If the coordinates of P,Q,R and S be(1,2,2),(2,4,0),(-3,0,1) and(-1,-2,2) respectively, find the projection of RS on PQ.​

The system of linear equations for the given graph is: y = 1/2x + 6;  y = -3x - 1

The graph of a linear equation follows a slope-intercept form y= mx + b, where m is the slope and b is the y-intercept. We can determine the graph of a linear equation by merely looking at the graph and finding two points on the graph from which the slope of the graph can be determined the represent it as a linear equation.

The linear equation can now be converted to a standard form to determine the system of the linear equation.

From the graph.

The first upper graph to the right shows the point (-2, 5) and (0,6)

The second graph to the left shows the point (-2, 5) and (0,-1)

The slope of the first graph = (6  - 5 )/(0--2) = 1/2; The y-intercept = 6

In slope-intercept form, we have:

y = 1/2x + 6 ----- (1)

The slope of the second graph = (-1 - 5)/(0--2) = -6/2 = -3

The y-intercept = -1

In slope-intercept form: y = -3x - 1   ------- (2)

y = 1/2x + 6

y = -3x - 1

Therefore, we can conclude that the system of linear equations for the given graph is: y = 1/2x + 6;  y = -3x - 1

Learn more about representing graphs as a system of linear equations here:

https://brainly.com/question/28732353

#SPJ1

The required simplified solution of the given expression is LHS is not equal to RHS as -33/10 ≠ -19/5.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
3 1/2+(-7 1/5) = 3+(-7) + 2/5 + (-1/5)
7/2 - 34/5 = -4 + 2/5 + -1/5
-33/10 =  -4 + 1/5
-33/10 ≠ -19/5

Thus, the required simplified solution of the given expression is LHS is not equal to RHS as -33/10 ≠ -19/5.

Learn more about simplification here:

https://brainly.com/question/12501526

#SPJ1

The correct equation of the circle is the first option which is

(x - 5)² + (y + 2)² = 9

What is a circle?

A circle is a collection of all points in a plane that is uniformly distanced from a fixed point. The fixed point is referred to as the circle's centre. The radius of a circle is the separation between the centre and any point along its circumference.

The general equation of the circle is

(x-h)² + (y-k)² = r²

where r = radius of the circle

          (h,k) = centre of the circle

Given,

      radius r = 3

    centre = (h,k) =  (5,-2)

According to the above equation,

(x-5)² + (y-(-2))² = 3²

(x-5)² + (y+2)² = 9

Therefore the correct equation of the circle is the first option.

To learn more about the circle, follow the link.

https://brainly.com/question/1506955

#SPJ1

The simplified monomials are:

Let's simplify each monomials we have.

3a³b² - 5a³b² = -2a³b² --> both exponents are already equal

5xy - 2x²y + 2xy = 7xy - 2x²y

                           = xy (7 - 2x)

-6w : -2w = 3

a⁴ . a³ = a⁽⁴⁺³⁾

          = a⁷

(-x⁵)² = - x ⁽⁵ˣ²⁾

        = - x¹⁰

k⁹ / k⁵ = k⁽⁹⁻⁵⁾

          = k⁴

-5x³ . (-3x⁴) = 15x⁷

(-2x²y)² . (-3xy³) = (4x⁴y²) . (-3xy³)

                          = -12x⁵y⁵

2a⁻⁵b⁶ . 5a²b² = 10 a⁻³b⁸

                       = 10b⁸ / a³

(-4y⁴)² = 16y⁸

(a²bc³)⁴ . (b²c)³ = (a⁸b⁴c¹²) . (b⁶c³)

                        = a⁸b¹⁰c¹⁵

(6cd⁻¹)⁻³ = 1 / (6cd⁻¹)³

              = (d/6c)³

              = d³ / 216c³

(4a)⁻³ . a⁻⁴ = 1/(4a)³ . (1/a⁴)

                 = 1/64a³ . 1/a⁴

                 = 1/64a⁷

(3xy)² . (-4x³y²)³ = (9x²y²) . (-64x⁹y⁶)

