10 points!
pls give explanation how you reached your answer!! question in the image

The fourth term in the expanded form of (x - 1)⁶ is  -20x³.

The fourth term in the expanded form of (x - 1)⁶  using the binomial theorem is calculated as follows;

The expanded form of (x - 1)⁶ using the binomial theorem is;

(x - 1)⁶ = 1x⁶ + (-6)x⁵ + 15x⁴ + (-20)x³ + 15x² + (-6)x + 1

(x - 1)⁶ = x⁶ -6x⁵ + 15x⁴ -20x³ + 15x² -6x + 1

To find the fourth term, we look for the fourth term from the left side to right side, which is  -20x³.

Therefore, the fourth term in the expanded form of (x - 1)⁶ is  -20x³.

Learn more about binomial theorem here: https://brainly.com/question/13602562

#SPJ1

The drop down menu is used to match each situation as below.

1. The rocket reached its maximum  the x-value of the vertex

height in 5 s.

2. ground level                                    the y-intercept

3. The rocket launcher was                the y-value of the point containing

on the ground.                                     the x-intercept on the right

4. The rocket was in the air 10           the x-intercept on the right                                                                                    

5. The maximum height of the           the y-value of the vertex

rocket is 50 ft.

6. the time the rocket was                the x-value of the point containing the

launched                                          y-intercept

The key features of the curve such as the x intercept is the point the launcher and the rocket were on ground.

The vertex is the point the rocket had the maximum and height.

Generally, the curve traces a parabolic path

Learn more about parabolic equation at

https://brainly.com/question/4061870

#SPJ1

Michel-Eugène Chevreul found that the greatest intensity came from placing complementary colors next to each other. The Option C is correct.

Chevreul made great contributions to the field of color theory as he made key findings was that placing complementary colors next to each other creates the greatest intensity.

These colors are opposite to each other on the color wheel such as red & green, blue & orange or yellow &  purple. When these color are placed next to each other, these colors create a visual contrast that makes them appear brighter and more intense.

Read more about complementary color

brainly.com/question/2668848

#SPJ1

Answer:

5/2

Step-by-step explanation:

Slope is rise over run, or how far it goes in the y direction over how far it goes in the x direction. In this case, y increases by a value of 5 at the same time x is increasing by a value of 2. This makes the slope 5/2, and it is positive since the values are increasing. If there is a problem your stuck on like this try graphing the points, desmos has a good graphing calculator :)

The requried equivalent fraction for the equivalent fraction to 3 3/4 and 1 2/3, is 45/12, and 20/12.

To find a common denominator for 4 and 3, we can multiply them together to get 12.

So, we can convert 3 3/4 as:

3 3/4 = 12/4 + 3/4 = 15/4

Similarly, we can convert 1 2/3 as:

1 2/3 = 5/3

Therefore, the equivalent fractions for 3 3/4 and 1 2/3 using a common denominator of 12 are:

15/4 = 45/12 and 5/3 = 20/12

Learn more about equivalent fractions here:

https://brainly.com/question/29766013

#SPJ1

Answer:

The second scatterplot does not suggest a linear relationship between x and y.

Answer:  C

Step-by-step explanation:

Think about y=[tex]x^{3}[/tex]     This is an odd function because the highest exponent(degree) is odd

A.  is wrong. Symmetry is where you can fold it and it would be the same.  If i folded y=[tex]x^{3}[/tex] along the y- axis it would not be the same.  

B is wrong. Transformations are where has it moved, which has nothing to do with odd functions in general

C.  is correct.  It is folded along y=x and flipped.

D. is wrong.  If folded y=x it's in the same quadrant but it's not the same, its' reversed.

The bearing of the cruise ship displacement from its initial position is 15.06°, which makes the second option correct

Bearing is usually measured in degrees, with 0° indicating the reference direction (usually North), and increasing clockwise to 360°. It refers to the direction or angle between a reference direction and a point or object.

We will get a right triangle from travels of the ship, such that we can call the initial position A, the point after 8 miles B and the point after 30 miles C

angle B = 30° + 60° = 90°

AB = 8

BC = 30

by Pythagoras rule;

AC = √(8² + 30²) = 31.04

using sine rule;

30/sinA = 31.04/sin90

A = sin⁻¹[(30 × sin90)/31.04]

A = 75.06°

bearing from initial position = (30° + 75.06°) - 90°

bearing from initial position = 105.06 - 90°

bearing from initial position = 15.06°

Therefore, the bearing of the cruise ship displacement from its initial position is 15.06°

Read more about bearing here:https://brainly.com/question/22518031

#SPJ1

The area of the given rectangle is 83.6cm²

We know that the area of a rectangle is equal to the product between the dimensions, here we can see that:

b = 11cm

h = 7.6cm

The formula for the area is:

A = b*h

Replacing the values we will get:

A = 11cm*7.6cm = 83.6cm²

that is the area.

