Find the value of x to the nearest tenth

If v = 4i and w = 2i + 5i, the angle between the vectors v and w is approximately 47.32 degrees.

To find the angle between two vectors, we can use the dot product formula, which relates the cosine of the angle between the vectors to their dot product and magnitudes. The dot product of two vectors v and w is given by:

v · w = |v| |w| cos(θ)

where |v| and |w| are the magnitudes of the vectors, and theta is the angle between them.

In this case, we are given the vectors v = 4i and w = 2i + 5j. We can compute their dot product as:

v · w = (4i) · (2i + 5j) = 8 + 0 = 8

We can also compute the magnitudes of the vectors as:

|v| = √((4² + 0²)) = 4

|w| = √((2² + 5²)) = √(29)

Substituting these values into the dot product formula, we get:

8 = 4 √(29) cos(θ)

Solving for cos(θ), we get:

cos(θ) = 2 / √(29)

Taking the inverse cosine of both sides, we get:

θ = cos⁻¹(2 / √(29)) = 47.32 degrees

To learn more about angle between vector click on,

https://brainly.com/question/29019969

#SPJ1

The expression (-3)0 has a value of 0 when evaluated because a number multiplied by 0 gives 0

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

(-3)0

The above statement is a product expression that multiplies the values of -3 and 0

Also, there is no need to check if there are like terms in the expression or not

This is  because we are multiplying the factors

So, we have

(-3)0 = 0

This means that the value of the expression is 0 i.e a number multiplied by 0 gives 0

Read more about expression at

brainly.com/question/15775046

#SPJ1

they are all absolute value, so the negatives are removed

thus the values are 10, 3, 6, 9 (biggest would be 10)

The integral of the greatest integer function ∫ [x]dx is equivalent to 0.

Given is to integrate the greatest integer function. We can write it as -

∫ [x]dx

We can expand the the integral as -

∫ [x]dx = [tex]\int\limits^0_b {x} \, dx +\int\limits^c_0 {x} \, dx[/tex], where b = - ∞ and c = ∞

∫ [x]dx = [tex]\int\limits^0_b {x} \, dx +\int\limits^c_0 {x} \, dx[/tex] =

- ∞ + ...... + (-5) + (-4) + (-3) + (-2) + (-1) + 0 + 1 + 2 + 3 + 4 + 5 + ..... + ∞

{ 1 + 2 + 3 + 4 + 5 + ..... + ∞ } + {- ∞ + ...... + (-5) + (-4) + (-3) + (-2) + (-1)}

{ 1 + 2 + 3 + 4 + 5 + ..... + ∞ } - {∞ + ...... + (5) + (4) + (3) + (2) + (1)}

{ 1 + 2 + 3 + 4 + 5 + ..... + ∞ } - {∞ + ...... + (5) + (4) + (3) + (2) + (1)}

{- 1/12 - (- 1/12)}                     {Ramanujan's infinite sum series}

-1/12 + 1/12

0

To solve more questions on integrals, visit the link-

https://brainly.com/question/18125359

#SPJ1

Answer:

the volume of the prism at the right is 56.7 cm³

Step-by-step explanation:

To find the volume of the prism at the right, we need to first find the area of the base, which is a triangle. The area of a triangle is given by A=21​bh

where A

is the area, b

is the base, and h

is the height of the triangle.

The base of the triangle is 4.2 cm and the height of the triangle is 3 cm. So, we can plug these values into the formula and get:

A=21​(4.2)(3)

A=6.3 cm2

Now that we have the area of the base, we can multiply it by the height of the prism, which is 9 cm. This will give us the volume of the prism:

V=B×h

V=6.3×9

V=56.7 cm3

[tex]2(x+1)^2[/tex]

let me know if there's anything that's still confusing

The value of x in the similar triangle is 2 units.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

Therefore, let's use the ratio to find the side length of x in the triangle.

Hence, the right angle triangle FHJ is similar to the right angle triangle GFJ. Using the similarity ratios,

GH / GF = GF / GJ

Hence,

GH = 9

GF = 3√11

GJ =  x + 9

9 / 3√11 = 3√11 / x + 9

cross multiply

9(x + 9) = (3√11)(3√11)

9x + 81 = 9(11)

9x + 81 = 99

9x = 99 - 81

9x = 18

divide both sides by 9

x = 18 / 9

x = 2

learn more on similar triangle here: https://brainly.com/question/26580326

#SPJ1

Inductive reasoning is the process of making generalizations based on specific observations or examples. Deductive reasoning, on the other hand, is the process of reasoning from general principles to specific examples.

To determine whether the type of reasoning used is inductive or deductive reasoning, we need to look at the nature of the argument being made. If the argument is moving from specific examples to a general conclusion, it is using inductive reasoning. If the argument is moving from general principles to specific examples, it is using deductive reasoning.

Learn more about inductive reasoning here:

https://brainly.com/question/8419798

#SPJ1

The pattern is empty the second pail, leaving the first and third pail full and the fourth and sixth pails empty.

Given that, there are 6 pails in a row. The first 3 pails are filled with water.

The easiest way to solve this problem is to empty the second pail, leaving the first and third pail full and the fourth and sixth pails empty. This will create the desired pattern of full, empty, full, empty, full, empty.

Therefore, empty the second pail, leaving the first and third pail full and the fourth and sixth pails empty.

Learn more about the pattern here:

https://brainly.com/question/23136125.

#SPJ1

The money multiplier is the inverse of the reserve requirement ratio. If the Federal Reserve sets the reserve rate to 2%, the reserve requirement ratio is 0.02, and the money multiplier is 1/0.02, which equals 50. Therefore, the correct answer is A. 50.

The graph represents the quadratic equation y = 2 · x² - 12 · x + 9. The values of the coefficients are b = - 12 and c = 9.

In this problem we find the graph of a quadratic equation and the expression in standard form with two missing coefficients, whose values can be found by considering two points of the graph. If we know that (x₁, y₁) = (3, - 9) and (x₂, y₂) = (5, - 1), then the coefficients are, respectively:

2 · 3² + b · 3 + c = - 9

2 · 5² + b · 5 + c = - 1

3 · b + c = - 27

5 · b + c = - 51

The solution to the system of linear equations is (b, c) = (- 12, 9).

To learn more on quadratic equations: https://brainly.com/question/1863222

#SPJ1

To create a three-column table, draw three vertical lines and label each column with the appropriate category. Enter the information row by row, be consistent with formatting, and consider using shading or color to improve readability.

To create a three-column table

A three-column table is a way of organizing information into three columns or columns. Each column represents a different category or piece of information. For example, a three-column table might be used to show a list of names, ages, and cities.

Here's how to create a three-column table, Draw three vertical lines on a piece of paper or in a document to create three columns. Label the columns with the appropriate categories. For example, if you're creating a table to show names, ages, and cities, you would label the columns "Name," "Age," and "City."

Enter the information into the table. Start by entering the information for the first row, then move on to the next row until you have entered all the information. Be consistent with your formatting. Use the same font and font size for all the text in the table.

Align the text in the columns so that it is easy to read and compare information. Consider using shading or color to make the table more visually appealing and easier to read.

To know more about three-column table:

https://brainly.com/question/30422989

#SPJ1

The probability of rolling a 3 or getting heads is 0.67

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

Using the above as a guide, we have the following:

P(3) = 1/6

This is because there is only 1 face with number 3 in a die

Also, we have

P(Head) = 1/2

Using the above as a guide, we have the following:

P(3 and Head) = 1/6 + 1/2

Evaluate

P(3 and Head) = 0.67

Hence the probability is 0.67

Read more about probability at

https://brainly.com/question/251701

#SPJ1

The volume of the prism is 14.67 units³

A prism is a solid shape that is bound on all its sides by plane faces.

The general formula for the volume of a prism is ;

V = base area × height

here the base area has already been calculated and the value is 7 1/3 unit²

The height of the prism is 2 units

Therefore ;

The volume of the prism = 7 1/3 × 2

= 22/3 × 2

= 44/3

= 14.67 units³

therefore the volume of the cuboid is 14.67 units³

learn more about volume of prism from

https://brainly.com/question/23963432

#SPJ1

After calculating the area of figure, we can conclude that it's area is 38.4 cm².

To find the figure of this area, we need to first divide the composite figure into two parts so that we can find it's area. So, it will be divided into a parallelogram and a rectangle.

Firstly, we will find the area of the parallelogram.

For parallelogram,

base = 4cm

height = 3.6 cm

area of parallelogram = base × height

= 4 × 3.6

= 14.4 cm²

Now, we will find the area of the rectangle:

We have been given Its length as 4cm and breadth as 6 cm

Area of rectangle = length × breadth

= 4 × 6

= 24 cm²

Now, to find the area of composite figure, we will add both the areas

Area of figure = Area of rectangle + area of parallelogram

= 24 + 14.4

= 38.4 cm²

To know more about area of figure:

https://brainly.com/question/23718948

#SPJ1

The part of a financial aid letter that shows what you will have to pay after deducting all gift aid is the D. net cost.

The net cost can be described as the amount that is usually meant for paying out of pocket or through loans after all gift aid.

The net cost can be calculated usually by subtracting all gift aid from the total cost of attendance.

The net cost is an important figure to consider when you want evaluate your financial aid package and also decide how to pay for college.

Learn more about the net cost on:

https://brainly.com/question/30854400

#SPJ1

We need 1.5 or 3/2 full cones to fill the cylinder completely.

We have,

Let's assume that the diameter and height of the cylinder are D and H, respectively.

Since the cone has the same diameter as the cylinder, its radius is half of the diameter or D/2.

Since the cone has half of the height of the cylinder, its height is H/2.

The volume of the cylinder is given by the formula.

V cylinder = π(D/2)² H.

The volume of the cone is given by the formula.

V cone = 1/3 π(D/2)² (H/2).

To fill the cylinder completely with water using the cone, we need to find out how many cones are required to fill the cylinder.

Let's set up an equation using the volumes of the cylinder and cone:

Number of cones needed = V cylinder / V cone

Substituting the formulas for the volumes.

Number of cones needed = [π(D/2)² H] / [1/3 π(D/2)² (H/2)]

Simplifying this expression, we get:

Number of cones needed = 3(H/2) / H

Number of cones needed = 3/2

Therefore,

We need 1.5 or 3/2 full cones to fill the cylinder completely.

Since we cannot have half a cone, we need 2 full cones to fill the cylinder completely.

Learn more about cones here:

https://brainly.com/question/13798146

#SPJ1

The missing parts of the right triangle are shown below.

A perfect 90-degree angle (a right angle) distinguishes a right triangle from other triangle types. The hypotenuse and legs are terms used to describe the two sides.

1) Sin 48 = x/5

x = 5 Sin 48

x = 3.7

2) Cos x = 11/23

x = Cos-1(11/23)

= 61.4 degrees

3) Tan 54 = x/8

x = 8 Tan54

x = 11.0

4) Sin 37 = x/12

x = 12Sin 37

= 7.2

5) Cos x = 6.5/10

x = Cos-1(6.5/10)

x = 49.5 degrees

6) Tan x = 47/25

x = Tan-1 (47/25)

x = 61.9 degrees

Learn more about the right triangle:https://brainly.com/question/6322314

#SPJ1

The solution is, the value of the variables are x = 40 and, y = 160.

Notice that "x" and "3x+20" are supplementary angles so their sum is 180°

(x) + (3x + 20) = 180

4x + 20 = 180

4x = 160

x = 40

To solve for "y", you have 2 options: either notice that "x" and "y-20" are supplementary angles so their sum is 180° or notice that "3x + 20" and "y - 20" are vertical angles so are equal to each other. I am going to solve using the first option because it is less work.

(x) + (y - 20) = 180°

40 + y - 20 = 180

y + 20 = 180

y = 160

Answer: x=40, y=160

The solution is, the value of the variables are x = 40 and, y = 160.

To learn more on angle click:

brainly.com/question/28451077

#SPJ1

complete question:

Find the value of each variable

The total surface area of the triangular figure is S = 160 m²

Given data ,

Let the total surface area of the triangular figure be S

Now , the area of the base be A

where the side length of the base a = 8 m

So , the area of base A = 8²

A = 64 m²

Now , the height of the triangle = 6 m

The base of the triangle = 8 m0

Now , the area of the four triangles = 4 ( 1/2 ) ( 6 ) ( 8 )

Area of four triangles = 96 m²

Therefore , the total surface area S = 64 + 96

S = 160 m²

Hence , the surface area of figure is 160 m²

To learn more about surface area of pyramid click :

https://brainly.com/question/15050758

#SPJ1

Answer: D. y=1/2x+1

Step-by-step explanation:

For every 2 x values on the table, y increases only by 1. To find the slope of the table you can also use the slope formula with two points. y2-y1/x2-x1=m

For example,

(4, 3) & (6, 4)

The first point has the ordered pair of x1 and y1. The second point is the ordered pair of x2 and y2. Plug the numbers into the equation and you'll find the slope.

So, 4-3 / 6-4 = 1/2.

Now that we have the slope we can use the point-slope formula to find the y-intercept. y-y1=m(x-x1)

This formula only requires 1 point from the table and the slope so you can use any point, I'll use (4,3). After that, you plug in your numbers into the equation and solve for y.

y-3=1/2(x-4)

y-3=1/2x-2

Add 3 to both sides

y=1/2x+1

And you're done :)

17.5, if both were the same difficulty homework for "Monie".

[tex]\begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} ~\hspace{7em} \begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \end{array} \\\\[-0.35em] ~\dotfill\\\\ 2\log(6)-\log(9)\implies \log(6^2)-\log(9)\implies \log\left( \cfrac{6^2}{9} \right)\implies \log(4)[/tex]

The combination is solved and the number of ways of choosing 7 cards from a set of 48 cards is ⁴⁸C₇ = 85,900,584 ways

Given data ,

Let the number of ways of choosing 7 cards from a set of 48 cards be C

Now , the number of cards = 48 cards in deck

The number of selected cards = 7

From the combination , we get

The number of ways that a player can have 7 cards from a 48-card deck, we can use the formula for combinations:

n choose r = n! / (r! * (n-r)!)

where n is the total number of items and r is the number of items chosen.

In this case, n = 48 (the number of cards in the deck) and r = 7 (the number of cards dealt to each player). So we can plug in these values and simplify:

⁴⁸C₇ = 48! / (7! * (48-7)!)

Hence , the combination is ⁴⁸C₇ = 85,900,584 ways

To learn more about combinations click :

https://brainly.com/question/28065038

#SPJ1

Answer:

Step-by-step explanation:

We know this is a combinations problem, so we have 48C7:

48C7=48!7!(48−7)!=48!7!41!=48⋅47⋅46⋅45⋅44⋅43⋅42⋅41!7⋅6⋅5⋅⋅⋅2⋅1⋅41!=73,629,072

That is, there are 73,629,072 ways to choose seven cards from forty-eight.

this is pt 2 of the knewton answer

The Inequality which ensure triangle exists is A. 7/4 < x < 11/2

Inequality is defined as the relation between two quantities with the sign of inequality that is >, <, ≤ , ≥ ."

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal.

Theorem used In ΔABC,

AB + BC >AC

AC+ BC >AB

AC + AB > BC

According to the question,

In triangle ABC.

AC = 18units

BC = 6x units,

AB = 2x + 4 units

Substitute the value in the inequality to ensure triangle exists we get 7/4 < x < 11/2. The correct option is A.

Learn more about inequalities on

https://brainly.com/question/24372553

#SPJ1