Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).

Answer: Y = X2

Step-by-step explanation:
A and C aren't proportional and D is increasng

As a consequence, the percentage decline from 498 to 0 is equal to 100% of the original value.

As a fraction of 100, a figure can be expressed as a percentage.  For instance, the decimal equivalent of 50% is 50/100 or 0.5. The comparison or representation of changes between two numbers is frequently done using percentages. For instance, a percentage increase or decline indicates how much something has changed from its starting point. Additionally, percentages are frequently used in daily contexts like interest rates, shopping discounts, and academic performance.

given

The formula below can be used to determine the percent reduction from 498 to 0:

(Original value - New value) / 100% of the original value equals the percent decline.

The initial number in this case was 498, and the updated value is 0.

Reduced percentage equals (498 - 0) / (498 x 100%)

% drop equals 100%

As a consequence, the percentage decline from 498 to 0 is equal to 100% of the original value.

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The equivalent expression value when {a} = 2, {b} = -3, {c} = -1 is 19.

A function is a relation between a dependent and independent variable. We can write the examples of functions as -

y = f(x) = ax + b

y = f(x, y, z) = ax + by + cz

Given is the algebraic expression as -

ab² - c³

For {a} = 2, {b} = -3, {c} = -1, we can evaluate the algebraic expression as -

ab² - c³

2(-3)² - (- 1)³

2 x 9 - (- 1)

18 + 1

19

Therefore, the equivalent expression value when {a} = 2, {b} = -3, {c} = -1 is 19.

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{Question in english -

Find the value of the expression if a =2, b= -3 and c=-1 ; ab2 -c3}

The length of the mid segment is 8 feet.

The bases of a trapezoid have lengths of 6 feet and 10 feet. Let's find the length of the mid segment of the trapezoid.

A midsegment of a trapezoid is the line segment connecting the midpoints of the two non-parallel sides of a trapezoid.

The length of the midsegment of trapezoid is half the sum of the lengths of the two parallel sides

Hence,

mid segment = 1  /2 (6 + 10)

mid segment = 16 / 2

mid segment = 8 feet

Therefore,

mid segment = 8 feet.

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The statement, Angle 1 and angle 5 are complementary angles,

As ∠2 = ∠5.

We know when a transversal intersects two parallel lines at two distinct points,

Two pairs of interior and alternate angles are formed such that the measure of interior angles are same and the measure of alternate angles is also the same.

We know when the sum of two angles is 180° they are supplementary.

Two angles are said to be adjacent angles if they share a common side.

Two angles are said to be complementary when the sum is 90°.

We know vertically opposite angles are in equal measure when a transversal intersects two parallel lines.

Therefore, ∠2 = ∠5.

Hence, ∠1 + ∠2 = ∠1 = ∠5 = 90°.

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Answer:   πr2h

=  π×282×34

=  26656π

=  83742.29377409 centimeters3

Step-by-step explanation:

Answer:

The volume of the composite figure is 12,719 cm³ to the nearest whole number.

Step-by-step explanation:

The composite figure is composed of a cone and a half-sphere.

To calculate the volume of the figure, sum the volume of the cone and the volume of the half-sphere.

[tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a cone}\\\\$V=\dfrac{1}{3} \pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]     [tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a half-sphere}\\\\$V=\dfrac{2}{3} \pi r^3$ \\\\ where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\\end{minipage}}[/tex]

Therefore, the equation for the volume of the composite figure is:

[tex]V=\dfrac{1}{3} \pi r^2 h+\dfrac{2}{3} \pi r^3[/tex]

From inspection of the given diagram:

As the diameter of a circle is twice its radius, r = 14 cm.

