Determine the magnitude and the ordered pair that represents the vector from (18,3) to (-4,16)

Final answer:

To find the third side of a triangle when two sides are known, you can use the Triangle Inequality Theorem or the Law of Cosines.

Explanation:

To find the third side of a triangle when two sides are known, you can use the Triangle Inequality Theorem or the Law of Cosines.

Triangle Inequality Theorem:

Take the two known sides of the triangle.

Add the lengths of the two sides together.

Subtract the sum from the total perimeter of the triangle.

Law of Cosines:

Label the two known sides as 'a' and 'b', and the angle between them as 'C'.

Use the formula c² = a² + b² - 2abcos(C) to find the square of the third side.

Take the square root of the result to find the length of the third side.

Answer:

the answer is 64%

Step-by-step explanation:

Answer: A.

Step-by-step explanation:

The product of equation is 18x² - 45x.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Both linear equations with one variable and those with two variables exist.

Given equation -9x(5 - 2x)

product  = -9x(5) - (-9x)(2x)

= -45x + 18x²

= 18x² - 45x

Hence the product is 18x² - 45x.

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Hello!

I believe the answer is A) p(x) = 13x -20.

I hope it helps!

Answer:

The length of BC is 11√2 ft.

Step-by-step explanation:

Given,

A right angled triangle ABC,

In which,

AC = 11 ft ( By diagram ),

∠A = 90°,

∠B = 45°,

By the law of sine,

[tex]\frac{sin B}{AC}=\frac{sin A}{BC}[/tex]

[tex]\implies BC\times sin B = AC\times sin A[/tex]   ( By cross multiplication )

[tex]\implies BC = \frac{AC\times sin A}{sin B}[/tex]

By substituting the values,

[tex]BC=\frac{11\times sin 90^{\circ}}{sin 45^{\circ}}[/tex]

[tex]=\frac{11}{\frac{1}{\sqrt{2}}}[/tex]

[tex]=11\sqrt{2}[/tex]

Hence, the length of BC is 11√2 ft.

Answer:

true

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The formula is S=a1/1-r

The series third has a sum of 5 option (C) is correct because the sequence represents the sum of the infinite terms.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have a series shown in the picture.

The geometric sequence is shown in the options.

As we know, in the geometric sequence there is a first term and common difference

In the first sequence:

First term a = 2

Common difference = 2(0.1)/2

Common difference d = 0.1

The sum of the infinite series is:

S = a/(1 - r)

S = 2/(1 - 0.1)

S = 2.22

In the second sequence:

First term a = 15

Common difference = 15(0.3)/15

Common difference d = 0.3

The sum of the infinite series is:

S = a/(1 - r)

S = 15/(1 - 0.3)

S = 21.42

In the third sequence:

First term a = 4

Common difference = 4(0.2)/4

Common difference d = 0.2

The sum of the infinite series is:

S = a/(1 - r)

S = 4/(1 - 0.2)

S = 5

Thus, the series third has a sum of 5 option (C) is correct because the sequence represents the sum of the infinite terms.

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The calculated area of the shape is 50.24 square units

Finding the area of the shape.

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

The shape

The area of the shape is calculated as

Area = 1/4πr²

Where

Radius, r = 8

Substitute the known values into the equation

Area = 1/4π * 8²

Evaluate

Area = 16π

So, we have

Area = 16 * 3.14

Evaluate

Area = 50.24

Hence, the area of the shape is 50.24 square units

Question

Find the area of the shape.

Use 3.14 for pi. Round your answer to the nearest hundredth.

Jenny will get 5 pieces of rope.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

To find out how many pieces of rope Jenny will get, we need to divide the total length of the rope by the length of each piece:

Total length of the rope = 7 1/2 = 15/2

Length of each piece = 3/4

Number of pieces = (15/2) ÷ (3/4)

We can simplify this expression by dividing the numerator and denominator of the left-hand side by 2:

Number of pieces = (15/2) × (4/3)

Number of pieces = 30/6

Number of pieces = 5

Therefore, Jenny will get 5 pieces of rope.

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Answer:

x + 6; where x ≠ -6, +6

Step-by-step explanation:

Answer: [tex]243.3\ mm^2[/tex]

Step-by-step explanation:

Given: The diameter of smaller circle = 13.2 mm

Then the radius of smaller circle r =[tex]\frac{13.2}{2}=6.6\ mm[/tex]

Also, the radius of larger circle R= [tex]6.6+4.4=11.0\ mm[/tex]

Now, the area of the washer is given by :-

[tex]\text{Area of washer=Area of larger circle-Area of smaller circle}\\\\\Rightarrow\\text{Area of washer}=\pi R^2-\p r^2\\\\\Rightarrow\\text{Area of washer}=\pi(R^2-r^2)\\\\\Rightarrow\\text{Area of washer}=(3.14159265359)((11.0)^2-(6.6)^2)\\\\\Rightarrow\\text{Area of washer}=243.284935094\approx243.3\ mm^2[/tex]

The area of the washer is 0 mm2.

To find the area of the washer, we first need to find the area of the larger circle and the area of the smaller circle. The formula for the area of a circle is A = πr^2.

The larger circle has a diameter of 13.2 mm, so the radius is half of that, which is 6.6 mm. Plugging this value into the formula, the area of the larger circle is approximately 136.78 mm2.

The smaller circle has a diameter of 13.2 mm, so the radius is again 6.6 mm. Using the same formula, the area of the smaller circle is also approximately 136.78 mm2.

To find the area of the washer, we subtract the area of the smaller circle from the area of the larger circle: 136.78 mm2 - 136.78 mm2 = 0 mm2. Rounded to the nearest tenth, the area of the washer is 0 mm2.

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Final answer:

To complete the square for the equation x^2-14x+33=0, the constant 33 is moved to the other side, and the number needed to make the left side a perfect square trinomial, 49, is added to both sides, resulting in factoring and solving (x - 7)^2 = 16 to find x = 11 and x = 3.

Explanation:

To complete the square for the equation x^2-14x+33=0, you need to form a perfect square trinomial on the left side of the equation. First, you'll move the constant term to the right side:

x^2 - 14x = -33

Next, find the value that completes the square for the x-terms. This value is obtained by taking half of the coefficient of x (which is -14 in this case) and squaring it, giving us (-7)^2 = 49.

Add 49 to both sides of the equation:

x^2 - 14x + 49 = -33 + 49

x^2 - 14x + 49 = 16

Now, the left side of the equation is a perfect square trinomial, and can be factored into:

(x - 7)^2 = 16

To solve for x, take the square root of both sides:

x - 7 = [tex]\sqrt{16}[/tex]

x - 7 = +- 4

Finally, solve for x by adding 7 to both sides:

x = 7 +- 4

x = 11 or x = 3

Answer:

896 cm^3

Step-by-step explanation:

formula for the triangle prism is

V= 1/3 Bh

V = 1/3 (8 x 3) (8)  The base is 8 seen the base of the rectangel prism is 8 to its consider as base to.

V= 1/3 (24 x 8)

V= 1/3 (192)

V = 64

Now we need to find the volume so the rectangle formula is

V= lwh

V= (13x 8) (8)

V= 832cm

Add your two answers and u get

832 + 64 = 896 cm^3

The solution is :  896 cm^3 is the volume of the composite figure.

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

Here, we have,

Volume formula for the triangle prism is

V= 1/3 Bh

V = 1/3 (8 x 3) (8)  

The base is 8 seen the base of the rectangle prism is 8 to its consider as base to.

V= 1/3 (24 x 8)

V= 1/3 (192)

V = 64

Now we need to find the volume so the rectangle formula is

V= lwh

V= (13x 8) (8)

V= 832cm

Add your two answers and u get

832 + 64 = 896 cm^3

Hence, The solution is :  896 cm^3 is the volume of the composite figure.

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Answer:

x = 3

Step-by-step explanation:

[tex]\dfrac{2}{5x}=-\dfrac{3}{15}+\dfrac{1}{x}\\\\\dfrac{1}{5}=\dfrac{5-2}{5x}\qquad\text{add $\frac{3}{15}-\frac{2}{5x}$}\\\\x=3\qquad\text{multiply by 5x}[/tex]

The correct answer is D (x - 5)(x - 2)

You can tell this because in the picture, we are looking for all of the cross sections to multiply to their appropriate boxes. In the bottom right corner, we see the number 10. This means that the bottom number and the right number must multiply to 10. This only happens in A and D, whereas in B and C those equal -10.

To determine between A and D, you must find the ones that have negatives, since the two x values are both negatives. D is the only one with negative numbers out of the ones we are left working with. Therefore, D is the correct answer.

Answer:

its C i just did that question

Step-by-step explanation:

The population of a major U.S. city = 8,550,405

Area of the city = 1213.4 sq.km

Density = [tex] \frac{Population}{area} [/tex]

Density = [tex] \frac{8,550,405}{1213.4} [/tex]

Density = 7046.6499 [tex] \frac{People}{km^{2}} [/tex]

As the density here will not be in decimal so after rounding the density in whole number,

Density = 7047 [tex] \frac{People}{km^{2}} [/tex]

Option A is the answer