A movie theater sends out a coupon for 25% off the price of a ticket. Write an equation for the situation, where y is the price of the ticket with the coupon, and x is the original price of the ticket. Use pencil and paper. Draw a graph of the equation and explain why the line should only be in the first quadrant.

Answer:

This is a ssa situation, no triangle is possible.

Step-by-step explanation:

"SSA" means "Side, Side, Angle".

In an SSA triangle, we are given two sides and an angle that is not the angle between the given sides.

In triangle ABC:

Given:

The angle that is between the sides a and b is angle C.

Therefore, as angle A is not the angle between the given sides, ΔABC is an SSA triangle.

Law of Sines

\(\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}\)

(where A, B and C are the angles and a, b and c are the sides opposite the angles)

To determine if any triangles are possible, substitute the given values into the Law of Sines to find angle B:

\(\implies \sf \dfrac{\sin 44^{\circ}}{12.6}=\dfrac{\sin B}{19}\)

\(\implies \sf \sin B=\dfrac{19\sin 44^{\circ}}{12.6}\)

\(\implies \sf \sin B=1.0475007...\)

As -1 ≤ sin B ≤ 1, there is no solution for angle B.

Therefore, although this is an SSA situation, no triangle is possible.

The value of b in x²+ bx + 16/49 is 8/7 and the squared binomial is (x + 4/7)²

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

X^2+bx+16/49

Rewrite properly

So, we have the following representation

x²+ bx + 16/49

When represented as a square, we have

x²+ bx + 16/49 = (x + a)²

Expand the bracket

So, we have the following representation

x²+ bx + 16/49 = x² + 2ax + a²

By comparison, we have

bx = 2ax

a² = 16/49

Take the square root of both sides

a = 4/7

Substitute a = 4/7 in bx = 2ax

bx = 2 * 4/7x

So, we have

b = 2 * 4/7

Evaluate

b = 8/7

In (a), we have

x²+ bx + 16/49 = (x + a)²

Where

a = 4/7

So, we have

x²+ bx + 16/49 = (x + 4/7)²

Hence, the binomial is (x + 4/7)²

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Answer:

\(\textsf{1)} \quad b = \dfrac{8}{7}\)

\(\textsf{2)} \quad \left(x+\dfrac{4}{7}\right)^2\)

Step-by-step explanation:

Perfect Square Trinomial

A trinomial that can be written as the square of a binomial.

For example the perfect trinomial  x²+2dx+d² can be written  as (x+d)².

Given trinomial:

\(x^2+bx+\dfrac{16}{49}\)

To express the given trinomial as a perfect square trinomial, determine the value of b.

As the coefficient of the x² term is one, b equals twice the square root of the constant of the trinomial:

\(\implies b = 2 \sqrt{\dfrac{16}{49}}\)

\(\implies b = 2 \cdot \dfrac{4}{7}\)

\(\implies b = \dfrac{8}{7}\)

Therefore, the perfect square trinomial is:

\(x^2+\dfrac{8}{7}x+\dfrac{16}{49}\)

To factor in the form of a squared binomial (x + d)², d is half the value of b:

\(\implies d = \dfrac{1}{2}b\)

\(\implies d = \dfrac{1}{2} \cdot \dfrac{8}{7}\)

\(\implies d=\dfrac{8}{14}\)

\(\implies d=\dfrac{4}{7}\)

Therefore, the perfect square trinomial as a squared binomial is:\(\implies \left(x+\dfrac{4}{7}\right)^2\)

Answer:

(3b - 1)(3b + 1).

Step-by-step explanation:

Difference of 2 squares:

a^2 - b^2 = (a - b)(a + b) so here we have:

9b^2 - 1 = (3b - 1)(3b + 1).

Answer:

56 degrees

Step-by-step explanation:

Here, I think you just accidentally put the value for the angle ZWX, which would be ZWP+PWX(56+56).

You actually already wrote it on the paper, so nothing wrong with your math here, just a thinking error :)

Therefore, sin θ = 4/5, csc θ = 5/4, and cot θ = -3/4 using trigonometric ratio.

We know that the point (-3, 4) is on the terminal side of the angle θ, and we can use the Pythagorean theorem to find the value of the hypotenuse:

r² = x² + y²

r² = (-3)² + 4²

r² = 9 + 16

r² = 25

r = 5

Now we can find the values of sin θ, csc θ, and cot θ:

sin θ = y/r = 4/5

csc θ = r/y = 5/4

cot θ = x/y = -3/4

Therefore, sin θ = 4/5, csc θ = 5/4, and cot θ = -3/4.

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Answer:

6x+36=11x-9

11x-6x=36+9

5x=45

X=45

now,

45+Z=180

Z=180-45

Therefore,Z=135

6x+36=11x-9

or,11x-6x=36+9

or,5x=44

:X=35

We know that,

45+Z=180

or,Z=180-45

:Z=135

Answer:

The series is convergent and: ∞∑n=12nn!=e2−1. Explanation: The ratio test states that a sufficient condition for a series: ∞∑n=0an.

