64+16x^2-72x+81=289 I don’t understand

The inequality that models the scenario is the first one:

$24 + $2*n ≤ $37

Solving that we conclude that Eli can buy at most 6 notebooks.

We know that Eli wants to buy a calculator that costs $24 and some notebooks, such that each notebook costs $2.

Then If Eli buys the calculator and n notebooks the total cost will be:

$24 + $2*n

We know that Eli has a total of $37 to spend, so that is the maximum amount he can spend. Thus, we can write the inequality:

$24 + $2*n ≤ $37

So the correct option is the first one.

Now also let's solve the inequality for n.

$24 + $2*n ≤ $37

$2*n  ≤ $37 - $24

$2*n ≤ $13.

n ≤ $13/$2

n ≤ 6.5

So Eli can buy at most 6 notebooks.

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Answer:

-0.3

Step-by-step explanation:

X---Y---Z. XY+Y ---} 7x+4x+3 ---} 10x+3=0 ---} 10x=-3 ---} x=-0.3

Answer: R(-6.5, 2)

Step-by-step explanation:

Given: M(-1,-3)  Q(4.5, -8)       R(x,y)=?

The coordinates of the point in the middle of the segment are equal to the arithmetic mean of the coordinates of its ends

\(\displaystyle\\Hence,\ x_M=\frac{x_Q+x_R}{2}\\\\-1=\frac{4.5+x_R}{2} \\\)

Multiply both parts of the equation by 2:

\(-2=4.5+x_R\\\\-2-4,5=4.5+x_R-4.5\\\\-6.5=x_R\\\\Thus,\ x_R=-6.5\)

\(\displaystyle\\y_M=\frac{y_Q+y_R}{2} \\\\-3=\frac{-8+y_R}{2}\)

Multiply both parts of the equation by 2:

\(-6=-8+y_R\\\\-6+8=-8+y_R+8\\\\2=y_R\\\\Thus,\ y_R=2\)

\(So,\ R(-6.5,2)\)

The probability that the randomly selected student chose running is; 12/57

Total number of students = 57

Total number of boys = 24

Total number of girls = 33

Number of Girls that chose football = 17

Number of boys that chose football = 14

Number of students that chose Tennis = 14

Now, number of students that chose running will be;

Number of students that chose running = 57 - (31 + 14) = 12

Thus, probability that a randomly selected student chose running = 12/57

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Answer:

Your answer is 15.

Step-by-step explanation:

I've done this before and got it right

Answer:

Step-by-step explanation:

pythagoras theorem

a^2+b^2=c^2

15^2+8^2=missing side^2

225+64=missing side^2

\(\sqrt{289\)=missing side

17=missing side

Answer:

n + 6 = 13

Step-by-step explanation:

let n be the number, then increasing by 6 means adding 6 to it , so

n + 6 = 13 ← linear equation

Answer:

It would be 8p+4

Step-by-step explanation:

dividing (48p + 24) by 6 involves factoring and simplifying the expression to obtain the result of 8p + 4

To divide (48p + 24) by 6, you first factor out the common factor of 6 from the expression, which yields

(48p + 24) = 6(8p + 4).

Then, you can further simplify by dividing each term by 6.

The result is 8p + 4.

This process of division distributes the division operation across all terms in the expression, and as a result, each term's coefficient is divided by 6.

In this case, it simplifies the original expression to 8p + 4.

In summary, dividing (48p + 24) by 6 involves factoring and simplifying the expression to obtain the result of 8p + 4

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Answer:

Completing the square is always confusing, but if you keep in mind it's just a way to write  (A + B )^2  so that the problem is in some easier form it makes a bit better sense.  A perfect square has some helpful properties.. anyway..

Step-by-step explanation:

Given: \(x^{2}\) - 12x +23 = 0   ( not a perfect square , tough to work with )

take 1/2 of the second term  coefficient  12/2 = 6   and square it

\(x^{2}\) - 12x + (\(-6)^{2}\) +23 = \((-6)^{2}\)

\(x^{2}\) -12x + \(6^{2}\) +23 = \(6^{2}\)

now there is a perfect square :)

(x - 6)^2 =36-23

(x - 6)^2 = 13

take the square root of both side now

x -6 = \(\sqrt{13}\)

x = \(\sqrt{13}\) +6

sooo  what is supposed to happen in these problems  is that square root of 13 is supposed to work out to something that is easy to find the root of ... maybe in your answers you left out the square roots?   so maybe A is right  :/

We want to solve a quadratic equation by completing squares.

