)

    The standard deviation is  \(s =  3.4\)

Generally given that the confidence level is 95% then the level of significance is  

       \(\alpha = (100 -  95)\%\)

=>     \(\alpha = 0.05 \)

Generally from the normal distribution table the critical value  of  \(\frac{\alpha }{2}\) is  

   \(Z_{\frac{\alpha }{2} } =  1.96\)

Considering question a

From the question  n  =  49

Generally the margin of error is mathematically represented as  

      \(E = Z_{\frac{\alpha }{2} } *  \frac{s }{\sqrt{n} }\)

=>   \(E = 1.96*  \frac{ 3.4 }{\sqrt{49} }\)

=>   \(E =  0.952 \)

Generally 95% confidence interval is mathematically represented as  

      \(\= x -E <  p <  \=x  +E\)

      \(34.5 -0.952 <  p < 34.5 + 0.952\)

=>    \(33.55 <  \mu < 35.5\)

Considering question b

From the question  n  =  196

Generally the margin of error is mathematically represented as  

      \(E = Z_{\frac{\alpha }{2} } *  \frac{s }{\sqrt{n} }\)

=>   \(E = 1.96*  \frac{ 3.4 }{\sqrt{196} }\)

=>   \(E =  0.4687 \)

Generally 95% confidence interval is mathematically represented as  

      \(\= x -E <  p <  \=x  +E\)

      \(34.5 -0.4687 <  p < 34.5 +0.4687\)

=>   \(34.03 <  \mu < 34.969 \)

Considering question c

Generally the width at  n =  49 is mathematically represented as

   \(w =  2 *  E\)

    \(w =  2 *  0.952 \)

     \(w =  1.904 \)

Generally the width at  n =  196 is mathematically represented as

   \(w =  2 *  E\)

    \(w =  2 *  0.4687 \)

     \(w =  0.9374  \)

Now when the sample size is quadrupled i.e from n = 49 to  n =  196  

The width of the  confidence interval  decrease by 2 from 1.904 to  0.9374  

The equations that can be used to determine the length of the room are:

y(y + 5) = 750

y²– 5y = 750

(y - 30) (y + 25) = 0

A rectangle is a 2-dimensional object that has four sides and four right angles. A rectangle has two diagonals of equal length which bisect each other at right angles.

Area of a rectangle = length x width

750 = y x (y - 5)

750 = y² - 5y

y² - 5y - 750 = 0

The factors of -750y² that add up to -5y are 25y and -30

(y² + 25y)(-30y - 750) = 0

y(y + 25) = 0

-30(y + 25) = 0

(y - 30) (y + 25) = 0.

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The amount of money she will have to pay for booking of the holidays would be = £220

The total amount of money that will cost Merrisa for booking of holidays = £660

The fraction of the total cost that she needs to deposit = 1/3

Therefore, the actual amount that she needs to deposit = 1/3 of £660

= 1/3× 660

= £220

Therefore, in conclusion, Merrisa would have to pay a total of £220 for booking of the holidays. This total amount is ⅓ of total cost of booking.

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The rational function graphed in this problem is given as follows:

D. F(x) = x/[(x + 4)(x - 1)]

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator, hence they are given as follows:

x= -4 and x = 1.

Hence the denominator of the function is given as follows:

(x + 4)(x - 1).

The intercept is given as follows:

x = 0.

Hence the numerator is:

x.

Thus the function is given as follows:

D. F(x) = x/[(x + 4)(x - 1)]

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Answer:

look cuh yo no sabo cuhhhhhh

Step-by-step explanation:

no sabo weys

For the given triangles:

(1) x = 5.4

(2)  x  =  √23

(3) θ = 25.84 degree

(4)   x = 9.5

(5) n = 41

(1) In the given triangle,

One angle = 16 degree

Perpendicular = x

Hypotenuse    = 20

Since we know that

Sinθ = opposite side of θ/hypotenuse

Therefore,

⇒ sin 16 = x/20

⇒   0.27 = x/20

⇒         x = 5.4

(2)  In the given triangle,

Hypotenuse = 12 km

Base = 11 km

perpendicular = x

We know that the Pythagoras theorem for a right angled triangle:

⇒  (Hypotenuse)²= (Perpendicular)² + (Base)²

⇒ (12)²= (x)² + (11)²

⇒ 144 = (x)² + 121

⇒   x² =  23

Taking square root both sides we get,

Hence,

⇒   x  =  √23

(3) In the given,

Base = 20

Perpendicular = 42

We know that the Pythagoras theorem for a right angled triangle:

⇒  (Hypotenuse)²= (Perpendicular)² + (Base)²

⇒ (Hypotenuse)² =  (42)² + (20)²

⇒ (Hypotenuse)² =  2164

Taking square root both sides,

⇒ (Hypotenuse)  = 46.51

⇒ cosθ = Adjacent/hypotenuse

             = 42/46.51

             = 0.90

Taking inverse of cosθ,

⇒ θ = 25.84 degree

(4) In the given triangle,

One angle = 30 degree

Base = x

Hypotenuse    = 11

Since we know that

cosθ = Adjacent/hypotenuse

Therefore,

⇒ cos 30  = x/11

⇒   √3/2 = x/11

⇒         x = 9.5

(4) In the given triangle,

Base = 40

Perpendicular = 9

Hypotenuse = n

We know that the Pythagoras theorem for a right angled triangle:

⇒  (Hypotenuse)²= (Perpendicular)² + (Base)²

⇒  n² = 9² + 40²

⇒  n² = 81 + 1600

⇒  n² = 1681

⇒  n = 41

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So,the value of the 30th percentile of the given data will be =P30=4

The cumulative distribution function of a real-valued random variable X, or simply the distribution function of X, assessed at x, is the likelihood that X will have a value less than or equal to x in probability theory and statistics.

Using the Cumulative Distribution Function to Calculate Probabilities

F(x) is a cumulative distribution function that calculates the likelihood that the random variable X is smaller than or equal to x:

To get the cumulative probability that X is less than or equal to 1, multiply P(X=0) by P(X = 0) by (P=1):

First, we will determine the value of the cumulative probability P(X<=x):

x         f(x)       P(X<=x)

1       0.02          0.02

2       0.01          0.03

3       0.2          0.23

4       0.17           0.4

5       0.39           0.79

6       0.2           0.99

7 0.01 1

30th percentile will be the x value,

below which less than or equal to 30% of the data falls.

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