                          = -576x¹¹y⁸

(4a⁻¹b⁵c⁻³)³ = (4b⁵ / ac³)³

                  = 64b¹⁵ / a³c⁹

9d⁸/3d¹⁰ = 3/d²

6a⁵b² / 4ab³ = 3a⁴/ 2b

32x³y²z⁵ / -8xyz² = -4x²yz³

(2y⁵)⁴ / 10y¹⁵ = 16y²⁰ / 10y¹⁵

                    = 8y⁵ / 5

(3x⁵y³ / x³y⁶)⁴ = (3x²/y³)⁴

                      = 81x⁸ / y¹²

(-6a⁵b)² - 8a³b = 36a¹⁰b² - 8a³b

12a⁷b                     12a⁷b

                        = 3a⁵b - 8a⁵b

                       = -5a⁵b

Learn  more about Monomials here: brainly.com/question/29113952

#SPJ1

It all depends on how you want your hamburger. If you're serving it as a main dish, 300 hamburger patties (each around 4 ounces) should be plenty to feed 300 people. If you utilize hamburger meat as a topping or filler in a meal, you'll need a different amount.

Arithmetic operations is a field of mathematics that studies numbers and the operations on numbers that are helpful in all other disciplines of mathematics. It consists mostly of operations like addition, subtraction, multiplication, and division. Arithmetic Operator is used to conduct mathematical operations on the supplied operands such as addition, subtraction, multiplication, division, modulus, and so on. The four basic arithmetic operations are addition, subtraction, multiplication, and division. Arithmetic mean is a number calculated by dividing the sum of a set's elements by the number of values in the set.

Here,

It all depends on how you want to eat the hamburger. If you're serving it as a main course, 300 hamburger patties, each weighing around 4 ounces, should plenty to satisfy 300 people. It will need a different quantity of hamburger meat if you use it as a topping or filler in a dish.

To know more about arithmetic operation,

https://brainly.com/question/29259404

#SPJ4  

Complete question:

How much hamburger will it take to make 300 three oz patties with a 20% shrinkage?

The value of the equation a = (1/4)×b in terms of a is b = 4a.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, An expression a = (1/4)×b.

Now, Making 'b' the subject is the same as solving for 'b'.

We know when a term is multiplied by another term moving it to the other side we have to take its reciprocal.

Therefore,  a = (1/4)×b.

b = a×(4/1).

b = 4a.

learn more about numerical expressions here :

https://brainly.com/question/29199574

#SPJ1

Based on the numerical data, we can estimate that 26 more labor hours will be necessary to satisfy the labor hours required without overtime.

The Fair Labor Standards Act, enacted by the federal government, places a cap on the number of hours per week (40 hours) that businesses may demand their employees to perform in exchange for regular pay. Employers were now required to give employees who put in more than 40 hours of work additional compensation in the form of overtime pay.

Hence,

Overtime pay is usually 1.5 times the employee's regular hourly wage.

So, if an employee is paid $15 per hour, their overtime rate is $22.50 per hour ($15 multiplied by 1.5).

If another employee is paid $25 per hour, overtime is $37.50 per hour ($25 x 1.5).

It would require 26 more labor hours will be necessary to satisfy the labor hours required without overtime.

Read more about overtime here:

https://brainly.com/question/901346

#SPJ1

The perimeter of the rectangle with a length of 4 meters and a width of 150 centimeters is 11 meters.

A rectangle is simply a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.

The perimeter of a rectangle is expressed as;

Perimeter = 2( length + width )

Given the data in the question;

Plug the values into the above equation.

Perimeter = 2( length + width )

Perimeter = 2( 4 meters + 1.5 meters )

Perimeter = 2( 5.5 meters )

Perimeter = 11 meters

Therefore, the perimeter is 11 meters.

Learn more about rectangles here: https://brainly.com/question/27612962

#SPJ1

In linear equation, $54.3  is  the original price of the jumper.

Which equation is 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.

17% of 319.41

17/100 * 319.41

= 54.2997

Learn more about linear equation

brainly.com/question/11897796

#SPJ1

Step-by-step explanation: To solve for e in this equation, you can start by isolating e on one side of the equation.

