The county fair charges $2.50 per ticket for the rides. Henry bought 15 tickets for the rides and spent a total of $55.50 at the fair. Henry spent his money only on ride tickets and fair admission. The price of the fair admission is the same for everyone. Use x to represent the number of ride tickets and y to represent the total cost.
Find the cost of admission to the fair. Explain how you found the cost of admission.
Write a linear equation that can be used to determine the cost for anyone who only pays for ride tickets and fair admission.
Explain what the coefficient of x and the constant of your linear equation represents.

Using the base and the acute angle on the base, to find the height of the dam, you would need to multiply the base by the tangent of the angle.

Height = 100 * tan(40)

Answer:

1, -4, 2 + 5i, 2 - 5i

Step-by-step explanation:

First, I factor x^2 + 3x - 4

==> I get: (x - 1) (x +4)

Then, I factor (x^2 - 4x + 29)

==> And I get (2 + 5i) (2 - 5i)

You can use the quadratic formula to factor or use the "X" to solve them.

Hope this help!

Applying the factor theorem, it is found that the roots of the equation are:

[tex]x = 1, x = -4, x = 2 + 5i, x = 2 - 5i[/tex]

The factor theorem states that if [tex]x_1, x_2, ..., x_n[/tex] are roots of a polynomial, it can be written as:

[tex](x - x_1)(x - x_2)...(x - x_n)[/tex]

In this problem:

[tex](x^2 + 3x - 4)(x^2 - 4x + 29) = 0[/tex]

Thus, the roots are the values of x for which either:

[tex]x^2 + 3x - 4 = 0[/tex]

Or

[tex]x^2 - 4x + 29 = 0[/tex]

First, [tex]x^2 + 3x - 4 = 0[/tex]

Which is a quadratic equation with [tex]a = 1, b = 3, c = -4[/tex], thus:

[tex]\Delta = 3^{2} - 4(1)(-4) = 25[/tex]

[tex]x_{1} = \frac{-3 + \sqrt{25}}{2} = 1[/tex]

[tex]x_{2} = \frac{-3 - \sqrt{25}}{2} = -4[/tex]  

Thus, [tex]x = 1[/tex] and [tex]x = -4[/tex] are roots.

Then, we solve [tex]x^2 - 4x + 29 = 0[/tex].

The coefficients are [tex]a = 1, b = -4, c = 29[/tex], so:

[tex]\Delta = (-4)^{2} - 4(1)(29) = -100[/tex]

[tex]x_{1} = \frac{-(-4) + \sqrt{100}}{2} = 2 + 5i[/tex]

[tex]x_{2} = \frac{-(-4) - \sqrt{100}}{2} = 2 - 5i[/tex]

Thus, [tex]x = 2 + 5i[/tex] and [tex]x = 2 - 5i[/tex] are also roots.

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Polygon A: 20 ft x 60 ft

           P = 2(20) + 2(60)

              =   40    +  120

              =         160

Polygon B: 3 ft x 9 ft

          P = 2(3) + 2(9)

             =   6   +   18

             =       24

Ratio of Perimeters: [tex]\frac{160}{24} = \frac{20}{3}[/tex]  = 20:3      

ANSWER

[tex]7.26451[/tex] correct  to 3 decimal places is [tex]7.265[/tex]

EXPLANATION

We start counting from the first number after the decimal point.

So starting from 2, we count 3 decimal places to the right and land on 4.

Next, we check to see if the number after 4, is greater or equal 5, then we round up, else we round down.

Since that number is 5, it is greater than or equal to 5.

Therefore we round up to obtain [tex]7.265[/tex]

7.264 51 correct to 3 decimal places is 7.265.

What is means to write a number to three decimal places is that after the decimal point, there should be three numbers. It means that the number should be rounded off to the nearest thousandth.

In order to round off to 3 decimal places take the following steps:

Examine the number in the ten thousandth place:

The number in the ten thousandth place is 5, so the number in the thousandth place increases by 1. The number becomes 7.265.

