100 POINTS! I REALLY NEED TO GET THIS CORRECT! Factor the quadratic trinomial.
x^2−3x−18
Hint: To use type an exponent, use the caret symbol (^) by using the keys shift + 6

A movie theater charges 8 dollars for adults and 4 dollars for seniors. On a particular day when 353 people paid an admission, the total receipts were 1688 dollars. How many who paid were adults? . How many who paid were seniors?

Answer:

There were 69 adults and 284 seniors

Solution:

Let "a" be the number of adults

Let "s" be the number of seniors

Cost of 1 adult = $ 8

Cost of 1 senior = $ 4

On a particular day when 353 people paid an admission

Therefore,

number of adults + number of seniors = 353

a + s = 353

a = 353 - s ---------- eqn 1

The total receipts were 1688 dollars

Therefore, we frame a equation as:

number of adults x Cost of 1 adult + number of seniors x Cost of 1 senior = 1688

[tex]a \times 8 + s \times 4 = 1688[/tex]

8a + 4s = 1688 ---------- eqn 2

Let us solve eqn 1 and eqn 2

Substitute eqn 1 in eqn 2

8(353 - s) + 4s = 1688

2824 -8s + 4s = 1688

4s = 2824 - 1688

4s = 1136

Substitute s = 284 in eqn 1

a = 353 - 284

Thus there were 69 adults and 284 seniors in movie theater

there were 55 adults and 284 seniors who paid admission.

Let's denote:

- ( A ) as the number of adults.

- ( S ) as the number of seniors.

Given:

- The price for adults is $9.

- The price for seniors is $5.

- The total number of people who paid admission is 339.

- The total receipts were $1915.

We can set up a system of equations based on the given information:

1. The total number of people who paid admission:

[tex]\[ A + S = 339 \][/tex]

2. The total receipts:

[tex]\[ 9A + 5S = 1915 \][/tex]

Now, we can solve this system of equations.

Let's solve equation 1 for one of the variables (let's solve for ( A )):

[tex]\[ A = 339 - S \][/tex]

Now, substitute this expression for( A ) into equation 2:

[tex]\[ 9(339 - S) + 5S = 1915 \][/tex]

Now, solve for \( S \):

[tex]\[ 3051 - 9S + 5S = 1915 \][/tex]

[tex]\[ -4S = 1915 - 3051 \][/tex]

[tex]\[ -4S = -1136 \][/tex]

[tex]\[ S = \frac{-1136}{-4} \][/tex]

[tex]\[ S = 284 \][/tex]

Now, we can find ( A ) using the value of ( S ) we found:

[tex]\[ A = 339 - 284 \][/tex]

[tex]\[ A = 55 \][/tex]

So, there were 55 adults and 284 seniors who paid admission.

complete question given below:

A movie theater charges 9$ for adults and 5 for seniors.on a particular day when 339 people paid an admission,the total receipts were 1915$ how many who paid were adults and how many who paid were seniors

The original price of one keyboard was $20.

Let's denote the original price of one keyboard as x.

The shop owner spent $540 to purchase a stock of computer keyboards. Therefore, the number of keyboards he purchased can be calculated as [tex]\( \frac{540}{x} \)[/tex].

If the price of each keyboard had been reduced by $2, the new price of one keyboard would be x - 2.

With this reduced price, the shop owner could have bought 3 more keyboards, so the total number of keyboards he could have purchased is [tex]\( \frac{540}{x-2} \)[/tex].

We are given that this value is 3 more keyboards than the original purchase, so we can set up the equation:

[tex]\[\frac{540}{x-2} = \frac{540}{x} + 3\][/tex]

To solve this equation, we first clear the fractions by multiplying both sides by (x(x-2):

[tex]\[540x = 540(x-2) + 3x(x-2)\][/tex]

Expanding and simplifying:

[tex]\[540x = 540x - 1080 + 3x^2 - 6x\][/tex]

[tex]\[0 = 3x^2 - 6x - 1080\][/tex]

Now, let's solve this quadratic equation for x.

