the sum of the measures of the angles in a triangle equal

Complex roots always appear in pairs, actually if a+ib is a root then a-ib is also a root. Then, at most there are 2 complex roots in a third degree polynomial.

Okay, here we have this:

Considering the provided information we are going to replace in the formula of continuous compound interest:

Now, let's solve for P:

Finally we obtain that should be invested $2,698.68.

Number of acres = 334

Number of days = 118 days

unit rate = Number of acres/Number of days

Unit rate = 334 acres/114 days

2 is common to both numerator and denominator

Divide both by 2:

Unit rate = 167/57

No other number asides 1 is common to both the numerator and denominator

Hence, the unit rate in acres per day is 167/57

In mixed fraction = 2 53/57

The given expression is

First, we multiply by 10 on each side.

Then, we sum 3 on each side.

Answer:

{-2,14}

Step-by-step explanation:

f(-4) = f(4) = 14

f(0) = -2

We can compare 2 fractions by means of the cross multiplication method. In our case, we have

since 50 is greater than 24 then 10/12 is greater than 2/5:

We want to find the sum of;

3 feet 6 in + 3 feet 6 in + 8 ft 2 in + 4in + 2ft 5in.

Recall that;

Adding we have;

ANSWER:

EXPLANATION:

Given:

Since the pyramid has a square base, therefore intersection of the horizontal plane will produce a shape that looks like a square.

The parametric equation for the rocket is given by

x = 24 t and y = 24√3 t

Given velocity = 48 ft per sec

∅ = 60°

Distance = speed × time

d = 48t

Displacement along the x-axis

= v cos ∅

= 48× t ×cos60°

=24 t

displacement along the y axis

= v sin ∅

=48 t sin 60°

=24√3 t

In mathematics, a parametric equation represents a set of numbers as functions between one or maybe more independent variables, often known as parameters.

When equations are used to indicate the dimensions of the constituent parts of a geometric object, such as a curve or surface, they are collectively referred to as the parametric representation (alternatively written as parametrization) of the object.

b) now we will use the parametric equation to calculate the rectangular equation.

we know that x = 24t and y = 24√3 t

again, x/24 = y/24√3

or, √3x = y

c) Hence we can see that the parametric equation for the projectile is given by x = 24 t and y = 24√3 t and the rectangular equation is given by

√3x = y .

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Given data:

The total weight of the apples Jeff have W=45 pounds.

The amount Jeff earned for every 3/4 pound of apple is A=$4.50.

The expression for the given statement is,

Multiple the above expression by 45 on both sides.

Thus, the amount Jeff earned is $270.

SOLUTION

Method:

The solution is gotten at the coordinates of the point of intersection.

The points of intersections are (-2, 0) and (4, -5)

Final answer:

(4, -5)

Answer: 12 students

Since we need to find how many students had at least 75 social interactions in the week, we will add up all the frequencies from at least 75 interactions. Looking at the given table, that would be 3, 6, 1, and 2.

Adding them up together and we will get:

Therefore, 12 students had at least 75 social interactions in the week.

We will determine the maximum height of the baseball as follows:

We will need the following formulas:

Here "u" represents the original speed, "t" represents the time, "a" the acceleration of the body and "s" is the total discance moved. [We will find s to solve the problem].

So:

First we have that the acceleation that the body will experience is -9.8m/s^2 [Since the object is going upwards and gravity is pulling on it towards the ground]. [acceleration of gravity using feet over second squared is 32.17 ft/s^2].

But the maximum height will be reached when the velocity after certain time has passed is 0 ft/s, so:

So, at approximately 1.3 seconds the maximum heigth willl be reached.

Now, we solve for s:

So, the maxumum altitude for the baseball will be 8 meters, but we have to add the initial 5 feet at which it was launched:

And taking that to feet we will have:

So, the solution must be the last option. [The discrepanc

We have to find the number that satisfies: "Four times a number plus two is equal to 3 times the number".

Four times a number is 4x.

Then, we can write and solve the expression as:

The number is -2.

297 different sundaes can you create using one of the ice cream flavors and one of the​ toppings.

We can rapidly determine the total number of things by multiplying. In order to do this, we will consider the number of groups with equal sizes and the number of items in each group.

The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers. When we need to merge groups of similar sizes, we employ it.

Given,

An ice cream shop offers 27 different flavors of ice cream and 11 different toppings.

Multiplying,

27 × 11

297

297 different sundaes can you create using one of the ice cream flavors and one of the​ toppings.

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You have the following equation:

y = -5x + 3

in order to determine if the point (0,3) is solution of the previous equation, replace the values of x = 0 and y = 3, and verify if the equation is consistent, as follow:

3 = -5(0) + 3

3 = 3

the equation is consistent for the given point, then, the point (0,3) is a olution of the given equation

Answer:

36%

Step-by-step explanation:

First, you would write that as a fraction, which would be 9/25. Then, you'd convert the fraction to a percentage by getting the denominator to 100. Multiply the numerator and denominator by 4 to achieve this. The answer would be 36/100, which translates to 36%.

To determine the area of the shaded region, we would subtract the area of the smaller or inner circle from the area of the bigger or outer circle.

From the information given,

diameter of inner circle = 26.2m

radius of inner circle = diameter/2 = 26.2/2 = 13.1m

B applying the formula for determining the area of a circle which is expressed as

Area = pie * r^2,

pie = 3.14

Area of inner circle = 3.14 * 13.1^2 = 538.86 m^2

Radius of outer circle = 10.7 + 13.1 = 23.8m

Area of outer circle = 3.14 * 23.8^2 = 1778.62m^2

Therefore,

Area of shaded region = 1778.62 - 538.86 = 1239.76m^2

Complex numbers z₁ = 6 · [tex]e^{i\,\frac{17\pi}{20} }[/tex] and z₂ = 6 · [tex]e^{i\,\frac{27\pi}{20} }[/tex] are the square roots of the complex number in polar form.

In this problem we find a complex number in polar form, that is, a complex number of the form:

z = r · [tex]e^{i\,\theta}[/tex]

Where:

The square root of this number can be found by means of the De Moivre's theorem:

[tex]\sqrt{z} = \sqrt{z} \cdot e^{i\,\left(\frac{\theta + 2\pi\cdot k}{n} \right)}[/tex], for k = {0, 1}

If we know that z = 36 and θ = 17π / 10, then the roots of the complex number are:

z₁ = 6 · [tex]e^{i\,\frac{\frac{17\pi}{10}}{2} }[/tex]

z₁ = 6 · [tex]e^{i\,\frac{17\pi}{20} }[/tex]

z₂ = 6 · [tex]e^{\frac{\frac{17\pi}{10} + 2\pi }{2} }[/tex]

z₂ = 6 · [tex]e^{i\,\frac{27\pi}{20} }[/tex]

The solutions are z₁ = 6 · [tex]e^{i\,\frac{17\pi}{20} }[/tex] and z₂ = 6 · [tex]e^{i\,\frac{27\pi}{20} }[/tex].

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Let's do the division:

Answer: x-3

I'm doing it on my notebook, hold on, it's easy

What to plus 57 divided by 134 is 83523.57

Let the first number be m while the second num

Let x be the amount invest at 8%

Let y be the amount invest at 16%

Paul has $50,000 to invest:

His intent is to earn 13% interest on his investment. He can invest part of his money at 8% interest and part at 16% interest.

Use the next system of equations to find x and y:

1. Solve x in the first equation:

2. Substitute the x in the second equation by the value you get in the previous step:

3. Solve y:

4. Use the value of y to solve x:

Solution for the system:

x=18,750

y=31,250

kmartinez2849, this is the solution:

Let's recall that:

1 inch/second = 5 feet/minute

Thus:

12 inch/second = 5 * 12 feet/minute

12 inch/second = 60 feet/minute

Let's recall that:

1 feet = 12 inches

1 minute = 60 seconds

Therefore:

1 inch/second * 60 = 60 inches/minute

Converting inches to feet

60 inches = 5 feet

In conclusion, 5 feet/minute

The tangent should be in fraction is 4/3

Calculation of the tangent:

Since in a right triangle with side lengths 3, 4, and 5

Here there is the larger acute angle in the 3, 4 and 5 so it should be lies between 3 and 5

So, it should be like

= opposite side ÷ adjacent side

= 4/3

Hence, The tangent should be in fraction is 4/3

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5

1) Translating that into a mathematical expression, we can write out the following. Let's call this number by "n":

Just one mistake: when we refer to the same number we use the same variable.

The object will be at rest if the resultant forces = 0

For the given object, a force of -5.5 Newtons applied to it

So, to be at rest we will add another force equal in magnitude and opposite in direction

So, the answer will be the required force = +5.5 newtons

The first step to answer this question is to find tan(2u) by using the double angle formula:

It means that tan(2u) is -65/72.

The next step is to rewrite the equations for sin(2u) and cos(2u) to have them in terms of the least number of variables possible, this way:

If we rewrite tan(2u) in terms of sin(2u) and cos(2u) we will have:

We know the values of tan(2u) and tan(u), so we can solve the equation for sin^2(u).

Using this value we can find the values of sin(2u) and cos(2u):

It means that sin(2u)=65/97, cos(2u)=-72/97 and tan(2u)=-65/72.