Factor each polynomial SHOW YOUR WORK please help me
X^2-6x+8
2x^2-9x+10

The function f(x) = x² - 1/x + 1, with domain [0, ∞), does not have an absolute maximum on its domain, but this does not contradict the extreme value theorem.

The extreme value theorem states that if a real-valued function f is continuous on a closed interval [a, b], then f must have both an absolute maximum and an absolute minimum on that interval.

However, the theorem does not apply to functions that have an open interval as their domain, such as f(x) = x² - 1/x + 1 with a domain of [0, ∞).

In this case, f(x) approaches infinity as x approaches 0, but it does not have a maximum value within the given domain. The lack of an absolute maximum for f(x) on [0, ∞) is consistent with the behavior of the function, and it does not violate the extreme value theorem since the domain is not a closed interval.

Therefore, the function f(x) = x² - 1/x + 1, defined on [0, ∞), lacks an absolute maximum, but this does not violate the extreme value theorem.

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Answer: 28 hours

Step-by-step explanation:

\(V=7(4)(1.2)\\\\v=33.6\ m^3\)

\(\displaystyle\\20\ l/min=\\\\\frac{20(60)}{1000} =\\\\\frac{1200}{1000}=\\\\1.2\ m^3/hour\)

\(\displaystyle\\v=\frac{V}{t} \\\)

Multiply both parts of the equation by t(t≠0):

\(vt=V\)

Divide both parts of the equation by v (v≠0):

\(\displaystyle\\t=\frac{V}{v} \\\\t=\frac{33.6}{1.2} \\\\t=28 \ hours\)

Answer:

We need to find the volume first.

We will use our famous volume of a rectangular solid formula:

V = l x w x h

So, V = 12 x 7 x 1.2 = 100.8 cubic meters.

Now, cost = 100.8 x 27.25 = 2746.8 PHP

Conclusion:The water will cost PHP 2,746.8.

The better buy is given by the following brand:

Brand A.

The better buy is obtained applying the proportions in the context of the problem.

A proportion is applied as the cost per ounce is given dividing the total cost by the number of ounces.

Then the better buy is given by the option with the lowest cost per ounce.

The cost per ounce for each brand is given as follows:

$8 per ounce is a lesser cost than $9.3 per ounce, hence the better buy is given by Brand A.

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Answer:

B. ΔRMS ≅ ΔRQS by AAS

I just took the test :)

Answer:B

Step-by-step explanation:just took the test

Answer:The value of 147 + (-43) + (-16) is 88.

Step-by-step explanation:

88

its basically 147 - 43 - 16=88

Expressing this function as a piecewise function, we get;

y = -x + 1         for x< -5

y = -1/2x + 4    for x> 4

According to the question, we can see that the graph is a line for x < -5. We will find two points on this line to find out the slope.

( - 5,6) and ( -8,9)

The slope is m= ( y2-y1)/(x2-x1)

m = ( 9-6)/(-8 - -5) = 3/ ( -8+5) = 3/-3

The slope is -1

Using point-slope form, we will find the general equation of this line

y-y1 = m(x-x1)  and the point ( -8,9)

y -9 = -1(x - -8)

y -9 = -1(x +8)

y-9 =  -x - 8

y = -x + 1   for x< -5

The graph is a line for  x > 4

(4,2) and ( 6,1)

The slope is m= ( y2-y1)/(x2-x1)

m = ( 1 - 2)/(6 - 4) = -1/ (2) = -1/2

The slope is -1/2

Using point-slope form

y-y1 = m(x-x1)  and the point (6,1)

y -1 = -1/2(x - 6)

y-1 = -1/2 x  + 3

y = -1/2x + 4   for x> 4

Therefore, expressing this function as a piecewise function, we get;

y = -x + 1         for x< -5

y = -1/2x + 4    for x> 4

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Answer:

The distance between the two villages is 16.5 Km

Step-by-step explanation:

Constant Speed Motion

It's a type of motion in which the distance of an object changes by an equal amount in every equal period of time.

If v is the constant speed, the object travels a distance x in a time t, given by the equation:

x=vt

Amar cycles at v=18 Km/h for t=55 minutes. We need to calculate the distance traveled between the two villages.

Since the speed and the time are given in different units, we convert the time to hours, recalling that 1 hour=60 minute.

t=55 min = 55/60 hours

For the sake of precision, we won't operate the division so far. Compute the distance:

x=18 *55/60=16.5 Km

The distance between the two villages is 16.5 Km

One common unit of measure that serves as a conversion factor between linear and angular measurements is the radian (rad).

A radian is defined as the angle subtended at the center of a circle by an arc of the circle equal in length to the radius of the circle.

Since the circumference of a circle is 2π times the radius, there are 2π radians in a full circle. Therefore, one can use the following conversion factors

1 radian = 180/π degrees (approx. 57.3 degrees)

1 degree = π/180 radians (approx. 0.01745 radians)

These conversion factors allow you to convert between linear measurements (such as arc length or circumference) and angular measurements (such as angles in degrees or radians) when dealing with circular motion or rotational systems.

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Answer:

The equation of line in point slope form is: \(\mathbf{y+5=-\frac{2}{3} (x-4)}\)

Option A is correct option.

Step-by-step explanation:

We need to identify an equation in point-slope form the line parallel to y=-2/3x+8 that passes through(4, -5).

The general equation of point slope form is: \(y-y_1=m(x-x_1)\)

where m is slope of the equation.

Finding slope of the equation.

Since the two lines are parallel so, both lines have same slope.

Equation of given line: y=-2/3x + 8

This equation is in slope-intercept form, comparing with general equation \(y=mx+b\) where m is slope , we get the value of m= -2/3

So, slope of given line = m = -2/3

Slope of required line = m =-2/3

Now, writing equation in point-slope form:

We are given point (4,-5) so, we have \(x_1=4, y_1=-5\) and slope is: m=-2/3

So, equation of line in point-slope form is:

\(y-y_1=m(x-x_1)\\y-(-5)=-\frac{2}{3}(x-4)\\y+5=-\frac{2}{3}(x-4)\)

So, the equation of line in point slope form is: \(\mathbf{y+5=-\frac{2}{3} (x-4)}\)

Option A is correct option.

Answer:

The answer is A.

Step-by-step explanation:

Yes, an angle in a right-angled triangle is always present.  Without any additional information about the triangle, it is impossible to determine the value of the angle in question.

In a right-angled triangle, one of the angles is a right angle, which measures 90 degrees. The other two angles in the triangle are acute angles and their measures always add up to 90 degrees.

To find the value of the angle in question, we need to know some additional information about the triangle. If we have the lengths of two sides of the triangle, we can use trigonometric ratios to find the measure of the angle.

For example, if we know the length of the side opposite the angle and the length of the hypotenuse (the longest side of the triangle), we can use the sine ratio to find the measure of the angle.

If we know the length of the side adjacent to the angle and the length of the hypotenuse, we can use the cosine ratio.

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The logarithmic equation 2log4 - log3 + 2logx - 4 = 0 can be solved by rewriting the equation using logarithmic properties and then solving for x. The exact value of x depends on the logarithmic base used.

To solve the logarithmic equation 2log4 - log3 + 2logx - 4 = 0, we can start by applying logarithmic properties. Using the properties

log(a) - log(b) = log(a/b) and log(a^b) = b log(a), we can rewrite the equation as log(4^2) - log(3) + log(x^2) - log(10,000) = 0.

Simplifying further, we have 2 log(16) - log(3) + 2 log(x) - 4 = 0.

Next, we can combine the logarithmic terms using the property

log(a) + log(b) = log(a * b). This gives us log(16^2 * x^2 / 3) - 4 = 0. Simplifying the logarithm, we have log(256x^2/3) - 4 = 0.

To isolate the logarithm, we can apply the property a = b implies 10^a = 10^b. In this case,

10^(log(256x^2/3) - 4) = 10^0. This simplifies to 256x^2/3 = 10^4.

Finally, we solve for x by rearranging the equation. Multiplying both sides by 3/256, we get x^2 = (3/256) * 10^4. Taking the square root of both sides, we have x = ±√(3/256) * 10^2. Thus, the exact value of x depends on the logarithmic base used, but this provides the general form of the solution.

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Answer:

See solutions below

Explanation

We are to find the equation of circle A and B

The equation of a circle is expressed as;

(x-a)^2 + (y-b)^2 = r^2

(a, b) is the centre and r is the radius

For Circle A that has center of (6, 7), and a radius of 4

Substitute;

(x-6)^2 + (y-7)^2 = 4^2

(x-6)^2+(y-7)^2 = 16

Hence the equation of circle A is (x-6)^2+(y-7)^2 = 16

For circle B:

If circle B has a center of (2, 4), and a radius of 16

The equation is expressed as;

(x-2)^2+(x-4)^2 = 16^2

(x-2)^2+(x-4)^2 = 256

Hence the required equation is (x-2)^2+(x-4)^2 = 256

Answer:

Hope this helps

Answer:

Middle and far right one

Step-by-step explanation:

X values cannot repeat

A poster of area 11760 cm2 has blank margins of 10 cm wide on the top and bottom and 6 cm wide on the sides. The dimensions that maximize the printed area are 500 cm x 23.52 cm.

The problem can be solved using the following concept:

Suppose we have a function f(x), then at the maximum/minimum point, it holds:

          f '(x) = 0

In the given problem, let:

q = length of the poster

p = width of the poster

Then,

p x q = 11760

or q = 11760/p

Let f(p,q) be the function of printed area, then:

f(p,q) = (p - 20)(q - 12)

f(p) = (p - 20) (11760/p - 12)

f(p) = -p² + 1000p - 980 x 20

At the maximum point:

f '(p) = 0

-2p + 1000 = 0

p = 500

Substitute p = 500 to get q:

q = 11760/p = 11760/500 = 23.52

Hence, the maximum printed area obtained if the dimensions are 500 cm x 23.52 cm

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Answer:

4 and -3

Step-by-step explanation:

By higher I think you mean greater

In this case, for a) 4 will be greater, and for b) -3 will be greater

Answer:

y + 1 = 1 × (x - 3)

Step-by-step explanation:

.................................

Answer:

An Overview of the Cell Cycle. The most basic function of the cell cycle is to duplicate accurately the vast amount of DNA in the chromosomes and then segregate the copies precisely into two genetically identical daughter cells. These processes define the two major phases of the cell cycle.

The percent increase in players from last year to this year = 20%

We know that the formula for the percentage change a quantity is :

(P) = [Final value - Initial value] / Initial value x 100

Here, a baseball team had 80 players show up for tryouts last year and this year 96 show up for tryouts.

initial number of players = 80

current number of players = 96

So, using above formula the percent increase in players is:

P = [(96 - 80) / (80)] x 100

P = (16 / 80) x 100

P = 0.20 x 100

P = 20%

Therefore, the percentage of increase in players =  20%.

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2:3 dhrhhrhrhrhrhrhrhrhrhdjfhjf

Answer:

\(y = \frac{29}{5} x \\ \frac{y}{x} = \frac{29}{5} \)

The assessed value of the property with a market value of $60,000 and an assessment rate of 45% is $27,000. T

To compute the assessed value of a property, you'll need to consider both the market value and the assessment rate. In this case, the market value is $60,000, and the assessment rate is 45%.

To find the assessed value, you can multiply the market value by the assessment rate. Using the provided values, you can calculate the assessed value as follows:

Assessed Value = Market Value x Assessment Rate
Assessed Value = $60,000 x 0.45

Assessed Value = $27,000

In this case, the assessed value of the property with a market value of $60,000 and an assessment rate of 45% is $27,000. This value represents the taxable amount on which property taxes will be calculated and is an essential factor for both property owners and tax authorities.

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Answer:

71.99

Step-by-step explanation:

89.99 x .20=17.998

89.99-17.998=71.992

Round

She paid $71.99

Answer:

The regular price is $1,889.79

Step-by-step explanation:

20% to 0.20

$89.99 divided by 0.20 equals 1,799.80

$1,799.80 plus $89.99 equals $1,889.79

Answer:

y= 2 x + 2 i think

Step-by-step explanation:

Answer: 7000

Note: 5 and up rounds up. 4 and below rounds down.

4 < 5 so that means we won't need to round up we round down.

7412 = 7000

If we were to round up then the answer would of been 7500.

The given options A (line) and B (ray) are correct.The one-dimensional figures that have infinite length are lines and rays.  

A line can be described as a one-dimensional geometric figure consisting of infinitely many points extending in two directions. It is straight and can be distinguished from a line segment, which connects two points.

A line has no end and extends indefinitely in both directions.

A ray is a one-dimensional geometric figure that consists of one initial point and extends infinitely in only one direction. It is referred to as half-line in geometry.

So, the correct answers are: A. Line B. Ray.

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Answer: The probability of 60% or less scared speechless out of a group of 50 customers (i.e. 30 customers) is 0.0932% or 0.000932.

Step-by-step explanation: Given problem meets all criteria for application of a binomial distribution with the probability of success; p=0.8 or 80% (which makes probability of failure; q=0.2 or 20%) and the total number of trials; n=50.

Let probability of 30 or less people scared (30 is 60% of 50 people) be P(x≤30), where x≤30 encapsulates all possibilities from 0 to 30 people scared speechless.

Then, by binomial distribution,

P(x≤30) =r=030nCr*pr*q(n-r)

Now we can substitute given values and find the desired probability,

P(x≤30) =r=03050!(50-r)!r!*(0.8)r*(0.2)(50-r)

P(x≤30) =r=03050!(50-r)!r!*(0.8)r*(0.2)-r*(0.2)50

P(x≤30) =(0.2)50*r=03050!(50-r)!r!*(0.8)r*(0.2)-r

P(x≤30) =(0.2)50*r=03050!(50-r)!r!*4r

The first value on the right hand side of equation is a very small number while the summation factor on second is a relatively larger number.

P(x≤30) = 0.000932

Thus, there is a 0.09% chance of 30 or less people scared speechless out of a group of 50.

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The probability of a password without repeating letters is 66.4%

What are permutations?

The permutation is the selection of some or all of the objects from a set and then arranging them by paying attention to the order

If the selected object cannot be repeated, then the permutation can be calculated as:

\(nPr = \frac{n!}{(n-r)!}\)

But if the selected object can be repeated, then the permutation can be calculated as:

\(nPr = n^{r}\)

where n is the total number of objects and r is the number of objects selected. Therefore, n cannot be less than r (n ≥ r)

In the above problem, we know that the number of letters in the alphabet is 26. To find out how many 5-letter passwords are generated without repeating letters, it can be calculated using the non-repetition permutation formula:

\(nPr = \frac{n!}{(n-r)!}\)

\(= \frac{26!}{(26-5)!}\)

\(= \frac{26 . 25 .24 .23 .22 .21!}{21!}\)

= 7893600 passwords

Meanwhile, the 5-letter password generated by repeating letters can be calculated using the permutation formula:

\(nPr = n^{r} \\= 26^{5}\)

= 11881376 passwords

So the probability of a password without repeating letters can be calculated as follows = 7893600 / 11881376 x 100% = 66.4%

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Answer:

$750,000

Step-by-step explanation:

$750,000 $680,000 $600,000 $880,000 $1,200,000 $760,000 $480,000

Write the prices in increasing order and choose the middle one.

$480,000 $600,000 $680,000 $750,000 $760,000 $880,000 $1,200,000

Answer: $750,000

Answer:

As AG = DG

so -4k +24 = 9k + 102

=> -4k - 9k = 102-24

=> -13k = 78

=> k = -6

So the length of DG = -4k + 24 = 24 + 24 = 48

As BG+DG = 2DG = 2(48) = 96 (ans)

So no. c is correct

Hope it helps