First, distribute the -2/5 on the left side of the equation:

-2/55 - 2/510e = e + 1/36e - 1/312

Now, you can combine like terms on both sides of the equation:

-2 - 4e = e + 2e - 4

Next, you can add e to both sides of the equation:

-2 - 3e = 2e - 4

Now you can add 3e to both sides of the equation:

-2 = 5e - 4

Now you can add 4 to both sides of the equation:

-6 = 5e

Finally, you can divide both sides of the equation by 5:

e = -6/5

So the value of e that satisfies the equation is -6/5.

Answer:

-2.5

Step-by-step explanation:

We can start by isolating h on one side of the equation:

4x + 5 = h(-2x + 5)

Divide both sides by -2x + 5:

(4x + 5) / (-2x + 5) = h

Now, since the equation has only one solution, the value of h must be well-defined for all values of x except those that would make the denominator equal to zero. This happens when -2x + 5 = 0, or when x = (5 - 5) / (-2) = -2.5.

So, the value of h cannot be determined when x = -2.5. This means that the value of h cannot be equal to -2.5.

Answer:

6,5

Step-by-step explanation:

The 15th term of the geometric progression is a₁₅ = 25/2048

A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.

The nth term of a GP is aₙ = arⁿ⁻¹

The general form of a GP is a, ar, ar2, ar3 and so on

Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )

Given data ,

Let the 15th term of the geometric progression be a₁₅

Now , the 4th term of the GP is a₄ = -25

The 9th term of the GP is a₉ = 25/32

Now , nth term of a GP is aₙ = arⁿ⁻¹

Substituting the values in the equation , we get

a₄ = ar³ = -25   be equation (1)

a₉ = ar⁸ = 25/32   be equation (2)

Divide equation (2) by equation (1) , we get

r⁵ = -( 1/32 )

r⁵ = - ( 1/2 )⁵

So , the common ratio r = -1/2

Now , the first term of the GP a is calculated by

ar³ = -25

when r = -1/2

a ( -1/2 )³ = -25

a/8 = 25

a = 200

Now , the 15th term of the geometric progression a₁₅ = ar¹⁴

Substituting the values in the equation , we get

a₁₅ = 200 ( -1/2 )¹⁴

a₁₅ = 200/16,384

a₁₅ = 25/2048

Hence , the 15th term of the GP is 25/2048

To learn more about geometric progression click :

https://brainly.com/question/1522572

#SPJ1

Answer:

Step-by-step explanation:

=63

The measure of arc ADC in circle B with the measure of minor arc AC= 126° is 234°.

Given that the measure of minor arc AC = 126°, we can find the measure of arc ADC using the following formula:

m/ADC = 360° - m/AC

Plugging in the values, we get:

m/ADC = 360° - 126° = 234°

Therefore, the measure of arc ADC is 234°.

Here is the explanation:

A minor arc is an arc that is less than 180°.

The measure of a minor arc is equal to the measure of the central angle that intersects it.

The measure of a whole circle is 360°.

Therefore, the measure of arc ADC is equal to the difference between the measure of the whole circle and the measure of minor arc AC. This difference is 360° - 126° = 234°.

To learn more about measure here:

https://brainly.com/question/29270640

#SPJ2

The value of the 7 in the one's place is 1/1000 times the value of the 7 in the thousand places.

According to the question,

The number is 7,567.23.

Place value in Maths describes the position or place of a digit in a number. Each digit has a place in the number.

The difference in place value in one's place and thousand places is 1000.

The 7 in the thousands place is 1000 times the value of the 7 in the one's place.

So, The value of the 7 in the one's place is 1/1000 times the value of the 7 in the thousand places.

Read more about place value:

https://brainly.com/question/569339

#SPJ4

The answer to option D) is yes. The likelihood of choosing a carnation at random from vase K is higher than the likelihood of choosing one at random from vase J.

The possibility is determined on the range of potential outcomes. the estimated number of outcomes that might occur. For instance, there is only one method to receive a head and there are a total of two possible outcomes, hence the chance of flipping the coin and receiving heads is 1 in 2. (a head or tail). We write P(heads) = 12 here.

