If lines a and b are perpendicular to line c, what word best describes how lines a and b relate to each other?
A.intersecting
B. Parallel
C. Perpendicular
D. Skew

The Reflexive property of congruence can be used to prove

ΔPQR≅ΔPSR .

Given:

∠QPR≅∠SPR

∠PQR≅∠PSR

What is Reflexive property of congruence ?

In geometry, the reflexive property of congruence states that an angle, line segment, or shape is always congruent to itself.

We learned that the reflexive property of equality means that anything is equal to itself. The formula for this property is a = a. This property tells us that any number is equal to itself. For example, 3 is equal to 3.

PR≅PR (Reflexive property of congruence)

If two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent.(AAS theorem)

Hence, ΔPQR≅ΔPSR.

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Answer:

it s b) 4 2 the power of 7

Step-by-step explanation:

Based on the given information and assuming the innocent men do not lie, Jones is the only suspect whose statement aligns with the statements of the other two, suggesting that Smith and Williams may be the murderers.

a. In this scenario, we cannot definitively determine the murderer based on the given information. The guilty man may or may not be telling the truth, so we cannot rely solely on their statements. Further investigation or evidence is needed to determine the actual culprit.

Williams states that he saw both Smith and Jones with Cooper on the day of the killing and that either Smith or Jones must have killed him. Based on the given information, we can conclude that Jones is the only suspect whose statement does not contradict the statements of the other two.   suspect whose statement aligns with the statements of the other two, suggesting that Smith and Williams may be the murderers.

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Answer:

Yes. 34.79 is a rational number because it can be written as a fraction.

Step-by-step explanation:

Hoped this helped.

Answer:

-7  -4  0 1 7

Step-by-step explanation:

x=0

x²-49=0

x²=49

x=±7

x²+3x-4= ² + 4 − − 4= ( + 4 ) − 1 ( + 4 )=(x+4)(x-1)=0

x+4=0

x=-4

x=1

Answer:

is 30 because 3 multiply by 10 is 30

The two square roots of the complex number 4√3 - 4i are:

x₀ = ±√2 cis(-π/12)

x₁ = ±√2 cis(5π/12)

The square roots of the complex number 4√3 - 4i, we can write it in polar form and use the properties of complex numbers.

First, let's convert 4√3 - 4i to polar form. We have:

r = √(4² + (-4)²)

= √(16 + 16)

= √32

= 4√2

θ = arctan(-4/4√3)

= arctan(-1/√3)

= -π/6 (since arctan(-1/√3) is in the fourth quadrant)

So, the polar form of the complex number is 4√2 cis(-π/6).

To find the square roots, we can use the square root property in polar form:

√z = ±(√r) cis(θ/2)

Let's calculate the square roots:

x₀ = ±(√(4√2)) cis((-π/6)/2) = ±(√(2√2)) cis(-π/12) = ±(√2) cis(-π/12)

x₁ = ±(√(4√2)) cis((π - π/6)/2) = ±(√(2√2)) cis(5π/12) = ±(√2) cis(5π/12)

Therefore, the two square roots of the complex number 4√3 - 4i are:

x₀ = ±√2 cis(-π/12)

x₁ = ±√2 cis(5π/12)

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Answer:

x=-13

Step-by-step explanation:

\(\frac{x}{6-5}=\left(-13\right)\)
\(\frac{x}{1}=\left(-13\right)\)
\(x=-13\)

Answer: x= -48

Step-by-step explanation:

x/6 -5 = -13                                              check answer

     +5 = +5                                                 (-48)/6 -5 =-13  

x/6 = -8                                                          -8 -5 = -13

6(x/6) = (-8)6                                                  -13 = -13  

x=-48

The options are: a. Less than 1.b. 4. c. Even number. d. Mo Out of the given options, the only example of a simple event is "4" as there is only one outcome associated with it. Therefore, the answer is option "b".

A simple event can be defined as an event that consists of only one outcome.  

Among the given options, "4" is the only example of a simple event as there is only one outcome associated with it. Therefore, the answer is option "b".

To write your answer within the limit of 250 words, you can follow the below format:A fair die has a total of 6 sides that are numbered from 1 to 6. When this die is rolled, each face of the die has an equal chance of landing face up. Thus,

we can conclude that the sample space of rolling a die is S = {1, 2, 3, 4, 5, 6}. An event can be defined as a subset of a sample space,

while a simple event is an event that consists of only one outcome. Given the sample space S = {1, 2, 3, 4, 5, 6}, we need to determine which of the following is an example of a simple event.

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Answer:

If you are asked if a point is a solution to an equation, we replace the variables with the given values and see if the 2 sides of the equation are equal (so is a solution), or not equal (so not a solution). A solution to a system of equations means the point must work in both equations in the system.

Output z obtained as: multiply w with 5 and then subtract 3 from the result: w --> *5 ---> -3 ---> z.

There are only one or two variables in a linear equation.

The given expression is:

z = 5w-3

Here:

Input value : 5w-3

Output value : z

So,

Output z obtained as:

multiply w with 5 and then subtract 3 from the result:

w --> *5 ---> -3 ---> z

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Answer:

(0,-23)

Step-by-step explanation:

Answer:

x>0

(0, infinity symbol)

The number of workers at a company increased 30 percent between 1990 and 2000. Employment increased 40 percent between 2000 and 2009. The employment in 2009 was 82 percent greater than in 1990.

Percentage generally refers to out of 100.

it is the term used to represent part of the whole or whole of the part.

Percentage can be calculated as \((\frac{Actual value}{Total value}) 100\).

Let the initial number of people in the company be x.

Between 1990 and 2000 employment increased = 30 %

Between 2000 and 2009 employment increased = 40 %

So, after both increment,

x(1 + 3/10)(1 + 4/10)

So required percentage change would be

[x(1 + 3/10)(1 + 4/10) /x] × 100

After solving we get total to be 82 % .

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We have 792 ways to pick five students for the student council from a group of twelve candidates.

We will use the combination formula, which is nCr = n! / r!(n - r)! is find  number of ways to pick five students.

In this case, we want to choose 5 students from 12 candidates:

12C5 = 12! / 5!(12 - 5)!

12C5 = (12 × 11 × 10 × 9 × 8) / (5 × 4 × 3 × 2 × 1)

12C5 = 95040 / 120

12C5 = 792

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Step-by-step explanation:

Slope intercept from is

y = mx + b     m = slope    b = y-axis intercept

y = 2/3 x -9

Answer:

<3 I want brainliest!!!

Step-by-step explanation:

1) 5.54 x 10^9

2) 2.5409 x 10^-5

Answer:

-4x

Step-by-step explanation:

3-7=-4 just add a x

Answer:

1.504 x 100 = 150.4

Explanation:

By multiplying the number by 100, we are moving the decimal two places to the right, which will make 0 in the one's place.

1.504

^ Here, 1 is in the one's place

150.4

   ^ Here, 0 is in the one's place

(Hint, the one's place is right in front of the decimal point)

The population parameter will always be between lower and upper bounds of the confidence interval. - True, whereas sample statistic will always be between lower and upper bounds of the confidence interval - False

With a certain degree of certainty, the population parameter is anticipated to lie between the lower and higher limits of the confidence interval. The confidence interval, which gives an interval estimate of the unidentified population parameter, is created based on the sample data. The interval's level of confidence shows the amount of ambiguity we are prepared to accept when determining the actual population parameter.

The confidence interval's lower and upper limits may or may not be met by the sample statistic used to compute them. A single point estimate, the sample figure is susceptible to sampling error. On the other hand, based on the observed sample data and the selected degree of confidence, the confidence interval is a range of values that we can be fairly confident includes the true population parameter.

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In  linear equation, 7/10 did he buy .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                            Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

multiply the fractions by each other.

7/8*4/5

7*4=28

8*5=40

28/40

"B" would be the correct answer but, it the fraction should be reduced to 7/10.

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If the best fit line is nearly horizontal, it suggests no significant relationship between height and head circumference.

In this scenario, the explanatory variable is the child's height, as it is being used to predict the head circumference.

The response variable is the head circumference itself, as it is the variable being predicted or explained by the height.

To draw a scatter diagram of the data, you would plot the child's height on the x-axis and the corresponding head circumference on the y-axis. Each data point would represent a child's measurement pair.

Once all the data points are plotted, you can then draw the best fit line, also known as the regression line, that represents the overall trend or relationship between height and head circumference.

By observing the scatter diagram and the best fit line, you can determine the relationship between a child's height and head circumference.

If the best fit line has a positive slope, it indicates a positive relationship, meaning that as height increases, head circumference tends to increase as well.

If the best fit line has a negative slope, it indicates a negative relationship, meaning that as height increases, head circumference tends to decrease.

By assessing the slope of the best fit line in the scatter diagram, you can determine whether the relationship between height and head circumference is positive, negative, or nonexistent.

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The velocity of the oxygen molecule at room temperature is 482 m/s.

The kinetic energy of an oxygen molecule at room temperature (300 K) is determined.

The mass of an oxygen molecule is 5.31 × 10-26 kg. As per the statement, the kinetic energy of the oxygen molecule at room temperature is 6.21 × 10-21 J.Kinetic energy

The kinetic energy of an object is the energy that it possesses because of its motion. It is a scalar quantity and has units of joules (J) in the SI system.

The formula for the kinetic energy of an object is given by 1/2mv²,

where m is the mass of the object, and v is its velocity.

The kinetic energy of a gas is calculated using the root mean square velocity of the molecules. RMS velocityRMS velocity is the square root of the average of the square of the velocities of the gas molecules.

It is calculated using the formula vrms = √(3RT/M)

where R is the ideal gas constant, T is the temperature in Kelvin, and M is the molar mass of the gas. We can obtain the velocity of a single molecule of gas by dividing the RMS velocity by the square root of Avogadro's number.

Here, we have a single oxygen molecule, so we can directly calculate its velocity from the RMS velocity. From the kinetic energy formula, we can get the velocity of the molecule, which is given by √(2KE/m)

Substitute the given values, we get,

Velocity of the molecule = √(2 × 6.21 × 10-21/5.31 × 10-26)= 482 m/s

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Answer:

Paralleogram Area = 98 cm²

Rectangle Area = 147 cm²

Total Area of Composite Figure = 245 cm²

Step-by-step explanation:

To find the area of paralleogram you have to take the odd part out and put it on the other side to make a rectangle. Then find the area of that rectangle. 7 * 14 = 98²

After that, Find the area of The regular rectangle. 7 * 21 = 147²

Then, do 98² + 147² = 245²

Thats how you get the answer of 245 cm²

:) hope it helped!

Answer:

C

Step-by-step explanation:

3 - (-12) = 15

6 + (-24) = (-18)

The magnitude of the upward force on the table due to the leg at (lx, 0) is Fx=W.

To find the upward force (Fx) on the table due to the leg at position (Lx, 0), you will need to consider the forces acting on the table. In this scenario, the force Fx is the force exerted by the leg to support the weight of the table and maintain equilibrium.  

To calculate Fx, you'll need to take into account the weight of the table (W) and any additional forces acting on it, such as objects placed on the table. Since the table is in equilibrium, the sum of all forces in the vertical direction should be equal to zero.

Using the principle of equilibrium:

ΣFy = 0

Where ΣFy represents the sum of all vertical forces acting on the table.

In this case, the upward force exerted by the leg (Fx) should be equal to the total downward force acting on the table:

Fx = W

Once you have determined the weight of the table and any additional forces, you can calculate the magnitude of the upward force Fx exerted by the leg at position (Lx, 0).

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Answer:

y= -2x - 1

Step-by-step explanation:

Take two of the points given by the data in the table.

Using the x-values 1 and 2, they have a y-value of -3 and -5, respectively.

Therefore, we can write these out as coordinate points: (1, -3) and (2, -5).

The equation to find the slope of a line is:

Substitute these points into this formula to find the slope of this linear function.

Simplify and solve for the slope m.

The slope of this linear function is -2. Now, we can use this slope and substitute it into the point-slope equation along with another one of the points on the function.

Point-slope equation:

Substitute m = -2 and the point (1, -3) into this equation.

Simplify this equation and put it into slope-intercept form: \(y=mx+b\).

The equation of the linear function represented by the table is y = -2x - 1.

Answer:

y= -2x - 1

Step-by-step explanation:

Take two of the points given by the data in the table.

Using the x-values 1 and 2, they have a y-value of -3 and -5, respectively.

Therefore, we can write these out as coordinate points: (1, -3) and (2, -5).

The equation to find the slope of a line is:

Substitute these points into this formula to find the slope of this linear function.

Simplify and solve for the slope m.

The slope of this linear function is -2. Now, we can use this slope and substitute it into the point-slope equation along with another one of the points on the function.

Point-slope equation:

Substitute m = -2 and the point (1, -3) into this equation.

Simplify this equation and put it into slope-intercept form: .

The equation of the linear function represented by the table is y = -2x - 1.

Answer:

(2,0)

Step-by-step explanation:

I think that the answer

Therefore, the expression for the number 'n' of bacteria after 't' hours is N(t) = 600 * (3)^t.

We can find the expression for the number 'n' of bacteria after 't' hours by using the following formula. The formula for exponential growth is given by:

P(t) = P0 * (1 + r)^t, Where P0 = initial population of bacteria, t = time in hours, r = rate of growth of bacteria.

P(t) = P0 * (3)^t

The initial population of bacteria is 600. So,

P0 = 600

And rate of growth of bacteria is 3. The formula for the number 'n' of bacteria after 't' hours is given by:

N(t) = 600 * (3)^t

Therefore, the expression for the number 'n' of bacteria after 't' hours is N(t) = 600 * (3)^t.

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