Substitute the values of r, h and π into the equation and solve for V:

[tex]\begin{aligned}\implies V&=\dfrac{1}{3} \pi r^2 h+\dfrac{2}{3} \pi r^3\\\\&=\dfrac{1}{3} (3.14) (14)^2 (34)+\dfrac{2}{3} (3.14) (14)^3\\\\&=\dfrac{1}{3} (3.14) (196) (34)+\dfrac{2}{3} (3.14) (2744)\\\\&=6974.98666...+5744.10666...\\\\&=12719.09333...\\\\&=12719\;\sf cm^3\;\;(nearest\;whole\;number)\end{aligned}[/tex]

Therefore, the volume of the composite figure is 12,719 cm³ to the nearest whole number.

for a f(5) is 1 and f(7) is 1/4

for b the domain is 16-1/4

for c the value is decreasing by 1/2 every time

The amount that I spent by using the equation y = 1/2x , according to my friend's expense is $7.5.

In its simplest form in algebra, the definition of an equation is a mathematical statement that two mathematical expressions are equal. For example, 3x + 5 = 14 is an equation where 3x + 5 and 14 are two terms separated by an equal sign. 

There are two types of equations:

Identities and conditionals. The identity applies to all values ​​of the variable. Constraint expressions apply only to specific values ​​of variables. Equations are written as two expressions separated by an equal sign ("="). 

Solution:

Given, amount spent by friend = $15

           Equation: y = 1/2x

So, amount spent by me is as follows

y = (1/2)×15

  =15/2

y  = $7.5

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The amount of money you are spending is $7.50 according to the given equation.

A mathematical equation is a statement that expresses the relationship between two values using mathematical symbols. An equation typically involves a variable, which is a symbol that stands for a number that can change, and an equals sign. Equations can be used to solve a variety of problems in mathematics.

The equation y = 1/2x states that 'y' is equal to one half of 'x'. This equation can be used in many different ways to solve real-life problems. In this case, 'x' represents the amount of money your friend spent at the carnival. 'y' represents the amount of money you spent. To solve for 'y', we divide the value of 'x' by 2.

In the question, your friend spent $15 at the carnival. Therefore, 'x' is equal to 15. We then divide 15 by 2, which gives us 7.5. This means that you spent $7.50 at the carnival.

The equation y = 1/2x is a simple but powerful tool for solving problems. It can be used for a variety of tasks, including finding out how much money you spent at the carnival if you spent half as much as your friend. All you have to do is plug in the value of 'x' and divide it by two.

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The terms from the highest to lowest power of the variable are 10b⁶, -b², -9b, -9.

Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression.

Here,
To write the terms from the highest to the lowest power of the variable, we need to first simplify the given expression by combining the like terms.

The given expression can be simplified as follows:

= 9b² + 10b⁵b + 4 + 7b² - 6 - 15b² - 9b

= 10b⁶ + (9b² + 7b² - 15b²) - 9b + (4 - 6)

= 10b⁶ - b² - 9

Now, we can write the terms from highest to lowest power of the variable as follows:

10b⁶ is the term with the highest power of the variable.

The next highest power of the variable is b². Therefore, we have -b².

The next term is -9b, which has the power of the variable 1.

Finally, the constant term is -9, which has no power of the variable.

Therefore, the terms from the highest to lowest power of the variable are 10b⁶, -b², -9b, -9.

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Answer:

$104,000

Step-by-step explanation:

For simple interest,

I = Prt

where I = interest earned

P = principal, amount invested

r = annual interest rate

t = time in years

I = $40,000 × 0.08 × 20

I = $64,000

The total amount saved is the principal amount plus the interest.

$40,000 + $64,000 = $104,000

25 pi^2

The circumference is diameter by pi. So you have to divide 50pi by pi, which gives you 50. Then, divide that by 2 to get your radius. 25. A=pi r^2. So you have to multiply 35 by pi, 25pi, and then make it squared.

The value of x in the equation below 18 = x - 10 is equal to 28.

In Mathematics, an expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).

Based on the information provided above, we have the following mathematical expression:

18 = x - 10

By rearranging and collecting like-terms, we have the following:

x = 18 + 10

x = 28.

