Graphing Quadratic Equations

Answer:

x = 4, -1

Step-by-step explanation:

Move all terms to the left side and set equal to zero. Then set each factor equal to zero.

have a good day :)

Answer:

28 inches.

Step-by-step explanation:

The side length of the square can be found by taking the square root of the area, which is 7 inches.

The perimeter of a square is simply 4 times the length of one of its sides, so the perimeter of this square paper is:

4 x 7 inches = 28 inches

The stack of  paper will be 3355.4432 meters high after stacking halves of it tearing up for 25 times by method of unit conversion from millimeters to meters.

A sheet of paper is 0.1 mm thick.
It is folded in halves for 25 times by tearing it.
The above information can be represented in an equation form as,
Height of the paper stack = (0.1)* ([tex]2^{n}[/tex]) in millimeters
where, n denotes the number of times paper is folded.
Thus, height of the paper stack after tearing it in halves for 25 times we get,
Height = (0.1)* ([tex]2^{25}[/tex]) in millimeters
= 3355443.2 millimeters
We can convert milimmillimeters in meters by the following way as,
1 millimeter = 0.001 meter
Therefore, 33355443.2 millimeters = (0.001)(3355443.2) meters
= 3355.4432 meters

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The correct statement regarding the meaning of the conditional probability P(B|A) is given as follows:

C. The probability that the sum is 11, given that the first number cube shows a 6.

Conditional probability is the probability of one event happening, considering the result of a previous event.

The notation is P(B|A), which is read as the probability of B happening, considering that A has happened.

The events in this problem are given as follows:

Hence the correct statement regarding the meaning, that is, B given A = sum of 11 given that a six was rolled first, is given by option C.

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The graph of y= √x-1 is given by the image presented at the end of the answer.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The parent function in the context of this problem is given as follows:

y= √x

Which has vertex at the origin.

The translated function is given as follows:

y = √x-1

Which is a translation down one unit of the parent function, hence it will have vertex at (0,-1).

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(a) Approximately 65.91% of SAT verbal scores are less than 550.

(b) Out of 1000 randomly selected SAT verbal scores, we can expect approximately 16 scores to be greater than 525.

(a) To find the percent of SAT verbal scores less than 550, we need to find the area under the normal curve to the left of 550. We can use the z-score formula to convert 550 to a z-score

z = (x - μ) / σ

where x is the score we're interested in, μ is the mean, and σ is the standard deviation.

z = (550 - 501) / 119 = 0.41

Using a standard normal distribution table or a calculator, we can find that the area to the left of z = 0.41 is 0.6591.

Therefore, approximately 65.91% of SAT verbal scores are less than 550.

(b) To find the number of SAT verbal scores greater than 525 out of 1000 randomly selected scores, we can use the normal distribution formula

z = (x - μ) / (σ / √(n)

where n is the sample size (1000 in this case).

z = (525 - 501) / (119 / √(1000)) = 2.12

Using a standard normal distribution table or a calculator, we can find that the area to the right of z = 2.12 is 0.0162.

Therefore, out of 1000 randomly selected SAT verbal scores, we can expect approximately 16 scores to be greater than 525.

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The inequality that describes and suitable for this situation is 9.99+1.29n≤50 under the condition that Lin got a $50 gift card to an online music store. She uses the gift card to buy an album for $9.99. Then the correct option is Option C.

Given,
Lin has a $50 gift card and she spends $9.99 on an album. The amount of money left on the gift card is $50 - $9.99
= $40.01.

In the event that Lin buys n songs at $1.29 each, the total cost of the songs will be evaluated as  $1.29n.

The total amount spent on the album and songs cannot reach the level to exceed the amount left on the gift card, which is determined as $40.01.

So we can write the inequality equation
9.99 + 1.29n ≤ 50

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The complete question is
Lin got a $50 gift card to an online music store. She uses the gift card to buy an album for $9.99. She also wants to use the gift card to buy some songs. Each song costs $1.29. Which of these inequalities describes this situation, where n is the number of songs Lin wants to buy?9.99+1.29n≥50

a) 9.99+1.29n≤50

b) 9.99−1.29n≥50

c) 9.99−1.29n≤50

If Mario asked "5-friends" about the amount they spent on boxes of cards last year, then only 3 friends spent less than $32.

We need to analyze the data given in the table and determine how many friends spent less than $32.00 on boxes of cards last year.

We are given the following data:

⇒ Friend 1 = $36,

⇒ Friend 2 = $32,

⇒ Friend 3 = $31,

⇒ Friend 4 = $12,

⇒ Friend 5 = $30.

We need to determine how many friends spent less than $32.00.

From the data given, we see that Friend 2 spent exactly $32.00, which is not less than $32.00.

