John is adding a curved edge to the landscaping in front of the high school. The curve is an arc of a circle with a radius of 1600 feet. The central angle that intercepts the curve measures π/8 radians. The length of the curve to the nearest foot is _____ feet.

Answers

Answer 1

By definition, the arc length is given by:
S = R * theta
Where,
Theta: central angle
R: radio
Substituting the values we have:
S = (1600) * (π / 8)
Rewriting we have:
S = 200π feet
S = 628.3185307 feet
Round to the nearest foot:
S = 628 feet
Answer:
The length of the curve to the nearest foot is 628 feet.

Answer 2

The length of the curve to the nearest foot is 628 feet.

To find the length of the curved edge, which is an arc of a circle, one can use the formula for the arc length [tex]$ L $[/tex] of a circle, given by the product of the radius [tex]$ r $[/tex] and the radian measure [tex]$ \theta $[/tex] of the central angle that intercepts the arc:

[tex]\[ L = r \cdot \theta \][/tex]

In this case, the radius [tex]$ r $[/tex] is given as 1600 feet, and the central angle [tex]$ \theta $[/tex] is given as [tex]$ \frac{\pi}{8} $[/tex] radians.

Plugging in the values, we get:

[tex]\[ L = 1600 \text{ feet} \cdot \frac{\pi}{8} \text{ radians} \][/tex]

To find the numerical value, we use the approximation [tex]$ \pi \approx 3.14159 $[/tex]:

[tex]\[ L \approx 1600 \cdot \frac{3.14159}{8} \] \[ L \approx 1600 \cdot 0.39269906 \] \[ L \approx 628.3185 \][/tex]

Since we are asked to round to the nearest foot, we consider the value 628.3185 feet. Rounding this to the nearest whole number, we get:

[tex]\[ L \approx 628 \text{ feet} \][/tex]

Therefore, the length of the curve to the nearest foot is 628 feet.

Related Questions

1. The graph shows the distance y, in centimeters, a pendulum moves to the left (negative displacement) and right (positive displacement), for a given number of seconds x. (a) From its resting position, how long does it take the pendulum to swing one direction, then the other, and then return to its resting position? (b) What is the pendulum’s maximum displacement? (c) What percent of a full cycle is completed within 1 s? (d) How is the pendulum moving during the time period from x = 5 to x = 5.625? (e) What is the equation of the graph?

Answers

The graph is shown in the picture attached.

A) In order to calculate how long it takes the pendulum to swing one direction, then the other, and then return to its resting position, you need to look at the graph and see where the function returns to zero after going once up and once down. This time is called period (T), which is defined as the time taken to perform one complete oscillation.
In our case, T = 5 s (see the second picture attached for reference).

B) In order to find the pendulum's maximum displacement, you need to look at the graph and see how high and low on the y-axis the function goes. This displacement is called amplitude (A), which is defined as the maximum displacement from the resting position in either direction.
In our case, A = 20 cm (see the second picture attached for reference).

C) Since the period of the pendulum is 5 seconds and it swings constantly, the fraction of a cycle completed in 1 second is calculated by simply dividing
p = 1 / 5 = 0.20
Therefore, in 1 second the pendulum completes 20% of its cycle.

D) During the time period from x = 5 to x = 5.625, we can see from the graph that the pendulum has just started its second oscillation, therefore it starts from the resting position and it moves towards the right (positive values of y)decreasing its velocity.

E) The equation of the graph is a sinusoidal function, therefore it will have an equation like
[tex]f(t) = A \cdot sin( \frac{2 \pi}{T} \cdot t - b) + c [/tex]

where:
A = amplitude
T = period
b and c = shifting constants

In order to find b and c, we recall that the graph starts at (0,0) and therefore it is not shifted either horizontally or vertically, and therefore we can infer that b = c = 0.

Substituting the values, we find:
[tex]f(t) = 20 \cdot sin( \frac{2 \pi}{5} \cdot t) [/tex]

Fran sells brownies $3 each she cuts pan of brownies into 6 pieces if she makes 4 pan of brownies how much money she make

Answers

Answer: 6•4•3=72$

Show your work: 6•4=24
24•3=72$

Written answer: If Fran sells all her brownies, she will make 72$

A number that divides evenly into another number is known as which of the following?