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Complete Question:

Find the value of x in the equation below. 18 = x - 10

The mean oil-change time for which there is a 10% chance of being at or below is approximately 15.92 minutes.

We can start by using the Central Limit Theorem.

Data given:

The population mean is μ = 16.9 minutes

population standard deviation is σ = 4.7 minutes

sample size of n = 40 oil changes performed between 10 A.M. and 12 P.M.

The standard error of the mean (SE) is given by:

SE = σ / √n

SE = 4.7 / √40

SE = 0.743

To find the mean oil-change time for which there is a 10% chance of being at or below, we need to find the z-score associated with the 10th percentile of the standard normal distribution, which is -1.28 (using a standard normal distribution table or calculator).

We can use the formula for a z-score:

z = (x - μ) / SE

where x is the desired mean oil-change time.

Substituting the known values and solving for x, we get:

-1.28 = (x - 16.9) / 0.743

x = -1.28 * 0.743 + 16.9

x = 15.92

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Michelle biked approximately 37.68 miles in the shape of a circle.

A circle's diameter and radius are connected because the diameter is twice as long as the radius. Mathematically, this connection may be written as d = 2r, where d stands for the diameter and r for the radius. On the other hand, we can alternatively state that the radius is equal to half the diameter's length: r = d/2

The circumference of a circle can be found using the formula:

C = πd

Given that,

Michelle biked around the trail 4 times.

The circumference is:

C = π x 3 = 9.42 miles

Also,

4 x 9.42 = 37.68 miles

Hence, Michelle biked approximately 37.68 miles in the shape of a circle.

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It will take 6.5 minutes to grade 338 test by the electronic grading machine.

The quality of the answer papers is a key element. The machine might not be able to reliably scan and evaluate the answers if the answer sheets are not filled out completely or if the paper has rips or smudges on it. Similar to this, the computer might not be able to recognize the right answers if the answer sheets are not properly aligned.

Given that, the machine can grade 52 test in 1 minute.

The, we can calculate the time taken to grade 338 test as follows:

time = number of tests / rate of grading

Plugging in the given values, we get:

time = 338 / 52 = 6.5 minutes

Hence, it will take 6.5 minutes to grade 338 test by the electronic grading machine.

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The common feature of the two functions is given as follows:

Vertical asymptote.

For this problem, neither of the functions is defined at x = -4, hence x = -4 is the vertical asymptote for both of the functions.

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The area of the figure is equal to:

A = 28[tex]unit[/tex]² + 7[tex]unit[/tex]² + 7[tex]unit[/tex]² =42[tex]unit[/tex]²

You could also draw the shape on a grid and count the squares there: The rectangle has a 15 surface area. For instance, if the space is 15 m2 and each square is one meter in size (15 square meters).

Answer:

42[tex]units[/tex]²

Step-by-step explanation:

we know that

The area of the figure is equal to the area of a rectangle plus the area of two triangles

Find the area of rectangle

Observing the graph

The area of rectangle is equal to

A= bh = (2+5)(2+2)= 28[tex]unit[/tex]²

Find the area of the top triangle

A = 1/2bh = 1/2(2+5)(2+2) = 7[tex]unit[/tex]²

Find the area of the bottom triangle

A = 1/2bh = 1/2(2+5)(2+2) = 7[tex]unit[/tex]²

the area of the figure is equal to

A = 28[tex]unit[/tex]² + 7[tex]unit[/tex]² + 7[tex]unit[/tex]² =42[tex]unit[/tex]²

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The volume of water that Keith's kitchen kettle holds when it is full is 1800 ml.

Assume that Keith's kitchen kettle has a "x" ml capacity when it is full.

The kettle is initially 80% full, which means it holds 0.8x ml of water, according to the problem.

20% of the water is poured out, leaving 80% of the original amount of water in the kettle, which is:

0.8x * 0.8 = 0.64x ml

We are informed that the 1152 ml of water that is left equates to:

0.64x = 1152

By multiplying both sides by 0.64, we obtain:

x = 1800

Consequently, Keith's cooking kettle has an 1800 ml capacity when it is full.

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The sample space for spinning the spinner two times is -

{Blue, Orange} {Blue, Red} {Orange, Red}

{Blue, Blue} {Red, Blue} {Orange, Blue}

{Red, Red} {Orange, Orange}

What is a sample?

A sample is characterised as a more manageable and compact version of a bigger group. A smaller population that possesses the traits of a bigger group. When the population size is too big to include all participants or observations in the test, a sample is utilised in statistical analysis.

The sample space for spinning the spinner two times can be found by listing all possible outcomes of the two spins.

Each spin has three possible outcomes, so the total number of outcomes for two spins is 3 x 3 = 9.

One way to list the sample space is to use a table where the rows and columns represent the outcomes of the first and second spins, respectively.

The entries in the table represent the ordered pairs of outcomes, with the first entry corresponding to the first spin and the second entry corresponding to the second spin.

Using this method, the sample space for spinning the spinner two times is -

Blue | Blue | (Blue, Blue) | Blue | Orange | (Blue, Orange) | Blue | Red | (Blue, Red)

Red | Blue | (Red, Blue) | Red | Orange | (Red, Orange) | Red | Red | (Red, Red)

Orange | Blue | (Orange, Blue) | Orange | Orange | (Orange, Orange) | Orange | Red | (Orange, Red)

Alternatively, we can list the outcomes as an unordered set of two elements, where the order of the elements does not matter.

In this case, the sample space for two spins would be -

{Blue, Orange} {Blue, Red} {Orange, Red}

{Blue, Blue} {Red, Blue} {Orange, Blue}

{Red, Red} {Orange, Orange}

Therefore, the sample space is obtained.

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Answer:

7.75 ; 7.81 ; 7.77 ; 7.84

If A file that is 278 megabytes is being downloaded and the download is 19.7% complete, then you just need to multiply the 278 megabytes with 19.7%

The calculation would be: 278 megabytes x 0.197 = 54.766 megabytes.

If you round up the answer to nearest tenth it will be 54.8 megabytes.

Answer: h(x) = 8x so choice A.

Step-by-step explanation:

f(x) = (x + 2)² - 1

g(x) = -(x - 2)² + 1

SOLVE:

h(x) = f(x) + g(x)

——————————————

Step 1: Put together

((x + 2)² - 1) + (-(x - 2)² + 1)

Step 2: Positive and Negative 1 add to 0

((x + 2)² - ) + (-(x - 2)² + )

Step 3: Rewrite

(x + 2)² - (x - 2)²

Step 3: Expand the expression

(x + 2)(x + 2) - (x - 2)(x - 2)

Step 4: Distribute

(x² + 4x + 4) - (x² - 4x + 4)

Step 5: Remove Parentheses (don't forget to distribute the negative)

x² + 4x + 4 - x² + 4x - 4

Step 6: Collect Like Terms

x² and -x² add to 0

+ 4 and - 4 add up to 0

Leaving only + 4x and + 4x which add up to 8x

Therefore, h(x) = f(x) + g(x), h(x) = 8x

Graph Letter A:

Answer: B. 50

Step-by-step explanation:

  To solve this, we will isolate the variable b.

   Given:

[tex]\frac{1}{5}[/tex]b + 4 = 14

   Subtract four from both sides of the equation:

[tex]\frac{1}{5}[/tex]b = 10

   Multiply both sides of the equation by 5:

b = 50

        B. 50

The growth rate of the plant shown in the graph is 1/2 centimeter per week

From the question, we are to determine the growth rate of the plant

To determine the growth rate of the plant, we will determine the slope of the line

To determine the slope of the line passing through the points (1, 1/2) and (3, 1 1/2), we can use the slope formula:

Slope = (Change in y) / (Change in x)

We first calculate the change in y by subtracting the y-coordinate of the first point from the y-coordinate of the second point:

Δy = 1 1/2 - 1/2 = 1

Next, we calculate the change in x by subtracting the x-coordinate of the first point from the x-coordinate of the second point:

Δx = 3 - 1 = 2

Finally, we can calculate the slope by dividing the change in y by the change in x:

Slope = Δy / Δx = 1 / 2

The slope of the line is 1/2.