Roughly simply, probability is the chance that everything will exist. When we wouldn't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes.

To know more about Probability visit :

https://brainly.com/question/30034780

#SPJ1

I found the answer with the ruluer it's 11.3

If we throw uniformly at random a point on segment [0,1], then its expected position is 1/2.  the expected positions 1/3 and 2/3 of two random points on segment [0,1] are [0,1/3],[1/3,2/3]and[2/3,1]

In geometry, the mean line segment length is the average length of a line segment connecting two points chosen uniformly at random in a given shape. In other words, it is the expected Euclidean distance between two random points, where each point in the shape is equally likely to be chosen. Given the interval is [0,1]

Then it's expected position is 1/2

So [0,1/2] and[1/2,1]

Now we get the two expected positions

I. E three intervals

So (1-0)/3

=1/3

So 1/3 and 2/3 are expected positions

They are [0,1/3],[1/3,2/3]and[2/3,1]

Learn more about expected distance between 2 points here :

https://brainly.com/question/20343143

#SPJ4

Answer:

1200

Step-by-step explanation:

4% of 2000 is 80 then do 80*15 and you get 1200

Fewer than 15% of coins were quarters. Exactly 80% of the coins were nickels, dimes, and quarters. Nickels, dimes, and quarters account for 95% of the total number of coins.

Quarters are coins that are used in many countries as a form of currency. Quarters are generally made of metal and are round in shape. They are typically smaller than other coins, such as dimes and nickels, and have a value of 25 cents (or one-fourth of a dollar). Quarters are often used in everyday transactions, such as buying candy or a newspaper, or to pay for parking. In the United States, there are five different designs of quarters in circulation, each representing a different state or territory.

To learn more about quarters

https://brainly.com/question/28840327

#SPJ1

1) The proof that ΔFEH ≅ΔFGH is given as follows:

ΔFH bisects ∠EFG (Given)

∠FEH ≅ ∠ FGH.

FH = HF (Given)

∠EFH ≅ ∠FHG (Angle Bisector Theorem)

Thus, ΔFEH ≅ΔFGH  (Angle  - Side - Angle Theorem)

2) The proof that ΔPQR ≅ ΔTSR is:

∠RPQ ≅ ∠RTS - Given

R is the midpoint of QS - Given the Definition of Midpoint

QR ≅ RS -  Definition of Midpoint

∠PRQ ≅ ∠SRT Vertical Angles

Thus: ΔPQR ≅ ΔTSR - Angle - Angle - Side Theorem.

3) the proof that ΔABC ≅ Δ DCB is given as follows:
ΔABC and ΔDCB are Right Angled Triangles

AB ≅ DC - Given

BC ≅CB - Reflective Properties; thus

ΔABC ≅ ΔDCB - Hypothenus Leg Theorem.

According to the hypotenuse-leg (HL) theorem, if the hypotenuse and a leg of a right triangle are both congruent with the corresponding hypotenuse and leg of another right triangle, the triangles are congruent. According to the HL theorem, these triangles are congruent.

There is one exception to this rule: when the angles are straight angles. Using words: The triangles are congruent if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle.

Learn more about the Hypothenus Leg Theorem:
https://brainly.com/question/16042583
#SPJ1

The probability that it takes more than 3 customers who buy an eligible item to find one who purchased the extended warranty = 0.493

Here, 21% of customers purchase extended warranty.

So, the probability p = 0.21

It takes more than 3 customers who buy an eligible item to find one who purchased the extended warranty is nothing but none of the first three buy.

This means, we find probability P(X = 0) when n = 3.

Using Binomial distribution formula for probability,

P(X = 0) = ³C₀ (0.21)⁰ (1 - 0.21)⁽³ ⁻ ⁰⁾

P(X = 0) =  ³C₀ (0.21)⁰ (0.79)⁽³ ⁻ ⁰⁾

P(X = 0) = 0.493

Therefore, the required probability is 0.493

Learn more about the probability here:

https://brainly.com/question/15124899

#SPJ4

The complete question is:

The transaction history at an electronic goods store indicates that 21 percent of customers purchase the extended warranty when they buy an eligible item. Suppose customers who buy eligible

items are chosen at random one at a time, until one is found who purchased the extended warranty. Let the random variable X represent the number of customers it takes to find one who

purchased the extended warranty. Assume customers' decisions on whether to purchase the extended warranty are independentWhich of the following is closest to the probability that X > 3;

that is, the probability that it takes more than 3 customers who buy an eligible item to find one who purchased the extended warranty?