A.) prime number
B.)factor
C.) multiple
D.) Integer

Answers

It should be multiple of that number:
the prime number is greater than one and cannot be divided by other numbers.
the factor is an element of a number.
multiple means it can be various numbers
An integer is a whole number from - infinity to positive infinity including zero.

A number that divides evenly into another number is known as factor.

The correct answer is

B.) factor.

A factor is a number that divides evenly into another number. To find the factors of a number, you can perform a process of division or use other mathematical methods.

Let's take an example to illustrate:

If we consider the number 12, its factors are the numbers that divide it evenly without leaving a remainder. We can start by dividing 12 by 1:

12 ÷ 1 = 12

Since there's no remainder, 1 is a factor of 12. Now, let's try dividing 12 by 2:

12 ÷ 2 = 6

Again, there's no remainder, so 2 is also a factor of 12. Continuing this process, we find that 3 is also a factor of 12:

12 ÷ 3 = 4

And finally, 12 ÷ 4 = 3

So, the factors of 12 are 1, 2, 3, 4, 6, and 12.

Each of these numbers divides evenly into 12, making them factors. Therefore, the correct answer is B.) factor.

Factors are essential in various mathematical concepts, including prime factorization, finding greatest common divisors, and simplifying fractions. Understanding factors helps in solving problems related to divisibility and multiplication. By identifying factors, we can break down complex numbers into simpler components, aiding in various mathematical computations and analyses. Hence, recognizing factors is fundamental in mathematics.

Complete question:

A number that divides evenly into another number is known as which of the following?

A.) prime number

B.)factor

C.) multiple

D.) Integer

1 cubic foot of sand weighs 100 lb. a square sandbox with 5 foot sides has a half of a foot of sand in it. how many pounds of sand is sandbox the holding?

Answers

1250. Cubic feet = volume and volume is length * width * height. The volume of this would be 5x5x(1/2), which equals 12.5 cubic feet. 12.5*100=1250

Final answer:

The sandbox with 5-foot sides and a half-foot depth of sand is holding 1250 pounds of sand, calculated using the volume of the sand and the known weight per cubic foot.

Explanation:

To calculate the weight of sand in the sandbox, we can use the formula for the volume of a cube, which is length × width × height. Given that the sandbox has 5-foot sides and is filled with a half of a foot of sand, the volume × weight of the sand can be calculated as follows:

The volume of sand = 5 ft (length) × 5 ft (width) × 0.5 ft (height) = 12.5 cubic feet.Since 1 cubic foot of sand weighs 100 lb, the total weight of the sand = 12.5 cubic feet × 100 lb/cubic foot = 1250 pounds.

Therefore, the sandbox is holding 1250 pounds of sand.

If Luis earns a base salary of $150.00 every week with an additional 14 % commission on everything he sells .Luis sold $6050.00 worth of items last week. what is Luis's total pay last week

Answers

6050x 14%= 847
847+150=$997 was Luis's total pay last week

Which of the following scenarios has a lower y-intercept than y = 4x + 5 ?

(a.) A 50 gallon tub is draining. Every 2 minutes, the amount of water decreases by 2 gallons.

(b.) Reginaldo had $17 in his account and for every book he buys, it costs him $4.

(c.) Sydney has collected 8 postcards. Each time a friend comes to visit, Sydney gives her a postcard.

(d.) Owen has 3 pets. He receives a new pet each time he has a birthday.

Answers

Comment
The key to this question is "What do you start with?" All of them (except D) start with something and then a condition reduces the starting point.
A
The condition (at zero) starts with 50 gallons. Every 2 minutes the amount taken away is 2 gallons.
The equation looks like this
y = -2x + 50
So what do you start with? You started with 50 gallons. That's your y intercept. It's big. A is NOT the answer.

