Values that are perfect squares? Which ones are


1. 64
2. 32
3. 18
4. 100

The entering basic value is α and the leaving basic variable is x2.

Given that the formula for the line passing through the points (2, 4, 3) and (4, 2, 4) can be written as (2,4,3)+α[(4,2,4)−(2,4,3)] = (2,4,3)+α(2,−2,1), where 0 ≤ α ≤ 1 for just the line segment between these points. After augmenting with the slack variables x4, x5, x6, x7 for the respective functional constraints, this formula becomes (2,4,3,2,0,0,0) + α(2,−2,1,−2,2,0,0).We have to use this formula directly to answer each of the following questions and relate the algebra and geometry of the simplex method as it goes through one iteration in moving from (2,4,3) to (4,2,4). The questions are:(a) What is the entering basic variable?The entering basic variable is the variable that increases in the formula which in this case is α.(b) What is the leaving basic variable?The leaving basic variable is the variable that makes one of the original basic variables zero and takes its place as a basic variable in the new basic feasible solution. Here, the leaving basic variable is x2.(c) What is the new BF solution?The new basic feasible solution is found by replacing the entering basic variable α for the leaving basic variable x2 and then using Gaussian elimination to solve the linear system. Here is how it is done:At α = 0, we have the point (2,4,3,2,0,0,0).At α = 1, we have the point (4,2,4,0,2,0,0).Let α be the entering basic variable, then we can take x2 to leave the basis. Thus, at α = 0, we have (2,4,3,2,0,0,0) as the BFS and at α = 1, we have (4,2,4,0,2,0,0) as the next BFS.Then we need to use Gaussian elimination to solve the linear system. After Gaussian elimination, we get the new basic feasible solution as (10/3,4/3,0,0,2/3,0,0).Hence, the new BF solution is (10/3,4/3,0,0,2/3,0,0).Thus, the entering basic variable is α, the leaving basic variable is x2, and the new BF solution is (10/3,4/3,0,0,2/3,0,0).

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The scale drawing of the room is 10 inches long and 8 inches wide. If his actual room is 16 feet wide, the actual length of the room is 10 feet.

The scale of Harry's living room drawing is 10 inches long and 8 inches wide. Let's say the actual width of the room is 16 feet. We can use proportions to find the length of the actual room using the scale drawing.

The proportion of the length of the scale drawing to the actual length of the room is the same as the proportion of the width of the scale drawing to the actual width of the room.

Using this proportion, we can set up the equation:

10 inches / x = 8 inches / 16 feet

Simplifying this equation gives us:

10 inches / x = 8 inches / 192 inches

Cross-multiplying gives us:

10 inches * 192 inches = 8 inches * x

Solving for x gives us:

x = 120 inches or 10 feet

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We want to see which of the listed situations can be modeled with linear equations. We will see that the situations that are linear are:

First, a linear equation shows a dependence of two variables as:

y = a*x + b

Where y and x are the variables, a is the slope and b is the y-intercept.

Let's see which situations can be written in this form.

"He sells 5 propane stoves each day for 4 consecutive days."

If we define y = number of propane stoves sold and x = number of days, then we can write this as:

y = 5*x

Where x goes from 0 to 4, so this can be represented with a linear equation.

"Cooper's profit decreases by $125 each day for 5 days."

Similar to before, we have a fixed change per day, so this again can be modeled with a linear equation.

"Cooper's profit doubles each month for 3 consecutive months."

This can not be modeled with a linear equation, the problem here is that the change is not fixed.

Because the profit is doubled, the change will depend on the value of the profit (so the double of 4 is not the same as the double of 5, just to give an example). Thus, this can not be modeled with a linear equation, this actually needs an exponential equation.

"Cooper sells 2 fewer fishing poles each day for 1 week."

Similar to the first and second case, each day he has 2 fewer fishing poles, a fixed number per day, thus, this can be modeled with a linear equation.

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The value of X and y using substitution method for the quadratic equation given above would be = -3.6 and - 2.8 respectively.

