6x ^ 2 + 96x - 13 = - 13
(X+A)^2=b

Answer:

x = 135 degrees

y = 45 degrees

Step-by-step explanation:

angle F = 90 = E  degrees

triangle EBF is isosceles so the angles at the base would be 180-90 = 90/2

which would equal 45.

Hence, y would equal 45.

45 + x = 180 (supplementary)

x = 135

Answer:

185 anle with the postive measure and a negative measure

a) To maximize its net savings, the company should use the new machine for 7 years.  b) The net savings during the first year of use of the machine are $405 (rounded off to the nearest dollar).  c) The net savings over the period determined in part a are $1,833.33 (rounded off to the nearest cent).

Step-by-step explanation: a) To determine for how many years should the company use the new machine to maximize its net savings, we need to find the value of x that maximizes the difference between the savings and the costs.To do this, we need to first calculate the net savings, N(x), which is given by:S'(x) - C'(x) = 175 - x² - (x² + 11x) = -2x² - 11x + 175To find the maximum value of N(x), we need to find the critical values, which are the values of x that make N'(x) = 0:N'(x) = -4x - 11 = 0 ⇒ x = -11/4The critical value x = -11/4 is not a valid solution because x represents the number of years of operation of the machine, which cannot be negative. (i.e., not use it at all).However, this answer does not make sense because the company would not introduce a new machine that it does not intend to use. Therefore, we need to examine the concavity of N(x) to see if there is a local maximum in the feasible interval.

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The function my squares[v, m, µ, σ] constructs m samples of v sums-of-squares of the deviation from the mean with the X drawn from the normal distribution N(µ,σ). The function histxsq [v, m, µ, σ] plots a PDF histogram of the samples, with the appropriate x² PDF plotted over the top of it.

First, let's define the mysquares[v, m, µ, σ] function. The function takes in four inputs:
- v: an integer representing the number of deviations from the mean to be squared and summed
- m: an integer representing the number of samples to be generated
- µ: a float representing the mean of the normal distribution
- σ: a float representing the standard deviation of the normal distribution



Here is the code for both functions:

```
import nu m p y as np
import matplotlib. py plot as plt
from scipy.stats import chi2

def mysquares(v, m, µ, σ):
   x = np.random.normal(µ, σ, (v, m))
   x_bar = np.mean(x, axis=0)
   return np.sum((x - x_bar)**2, axis=0)

def histxsq(v, m, µ, σ):
   x_sq = mysquares(v, m, µ, σ)
   chi_sq = chi2.pdf(np.linspace(0, np.max(x_sq), 100), v)
   plt.hist(x_sq, bins='auto', density=True, alpha=0.7)
   plt.plot(np.linspace(0, np.max(x_sq), 100), chi_sq, linewidth=2)
   plt.show()
```

Let's test the functions with the provided inputs. We will plot histograms for the following cases:
- v = 2, µ = 1, σ = 2
- v = 6, µ = 3, σ = 10
- v = 16, µ = 0, σ = 1

```
histxsq(2, 10000, 1, 2)
histxsq(6, 10000, 3, 10)
histxsq(16, 10000, 0, 1)
```

The resulting histograms show that the x² distribution fits the samples quite well.

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If the small holds 36 units, the large one holds 144 units.

In the given problem, it is mentioned that if the small holds 36 units. Therefore, we need to find the quantity that the large unit can hold. So let the large unit hold x units. The small unit holds 36 units. So, we can write the proportion as: Small unit: Large unit = 36: x.

We know that the ratio of the small unit and large unit is the same, so we can write the cross-product of these two terms as 36 * x = Small unit * Large unit. Therefore, x = (Small unit * Large unit) / 36Given, small unit = 36So, x = (36 * Large unit) / 36. Canceling the common factor, we get, x = Large unit.

Therefore, the large unit can hold 144 units.

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For Aₙ = aₙ₋₁ + n and a₁ = 4, the first four terms will be 4, 6, 9, 13 respectively.

We will use the recursive formula  aₙ = aₙ₋₁ + n for the recursive series to get the first four terms of the sequence, with a₁ set to 4 for the series.

a₁ = 4 (given),

a₂ = a₁+2

⇒ a₂ = 4+2

⇒ a₂ = 6,

a₃ = a₂+3

⇒ a₂ = 6+3

⇒ a₃ = 9,

a₄ = a₃+4

⇒ a₄ = 9+4

⇒ a₄ = 13,

As can be seen, one term is utilized to locate the next term in the sequence, which is why it is referred to as recursive. So the series' first four terms are 4, 6, 9, 13.

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The given fractions have equal value, so Liam is correct.

Equivalent fractions are defined as fractions that have different numerators and denominators but the same value. For example, 2/4 and 3/6 are equivalent fractions because they are both equal to 1/2. A fraction is part of a whole. Equivalent fractions represent the same part of a whole.  

Liam is claiming that the fraction -(5/12) is equivalent to 5/-12.

Thus, we can say that:

The fraction  -(5/12) can be described as the opposite of a positive number divided by a positive number. A positive number divided by a positive number always results in a positive quotient and its' opposite is always negative.

The fraction 5/-12 can be described as a positive number divided by a negative number which always results in a negative quotient

The fractions have equal value, so Liam is correct

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The tendency to perceive meaningful patterns in random sequences of outcomes often leads us to underestimate the extent to which outcomes result from CHANCE .

The word "chance" describes unpredictability or the unexpected in relation to things like events that happen without a clear reason why and without human intention.

The conclusion is that chance is the tendency of people to recognize different kinds of significant patterns in a random order or sequence in addition to evaluating any kind of outcome. Because chance can also result in an underestimating of a system's conclusion or result, it is crucial to consider it when conducting an investigation.

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The derivative of y = 6x^3 with respect to x is dy/dx = 18x^2.

From the question, we have the following parameters that can be used in our computation:

y = 6x^3

To find the derivative of y with respect to x, we can use the power rule of differentiation, which states that the derivative of x^n with respect to x is n*x^(n-1).

Using this rule, we can differentiate y = 6x^3 as follows:

dy/dx = d/dx (6x^3)

= 6 * d/dx (x^3)

= 6 * 3x^2 (applying the power rule with n=2)

= 18x^2

Therefore, the derivative of y = 6x^3 with respect to x is dy/dx = 18x^2.

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Answer:

Horizontal

Step-by-step explanation:

Answer:

y = 9 is a horizontal line :)

Step-by-step explanation:

y=9 is the equation of a horizontal line. The slope is 0. This means that for any value of x that is chosen, the y-value is always 9 Hence y=9 .

Answer:

Y=2x+2

Step-by-step explanation:

The value of the expression is approximately 1.132. First, we need to convert the angles from degrees to radians because trigonometric functions in calculators typically use radians as input.

To convert degrees to radians, we use the formula: radians = degrees x (π / 180)

So, we have:

 = 38.2° = 0.666 radians (approx.)

B = 146.4° = 2.552 radians (approx.)

Next, we can plug these values into the expression:

2cos(Â) + cos^2(B)

Substituting  and B with their respective values, we get:

2cos(0.666) + cos^2(2.552)

Using a calculator, we can evaluate this expression as follows:

2cos(0.666) + cos^2(2.552) ≈ 1.132

Therefore, the value of the expression is approximately 1.132.

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Using L'Hôpital's Theorem, we can evaluate the limit of x * arcsin(x) as x approaches 0. The limit is 0.

To evaluate the limit, we can apply L'Hôpital's Rule, which states that if the limit of a ratio of two functions is indeterminate (such as 0/0 or ∞/∞), then we can differentiate the numerator and denominator and take the limit again. In this case, we have the limit of x * arcsin(x) as x approaches 0. Both the numerator and denominator approach 0 as x approaches 0. By differentiating the numerator and denominator, we get 1 * arccos(x) / 1, which simplifies to arccos(0) = π/2. Therefore, the limit is 0.

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An infant may have had birthing complications that reduced the amount of oxygen in her blood if her Apgar score ranges from 7 at 1 minute to 9 at 5 minutes. In this situation, the hospital nurses will most likely vigorously dry her with a towel while holding oxygen under her nose.

The Apgar score is a recognized and practical way to report on the newborn baby's condition right after birth and their reaction to resuscitation, if necessary. One's particular neonatal mortality or neurologic prognosis cannot be predicted by the Apgar score alone, nor can it be regarded as a result of suffocation. It should also not be utilized to do so. An infant's spontaneous breathing score and the Apgar score given after resuscitation are not the same thing. An enhanced Apgar score reporting form that takes into account concurrent resuscitative treatments is encouraged by both the American Academy of Pediatrics and the American College of Obstetricians and Gynecologists.

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Step-by-step explanation:

no

because it will become

3(3)>9

9>9

it must be more than 9 unless the symbol is

\( \geqslant\)

Answer:

c = 5cm

Step-by-step explanation:

a^2 + b^2 = c^2

4^2 + 3^2 = c^2

16 + 9 = c^2

25 = c^2

do the square root of 25 and c to solve for c

the square root of c^2 is c

therefore, c= 5cm

Answer:

(i) see first attached diagram

(ii) QR = 22.67 km (2 dp)

(iii) 243°

Step-by-step explanation:

A bearing is the angle in degrees measured clockwise from north.

Part (i)

see first attached diagram

Part (ii)

The angles marked in blue on the second attached diagram are Consecutive Interior Angles.  In this case they add to 180° as the North lines are parallel.

The sum of angles around a point is 360°

⇒ m∠QPR (shown in red on the second attached diagram) = 360 - 150 - (180 - 15) = 45°        

To calculate the distance between Q and R (marked in red on the attached diagram), use the cosine rule.

⇒ QR² = PR² + QP² - 2(PR)(QP)cos(QPR)

⇒ QR² = 32² + 24² - 2(32)(24)cos(45)

⇒ QR² = 513.8839841...

⇒ QR = √513.8839841...

⇒ QR = 22.67 km (2 dp)

Part (iii)

We need to find the angle marked in green on the third attached diagram.

To do this, we need to find the angle marked in pink and the angle marked in orange, then subtract them from 360°

Pink angle = 180 - 150 = 30° (using the same consecutive angle theorem as before)

Orange angle (o) using the sine rule:

⇒ sin(o)/32 = sin(45)/QR

⇒ sin(o) = 32sin(45)/22.67

⇒ sin(o) = 0.9981652337...

⇒ o = 86.52868176...°

Therefore, the green angle = 360 - 30 - 86.52868176... = 243° (nearest degree)

Answer:

10y-12

Step-by-step explanation:

Answer:

The slope of the line that contains diagonal OE will be = -3/2

Step-by-step explanation:

We know the slope-intercept form of the line equation

y = mx+b

Where m is the slope and b is the y-intercept

Given the equation of the line that contains diagonal HM is y = 2/3 x + 7

y = 2/3 x + 7

comparing the equation with the slope-intercept form of the line equation

y = mx+b

Thus, slope = m = 2/3

As we have to determine the slope of the line that contains diagonal OE.

As the slope of the line that contains diagonal HM = 2/3

We also know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line.

Therefore, the slope of the line that contains diagonal

OE will be = -1/m = -1/(2/3) = -3/2

Hence, the slope of the line that contains diagonal OE will be = -3/2

We have a continuous random variable over -2 < x < 5 so p(x = 1) = 0 because the probability at any given point for any continuous random variable is always 0.

Probability is a measure of the likelihood of a particular event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to happen.

Probability at any given position is always zero for any continuous random variable. This is because the probability of a single value occurring for a continuous random variable is always 0 because the range of values for the random variable is infinite and therefore the probability of a single value occurring is 0.

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The area of the figure after the triangle is removed from the parallelogram is 5,160 square centimeters.

rrTo find the area of the figure after the triangle is removed from the parallelogram, we first need to calculate the area of the parallelogram and the area of the triangle.

The area of a parallelogram is given by the formula: Area = base * height.

In this case, the base of the parallelogram is 86 centimeters and the height is 80 centimeters. So, the area of the parallelogram is: Area_parallelogram = 86 cm * 80 cm = 6,880 square centimeters.

Next, we need to find the area of the triangle. The base and height of the triangle are half of the base and height of the parallelogram, respectively. So, the base of the triangle is 86 cm / 2 = 43 centimeters, and the height of the triangle is 80 cm / 2 = 40 centimeters.

The area of a triangle is given by the formula: Area = (base * height) / 2.

Substituting the values, we have: Area_triangle = (43 cm * 40 cm) / 2 = 1,720 square centimeters.

Now, to find the area of the figure after the triangle is removed, we subtract the area of the triangle from the area of the parallelogram:

Area_figure = Area_parallelogram - Area_triangle

Area_figure = 6,880 square centimeters - 1,720 square centimeters

Area_figure = 5,160 square centimeters.

Therefore, the area of the figure after the triangle is removed from the parallelogram is 5,160 square centimeters.

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Answer:

1,980

Step-by-step explanation:

using the formula

(n – 2) × 180°

= (13 – 2) × 180°

= 11 × 180

= 1,980

if we were asked to find the interior angle

we will use this formula

\(interior \: angle \: of \: a \: polygon = \frac{sum \: of \: interior \: angle}{number \: of \: sides} \)

= 1,980/13

= 152.3°

i hope all this helped

The respective sides of the two square pyramids are proportionate since they are comparable. Let's use A cm2 to represent the smaller pyramid's surface area.

The square of the ratio of the corresponding side lengths of comparable pyramids is equal to the ratio of their surface areas. As a result, we may construct the equation shown below:

(s_small / s_large) = (A / 2304)²

where the sides of the smaller and larger pyramids, respectively, are represented by the lengths s_small and s_large, respectively.

We are unable to immediately solve for A since we lack the precise side length data. The ratio of the surface areas is still measurable, though:

(s_small / s_large) = (A / 2304)²

Using the information provided, we can determine that the surface area of.

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The remainder when 7x⁴ - 3x is divided by x - 1 is 4.

knοwn as indeterminates) and cοefficients, which are cοmbined using the οperatiοns οf additiοn, subtractiοn, and multiplicatiοn. A pοlynοmial can have οne οr mοre variables, but each term in the pοlynοmial must have nοn-negative integer expοnents οn the variables. The degree οf a pοlynοmial is the highest pοwer οf its variables with a nοn-zerο cοefficient.

Fοr example, the pοlynοmial 3x² - 2x + 5 has a degree οf 2, with the term 3x² being the highest degree term. The cοefficient οf the term 3x^2 is 3, and the cοefficient οf the term -2x is -2.

Pοlynοmials are used in a variety οf mathematical applicatiοns, including algebra, calculus, and geοmetry. They are used tο represent mathematical functiοns, tο apprοximate cοmplex curves, and tο sοlve equatiοns. Sοme cοmmοn οperatiοns οn pοlynοmials include additiοn, subtractiοn, multiplicatiοn, divisiοn, and factοring.

Tο find the remainder when the pοlynοmial 7x⁴ - 3x is divided by x - 1, we can use pοlynοmial lοng divisiοn οr synthetic divisiοn.

7x³ + 7x² + 7x + 4

x - 1 | 7x⁴ + 0x³ - 3x² + 0x + 0

     - (7x⁴ - 7x³)

           7x³ - 3x²

           - (7x³ - 7x²)

                 4x² + 0x

                 - (4x² - 4x)

                        4x

                        - (4x - 4)

                             4

Therefore, the remainder when 7x⁴ - 3x is divided by x - 1 is 4.

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To solve the system of equations, we need to find the values of x, y, and z that satisfy all three equations.

The given equations are:

2x – 3y + 2z = 14
-x – y + Oz = 4
3x + Oy + 2z = -3

To solve this system, we can use the method of substitution.