B
Renaldo starts with 17 dollars. He hasn't done anything, and he still has 17 dollars. If he buys a book, he has 4 dollars less. So his equation is
y = -4x + 17. The y intercept is 17 if he has bought no books. The answer is NOT B

C
Sydney starts with 8 postcards. Every time a friend comes, Sydney has 1 less post card. Her equation is
y = 8 - x That's not the answer either.

D
What do you start with? 3 pets, correct? Every birthday Owen get's one more. But the starting point is three. So his equation is
y= 3 + x where x is the number of birthdays.
D has the lowest starting point.

D <<<< Answer

The square of mark's age 3 years ago is 6 times the age he will be in 9 years. what is his age now? 9 12 15

Answers

This is how you do it!

(x-3)^2=6(x+9)
x^2 - 6x + 9 = 6x + 54
x^2 - 12x + 9 = 54
x^2 - 12x - 45 = 0
Then Factor the left side
(x + 3)(x - 15) = 0
x + 3 = 0 and x - 15 = 0
x = -3 and x = 15

The only option that can be an age is 15

Therefore the answer is 15

Answer:

mos def 15

Step-by-step explanation:

The figure has 60 edges and 30 vertices. Use Euler’s formula to find the number of faces in the given polyhedron.

Answers

Let the number of faces ⇒⇒⇒ F
Number of Vertices        ⇒⇒⇒ V
Number of Edges          ⇒⇒⇒ E

Euler's Formula ⇒⇒⇒⇒⇒ F + V − E = 2

given:⇒⇒⇒ 60 edges and 30 vertices
∴ E = 60    and    V = 30
∴ F + 30 - 60 = 2
∴ F = 2 + 60 - 30 = 32

Number of faces = 32

An investment banker is responsible for investing a customer’s money into the greatest interest earning account. The banker has the following options for his customer’s investment: Account A: interest rate = 4.8% term of investment = 10 years interest compounded monthly Account B: interest rate = 4.9% term of investment = 10 years interest compounding continuously Which account, A or B, will earn the customer the greatest amount of interest on his $150,000 investment? In your final answer, include all of your calculations.

Answers

The more often an interest rate is compounded, the better the return it provides. Continuous compounding at 4.9% would give a better return than monthly compounding at the same rate. Monthly compounding at 4.9% would give a better return than monthly compounding at 4.8%.

Account B will earn the customer the greatest amount of interest.

_____
The question is a qualitative one; no calculations are necessary. One simply needs to observe that 4.9 > 4.8.

(If the numbers were reversed, monthly compounding at 4.9% would give a better return than continuous compounding at 4.8%. A calculation is needed in order to come to that conclusion.)

Find the center, vertices, and foci of the ellipse with equation 2x2 + 9y2 = 18.

Answers

we have that
2x² + 9y² = 18------> divided by 18
so
2x² /18+ 9y²/18 = 18/18------> x/9² + y²/2 = 1

Part a)
the equation of the ellipse if of the form
(x-h)²/a²+(y-k)²/b²=1
where (h,k) is the center
in this problem
(h,k) is (0,0) ------> is the origin
a²=9------> a=3
b²=2-----> b=√2

Part b)
vertices are
(h+a,k) and (h-a,k)
(0+3,0)-----> (3,0)
(0-3,0)----> (-3,0)

Part c)
foci are
(h+c.k) and (h-c, k)
where
c²=a²-b²-----> c²=9-2-----> c²=7-----> c=√7

the foci are
(0+√7, 0)-----> (√7,0)
(0-√7,0)------> (-√7,0)

Item 12 a regular triangular pyramid has a base and lateral faces that are congruent equilateral triangles. it has a lateral surface area of 57 square centimeters. what is the surface area of the regular triangular pyramid?

Answers

Answer:

Step-by-step explanation:

im short on time sorry for no explanation.

When wrapping a birthday gift for his mother kemji adds additional 2.5 square feet of gift wrap to allow for overlap. how many squares feet of gift wrap will kenji use to wrap a gift 3.5 ft long 18 in wide and 2 ft high?