So, we need to look at the remaining four friends to determine how many of them spent less than $32.00.

We can see that Friend 3 spent $31.00, which is less than $32.00.

So, at least one friend spent less-than $32.00.

Friend 4 spent only $12.00, which is much less than $32.00.

So, at least two friends spent less than $32.00.

Friend 5 spent $30.00, which is also less than $32.00.

So, at least three friends spent less than $32.00 on boxes of cards last year.

Therefore, three friends spent less than $32.00.

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The given question is incomplete, the complete question is

Mario asked 5 friends how much they spent on boxes of cards last year.

He organized the data in a table.

Friend 1  = $36,

Friend 2 = $32,

Friend 3 = $31,

Friend 4 = $12,

Friend 5 = $30.

How many friends spent less than $32.00?

Answer:

15

Step-by-step explanation:

[tex]\frac{5}{3}[/tex] = [tex]\frac{25}{x}[/tex]

5 x 5 = 25

3 x 5 = 15

Helping in the name of Jesus.

Answer:

# > 1

Step-by-step explanation:

12x? > 12

/ 12.     /12.

? > 1

Any number larger than 1 makes this true.

The volume, in cubic feet, of the sandbox is 12 cubic feet.

The volume V of a rectangular prism is given by the formula:

V = lwh

Where:

l is the representation of length, w is the representation of width, and h is the representation of height.

As per the given information, the length l = 4 1/2 feet, the width w = 5 1/3 feet, and the height h = 1/2 foot.

We need to convert the mixed numbers to improper fractions:

l = 4 1/2 = 9/2

w = 5 1/3 = 16/3

h = 1/2

Substitute the values to the given  formula,

V = (9/2) x (16/3) x (1/2)

V = 48/4

V = 12 cubic feet.

Therefore, the volume of the sandbox is 12 cubic feet.

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The 95% confidence interval for the proportion of people who reported problems getting to sleep after watching a horror film is approximately (0.550, 0.810).

CI is the confidence interval, p is the sample proportion, Z is the Z-score corresponding to the desired confidence level (1.96 for 95%), and n is the sample size.

First, calculate the sample proportion (p):

p = 34 / 50 = 0.68

Next, apply the formula:

CI = 0.68 ± 1.96 * sqrt(0.68 * (1 - 0.68) / 50)

CI = 0.68 ± 1.96 * sqrt(0.68 * 0.32 / 50)

CI = 0.68 ± 1.96 * sqrt(0.2176 / 50)

CI = 0.68 ± 1.96 * sqrt(0.004352)

CI = 0.68 ± 1.96 * 0.065975

CI = 0.68 ± 0.129512

Lower limit: 0.68 - 0.129512 = 0.550488

Upper limit: 0.68 + 0.129512 = 0.809512

So, the 95% confidence interval for the proportion of people who reported problems getting to sleep after watching a horror film is approximately (0.550, 0.810).

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Step-by-step explanation:

A  true   opposite side are congruent and parallel

B   false   opposite sides are not perpindicular

C  true opposite sides are equal and parallel

D  false   not perpindicular

E false    not necessarily 90 degrees  

Step-by-step explanation:

The formula to find the arc length of a circle is:

arc length = (central angle / 360 degrees) x 2πr

where r is the radius of the circle.

In this case, we are given the central angle of the arc, which is 36 degrees, and the length of the chord AB, which is 3 units. To find the radius of the circle, we need to use some trigonometry.

Since angle ABC is an inscribed angle that intercepts arc AC, it is half the measure of arc AC. So, we can find the measure of arc AC as 2 times the measure of angle ABC, which is:

m(arc AC) = 2 x m∠ABC

m(arc AC) = 2 x 36

m(arc AC) = 72 degrees

Now, let's use the law of cosines to find the radius of the circle:

c^2 = a^2 + b^2 - 2ab cos(C)

where a and b are the sides of the triangle and c is the side opposite the angle C.

In triangle ABC, we know that side AB has length 3 units and angle ABC has measure 36 degrees. We also know that angle BAC is a right angle, since it is formed by a chord and a radius of a circle. So, we can use trigonometry to find the length of side AC:

sin(36) = AC / 2r

2r = AC / sin(36)

r = AC / (2 sin(36))

Using the law of cosines, we can find AC:

c^2 = a^2 + b^2 - 2ab cos(C)

AC^2 = 3^2 + (2r)^2 - 2(3)(2r) cos(36)

AC^2 = 9 + 4r^2 - 12r cos(36)

Substituting the expression for r from above, we get:

AC^2 = 9 + 4/((2 sin(36))^2) - 12/((2 sin(36))) cos(36)

AC^2 = 9.259

Taking the square root of both sides, we get:

AC ≈ 3.04 units

Now that we know the radius of the circle and the central angle of the arc, we can use the formula for arc length to find the length of arc AC:

arc length = (central angle / 360 degrees) x 2πr

arc length = (72 / 360) x 2π(3.04)

arc length ≈ 3.03 units

Therefore, the length of arc AC is approximately 3.03 units, rounded to the nearest hundredth.

Answer: Cant really show you but use the picture below

Step-by-step explanation:

The slope is 2/5 or basically use the rise over run method. I would start with using x as 0. If so the y would be 3 as seen. So one point is (0,3). From there you can use another number and input it.

Answer:

[tex]9\frac{1}{3}[/tex] cans

Step-by-step explanation:

Gianna used 3[tex]\frac{1}{2}[/tex] cans, which can be written as [tex]\frac{7}{2}[/tex] (since 3 is 6 halves, plus the one half). Seyon used 2 and [tex]\frac{2}{3}[/tex] times as many, which is [tex]\frac{8}{3}[/tex] times as many (2 is six thirds, plus the two thirds).

Now, we multiply [tex]\frac{7}{2}[/tex] by [tex]\frac{8}{3}[/tex]:

[tex]\frac{7}{2}[/tex] * [tex]\frac{8}{3}[/tex] = [tex]\frac{56}{6}[/tex] = [tex]\frac{28}{3}[/tex] = [tex]9\frac{1}{3}[/tex] cans

Hope this helps! :D

Answer: y = |x - 1| - 1

Step-by-step explanation:

We will use this form of absolute value equations. a is the slope, which is 1. h is the horizontal shift and k is the vertical shift.

     y = a|x - h| + k

First, we see this graph is shifted one unit down from the parent function (absolute value). We will subtract 1 from the parent function.

     y = |x| - 1

Next, we see it is shifted one unit right from the parent function. We will add this to the equation above. Since we are adding one unit, we will subtract one unit as it's reversed (" -h" in the equation above).

     y = |x - 1| - 1

Answer: Holly has not made a mistake, she has correctly identified the lower bound of x as 1.8 based on the fact that x truncated to 1 decimal place is 1.8. However, she has not identified the upper bound of x, which should be 1.9 based on the fact that x truncated to 1 decimal place could not be greater than 1.9. Therefore, the correct answer is: 1.8 ≤ x ≤ 1.9.

Step-by-step explanation:

[tex]\cos(18^o )=\cfrac{\stackrel{adjacent}{x}}{\underset{hypotenuse}{23}} \implies 23\cos(18^o)=x \implies 21.87\approx x[/tex]

Make sure your calculator is in Degree mode.

Step-by-step explanation:

A: 3x-4y=-2

3x=-2+4y

x =(-2+4y)/3

B: x-y⁴=0

x=y⁴

C: x²-3y=0

x²=3y

x=±√3y

D: |x| + |y| =2

x + y= 2

x =2-y

The number of miles she will run each day to meet her daily goal of 42-1/2 miles dor work is 5.5 miles per day, under the given condition that She runs 9-1/2 miles on Sunday furthermore she runs the same distance on each of the 6 remaining day.

In order to find out how many miles she needs to run each day, we have to perform  division of  the total number of miles she needs to run by the number of days she has left

33 miles ÷ 6 days = 5.5 miles per day

Hence, Sam needs to run 5.5 miles per day for the remaining six days in order to meet her goal of running 42-1/2 miles for the week.

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The measure of the secant line VZ is 36.

From the diagram:

Using the Intersecting Secants Theorem:

VY × VZ = VW × VX

Plug in the values and solve for x.

( x + 2 ) × ( x + 2 + 29 ) = ( x + 4 ) × (  x + 4 + 19 )

( x + 2 ) × ( x + 31 ) = ( x + 4 ) × (  x + 23 )

Aplly distrubutive property

x( x + 31 ) + 2( x + 31 ) = x(  x + 23 ) + 4(  x + 23 )

x² + 31x + 2x + 62 = x² + 23x + 4x + 92

Collect and add like terms

x² -  x² + 31x + 2x - 23x - 4x = 92 - 62

31x + 2x - 23x - 4x = 92 - 62

6x = 92 - 62

6x = 30

x = 30/6

x = 5

Now, the value of line VZ will be:

VZ = x + 2 + 29

Plug in x = 5

VZ = 5 + 2 + 29

VZ = 5 + 2 + 29

VZ = 36

Therefore, line VZ is 36.

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Answer:

Rise/run = - 4/3

The rise is vertical, run is from left to right.  I counted 4 units down from (-3, 2) to (-3, -2) and since it is down, it's negative.  Then, I counted 3 units to the right from (-3, -2) to (0, -2) and the run will always be positive.  Because there is a negative in one of the numbers, the slope will be negative: - 4/3

The equation that represents the average sales each day for the real estate company is s = 1/(2h)

To find the equation for f, we need to use the information given in the question. The company hopes to sell houses every other day of the month, which means they sell houses on days 1, 3, 5, 7, and so on. We can write this as:

t = 2n - 1

where n is an integer that represents the number of days since the first of the month.

Now, we need to express the average sales each day, f(t), in terms of n. We can assume that the company sells the same number of houses on each of the days they sell (i.e., on days 1, 3, 5, 7, and so on). Let's call this number of houses "h". Then, the total number of houses sold on the days they sell is:

h + h + h + ... (n times) = hn

The total number of days they sell houses in the month is:

n/2 (since they sell houses every other day)

Therefore, the average number of houses sold each day, f(t), is:

f(t) = hn / (n/2) = 2h

Substituting t = 2n - 1, we get:

f(t) = 2h

So, the equation that represents the average sales each day for the real estate company is:

s = 1/f(t) = 1/(2h)

where h is the average number of houses sold on each of the days they sell (i.e., on days 1, 3, 5, 7, and so on).

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About 1144π cubic inches (or approximately, 3591 cubic inches) of additional air is needed to fully fill the sphere-shaped balloon.

The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius.

In this case, the radius is 8 inches, so the volume of the balloon is:

V = (4/3)π(8^3)

V = 2144π cubic inches

The balloon already has 1000 cubic inches of air, so the amount of air still needed to fill the balloon is:

2144π - 1000 = 1144π cubic inches (rounded to the nearest whole number, this is approximately 3591 cubic inches).

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(a) Yes the wavelengths is shorter for the finite square well compared with the infinite well.

(b) The physical arguments to decide whether the energies are smaller for the finite square-well than for the infinite square well.

(c) The energy levels of each potential can also be calculated using the Schrödinger equation, and the comparison of the energies involves comparing the magnitude of the potential energy term for each potential.

When considering the wavelengths of particles in the square well potentials, we can use the de Broglie wavelength, which relates the momentum of a particle to its wavelength.

Finally, the finite square well has a finite number of bound energy states because as the width of the well increases, the energy of the particle becomes less negative and eventually becomes positive, allowing the particle to escape from the well.

Mathematically, the comparison of the two potentials involves solving the Schrödinger equation for each potential. In the case of the infinite square well, the solution is a sine wave, with wavelengths determined by the width of the well. In the case of the finite square well, the solution is a combination of sine and exponential functions, with the wavelength depending on the width of the well.

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Complete Question:

Compare the results of the infinite and finite square-well potentials. (a) Are the wavelengths longer or shorter for the finite square well compared with the infinite well? (b) Use physical arguments to decide whether the energies (for a given quantum number n) are (i) larger or (ii) smaller for the finite square-well than for the infinite square well? (c) Why will there be a finite number of bound energy states for the finite potential?

The lateral surface area of the cylinder will be 32.34 square cm.

Given that:

Radius, r = 3 cm

Height, h = 10.5 cm

Let r be the radius and h be the height of the cylinder. Then the surface area of the cylinder will be given as,

SA = 2πr (h + r) square units

The lateral surface area is calculated as,

SA = 2 x 3.14 x 3 x (10.5 + 3)

SA = 18.84 x 13.5

SA = 32.34 square cm

The lateral surface area of the cylinder will be 32.34 square cm.

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The graph that best represents this situation is a line graph. A line graph is a type of chart that uses lines to show the relationship between two variables. In this case, the two variables are the number of stuffed animals Nicole has left and the number of months that have passed. The line graph will start at 60 stuffed animals and decrease by 5 stuffed animals each month until it reaches 0 stuffed animals.

Here is an example of a line graph that represents this situation:

[Image of a line graph with the number of stuffed animals on the y-axis and the number of months on the x-axis. The line starts at 60 and decreases by 5 each month until it reaches 0.]

I hope this helps! Let me know if you have any other questions.

Step-by-step explanation:

yes, the inequality is almost correct.

this is the fully correct one :

27 <= 12 + 6x

we want to get at least 27 gallons in the pool.

that means, if we hit exactly 27 gallons, it is a valid solution. therefore we need the "<=".

we want to get at least 27 gallons by starting with already existing 12 gallons and then adding 6 gallons for every minute (e.g. 5 minutes give us 5×6 = 30 gallons additional water).

so, now, let's solve :

27 <= 12 + 6x

15 <= 6x

15/6 <= x

2.5 <= x

therefore, it will take at least 2.5 minutes to fill the pool with at least 27 gallons.