Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS.

P(-2,1,0), Q(2,3,2), R(1,4,-1), S(3,6,1)

Answers

Answer 1

The volume of the parallelepiped with adjacent edges PQ, PR, and PS     is V=4  

Given three vectors, there is a product, called scalar triple product, that gives (the absolute value of it), the volume of the parallelepiped that has the three vectors as dimensions.

So

PQ=(-2-2,1-3,0-2)=(-4,-2,-2)

PR=(-2-1,-1-4,0+1)=(-3,-5,1)

PS=(-2-3,1-6,0-1)=(-5,-5,-1)

The scalar triple product is given by the determinant of the matrix (3×3)

that has in the rows the three components of the three vectors:

|-4 -2 -2|

|-3 -5 +1|

|-5 -5 -1|

and the determinant is given for example with the Laplace rule choosing the first row:

a(ad-bc)-b(ad-bc)+c(ad-bc)

=-4[(−5)(−1)−(1)(−5)]−(−2)[(−3)(−1)−(1)⋅(-5)]+(−2)[(−3)(−5)−(−5)(-5)]

=-4[5+5]+2[8]-2[-10]

-4(10)+16+20

=-40+36

V=-4

So the volume is: V=|−4|=4

To know more about the volume of the parallelepiped:

https://brainly.com/question/28174749

#SPJ4


Related Questions

How do you determine a value in a ratio when the difference between two amounts is given?

Answers

To determine the value in a ratio when the difference between two amounts is given, divide the difference by the ratio. For example, if the ratio is 3:2 and the difference between the two amounts is 12, then the value of the first amount is 18 (12/3 = 4 x 3 = 18). The value of the second amount is 12 (18 - 12 = 6 x 2 = 12).

1. Identify the ratio given in the problem.

2. Identify the difference between the two amounts.

3. Divide the difference by the ratio to determine the value of the first amount.

4. Subtract the difference from the first amount to determine the value of the second amount.

To determine the value in a ratio when the difference between two amounts is given, divide the difference by the ratio. For example, if the ratio is 3:2 and the difference between the two amounts is 12, then the value of the first amount is 18 (12/3 = 4 x 3 = 18). The value of the second amount is 12 (18 - 12 = 6 x 2 = 12).

Learn more about ratio here

https://brainly.com/question/13419413

#SPJ4

Please answer a and b its urgent

Answers

Answer: 1200 mm/s

Step-by-step explanation:

Step 1: As for point B, each small case represent 2mm/s. So, when A is 3 mm/s, B is 12 mm/s

Step 2: Assuming point A: x, Point B: y and y= k, x through (0,0) and (3,12)

So, 12=3k=k=4

so, y=4x

then, x=300 and y = 4×300

which is 1200 mm/s

To know more about rates:

https://brainly.com/question/12786410

What is the range of slope?

Answers

Range of slope is from 0 to 90 degrees.

What are formula questions?

Answers

Formula questions are those questions which require an answer that is numerical in value, including a specific value or a set of values.

These questions require you to apply certain mathematical formulas and use numeric data to come up with solutions. It will contain random numerical data that will be changed and the student has to find a solution for the same. Any numeric value can be modified and hence, the answer is not fixed. There can be different answers depending on the set of numbers presented in the formula question. The answer can be found by using the necessary formulas that exist.

Learn more about formula question here:

https://brainly.com/question/11812554

#SPJ4

How to find the height of a triangle using Pythagorean Theorem?

Answers

Answer:

Step-by-step explanation:

We can find height of triangle by using pythagoras theorem

By theorem  (hypotenuse)^2 = (perpendicular or height)^2 + (base)^2

            =>    Height of triangle = sqrt{(hypotenuse)^{2} - (base)^{2}

a small computing center has found that the number of jobs submitted per day to its computers has a distribution that is approximately mound-shaped and symmetric, with a mean of 84 jobs and a standard deviation of 9. where do we expect approximately 95% of the distribution to fall?

Answers

Our confidence interval is (66, 102).

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts. Therefore, it can be concluded that there is a 95% probability that the true value falls within that range if a point estimate of 10.00 is produced using a statistical model with a 95% confidence interval of 9.50 - 10.50.

Now, here:

Mean, μ = 84

Standard deviation, σ = 9

It is a 95% confidence interval. We know that, within 2 standard deviations of the mean lies 95% of the population. Hence, z = 2.