Answers

For this case, the first thing to do is find the surface area of a rectangular prism.
A = 2 * (h) * (l) + 2 * (h) * (w) + 2 * (w) * (l)
Where,
h: height
l: long
w: width
Substituting values:
A = 2 * (2) * (3.5) + 2 * (2) * (18/12) + 2 * (18/12) * (3.5)
A = 30.5 ft ^ 2
Then, the amount of wrapping paper is:
W = A + 2.5
W = 30.5 + 2.5
W = 33 ift ^ 2
Answer:
kenji will use 33 ft ^ 2 of gift wrap to wrap a gift

if a crate contains 25,500 ounces of rice , about how many kilograms does it contain?

Answers

well, we know there are 16oz in 1lb, and we know there are 2.2lbs in 1Kg, so

[tex]\bf 25500~\underline{oz}\cdot \cfrac{1~\underline{lb}}{16~\underline{oz}}\cdot \cfrac{1kg}{2.2~\underline{lb}}\implies \cfrac{25500\cdot 1\cdot 1~kg}{16\cdot 2.2}\qquad \approx \qquad 724.43\overline{18}~kg[/tex]

Michael has $1.95 totally in his collection, consisting of quarters and nickels. The number of nickels is three more than the number of quarters. how many quarters and nickels does Michael have?

Answers

1 nickel=$0.05
1 quarter=$0.25
let the number of quarters be x, the number of nickels will be 3+x
thus:
0.05(3+x)+0.25x=1.95
0.05x+0.15+0.25x=1.95
0.30x=1.8
x=6
thus the number of quarters is 6
the number of nickels=6+3=9

Which point lies outside the circle with equation (x - 2)2 + (y + 3)2 = 4?

(1, -4)

(0, -3)

(2, 0)

(2, -4)

Answers

Graphing the circle and the points shows that the point that lies outside the circle is ...
(2, 0)

The only point outside of the line is (2, 0)

In order to find if a point is outside, inside or on the line, you simply have to put the number into the equation. If the result is both sides are equal, then it is on the line. If the left side is bigger than the right side, then it is outside of the line. If the right side is bigger than the left, then it is inside of the line. So lets plug in and see where (2, 0) falls.

(x - 2)^2 + (y + 3)^2 = 4

(2 - 2)^2 + (0 + 3)^2 = 4

0^2 + 3^2 = 4

0 + 9 = 4

9 = 4

Since the left side is bigger than the right, we know it is outside of the line

The area of the circle shown below is 100π. What is the diameter (D) of the circle?

Answers

[tex]\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\ -----\\ A=100\pi \end{cases}\implies 100\pi =\pi r^2 \\\\\\ \cfrac{100\pi }{\pi }=r^2\implies 100=r^2\implies \sqrt{100}=r\implies \boxed{10=r}[/tex]

since a diameter is twice as long as the radius, this one is also 2r.

Answer: 20 units

Step-by-step explanation:

We know that the area of a circle is given by :-

[tex]\text{Area}=\pi r^2[/tex], where r is the radius of the circle.

We are given that the area of the circle = [tex]100\pi[/tex] square units.

[tex]\Rightarrow\ 100\pi=\pi r^2\\\\\Rightarrow\ r^2 =100[/tex]

Taking square root on both the sides , we get

[tex]\\\\\Rightarrow\ r=10[/tex]

The diameter of the circle is given by :-

[tex]d=2r=2(10)=20\text{ units}[/tex]

At 59 F, crickets chirp at a rate of 76 times per minute, and at 65 F they chirp 100 times per minute. Write an equation in slope-intercept form that represents the situatio.

Answers

y = 4x-160 is your simplified answer to this question.

Final answer:

The rate of crickets chirping is linearly dependent on the temperature and can be represented by the equation y = 4x -100, whereby y is the number of chirps per minute, and x is the temperature in °F.

Explanation:

This is essentially a linear equation problem where the rate of cricket chirps is related to the temperature.

Firstly, we list our two points: (59, 76) and (65, 100).

We can then calculate the slope (m). m = (y2-y1) / (x2-x1) = (100-76)/(65-59) = 24/6 = 4.

We have the rate of cricket chirps increasing by 4 chirps per increase in 1°F. Our equation is now of the form y= 4x + b.

Finally, we'll calculate the y-intercept (b) by plugging one of our points into the equation. If we choose the point (59, 76), we get 76 = 4*59 + b. Solving for b, we get b = -100.

So, the equation is y = 4x -100, where y is the number of chirps per minute, and x is the temperature in °F.

Learn more about Linear Equations here:

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After 7 years, Abner earned $1575 in simple interest from a CD into which he initially deposited $6000. What was the annual interest rate of the CD?

Answers

The answer is C. 3.75%

The annual interest rate of the CD was 3.75 %

Explanation

Simple Interest formula is : [tex] I =P*r*t [/tex] , where [tex] I= [/tex] Amount of interest, [tex] P= [/tex] Principal/Initial amount, [tex] r= [/tex] rate of interest in decimal form and [tex] t= [/tex] time in years

Here Abner earned $1575 in simple interest and he initially deposited $6000. So, [tex] I=1575 [/tex] dollar and [tex] P= 6000 [/tex] dollar

Also given that, [tex] t = 7 [/tex] years

Now according to the formula...

[tex] I= P* r*t\\ \\ 1575= 6000*r*7\\ \\ 1575= 42000*r\\ \\ r= \frac{1575}{42000}= 0.0375 [/tex]

For getting the interest rate in percentage, we will multiply it by 100%. So... (0.0375 × 100) % = 3.75 %

So, the annual interest rate of the CD was 3.75 %

If VX = WZ = 40 cm and m∠ZVX = m∠XWZ = 22°, can ΔVZX and ΔWXZ be proven congruent by SAS? Why or why not?

Yes, along with the given information, ZX ≅ ZX by the reflexive property.
Yes, the triangles are both obtuse.
No, the sides of the triangles intersect.
No, there is not enough information given.

Answers

No, there is not enough information given to prove that ΔVZX and ΔWXZ are congruent by SAS.

What are congruent triangles?

Two triangles are said to be congruent if their corresponding sides and angles are equal.

The given information only provides the lengths of two sides and the measures of two angles in the triangles, but we do not know if the third side is congruent, and we cannot assume that it is by the given information.

Additionally, the given information does not specify that one of the congruent sides is included between the congruent angles, which is necessary for the SAS postulate to be used to prove congruence.

Therefore, there is not enough information given to prove that ΔVZX and ΔWXZ are congruent by SAS.

Learn more about congruent triangles here:

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(x^ 3 + y ^3) divided by (x - y)

Answers

x^2+xy+y^2 is the anwer

Identify the transformations that describe the graph of an even function. Select all that apply.

reflection over the x-axis
reflection over the y-axis
reflection over the line y = x
90° rotation around the origin
180° rotation around the origin

Answers

The function becomes even when f(-x) = f(x)
So, if f is even function and y = f(x)
∴ y = f(-x)
∴ (x,y) and (-x,y) on the same graph
or we can say (-x,y) is an image for (x,y)
So, the rule of transformation becomes (x,y) ⇒⇒⇒ (-x,y)
Which is the same rule of reflection over the y-axis.

∴ The correct choice is the second option

Answer:

reflection over the y-axis

Step-by-step explanation:

Which equation does not represent a function? A) y = 2x + 3 B) x = 4y + 7 C) 6x - 5y = 8 D) y2 = -5x - 8

Answers

D. It is not a function because there are multiple outputs for one input.

Answer:

D) y2 = -5x - 8

Step-by-step explanation:

A function is a rule between two sets A and B so that each element of set A (Domain) corresponds to a single element of set B (Range). Mathematically they can be expressed as:

[tex]f: A\rightarrow B\\\\a\rightarrow b =f(a)[/tex]

So:

[tex]y^2=-5x-8\\\\y=\pm \sqrt{-5x-8}[/tex]

Isn't a function because the elements of the domain don't corresponds to a single element of the range.

We can see this in an easier way using the vertical line test, which is a visual way to determine if a curve is a graph of a function or not. If a vertical line intersects a curve in an xy plane more than once, then for a value of x the curve has more than one value of y, and then the curve does not represent a function.

I attached you the graphs, so you can corroborate the results visually.

Bonnie can complete her paper route in 45 min. when her sister jean helps her it takes them 18 min to complete the route. how long would it take jean alone?

Answers

We know that Bonnie complete her paper route in 45min. So, in 1min she can complete:

[tex]\frac{1}{45}[/tex] of her paper route.

We need to know how long it would take Jean alone, then we will call this time x. Working together they last 18min, so in 1min they can complete:

[tex]\frac{1}{18}[/tex] of the paper route.

The paper route working together satisfies the following equation:

[tex]\frac{1}{18} = \frac{1}{45} + \frac{1}{x}[/tex]

Solving this equation:

[tex]\frac{1}{x} = \frac{1}{18} - \frac{1}{45} = \frac{45-18}{810} = \frac{27}{810}[/tex]
[tex]x = \frac{810}{27} = 30min[/tex]

Finally:
It takes 30min to complete the paper route by Jane alone.

How many different ways can you choose a council with exactly 3 sophomores, 1 junior, and 2 seniors?

Answers

I think it's just 1 way; 3 sophomores, 1 junior and 2 seniors.

Triangle GHI has the angle measures of G = (2x + 5)°, H = (6x − 10)°,
and I = (x + 5)°. What is the actual measurement of angle H?

Answers

The sum of the angles of a triangle is equal to 180 degrees.
We then have the following equation:
G + H + I = 180
Substituting values:
(2x + 5) + (6x - 10) + (x + 5) = 180
Clearing x we have:
(2x + 6x + x) + (5-10 + 5) = 180
9x + 0 = 180
9x = 180
x = 180/9
x = 20
Then, for the angle H we have:
H = (6x - 10) °
Substituting:
H = (6 (20) - 10) °
H = (120 - 10) °
H = 110 °
Answer:
the current measurement of angle H is:
H = 110 °

The actual measurement of angle H is thus 110 degrees.

To find the actual measurement of angle H in triangle GHI, we can use the fact that the sum of the interior angles in any triangle is always 180 degrees. Given the expressions for angles G, H, and I as G = (2x + 5)", H = (6x − 10)", and I = (x + 5)", we can set up the equation (2x + 5) + (6x - 10) + (x + 5) = 180 to find the value of x. After determining x, we substitute it back into the expression for angle H to get the desired measurement.

Setting up the equation we have:
(2x + 5) + (6x - 10) + (x + 5) = 180

Combine like terms to get 9x = 180

Divide both sides by 9 to find x: x = 20 degrees

Now plug this value into the expression for angle H: H = 6(20) - 10

We find that H = 120 - 10 degrees, so H = 110 degrees

To find the measurement of angle H in triangle GHI, we apply the fact that the sum of angles in a triangle is always 180 degrees. By solving the equation that sets this sum, we find the value of x, and then use it to determine that angle H measures 110 degrees.

A college basketball player makes 5/6 of his free throws. Assuming free throws are independent, the probability that he makes it exactly three of his next four free throws is

Answers

Final answer:

The probability that a college basketball player makes exactly three of his next four free throws is calculated using binomial probability, resulting in approximately 38.58%.

Explanation:

The probability that a college basketball player makes exactly three of his next four free throws, given that he makes 5/6 of his free throws, involves calculating a binomial probability. We have four independent events (four free throws), and we want exactly three successes (made throws) and one failure (missed throw). We use the following formula for the binomial probability:

P(X=k) = C(n, k) × p^k × (1-p)^(n-k)

where:

C(n, k) is the number of combinations of n items taken k at a time.p is the probability of success on any given trial.n is the number of trials (4 in this case).k is the number of successes (3 in this case).(1-p) is the probability of failure on any given trial.

In this problem:

p = 5/6 (probability of making a throw)(1-p) = 1/6 (probability of missing a throw)n = 4 (total number of free throws)k = 3 (number of free throws made)

Plugging in the values:

P(X=3) = C(4, 3) × (5/6)^3 × (1/6)^1

C(4, 3) is 4, since there are four different ways to make three throws and miss one (MMM-M, MM-MM, M-MMM, MMMM-). So the calculation gives:

P(X=3) = 4 × (5/6)^3 × (1/6) = 4 × (125/216) × (1/6) = 500/1296, which simplifies to about 0.3858 or 38.58%.

