When written in standard form,which polynomial had a leading coefficient of 5?

Answer:

√500

Step-by-step explanation:

It is given that a set of real numbers s is non-empty and bounded. The objective is to prove that inf s ≤ sup s. This statement can be justified as below.

Firstly, as per the definition of bounded set, it is known that the set s has both lower and upper bounds. Thus, the infimum and supremum of s exist and are denoted as inf s and sup s, respectively.

Since s is non-empty and bounded, it can be observed that every element of the set s is greater than or equal to inf s and less than or equal to sup s.

Therefore, inf s is the greatest lower bound of s and sup s is the least upper bound of s, implying that inf s ≤ sup s. Hence, it is proven that inf s ≤ sup s for a non-empty set s of real numbers that is bounded.

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Answer:

Step-by-step explanation:When a quadratic function is graphed in the coordinate plane, the resulting parabola and corresponding axis of symmetry are vertical. The graph of the parabola represented by the quadratic function y = a( x - p )2 + q has an axis of symmetry represented by the equation of the vertical line x = p.

Answer:

x=2

Step-by-step explanation:

symmetry= the hightest number x value. basically the halo of the quadratic.

False, The eigenvalues of a matrix A are not same as the eigenvalues of the reduced row echelon form of A.

A matrix's eigenvalues are not the same as those of the matrix's reduced row echelon form, contrary to what is claimed.

This is due to the fact that when a matrix is reduced to its echelon form via row operations, its eigenvalues may not always stay the same. The eigenvalues of a matrix may be different in the reduced row echelon form than they are in the original matrix as a result.

Think about these matrices as an illustration:

Likewise, B's reduced row echelon form is B, and B's eigenvalues are both 1.

A = [1 2; 2 1]

and

B = [1 0; 0 1].

The eigenvalues of a matrix and its reduced row echelon form are thus typically not the same.

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FALSE. The eigenvalues of a matrix A are NOT the same as the eigenvalues of the reduced row echelon form of A.

Explanation:

Eigenvalues are scalar values that, when multiplied by an eigenvector, produce the same effect as the original matrix A on that eigenvector. Mathematically, for a matrix A and its eigenvector v, Av = λv, where λ is the eigenvalue.

Row echelon form is a matrix transformation using elementary row operations to obtain a triangular form. The reduced row echelon form (RREF) is a further simplified version of the row echelon form.

However, transforming a matrix A to its RREF changes the properties of the matrix, and therefore the eigenvalues of matrix A and its RREF are generally not the same. The eigenvalues are preserved only under specific matrix transformations, such as similarity transformations, which row echelon form is not one of them.

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Adding too much MgSO4 could lead to an overestimation of the mass of the sample. This could cause the results to be inaccurate, as the sample would be heavier than it actually is.

Additionally, if MgSO4 is present in the sample, it could interfere with the results of the experiment and lead to incorrect measurements.

1. Adding too much MgSO4 could lead to an overestimation of the mass of the sample. This is because MgSO4 is heavier than the sample and adding too much could increase the total mass of the sample.

2. This could cause the results to be inaccurate, as the sample would be heavier than it actually is. This means that the measurements taken during the experiment might not be reflective of the actual mass of the sample.

3. Additionally, if MgSO4 is present in the sample, it could interfere with the results of the experiment and lead to incorrect measurements. MgSO4 can act as a catalyst or interfere with the reaction, leading to inaccurate results.

Adding too much MgSO4 could lead to an overestimation of the mass of the sample, causing inaccurate results. This is because MgSO4 is heavier than the sample and adding too much could increase the total mass of the sample. Additionally, if MgSO4 is present in the sample, it could interfere with the reaction and lead to incorrect measurements. This could lead to inaccurate results, as the measurements taken during the experiment might not be reflective of the actual mass of the sample. Therefore, adding too much MgSO4 can impact the results of the experiment, leading to incorrect measurements and inaccurate results.

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In the analyze stage of the data life cycle, the data analyst will use the spreadsheet to aggregate the data and use the formulas to perform the calculations

The data life cycle is defined as the time period that that data exist in you system. Usually the data management experts finds the six or more stages in the data life cycle

The data analyst is the person who use the interpreted data and analyze the data in order to solve the problems

The analyze stage is the one of the main stages of the data life cycle. In the stage data analyst will use the spreadsheet to aggregate the data in the system and use the formulas to perform the calculations in the system

Therefore, the data analyst will use the spreadsheet to aggregate the data and use the formulas to perform the calculations

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The perimeter (p) can be expressed as: p = s + s + s = 3s.