Step-by-step explanation:

hope i helped

Answer:

rate of the boat in still water:  81 km/h

rate of the current:  18 km/h

Step-by-step explanation:

Rate of the boat in still water:81 km/h

Rate of the current: 18km/h

Speed tells us how fast something or someone is travelling. You can find the average speed of an object if you know the distance travelled and the time it took. The formula for speed is speed = distance ÷ time.

Given

b= speed of boat in still water c=speed of current

"boat travels 693 kilometers in 7 hours going downstream" Going downstream, the boat travels b+c km per hour. b+c km/hr =  693 km/7hr =  99 km/hr

b+c=99

"boat travels 189 kilometers in 3 hours going upstream" Going upstream, the boat travels b-c km per hour. b-c km/hr = 189 km/3hr = 63 km/hrb-c=63

Add the equations together to eliminate the c terms: b+c=99 b-c=63 2b = 162, therefore, b= 81

b+c= 99, so c = 99 - b= 18

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The monthly Payment for the loan is approximately $271.24.

To calculate the monthly payment for the loan, we can use the formula for calculating the monthly payment on an intermediate-term loan. The formula is:

Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Months))

Given:

Loan Amount = $50,000

Interest Rate = 6.5% per year

Number of Years = 5

First, we need to convert the annual interest rate to a monthly interest rate. Since there are 12 months in a year, the monthly interest rate is:

Monthly Interest Rate = (6.5% / 100) / 12 = 0.00541667

Plugging in the values into the formula, we get:

Monthly Payment = ($50,000 * 0.00541667) / (1 - (1 + 0.00541667)^(-5 * 12))

              = $271.24

Therefore, the monthly payment for the loan is approximately $271.24.

The owners of the restaurant want to use the loan to renovate the kitchen and expand the dining room, which they expect will generate additional monthly revenue between $2,000 and $5,000.

If we assume a conservative estimate of $2,000 per month in additional revenue, the loan payment of $271.24 represents approximately 13.56% of the additional revenue. This means that the owners would still have a significant portion of the additional revenue available for other expenses or profit.

On the other hand, if we consider the higher estimate of $5,000 per month in additional revenue, the loan payment would represent only about 5.42% of the additional revenue, leaving a substantial amount of money for other purposes.

Considering these calculations, it appears that taking this loan is a smart business decision. The monthly payment is manageable and leaves a significant portion of the additional revenue for the restaurant's operation and potential profit. However, it is essential for the owners to ensure that the projected additional revenue is realistic and sustainable to cover the loan payment and other business expenses.

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The system A has no solution.

The system B has the solution y=( 3-x )/3

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

System A:

x+3y=9..........(1)

-x-3y=9 ..........(2)

(1) => x=9-3y........(3)

Substitute (3) into (2)

(2) = >  - ( 9-3y ) - 3y = 9

          -9 + 3y - 3y = 9

          -9 =9

This is false.

So, the system has no solution.

System B:

-x-3y=-3..........(1)

x+3y=3..........(2)

(2) => x=3-3y........(3)

Substitute (3) into (1)

-(3-3y)-3y=-3

-3+3y-3y= -3

-3=-3

This is true,

So, the solution is:

x=3-3y

=> 3y= 3-x

=> y=( 3-x )/3

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The measures of angle 4 (m<4) and angle 7 (m<7) are 42° and 96°, respectively.

To find the measures of angles 4 and 7, we need to apply some geometric principles. Since the top and bottom pieces of the crib are parallel to each other, we can use the property of alternate interior angles.

Angle 4 (m<4) is formed by a transversal (the line connecting the top and bottom pieces of the crib) intersecting two parallel lines. Given that angle m<2 is 42°, we know that angle 4 is congruent to angle 2. Therefore, m<4 = m<2 = 42°.

Angle 7 (m<7) is formed by a transversal intersecting two parallel lines as well. However, in this case, angle 7 is an exterior angle, which is equal to the sum of the two remote interior angles. The remote interior angles are angles 2 and 4. We know that m<2 = 42° (as given) and m<4 = m<2 = 42° (as explained above). Therefore, the sum of angles 2 and 4 is 42° + 42° = 84°. Since angle 7 is an exterior angle, it is equal to 180° minus the sum of the remote interior angles. Thus, m<7 = 180° - 84° = 96°.

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21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100 are all composite numbers greater than 20. Next time do a quick search before resorting to brainly.

Answer:

two of them are possible which one is the correct

Answer: 144 styles.

Step-by-step explanation:

6 ⇒ different colours

4 ⇒ different engines

3 ⇒ different seat layouts

(6 x 4 x 3 x 1) +  (6 x 4 x 3)

= 72 + 72

= 144 styles

Answer: 144 styles

Step-by-step explanation:

6 ⇒ different colours

4 ⇒ different engines

3 ⇒ different seat layouts

(6 x 4 x 3 x 1) +  (6 x 4 x 3)

= 72 + 72

= 144 styles

Answer:

The range: { -11, 11, 24}

Step-by-step explanation:

f(x) = 5x + 9   Substitute each number in the domain, which is the x-value, in the equation and solve.

f(-4) = 5(-4) + 9 ;  f(-4) = -20 + 9;  f(-4) = -11

f(2/5) = 5(2/5) + 9; f(-2/5) = 10/5 + 9;  f(2/5) = 2 + 9; f(2/5) = 11

f(3) = 5(3) + 9;  f(3) = 15 + 9; f(3) = 24

The range: { -11, 11, 24}

For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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Answer:

\(V=9\pi\sqrt{3}\)

Step-by-step explanation:

In order to solve this problem we must start by graphing the given function and finding the differential area we will use to set our integral up. (See attached picture).

The formula we will use for this problem is the following:

\(V=\int\limits^b_a {\pi r^{2}} \, dy\)

where:

\(r=6-(6-3 sec(y))\)

\(r=3 sec(y)\)

a=0

\(b=\frac{\pi}{3}\)

so the volume becomes:

\(V=\int\limits^\frac{\pi}{3}_0 {\pi (3 sec(y))^{2}} \, dy\)

This can be simplified to:

\(V=\int\limits^\frac{\pi}{3}_0 {9\pi sec^{2}(y)} \, dy\)

and the integral can be rewritten like this:

\(V=9\pi\int\limits^\frac{\pi}{3}_0 {sec^{2}(y)} \, dy\)

which is a standard integral so we solve it to:

\(V=9\pi[tan y]\limits^\frac{\pi}{3}_0\)

so we get:

\(V=9\pi[tan \frac{\pi}{3} - tan 0]\)

which yields:

\(V=9\pi\sqrt{3}\)]

Answer:

522.50

Step-by-step explanation:

Simply take the total amount of money (salary) you're paid for the year and divide it by 12. For example, if you're paid an annual salary of $75,000 per year, the formula shows that your gross income per month is $6,250.

The value of x, considering the vertical angles in this problem, is given as follows:

x = 11.

Vertical angles are angles that are opposite by the same vertex on crossing segments, hence they share a common vertex, thus being congruent, meaning that they end up having the same angle measure.

The vertical angles for this problem are given as follows:

As the vertical angles are congruent, the value of x is obtained as follows:

2x - 4 = x + 7

x = 11.

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The equation of the line perpendicular ton the given line is y = -3x +6

A equation of a straight line is given by

y = mx+c ,

where m is the slope and c is the intercept on y axis.

The given line is

y = (1/3)x +4

The slope is 1/3

Te slope of the line perpendicular to a line is given by

m * m' = -1

(1/3) * m' = -1

m' = -3

The equation of the line is

y = -3x + c

The  x intercept is 2

At y = 0, x =2

0 = -6 +c

c =6

Therefore the equation of the line perpendicular ton the given line is

y = -3x +6

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The values of {m} that is greater than 4.6 represent the solution of the given inequality.

An inequality is used to compare two or more expressions or numbers.

For example -

2x > 4y + 3

x + y > 3

x - y < 6

The given inequality is -

5m - 7 > 16

Adding 7 on both sides, we get -

5m - 7 + 7 > 16 + 7

5m > 23

m > 23/5

m > 4.6

Therefore, the values of {m} that is greater than 4.6 represent the solution of the given inequality.

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Answer:

Step-by-step explanation:

Range is largest value - smallest value. 12-3=9! EZ

Answer:

the first option

Step-by-step explanation:

for a number to be rational, it should be able to be expressed as a fraction.  Non terminal decimals must have a repeating pattern. Square roots of random numbers aren’t rational. Just like the first rule with decimals, the third number cannot be expressed as a fraction

Answer:

Step-by-step explanation:

it’s the first one

For the function, the x-intercept of g(x) is at (5,0).

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input.

Given f(x) = ln(x)

and g(x) = -f(x - 4)

the function is

g(x) = -ln(x - 4)

when x = 5

g(x) = -ln(5 - 4)

g(x) = -ln1

g(x) = 0

the coordinates are (5, 0)

Hence the x-intercept is (5, 0).

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The quadrant of the terminal side for 15) is fourth quadrant.

To change from radians to degrees, you need to the multiple the number of radians by 180/π.

Multiple the number of radians by 180/π.

15) 5 radians = 5 * (180/π)

16) 11π/6 = (11*180)/6 = 330.

19) 3.5 = 3.5*(π/180) degree.

20) 1 = 1*(π/180) degree.

therefore, terminal side for 15) is fourth quadrant.

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Answer:

Anything known? I mean the lenght of bottle or anything like that?