The equations given are;

2x - 7y = 13. ----> equation 1

3x + y = 8 --------> equation 2

From equation 2 make y that subject of formula;

y = 8 - 3x

Substitute y = 8 - 3x into equation 1

2x - 7(8 - 3x) = 13

2x - 56 - 21x = 13

-19x = 13+56

-19x = 69

X = -69/19

X = - 3.6

Substitute X = -3.6 into equation 2

3(-3.6) + y = 8

y= 8 - 10.8

= - 2.8

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Answer:

Oblique Because the slopes are different

Step-by-step explanation:

Answer:

i belive it oblique . Not sure tho but good luck !!

Step-by-step explanation:

The mean (μ) for the given binomial distribution is 0.50.

To calculate the mean (μ) of a binomial distribution, we multiply the number of trials (n) by the probability of success in a single trial (π). Let's examine each scenario in detail:

a. When n = 5 and π = 0.10:

μ = 5 * 0.10

  = 0.50

For this binomial distribution, with 5 trials and a success probability of 0.10, the mean (μ) is 0.50. This means that, on average, we would expect to have 0.50 successes per trial.

b. When n = 3 and π = 0.40:

μ = 3 * 0.40

  = 1.20

In this case, the mean (μ) of the binomial distribution is 1.20. It indicates that, on average, there would be 1.20 successes per trial when there are 3 trials and a success probability of 0.40.

c. When n = 5 and π = 0.50:

μ = 5 * 0.50

  = 2.50

For a binomial distribution with 5 trials and a success probability of 0.50, the mean (μ) is 2.50. This means that, on average, we would expect to have 2.50 successes per trial.

d. When n = 3 and π = 0.80:

μ = 3 * 0.80

  = 2.40

In this scenario, the mean (μ) of the binomial distribution is 2.40. It suggests that, on average, we would expect to have 2.40 successes per trial when there are 3 trials and a success probability of 0.80.

The mean (μ) provides a measure of the central tendency or the average number of successes in a binomial distribution based on the given parameters.

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The solution to the inequality f(x) ≤ 0 is the interval [-6, 2]. In other words, the values of x that satisfy the inequality are those that lie between -6 and 2, inclusive.

To solve the inequality f(x) ≤ 0, we need to find the values of x for which the function f(x) is less than or equal to zero.

We start by factoring the quadratic expression f(x) = x^2 + 4x - 12:

f(x) = (x + 6)(x - 2)

Setting this expression to zero, we get:

(x + 6)(x - 2) = 0

This gives us two solutions: x = -6 and x = 2.

Now, we need to determine the sign of f(x) in the intervals between these two solutions. We can use a sign chart to do this:

x f(x)

-∞ +

-6 0

2 0

+∞ +

From the sign chart, we see that f(x) is positive for x < -6 and for x > 2, and it is negative for -6 < x < 2.

To summarize, the solution to the inequality f(x) ≤ 0 for the function f(x) = x^2 + 4x - 12 is the interval [-6, 2].

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The coordinates of the new triangle are P' = (5, 3), K' = (3, 1) and Y' = (1, 4)

The coordinates of the triangle in the figure are

P = (-5, -3)

K = (-3, -1)

Y = (-1, -4)

The transformation is given as 180 degrees rotation

The rule of this transformation is

(x, y) = (-x, -y)

When this is applied on the triangle, we have the coordinates of the new triangle to be

P' = (5, 3)

K' = (3, 1)

Y' = (1, 4)

Hence, the coordinates of the new triangle are P' = (5, 3), K' = (3, 1) and Y' = (1, 4)

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The mean(μ) of 45 months and a standard deviation(σ) of 8 months. So, the Normal distribution is 34.72 months.

a) Locate\(Pr[x\leq 36]\)  Convert the x-rating to z-score and then use the regular distributiontable

 \(Pr[x\leq 36]=Pr[z\leq \frac{36-45}{8}]=Pr[z\leq -1.13]\)  ˜ 0.1292  or 12.92%.

b) The query is looking whatx-rating is 10% of the facts to the left of. So, we lookat the everyday distribution table and discover the closest probabilityto .one thousand. the closest is between a z-rating of -1.28 and-1.29, so allow's use -1.285.

The usage of the z-conversion components backwards, we are able to find out x

\(z=\frac{x-\mu}{\sigma}= > -1.285=\frac{x-45}{8}\)

Solving the equation for x we get:  

x = 34.72  months

Normal distribution, also known as Gaussian distribution, is a probability distribution that represents a set of random variables that are symmetrically distributed around a mean value. It is characterized by its bell-shaped curve, where the majority of the data falls around the mean, with fewer data points as we move further away from the mean in either direction.

The normal distribution is widely used in statistics and probability theory, as it occurs naturally in many real-world phenomena, such as height and weight measurements of a population, test scores, and errors in measurements. The distribution is determined by two parameters: the mean, which represents the central tendency of the distribution, and the standard deviation, which measures how spread out the data is from the mean.

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Complete Question: -

Quick Start Company makes a 12-volt car batteries. After manyyears of product testing, the company knows the average life of aQuick Start battery is normally distributed, with mean=45 months and a std. deviation = 8 months.

If Quick start guarantees a full refund on any battery that failswithin the 36 month period after purchase, what percentage of itsbatteries will the company expect to replace?

If quick Start does not want to make refunds for more than 10% ofits batteries under the full refund guarantee policy, for how longshould the company guarantee the batteries (to the nearestmonth)

2, 3, 5, 7, 11, 13, and 17 are not factors of n = 2 · 3 · 5 · 7 · 11 · 13 · 17 + 1 because 1 is added to the product of the factors

The product is given as:

n = 2 · 3 · 5 · 7 · 11 · 13 · 17 + 1

Let 2 · 3 · 5 · 7 · 11 · 13 · 17 be represented by x.

So, we have:

n = x + 1

Given the above equation.

The factors of x cannot be the factors of n

This is so because of the 1 that is added to x to given n

Hence, 2, 3, 5, 7, 11, 13, and 17 are not factors of n = 2 · 3 · 5 · 7 · 11 · 13 · 17 + 1 because 1 is added to the product of the factors

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Solution:

Given:

The numbers are represented on the number line below;

The distance between the numbers can be gotten by moving from one number to the other counting the number of steps taken.

Hence,

Therefore, the distance between the numbers on the number line is 17.

Answer:

\({ \tt{x + 83 = 180}}\)

[ Property of angles on a straight line ]

\({ \tt{x = 180 - 83}} \\ \\ { \boxed{ \tt{x = 97 \degree}}}\)

\({ \tt{(4y - 27) = x}} \\ \)

[ Property of alternate angles ]

\({ \tt{4y - 27 = 97}} \\ { \tt{4y = 124}} \\ { \tt{ \frac{4y}{4} = \frac{124}{4} }} \\ \\ { \boxed{ \tt{y = 31 \degree}}}\)

It cannot be determined. At least one other point on the line is needed to determine if x is proportional to y

Given data ,

A point on a straight line has an x-coordinate of 3 and a y-coordinate of 6

Now , A single point on a straight line does not define the connection between x and y. We must evaluate the connection between x and y for several places on the line in order to establish if x is proportional to y.

As a result, the relationship between x and y cannot be inferred only from the supplied location (3, 6). To establish the proportionality between x and y, at least one more point on the line is required

Hence , the equation of line is solved

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Answer:22

Step-by-step explanation:

Answer:

See attached graph

Step-by-step explanation:

The equation that has a slope of 10 and intersects (0,0) is:

y = 10x

The slope-intercept form of a straight line equation is y=mx+b, where m is the slope and b the y-intercept (the value of y when x = 0).  

In this case:

m = 10

b is 0 since the value of y when x = 0 is 0 (0,0).

See attached graph.

\(\huge\fbox{Hi\:there!}\)

We are given the slope of the line and a point that it passes through, so we can use the Point-Slope formula:

\(\rm{y-y1=m(x-x1)\)

Where

y1 is the y-coordinate of the point, m is the slope and x1 is the x-coordinate.

In this case:

y1=0

m=10

x1=0

Plug in the values:

\(\bf{y-0=10(x-0)\)

Solve:

\(\bf{y-0=10x\)

\(\bf{y=10x}\)

Now, how to graph the line?

Let's look at its equation.

First of all, it has a y-intercept of 0, which means the line touches the y-axis at (0,0)

Now, what about the slope? The slope is 10.

Thus

We move "up 10, over 1, up 10, over 1" and so on, until we have a line.

Then all we have to do is take a ruler and connect the points.

Hope it helps!

~Just a determined gal

#HaveAGreatDay

\(\bf{-MistySparkles^**^*\)

Step-by-step explanation:

Triangle a) is half of an equilateral triangle therefore the height divides the base into two equal parts, same thing for triangle b), triangle c) instead is half square, therefore congruent catheti.

a)

n = 6 : 2

n = 3

m = √(6²+3²)

m = √45

b)

x = 10 x 2 = 20

y = √(20²-10²)

y = √300

c)

a = √(5²+5²)

a = √50

Draw an equilateral triangle with side lengths of 1. Each angle here is 60 degrees, which is true of any equilateral triangle.

Now draw another equilateral triangle that has side lengths of 2 units. Clearly this triangle is not the same size as the previous one, but the angles are all still 60 degrees.

We have an example in which there are 2 triangles with the same angles, but the triangles are not congruent. Therefore, having info about congruent angles only isn't sufficient to prove triangles to be congruent.

Answer:

Step-by-step explanation:

The final answer is -18. hope it helped.

To solve the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0, we can use algebraic methods and the unit circle to determine the values of x that satisfy the equation.

1. Start by rearranging the equation to a quadratic form: \(6sin^2(x)\) + 6sin(x) + 1 = 0.

2. Notice that the equation resembles a quadratic equation in terms of sin(x). Let's substitute sin(x) with a variable, such as u: \(6u^2\) + 6u + 1 = 0.

3. Solve this quadratic equation for u. You can use the quadratic formula or factorization methods to find the values of u. The solutions are u = (-3 ± √3) / 6.

4. Since sin(x) = u, substitute back the values of u into sin(x) to obtain the values for sin(x): sin(x) = (-3 ± √3) / 6.

5. To find the values of x, we can use the inverse sine function. Take the inverse sine of both sides: x = arcsin[(-3 ± √3) / 6].

6. The arcsin function has a range of [-π/2, π/2], so the values of x lie within that range. Use a calculator to find the approximate values of x based on the values obtained in step 5.

7. Plot the obtained x-values on the graph to show the solutions of the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0. The graph will illustrate the points where the curve intersects the x-axis.

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Answer: C

Step-by-step explanation: The graph shows "Height" and "Seconds" not only the height, meaning its "the number of seconds it takes the ball to reach its maximum height"

Answer:

C

Step-by-step explanation:

The number of seconds it takes the ball..

Answer:

False

Step-by-step explanation:

4/8 equals to 1/2 but 6/10 equals to 3/5. Correct would be if it was 5/10

Answer:

2x^2 + 2x - 83 = 0

Step-by-step explanation:

Consecutive integers differ by 1

Let the first number be x

The next will be (x+1)

The sum of the squares of these two numbers is 85

so we have;

x^2 + (x + 1)^2 =85

= x^2 + x^2 + 2x + 2 = 85

2x^2 + 2x + 2-85 = 0

2x^2 + 2x - 83 = 0

Answer:

y=8x+2

Step-by-step explanation:

the slope is 8 and the y intercept is 2

the slope is 8 dollars the increase of the price per hour. the yintercept is the amount she get for 0 hours (2 dollars)

1,10

2,18

8/1 is 8

10=8*1+b

10=8+b

2=b

Answer:

x=9

Step-by-step explanation:

plug in the number 9

-2(9)= -18

-18+3= -15

Using PEMDAS rule , we can evaluate the provide expression . The required result is thirteen that's the value is L= 13.

PEMDAS order of operations: The order of operations is a rule that tells the correct sequence of steps for evaluating a given mathematical expression. We can remember the order using "PEMDAS" where

P --> Parentheses

E --> Exponents (2⁵ is 2 raised to the power of 5)

M------> Multiplication and

D---->Division (from left to right)

A--->Addition

S--->Subtraction (from left to right).

We have given that

3/4 ( 2³ + 4² )

let given expresion equal to L i.e

L = 3/4 ( 2³ + 4² )

Now, we have to solve it

Using "PEMDAS" rule ,

L = 3/4 ( 2³ + 4²)

= 3/4 ( 8 + 4²)

= 3/4 ( 8 + 16 )

= 3/4 ( 24)

= 3/4 ×24

= 24×3/4

= 72/4

L = 1 3

Hence, the given expresion is equal to 13 .

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The "4" in the integral is actually the height (or thickness) of each slice that we are using to find the volume of the solid.

In this case, we are taking infinitesimal slices perpendicular to the x-axis and the height of each slice is 4.

Let's consider the cross-sectional area of each slice. The cross-section is a square with side length equal to the diameter of the semicircular base, which is 2 * 9 = 18. The area of the square is 18^2 = 324.

However, we also need to take into account the shape of the semicircle. As we move up the solid, the area of the cross-section decreases as the height of the slice decreases. This is because the cross-sectional square is inscribed inside the semicircle, and as the height decreases, so does the width of the square. To account for this, we need to find the width of the square as a function of the height of the slice.

Let y be the height of the slice, then the width of the square is equal to the diameter of the semicircle minus twice the height of the slice. The diameter of the semicircle is 18, so the width of the square is 18 - 2y.

The area of the cross-section at height y is then given by:

A(y) = (18 - 2y)^2

A(y) = 324 - 72y + 4y^2

To find the volume of the solid, we integrate the area of the cross-section with respect to the height of the slice, from 0 to 9:

V = ∫_0^9 A(y) * 4 dy

V = ∫_0^9 (324 - 72y + 4y^2) * 4 dy

V = ∫_0^9 1296 - 288y + 16y^2 dy

V = 1296 * y - 144y^2 + 8y^3 |_0^9

V = 1296 * 9 - 144 * 9^2 + 8 * 9^3

V = 11304 - 1296 + 729 = 8737 cubic units

So, the volume of the solid is 8737 cubic units.

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Let's consider the cross-sectional area of each slice. The cross-section is a square with side length equal to the diameter of the semicircular base, which is 2 * 9 = 18. The area of the square is 18^2 = 324.

A(y) = (18 - 2y)^2

A(y) = 324 - 72y + 4y^2

V = ∫_0^9 A(y) * 4 dy

V = ∫_0^9 (324 - 72y + 4y^2) * 4 dy

V = ∫_0^9 1296 - 288y + 16y^2 dy

V = 1296 * y - 144y^2 + 8y^3 |_0^9

V = 1296 * 9 - 144 * 9^2 + 8 * 9^3

V = 11304 - 1296 + 729 = 8737 cubic units

Step-by-step explanation:

because

ST = QR = 16

that means that also the distance from the center point is the same.

in other words :

UC = VC

therefore,

2x = 5x - 9

0 = 3x - 9

9 = 3x

x = 3

The absolute value model |x - 30| = 10 represents the time required for Jack to fold his laundry. (Correct choice: D)

Absolute values are functions used in mathematics that represents the magnitude of a number, whose definition is summarized below:

In this case, we must determine an absolute value model that contains the maximum and minimum times required by Jack to fold his laundry, This is represented by the following model:

|x - a| = b

Where:

If we know that a = 30 min and b = 10 min, then the absolute value model is:

|x - 30| = 10

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The m values that allow the quadratic equation \(x^2 + mx + 4\) to have two independent real roots are m in the open range (-∞ , -4) (4 , ∞). This may be expressed in interval notation as:

m ∈ (-∞, -4) ∪ (4, ∞).

The quadratic formula tells us that the quadratic equation's roots

\(x^2 + mx + 4 = 0\)

are provided by:

\(x = (-m\) ± \(sqrt(m^2 - 16))/2\)

The discriminant \((m^2- 16)\)must be positive, i.e., \(m^2\) > 16, for the quadratic to have two separate real roots. As a result, we have two instances to consider:

Case 1: m > 4. Because \((-m + sqrt(m^2 - 16)/2\)and\((-m - sqrt(m^2 - 16)/2\)are both real and unique in this case, the quadratic has two separate real roots.

Case 2: m < -4. In this situation, \((-m + sqrt(m^2 - 16)/2\) is negative, whereas\((-m - sqrt(m^2 - 16)/2\) is positive, indicating that the quadratic has two separate real roots.

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Answer: She is using the counting-on technique.

Step-by-step explanation: