r=14costheta in rectangular form

Answer is A) Acute due to the lengths

Answer:

A

Step-by-step explanation:

Answer:

This situation involves a combination as the team will be the same no matter what order the students are chosen in.

There are 1402410240 possibilities for the six student team

Step-by-step explanation:

Each time a student is chosen, they cannot be chosen again, so the number of available students decreases each time that one is chosen.

[tex]36*35*34*33*32*31=1402410240[/tex]

Answer:

The second degree polynomial is f(x) = 4x² - 28x + 40

Step-by-step explanation:

* Lets revise the general form of the second-degree polynomial

- The general form of the second degree polynomial is

 f(x) = ax² + bx + c, where a , b , c are constant

- The highest power of the variable that occurs in the polynomial

 is called the degree of a polynomial.

- The leading term is the term with the highest power, and its

 coefficient is called the leading coefficient.

- The leading coefficient is the coefficient of x²

∴ a = 4

∴ f(x) = 4x² + bx + c

- The roots of a polynomial are also called its zeroes, because

 the roots are the x values at which the function equals zero

∴ When f(x) = 0, the values of x are 5 and 2

* To find the value of b and c substitute the values of x in f(x) = 0

- At x = 5

∵ 4(5)² + b(5) + c = 0 ⇒ simplify it

∴ 100 + 5b + c = 0 ⇒ subtract 100 from both sides

∴ 5b + c = -100 ⇒ (1)

- At x = 2

∵ 4(2)² + b(2) + c = 0 ⇒ simplify it

∴ 16 + 2b + c = 0 ⇒ subtract 16 from both sides

∴ 2b + c = -16 ⇒ (2)

- Subtract (2) from (1)

∴ 3b = -84 ⇒ divide both sides by 3

∴ b = -28

- Substitute the value of b in (1) or (2) to find c

∵ 2(-28) + c = -16

∴ -56 + c = -16 ⇒ add 56 to both sides

∴ c = 40

∴ f(x) = 4x² - 28x + 40

* The second degree polynomial is f(x) = 4x² - 28x + 40

Answer:

d

Step-by-step explanation:

For this case we have the following system of equations:

[tex]y = -6x + 9\\y = -3x + 3[/tex]

Equating the equations we have:

[tex]-6x + 9 = -3x + 3[/tex]

Adding 3x to both sides of the equation:

[tex]-6x + 3x + 9 = 3\\-3x + 9 = 3[/tex]

Subtracting 9 from both sides of the equation:

[tex]-3x = 3-9\\-3x = -6[/tex]

Dividing between -3 on both sides of the equation:

[tex]x = \frac {-6} {- 3}\\x = 2[/tex]

We look for the value of "and":

[tex]y = -3 (2) +3\\y = -6 + 3\\y = -3[/tex]

Thus, the solution of the system is (2, -3)

Answer:

(2, -3)

[tex]r=\dfrac5{1+\cos\theta}\implies r(1+\cos\theta)=5\implies r+r\cos\theta=5[/tex]

In converting between polar and rectangular coordinates, we take

[tex]x^2+y^2=r^2\implies r=\sqrt{x^2+y^2}[/tex]

[tex]x=r\cos\theta[/tex]

so that the equation becomes

[tex]\sqrt{x^2+y^2}+x=5[/tex]

which we can rewrite as

[tex]\sqrt{x^2+y^2}=5-x[/tex]

[tex]x^2+y^2=(5-x)^2[/tex]

[tex]x^2+y^2=25-10x+x^2[/tex]

[tex]\implies\boxed{y^2=25-10x}[/tex]

so the answer is C.

The expanded algebraic expression is x⁶ - 12x⁵ + 64x⁴ - 160x³ + 256x² - 192x + 64

How to expand the algebraic expression

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

(x - 2)⁶

This is a binomial expression that can be expanded using Pascal triangle

The power of the expression is 6

At n = 6, we have the following coefficients

1   6  16  20  16  6 1

So, we have

(x - 2)⁶ = 1 * x⁶ + 6 * x⁵ * (-2) + 16 * x⁴ * (-2)² + 20 * x³ * (-2)³ + 16 * x² * (-2)⁴ + 6 * x * (-2)⁵ + 1 * (-2)⁶

Expand the exponents

(x - 2)⁶ = x⁶ - 12x⁵ + 64x⁴ - 160x³ + 256x² - 192x + 64

Hence, the expanded algebraic expression is x⁶ - 12x⁵ + 64x⁴ - 160x³ + 256x² - 192x + 64

Final answer:

To create a 95% confidence interval for y when x=8, we need the sample mean and the standard deviation to calculate the Error Bound for the Mean (EBM). The CI is the sample mean ± EBM. Estimating the standard deviation of y involves using the sample standard deviation as an estimate or the known population standard deviation.

Explanation:

To develop a 95% confidence interval for the expected value of y when x = 8, we first need to know the sample mean (μ) and the standard deviation of the population or an estimate from the sample (known as σ or s, respectively). When we have these statistics, we can use the normal distribution to calculate the error bound for the mean (EBM), which is the margin of error. The confidence interval (CI) is then constructed as (sample mean - EBM, sample mean + EBM).

To estimate the standard deviation of an individual value of y when x = 8, which is essentially the standard deviation of the population (σ), you need to use the sample standard deviation (s) as an estimate unless the population standard deviation is known.

Remember, the EBM for the confidence interval depends on the chosen confidence level, the standard deviation, and the size of the sample. With a higher confidence level, you get a wider interval. In practice, the confidence interval gives us a range where we expect the true population parameter lies with a certain level of confidence, acknowledging there's still a small chance the true value lies outside of this range.

Answer:

4

Step-by-step explanation:

Since perpendicular lines have negative reciprocals, we have to find out the negative reciprocal of -1/4.

To get the negative reciprocal of -1/4, we have to switch the numbers in the numerator and denominator.

That becomes 4/-1, and then we have to remove the negative, which makes the final answer 4/1.

4/1 = 4

Therefore, the negative reciprocal of -1/4 is 4.

Hope this Helps!

The slope of the red perpendicular line is 4.

Slope of a straight line is defined as the inclination of the line with respect to the coordinate axis. The slope is also measure of the tangent of angle with which the line is inclined to the axis.

If the slope of a given straight line is m then the slope of its corresponding perpendicular line will be negative reciprocal of the given slope which is -(1/m).

It is said that the lines shown below are perpendicular. Also it is mentioned that the green line has a slope of -1/4 .

As the red line is perpendicular to the green line, thus its slope is negative reciprocal of the given slope of green line.

Slope = -(-4) = 4 .

Therefore, the slope of the red perpendicular line is 4.

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Answer:

$31,045.50

Step-by-step explanation:

Revenue from sales = ($855/item)p

Expenses:  $6,780

Revenue if p = 250 is R(250) = ($855/item)(250 items) = $213,750

Subtracting expenses, we get a profit of $206,970.

The CEO of the company earns 15% of this profit, or:

0.15($206,970) = $31,045.50

Answer:

Most likely Perimeter of the pad is 42 ft.

Step-by-step explanation:

Area of the Cement pad = 108 feet²

Length of the dumpster = 9 ft

Width of the dumpster = 8 ft

Cement pad surface is greater than dumpster to hold it.

Area of pad = 108 ft²

length × width = 108

we choose length and width such that they are greater than length and width of the dumpster.

So, length of the pad = 12 ft

Width of the pad = 9 ft

Thus, Perimeter = 2 × (length +  width) = 2 × ( 12 + 9 ) = 2 × 21 = 42 ft

Therefore, Most likely Perimeter of the pad is 42 ft.

It would be $9.95 x 3

Answer:

π(10 in)² - π(8 in)²  

Step-by-step explanation:

Area between the two circles=

   Area of larger circle   less  area of smaller circle, or

          π(10 in)² - π(8 in)²         Since the difference in the radii of the

                                                 two circles is 2, that means the smaller

                                                  circle has radius 10 - 2, or 8 (inches)

Next time, please share the answer choices.  Thank you.

To find the shaded area between the two circles, subtract the area of the smaller circle from the area of the larger circle. The area of a circle is calculated using the formula A = πr^2. By finding the radius of the smaller circle, we can calculate its area and subtract from the larger circle's area to find the shaded area.

The shaded area between the two circles can be found by subtracting the area of the smaller circle from the area of the larger circle. The radius of the larger circle is given as 10 inches and the distance between the two circles is given as 2 inches. To find the area of the shaded region, we first need to find the radius of the smaller circle. Since the distance between the two circles is equal to the sum of their radii, the radius of the smaller circle is 10 inches - 2 inches = 8 inches.

The area of the larger circle is calculated using the formula A = πr^2, where r is the radius. Therefore, the area of the larger circle is A = π(10 inches)^2 = 100π square inches.

The area of the smaller circle is calculated in the same way, using the radius of 8 inches. Therefore, the area of the smaller circle is A = π(8 inches)^2 = 64π square inches.

To find the shaded area, we subtract the area of the smaller circle from the area of the larger circle: 100π square inches - 64π square inches = 36π square inches.

Answer:

B. qualitative

Step-by-step explanation:

Answer:

The perimeter of the triangle is [tex]12\ units[/tex]

Step-by-step explanation:

Let

[tex]A(-3,1),B(1,1),C(1,-2)[/tex]

we know that

The perimeter of triangle is equal to

[tex]P=AB+BC+AC[/tex]

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

step 1

Find the distance AB

[tex]A(-3,1),B(1,1)[/tex]

substitute in the formula

[tex]AB=\sqrt{(1-1)^{2}+(1+3)^{2}}[/tex]

[tex]AB=\sqrt{(0)^{2}+(4)^{2}}[/tex]

[tex]AB=4\ units[/tex]

step 2

Find the distance BC

[tex]B(1,1),C(1,-2)[/tex]

substitute in the formula

[tex]BC=\sqrt{(-2-1)^{2}+(1-1)^{2}}[/tex]

[tex]BC=\sqrt{(-3)^{2}+(0)^{2}}[/tex]

[tex]BC=3\ units[/tex]

step 3

Find the distance AC

[tex]A(-3,1),C(1,-2)[/tex]

substitute in the formula

[tex]AC=\sqrt{(-2-1)^{2}+(1+3)^{2}}[/tex]

[tex]AC=\sqrt{(-3)^{2}+(4)^{2}}[/tex]

[tex]AC=5\ units[/tex]

step 4

Find the perimeter

[tex]P=AB+BC+AC[/tex]

substitute the values

[tex]P=4+3+5=12\ units[/tex]

Answer:

340 units squared

Step-by-step explanation:

in the trapezoid, there is a square and an isosceles triangle

find the area of the square: 17×(23-6) =17×17 =289

find area of the triangle: 17×6 /2 =51

add the two together: 289 +51 =340

Answer:

Line MN = 23 -3 -3 = 17

Middle Area = 17 * 17 = 289

Area of BOTH Ends = 17 * 3 = 51

TOTAL Area = 289 + 51 = 340

Step-by-step explanation:

Answer:

$14,450

Step-by-step explanation:

y=20,000(1-0.15)^x

Hope This Helps :D

Answer:

D $50

Step-by-step explanation:

50x.10=5

5+50=55

For this case we propose a rule of three:

$ 50 -------------> 100%

x -----------------> 10%

Where the variable "x" represents the amount of the tip.

[tex]x = \frac {10 * 50} {100}\\x = 5[/tex]

So, the tip was 5 dollars.

If we subtract that amount to what Matt paid at the restaurant we will have the amount of the check before the tip.[tex]55-5 = 50[/tex]

ANswer:

Option D

Answer:

37.76

Step-by-step explanation:

(What we know)

V = 4*4*4 = 64

Density = 0.59

___________________

Density = Mass/Volume

Mass = (Density)(Volume)

So

Mass = (0.59)(64)

or

Mass = .59 * 64

Mass = 37.76

_____________________________

So the answer would be 37.76

Hope this helps, if you see an error please correct me.

Answer:

215.6 m²

Step-by-step explanation:

The area (A) of the polygon is

A = [tex]\frac{1}{2}[/tex] × perimeter × apothem

perimeter = 7 × 7.7 = 53.9 m, so

A = 0.5 × 53.9 × 8 = 215.6

The area of regular polygon with 7 sides is 215.6 m².

Polygon, in geometry, any closed curve consisting of a set of line segments (sides) connected such that no two segments cross.

Here, the area (A) of the polygon is

A =  1/2 × perimeter × apothem

perimeter = length X width

                   = 7 × 7.7

                   = 53.9 m,

so, A = 0.5 × 53.9 × 8

         = 215.6 m²

Thus, the area of regular polygon with 7 sides is 215.6 m².

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Answer:

[tex]7\frac{1}{2}[/tex] pages

Step-by-step explanation:

Method 1: Working with minutes

Let us assume that, Sandra's printer can print x pages in 1 minute.