Now, calculating μ - z.σ and μ + z.σ to find the intervals.

μ - z.σ  = 84 - 2x9 = 66

μ + z.σ = 84 + 2x9 = 102

Thus, our confidence interval is (66, 102).

To learn more about confidence intervals in statistics, visit the link:

brainly.com/question/29680703

#SPJ4

the sum of twice a number, x, and 6 is equal to 4 more than the number, x. what is the vaule of x.

Answers

Answer:

2x+6=x+4

2x-x = 4-6

x= -2

Answer:

x=-2

Step-by-step explanation:

cuz , if u added them together the sum would be -2+6=4 , is that ur question? or I've answered smth that has nothing to do?

Choose the solution to the system shown in the table of values.
5)
LINE 1
-2
-1
0
1
2
-1
1
3
5
7
LINE 2
A. (5,5)
B. (0,5)
C. (5,0)
D. (0,7)
1
3
5
7
9
6
4
2
0
-2
3 -2
-1
y-axis
8-
7-
5-
4
3-
2
1
-
-2
2
3
X-ROS

Answers

The solution to the system in given tables of line 1 and line 2, using linear equation is (b) (0,5)

What is linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

from the table of line 1, the equation of line is

y = 2x +5.

from the table of line 2, the equation of line is

y = 5 - x

to find the solution of the system, we compare both of the equation, we get

2x + 5 = 5 - x

add x from both side, we get

3x + 5 = 5

subtract 5 from both side, we get

3x = 0

So that, x = 0

putting the value of x in the equation of line 2

y = 5 - x

y = 5 - 0

y = 5

The solution to the system in given tables of line 1 and line 2 is (0,5)

To learn more about linear equation visit:

brainly.com/question/21835898

#SPJ1

X is the midpoint of UV, Y is the midpoint of UW, and T is the midpoint of VW. If mZU= 56° and mZV=41°, find mZTYW.

Answers

Answer: We know that T is the midpoint of VW, which means that ZW = ZV. So we can say that ZV = ZW = 41°.

Also, we know that Y is the midpoint of UW, so the angle ZYU is half of ZUW. So we can say that ZYU = ZUW/2.

We know that X is the midpoint of UV, so the angle ZXU is half of ZUV. So we can say that ZXU = ZUV/2.

Since Y is the midpoint of UW, ZYU + ZXU = ZUW/2 + ZUV/2 = ZUW/2 + (ZUW - ZXU)/2 = ZUW/2 + (ZUW - ZUV/2)/2 = ZUW/2 + (ZUW - ZUW/2)/2 = ZUW/2 + ZUW/4 = (3/4)ZUW

We know that X is the midpoint of UV, so ZXU + ZVU = ZUV/2 + ZUV = ZUV

The angle ZTYW is supplementary to the angle ZXU + ZVU + ZYU so mZTYW = 180 - ( ZXU + ZVU + ZYU)

Therefore, mZTYW = 180 - ( ZUV + (3/4)ZUW + 41)

mZTYW = 180 - (56 + (3/4)56 + 41) = 180 - (56 + 42 + 41) = 180 - 139 = 41 degrees

Step-by-step explanation:

1. last year, justin and his sister, karin, earned a
total of $468 in allowance. if justin earned $52
more than karin in allowance, write a system of
equations that represents their allowances.

Answers

Answer:

j+k=468

j=52 + j

are the correct equations

there is a linear relationship between the number of chirps made by the striped ground cricket and the air temperature. a least-squares fit of some data collected by a biologist gives fahrenheit. what is the predicted increase in temperature for the model , where x is the number of chirps per minute and is the estimated temperature in d

Answers

The increase in the temperature for an increase of 5 chirps per minute is 41.7 Fahrenheit.

What is Linear relationship?

A Linear relationship, describes a straight-line relationship between two variables.

Given that, There is a linear relationship between the number of chirps made by the striped ground cricket and the air temperature.  A biologist gives the model = 25.2 + 3.3x, where x is the number of chirps per minute.

there is a linear relationship between the number of chirps made by the striped ground cricket and the air temperature. a least-squares fit of some data collected

Here x = 5, putting it in the given model,

Temperature = 25.2 + 3.3 (5) = 41.7 F

Hence, the required prediction of increase in temperature is 41.7 F

For more references on Linear relationship, click;

brainly.com/question/11663530

#SPJ4

–10.9p + 3.9 = –9.18

Answers

Answer:

Step-by-step explanation:

-10.9p + 3.9

-10.9p turns positive.

