The sides of a regular 9-sided polygon have been
extended to make a star, as shown below.
Calculate the size of angle x.
Give your answer in degrees (°).
x

The second term if the recursive formula is tn + 1 = 5 • t1 and the first term is t1 = 7 is 34

Recursive formula; tn + 1 = 5 • t1

Find t2, second term

tn + 1 = 5 • tn

t2 + 1 = 5 × 7

t2 + 1 = 35

t2 = 35 - 1

t2 = 34

Therefore, the second term if the recursive formula is 34

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Step-by-step explanation:

a.) 9

When you divide with a fraction you do the reciprocal of the fraction (basically flipping numerator and denominator) then multiplying (since the opposite of division is multiplication.

So if you flip

\(\frac{1}{9} \)

It would be:

\( \frac{9}{1} \)

9/1 is the same as 9 so:

1 times 9 = 9

b.) 15

Same thing like we did above, just do the reciprocal the multiply.

\( \frac{1}{5} \)

Becomes

\( \frac{5}{1} \)

5/1 is the same as 5.

3 times 5 = 15

Answer:

\((x+(3+\sqrt{11}i)) (x+(3-\sqrt{11}i))\)

Step-by-step explanation:

The first step to this problem is to look at the key features of the initial expression given to us. Namely, the middle term.

Notice that it is just \(+6x\). This indicates that the square root terms cancel out, meaning that their signs need to be opposite, but the threes need to have the same, positive sign. This indicates that our answer is option C, but you should always double check by multiplying the expression out to confirm. Here are the steps:

\((x+(3+\sqrt{11}i)) (x+(3-\sqrt{11}i))\)

\(x^{2} +(3+\sqrt{11}i)x+(3-\sqrt{11}i)x+(3+\sqrt{11}i)(3-\sqrt{11}i)\)\(x^{2}+3x+\sqrt{11}ix+3x-\sqrt{11}ix+9+3\sqrt{11}i-3\sqrt{11}i-(\sqrt{11})^{2}(i^{2})\)\(x^{2}+6x+9-(11)(-1)\)

\(x^{2}+6x+9+11\)

\(x^{2}+6x+20\)

Therefore as we suspected, the answer is C.

Answer:

-10

Step-by-step explanation:

See image below:)

Answer:

x = -10

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

Identify

-4/5x = 8

Step 2: Solve for x

Answer:

B. x=5±√3

Step-by-step explanation:

Let's solve your equation step-by-step.

(x−5)²=3

Step 1: Simplify both sides of the equation.

x²−10x+25=3

Step 2: Subtract 3 from both sides.

x²−10x+25−3=3−3

x²−10x+22=0

For this equation: a=1, b=-10, c=22

1x²+−10x+22=0

Step 3: Use quadratic formula with a=1, b=-10, c=22.

x=−b±√b²−4ac/2a

x=−(−10)±√(−10)²−4(1)(22)/2(1)

x=10±√12/2

x=5+√3 or x=5−√3

The algebraic rule for translating the figure 3 units left and 2 units up is (x-3, y+2).  Option B.

To translate a figure 3 units to the left and 2 units up, we need to adjust the coordinates of the figure accordingly. The algebraic rule that represents this translation can be determined by examining the changes in the x and y coordinates.

When we move a figure to the left, we subtract a certain value from the x coordinates. In this case, we want to move the figure 3 units to the left, so we subtract 3 from the x coordinates.

Similarly, when we move a figure up, we add a certain value to the y coordinates. In this case, we want to move the figure 2 units up, so we add 2 to the y coordinates.

Taking these changes into account, we can conclude that the algebraic rule for translating the figure 3 units left and 2 units up is (x-3, y+2). The x coordinates are shifted by subtracting 3, and the y coordinates are shifted by adding 2. SO Option B is correct.

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The subsets of the set {e, n, t} are given as follows:

{{}, {e}, {n}, {t}, {e,n}, {e,t}, {n,t}, {e,n,t}}.

Considering a set with n elements, the number of subsets in the set is the nth power of 2, that is:

\(2^n\)

The set for this problem is given as follows:

{e, n, t}

The cardinality is given as follows:

n = 3.

Hence the number of subsets is given as follows:

2³ = 8.

The subsets are given as follows:

{{}, {e}, {n}, {t}, {e,n}, {e,t}, {n,t}, {e,n,t}}.

In which {} is the empty set.

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Answer:

x = - 1

Step-by-step explanation:

- 9(1 + 6x) = 42 - 3x ← distribute parenthesis on left side by - 9

- 9 - 54x = 42 - 3x ( add 3x to both sides )

- 9 - 51x = 42 ( add 9 to both sides )

- 51x = 51 ( divide both sides by - 51 )

x = - 1

Answer:-1=x

Step-by-step explanation:

-9(1+6x)=42-3x

-9-54x=42-3x

+54x          +54x

-9=42+51x

-42     -42

-51/51=51x/51

-1=x

Intersection of B'∩C = {k, y}

To find the intersection of B' and C, we need to first find the complement of set B (B') and then find the intersection between B' and C.

1. Complement of set B (B'):

The complement of set B (B') consists of all elements in the universal set U that are not in set B. From the given information, set B is defined as {k, s, y}', which means it contains all elements in U except for k, s, and y. Therefore, the complement of set B is {f, m, x, z}.

2. Intersection between B' and C:

Now, we need to find the intersection between B' (complement of B) and set C. From the given information, set C is defined as {s, z}. To find the intersection, we need to identify the common elements between B' and C.

The elements present in both B' and C are k and y. Therefore, the intersection of B' and C is {k, y}.

So, the answer to (b) is B'∩C = {k, y}.

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To change a word equation into a numerical equation, we can replace keywords with numbers or operations.

We're given:

6 × 2x = 72

Full question attached

Answer and  explanation:

Answer and explanation attached

Answer:

30.4

Step-by-step explanation:

8 boxes = 243.20

find 1 boxes

= 243.20 ÷ 8

= 30.40 / 30.4

Answer: 39 ft2

Step-by-step explanation:

The area of the trapezoid is 39 square feet.

To find the area of a trapezoid, you can use the formula:

Area = (1/2) × (base1 + base2) × height

Given that the bases of the trapezoid are 16 feet and 10 feet, and the height is 3 feet, we can substitute these values into the formula:

Area = (1/2) × (16 + 10) × 3

Area = (1/2) × 26 × 3

Area = (1/2) × 78

Area = 39 ft^2

Therefore, the area of the trapezoid is 39 square feet.

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Answer:

3(6+4)

Step-by-step explanation:

The corrective action that offices that consistently charged excessive fees would be subject to by JTFH is a. The office will immediately be terminated from the Program.

JTH Financial, LLC (JTHF)  is a company that was formed in 2010 in Virginia and their goal and mode of operation is to help customers with tax settlement products that can help them get the best amount to pay for taxes.

JTH Financial, LLC has affiliate offices that engage in tax preparation for clients around the United States but they monitor these offices to ensure that their tax preparation fee averages is not excessive. If an office consistently has excessive fees charged to its customers, then JTH Financial terminates them from the program to protect its customers.

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Answer:

B

Step-by-step explanation:

Answer:

2³ = 8

-5*8 = -40

-40 + 7 == -33

Step-by-step explanation:

2³ = 8

-5*8 = -40

-40 + 7 == -33

Answer:

Average time per day = 1.2 hours per day
Average time per day = 72 minutes per day

Step-by-step explanation:

To find Clarence's average time per day, we need to divide the total time he takes to walk the 15.5 miles by the number of days he walks, which is five.

Let's calculate his average time per day:

Average time per day = Total time / Number of days

Since Clarence takes a total of 6 hours to walk the 15.5 miles, we'll divide 6 by 5 to find his average time per day:

Average time per day = 6 hours / 5

Average time per day = 1.2 hours per day

To convert hours to minutes, we'll multiply the average time per day by 60:

Average time per day = 1.2 hours * 60 minutes

Average time per day = 72 minutes per day

Therefore, Clarence's average time per day is 72 minutes.

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

Explanation:

If there were 7 boys and 5 girls, then we'd have the ratio of 7:5. The boys are listed first because of how your teacher mentions boys first to set up the ratio. The order is important. That means 7:5 is different from 5:7.

With 7 boys and 5 girls, we see that there are 7-5 = 2 more boys compared to girls, and not 8. The jump from 2 to 8 is "times 4", which means we'll need to multiply each gender count by 4 to get to the class size we want

boys: 7 ---> 7*4 = 28

girls: 5 ---> 5*4 = 20

Having 28 boys and 20 girls will lead to the ratio 28:20, and it reduces fully to 7:5 when we divide both parts by the GCF 4.

The total number of students is 28+20 = 48

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

Here's another way we can solve.

x = number of girls

x+8 = number of boys, since there are 8 more

The ratio of boys to girls is 7:5, meaning,

(number of boys)/(number of girls) = 7/5

(x+8)/x = 7/5

(x+8)*5 = x*7 .... cross multiply

5x+40 = 7x

40 = 7x-5x

40 = 2x

2x = 40

x = 40/2

x = 20

There are x = 20 girls and x+8 = 20+8 = 28 boys. So 20+48 = 48 total.

The numbers on the cards are 5,5,8,12,15

Number of cards = 5

Median value = 8

Hence, the third number on the cards is 8.

With a modal value of 5, then the value must have appeared more than once.

Since values would be arranged in ascending order, then the two cards before the median would be 5.

Hence , we have 5, 5, 8

The range = 10 ;

Range = maximum - minimum

minimum = 5

10 = maximum - 5

maximum= 10 + 5 = 15

Now , we have : 5,5,8, _,15

Last card value = 45 - (15+8+5+5)

Last value = 45 - 33 = 12

Hence, the values are : 5,5,8,12,15

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Answer:

If the slope of a line is negative, it means that the line is sloping downward from left to right. In other words, as the value of x increases, the value of y decreases. This is in contrast to a positive slope, where as the value of x increases, the value of y also increases. So, if the slope of the line y = x is changed to a negative value, the line will still have the same general shape, but it will be flipped upside-down and will slope downward from left to right

(a) f(x) =  \(log_2(x)\) is a logarithmic function

(b) g(x) = ∜x is a root function

(c) h(x) = \(2x^3/(1 - x^2)\) is a rational function

(d) u(t) = 1 - 1.1t + \(2.54t^2\) is a polynomial of degree 2

(e) v(t) = \(5^t\)is an exponential function

(f) w(θ) = sin θ \(cos^{2}\theta\) is a trigonometric function.

(a) f(x) = \(log_2(x)\) is a logarithmic function. Logarithmic functions have the logarithm of the independent variable as the output. Here, the logarithm base is 2.

(b) g(x) = ∜x is a root function. Root functions have the square root or higher roots of the independent variable as the output. Here, the root is a cube root.

(c) h(x) = \(2x^3/(1 - x^2)\) is a rational function. Rational functions are functions that are expressed as the quotient of two polynomials. Here, the numerator is a cubic polynomial and the denominator is a quadratic polynomial.

(d) u(t) = 1 - 1.1t + \(2.54t^2\) is a polynomial of degree 2. Polynomials are functions that are expressed as a sum of powers of the independent variable, with coefficients. The degree of a polynomial is the highest power of the independent variable.

(e) v(t) = \(5^t\) is an exponential function. Exponential functions have the independent variable as the exponent. Here, the base is 5.

(f) w(θ) = sin θ \(cos^{2}\theta\) is an algebraic function and a trigonometric function. Algebraic functions are functions that can be expressed using arithmetic operations and algebraic expressions. Trigonometric functions are functions that involve the ratios of the sides of a right triangle. Here, the function is a combination of sine and cosine functions.

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The complete question is -

Classify each function as a power function, root function, polynomial (state its degree), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function.

(a) f(x) =  \(log_2(x)\)    

(b) g(x) = ∜x    

(c) h(x) = \(2x^3/(1 - x^2)\)    

(d) u(t) = 1 - 1.1t + \(2.54t^2\)                    

(e) v(t) = \(5^t\)    

(f) w(θ) = sin θ \(cos^{2}\theta\)

Answer:

15 shirts

Step-by-step explanation:

Store A charges 12.50 for a custom shirt with 0.40 per each custom character. Store B charges 14.75 for the same shirt but charges 0.25 per each custom character would make the cost from both stores the same

A: 12.5 + 0.40x

B: 14.75 + 0.25x

12.5 + 0.40x = 14.75 + 0.25x

subtract 12.5 from both sides:

12.5 + 0.40x - 12.5 = 14.75 + 0.25x - 12.5

0.40x = 2.25 + 0.25x

subtract 0.25x from both sides:

0.40x - 0.25x = 2.25 + 0.25x - 0.25x

0.15x = 2.25

divide both sides by 0.15:

0.15x/0.15 = 2.25/0.15

x = 15

According to the quantity theory of money, changes in the money supply will lead directly to changes in the price level if velocity and real GDP are unaffected by the change in the money supply.Velocity can change over time, and changes in velocity may be caused by various factors.

For example, changes in velocity can be caused by shifts in payment practices, changes in the use of credit, changes in the availability of bank deposits or cash, or shifts in demand patterns.Changes in velocity may be related to changes in the money supply.

For example, if the money supply increases, the demand for money may increase, causing the velocity of money to decrease. Conversely, if the money supply decreases, the demand for money may decrease, causing the velocity of money to increase.

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Answer: 7x -4

Step-by-step explanation:

Answer:

a = 0.9

Step-by-step explanation:

For the quadratic equation \(\boxed{ax^2 + bx + c = 0}\) to have exactly one real root, the value of its discriminant, \(\boxed{b^2 - 4ac}\), must be zero.

For the given equation:

\(y = ax^2 - 6x + 10\),

• a = a

• b = -6

• c = 10.

Substituting these values into the formula for discriminant, we get:

\((-6)^2 - 4(a)(10) = 0\)

⇒ \(36 - 40a = 0\)

⇒ \(36 = 40a\)

⇒ \(a = \frac{36}{40}\)

⇒ \(a = \bf 0.9\)

Therefore the value of a is 0.9 when the given quadratic has exactly one root.

Answer:

$26,986.29

Step-by-step explanation:

We can use the formula for calculating the depreciation of an asset over time:

wor

\(\bold{D = P(1 - \frac{r}{100} )^t}\)

where:

D= the current value of the asset

P = the initial purchase price of the asset

r = the annual depreciation rate as a decimal

t = the number of years the asset has been in use

In this case, we have:

P = $39,600

r = 12% = 0.12

t = 3 years

Substituting these values into the formula, we get:

\(D= 39,600(1 - \frac{12}{100})^3\\D= 39,600(1 - 0.12)^3\\D= 39,600*0.88^3\\D= 39,600*0.681472\\D=26986.2912\)

Therefore, the car is worth approximately $26,986.29 after 3 years of depreciation at a rate of 12% per annum.

Answer:

$26,986.29

Step-by-step explanation:

As the car's value depreciates at a constant rate of 12% per annum, we can use the exponential decay formula to create a function for the value of the car f(t) after t years.

\(\boxed{f(t)=a(1-r)^t}\)

where:

In this case, the initial value is $39,600, and the rate of depreciation is 12% per year. Therefore, the function that models the value of the car after t years is:

\(f(t)=39600(1-0.12)^t\)

\(f(t)=39600(0.88)^t\)

To calculate the value of the car after 3 years, substitute t = 3 into the function:

\(\begin{aligned} f(3)&=39600(0.88)^3\\&=39600(0.681472)\\&=26986.2912\\&=26986.29\;(\sf 2\;d.p.)\end{aligned}\)

Therefore, the car is worth $26,986.29 after 3 years.

Answer:

20:9

Step-by-step explanation:

Here we will simplify the ratio to 40:18 for you and show you how we did it.

To simplify the ratio 40:18, we find the greatest common divisor of 40 and 18, and then we divide 40 and 18 by the greatest common divisor.

The greatest common divisor that you can use to simplify 40:18 is 2. This means the answer to ratio 40:18 simplified is:

20:9

The angle that is supplementary to the angle DEA is angle DEC

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

Also from the question, we have

Angle = DEA

As a general rule;

Two angles are said to be supplementary if their sum add up tp 180 degrees

This means that the angles are on a straight line

The angle are on the same straight line with ange DEA is DEC

Hence, the angle is angle DEC

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