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[tex]-67\geq5+3n-21\\\\-67\geq3n+(5-21)\\\\-67\geq3n-16\ \ \ \ |+16\\\\-51\geq3n\ \ \ \ |:3\\\\-17\geq n\to n\leq-17\\\\Answer:\ \boxed{B.\ n\leq-17}[/tex]

Answer: Solve by combining like terms.

Solve for x by simplifying both sides of the equation, then isolating the variable.

x > [tex]-\frac{99}{4}[/tex]

As a decimal is: x > −24.75

On simplify both sides of the inequality the solution for the inequality -2/5x - 9 < 9/10 is x > -247.5.

To simplify both sides of the inequality, we'll perform the necessary mathematical operations step by step:

-2/5x - 9 < 9/10

Step 1: Add 9 to both sides of the inequality to isolate the term with "x":

-2/5x - 9 + 9 < 9/10 + 9

Simplify:

-2/5x < 9/10 + 90/10

Step 2: Combine the fractions on the right side:

-2/5x < (9 + 90)/10

-2/5x < 99/10

Step 3: To eliminate the fraction, multiply both sides by the reciprocal of (-2/5), which is (-5/2). When you multiply an inequality by a negative number, remember to flip the inequality sign:

(-5/2) * (-2/5x) > (-5/2) * (99/10)

Simplify:

x > -5/2 * (99/10)

x > -495/20

Step 4: Reduce the fraction on the right side:

x > -247.5

Now, the simplified inequality is:

x > -247.5

So, the solution for the inequality is "x > -247.5."

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Final answer:

When considering that yards vary directly as feet and 2 feet represent 30 yards, we determine that 3 feet represent 45 yards by setting up a direct variation proportion.

Explanation:

In the problem where yards vary directly as feet, we are given that 2 feet represent 30 yards. To find out how many yards represent 3 feet, we need to set up a proportion based on the given information that 1 yard equals 3 feet. Using the direct variation, we can create the equation: 2 feet / 30 yards = 3 feet / x yards, where x represents the unknown number of yards.

If we simplify the first ratio, 2 feet is to 30 yards as 1 foot is to 15 yards, since dividing both sides by 2 gives us: 1 foot / 15 yards. Therefore, we can continue the proportion as: 1 foot / 15 yards = 3 feet / x yards.

Now, let's solve for x by multiplying both sides of the equation by the denominator on the right side (x yards) to eliminate the fraction: 1 foot / 15 yards = 3/x, which simplifies to x = 3 * 15. After performing the multiplication, we get x = 45 yards. Therefore, 3 feet represent 45 yards on the drawing scale.

Your answer is 5/2.

Steps:

Convert element to fraction

Multiply fractions

Cancel the common factor (1)

--

Hope this helped!

Answer:

Rate of Pratap in still water is 4.5 miles/hour and rate of current is 0.5 miles/hour.

Step-by-step explanation:

Pratap Puri rowed 10 miles down a river in 2 ​hours, but the return trip took him 2.5 hours.

We know that, [tex]Speed = \frac{Distance}{Time}[/tex]

So, the speed of Pratap with the current will be:  [tex](\frac{10}{2})miles/hour = 5[/tex] miles/hour

and the speed of Pratap against the current will be:  [tex](\frac{10}{2.5})miles/hour = 4[/tex] miles/hour.

Suppose, the rate of Pratap in still water is [tex]x[/tex] and the rate of current is [tex]y[/tex].

So, the equations will be........

[tex]x+y= 5 .............................. (1)\\ \\ x-y=4 .............................. (2)[/tex]

Adding equation (1) and (2) , we will get......

[tex]2x=9\\ \\ x=\frac{9}{2}= 4.5[/tex]

Now, plugging this [tex]x=4.5[/tex] into equation (1), we will get.....

[tex]4.5+y=5\\ \\ y=5-4.5 =0.5[/tex]

Thus, Pratap can row at 4.5 miles per hour in still water and the rate of the current is 0.5 miles/hour.

Pratap's rowing speed in still water is 4.5 miles per hour, and the speed of the current is 0.5 miles per hour.

First, we need to understand that Pratap's velocity, or speed, is the sum of his own rowing speed and the speed of the current when he rows downstream, and the difference of his speed and the current when he rows upstream. To find these speeds, we can use the formula for speed, which is distance/time.

When Pratap is rowing downstream (with the current), he covers 10 miles in 2 hours, giving a speed of 10/2 = 5 miles per hour. When rowing upstream (against the current), he covers the same distance in 2.5 hours, giving a speed of 10/2.5 = 4 miles per hour.

Now, if we add these two speeds together and divide by 2, we get the rowing speed of Pratap in still water (since half the time he gets an assist from the current, and half the time he is fighting against it). This is (5+4)/2 = 4.5 miles per hour.

The speed of the current would be the difference between Pratap's rowing speed and the overall speed when he is rowing downstream, which is 5 - 4.5 = "0.5 miles per hour".

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Final answer:

The smallest power of 10 that exceeds 999,999,999,991 is 10¹² because 999,999,999,991 is just one less than 1,000,000,000,000, which can be expressed as 10¹² in exponential form.

Explanation:

The question asks for the smallest power of 10 that would exceed 999,999,999,991. Understanding how to convert numbers into their exponential form plays a crucial role here. For a power of 10, the exponent tells you how many zeros you'd add to the digit 1 to express that number in long form. For example, 10² is 100, which is a 1 followed by 2 zeros. In the case of 999,999,999,991, we need to find a power of 10 that is just larger than this number.

Observing the number 999,999,999,991, it is just one less than 1,000,000,000,000. If we were to express 1,000,000,000,000 in exponential form, it would be 10¹², because it is a 1 followed by 12 zeros. Therefore, the smallest power of 10 that exceeds 999,999,999,991 is 10¹². This example illustrates how understanding integer powers and exponential notation is essential in solving problems of this nature effectively.

[tex]1.\\\dfrac{9}{2}(8-x)+36=102-\dfrac{5}{2}(3x+24)\ \ \ \ |\text{multiply both sides by 2}\\\\\not2^1\cdot\dfrac{9}{\not2_1}(8-x)+2\cdot36=2\cdot102-\not2^2\cdot\dfrac{5}{\not2_1}(3x+24)\\\\9(8-x)+72=204-5(3x+24)\ \ \ \ |\text{use distributive property}\\\\(9)(8)+(9)(-x)+72=204+(-5)(3x)+(-5)(24)\\\\72-9x+72=204-15x-120\ \ \ \ |\text{use commutative and associative property}\\\\-9x+(72+72)=-15x+(204-120)\\\\-9x+144=-15x+84\ \ \ \ |\text{subtract 144 from both sides}[/tex]

[tex]-9x=-15x-60\ \ \ \ |\text{add 15x to both sides}\\\\6x=-60\ \ \ \ |\text{divide both sides by 6}\\\\\boxed{x=-10}[/tex]

[tex]2.\\-12x-0.4 > 0.2(36.5x+80)-55\ \ \ \ |\text{use distributive property}\\\\-12x-0.4 > (0.2)(36.5x)+(0.2)(80)-55\\\\-12x-0.4 > 7.3x+16-55\ \ \ \ |\text{use associative property}\\\\-12x-0.4 > 7.3x+(16-55)\\\\-12x-0.4 > 7.3x-39\ \ \ \ |\text{add 0.4 to both sides}\\\\-12x > 7.3x-38.6\ \ \ \ |\text{subtract 7.3x from both sides}\\\\-19.3x > -38.6\ \ \ \ \ |\text{change the signs}\\\\19.3x < 38.6\ \ \ \ |\text{divide both sides by 19.3}\\\\\boxed{x < 2}[/tex]

2)

-12x - 0.4 > 0.2(36.5x + 80) - 55

Distributive property

-12x - 0.4 > 7.3x + 16 - 55

Combine like terms

-12x - 0.4 > 7.3x -39

Subtract both sides by 7.3x

-19.3x - 0.4 > - 39

Add 0.4 to both sides

-19.3x > -38.6

Divide both sides by -19.3 (remember when dividing a negative number, the sign will be flipped)

x < 2

1)

9/2(8 -x) + 36 = 102 - 5/2(3x+24)

Multiply both sides by 2

9(8 -x) + 72 = 204 - 5(3x+24)

Distributive propery

72 - 9x + 72 = 204 - 15x - 120

Combine like terms

- 9x + 144 = -15x + 84

Add 15x to both sides

6x + 144 = 84

Subtract 144 from both sides

6x = -60

 x = -10

Hope they help.

The measure of the indicated angle [tex]\angle A$ is 46 degrees[/tex]

We can use the fact that the sum of the angles in a triangle is 180 degrees to solve for the missing angle.

Since we are given that [tex]\angle C = 46^\circ$,[/tex]  we can write the following equation:

[tex]m\angle A + m\angle B + 46^\circ = 180^\circ[/tex]

Solving for [tex]$m\angle A[/tex] we get:

[tex]m\angle A = 180^\circ - m\angle B - 46^\circ[/tex]

Since [tex]$\angle B$[/tex]  is the missing angle, we can substitute the given information into the equation to solve for its measure:

[tex]m\angle A = 180^\circ - 46^\circ - 46^\circ = 98^\circ - 92^\circ = 46^\circ[/tex]

Therefore, the measure of the indicated angle $\angle A$ is 46 degrees.

For similar question on missing angle.

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For a line you would draw a straight line with arrows on each end and for a ray you would draw a straight line with an arrow on only one end (depends on which way ray is pointing)

:)

This is your answer thanks!

Answer:

they are perpendicular to each other

Step-by-step explanation:

600,000 would be your answer

vote on my answer pplz

B. 0.6 seconds

Because they want you to round to the nearest 10th and 0 is the ground.

Answer:

Option B. 0.6 seconds

Step-by-step explanation:

As given in the table at time t = 0 the maximum height of the penny is 2 meters.

In simpler way we can say the penny has been throw from a height of 2 meters.

Now this process can be represented by the equation of motion

[tex]h=ut+\frac{1}{2}gt^{2}[/tex]

For free fall u = 0

So [tex]h=\frac{1}{2}gt^{2}[/tex]

where h = 2 meters

and g = 9.81 m/sec²

By putting these values in the equation

[tex]2=\frac{1}{2}(9.81)(t)^{2}=4.905t^{2}[/tex]

[tex]t^{2}=\frac{2}{4.905}=0.4077[/tex]

t = √0.4077 = 0.6385 seconds

or t = 0.6 seconds

Answer is option B. 0.6 seconds

The slope-intercept form of a line:

y = mx + b

m - slope

b - y-intercept

We have

[tex]y=\dfrac{2}{3}x+2[/tex]

therefore the y-intercept is 2

C is the correct answer

y=-1/4x+3/4

Pq Slope * Vt Slope should equal -1

4 * -1/4 = -1 Yes they are perpendicular.

The slope for the first equation is 4, and after transforming the second equation into slope-intercept form the slope is -0.25. Since these slopes are negative reciprocals of each other, the lines pq and vt are perpendicular.

The given equations are y=4x+3 (equation of line pq), and 2x+8y=6 (equation of line vt). To find out if these lines are perpendicular, we need to rewrite the second equation in slope-intercept form (y=mx+b). You can achieve this by isolating y.

Here are the steps:

At this point, you can see that the slope of this line is -0.25.

Line pq has a slope of 4, and line vt has a slope of -0.25. Two lines are perpendicular if their slopes are negative reciprocals of each other. The negative reciprocal of 4 is -0.25, so we can conclude that lines pq and vt are perpendicular.

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I just took the test. For PLATO the first blank is 30 and the second blank is 2.

Answer:

Part 1) The inequality that describes the relationship between the number of cookies each one of them has is [tex]x^{2} -30x+224\geq 0[/tex]

Part 2) Jessica has at least 2 cookies more than Martha.

Explanation:

Let Jessica has x cookies.

Let Martha has y cookies.

Total cookies they have = 30

Equation forms:

[tex]x+y=30[/tex] or [tex]y = 30-x[/tex]      .....(1)

Each of them ate 6 cookies from their bag.

Cookies left with Jessica = [tex]x-6[/tex]

Cookies left with Martha = [tex]y-6[/tex]

The product of the number of cookies left in each bag is not more than 80.

[tex](x-6)(y-6) \leq 80[/tex]    ....(2)

Substituting [tex]y = 30-x[/tex] in equation (2)

[tex](x-6)(30-x-6) \leq 80[/tex]

=> [tex](x-6)(24-x) \leq 80[/tex]

=> [tex]24x-x^{2}-144+6x \leq 80[/tex]

=> [tex]-x^{2}+30x-144 \leq 80[/tex]

=> [tex]-x^{2}+30x-224 \leq 0[/tex]

Multiplying both sides by -1.

[tex]x^{2} -30x+224 \geq 0[/tex]

Solving this quadratic equation, we get

[tex]x\leq 14[/tex] or [tex]x\geq 16[/tex]

We will take x = 16 (bigger value as Jessica has more cookies)

And y = [tex]30-16=14[/tex]

y = 14

So, Jessica has 16 cookies.

Martha has 14 cookies.

Cookies left in the bag :

Jessica : [tex]16-6=10[/tex] cookies

Martha  : [tex]14-6=8[/tex] cookies

Therefore, Jessica has at least 2 cookies more than Martha.

Final answer:

The solution to the inequality [tex]x^2 - 3x - 28[/tex]≥ 0 is found by factoring the quadratic equation to find its roots, which are x = 7 and x = -4. The solution to the inequality is x ≤ -4 or x ≥ 7.

Explanation:

To determine the solution to the quadratic inequality  [tex]x^2 - 3x - 28[/tex] ≥ 0, we first need to find the roots of the equation  [tex]x^2 - 3x - 28 = 0.[/tex]We can do this by factoring the quadratic expression.

We look for two numbers that multiply to give -28 and add to give -3. These numbers are -7 and +4. So we can rewrite the equation as (x-7)(x+4) = 0. Setting each factor equal to zero gives us the roots x = 7 and x = -4.

Now, we test intervals that are determined by these roots to see where the inequality holds true. The intervals are (-infinity, -4), (-4, 7), and (7, infinity). If we test a number from each interval in the inequality [tex]x^2 - 3x - 28[/tex] ≥ 0, we find that the inequality is true for x ≤ -4 and x ≥ 7. Therefore, the solution to the inequality is x ≤ -4 or x ≥ 7.

Area of Bull's Eye:

A = π r²

   = π (1)²

   = π

Area of Inner Ring:

A = π r²

   = π (3-1)²

   = 4π

Ratio between Inner Ring and Bull's Eye:

[tex]\frac{InnerRing}{Bull's Eye} = \frac{4\pi }{\pi} = 4[/tex]

Answer: It is 4 times harder to hit the Bull's Eye than it is to hit the Inner Ring

Final answer:

The Inner Ring is 8 times larger than the Bull's Eye.

Explanation:

To determine how much harder it is to hit the Bull's Eye compared to the Inner Ring, we can compare their areas.

The area of a circle is calculated using the formula A = πr^2, where A is the area and r is the radius of the circle.

The area of the Bull's Eye can be calculated as A = π(1)^2 = π square inches.

The area of the Inner Ring can be calculated as A = π(3)^2 - π(1)^2 = 9π - π = 8π square inches.

Therefore, the Inner Ring is 8 times larger than the Bull's Eye.

Answer:

As you know that Additive inverse of any number

 A = - A  , For example additive inverse of 2 is -2

or additive inverse of (-2) is 2.

Now, According to the question given

Emily has fixed monthly expenses that are taken directly out of her bank account.

As she wants to know,  how much money she must deposit in her account each month to cover these expenses.

So, Expenses are Additive inverse of Deposit or Deposit are additive inverse of Expenses.

Out of the given Options Option D which is, Emily can add (–48) + (–12) + (–44) to find her total expenses. The additive inverse of this number is the amount Emily must deposit each month. is correct.

Answer:

d

Step-by-step explanation:

He has:

45 red tiles

90 blue tiles

75 yellow tiles

Greatest number of stones Marco can make is the GCF of the three numbers above which is 3 × 5 = 15 (Solution attached below)

its d. i know for sure had the same question promise no lie