The (p) is isolated.

10.9 - 3.9= 9.18 = -9.18

Answer

-9.18

Annual Salary: $24,872; personal exemptions: $1,500.
This person is paid semimonthly.
Use the following graduated income tax rates and find the income tax withheld per pay
period.
First $10,000 is 2.75%
Next $15,000 is 3.25%

Answers

If Annual Salary: $24,872; personal exemptions: $1,500.  the income tax withheld per pay is: $29.57 per pay period.

How to find the income tax withheld per day?

Total taxable income = $24,872 - $1,500

Total taxable income = $23,372

The first $10,000 is taxed at a rate of 2.75%.  The tax owed on the first $10,000 is:

$10,000 * 0.0275

= $275.

The remaining $13,372 ($23,372 - $10,000) is taxed at a rate of 3.25%, so the tax owed on this amount is:

$13,372 * 0.0325

= $434.57

The total tax owed is:

$275 + $434.57

= $709.57

Since the person is paid semimonthly, we divide the annual tax owed by 24 to find the tax withheld per pay period:

$709.57 / 24

= $29.57 per pay period

Therefore the income tax withheld per pay is: $29.57 per pay period.

Learn more about income tax withheld per day here:https://brainly.com/question/10020985

#SPJ1

The answer and explanation

Answers

The requried value of 'a' in the given expression is a = -12.

What is simplification?

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,
8⁻⁵⁵ / 8ᵃ = 8⁻⁴³
8ᵃ = 8⁻⁵⁵ / 8⁻⁴³
8ᵃ = 8 ⁻⁵⁵ ⁺ ⁴³
8ᵃ = 8⁻¹²

Taking logs on both sides
a ln 8 = -12 ln 8   [lnbˣ = x lnb]
a = -12

Thus, the requried value of 'a' in the given expression is a = -12.

Learn more about simplification here:

https://brainly.com/question/12501526

#SPJ1


Given:AD,CB,and MD~MB
Prove:Am=Cm
Help pls!

Answers

Answer:

ΔMDA ≅ ΔMBC by ASA

Step-by-step explanation:

Congruent triangles:

∠DMA ≅ ∠BMC          

MD ≅ MB

∠MDA ≅ ∠MBC

Two angles are congruent and the sides in between the congruent angles are equal. So, the two triangles are congruent by Angle Side Angle congruency.

Solve each equation by completing the square
X2+6x+8=0

Answers

Answer:

x = - 2 and x = - 4  

---------------------------------

Given equation:

x² + 6x + 8 = 0

Recall the identity for a square of a sum:

(a + b)² = a² + 2ab + b²

Complete the square by adding the missing part:

x² + 6x + 8 = 0x² + 2*3*x + 8 = 0                                   Missing part is 3²   x² + 2*3*x + 3² + 8 = 3²                          Add 3² to both sides(x + 3)² + 8 = 9                                        Subtract 8 from both sides(x + 3)² = 1                                               Square root both sidesx + 3 = ± 1x = - 3 + 1 and x = -3 - 1                           Add -3 to both sidesx = - 2 and x = - 4                                    Solution

Answer:

x = -2, x = -4

Step-by-step explanation:

Given quadratic equation:

[tex]x^2+6x+8=0[/tex]

Solve by the method of Completing the Square.

Step 1

When completing the square for a quadratic equation in the form ax²+bx+c=0, the first step is to move the constant to the right side of the equation:

[tex]\implies x^2+6x=-8[/tex]

Step 2

Add the square of half the coefficient of the term in x to both sides to form a perfect square trinomial on the left side:

[tex]\implies x^2+6x+\left(\dfrac{6}{2}\right)^2=-8+\left(\dfrac{6}{2}\right)^2[/tex]

Simplify:

[tex]\implies x^2+6x+3^2=-8+3^2[/tex]

[tex]\implies x^2+6x+9=-8+9[/tex]

[tex]\implies x^2+6x+9=1[/tex]

Step 3

Factor the perfect square trinomial on the left side:

[tex]\implies (x+3)^2=1[/tex]

Step 4

Square root both sides:

