eight more than the product of two and a number x

Answer:

A. definition of perpendicular bisector

Step-by-step explanation:

I JUST TOOK THE TEST!!!!!!

Answer:

The correct option is a) perpendicular bisector definition.

Step-by-step explanation:

Given :

Triangle QPT is similar to triangle QRT.

[tex]\rm SP \cong SR[/tex]

To find : Why [tex]\rm PT \cong RT[/tex]

Solution :

According to perpendicular bisector definition -

Perpendicular Bisector is a line or a segment perpendicular to a segment that passes through the midpoint of the segment. Any point on the perpendicular bisector is equidistant from the endpoints of the line segment.

Therefore, [tex]\rm PT \cong RT[/tex]

Hence option a) is correct.

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Answer:

Option A is correct

Step-by-step explanation:

In the given figure to draw the parallel line to AC passing through B we have to tell the next step.

As lines AC and AB given and we know if lines are parallel then alternate angles are equal.

Hence, if line through B parallel to AC drawn then alternate angles ∠BAC and ∠ABD equal.

∴ To draw parallel lines our next step is to use a protractor to measure ∠BAC so that the same angle through B is drawn results in equal alternate interior angles.

Hence, Option A is correct.

The margin of error can be calculated using the t statistic. The formula for margin of error is given as:

Margin of error = t * s / sqrt (n)                                 ---> 1

Where,

t = the t score based on the given confidence level and degrees of freedom

n = number of samples = 21

s = standard deviation = 7.1

Degrees of freedom = n – 1 = 21 – 1 = 20

Based on the standard probability tables for t, the t score is:

t = 0.860

Substituting into equation 1:

margin of error = 0.860 * 7.1 / sqrt (21)

margin of error = 1.33

The range is:

range = 30.1 ± 1.33

range = 28.77, 31.43

Therefore the commute time to work is between 28.77 minutes and 31.43 minutes.

Answer:

its D

Step-by-step explanation:

Answer:  The required ratio is [tex]\dfrac{12}{13}.[/tex]

Step-by-step explanation:  In the given triangle, we are to find the ratio of sinθ.

We know that

in a right-angled triangle, the ratio sine of an angle is given by the length of the perpendicular divided by the length of the hypotenuse.

For the given right-angled triangle, we get

[tex]\sin\theta=\dfrac{perpendicular}{hypotenuse}\\\\\\\Rightarrow \sin\theta=\dfrac{36}{39}\\\\\\\Rightarrow \sin\theta=\dfrac{12}{13}.[/tex]

Thus, the required ratio is [tex]\dfrac{12}{13}.[/tex]

In this problem, the student can use the properties of a 45°-45°-90° triangle to determine that the hypotenuse KL is 7 * √2 which is approximately equal to 9.9.

In a triangle where you know one angle (45°) and one side (7 units) across from the right angle, it is a typical example of a situation where trigonometry can be used. In this case, you're dealing with a 45°-45°-90° triangle, also known as an isosceles right triangle. In such a triangle, the sides are in a specific ratio. The sides opposite the 45° angles are the same length (let's call it 'a'), and the hypotenuse is a√2.

Given that LM = 7 and angle K is 45°, triangle KLM is therefore an isosceles right triangle and KL (the hypotenuse) is equal to LM multiplied by √2. So, KL = 7 * √2 which approximately equals to 9.9.

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Answer:

Step-by-step explanation:

The prefix Pre stands for before and algebra is math so pre algebra is informing you about what you will be learning before it actually happens.

Algebra is math for ninth graders that if you fail makes you have to take it until you pass it.

opposite angles have to equal 180

 so 180-111 = 69

 angle 2 is 69 degrees

Answer: [tex]sec \theta[/tex].

Step-by-step explanation: Given expression : [tex]\frac{sin \theta \ sec \theta }{cos \theta \ tan \theta} .[/tex]

We know,

[tex]sec \theta = \frac{1}{cos \theta}[/tex]

[tex]tan \theta = \frac{sin \theta}{cos \theta}[/tex]

Substituting those values in given expression, we get

[tex]\frac{sin \theta \ sec \theta }{cos \theta \ tan \theta} .[/tex] =[tex]\frac{sin \theta\ \frac{1}{cos \theta} } {cos \theta\ \frac{sin \theta}{cos \theta} }[/tex]

= [tex]\frac{sin \theta \ cos \theta}{cos \theta \ cos \theta \ sin \theta}[/tex]

Crossing out [tex]sin \theta \ cos \theta[/tex] from top and bottom, we get

=[tex]\frac{1}{cos \theta }[/tex]

= [tex]sec \theta[/tex].

Answer:

The simplified form of the given expression [tex]\frac{\sin\theta \cdot \sec\theta}{\cos\theta\cdot \tan\theta}[/tex] is  [tex]\sec\theta[/tex]

Step-by-step explanation:

Given: Expression [tex]\frac{\sin\theta \cdot \sec\theta}{\cos\theta\cdot \tan\theta}[/tex]

We have to writ the given expression in simplified form.

Consider , The given expression [tex]\frac{\sin\theta \cdot \sec\theta}{\cos\theta\cdot \tan\theta}[/tex]

Since, we know,

[tex]\sec\theta=\frac{1}{\cos\theta}[/tex]

and  [tex]\tan\theta=\frac{\sin\theta}{\cos\theta}[/tex]

Substitute, we have,

[tex]\frac{\sin\theta \cdot \sec\theta}{\cos\theta\cdot \tan\theta}=\frac{\sin\theta \cdot\frac{1}{\cos\theta}} {\cos\theta\cdot \frac{\sin\theta}{\cos\theta} }[/tex]

Simplify, we have,

[tex]=\frac{\frac{1}{\cos\theta}} {\cos\theta\cdot \frac{1}{\cos\theta} }[/tex]

Simplify further, we get,

[tex]=\frac{1}{\cos\theta}=\sec\theta[/tex]

Thus, The simplified form of the given expression [tex]\frac{\sin\theta \cdot \sec\theta}{\cos\theta\cdot \tan\theta}[/tex] is  [tex]\sec\theta[/tex]

volume = 4/3 x PI x r^3

 in terms of pi. multiply r^3 x 4/3 = 18432PI

surface area = 4pir^2

in terms of pi multiply r^2 x 4 = 2304PI

The given system of equations, x - 2y = 2 and x - 2y = -2, are parallel lines and do not intersect, thus there is no common solution to the system.

In mathematics, to find the solution to a system of equations, we generally try to find the values of variables that satisfy all the equations in the system. When looking at the given equations: x - 2y = 2 and x - 2y = -2, we can see that there is something strange. These two equations are equivalent to each other, meaning they represent the same line. This is due to the fact that both equations have the same coefficients for the x and y variables (1 and -2 respectively). So, if two lines are equivalent, they are essentially the same line. This means there are infinitely many solutions which satisfy this system of equations, since all points on the line satisfy both equations. However, if two lines have the same coefficients but different constants (the numbers without the variables), as in our case, then they are parallel and do not intersect, indicating that there's no solution for the system of equations. Therefore, this system of equations has no solution.

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The area of a computer monitor with dimensions of 13.93 inches by 10.45 inches is approximately 0.09381 square meters.

To calculate the area of your computer monitor, you first need to convert the dimensions from inches to meters because the area is asked for in square meters. There are approximately 0.0254 meters in an inch. So the width is 13.93 inches * 0.0254 m/inch equals to approximately 0.354 meters, and the height is 10.45 inches * 0.0254 m/inch equals to approximately 0.265 meters.  

Then, we can calculate the area using the formula: Area = width * height. Substituting the converted measurements into the formula: Area = 0.354 m * 0.265 m which equals to approximately 0.09381 square meters.

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