(3a+b)³ please help me​

The equation of the plane passing through (0, -3,1) that is orthogonal to the planes 3x + 2y - 4z = 0 and - X+ 2y + 4z = 7 is 16x - 8y + 8z = 32

We know that the equation of plane passing through point (x₁, y₁, z₁) is given by,

A(x - x₁) + B(y - y₁) + C(z - z₁) = 0

where, A, B, and C are direction ratios

In the question,  the plane passes through point (0, -3,1)

Let (x₁, y₁, z₁)  = (0, -3,1)

Using above formula the equation of the plane will be in the form,

A(x -0) + B(y - (-3))+C(z - 1) = 0            

Ax + B(y + 3)+C(z - 1) = 0                   ..........(1)

The required plane is orthogonal to the planes 3x + 2y - 4z = 0 and - X+ 2y + 4z = 7.

So, their normal to the required plane would be perpendicular to the normal of both the planes.

The normal to the required plane is a cross-product of the normals of planes.

A cross-product of the normals of planes 3x + 2y - 4z = 0 and - X+ 2y + 4z = 7 is 16i - 8j + 8k

So, the direction ratios,

A = 16, B = -8, C = 8

So equation (1) becomes,

16x - 8(y + 3) + 8(z - 1) = 0  

16x - 8y - 24 + 8z - 8 = 0

16x - 8y + 8z - 32 = 0 is the required equation of the plane

Learn more about the equation of the plane here:

https://brainly.com/question/27190150

#SPJ4

Answer:

m reprecents $100

Hope this helps

The smallest positive integer that begins with the digit 1 when written in base 10 and is tripled when the 1 is transferred to the end is 12.

To solve this problem, we need to use some algebraic equations. Let's represent the positive integer as "x" and write it in base 10 as 10a+b, where a and b are digits. We know that x begins with the digit 1, so a must be 1.

Now we transfer the digit 1 to the end of the number, making it 10b+1. We also know that when we triple this number, we get 3(10b+1) = 30b+3x.

Setting this equal to our original number, 10a+b=x, we get the equation 30b+3x=10a+b. Substituting a=1, we can simplify this to 27b=7+x.

We want to find the smallest integer that satisfies this equation, so we start by setting x=1 and solving for b. We get b=2, which means our original number was 12.

For more about integer:

https://brainly.com/question/15276410

#SPJ11

Using the properties of similar triangles and ratio and proportion we get the vale of x as 2.8 units.

In the given figure the triangle ΔKFG and ΔFJH

KG is parallel to JH

Hence ΔKFG is similar to ΔFJH

Now using the property of similarity and proportion we can say that:

FG/FH = KF/JF

putting the values in the above proportion we get:

7 /(7+x) = 5/ 7

or, 49 = 35 +5 x

or, 14 = 5x

or, x =14/5

or, x = 2.8

The majority of ratio and percentage explanations involve using fractions.

A proportion states that two variables are equal, whereas a ratio is a fraction that is written as a:b. The two ratios given are equal to one another, as demonstrated by the proportional equation.

Hence the value of x is 2.8 units.

To learn more about proportion visit:

https://brainly.com/question/21570782

#SPJ9

-78

Step-by-step explanation:

(7-8)(78)

(-1)(78)=-78

Answer:

5xy^2

Step-by-step explanation:

Answer:

Brooklyn would get paid 16.30 hourly. So she will have to work 15 hours the next week to earn 244.50.

Step-by-step explanation:

Divide 179.30 by 11 and you would get 16.30 which is her hourly wage. Then you divide 244.50 by 16.30 to see how many hours she would have to work to earn 244.50.

Answer:

15 Hours

Step-by-step explanation:

179.30 / 11 = $16.3 an hour

244.5 / 16.3 = 15 hours

The point of concurrency of the altitudes of a triangle is called the orthocenter.

The orthocenter is the intersection point of the three altitudes of a triangle. An altitude is a line segment drawn from a vertex of a triangle perpendicular to the opposite side. The altitudes of a triangle can intersect inside, outside, or on the triangle itself. When they intersect, the point of intersection is the orthocenter. The orthocenter plays an important role in triangle geometry and has several interesting properties. For example, it is always inside an acute triangle, outside an obtuse triangle, and on a right triangle's vertex. It is also the center of symmetry for the triangle's circumcenter and is related to the triangle's Euler line. The orthocenter is a key point that helps define and analyze various geometric properties and relationships within a triangle.

learn more about  point of concurrency here

brainly.com/question/29774114

#SPJ11

The combined present worth of the costs associated with the proposed bridge design, including construction and annual operating costs, is $10,583,333.

To calculate the combined present worth of costs, we need to consider the construction cost and the annual operating cost over the infinite life of the bridge. We will use the concept of present worth, which is the equivalent value of future costs in today's dollars.

The present worth of the construction cost is simply the initial cost itself, which is $9,000,000. This cost is already in present value terms.

For the annual operating cost, we need to calculate the present worth of perpetuity. A perpetuity is a series of equal payments that continue indefinitely. In this case, the annual operating cost of $700,000 represents an equal payment.

To calculate the present worth of the perpetuity, we can use the formula PW = A / MARR,

where PW is the present worth, A is the annual payment, and MARR is the minimum attractive rate of return (also known as the discount rate). Here, the MARR is given as 12%.

Plugging in the values, we have PW = $700,000 / 0.12 = $5,833,333.

Adding the present worth of the construction cost and the present worth of the perpetuity, we get $9,000,000 + $5,833,333 = $14,833,333.

However, since we are looking for the combined present worth, we need to subtract the salvage value, which is zero in this case. Therefore, the combined present worth of the costs associated with the proposed bridge design is $14,833,333 - $4,250,000 = $10,583,333, rounded to the nearest dollar.

Learn more about present worth here:

https://brainly.com/question/14962478

#SPJ11

On solving the equations by elimination method, the value of x is 4 and y is -8.

'The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with multiplication or division of coefficients of the variables.'

According to the given problem,

Given equations = 2x - 2y =  24   (1)

                               4x + 7y = -40  (2)

Now, Multiplying equation (1) with 2,

⇒ 2( 2x - 2y ) = 2 × 24

⇒ 4x - 4y = 48  (3)

Now subtracting Equation (3) from equation (1),

⇒  4x + 7y - (4x - 4y) = -40 - 48

⇒ 4x + 7y - 4x + 4y = -88

⇒ 11y = -88

⇒ y = -8

Now, putting value of y in equation (1),

⇒ 2x - 2(-8) =  24

⇒ 2x + 16 = 24

⇒ 2x = 24 - 16

⇒ 2x = 8

⇒ x = 4

Hence, we can conclude the value of x = 4 and y = -11 by elimination method.

Learn more about elimination method here:

https://brainly.com/question/14619835

#SPJ2

Answer:

p = 22/5

Step-by-step explanation:

50p+5=225

Subtract 5 from each side

50p+5-5=225-5

50p = 220

Divide by 50

50p/50 = 220/50

p = 22/5

Answer:

50p+5=225

(50p+5) + (-5) =225 + (-5)

50p + 5 - 5 = 225 - 5

50p = 220

(fraction: 50p/50 = fraction: 220/50)

Sorry but you need to finish it because i cant do exponits sorry...

Answer:

42,195

Step-by-step explanation:

The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

Given a function:

f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6

where c is a constant.

The solution to the question is shown below.

Step 1: We have given a function:

f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6

We have to find the number of words we have to write to express this function in words.

Step 2: Solution

f(t) = et5+4t + ln(t²+3c)⁷ +te-1+5e⁶

Where,

et5+4t = exponential function

ln(t²+3c)⁷ = natural logarithmic function

te-1 = linear function

e⁶ = exponential function

Therefore, f(t) can be expressed in words as:

The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

Step 3: Conclusion

Hence, the function f(t) can be expressed in words with:The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

To know more about natural logarithm visit:

https://brainly.com/question/29154694

#SPJ11

The answer is 208 4/25 or if you need decimal form 208.16

answer is

\(208 \frac{4}{25} \)

in decimal form.. it will be,

\(208.16\)

Answers:

For original triangle, perimeter is 60. The area is 120.

The dilated triangle, perimeter is 180. The area is 1080.

Step-by-step explanation:

24 times 3=72

10 times 3=30

26 times 3=78

72+30+78=180

Perimeter of diliated triangle

1/2btimesh=area

1/2 30 times 72=1080 square units

Perimeter of original triangle

24+10+26=60 units

1/2 10 times 24=120 square units

From the picture attached,

Measure of the base of the small right triangle = 10 units

Height of the triangle = 24 units

Measure of the Hypotenuse = 26 units

Since, Perimeter of the triangle = Sum of the measures of the sides of the triangle

Therefore, Perimeter = 10 + 24 + 26

                                   = 60 units

Area of the triangle = \(\frac{1}{2}(\text{Base})(\text{Height})\)

                                 = \(\frac{1}{2}(10)(24)\)

                                 = 120 units²

Given triangle is dilated by a scale factor of 3 to form the bigger triangle,

Scale factor = 3

Since, expression for the scale factor is given by,

Scale factor = \(\frac{\text{Dimension of the image}}{\text{Dimension of the original}}\)

Therefore, length of the base of the dilated (bigger) triangle will be,

\(3=\frac{\text{Measure of the base of the original}}{10}\)

Measure of the base of the original = 30 units

Height of the dilated triangle will be,

\(3=\frac{\text{Height of the dilated triangle}}{24}\)

Height = 24 × 3

            = 72 cm

Hypotenuse of the dilated triangle will be,

\(3=\frac{\text{Hypotenuse of the dilated triangle}}{26}\)

Hypotenuse = 78 cm

Now the perimeter of the dilated triangle = 30 + 72 + 78

                                                                     = 180 cm

Area of the dilated triangle = \(\frac{1}{2}(30)(72)\)

                                             = 1080 cm²

Learn more,

https://brainly.com/question/8517549

The probability that an arriving student will find at least one other student waiting in line is approximately 0.167.