Then we can write the equation:

[tex]x:1=5:\frac{2}{3}[/tex]

We can rewrite the ratios as a fraction.

[tex]\frac{x}{1}=\frac{5}{\frac{2}{3}}[/tex]

This simplifies to

[tex]x=\frac{15}{2}[/tex]

Or

[tex]x=7\frac{1}{2}[/tex]

Method 2: Working with seconds

If 5 pages corresponds to 40 seconds, then we can write: [tex]5:40[/tex]

Let y corresponds to 60 seconds (1 minutes).

Then:

[tex]y:60=5:40[/tex]

We rewrite as fraction:

[tex]\frac{y}{60}=\frac{5}{40}[/tex]

Multiply both sides by:

[tex]y=\frac{5}{40}\times 60[/tex]

[tex]y=\frac{300}{40}[/tex]

[tex]y=\frac{15}{2}[/tex]

[tex]y=7\frac{1}{2}[/tex]

A is the correct answer but I did do it in my head so fair warning

Answer:

2

Step-by-step explanation:

The equation of a horizontal line is y = c

where c is the value of the y- coordinates the line passes through

Thus y = 3 ← is the equation of a horizontal line

Answer:

  B.  17 days

Step-by-step explanation:

We want to know how many days it took, so it is convenient to define the variable x as the number of days. Then the number of square feet is (x+269) and the total cost is ...

  124.26x +3.92(x+269) = 3233.54

  128.18x + 1054.48 = 3233.54 . . . . . . . . simplify

  128.18x = 2179.06 . . . . . . . . . . . . . . . . . . subtract 1054.48

  2179.06/128.18 = x = 17 . . . . . . . . . . . . . divide by the coefficient of x

The renovation took 17 days.

For solving the problem, we first divide the question into two equations, and then substitute and solve the equations. The renovation took around 17 days that is option B)

This is a system of equations problems in Mathematics. Let's denote the number of days as 'd' and the square footage as 'f'. According to the problem, we know that:

1. Costs of materials + Costs of labor = Total spent

2. The square footage is 269 more than the number of days. So:

We can replace 'f' from the second equation with the first one: $3.92(d + 269) + $124.26d = $3233.54. Simplifying this, we get $1052.48 + $4.93d = $3233.54, and solving for 'd', we get 'd' approximately equal to 17 days, so the answer is (B).

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Answer: 13

Step-by-step explanation: because I have the whole bookanswer duh

Answer:

  31%

Step-by-step explanation:

Of the 6101 students on financial aid, 1879 are graduates. This fraction is ...

  1879/6101 × 100% ≈ 30.798% ≈ 31%

Answer:

true

Step-by-step explanation:

For this case we have that by definition:

[tex]Sin (90) = 1\\Cos (90) = 0[/tex]

Now, the tangent of 90 is given by:

[tex]tg (90) = \frac {Sin (90)} {Cos {90}} = \frac {1} {0}[/tex]

Thus, it is observed that the tangent of 90 degrees is not defined.  Is obtained ∞.

Similarly:

[tex]Sin (-90) = - 1\\Cos (-90) = 0[/tex]

Now, the tangent of -90 is given by:

[tex]tg (-90) = \frac {Sin (-90)} {Cos {-90}} = \frac {-1} {0}[/tex]

Thus, it is observed that the tangent of -90 degrees is not defined.

Answer:

False

Answer:

$42.5

Step-by-step explanation:

Answer:

42.5

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The graph of the parabola has no points of intersection with the real x- axis

and therefore has no real solutions

Complex roots occur in conjugate pairs so cannot be C

The solution would be 2 complex roots → A

Answer:

A

Step-by-step explanation:

The graph has no intersection with x-axis therefore has no real roots.

Answer:

x-axis

Step-by-step explanation:

The asymptote is a straight line that the curve gets closer and closer to but never touches it.

The given exponential function is [tex]f(x)=3^x[/tex].

The given graph has a horizontal asymptote,

The equation of this horizontal asymptote is y=0.

This is also refers to as the x-axis.

Therefore the asymptote is the x-axis.

Answer:

s = +√A

Step-by-step explanation:

Start with the area formula, A = s².  Solve this for the side length, s, as follows:

s = +√A

In words, if you're given the area of a square, find the square root of this area to determine the side length.