First, let's solve the second equation for O:

-x – y + Oz = 4
Oz = x + y + 4
O = (x + y + 4)/z

Now, we can substitute this expression for O into the first and third equations:

2x – 3y + 2z = 14
3x + (x + y + 4)/z + 2z = -3

Next, we can simplify the third equation by multiplying both sides by z:

3xz + x + y + 4 + 2z^2 = -3z

Now, we can rearrange the equations and solve for one variable:

2x – 3y + 2z = 14
3xz + x + y + 4 + 2z^2 = -3z

From the first equation, we can solve for x:

x = (3y – 2z + 14)/2

Now, we can substitute this expression for x into the second equation:

3z(3y – 2z + 14)/2 + (3y – 2z + 14)/2 + y + 4 + 2z^2 = -3z

Simplifying this equation, we get:

9yz – 3z^2 + 21y + 7z + 38 = 0

This is a quadratic equation in z. We can solve it using the quadratic formula:

z = (-b ± sqrt(b^2 – 4ac))/(2a)

Where a = -3, b = 7, and c = 9y + 38.

Plugging in these values, we get:

z = (-7 ± sqrt(49 – 4(-3)(9y + 38)))/(2(-3))
z = (-7 ± sqrt(13 – 36y))/(-6)

Now that we have a formula for z, we can substitute it back into the equation for x and solve for y:

x = (3y – 2z + 14)/2
y = (4z – 3x – 14)/3

Plugging in the formula for z, we get:

x = (3y + 14 + 7/3sqrt(13 – 36y))/2
y = (4(-7 ± sqrt(13 – 36y))/(-6) – 3(3y + 14 + 7/3sqrt(13 – 36y)) – 14)/3

These formulas are a bit messy, but they do give the solution for the system of equations.

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7x(4x-5)

Distribute

28x^2-35x

Ans : 28x^2-35x

Answer:

28x - 5

Step-by-step explanation:

coeffecients with the same variable can be multiplied added subtracted divided so i multiplied 7 and 4 because they have the same variable which is X so it would be 28x and you can't multiply 7x by 5 because it doesnt have a variable consider multiplying if it has the same variable when it has a variable. so it would just be 28x - 5

Answer:

Step-by-step explanation:

Slope of a line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by,

Slope = \(\frac{y_2-y_1}{x_2-x_1}\)

8). Slope of the line passing through (0, 4) and (-1, 6) will be,

Slope = \(\frac{6-4}{-1-0}\)

          = -2

9). Slope of a line passing through (10, 15) and (9, 0),

Slope = \(\frac{15-0}{10-9}\)

          = 15

10). Slope of a line passing through (0, -9) and (4, -7),

Slope = \(\frac{-9+7}{0-4}\)

          = \(\frac{1}{2}\)

11). Slope of a line passing through (2, 20) and (4, 17),

Slope = \(\frac{20-17}{2-4}\)

          = \(-\frac{3}{2}\)

Complete Question

A rectangular rug feet is x ft long and y feet wide with a perimeter of 60 ft both X and Y are whole numbers between 10 and 20. Fill in the blanks to complete the sentence. The Area of the rug is greater than___but less than__.

Answer:

he Area of the rug is greater than  but less than \(441ft\)

Step-by-step explanation:

From the question we are told that:

Perimeter \(P=60ft\)

Value Range:Between 10-20

Generally the Area of the rug is greater than for values of X and Y greater than 9

Therefore Area is greater than from whole number 9

Generally the equation for Area greater than \(A_g\) is mathematically given by

\(A_l=X*Y\)

Where

\(X=9\\Y=9\)

Therefore

\(A_l=X*Y\)

\(A_l=9*9\)

\(A_l=81ft\)

Generally the Area of the rug is less than for values of X and Y less than 21

Therefore Area is less than from whole number 21

Generally the equation for Area greater than A_l is mathematically given by

\(A_g=X*Y\)

Where

\(X=21\\Y=21\)

Therefore

\(A_g=X*Y\)

\(A_g=21*21\)

\(A_g=441ft\)