Hence, the growth rate is 1/2 centimeter per week

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Answer:

The greatest possible distance between two points on the walls in the room is 17 feet.

Step-by-step explanation:

The room can be modelled as a rectangular prism with the following dimensions:

The greatest possible distance between two points on the walls in the room is the line between diagonally opposite corners. This is marked as the blue line (x) on the attached 3D diagram.

This distance is the hypotenuse of a right triangle with a base of the diagonal of the floor and a height of the height of the room.

The diagonal of the floor (marked "y" on the attached diagram) is the hypotenuse of a right triangle with legs of the width and length of the room.  To calculate the diagonal of the floor, use Pythagoras Theorem.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

Substitute a = 8, b = 12 and c = y into the formula and solve for y:

[tex]\implies 8^2+12^2=y^2[/tex]

[tex]\implies 64+144=y^2[/tex]

[tex]\implies y^2=208[/tex]

[tex]\implies y=\sqrt{208}\; \sf ft[/tex]

Therefore, the diagonal of the floor (y) is √(208) feet in length.

We can now use Pythagoras Theorem again to find the length x.

Substitute a = y, b = 9 and c = x into the formula:

[tex]\implies y^2+9^2=x^2[/tex]

Substitute the found value of y and solve for x:

[tex]\implies (\sqrt{208})^2+9^2=x^2[/tex]

[tex]\implies 208+81=x^2[/tex]

[tex]\implies 289=x^2[/tex]

[tex]\implies x=\sqrt{289}[/tex]

[tex]\implies x=17 \sf \; ft[/tex]

Therefore, the greatest possible distance between two points on the walls in the room is 17 feet.

According to the given values London's statement is incorrect.

Simple interest is a type of interest that is calculated based on the principal amount of a loan or investment and the length of time for which the money is borrowed or invested. It is called "simple" because the interest is calculated only on the initial principal amount and does not take into account any interest that may have accrued in previous periods.

Let's calculate the interest earned by each person after one year:

London:

The amount deposited by London is $100. The simple interest rate is 3.4%. Therefore, the interest earned by London after one year is:

[tex]$$\text{Interest}[/tex] = [tex]\text{Principal} \times \text{Rate} \times \text{Time}[/tex] = [tex]$100 \times 3.4%[/tex] [tex]\times 1[/tex]= [tex]$3.40$$[/tex]

Chen:

The amount deposited by Chen is $200. The simple interest rate is 2.2%. Therefore, the interest earned by Chen after one year is:

[tex]$$\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}[/tex]= [tex]$200 \times 2.2%[/tex] [tex]\times 1[/tex] = [tex]$4.40$$[/tex]

As we can see, even though London's interest rate is higher than Chen's, Chen will earn more interest in one year because he deposited a larger amount of money.

Therefore, according to the given values London's statement is incorrect.

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Answer:

[tex]x=1[/tex]

Step-by-step explanation:

First, square both sides.

[tex]\left(\sqrt{3+\dfrac{\left(4 + \sqrt{x+3} \, \right)^2}{6}}\, \right)^2= 3^2[/tex]

[tex]3+\dfrac{\left(4 + \sqrt{x+3} \, \right)^2}{6} = 9[/tex]

This eliminates the square root over the entire left side of the equation.

Next, multiply both sides by 6 to get rid of the fraction on the left side.

[tex]6\left(3+\dfrac{\left(4 + \sqrt{x+3} \, \right)^2}{6}\right) = 6( 9)[/tex]

[tex]6(3) + \left(4 + \sqrt{x+3} \, \right)^2 = 6(9)[/tex]

[tex]18 + \left(4 + \sqrt{x+3} \, \right)^2 = 54[/tex]

Then, subtract 18 from both sides to isolate the squared term.