If "s" represents the measure of one side of the equilateral triangle, then:

The perimeter (p) of an equilateral triangle can be found by adding up the length of all three sides. Since all sides of an equilateral triangle are equal, the perimeter (p) can be expressed as: p = s + s + s = 3s.

Another way to express the perimeter (p) of an equilateral triangle is to use multiplication. Since all three sides are equal, we can simply multiply the length of one side (s) by 3 to get the perimeter (p): p = 3s.

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Answer:

16: 24ab, a negative times a negative always makes a positive by the way

17: 6x^4

18: 15, 15-8=7, then 7x3=21

19: -2x+8

20: 8a

21: y x y x y

22: 2a+3b

23: 6a^4

24: x times x times x times x

25: 49y^2

200 is the mean absolute deviation. Therefore, choice three (200) is the right one.

The absolute difference between the predicted and actual values must be determined, added together, and divided by the total number of periods.

Forecasted values are as follows: 1,500 and 1,400

Values in actuality: 1,200 and 1,500

Absolute differences:

|1,500 - 1,200| = 300

|1,400 - 1,500| = 100

Now, we calculate the MAD:

MAD = (300 + 100) / 2 = 400 / 2 = 200

Therefore, 200 is the mean absolute deviation. Therefore, choice three (200) is the right one.

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Answer:

$29

Step-by-step explanation:

You divide 2.5 by 100 the you multiply that by 725 and sense its months it would be converted to 1.6 so you multiply 725 1.6 and the answer to 2.5 divide by 100

Answer:

The interval estimate is:

41.5 - 2.45 ≤ true average time ≤ 41.5 + 2.45

or

38.05 ≤ true average time ≤ 44.95

Inequality notation:

[38.05, 44.95]

The interval estimate that will estimate the true average time that people spend brushing their teeth is [39.05, 43.95] seconds.

Given that the mean time spent brushing teeth from the sample is 41.5 seconds, and the margin of error is 2.45 seconds, we can construct a confidence interval estimate using the formula:

(sample mean) ± (margin of error)

Substituting the given values, we get:

41.5 ± 2.45

Simplifying, we get:

[39.05, 43.95]

Therefore, we can be 95% confident that the true average time that all people spend brushing their teeth falls within this interval.

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\( \frac{19}{6} \pi \times \frac{360}{75} = \frac{19}{6} \pi \times \frac{24}{5} = \frac{76}{5} \pi\)

\( {x}^{2} \times \pi = \frac{76}{5} \pi\)

\(x = \frac{2 \sqrt{95} }{5} = 3.9\)

9514 1404 393

Answer:

  a.  f(x) = (4x +5)(x -3)

  b.  x-intercepts: {-1.25, +3}

  c.  f(x) goes to +infinity as x goes to ±infinity

  d. plot the x-intercepts, the vertex, and a few other points; draw a smooth curve through them

Step-by-step explanation:

a. Here, you're looking for factors of (4)(-15) = -60 that have a sum of -7. Those factors will be -12 and +5, so we can factor the function as ...

  f(x) = (4x -12)(4x +5)/4

  f(x) = (x -3)(4x +5)

__

b. The x-intercepts are the values of x that make the factors zero:

  x -3 = 0   ⇒   x = 3 . . . . (add 3)

  4x +5 = 0   ⇒   x = -5/4 . . . . (add -5, divide by 4)

__

c. As with all even-degree polynomials with positive leading coefficients, the end behavior of f(x) matches that of |x|:

  as x → ∞, f(x) → ∞

  as x → -∞, f(x) → ∞

__

d. The vertex of the function will be located halfway between the x-intercepts, at x = (3-5/4)/2 = (7/4)/2 = 7/8. The value of f(x) there is ...

  f(7/8) = (4(7/8) +5)(7/8 -3) = -289/16 = -18.0625

Since the leading coefficient is 4, the normal x^2 function behavior is stretched vertically by a factor of 4. So, additional points would be

  x = 7/8 ±1, f(x) = -18.0625 +4·1 = -14.0625

  x = 7/8 ±2, f(x) = -18.0625 +4·2^2 = -2.0625

The answers of part B locate two points on the graph, and help find the vertex. The answer of part C confirms the graph as opening upward.

__

Additional comment

I find a graphing calculator to be very helpful finding the roots and making the graph.

Answer:

177 kg

Step-by-step explanation:

Find the weight of the third article by finding the difference between 502 and 856, since 856 kg is the total weight and 502 kg is the weight of the other 2 articles:

856 - 502

= 354

Now, find 1/2 of the weight, by dividing this by 2:

354/2

= 177

So, 1/2 the weight of the third article is 177 kg

Answer:

m = 10

Step-by-step explanation:

The values of w is inversely proportional to m

Mathematically the above statement is expressed as:

w ∝ 1/m

w = k × 1/m

w = k/m

Where k is the Proportionality Constant

First step

Solve for k

If w=8 then m=25

w = k/m

8 = k/25

Cross Multiply

k = 25 × 8

k = 200

Second step

what is m when w=20? Show me the steps please

We solve for m

w = k/m

k = 200

20 = 200/m

Cross Multiply

20m = 200

m = 200/20

m = 10

Answer:

Step-by-step explanation:

x/3+5>2

x/3>-3

x>-9

answer: x>-9

Answer:

x>-9

Step-by-step explanation:

First, do -5 on 2 and cross out +5.

then u have 2-5 which is -3

so it would x/3>-3

then u multiply 3 times -3 which is -9 so its x>-9

The largest right circular cone that can fit within a cube has a volume of 718.67 cm3.

When a cone's axis is the line from the vertex to the circular base's midpoint, the cone is said to be right circular. In other words, a right angle is formed when the center of the circular base joins the cone's peak.

A three-dimensional form called an inverted frustum that resembles a conical cylinder. When the vertex of a cone is inverted after being sliced by a plane parallel to the shape's base, it is said to have this shape.

The formula r2+rl, where r is the radius of the circular base, h is the height of the cone, l is the slant height, and is an approximation, is used to determine the surface area of a cone as 3.14

Side of cube: 14 cm

Cube's radius is 14/2 cm, or 7 cm.

h=14cm for height

Volume'=1/3piR x 2hM =1/3 x 22 x 7 x 7 x7

= 718.67 cm3.

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The simplification of the expression m²n³+ 18m³n² + 10m²n+2m²n is m²n ( n²+18mn+ 12)

Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do.

m²n³+ 18m³n² + 10m²n+2m²n = m²n³ + 18m³n² +12m²n

Therefore we factorize the common factors out, they are m²n

= m²n ( n²+18mn+ 12)

therefore the simplification of the expression m²n³+ 18m³n² + 10m²n+2m²n is m²n ( n²+18mn+ 12)

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The slope of the new road is zero.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Take points from the Graph (5, 0) and (5, 4).

Slope of a line = m = tanθ

where θ is the angle made by the line with the x−axis.

For a line parallel to y−axis ,θ= π/2.

​

∴m = tan π/2 = undefined

The new road will therefore have 0° of inclination if it is perpendicular to D street because if they are perpendicular and D street is vertical, the new road is level and has 0° of inclination.

An horizontal line now has zero slope.

The new road has a zero slope as a result.

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Answer:

He volunteered 10 hrs 15 min on average.

Step-by-step explanation:

The first week: 8 hrs

The second week: 12 hrs

The third week: 12 hrs

The fourth week: 9 hrs

8 + 12 + 12 + 9 = 41 hrs total

41 hours/4 weeks = 10.25 hrs (10 hrs 15 min)

Answer: 10.25 hours/week (On average, William volunteered 10.25 hours per week during these four weeks)

Step-by-step explanation:

To find an average, you need to add up each entity:

8+12+12+9=41

After that, you divide that number by n (the number of weeks)

41/4=10.25 hours

Step-by-step explanation:

A

y=10x

x:y=x:10x=1:10

Answer:

See Below.

Step-by-step explanation:

Please refer to the attachment below.

In order to complete the proof, we create a new segment DE that extends from D and is equal to AD. The endpoint of DE will be connected to B.