Therefore, the probability that he makes exactly three of his next four free throws is 0.3858 or 38.58%.

A pair of fair dice is rolled once. suppose that you lose $ 8 if the dice sum to 3 and win $ 13 if the dice sum to 10 or 12. how much should you win or lose if any other number turns up in order for the game to be fair?

Answers

You should lose $1.20 for any other outcome to make it a fair game.

There are 2 ways to get a sum of 3 out of 36 outcomes; this probability is 2/36.
There are 4 ways to get a sum of 10 or 12 out of 36 outcomes; this probability is 4/36.
There are 36-(2+4) = 36-6 = 30 other outcomes out of 36; this probability is 30/36.

We lose $8 if we get a sum of 3; this expected value is -8(2/36) = -16/36.
We win $13 if we get a sum of 10 or 12; this expected value is 13(4/36) = 52/36.
Using x as the amount we win or lose for the other outcomes, the expected value is 30x/36.

In order to be a fair game, the amount we win and/or lose should come outto( $0 total.

Together we have the equation
-16/36+52/36+30x/36 = 0

Adding the fractions, we have
(-16+52+30x)/36 = 0
(30x+36)/36 = 0

Multiplying both sides by 36,
30x+36=0*36
30x+36=0

Subtracting 36 from both sides,
30x+36-36=0-36
30x=-36

Dividing both sides by 30,
30x/30 = -36/30
x=-36/30 = -1.2

Thus we should lose $1.20 for any other roll.

Solve the quadratic in form equation x^4-14x^2+45=0

Answers

x⁴-14x²+45=0
(x²) ²-14x²+45=0
let y=x²
y²-14y+45=0
(y-9) (y-5) =0
y=9 or y=5
x²=9 or x²=5
x=±3 or x=±√5

identify the type of conic section that has the equation 4x^2+25y^2=100 and identify its domain and range.

Answers

4x^2+25y^2=100

[tex]4x^2+25y^2=100 \\\\ Dividing \;both \;sides \;by \;100 \\\\ \frac{4x^2}{100}+ \frac{25y^2}{100}= \frac{100}{100} \\\\ \frac{x^2}{25}+ \frac{y^2}{4}= 1 \\\\ \frac{x^2}{5^2}+ \frac{y^2}{2^2}= 1 \\\\ This \;is \;an \;ellipse. \\\\

\frac{x^2}{a^2}+ \frac{y^2}{b^2}= 1 [/tex]

Domain of an ellipse is x ∈ [-a,a] and Range of an ellipse is y ∈ [-b,b].

So, given equation is an Ellipse where Domain is x ∈ [-5,5] and Range is y ∈ [-2,2].

Solve the system of equations using a matrix. Separate the x and y values with a comma. 2x-y=6 & 3x-y=11

Answers

[tex]\left\{\begin{array}{ccc}2x-y=6\\3x-y=11\end{array}\right\\\\ \left[\begin{array}{ccc}2&-1\\3&-1\end{array}\right\left|\begin{array}{ccc}6\\11\end{array}\right]\xrightarrow{r_1-r_2} \left[\begin{array}{ccc}-1&0\\3&-1\end{array}\right\left|\begin{array}{ccc}-5\\11\end{array}\right]\xrightarrow{r_2+3r_1}[/tex]
[tex]\left[\begin{array}{ccc}-1&0\\0&-1\end{array}\right\left|\begin{array}{ccc}-5\\-4\end{array}\right]\xrightarrow{(-1)r_1;(-1)r_2}\left[\begin{array}{ccc}1&0\\0&1\end{array}\right\left|\begin{array}{ccc}5\\4\end{array}\right]\\\\Answer:\ \left\{\begin{array}{ccc}x=5\\y=4\end{array}\right\to(5;\ 4)[/tex]

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