[tex]\implies \sqrt{(x+3)^2}=\sqrt{1}[/tex]

[tex]\implies x+3=\pm1[/tex]

Step 5

Subtract 3 from both sides:

[tex]\implies x+3-3=\pm1-3[/tex]

[tex]\implies x=-4, -2[/tex]

Solutions

Therefore, the solutions of the given quadratic equation are:

[tex]x=-4, \;\; x=-2[/tex]

Learn more about completing the square here:

https://brainly.com/question/27933930

Pham burgers has beginning net fixed assets of $684,218, ending net fixed assets of $679,426, and depreciation expense of $48,859. What is the net capital spending for the year if the tax rate is 21 percent?.

Answers

If Pham burgers has beginning net fixed assets of $684218 , ending net fixed assets of $679426 and depreciation expense of $48859 , then the net capital spending for the year is $44067  .

For the Pham burgers , the Beginning Net Fixed Assets is = $684218 ;

the ending net fixed assets for Pham burgers is = $679426  ;

the depreciation expense for Pham burgers is = $48859 ;

the tax rate is 21% , which is not relevant for this question ;

The Net capital Spending for the year can be calculated using the formula :

[tex](Ending \; Net \; Fixed \;Assets - Beginning \; Net\; Fixed \; Assets) + Depreciation[/tex] ;

substituting the required values ,

we get ;

Net Capital Spending for year is = ($679426 - $684218) + $48859 ;

On simplifying ,

we get ;

= $44067 .

Therefore , the Net Capital Spending for the year is $44067  .

Learn more about Net Capital Spending here

https://brainly.com/question/17031145

#SPJ4

simplify log10^8-log10^4​

Answers

The simplified form of the expression given is 4.

What are Expressions?

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given is a logarithmic expression.

㏒ 10⁸ - ㏒ 10⁴

We have a rule for logarithms ㏒ aᵇ = b ㏒ a

So the expression becomes,

㏒ 10⁸ - ㏒ 10⁴ = 8 ㏒ (10) - 4 ㏒ (10)

The value of log 10 is 1.

㏒ 10⁸ - ㏒ 10⁴ = 8 - 4 = 4

Hence the expression can be simplified to 4.

Learn more about Expressions here :

https://brainly.com/question/14083225

#SPJ1

A simple random sample of 40 items resulted in a sample mean of 25. The population standard deviation is 5.a. What is the standard error of the mean? round answer to 2 decimal place.b. At 95% confidence, what is the margin of error? round answer to 2 decimal place

Answers

The standard error of the mean 0.79

The margin of error  1.55

The standard error of the mean is one of the components of the margin of error.

The margin of error is the multiplication of standard error of the mean and critical value. Margin of error is denoted by E

sample size, n= 40,

Sample mean,   = 25 and

population standard deviation, [tex]\alpha[/tex]= 5

[tex]SE_{x}[/tex]

The standard error of the mean, [tex]SE_{x}[/tex]

[tex]SE_{x}[/tex] = [tex]\alpha[/tex]/√n

[tex]SE_{x}[/tex] = 5/√40

[tex]SE_{x}[/tex] = 5/6.3246

[tex]SE_{x}[/tex] = 0.79

We have to find the critical value  

[tex]\alpha[/tex]/2 = 0.05/2 = 0.025 is ± 1.96

The margin of error, E

E =  [tex]Z_{\alpha /2 }[/tex] * [tex]SE_{x}[/tex]

E= 1.96×0.79

E= 1.55

The standard error of the mean 0.79

The margin of error  1.55

To know more about standard error visit brainly.com/question/29296846

#SPJ4

What type of triangle has side lengths of 6cm 8cm and 10 cm?

Answers

A triangle with the given side lengths 6cm , 8cm , and 10cm represents a scalene right angled triangle.

As given in the question,

For the given triangle,

Side lengths of the given triangle is equal to :

6cm , 8cm , and 10cm

Longest side length of the given triangle is equal to 10cm.

Apply Pythagoras theorem to check whether the given triangle is right angled triangle or not.

( longest side ) ² = ( side 1)² + ( Side 2)²

Hypotenuse = longest side

Side 1 = base

Side 2 = Altitude

In the given triangle,

10²

= 100

= 36 + 64

= 6² + 8²

which satisfies the condition of Pythagoras triplets.

All the sides are of different measure so it is a scalene triangle.

Therefore, a triangle with given side lengths is a scalene right angles triangle.

Learn more about triangle here

brainly.com/question/2773823

#SPJ4

A bag contain one blue marble and even green marble. What i the probability of picking a blue or green marble?

Answers

50/50 for getting each blue or green marble

Find a vector equation and parametric equations for the line. (Use the parameter t.) The line through the point (0, 15, −9) and parallel to the line x = −1 + 4t, y = 6 − 2t, z = 3 + 9t. r(t)  = . (x(t), y(t), z(t))  = .

Answers

A vector theory and descriptive coefficients for the line are provided by the statement: r(t) = 0,15,-9> +t4,-2,9>.

What is a class 12 vector?

There are different quantities, which include direction and magnitude. If the quantity has both magnitude and direction, it is said to be a vector. These are referred to as vector quantities. Examples include displacement, speed, acceleration, energy, weight, impetus, and electric intensity. Consequently, the vector quantity is and the SI unit for it is m/s².

The given line is-

x = -1+4t, y = 6-2t, z = 3+9t

That is,

r(t) = <-1+4t, 6-2t, 3+9t> = < -1,6,3> +t<4, -2,9>

The line concurrent to the given line's direction vector is

u = <4,-2,9>

Equation for line going through point (x0,y0,z0) and has direction vector u is line passing through point (0,15,-9)

r(t) = < x0, y0,z0> +tu

That is

r(t) = <0,15, -9> +t<4,-2,9>

To know more about Vector visit:

https://brainly.com/question/15519257

#SPJ4

amar keeps picking playing cards out of a standard deck of 52 cards in the hopes that he will draw a spade there are 13 spades in the deck after looking at each card he places it back in the deck what is probability that amar will draw a spade in the first five attempts

Answers

The probability of Amar drawing a spade in the first five attempts is approximately 24.5%, as there are 13 spades in a deck of 52 cards.

The probability of drawing a spade in the first attempt is 13/52 or 25%.

The probability of drawing a spade in the second attempt is 12/51 or 23.5%.

The probability of drawing a spade in the third attempt is 11/50 or 22%.

The probability of drawing a spade in the fourth attempt is 10/49 or 20.4%.

The probability of drawing a spade in the fifth attempt is 9/48 or 18.8%.

The total probability of drawing a spade in the first five attempts is the sum of the above probabilities, which is 24.5%.

The probability of drawing a spade in the first five attempts is 24.5%, calculated by summing the separate probabilities.

Learn more about probability here

https://brainly.com/question/11234923

#SPJ4

A scale model of a house uses a scale 14
inch = 3 feet. If the model is 4.25
inches tall, what is the actual height of the
house?

Answers

The actual height of the house is 0.910 feet.

What is Scale factor?

When both the original dimensions and the new dimensions are known, the scale factor may be determined. When employing the scale factor, there are two terms that must be understood. When a figure's size is increased, we refer to this as scaling up, and when its size is decreased, we refer to this as scaling down.

Given:

Scale : 14 inch = 3 feet

So, 1 inch is represented by

= 3/14

So, 4.25 inch represented as

= 3/14 x 4.25

= 0.910 feet

Hence, the actual height is 0.910 feet.

Learn more about Scale factor here:

https://brainly.com/question/21405304

#SPJ1

Pls help almost due ​

Answers

Answer:

y = -0.5x + 5.5

Step-by-step explanation:

A linear function can be represented in the form of y = mx + b, where m is the slope and b is the y-intercept. The slope of a line is the ratio of the change in y to the change in x (rise over run) and the y-intercept is the point where the line crosses the y-axis.

To find the rule for this linear function, we can use the two points (x1, y1) and (x2, y2) to find the slope m:

m = (y2 - y1) / (x2 - x1)

If we use the points (7, 2) and (5, 3) to find the slope, we have:

m = (3 - 2) / (5 - 7) = 1 / (-2) = -0.5

We can also use the point (x1, y1) to find the y-intercept b:

b = y1 - m * x1

If we use the point (7, 2) to find the y-intercept, we have:

b = 2 - (-0.5) * 7 = 2 + 3.5 = 5.5

So the rule for the linear function is:

y = -0.5x + 5.5

We can confirm this rule by checking the point (x=-1,y=6)

y = -0.5(-1) + 5.5 = 6

Find the sum of 5.2 c -7 and -3.9c + 8.5 what is the sum

Answers

Answer:

