What is the simplified form of the quantity of x plus 5, all over the quantity of 9 − the quantity of x plus 4, all over the quantity of x plus 6

The cotangent of the angle is [tex]\(\frac{4}{3}\).[/tex]

In triangle ABC, where angle ABC is a right angle (90 degrees) and sides AB, BC, and AC are given as 6, 8, and 10 units respectively, we can use the cosine and cotangent functions to find the cotangent of angle ABC.

The cosine of an angle in a right-angled triangle is defined as the ratio of the adjacent side to the hypotenuse.

In this case,[tex]\(\cos(\angle ABC) = \frac{BC}{AC} = \frac{8}{10} = \frac{4}{5}\).[/tex]

The cotangent [tex](\(\cot\))[/tex] of an angle is the reciprocal of the tangent (tan).

The tangent is the ratio of the opposite side to the adjacent side.

Therefore,[tex]\(\cot(\angle ABC) = \frac{1}{\tan(\angle ABC)}\).[/tex]

Since [tex]\(\tan(\angle ABC) = \frac{AB}{BC} = \frac{6}{8} = \frac{3}{4}\)[/tex], we can find the cotangent:

[tex]\[ \cot(\angle ABC) = \frac{1}{\tan(\angle ABC)} = \frac{1}{\frac{3}{4}} = \frac{4}{3} \][/tex]

Therefore, the cotangent of the angle is [tex]\(\frac{4}{3}\).[/tex]

The probable question may be:

The cosine of a certain angle is 4/5. What is the cotangent of the angle?

In triangle ABC , Angle ABC=90 degree, AB=6, BC=8 AC=10

Final answer:

The cosine of an angle being 4/5 means that the ratio of the adjacent side to the hypotenuse in a right triangle is 4/5.

Explanation:

The given question states that the cosine of an angle is 4/5. In trigonometry, the cosine function is defined as the ratio of the adjacent side to the hypotenuse in a right triangle. So, if we have a right triangle with an angle A, and the cosine of A is 4/5, it means that the ratio of the length of the adjacent side to the hypotenuse is 4/5.

Thus, we can say that if the length of the adjacent side is 4 units, then the length of the hypotenuse would be 5 units, assuming the units are consistent. This relationship holds true for any right triangle with an angle whose cosine is 4/5.

For example, if we have a right triangle with an adjacent side of 8 units, then the hypotenuse would be 10 units.

angles in a triangle need to equal 180 degrees

 so x = 180 - 47 - 58

x = 180-105

 x= 75 degrees

To determine if a relation is a function, check for repeated x-values. The relations that represent a function are {(1,-3),(-2,0),(1,4)} and {(3,-8),(-2,0),(4,1)}.

In order for a relation to represent a function, each input (x-value) must correspond to exactly one output (y-value). We can determine if a relation is a function by checking for any repeated x-values. If there are no repeated x-values, then the relation is a function. Let's apply this to the given relations:

The relation {(1,-3),(-2,0),(1,4)} represents a function because each x-value is unique.

The relation {(-2,0),(3,0),(-2,1)} does not represent a function because there is a repeated x-value (-2).

The relation {(3,-8),(-2,0),(4,1)} represents a function because each x-value is unique.

The relation {(4,12),(4,13),(-4,14)} does not represent a function because there is a repeated x-value (4).

So, the relations that represent a function are {(1,-3),(-2,0),(1,4)} and {(3,-8),(-2,0),(4,1)}.

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If the coordinate B is reflected over x-axis, the resulting coordinate will be (5, -9)

If an image is reflected over the x-axis, the resulting coordinate will be (x, -y). The reflections shows the mirror image of a figure.

Given the coordinate B before reflection as (5, 9)> If the coordinate is reflected over x-axis, the resulting coordinate will be (5, -9)

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Refer to the diagram shown below, which shows two of 16 equally-spaced cars attached to the center of the wheel.

The total central angle around the wheel is 2π.

Therefore the central angle between two cars is

(2π)/16 = π/8 = 0.39 radians (nearest hundredth)

The arc length between two cars is

s = (20 ft)*(π/8 radians) = 2.5π = 7.85 ft (nearest hundredth)

The area of a sector formed by two cars is

(1/16)*(π*20²) = 78.54 ft² (nearest hundredth)

Answers: (to the nearest hundredth)

Between two cars,

Central angle = 0.39 radians (or 71.4°)

Arc length = 7.85 ft

Area of a sector = 78.54 ft²

Please see attached file for the triangle’s figure:

Going with the image attached, if DE is parallel to BC
then
4: (4 + 5) = 6 : (6 + 7).

Therefore, the inequality that she will use to contradict the assumption is 4:9 ≠ 6:13.

To add, a relation that holds between two values when they are different in mathematics is called an inequality. A is not equal to b also means the notation a ≠ b.

Answer:

4:9 ≠ 6:13.

Step-by-step explanation:

Answer:

b edge

Step-by-step explanation:

Answer:

[tex]AC=\sqrt{130}[/tex]

Step-by-step explanation:

AC is the geometric mean.  Solve it using this proportion:

[tex]\frac{BC}{AC}=\frac{AC}{CD}[/tex]

Now fill in the values we know:

[tex]\frac{5}{AC}=\frac{AC}{26}[/tex]

Cross multiply to get

[tex](AC)^2=130[/tex]

That means that

AC = [tex]\sqrt{130}[/tex], which, in decimal form is

AC = 11.40175425

the figure is an equilateral triangle, which all angles are 60 degrees

 angle 3 divides a 60 degree angle in half so angle 3 = 30 degrees

 the base is a right triangle which is 90 degrees

 90+30 = 120

180-120 = 60

 Angle 2 is 60 degrees

since the 6th comic will be last you need to know how many different ways to schedule 5 comics

5x4x3x2 = 120

 there are 120 different ways.

Answer:

Volume of the cone = 7 unit³

Step-by-step explanation:

Soda can has the shape of a cylinder.

Volume of soda can = πr²h

where r = [tex]\frac{6}{2}=3[/tex] units

and volume = 21 unit³

We put the values in the formula to get the value of h.

21 = πr²h

[tex]h=\frac{21}{\pi r^{2} }[/tex]

Now If we fit a cone inside the can, radius of the cone will be equal to the radius of the cylinder and height of the cylinder will be equal to the height of the cone fit inside.

By the formula of volume of cone

Volume = [tex]\frac{1}{3}\pi r^{2}h[/tex]

= [tex]\frac{1}{3}\pi r^{2}( \frac{21}{\pi r^{2} })[/tex]

= [tex]\frac{21}{3}=7[/tex] units³

Volume of the cone is 7 unit³

To area under the standard normal curve between z = -1.5 and z = 2.5 is 0.927

A standard normal curve, also known as the standard normal distribution, is a bell-shaped, symmetrical probability distribution with a mean of 0 and a standard deviation of 1. It serves as a reference for many statistical analyses and is often denoted as the Z-distribution.

To find the area under the standard normal curve between z = -1.5 and z = 2.5, we need to use the z-table. The z-score of -1.5 corresponds to an area of 0.0668 and the z-score of 2.5 corresponds to an area of 0.9938. To find the area between these two z-scores, we subtract the smaller area from the larger area:

= 0.9938 - 0.0668

= 0.927

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The area between these z-scores is 0.9270.

The area under the standard normal curve between z = -1.5 and z = 2.5 can be found using the z-table.

First, find the area to the left of

z = -1.5, which is 0.0668.

Next, find the area to the left of

z = 2.5, which is 0.9938.

Subtract these two values to get the area between z = -1.5 and z = 2.5 :

0.9938 - 0.0668

 = 0.9270.