[tex]18 + \left(4 + \sqrt{x+3} \, \right)^2 = 54\\\underline{-18 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \: } \ \ \ \ \ \underline{ - 18}[/tex]

[tex]\left(4 + \sqrt{x+3} \, \right)^2 = 36[/tex]

Now, we can square root both sides.

[tex]\sqrt{\left(4 + \sqrt{x+3} \, \right)^2} = \sqrt{36}[/tex]

[tex]4 + \sqrt{x+3} = \pm 6[/tex]

Remember to use apply the even root property, so that the right side (6) is positive or negative (indicated by the plus or minus sign).

Next, subtract 4 from both sides.

[tex]4 + \sqrt{x+3} = \pm 6 \\ \underline{-4\ \ \ \ \ \ \ \ \ \ \: } \ \ \ \ \ \underline{ - 4}[/tex]

[tex]\sqrt{x+3} = \pm 6 - 4[/tex]

Then, square both sides to get rid of the square root on the left side.

[tex]\left(\sqrt{x+3}\right)^2 = (\pm 6 - 4)^2[/tex]

[tex]x+3 = 2^2[/tex]    OR    [tex]x+3 = (-10)^2[/tex]

We can see that there are two resulting expressions, each of which we can solve individually.

[tex]x+3 = 4[/tex]    OR    [tex]x+3 = 100[/tex]

[tex]\boxed{x = 1}[/tex]                 [tex]\boxed{x\ne97}[/tex]

The reason that x = 97 is crossed out is because when we plug that x-value back into the original equation, it does not come out to be true. Therefore, 97 is an extraneous solution.

Also, see the attached image for another solution (that implores another method).

Answer:

  x = 1

Step-by-step explanation:

You want to solve for x:

  [tex]\sqrt{3+\dfrac{(4+\sqrt{x+3})^2}{6}}=3[/tex]

At any stage where there is a root, you isolate the radical and raise both sides of the equation to a power sufficient to eliminate the radical. Repeat as necessary.

The radical is already on one side of the equation by itself, so we simply square both sides:

  [tex]3+\dfrac{(4+\sqrt{x+3})^2}{6}=9\\\\(4+\sqrt{x+3})^2=6^2\qquad\text{subtract 3, multiply by 6}\\\\|4+\sqrt{x+3}|=6\qquad\text{take the square root}[/tex]

At this point, we note that the sum cannot be negative, so the absolute value bars are irrelevant. Isolating the radical and squaring both sides, we can finish the solution.

  [tex]4+\sqrt{x+3}=6\\\\\sqrt{x+3}=2\qquad\text{subtract 4}\\\\x+3=4\qquad\text{square both sides}\\\\\boxed{x=1}\qquad\text{subtract 3}[/tex]

This is the only solution, as the attached graph shows.

__

Additional comment

Generally, the square root symbol means the positive square root. That is, √z is usually considered to be non-negative.  This is why we use ±√z when we want both signs of the root.

In this problem, the only root we're taking as part of the solution is the root of a square. The possibility of a negative value for the term being squared is handled by using the absolute value brackets: √(z²) = |z|.

For solving these using a graphing calculator, we like to rewrite the equation to the form f(x)=0. That way, the solutions are the x-intercepts.

Answer:

1 buck

Step-by-step explanation:

Alright man im not a pro at this, so im not gonna have a professional explanation, but the final answer will be correct.

So listen up a dice has 6 sides labeled 1,2,3,4,5,6

3 of those are even

3 of those are odd

so you have a 50% chance of landing on an evan numbered side

and a 50% chance of landing on an odd-numbered side

So basically, if we play one round, there are 2 possibilities. We get even and win 2 bucks, or we get odd and lose a buck. We dont need to worry about probability as they are both 50%. Therfore, the value is 2-1 = 1 dollar. I found the value by subtracting the possbilities.

Total amount/Working days

Step-by-step explanation: