7. John has two coupons to use at a clothing store. One is for $20 off and the other is for 20% off. John wants to purchase a shirt with one of the coupons and wants to pay the least amount that he can. Choose the answer that BEST describes the situation. * 1 point A. The shirt will have the lowest price with the $20 off coupon. B. The shirt will have the lowest price with the 20% off coupon. C. The shirt will cost the same with either coupon. D. It depends on the cost of the shirt as to which coupon will help John pay the lowest price.

The sum of the real and imaginary parts of $c$ is$$\operatorname{Re}(c) + \operatorname{Im}(c) = \frac{\operatorname{Re}(2c)}{2} + \frac{\operatorname{Im}(2c)}{2}$$$$= \frac{\operatorname{Re}(z_0+z_2)}{2} - \frac{\operatorname{Im}(z_0)}{2}(1-\cos(\theta/2)) - \frac{\operatorname{Re}(z_0)}{2}\sin(\theta/2)$$$$+ \frac{\operatorname{Im}(z_0+z_2)}{2} - \frac{\operatorname{Re}(z_0)}{2}(1-\cos(\theta/2)) + \frac{\operatorname{Im}(z_0)}{2}\sin(\theta/2).$$

The given problem can be solved using algebraic and geometric methods. We can use algebraic methods, such as the equations given in the problem, and we can use geometric methods by visualizing what the problem is asking. To start, let's translate the given problem into mathematical equations. Let $z_0$ be the original complex number. We want to rotate this point by 90 degrees counter-clockwise about some complex number $c$ to get $z_2$. Thus,$$z_2 = c + i(z_0 - c)$$$$=c + iz_0 - ic$$$$= (1-i)c + iz_0.$$We also know that this transformation will rotate the point $z_1 = (z_0 + z_2)/2$ by 45 degrees. Thus, using similar logic,$$z_1 = (1-i/2)c + iz_0/2.$$Now let's use the formula for rotating a point about the origin by $\theta$ degrees (where $\theta$ is measured in radians) to find a relationship between $z_1$ and $z_0$.$$z_1 = z_0 e^{i\theta/2}$$$$\implies (1-i/2)c + iz_0/2 = z_0 e^{i\theta/2}$$$$\implies (1-i/2)c = (e^{i\theta/2} - 1)z_0/2.$$We can solve for $c$ by dividing both sides by $1-i/2$.$$c = \frac{e^{i\theta/2} - 1}{1-i/2}\cdot\frac{z_0}{2}.$$We can now use the information given in the problem to solve for the sum of the real and imaginary parts of $c$. We know that rotating $z_0$ by 90 degrees counter-clockwise will result in the complex number $z_2$. Visually, this means that $c$ is located at the midpoint between $z_0$ and $z_2$ on the line that is perpendicular to the line segment connecting $z_0$ and $z_2$. We can use this geometric interpretation to solve for $c$. The midpoint of the line segment connecting $z_0$ and $z_2$ is$$\frac{z_0+z_2}{2} = c + i\frac{z_0-c}{2}.$$Solving for $c$, we get$$c = \frac{z_0+z_2}{2} - \frac{i}{2}(z_0-c)$$$$\implies 2c = z_0+z_2 - i(z_0-c)$$$$\implies 2c = z_0+z_2 - i(z_0- (e^{i\theta/2} - 1)(z_0/2)/(1-i/2)).$$We can now find the real and imaginary parts of $c$ and add them together to get the desired answer. Let's first simplify the expression for $c$.$$2c = z_0+z_2 - i(z_0 - (e^{i\theta/2} - 1)\cdot(z_0/2)\cdot(1+i)/2)$$$$= z_0 + z_2 - i(z_0 - z_0(e^{i\theta/2} - 1)(1+i)/4)$$$$= z_0 + z_2 - i(z_0 - z_0e^{i\theta/2}(1+i)/4 + z_0(1-i)/4)$$$$= z_0 + z_2 - i(z_0(1-e^{i\theta/2})/4 + z_0(1-i)/4)$$$$= z_0 + z_2 - i(z_0/4(1-e^{i\theta/2} + 1 - i))$$$$= z_0 + z_2 - i(z_0/2(1-\cos(\theta/2) - i\sin(\theta/2)))$$$$= z_0 + z_2 - i(z_0(1-\cos(\theta/2)) + z_0\sin(\theta/2) - i(z_0\cos(\theta/2))/2.$$Now we can find the real and imaginary parts of $2c$ and divide by 2 to get the real and imaginary parts of $c$. We have$$\operatorname{Re}(2c) = \operatorname{Re}(z_0+z_2) - \operatorname{Im}(z_0)(1-\cos(\theta/2)) - \operatorname{Re}(z_0)\sin(\theta/2)$$$$\operatorname{Im}(2c) = \operatorname{Im}(z_0+z_2) - \operatorname{Re}(z_0)(1-\cos(\theta/2)) + \operatorname{Im}(z_0)\sin(\theta/2).$$Thus, the sum of the real and imaginary parts of $c$ is$$\operatorname{Re}(c) + \operatorname{Im}(c) = \frac{\operatorname{Re}(2c)}{2} + \frac{\operatorname{Im}(2c)}{2}$$$$= \frac{\operatorname{Re}(z_0+z_2)}{2} - \frac{\operatorname{Im}(z_0)}{2}(1-\cos(\theta/2)) - \frac{\operatorname{Re}(z_0)}{2}\sin(\theta/2)$$$$+ \frac{\operatorname{Im}(z_0+z_2)}{2} - \frac{\operatorname{Re}(z_0)}{2}(1-\cos(\theta/2)) + \frac{\operatorname{Im}(z_0)}{2}\sin(\theta/2).$$

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The percentage increase is 22.72%

The given parameters are:

Initial = 440 coins

Final = 540 coins

The percentage increase is calculated as:

%Increase = (Final - Initial)/Initial * 100%

So, we have:

%Increase = (540 - 440)/440 * 100%

Evaluate the difference

%Increase = 100/440 * 100%

Evaluate the quotient

%Increase = 0.2272 * 100%

Evaluate the product

%Increase = 22.72%

Hence, the percentage increase is 22.72%

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Answer:

15

Step-by-step explanation:

(2x-1)+(x+17)+(4x-15)=106º

2x+x+4x=7x

-1+17-15=1

7x+1=106º

         -1

7x=105º

/7     /7

x= 15

Answer:x=y-bm

Step-by-step explanation:

Answer:

x = y-b/m

Step-by-step explanation:

Step 1:  y = mx + b

Step 2: Bring b to the left side of the equation

Step 3: y - b = mx

Step 4: To isolate for x, we must get rid of m. Therefore, divide m on both sides of the equation

Step 5: y-b/m = mx/m

Step 6: On the right side of the equation, m and m crosses out.

Step 7: All we have left is: y-b/m = x

(Or you can write it as x = y-b/m)

Hope this helps.

Answer:

It does not display exponential behavior, so no.

Step-by-step explanation:

x values are consistently decreasing by 3

y values are consistently decreasing by 7

Yes, the set of data shown in the table displays exponential behavior.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The exponential function is given as f(x) = \(a^x\)

From the table,

f(x) = \(a^x\)

30 = c\(a^{21}\) _____(1)

23 = c\(a^{18}\) ______(2)

Now,

From (1) and (2)

30/\(a^{21}\) = 23/\(a^{18}\)

\(a^{18 - 21}\) = 23/30

\(a^{-3}\) = 23/30

1/\(a^3\) = 23/30

a³ = 30/23

a = ∛(30/23)

a = 1.09

Now,

30 = c\(a^{21}\)

30 = c x \(1.09^{21}\)

c = 30 / 6.11

c = 4.91

Now,

The function from the table is f(x) = 4.91 x \(1.09^x\)

Thus,

The set of data is an exponential function.

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Answer:

x = 72°

y = 61°

Step-by-step explanation:

Properties of a kite,

1). At least on pair of opposite angles of a kite are equal.

2). Diagonal of a kite intersect each other at 90°.

3). Diagonals are the angle bisectors of opposite angles.

By these properties,

m∠AED = 90°

In ΔAED,

m∠AED + m∠EDA + m∠DAE = 180° [Triangle sum theorem]

90° + 18° + m∠DAE = 180°

m∠DAE = 180° - 108°

             = 72°

Since, diagonal AC is an angle bisector of angle DAB,

x = 72°

In ΔABC,

m∠ABC + m∠BCA + m∠CAB = 180°

m∠ABC + 29° + x° = 180°

m∠ABC + 29° + 72° = 180°

m∠ABC = 180° - 101°

m∠ABC = 79°

Since, opposite angles ∠ADC and ∠ABD are equal in measure,

m∠ABC = m∠ADC = 79°

79° = (18 + y)°

y = 79 - 18

y = 61°

| 5 -4 -6 | -3 |

| 1  -3   1 | -1 |

|-3 -6  7 |  1 |

is the augmented matrix for given system of equations.

What is augmented matrix?

An augmented matrix is a matrix that represents a system of linear equations by having the coefficients of the variables and the constants on the right side in a single matrix.

It is obtained by placing the coefficients of each equation in a row and placing the constant term at the end of the row. The vertical bar in the matrix separates the coefficient matrix and the constant terms. For example, the augmented matrix for the system of equations:

5x - 4y - 6z = -3

x - 3y + z = -1

-3x - 6y + 7z = 1

would be:

| 5 -4 -6 | -3 |

| 1  -3   1 | -1 |

|-3 -6  7 |  1 |

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Answer:

The expression for the truck's position in terms of t would be xtruck = t × vtruck, where vtruck is the truck's velocity. The expression for the car's position in terms of t would be xcar = t × vcar + x0, where vcar is the car's velocity and x0 is the car's initial position. For the vehicles to eventually meet, these two equations must be equal, so vtruck = vcar + (x_0/t).

Answer:

Step-by-step explanation:

Let's solve for x.

1.5x+0.5y=12

Step 1: Add -0.5y to both sides.

1.5x+0.5y+−0.5y=12+−0.5y

1.5x=−0.5y+12

Step 2: Divide both sides by 1.5.

1.5x

1.5

=

−0.5y+12

1.5

x=−0.333333y+8

Answer:

x=−0.333333y+8

Answer: 15

Step-by-step explanation:

This is a right angle and right angles always add up to 90 degrees.

You would take away 30 from 90 which equals 60.

Then because it is 4x you would do the inverse and divide 60 by 4 to get x on its own.

60/4=15

Step-by-step explanation:

log (√1000000x)

Rewrite √1000000x as (1000000x)1/2.

expand long ((1000000x)1/2) by moving 1/2

oby moving logarithm.

1/2 longth (1000000x)

Rewrite

log

(1000000x) as log(1000000)+log(x).

1/2(log(1000000)+log(x))

Logarithm base 10 of 1000000 is 6.

1/2(6+log(x))

Apply the distributive property.

1/2.6+1/2 log(x)

Cancel the common factor of 2.

3+1/2 long(x)

Combine 1/2 and log(x)

3+ long(x)/2

Step-by-step explanation:

See the steps below:

\(log\sqrt{1000000x} =\\(1/2)log 1000000x=\\(1/2)log10^6+(1/2)logx=\\(1/2)(6) + (1/2)logx=\\3+(1/2)logx\)

Answer:

thanks...

Step-by-step explanation:

Answer:

They are all 23 because all the sides are equal.

Step-by-step explanation:

The average rate of change of the function r(x) = x² + 2x - 5 over the interval [0,3] is given as follows:

r = 5.

The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function.

The function for this problem is defined as follows:

r(x) = x² + 2x - 5.

The numeric values of the function are given as follows:

Hence the average rate of change is given as follows:

r = (10 - (-5))/(3 - 0)

r = 5.

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The missing statements and proofs that complete the proof in the question are;

Statement 2; m∠ PQA = m∠ RQA : Bisector

Statement 4; m∠ QXA = m∠ QYA : Right angles are congruent

Statement 6; ΔQXA = ΔQYA: AAS congruence Postulate

The statements and reasons that give the proof are;

1) Bisector:

An angle bisector or angle bisector is a ray that divides an angle into two equal parts. For example, if ray AX divides a 60 degree angle into two equal parts, each measurement equals 30 degrees. Every angle has an angle bisector.

Statement 1; QA is the bisector of ∠PQR

Reason 1; The reason is because we are Given.

2) Bisector:

An angle bisector or angle bisector is a ray that divides an angle into two equal parts. For example, if ray AX divides a 60 degree angle into two equal parts, each measurement equals 30 degrees. Every angle has an angle bisector.

Statement 2; m∠ PQA = m∠ RQA

Reason 2; Definition of Bisector

3) The reason is mentioned in the question.

Statement 3; ∠QXA and ∠QYA are right angles.

Reason 3; Given

4) Two angles are congruent if they are the complements of the same angle (or congruent angles). All right angles are congruent. Two angles are right angles if they are congruent and complementary.

Statement 4; m∠ QXA = m∠ QYA

Reason 4; All right angles are congruent  

5) The recursive property of a set dictates that each element of the set is related to itself. If the relation defined on sets is congruence, it is called congruence recursion, and if the relation defined on sets of numbers is equality, it is called equality recursion.

Statement 5; QA = QA

Reason 5; Reflexive Property

6)The AAS assumption states that triangles are congruent if the two angles and non-inclusive sides of the triangle are congruent with the two corners and non-inclusive sides of a second triangle.

Statement 6; ΔQXA = ΔQYA

Reason 6; AAS Congruence Postulate

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Answer:

25 MP3 downloads

Step-by-step explanation:

If he starts off with $50 then these are the steps

$50 - $1.50 = $48.50 for 1 MP3

$48.50 - $1.50 = $47.00 for 2

$48.50 - $1.50 = $45.50 for 3

then repeat that until we have $12

it doesnt give us exactly $12 but it gives us $12.50 reminder

So he can but 25 MP3 downloads and still have at least $12 remining

Hope this helps plz give me brainliest I worked really hard

Answer:

112

Step-by-step explanation:

Supplementary Angle Theorem

Answer:

B. positive

Step-by-step explanation:

Answer:

Step-by-step explanation:

1.Collect pairs of data where a relationship is suspected.

2.Draw a graph with the independent variable on the horizontal axis and the dependent variable on the vertical axis. ...

3.Look at the pattern of points to see if a relationship is obvious. ...

4.Divide points on the graph into four quadrants.

As previously stated, a system will not be stable if its eigenvalues have any non-negative real parts, the system will be unstable if an eigenvalue has no imaginary part and is equal to zero. A trivial instance of the complex eigenvalue with a zero component exists here.

When both eigenvalues are zero, what takes place?

A zero eigenvalue implies the network being referred to is particular.The null space of the matrix is based on the eigenvectors that correspond to the zero eigenvalues.

When one eigenvalue is zero, what does this mean?

If and only if A is not invertible, then the number 0 is an eigenvalue of A.

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The answer is 3/25

The calculation as follows.

First, convert to fraction version of the decimals.

0,12 means 12/100

Second, simplify both up and bottom value of the fraction by dividing it with 4

(12:4)/(100:4) = 3/25

So, the answer is 3/25

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Answer:

Yes

Step-by-step explanation:

They have the same length. The length is 1.

I hope this helps!

Answer: C)The two triangles may be congruent, but additional measurements are needed.

Step-by-step explanation:Not 100% sure

Answer:

X = 3   Y = -3

Step-by-step explanation:

The arrow is on X = 3 and the other side of arrow is on Y = -3

Hope I helped

The 95% confidence interval estimate for the population proportion of car deals that used 0% financing is (0.1612, 0.2308). So, the correct option is (b).

To construct a confidence interval estimate for the population proportion of car deals that used 0% financing, we can use the formula

CI = p ± z√((p(1-p))/n)

where

p = sample proportion = 98/500 = 0.196

n = sample size = 500

z = z-score for the desired level of confidence, which is 95% in this case. From a standard normal distribution table, the z-score corresponding to 95% confidence level is approximately 1.96.

Substituting the values, we get

CI = 0.196 ± 1.96√((0.196(1-0.196))/500)

= (0.1612, 0.2308)

Therefore, the 95% confidence interval estimate is (0.1612, 0.2308).

The correct answer is (b).

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To estimate the number of new users that would be added during time period 7, we can use the Bass diffusion model, which is commonly used to model the adoption of new products or technologies.

The Bass diffusion model is given by the formula:

\(\[N(t) = \frac{{p \cdot q}}{{q + (p/q) \cdot e^{-((p+q) \cdot t)}}}\]\)

where:

- N(t) represents the cumulative number of adopters at time \(t\).

- p is the innovation parameter, representing the coefficient of innovation.

- q is the imitation parameter, representing the coefficient of imitation.

- e is the base of the natural logarithm.

Given a population size of 67 million, an innovation parameter of 0.005, and an imitation parameter of 0.84 for Color TV, we can substitute these values into the Bass diffusion model and calculate the number of new users added during time period 7.

\(\[N(7) - N(6) = \frac{{p \cdot q}}{{q + (p/q) \cdot e^{-((p+q) \cdot 7)}}} - \frac{{p \cdot q}}{{q + (p/q) \cdot e^{-((p+q) \cdot 6)}}}\]\)

Substituting the given values into the equation:

\(\[N(7) - N(6) = \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 7)}}} - \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 6)}}}\]\)

Evaluating the expression will give us the estimated number of new users added during time period 7.

In LaTeX, the solution can be represented as:

\(\[N(7) - N(6) = \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 7)}}} - \frac{{0.005 \cdot 0.84}}{{0.84 + (0.005/0.84) \cdot e^{-((0.005+0.84) \cdot 6)}}}\]\)

After evaluating this expression, you will obtain the estimated number of new users added during time period 7.

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We can conclude that gcd(a, b) divides 15 if and only if there exist integers s and t such that as + bt = 15.

If there are integers s and t such that as + bt = 15, then we can conclude that gcd(a, b) divides 15. This is known as Bézout's identity, which states that for any two integers a and b, there exist integers s and t such that as + bt = gcd(a, b).

To see why this is true, consider the set of all linear combinations of a and b, that is, the set {ax + by : x, y are integers}. This set contains all multiples of gcd(a, b) since gcd(a, b) divides both a and b.

Therefore, gcd(a, b) is the smallest positive integer that can be expressed as a linear combination of a and b.

Now, if as + bt = 15, then 15 is a linear combination of a and b, which means that gcd(a, b) divides 15.

Conversely, if gcd(a, b) divides 15, then we can find integers s and t such that as + bt = gcd(a, b), and we can scale this equation to obtain as' + bt' = 15, where s' = (15/gcd(a, b))s and t' = (15/gcd(a, b))t.

Therefore, we can conclude that gcd(a, b) divides 15 if and only if there exist integers s and t such that as + bt = 15.

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There are two solutions: x = -3 and x = -7.

Let's analyze each equation to determine the number of solutions and provide explanations:

x² - 144 = 0

This equation can be rewritten as (x - 12)(x + 12) = 0. It is a quadratic equation in the form of (x - a)(x + a) = 0, where a is a constant. In this case, a = 12.

Since we have two factors that multiply to give zero, either (x - 12) = 0 or (x + 12) = 0 must be true for the equation to hold.

Thus, there are two solutions: x = 12 and x = -12.

x² + 1440

This equation does not contain an equal sign, so it is not an equation. It is an expression. Therefore, it does not have any solutions.

x (x - 5) = 0

This equation is a product of two factors equal to zero. Either x = 0 or (x - 5) = 0 must be true for the equation to hold. Thus, there are two solutions: x = 0 and x = 5.

(x - 8)² = 0

This equation is a perfect square trinomial. The square of any number is always non-negative, and it only equals zero when the number itself is zero. Thus, the equation (x - 8)² = 0 has only one solution: x = 8.

(x + 3)(x + 7) = 0

This equation is a product of two factors equal to zero. Either (x + 3) = 0 or (x + 7) = 0 must be true for the equation to hold. Thus, there are two solutions: x = -3 and x = -7.

To summarize:

x² - 144 = 0 has two solutions: x = 12 and x = -12.

x² + 1440 does not have any solutions.

x (x - 5) = 0 has two solutions: x = 0 and x = 5.

(x - 8)² = 0 has one solution: x = 8.

(x + 3)(x + 7) = 0 has two solutions: x = -3 and x = -7.

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The number 3600 at the end of solving the problem represents the final result.

In order to understand where the number 3600 came from at the end of solving the problem, we need to examine the steps taken during the solution process.

Let's assume we were solving a mathematical problem and arrived at the equation 120 + 3600 = 3720. The equation implies that by adding 120 and 3600 together, we obtain the sum of 3720. However, in this context, we are specifically interested in the origin of the number 3600.

To determine where this number came from, we would need to review the specific calculations or operations conducted before arriving at the final equation.

It could be the result of performing a series of mathematical operations such as multiplication, division, or exponentiation. The detailed calculations leading up to the addition of 120 and 3600 would provide the necessary context to understand the origin of the number 3600.

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The number 56% as a fraction is 14/25.

A fraction is a part of the whole represented by a/b, where a and b are any integers.

The given number is 56%.

Write the number as a fraction,

56%

= 56/100

= 14/25

Hence, the number 56% as a fraction is 14/25.

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