Learn more about rectangles at.

https://brainly.com/question/17297081

#SPJ1

The new surface area of the hemisphere-shaped mole would be = 102mm².

A hemisphere-shaped mole has a shape that has one surface that is curved and the other surface a flat circular base.

Since the surface area of one hemisphere has been given, the second hemisphere can be determined.

To calculate the new surface area of the hemisphere-shaped moles the following is carried out;

Radius of the initial mole = 5.7/2 = 2.85 mm

If 2.85mm radius = 51 mm²

2(2.85mm) radius = x

Make X the subject of formula;

X = 2×2.85 × 51/2.85

= 102 mm²

Learn more about area here:

https://brainly.com/question/28470545

#SPJ1

Based on the figure, we can see that triangles OHJ and OIX are similar because they share the same angle at O and HI and HJ are tangent to the circle. Thus, we can set up the following proportion:

OH / OI = HJ / (HJ + 9)

Substituting the given values:

6.5 / 3.9 = HJ / (HJ + 9)

Cross-multiplying:

6.5(HJ + 9) = 3.9HJ

Distributing:

6.5HJ + 58.5 = 3.9HJ

Simplifying:

2.6HJ = -58.5

HJ = -22.5

However, this answer doesn't make sense in the context of the problem. Since HJ represents a length, it cannot be negative. Therefore, we need to re-examine our work.

Looking back at our proportion, we can see that the ratio of OH to OI is greater than 1, which implies that HJ is greater than 9. This makes sense since HJ is a chord of the circle and thus must be longer than the radius.

Let's try the problem again, but this time we'll rearrange the proportion to solve for HJ:

HJ / (HJ + 9) = OI / OH

Substituting the given values:

HJ / (HJ + 9) = 3.9 / 6.5

Cross-multiplying:

6.5HJ = 3.9HJ + 35.1

Simplifying:

2.6HJ = 35.1

HJ = 13.5

Therefore, HJ is equal to 13.5.

The solutions to the expressions are (m-8)² = m² - 16m + 64 and 2m²-16m + m²-8m+161 = 3m²- 24m + 161

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

(m-8)²

Expand

So, we have

m² - 16m + 64

Next, we have

2m²-16m + m²-8m+161

Evaluate the like terms

3m²- 24m + 161

Read more about expressions at

https://brainly.com/question/15775046

#SPJ1

Answer:

12/2

Step-by-step explanation:

(x - h)^2 + (y - k)^2 = r^2

where (h,k) is the center of the circle and r is the radius.

Comparing this to the given equation, we see that the center of the circle is (-10,0) and the radius is sqrt(9) = 3.

The diameter of the circle is twice the radius, so:

diameter = 2(radius) = 2(3) = 6

Therefore, the diameter of the circle is 6.

We can write this in simplified, rationalized form as:

diameter = 6 = 6/1 = 12/2

Answer:

----------------------------

Find the composition of the functions f(x) and g(x), which is written as f(g(x)).

Given functions:

Find f(g(x)):

Evaluate f(g(2)):

So, (f·g)(2) = 14.

Answer: A,E or F.

Step-by-step explanation: That's the only ones that have X's and then x is 0

Answer:

Length= 43.98 cm

Step-by-step explanation:

Circumference=2πr

r=7cm

C=2π(7)

C=43.98 cm

circumference is equal to the length of ribbon along the outside of the circular object

The three equivalent numerical expressions are  1/32, 0.03125, 3.125 x 10^-2

Using the exponential rules, we can simplify the expressions as:

(2^-3)(2^5)/2^7)

= 2^(5-3)/2^7

= 2^2/2^7

= 1/2^(7-2)

= 1/2^5

= 1/32

Therefore, three equivalent numerical expressions for the given expression are: 1/32, 0.03125, 3.125 x 10^-2

Learn more about expressions at https://brainly.com/question/1859113

#SPJ1

Answer:

w=0,

w=-7

Step-by-step explanation:

The sum of 3√5 and 4√25 is an irrational number.

First, simplify the expressions inside the square roots:

3√5 = 3√(5×1) = 3√5

4√25 = 4√(25×1) = 4×5 = 20

Now, we add them together:

3√5 + 4√25 = 3√5 + 20

This is the simplest form since 20 is already a rational number and we cannot simplify the square root of 5 any further.