1.3 * c + 1.5

Step-by-step explanation:

(5.2c-7) + (-3.9c + 8.5)

5.2 * c - 7 - 3.9 * c + 8.5

1. add constants ( - 7 and 8.5)

5.2 * c - 3.9 * c + 1.5

2. add both of the coefficients of c

when a variable is multiplied by a coefficient, we can add another coefficient * variable combination if the variable is the same. for example, 1 * x + 2 * x = 3 * x by adding the 1 and 2 together

similarly, 5.2 * c - 3.9 * c = (5.2 - 3.9) * c = 1.3 * c

1.3 * c + 1.5

Identify a quadratic function that fits the points (−3, −7),(0, −4), and (2, −12).

Answers

By solving a system of equations we will see that the quadratic equation is:

y = 3*x^2 - 10*x - 4

Which system of equations has the given points?

We know that a general quadratic function can be written as:

y = a*x^2 + b*x + c

Here we know that the equation passes through (0, -4), replacing these values:

-4 = a*0^2 + b*0 + c

-4 = c

Then the quadratic equation is:

y = a*x^2 + b*x - 4

Now we can use the other two points (-3, -7) and (2, -12), replacing these values we will get a system of equations:

-7 = a*(-3)^2 + b*(-3) - 4

-12 = a*(2)^2 + b*(2) - 4

We can simplify these equations to get:

-3 = 9a + 3b

-8 = 4a + 2b

We can isolate b on the second equation to get:

2b + 4a = -8

2b = -8 - 4a

b = (-8 - 4a)/2

b = -4 - 2a

Now we can replace that in the other equation to get:

-3 = 9a + 3*(-4 - 2a)

-3 = 9a -12 - 6a

-3 + 12 = 3a

9 = 3a

9/3 = a

3 = a

And the value of b is:

b = -4 - 2a

b = -4 - 2*3

b = -4 - 6 = -10

Then the quadratic equation is:

y = 3*x^2 - 10*x - 4

Learn more about systems of equations at:

https://brainly.com/question/13729904

#SPJ1

(02.04 HC)
Two functions are given below: f(x) and h(x). State the axis of symmetry for each function and explain how to find it.
f(x)
f(x) = -2(x-4)2 +2
X
-4-3-2
h(x)
Ñ

Answers

For [tex]f(x)[/tex], the axis of symmetry is the vertical line passing through the vertex. Matching with vertex form, we see the vertex of the graph of [tex]f(x)[/tex] has coordinates [tex](4,2)[/tex]. Thus, the axis of symmetry has equation [tex]x=4[/tex].

Similarly, for [tex]h(x)[/tex], the axis of symmetry is the vertical line passing through the vertex. The vertex of the graph of a quadratic function is either the minimum or maximum point (it depends on the leading coefficient of the function). Here, there is a maximum point, which has coordinates [tex](-2,2)[/tex]. Thus, the axis of symmetry has equation [tex]x=-2[/tex].

Find the value of (x − 6)² if x² – 12x = 30, and x > 0.

plsss answer ​

Answers

Answer:

65.9

Step-by-step explanation:

The equation x² – 12x = 30 (x>0) promises that we can determine possible values of x if we solve the equation.  So let's start there:

We can factor the equation or solve it with the quadratic equation.

Factor

  x² – 12x = 30

  x² – 12x - 30 = 0

I don't see an easy factor solution.  One possibility is to first rewrite the equation as

  (x-12)x-30 = 0

  (x-6)^2 - 66 = 0

 -(-x+[tex]\sqrt66}[/tex]+6)(x+[tex]\sqrt{66}[/tex]-6)

The roots are:

x = 6-[tex]\sqrt{66}[/tex] and

x = 6+[tex]\sqrt{66}[/tex]

Since x>0, only the second root is valid:  x = 6+[tex]\sqrt{66}[/tex]

x = 6 + (8.12)

x = 14.12

[That was painful]

Quadratic Equation

Solving with the quadratic equation gives values of:

14.12, and -2.12  Again, only the positive value is valid:  14.12

[The quadratic approach was far easier than factoring, in this case]

==

Since we established x = 14.12, (x − 6)² bcomes:

  (14.12 − 6)²

 (8.12)² = 65.9

 

Find the length of AG

Answers

Answer:

58.27 mm (2 d.p.)