Answer: B, C, A.

Step-by-step explanation: positive, not negative

Answer:

No, it would not fit because one cup is 8 ounces and if you times 8 and 13 it 104 so it would not fit they would need another container.

Step-by-step explanation:

hope it helps

Answer:

Step-by-step explanation:

The relationship between tan A and tan B is: tan A * tan B = 1

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

angle A + angle B = 90 deg

When angle A + angle B = 90 degrees,

The two angles are complementary, meaning they add up to 90 degrees.

In this case, the relationship between tan A and tan B is:

tan A * tan B = 1

This is known as the tangent addition formula.

Read more about trigonometry at

https://brainly.com/question/24349828

#SPJ1

If the chi square value of a dihybrid analysis is 0.47 , and degree of freedom in analysis were 3 , then the null hypothesis will not be rejected because 0.47 < 7.815  .

To determine whether to reject or accept the Null Hypothesis, a critical value of chi-square with a given level of significance is used.

If the calculated chi-square value is greater than the critical value, then the null hypothesis is rejected. and

If the calculated chi-square value is less than or equal to the critical value, then the null hypothesis is not rejected.

The critical value of chi-square for a level of significance and degrees of freedom can be found using a chi-square distribution table.

With a level of significance of 0.05 and 3 degrees of freedom, the critical value of chi-square is 7.815.

that means ⇒ 0.47 < 7.815, the null hypothesis would not be rejected at a level of significance of 0.05    .

Learn more about Null Hypothesis here

https://brainly.com/question/30115273

#SPJ4

Answer:

37.17

Step-by-step explanation:

I took the test

Answer: The circumference of the pizza is 37.7 inches.

Given data :

Diameter of the pizza = 12 inches

So,

Radius of the pizza = 12/2

= 6 inches

So,

Circumference of the pizza

= 2×π×radius

= 2×22/7×6

= 37.7 inches (answer)

take upper base = 12

take upper base = 12right side= 20

take upper base = 12right side= 20apply pythagorus

take upper base = 12right side= 20apply pythagorus .

take upper base = 12right side= 20apply pythagorus .= 13

now semi circle= 2 pi r/2 = pi × (11/2)

add all

12 +20+13× 5.5pi

Answer:

64.27cm

Step-by-step explanation:

Total perimeter =

semicircle +  Length of rectangle +  Breadth of rectangle and triangle +

hypotenuse of Triangle

semicircle = pi x r     (r = radius)

= 3.14 x 11/2

= 17.27 cm   -----------------(1)

Length of rectangle = 12cm  (Given) ----------------------(2)

Base (rectangle and triangle) = 20cm (Given) --------------------(3)

Hypotenuse = Root of (20-11)^2 + 12^2

= Root of  9^2 + 12^2

= Root of 81 + 144

= Root of 225

= 15cm ---------------------------(4)

By adding (1), (2), (3) and (4) we get

= 17.27 + 12 + 20 + 15

= 64.27cm

The variance of 'x'  for the continuous distribution over the interval 40 to 44 is approximately b) 1.333

The variance of a continuous uniform distribution over the interval [a, b] is:

Calculate the variance using the formula:

                                       Var(x) = (b-a)^2/12

where [a, b] is the interval over which the continuous uniform distribution is defined

But putting a= 40 and b = 44, calculate the variance by putting them in the above formula

So, Var(x) = (44-40)^2/12

     Var(x) = 4^2/12

     Var(x) = 16/12

     Var(x) = 4/3

     Var(x) = 1.333

Therefore, the variance of 'x' for the continuous distribution over the interval 40 to 44 is approximately b) 1.333

To learn more about Variance here:

brainly.com/question/28426562

#SPJ4