What we need to use is the general relation:

\((a + b)^2 = a^2 + 2ab + b^2\)

We will see that the solutions are:

\(x = 6 \pm \sqrt{13}\)

We start with the equation:

\(x^2 - 12x + 23 = 0\\\)

We can rewrite the middle term as:

\(x^2 - 2*6*x + 23 = 0\\\)

Now remember that 6*6  = 36

Then we can add 13 and subtract 13 to get:

\(x^2 - 2*6*x + 23 + 13 - 13 = 0\\x^2 - 2*6*x + 36 - 13 = 0\\x^2 - 2*6*x + (-6)^2 - 13 = 0\\(x - 6)^2 - 13 = 0\)

Then the solutions are:

\((x - 6) = \pm \sqrt{13} \\\\x = 6 \pm \sqrt{13}\)

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We have three equations with three unknowns: \(y[0]\), \(y[1]\), and \(y[2]\). By solving this system of equations, we can find the output signal \(y[n]\).

To determine the output of the LTI system, we can substitute the given values of the input signal \(x[n]\) into the difference equation:

\(y[n] + \frac{1}{2} y[n-2] = x[n] - \frac{1}{4} x[n-1]\)

Given \(x[n] = \{2, 0, 1\}\), we can substitute these values into the equation:

For \(n = 0\):

\(y[0] + \frac{1}{2} y[-2] = x[0] - \frac{1}{4} x[-1]\)

\(y[0] + \frac{1}{2} y[-2] = 2 - \frac{1}{4} \cdot x[-1]\)

\(y[0] + \frac{1}{2} y[-2] = 2 - \frac{1}{4} \cdot x[-1]\)

For \(n = 1\):

\(y[1] + \frac{1}{2} y[-1] = x[1] - \frac{1}{4} \cdot x[0]\)

\(y[1] + \frac{1}{2} y[-1] = 0 - \frac{1}{4} \cdot 2\)

\(y[1] + \frac{1}{2} y[-1] = -\frac{1}{2}\)

For \(n = 2\):

\(y[2] + \frac{1}{2} y[0] = x[2] - \frac{1}{4} \cdot x[1]\)

\(y[2] + \frac{1}{2} y[0] = 1 - \frac{1}{4} \cdot 0\)

\(y[2] + \frac{1}{2} y[0] = 1\)

We have three equations with three unknowns: \(y[0]\), \(y[1]\), and \(y[2]\). By solving this system of equations, we can find the output signal \(y[n]\).

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Answer: y = 5x + 26

Step-by-step explanation:

To find the equation of a line that is perpendicular to the given line y = -1/5x + 1 and passes through the point (-5, 1), we need to determine the slope of the perpendicular line. The given line has a slope of -1/5. Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the perpendicular line will be the negative reciprocal of -1/5, which is 5/1 or simply 5. Now, we have the slope (m = 5) and a point (-5, 1) that the perpendicular line passes through.

We can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Substituting the values, we get:

y - 1 = 5(x - (-5))

Simplifying further:

y - 1 = 5(x + 5)

Expanding the brackets:

y - 1 = 5x + 25

Rearranging the equation to the slope-intercept form (y = mx + b):

y = 5x + 26

Therefore, the equation of the perpendicular line that passes through the point (-5, 1) is y = 5x + 26.

Step-by-step explanation: Formula for simple interest is P x R x T , which is

Principal amount x Rate x Time (in years)

=> 9000 x \(\frac{2}{100}\) x 3 = 540

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Answer:

To find the greatest common factor (GCF) of the list of terms 30x^3, 110x^4, and 60x^5, we can begin by factoring each term into its prime factors:

30x^3 = 2 * 3 * 5 * x * x * x

110x^4 = 2 * 5 * 11 * x * x * x * x

60x^5 = 2 * 2 * 3 * 5 * x * x * x * x * x

Next, we can identify the common factors among the three terms. These are 2, 5, and x^3. The GCF is the product of these common factors:

GCF = 2 * 5 * x^3 = 10x^3

Therefore, the greatest common factor of 30x^3, 110x^4, and 60x^5 is 10x^3.

Step-by-step explanation:

Find the biggest common factor between the ratio's two terms to write the ratio in its simplest form. The largest number that equally divides both numbers is known as the greatest common factor of two numbers.

1 : 1/2 = 2 : 1

Add whole numbers to the values.

Create a fraction with the full number 1 as the denominator.

Next, we have:

1 : 1/2 = 1/1 : 1/2

Remove the denominators from fractions to convert them to integers.

We discover the Least Common Denominator and rewrite our two fractions as necessary using the common denominator because our two fractions have unlike denominators.

1 1/3 : 4 4/7 = 7 : 24

There are now:

1 1/3 : 4 4/7 = 4/3 : 32/7

Remove the denominators from fractions to convert them to integers.

We discover the Least Common Denominator and rewrite our two fractions as necessary using the common denominator because our two fractions have unlike denominators.

0.360 : 0.153 = 40 : 17

Add whole numbers to the values.

By multiplying both sides by 103 = 1000 to remove all three decimal places, you can convert any decimal values to integers.

Next, we have:

0.360 : 0.153 = 360 : 153

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The researcher randomly selected and interviewed fifty male and fifty female teachers can be categorized as:

iii. random - The selection of teachers is done randomly, without any specific criteria or pattern.

To solve the absolute-value inequality |8 - x| ≥ 5, we can consider two cases:

Case 1: (8 - x) ≥ 5

To solve this inequality, we have:

8 - x ≥ 5

-x ≥ 5 - 8

-x ≥ -3 (multiplying by -1 and reversing the inequality)

x ≤ 3 (dividing by -1 and reversing the inequality)

Case 2: -(8 - x) ≥ 5

To solve this inequality, we have:

-8 + x ≥ 5

x ≥ 5 + 8

x ≥ 13

Combining the solutions from both cases, we have:

x ≤ 3 or x ≥ 13

So, the solution to the absolute-value inequality |8 - x| ≥ 5 is x ≤ 3 or x ≥ 13.

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Answer:

26%

Step-by-step explanation:

Given that Dan has 59 new email messages and 13 have attachment then the proportion that have attachments may be expressed as a ratio of the number with attachments to the total number of emails.

Hence proportion of the email messages have attachments as a percentage

= 13/50 * 100%

= 26%

This means that 26% of the emails received have attachments

area cylinder= pi× r² × h, but the drawing shows only half of the cylinder so: area= (pi×r²×h)/2

area= (pi×(6/2)²×25)/2 (the radius is 6/2 because the

drawing indicates the whole

diameter)

area= 225pi / 2

area≈353.43cm³

Answer:

  413.9 cm²

Step-by-step explanation:

The total surface area of the solid is the sum of the curved area, semicircular end area, and rectangular base area.

The area of the curved surface is the lateral area of half a cylinder. The area of the semicircular ends is half the end area of a cylinder. The area of these surfaces together is half the area of a cylinder:

  A = 1/2(2πr)(r +h) = πr(r +h)

The radius is half the given diameter, so the area of the half-cylinder we can see is ...

  A = π(3 cm)(3 cm +25 cm) = 84π cm²

The rectangular bottom of the figure is hidden from view. Its dimensions are given as 6 cm wide by 25 cm long. Its area is given by the formula for the area of a rectangle:

  A = LW

  A = (25 cm)(6 cm) = 150 cm²

The total surface area of the figure is the sum of the half-cylinder area and the area of the base:

  total area = (84π +150) cm² ≈ 413.9 cm²

The surface area of the figure is about 413.9 square centimeters.

The value of x in the parallel line is as follows:

1. x = 50

2. x = 55

3. 102 - 2v

When parallel lines are cut by a transversal line, angle relationships are formed such as alternate interior angles, alternate exterior angles, corresponding angles, vertically opposite angles, linear angles etc.

Therefore, let's use the angle relationship to find the value of x as follows:

1.

m∠1 = m∠8(alternate interior angles)

2x + 25 = x + 75

2x - x = 75 - 25

x = 50

2.

m∠2 = m∠6(corresponding angles)

3x - 10 = 2x + 45

3x - 2x = 45 + 10

x = 55

3.

m∠3 + m∠8 = 180(same side interior angles)

4v - 31 + 2x + 7 = 180

2x = 180 + 31 - 7 - 4v

2x = 204 - 4v

x = 102 - 2v

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The coordinate of point P is (1, 5).

Here we have to find the coordinate of the point P, which is on the line between x(-1,2) and y(7,14) which are partitions in the ratio 1:3.

The formula of the coordinate when two points are separated in the ratio m:n

Let a and b be the coordinate of P.

a = 7m + (-1)n/ m+n

b = 14m + 2n / m+n

Now put the value m: n as 1:3

a = 7×1 +(-1)×3/ 1+3

 = 7 - 3/ 4

 = 4/4

 = 1

b = 14×1 + 2×3/ 1 +3

  = 14 + 6/ 4

  = 20/4

  = 5

Therefore the coordinate of P is (1,5).

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The net present value (NPV) of the project is $16,723.13. Since the NPV is positive, the investment of replacing old equipment should be accepted according to the net present value criterion.

To determine the net present value (NPV) of the project, we need to calculate the present value of the cash flows associated with the investment. The initial outlay is $130,000, which occurs immediately. The cash flow of $31,000 per year for 6 years can be viewed as an ordinary annuity. Using the formula for the present value of an ordinary annuity, we can calculate the present value of the savings:

PV = CF * (1 - (1 + r)^(-n)) / r

Where CF is the annual cash flow, r is the discount rate, and n is the number of years.

Using this formula with CF = $31,000, r = 8%, and n = 6, we find PV = $160,024.29.

The additional outlay of $20,000 that occurs five years from now needs to be discounted back to the present value using the compound interest formula:

PV = FV / (1 + r)^n

Where FV is the future value and n is the number of years.

Using this formula with FV = $20,000, r = 8%, and n = 5, we find PV = $13,301.16.

Now we can calculate the NPV by subtracting the initial outlay and the present value of the additional outlay from the present value of the savings:

NPV = PV of savings - Initial outlay - PV of additional outlay

    = $160,024.29 - $130,000 - $13,301.16

    = $16,723.13

Since the NPV is positive ($16,723.13), the investment should be accepted according to the net present value criterion.

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0.000181130666

Step-by-step explanation:

The area of a circle can be represented by the equation A = πr^2, where r is the radius. If the area of a circle is 4π cm^2, then we can solve for the radius, r:

4π = πr^2

Dividing both sides by π:

4 = r^2

Taking the square root of both sides:

r = 2 cm

The circumference of a circle can be represented by the equation C = 2πr, where r is the radius. Using the value of r we found earlier, we can now find the circumference of the circle:

C = 2π(2)

C = 4π cm

The circumference of the circle is 4π centimeters.

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By using factoring by grouping or synthetic division, we find that \(x = -2\) is a real solution.

Checking for Rational Roots

Using the rational root theorem, the possible rational roots of the polynomial are given by the factors of the constant term (24) divided by the factors of the leading coefficient (-4).

The possible rational roots are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24.

By substituting these values into \(f(x)\), we find that \(f(-2) = 0\). Hence, \(x + 2\) is a factor of \(f(x)\).

Dividing \(f(x)\) by \(x + 2\) using long division or synthetic division, we get:

Now, we have reduced the problem to factoring \(-4x³ + 18x² - 16x + 12\).

Attempt 2: Factoring by Grouping

Rearranging the terms, we have:

Factoring out common factors, we obtain:

Now, we have \(2x^2(-2x + 9) + 4(4x - 3)\). We can further factor this as:

Therefore, the fully factored form of \(f(x) = -4x⁴  + 26x³  - 50x² + 16x + 24\) is \(f(x) = (x + 2)(2x² + 4)(-2x + 9)\).

Solutions to the polynomial equations:

Using polynomial division or synthetic division, we can find the quadratic equation \((x + 2)(x² + 2x - 3)\). Factoring the quadratic equation, we get \(x² + 2x - 3 = (x +

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The mass of salt in the tank at time t.

dS/dt = 10 - S/400

S(0) = 100 grams

The solution is S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

A tank holds water V(0) = 4000 liters in which salt S(0) = 100 grams.

So dS/dt = S(in) - S(out)

S(in) = 1 × 10 = 10 gram/liters

S(out) = S/V × 10 = 10S/V gram/liters

V = V(0) + q(in) - q(out)

V = 4000 + 10t - 10t

V = 4000 liters

dS/dt = 10 - 10S/V

dS/dt = 10 - 10S/4000

dS/dt = 10 - S/400

Now given; S(0) = 100.

Here, p(t) = 1/400, q(t) = 10

\(\int p(t)dt = \int\frac{1}{400}dt\)\(\int p(t)dt = \frac{1}{400}t\)

\(\mu=e^{\int p(t)dt}\)

\(\mu=e^{\frac{t}{400}}\)

So, S(t) = \(\frac{\int\mu q(t)dt+C}{\mu}\)

S(t) = \(\frac{\int e^{\frac{t}{400}} \cdot10dt+C}{e^{\frac{t}{400}}}\)

S(t) = \(e^{\frac{-t}{400}} \left({\int e^{\frac{t}{400}} \cdot10dt+C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({10\times\frac{e^{\frac{t}{400}}}{1/400} +C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({4000\times{e^{\frac{t}{400}} +C}\right)\)

Now solving the bracket

S(t) = 4000 + \(e^{\frac{-t}{400}}\)C.....(1)

At S(0) = 100

100 = 4000 + \(e^{\frac{-0}{400}}\) C

100 = 4000 + \(e^{0}\) C

100 = 4000 + C

Subtract 4000 on both side, we get

C = -3900

Now S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

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The complete question is:

A tank holds 4000 liters of water in which 100 grams of salt have been dissolved. Saltwater with a concentration of 1 grams/liter is pumped in at 10 liters/minute and the well mixed saltwater solution is pumped out at the same rate. Write initial the value problem for:

The mass of salt in the tank at time t.

dS/dt =

S(0) =

The solution is S(t) =

The four criteria that can be used to prove triangles are congruent and can be used to prove the triangles are congruent.

Triangle congruence: Two triangles are said to be congruent if all three of their corresponding sides and all three of their corresponding angles have the same measurements. These triangles can be moved around, rotated, flipped, and turned to have a same appearance. They match up with one another when moved.

The four criteria that can be used to prove triangles are congruent are SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and SSS (Side-Side-Side). Additionally, CPCTC (Corresponding Parts of Congruent Triangles are Congruent) can be used to prove the triangles are congruent.

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Answer: Elena's running speed = 5 miles per hour.

Step-by-step explanation:

Length of track = \(\dfrac14 \text{ mile}\)

Time taken to complete one lap = \(\dfrac{1}{20}\) of an hour.

Elena's running speed = \(\dfrac{Distance}{Time}\)

\(=\dfrac{\dfrac14}{\dfrac1{20}}\text{ miles per hour}\\\\=\dfrac{20}{4}\text{ miles per hour}\\\\=5\text{ miles per hour}\)

Hence, Elena's running speed = 5 miles per hour.

Answer: 52.73

Explain: 56.40 - 3.67 = 52.73

_____________________

Solution:

Exact Form:

\(\frac{4}{7}-(-\frac{3}{8}) = \frac{53}{56}\)

______________________

(^Note^)

To subtract fractions, find the LCD (Least Common Denominator), then combine.

Hope this helps! If so, please lmk! Thanks and good luck!

Answer: 53/56

Step-by-step explanation:

sorry if im wrong but since there is 2 negative signs it is going to become positive. so..

4/7+3/8

then make the denominators the same (56)

then multiply the numerators by the number you multiplied for the denominator for the question.

answer: 32/56+21/56 = 53/56

Answer:

Exact Form: n = 4/5

Decimal Form: n = 0.8

Step-by-step explanation: Hope it helped :D

Please mark me brainliest ◉‿◉

Answer: 0.8

Step-by-step explanation: I'm super smart

Hope this helps  : D

(P.S. I promise I did not copy that other guy).