Step-by-step explanation:

Assuming the given prism is a rectangular prism, triangles ADC and ACG are right triangles.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Cos trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

AC is the hypotenuse of right triangle ADC.  

Therefore, we can use the cos trigonometric ratio to create an expression for the length of AC:

[tex]\implies \cos\left(36^{\circ}\right)=\dfrac{AD}{AC}[/tex]

[tex]\implies \cos\left(36^{\circ}\right)=\dfrac{42}{AC}[/tex]

[tex]\implies AC=\dfrac{42}{\cos\left(36^{\circ}\right)}[/tex]

AC is the hypotenuse of right triangle ACG.  

Therefore, we can use the cos trigonometric ratio to create an expression for the length of AG:

[tex]\implies \cos\left(27^{\circ}\right)=\dfrac{AC}{AG}[/tex]

[tex]\implies AG=\dfrac{AC}{\cos\left(27^{\circ}\right)}[/tex]

To find the length of AG, substitute the found expression for AC into the expression for AG:

[tex]\implies AG=\dfrac{\frac{42}{\cos\left(36^{\circ}\right)}}{\cos\left(27^{\circ}\right)}[/tex]

[tex]\implies AG=\dfrac{42}{\cos\left(36^{\circ}\right)} \times \dfrac{1}{\cos\left(27^{\circ}\right)}[/tex]

[tex]\implies AG=\dfrac{42}{\cos\left(36^{\circ}\right)\cos\left(27^{\circ}\right)}[/tex]

[tex]\implies AG=58.2654039...[/tex]

[tex]\implies AG=58.27\;\sf mm \;(2\;d.p.)[/tex]

Other Questions
Is body language important in public speaking? What does the sky do in the morning. a pregnant woman who is at 38 weeks' gestation arrives at the emergency department. she reports the presence of bright red vaginal bleeding and denies the presence of any pain. based on this information, what does the nurse determine the client may be experiencing? What is the most common use of land in the Pontotoc Ridge region? O cotton fields O fruit orchards O timberlands O peanut farms work out the area of this shape which of the following statements about inventory management is/are true? multiple select question. one of the goals is to achieve good customer service. the decision when to order need not be made, it's automated in the system. one of the goals is to keep inventory costs within reasonable bounds. excess inventory is preferable to too little inventory. inventory managers must decide how much to order. Which Russian leader does Napoleon most resemble? Write a disassociation equation for each of the following(Also please write an explanation on how you did it) How does Stevenson create an unnerving sense of horror at the start of chapter 4? how does perseus express his concern about the journey? You purchae a computer for $1999. 99 plu 7% ale tax. The electronic tore offer an intallment loan that allow you to pay for the computer by making 12 equal monthly payment of $203. 30. What i the cot of credit, in dollar, for thi loan? our water polo team has 15 members. i want to choose a starting team consisting of 7 players, one of whom will be the goalie (the other six positions are interchangeable, so the order in which they are chosen doesn't matter). in how many ways can i choose my starting team? 37) Kelly opened a bank account that earns 1.2% simple interest each year. After 7 years, Kelly will earn $126 in interest. How much did Kelly deposit when she opened the account? _ What were the 3 main reasons for European imperialism in Africa? A botanist is studying the growth of the sequoia tree. He selects one sequoia tree and records its hight each year. What is the equation of the line in slope-intercept form? Define your variables. Show your work when a buyer hands over an earnest money check to you as the buyer's agent, what's your responsibility? Select the correct answer.Which type of investment offers both capital gains and interest income?. property B. CDsC. stocksD. bonds calculate the net price factor and net price (in dollars). for convenience, round the net price factor to five decimal places and the net price to the nearest cent, when necessary. list price trade discount rate net price factor net price $0.49 20/9/4 0.83333 incorrect: your answer is incorrect. $ 0.41 incorrect: your answer is incorrect. Complete this table relating the values of Ecell and G to the Q/K ratioQ/KEcellG1Drag these labels into table as appropriate:>0, =0, in most markets, the variety and assortment of breakfast cereals available exceeds the amount that can be consumed by customers. this leads to greater and more effective competition among breakfast cereal producers. this scenario demonstrates the . multiple choice question.