Statements:                                             Reasons:

\(1)\text{ } AD\text{ bisects } CB\)                                     Given

\(2)\text{ } CD=DB\)                                            Definition of Bisector

\(3)\text{ } AE=DE\)                                            Given

\(4)\text{ } \angle ADC \cong \angle EDB\)                                 Vertical Angles are Congruent

\(5)\text{ } \Delta ADC\cong \Delta EDB\)                                SAS Congruence

\(6)\text{ } \angle BED\cong \angle CAD\)                                CPCTC

\(7)\text{ } AD\text{ bisects } \angle A\)                                    Given

\(8)\text{ } \angle CAD\cong \angle BAD\)                                 Definition of Congruence

\(9)\text{ } \angle BED\cong\angle BAD\)                                 Substitute

\(10)\text{ } BE=BA\)                                          Isosceles Triangle Theorem

\(11) \text{ } BE=CA\)                                          CPCTC

\(12)\text{ } CA=BA\)                                          Substitute

\(13)\text{ } \Delta ABC\text{ is isosceles}\)                             Isosceles Triangle Definition

Answer:

this is your answer look it once.thank you.

Answer:

$2.24 per Gallon

Step-by-step explanation:

36.96 divided by 16.5 is 2.24, then to check that multiple 2.24 by 16.5 and you get the total cost of 36.96. Hope this helps.

Answer:

b= 2 if you need a perfect square

Step-by-step explanation:

If we need to "Find the value of b? " so that the quadratic equation can be written as a perfect square

y= -x²+bx - 1, factor the -1

y= - (x² -bx +1), we know (a+b)² = a²+2ab+b² = x²-bx+1 , so b must be 2

y= - (x² -2x +1), rewritten as a perfect square

y= - (x -1)²

Answer:

Here, Hope it helps its only the answer

Answer:

(4x-9)²

Step-by-step explanation:

If you want to simplify 16x² - 72x + 81, you can use a cool trick called the square of a binomial rule. This rule says that if you have something like (a + b)², you can expand it as a² + 2ab + b². So, how do we apply this rule to our problem? Well, first we need to find a and b that make our expression look like (a + b)². We can do this by noticing that 16x² is the same as (4x)² and 81 is the same as 9². Then we can check that the middle term is -2 times the product of 4x and 9, which is -72x. So we can write our expression as (4x - 9)². That's it! We have simplified our expression using the square of a binomial rule.

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.

\((\stackrel{x_1}{3}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{9}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{9}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{3}}} \implies \cfrac{ 5 }{ 5 } \implies 1\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{ 1}(x-\stackrel{x_1}{3}) \\\\\\ y-4=x-3\implies {\Large \begin{array}{llll} y=x+1 \end{array}}\)

Answer:

Weight of Train A = A = 237 tons

Weight of Train B = B = 96 tons

Step-by-step explanation:

Two trains train a and be weigh a total of 333 tons. Train A is heavier than train B.The difference of their weight is 141 tons… What is the weight of each train??

Let us represent:

Weight of Train A = A

Weight of Train B = B

Our system of Equations is given as:

A + B = 333 tons..... Equation 1

A - B = 141 tons....... Equation 2

We solve using Elimination method

We Add Equation 1 and 2 together to Eliminate B

Hence:

2A = 474 tons

A = 474 tons/2

A = 237 tons

Solving for B using Equation 1

A + B = 333 tons..... Equation 1

237 tons + B = 333 tons

B = 333 tons - 237 tons

B = 96 tons

Therefore:

Weight of Train A = A = 237 tons

Weight of Train B = B = 96 tons

A hypothesis can be differentiated from a theory because it is a specific prediction arising from the theory. The statement that is true is, a hypothesis can be differentiated from a theory because it is a specific prediction arising from the theory. A hypothesis is a suggested explanation of a phenomenon or observed data that is testable.

Hypotheses are more detailed, and are written to explain precisely what you think is going to occur in your research and the reason for that prediction. A hypothesis will be rejected if it does not fit the data, whereas a theory will be modified to fit the data.

A hypothesis is more like a forecast, and a theory is more like a law that explains how certain events operate. Thus, we can conclude that a hypothesis is a specific prediction arising from the theory.

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