To determine whether the result is rational or irrational.

Since 3√5 is irrational and cannot be simplified any further, the expression as a whole is also irrational.

Therefore, the sum of 3√5 and 4√25 is an irrational number.

Learn more about the irrational number here:

https://brainly.com/question/28758979

#SPJ1

The interest earned and the future value of an annuity with monthly payments of $200 for two years that pays 6% interest per year compounded monthly is $25.43 and $225.43

Principal,P = $200

Time, t = 6%

Number of periods, n = 12

Interest rate, r = 6%

= 6/100

= 0.06 rate per year,

FV = P(1 + r/n)^nt

FV = 200.00(1 + 0.06/12)^(12)(2)

FV = 200.00(1 + 0.005)^(24)

FV = $225.43

Therefore,

Principal = $200.00

Interest = $25.43

Read more on compound interest:

https://brainly.com/question/24274034

#SPJ1

The area of one face of the cube that has a volume of 3375 cubic inches is: 225 square inches.

A cube has equal edge length, and therefore has faces with the same area. The formula for finding the volume of a cube is given as:

Volume of cube = s³, where s is the side length of the cube.

Also, to find the area of one face of a cube, we would use the formula below:

Area of one face of a cube = s².

Given the following:

Volume of a cube = 3375 cubic inches

Find s as shown below:

s = ∛3375

s = 15 inches.

Therefore, we have:

Area of one face of a cube = 15² = 225 square inches.

Learn more about the cube on:

https://brainly.com/question/26726803

#SPJ1

The side AC corresponds to the side AC in the other triangle and the length of BC is 15 units

For two triangles to be similar, the corresponding sides of the triangles must be in proportion

Having said  that

The side AC corresponds to the side AC in the other triangle

The length BC is calculated as

BC/9 = 25/15

Express as products

So, we have

BC = 9 * 25/15

Evaluate the products

BC = 15

Hence, the length of BC is 15 units

Read more about similar triangles at

https://brainly.com/question/14285697

#SPJ1

The probability that both events will occur is 23.76%.

Given that, you have 100 tiles and 98 are letters and 2 are blank you randomly drawl 2 title the first is a consonant and the 2nd is a vowel.

Consonants (A) = 56

Vowels (B) = 42

Blank = 2

Total letters = 100

Two letters are drawn with replacement.

P(A) = 56/100 = 0.56

P(B) = 42/ (100-1) = 0.424

P(A).P(B) = 0.56*0.424 = 0.2376

Hence, the probability that both events will occur is 23.76%.

Learn more about probability, click;

https://brainly.com/question/30034780

#SPJ1

Complete question is attached.

The most likely number of minutes of usage recorded by Jason is A . approximately 50.

We can see that initially, the temperature of the electronic system began to increase as the time increased. It then began to decrease from the 20 minute and ketp decreasing till the 40th minute.

Assuming that the temperature keeps decreasing, it would mean that at 50 minutes, the temperature would be more than the temperature at 40 minutes and so would most likely be 48 degrees.

Find out more on usage at https://brainly.com/question/21444630

#SPJ1

Answer:

∠ C = 84°

Step-by-step explanation:

A quadrilateral inscribed in a circle is a cyclic quadrilateral.

the opposite angles sum to 180° , that is

∠ A + ∠ C = 180 , then

x² + 60 + 8x + 36 = 180

x² + 8x + 96 = 180 ( subtract 180 from both sides )

x² + 8x - 84 = 0 ← in standard form

(x + 14)(x - 6) = 0 ← in factored form

equate each factor to zero and solve for x

x + 14 = 0 ⇒ x = - 14

x - 6 = 0 ⇒ x = 6

x > 0 , then x = 6 , so

∠ C = 8x + 36 = 8(6) + 36 = 48 + 36 = 84°

Answer:

The pattern of association between time and distance is positive and linear.

The value of P(A∩B) rounding to the nearest thousandth, if necessary is:  0.086

The parameters given are:

P(A) = 0.12

P(B) = 0.3

P(A ∪ B) = 0.334

We want to find the probability P(A∩B)

The P(A∪B) probability formula is given as:

P(A∪B) = P(A) + P(B) - P(A∩B)

where:

P(A) is Probability of event A happening

P(B) is Probability of event B happening

P(A∩B) is Probability of happening of both A and B.

Thus:

0.334 = 0.12 + 0.3 - P(A∩B)

P(A∩B) = 0.12 + 0.3 - 0.334

P(A∩B) = 0.086

Read more about probability formula at: https://brainly.com/question/27726507

#SPJ1