Check PictureGraph the polynomial given below by first selecting the number of points, then moving the points. You will need a point for each x intercept, and one for the y intercept.f(x)=17(x−1)(x+3)(x+7)

The polar coordinates for each point are given as follows:

a. [tex](r, \theta) = \left(2\sqrt{5}, \frac{7\pi}{4}\right)[/tex]

b. [tex](r, \theta) = \left(6, \frac{\pi}{3}\right)[/tex]

Suppose we have a point with Cartesian coordinates given as follows:

(x,y).

The polar coordinates will be found as follows:

For item a), the Cartesian coordinates are as follows:

(-4, 4).

Hence the polar coordinates will be given as follows:

For item a), the Cartesian coordinates are as follows:

(3, 3sqrt(3)).

Hence the polar coordinates will be given as follows:

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A lineal equation has the next form:

where m is the slope and is calculated as follow:

For this case

y1=20

y2= 25

x1=12

x2= 5

so:

then the equation will be:

Using one of the points we calculate the b

we are going to use y=25 x=5

Clearing the b we get:

b=200/7 or b=28.57

A lineal equation has the next form:

where m is the slope and is calculated as follow:

For this case

y1=20

y2= 25

x1=12

x2= 5

so:

then the equation will be:

Using one of the points we calculate the b

we are going to use y=25 x=5

Clearing the b we get:

b=200/7 or b=28.57

Explanation:

We have the expression:

where i represents the complex number i defined as follows:

To find if i^3 is real or complex, we represent it as follows:

And we find the value of i^2 using the definition of i:

Since the square root and the power of 2 cancel each other

And therefore, using this value for i^2, we can now write i^3 as follows:

This simplifies to -i

Because -i is still a complex number, that means that i^3 is a complex number.

Answer: Complex

The value of x nodes given quadrilateral ​is 80° which is determined by the measure of the supplemental interior angle.

A quadrilateral is a polygon with four sides. This also indicates that a quadrilateral has four vertices and four angles.

Exterior Angle is defined as an angle produced on the outside of a polygon by extending the sides of the polygon.

First, we have to find the measure of the supplemental interior angle

Here take the exterior angle1 = 100° and  exterior angle2 = 60°, find its interior angles

⇒ 100 + int.1 = 180 ⇒ int.1 = 180 - 100 = 80°

⇒ 60 + int.2 = 180 ⇒ int.2 = 180 - 60 = 120°

Since the sum of all interior angles of a polygon = 360°

As per the given figure,

x + 80 + x + 120 = 360

2x = 360 - 200

2x = 160

x = 80°

Therefore, the value of x nodes given quadrilateral ​is 80°.

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Answer: 77 = 46 + r, r = 31

Step-by-step explanation:

      We will write an equation to represent this situation. Then, we will solve for r by isolating the variable.

  Seventy-seven is forty-six more than r.

77 is forty-six more than r.

77 = forty-six more than r.

77 = 46 more than r.

  77 = 46 + r

  77 = 46 + r

(77) - 46 = (46 + r) - 46

31 = r

  r = 31

The two ships are 1933.32 ft apart

Given:

The height of the lighthouse = 350 ft

The angles of depression to the ships are 4 degree and 6.5 degree

To find:

the distance between the two ships

To determine the distance, we will use an illustration of the situation

First we will find the value of y as we need to know this value to get x

To get y, we will apply tan ratio (TOA)

Next is to find x using tan ratio (TOA):

Okay, here we have this:

We need to identify the x-value at which the-following function touches but does not cross the x-axis in the following function: 3x^3- 18^2 + 27x. So, considering that if is a zero with even multiplicity, the graph touches the x-axis and bounces off of the axis. And if it is a zero with odd multiplicity, the graph crosses the x-axis at a zero.

According with this let's

Given data:

The diameter of cylinder is d=12 cm.

The height of the cylinder is h= 27 cm.

The dimension of the aquarium is V=(35 cm)(40 cm)( 42 cm).

The volume of the cylinder is,

The volume of the aquarium is,

The number of cylinders that can be pour into aquarium is,

Thus, the number of cylinders that can be pour into aquarium is 19.25.

AB in 1:3 ratio, Find a pointwhere on one side there is 1/4 of AB and in the other side 3/4 of AB:

Part b.

In this case, we have the following function:

First, we need to solve for x. Then, by applying natural logarithm to both sides, we have

By the properties of the logarithm, it yields

By moving log5 to the left hand side, we have

By moving log2.4 to the left hand side, we obtain

Therfore, the answer is

Part C.

In this case, the given function is

and we need to solve x. Then, by raising both side to the power 10, we have

By moving 17 to the left hand side, we get

Therefore, the answer is

Volume of sandbox (to be built) = 50,445 cubic inches

A sandbox is the shape of a cuboid and is calculated by the formula

Volume = Length * Width * Height

Volume = 50,445 cubic inches, Length = 59 in. Width = 57 in, Height = ?

50,445 = 59 * 57 * h

Make h the subject of the formula, we have:

h = 50445 / (59 * 57) = 15 in

To solve this equation, we need to subtract both, 9c - 3c:

Dividing by 6 at both sides of the equation

Then

Then the answer C = 8. (Option D)

Given the number

We can express it in scientific notation below;

Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. For example, 650,000,000 can be written in scientific notation as 6.5 ✕ 10^8.

Therefore, in the given question, we will have;

Answer: Option C

The formula to find the volume of a triangular prism is the following:

where:

h - height

b - base length

w - width

for this problem:

h = 8 cm

b = 5 cm

w = 7 cm

then

solving this, we obtain that the volume of the triangular prism is 140 cm^3 or cubic centimeters

it would be 75 ur welcome

We have the next functions

Function notation

Describe the transformation in words

we have 2 transformations, the 2 that multiplies the function f(x) means that we will have an expansion in the y axis by 2, the one means that we will have a shift up by one unit

Given the folllowing equation:

You need to solve for "x" in order to find its value. To do this, you can follow the steps shown below:

1. You can apply the Addition property of equality by adding 0.04 to both sides of the equation:

2. Now you need to add the like terms on the left side of the equation:

3. Finally, you can apply the Division property of equality by dividing both sides of the equation by 0.41:

The answer is:

Let's convert the given equation first into a vertex form.

where (h, k) is the vertex.

The vertex form of the equatio that we have is:

Hence, the vertex of the equation is at the origin (0, 0).

Since "a" is negative, our parabola is opening downward.

Let's identify two points to the left of the vertex. Let's say at x = -1. Replace "x" with -1 in the equation.

Hence, we have a point to the left of the parabola at (-1, -2).

Let's say x = -2. Replace "x" with -2 in the equation.

Hence, we also have another point to the left of the parabola at (-2, -8).

If our x is to the right of the vertex, say, x = 1. Replace "x" with 1 in the equation.

We have a point to the right of the parabola at (1, -2).

If x = 2, let's replace "x" with 2 in the equation.

Hence, we also have another point to the right of the parabola at (2, -8).

The graph of this equation is:

she spent 525 on Food

she spent 750 on rent

she spent 775 on others

she spent 450 on fun

Explanation

to find the value of the percentage of any number just use this formula

so

to find the values, apply the formula

Step 1

a) food :21 %

so

it means she spent 525 on Food

Step 2

b) Rent:30 %

so

it means she spent 750 on rent

Step 3

c)other:31 %

so

it means she spent 775 on others

Step 4

d)Fun:18 %

so

it means she spent 450 on fun

I hope this helps you

Answer:

**NEED USEFUL ANSWER ASAP, H.W QUESTION**

Given that hotter blackbodies produce more energy than cooler blackbodies, why do cooler red giants have much higher luminosities than much hotter white dwarfs?

Step-by-step explanation:

Given:

Population in 2000 = 572 thousand

Rate of growth per year = 1.15%

Let's solve for the following:

(a) Explicit formula for the population years after 2000.

Where:

In year 2000, t = 0

To write the explicit formula, apply the exponantial growth function formula:

Where:

a is the initial amount

r is the growth rate.

Thus, we have:

Therefore, the explicit formula for the population years after 2000 is:

(b) What will be the district's population in 2025.

Where:

In the year 2000, t = 0

In the year 2025, t will be = 25

To find the population in 2025, substitute 25 for t in the explicit formula for evalaute:

The population in 2025 if the trend continues will be approximately 761 thousand.

(c) When does the model predict the population to exceeed 800 thousand.

Substitute 800 for Pt and solve for t.

We have:

Divide both sides by 572:

Take the natural logarithm of both sides:

Divide both sides by 0.01143:

When t = 29, the year is 2000 + 29 = 2029

Therefore, using this model, DC's population will exceed 800 thousand in the year 2029.

ANSWERS:

A rational value that is less than zero is -√4.

An irrational value greater than five is 5 1/9.

A rational value between 10 and 20 is √225.

A rational number is a number that can be expressed as a fraction of two integers. A rational number can either be a positive number, negative number, whole number, decimal or fraction.  Examples of rational numbers are 100, -0.5.

A irrational number is a number that cannot be expressed as a fraction of two integers. An irrational number can either be a positive number, negative number, whole number, decimal or fraction.  Examples of irrational numbers are 22/7, 1-/9.

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The length of rectangle is : 6ft .

Width of rectangle is : 5.5ft .

The area of rectangle is :

A = l × w

Here given,

length is 5ft less than twice the width,

So the equation can be represented in terms of length as,

l = 2w - 5

Given area = 33sqft

By substituting value of length,

33 = (2w - 5) × w

By applying distributive property,

33 = 2w² - 5w

= 2w² - 5w - 33

By factoring the equation:

(2w - 11)(w + 3) = 0

To find value of zeros,

2w - 11 = 0

2w = 11

w = 5.5

Similarly,

w + 3 = 0

w = -3

Since width cannot be negative , the width will be:

the width = 5.5 ft.

Also find length by substituting value of width in equation,

33 = 5.5l

33/5.5 = l

l = 6 ft.

∴ The  length = 6ft, and width = 5.5ft.

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The change of base formula states that:

this means that we can caculate any logarithm using the natural logarithm if we make the quotient of the natural logarithm of the original value and the natural logarithm of the original base.

In this case we have:

Then, using the change of base formula, we have:

Once we have the expression we just evaluate the expression on the right to get the appoximation we need:

Answer:

The two lines are parallel.

Explanation:

We have the equations:

Let's solve the first one for y, so we get the same formatting on both euqations:

SInce the two lines have the same slope, 2/5, the two lines are parallel.

Since the critical value of the test is greater than the absolute value of the test statistic, there is not enough evidence to conclude that the proportion is different of 20%.

At the null hypothesis, it is tested if the proportion is of 20%, that is:

[tex]H_0: p = 0.2[/tex]

At the alternative hypothesis, it is tested if the proportion is different of 20%, hence:

[tex]H_1: p \neq 0.2[/tex]

We have a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.05, hence the critical value is of:

|z| = 1.96.

The test statistic is given by the rule presented as follows:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

In the context of this problem, the parameters are given as follows:

[tex]p = 0.2, n = 200, \overline{p} = \frac{38}{200} = 0.19[/tex]

Hence the test statistic is:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.19 - 0.2}{\sqrt{\frac{0.2(0.8)}{200}}}[/tex]

z = -0.35.

|z| < 1.96, hence there is not enough evidence to conclude that the proportion is different of 20%.

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Answer:

The expression is c-6. She gave away 6 cards so subtract 6 from the original number which is c.

x-intercepts

1) In a quadratic equation, the Real solutions correspond to the points in which the parabola intercepts the x-axis.

2) Note that when the roots are not real solutions, then we'd have complex numbers and the parabola wouldn't intercept the x-axis.

3) Therefore, the answer is: x-intercepts