Dividing both sides by 3:

[tex]\[x^2 - 2x - 360 = 0\][/tex]

Now, we can use the quadratic formula to solve for x:

[tex]\[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\][/tex]

Where a = 1, b = -2, and c = -360:

[tex]\[x = \frac{-(-2) \pm \sqrt{(-2)^2 - 4 \times 1 \times (-360)}}{2 \times 1}\][/tex]

[tex]\[x = \frac{2 \pm \sqrt{4 + 1440}}{2}\][/tex]

[tex]\[x = \frac{2 \pm \sqrt{1444}}{2}\][/tex]

[tex]\[x = \frac{2 \pm 38}{2}\][/tex]

So, x can be either:

[tex]\[x = \frac{2 + 38}{2} = \frac{40}{2} = 20\][/tex]

or

[tex]\[x = \frac{2 - 38}{2} = \frac{-36}{2} = -18\][/tex]

Since the price of a keyboard cannot be negative, the only valid solution is x = 20.

Therefore, the original price of one keyboard is $20.

Answer:

B

Area measures the amount of any certain single unit (inches, feet, miles, etc.) that can be contained inside the flat plane of a given shape.

Step-by-step explanation:

Final answer:

To solve the inequality, simplify the expression and isolate the variable y. The solution is y > 43/37, so the correct answer is option (c).

Explanation:

To solve the inequality 2y - 1/5 - 2 + 7y/15 > 2/3, we can simplify and isolate the variable y. Combining like terms, we have 2y + 7y/15 - 1/5 - 2 > 2/3. Multiplying all terms by 15, we get 30y + 7y - 3 - 30 > 10. Simplifying further, we have 37y - 33 > 10. Adding 33 to both sides, we have 37y > 43. Finally, dividing both sides by 37, we find that y > 43/37.

So the correct answer is option (c), y > 43/37.

Answer:

The percent (relative) change is 7.14 percent (%).

Step-by-step explanation:

We are given that the original support value is at 42%.

Then the support increased by 3%, to reach 45%.

We want the Percentage Change (i.e. relative) change of this increase, which can be computed as:

[tex]\frac{X_{F}-X_{O}}{X_{O}}*100[/tex]

where [tex]X_{F}[/tex] is the final value reached

           [tex]X_{O}[/tex] is the original value

So plugging in our known values and computing we have:

[tex]\frac{45-42}{42}*100= \frac{3}{42}*100 = 0.071428*100=7.14[/tex] percent increase.

Now lets go back and check if we are correct.

[tex]42+42\frac{7.14}{100}=42+2.9988=42+3=45[/tex]

So it works!

Answer:

5/4

Step-by-step explanation:

2(8x-3)-4(3x-5)=19

16x-6-12x+20=19

16x-12x-6+20=19

4x+14=19

4x=19-14

4x=5

x=5/4

Answer:

14838388÷+113

Step-by-step explanation:

because it has two zeros

Answer:

its b

Step-by-step explanation:trust

Riley will need to work approximately 13 weeks to save enough money to buy a new television.

Riley needs to save $1,212.61 to buy a new television and already has $200.30, meaning she requires an additional $1,212.61 - $200.30 = $1,012.31. As her weekly earning is $77.87, she must save for several weeks to accumulate the required amount. To find the number of weeks, divide the total amount she needs to save by her weekly earnings. Therefore: $1,012.31 / $77.87 = approximately 13 weeks. Therefore, Riley will need to work for about 13 weeks to accumulate the required amount to purchase the television.

https://brainly.com/question/21124675

#SPJ12

Answer:

Each crest takes 5 seconds to pass the observer

Step-by-step explanation:

First, we need to convert all the units to be the same.

Speed is given in meters per second and length in kilometers, so we will convert kilometers to meters:

One kilometer has 1000 meters, so that means that 0.02 km has 20 meters.

Now, we can solve the problem:

speed equals to length over time, or in equation v = s/t

That means that t = s/v

t = 20m / 4 m/s

t = 5 s

Answer:

The amount for social security for all 3 months will $558 and the contribution for medicare will be $130.5

Step-by-step explanation:

Given that the salary is paid in US dollars, we can assume that Renae Walters falls under the social security and medicare tax rates for the United States. These rates, as of 2020, fall at 6.2% for social security and 1.45% for medicare.

By formula:

-Social security contribution= Social security tax rate * Income earned

January for example Social Security= 0.062* $9000= $558                      

-Medicare contribution= Medicare tax rate * Income earned

  January for example Medicare = 0.0145* $9000= $130.5

The above method will apply through the months without changes.

Remember: The social security wage base for 2020 is fixed at $137,700. Any income above this amount is not subject to social security tax. This implies that if the total yearly income is above $137,700, the individual is only liable to pay for the amount below. In this case, this is not possible as the yearly income reaches $108,000 and hence payment has to be made for all 12 months. There is no wage base for medicare, so payments remain unaffected.

Answer:

Social security:558, Medicare: 130.50 for all three months

Step-by-step explanation:

A. 9000X.062=558 social security

9000x.0145=130.50

b. Same answer as a.

c. Same answer as a.

the amounts are the same for all 3 months.

Answer:

24

Step-by-step explanation:

First find the exterior angle: 180 - 165 = 15

Then 360 ÷ 15 because 360 divided by he exterior angle of a regular polygon is equal to the number of sides.

Answer:

Hello, 24

Step-by-step explanation:

Ingerior angle = 165

Exterior angle = 180 - 165 = 15

The sum of exterior angles of any polygon is 360

Number of sides = 360/15 = 24 A polygon is any two dimensional shape formed with the straight lines. Triangles, pentagons, quadrilaterals, and hexagons are all examples of the polygons. The name itself tells as to how many sides the shape has. For example, a triangle has three sides, whereas a quadrilateral has four sides.

Thus, when the regular polygon have if each of its interior angle is 165° then,

The corresponding exterior angle must be 180-165 = 15°

The sum of ALL the exterior angles is 360°

Sides of exterior angles is 360/15 = 24

Therefore the number of sides a regular polygon will have is 24                           Have a Awesome Day!

The percent of change is 42 %

Solution:

Given that, Hollister boys shirts for 26 dollars and sells them for 37 dollars

We have to find the percent of change

The percent change is given by formula:

[tex]Percent\ Change = \frac{\text{final value - initial value}}{\text{Initial value}} \times 100[/tex]

Here given that,

Initial value = 26 dollars

Final value = 37 dollars

Substituting the values we get,

[tex]Percent\ Change = \frac{37-26}{26} \times 100\\\\Percent\ Change = \frac{11}{26} \times 100\\\\Percent\ Change =0.423 \times 100\\\\Percent\ Change =42.3 \approx 42[/tex]

Thus percent of change is 42 %

Answer:

Step-by-step explanation:

1)y=-6x-14   ---------(i)

-x-3y=-9  ---------- (ii)

Substitution method:

Substitute y  value in equ (i)

-x -3*(-6x-14) = -9

-x - 3*-6x -3*(-14)= -9

-x + 18x + 42 = -9

17x = -9 -42

17x = -51

x = -51/17

x = -3

Substitute x value in equation (i)

y = -6*-3 -14

y =18-14

y = 4

Step-by-step explanation:

I'm using substitute in the first and something I don't know the name of in the rest.

The graph representing the solution to the system of inequalities y < 2x - 5 and y > -3x + 1 would have a dashed line for the first inequality and a solid line for the second one, with the intersected shading to the left of the lines.

The student's question centers around identifying which graph depicts the solution to the given system of linear inequalities: y < 2x - 5 and y > -3x + 1. The solution to a system of inequalities is represented by the area of intersection between the two shaded regions of the graphs. The first inequality, y < 2x - 5, is a line with a positive slope that passes through (0, -5) and the shading is below the line because 'y' is less than the expression on the right. The second inequality, y > -3x + 1, is a line with a negative slope that passes through (0, 1), and the shading is above the line because 'y' is greater than the expression on the right. Based on these conditions, the correct graph would be the one with a dashed line (indicating 'less than' or 'greater than' but not 'equal to') for the first equation and a solid line (indicating 'less than or equal to' or 'greater than or equal to') for the second equation where the shading on the left side of the lines intersect.

Remember, the slope of a line indicates how steep the line is and is calculated by rise over run. The y-intercept of a line is where the line crosses the y-axis. These key features, along with the type of inequality symbol, determine where and how to shade the graph for a system of linear inequalities.

https://brainly.com/question/25731466

#SPJ12

Answer:

Since you didn't provide any choices, a possible equations would be h = (m - 10) / 5

Step-by-step Solution:

Since we know that the flat-rate 10 doesn't have anything to do with the hourly rate, we first subtract that. Then, we divide that number by 5 to get rid of it, so we're only left with h.

This process of removing things from the equation by reversing their methods can be applied all over math and is a strategy vary commonly used.

Answer:

Step-by-step explanation:

Problems like these are aided immensely by your knowledge of multiplication tables.

1) 36 = 1·36 = 2·18 = 3·12 = 4·9 = 6·6

  27 = 1·27 = 3·9

The greatest common factor is 9, so the sum can be written as 9(4+3).

__

2) 45 = 1·45 = 3·15 = 5·9

  25 = 1·25 = 5·5

The greatest common factor is 5, so the sum can be written as 5(9+5).

__

3) 16 = 1·16 = 2·8 = 4·4

  72 = 1·72 = 2·36 = 3·24 = 4·18 = 6·12 = 8·9

The greatest common factor is 8, so the sum can be written as 8(2+9).

The height of the branch is 9.54 ft

Step-by-step explanation:

Apply Pythagorean relationship in this question where the length of the ladder is the hypotenuse, and the distance from the tree base is the shortest side.Finding the height will be;

a²+b²=c²

a²+3²=10²

a²=10²-3²

a²=100-9

a²=91

a=√91=9.54 ft

Learn More

Pythagorean relationship:https://brainly.com/question/11967357

Keywords: cat, stuck, tree. rescue,base, ladder, height , branch

#LearnwithBrainly

Answer:

-50/7

Step-by-step explanation:

-7 1/7=-50/7

Because 7*7+1=49+1=50, and don't forget the negative sign.

Answer:

Since h(x) is a one-to-one function, this means its inverse is also a function

Step-by-step explanation:

The key idea here is knowing that a function needs to be a 'many - to -one' operation (Many could also include one-to-one functions. The key if that for any x, there is only one f(x) value).

This means that for a function to have an inverse, it needs to be one-to-one. Since the domain and range switch when we look at inverse relations, and so if we have a many-to-one function, then it's inverse would be one-to-many. But we need it to be one-to-one. So the original function would need to be one-to-one.

However the short answer is to just know the 'theorem' which says that a function has an inverse function if and only if it is a one-to-one function.

Answer: c, the graph of the inverse of h(x) passes through the horizontal line test.

Step-by-step explanation:

Edge 2020

Final answer:

Calculating the least common multiple (LCM) of 3 and 5 to determine that 6 students will receive both a medal and a ribbon at a swim meet of 100 students.

Explanation:

To find the number of students at the swim meet who will receive both a medal and a ribbon, we need to look for the common multiples of 3 and 5, as medals are given to every 3rd finisher and ribbons to every 5th finisher. The least common multiple (LCM) of 3 and 5 is 15, which means every 15th student will receive both a medal and a ribbon. Since there are 100 students, we simply divide 100 by 15 and then take the integer part of the result, because we can't have a fraction of a person.

100 ÷ 15 equals approximately 6.66. The integer part is 6, which means 6 students will receive both a medal and a ribbon.

Answer:

Shorter leg: 8 units

Longer leg: 15 units

Hypotenuse: 17 units

Step-by-step explanation:

We are given [tex]h=1+2s[/tex] where [tex]h[/tex] is the hypotenuse and [tex]s[/tex] is the length of the shorter leg.

We got this equation from reading that the "hypotenuse of a triangle is 1 foot more than twice the length of the shorter leg". I replaced the "hypotenuse of a triangle" with [tex]h[/tex], "is" with [tex]=[/tex], "1 foot more than" with [tex]1+[/tex] and finally "twice the length of the shorter leg" with [tex]2s[/tex].

We also have "longer leg is 7 feet longer than the shorter leg".

I'm going to replace "longer leg" with [tex]L[/tex].

I'm going to replace "is" with [tex]=[/tex].

I'm going to replace "7 feet longer than the shorter leg" with [tex]7+s[/tex].

So we have the equation [tex]L=7+s[/tex].

So we have a right triangle since something there is a side being referred to as the hypotenuse. We can use Pythagorean Theorem to find a relation between all these sides.

So by Pythagorean Theorem, we have: [tex]s^2+L^2=h^2[/tex].

Let's make some substitutions from above:

[tex]s^2+(7+s)^2=(1+2s)^2[/tex]

Let's expand the powers using:

[tex](a+b)^2=a^2+2ab+b^2[/tex]

Applying this now:

[tex]s^2+(49+2(7)s+s^2)=(1+2(1)(2s)+(2s)^2)[/tex]

[tex]s^2+49+14s+s^2=1+4s+4s^2[/tex]

Combine like terms on right hand side:

[tex]2s^2+49+14s=1+4s+4s^2[/tex]

Subtract everything on left hand side to get 0 on that side:

[tex]0=(1-49)+(4s-14s)+(4s^2-2s^2)[/tex]

Simplify:

[tex]0=(-48)+(-10s)+(2s^2)[/tex]

Reorder into standard form for a quadratic:

[tex]0=2s^2-10s-48[/tex]

Every term is even and therefore divisible by 2. I will divide both sides by 2:

[tex]0=s^2-5s-24[/tex]

I'm going to see if this is factoroable.

We need to see if we can come up with two numbers that multiply -24 and add up to be -5.

Those numbers are -8 and 3.

So the factored form is:

[tex]0=(s-8)(s+3)[/tex]

This implies that either [tex]s-8=0[/tex] os [tex]s+3=0[/tex].

The first equation can be solved by adding 8 on both sides: [tex]s=8[/tex].

The second equation can be solved by subtracting 3 on both sides: [tex]s=-3[/tex].

The only solution that makes sense for [tex]s[/tex] is 8 since it can't the shorter length cannot be a negative number.

[tex]s=8[/tex]

[tex]L=7+s=7+8=15[/tex]

[tex]h=1+2s=1+2(8)=1+16=17[/tex]

So the dimensions of the right triangle are:

Shorter leg: 8 units

Longer leg: 15 units

Hypotenuse: 17 units

The value of m is [tex]-\frac{1}{5}[/tex]

Step-by-step explanation:

The relation between the slopes of two perpendicular line is

∵ The equation of the perpendicular line is y = mx + b

∴ The slope of the perpendicular line is m

∵ The equation of the given line is y = 5x - 2

- The slope of the given line is the coefficient of x

∴ The slope of the given line = 5

- To find the slope of the perpendicular line to the given line

   reciprocal the slope of the given line and change its sign

∵ The reciprocal of 5 is [tex]\frac{1}{5}[/tex]

∴ The slope of the perpendicular line = [tex]-\frac{1}{5}[/tex]

∵ m is the slope of the perpendicular line

∴ m =  [tex]-\frac{1}{5}[/tex]

The value of m is [tex]-\frac{1}{5}[/tex]

Learn more:

You can learn more about the slopes of the perpendicular lines in brainly.com/question/9527422

#LearnwithBrainly

Answer:

x=1850

Step-by-step explanation:

C(x) is a stand-in for total cost

since we are given the total cost we can replace the variable with its value

385000=107500+150x

now all we have to do is solve

start by subtracting 107500 from both sides

385000=107500+150x

277500=150x

now we finish solving by dividing both sides by 150

277500=150x

x=1850

please leave a like or brainliest if this was helpful :)

Answer:

Step-by-step explani think its power 10 wizard cards

ation:

Answer:

Step-by-step explanation:

Answer:

Subtract 5.5 from both sides

Or

Add -5.50 to both sides

Step-by-step explanation:

The given equation is :

27.75n + 5.50= 144.25

To get 27.75n on one side of the equation.

We subtract 5.50 from both sides to get:

27.75n + 5.50-5.50= 144.25-5.50

This simplifies to:

27.75n= 138.75

Therefore the answer is subtract 5.50 from both sides

Answer:

Step-by-step explanation:

3x^2 + 3 + 3x^2 + x + 4....combine like terms

6x^2 + x + 7 <===

Answer:

Step-by-step explanation:

P(heads) = 1/2

P(blue) = 1/4

P (heads and blue) = 1/2 * 1/4 = 1/8

Answer:

x = 215.83654587...

Answer:

Exact Form:

x=279940/1297

Decimal Form:

x=215.83654587…

Mixed Number Form:

x=215[tex]\frac{1085}{1297}[/tex]

hope this helps:)