To solve this problem, we'll use the M/M/1 queueing model with Poisson arrivals and exponential service times. Let's calculate the required values: (a) Percentage of time Judy is idle: The utilization of the system (ρ) is the ratio of the average service time to the average interarrival time. In this case, the average service time is 10 minutes, and the average interarrival time is 12 minutes. Utilization (ρ) = Average service time / Average interarrival time = 10 / 12 = 5/6 ≈ 0.8333

The percentage of time Judy is idle is given by (1 - ρ) multiplied by 100: Idle percentage = (1 - 0.8333) * 100 ≈ 16.67%. Therefore, Judy is idle approximately 16.67% of the time. (b) Average waiting time for a student:

The average waiting time in a queue (Wq) can be calculated using Little's Law: Wq = Lq / λ, where Lq is the average number of customers in the queue and λ is the arrival rate. In this case, λ (arrival rate) = 1 customer per 12 minutes, and Lq can be calculated using the queuing formula: Lq = ρ^2 / (1 - ρ). Plugging in the values: Lq = (5/6)^2 / (1 - 5/6) = 25/6 ≈ 4.17 customers Wq = Lq / λ = 4.17 / (1/12) = 50 minutes. Therefore, on average, a student spends approximately 50 minutes waiting in line.

(c) Average length of the line: The average number of customers in the system (L) can be calculated using Little's Law: L = λ * W, where W is the average time a customer spends in the system. In this case, λ (arrival rate) = 1 customer per 12 minutes, and W can be calculated as W = Wq + 1/μ, where μ is the service rate (1/10 customers per minute). Plugging in the values: W = 50 + 1/ (1/10) = 50 + 10 = 60 minutes. L = λ * W = (1/12) * 60 = 5 customers. Therefore, on average, the line consists of approximately 5 customers.

(d) Probability of finding at least one student waiting in line: The probability that an arriving student finds at least one other student waiting in line is equal to the probability that the system is not empty. The probability that the system is not empty (P0) can be calculated using the formula: P0 = 1 - ρ, where ρ is the utilization. Plugging in the values:

P0 = 1 - 0.8333 ≈ 0.1667. Therefore, the probability that an arriving student will find at least one other student waiting in line is approximately 0.167.

To learn more about Probability, click here: brainly.com/question/16988487

#SPJ11

Answer:

Im pretty sure its just giving you the steps on how to solve things like that! If not, then im not sure

Step-by-step explanation:

Hope this helped!

-Akito

Answer:

0

Step-by-step explanation:

As x aproaches a, (x-a) will aproach 0, so the numerator will aproach 0, and because 0 divided by anything=0, the whole function will become 0. So, the answer is 0.

The probability that the tosses are all the same is 1/2^n, where n is the number of tosses.

This is because the probability of each toss being the same is 1/2 (heads or tails). So the probability of all three tosses being the same is the product of the probabilities of the individual tosses:

1/2 * 1/2 * 1/2 = 1/2^3 = 1/8.

The reason for this is that the probability of each toss being the same is independent of the others. That is, the result of one toss does not affect the result of another toss.

As a result, the probability of all tosses being the same is the product of the probabilities of the individual tosses.

In summary, the probability of all tosses being the same is 1/2^n, where n is the number of tosses.

To know more about probability refer here:

https://brainly.com/question/30034780

#SPJ11

a) Both functions 3x + 7 and x are of the same order, which is the first order or linear order. (a) is the correct option.

In order to determine if two functions are of the same order, we compare their growth rates as the input approaches infinity. If the ratio of the two functions approaches a constant value, then they are of the same order.

a) For the functions 3x + 7 and x, as x approaches infinity, the ratio (3x + 7) / x approaches 3. Therefore, they are of the same order, which is the first order or linear order.

b) The functions 2x^2 + x - 7 and x^2 are of the same order, which is the second order or quadratic order.

c) The functions x + 1/2 and x are of the same order, which is the first order or linear order.

d) The functions log(x^2 + 1) and log2 x are of the same order, which is the logarithmic order.

e) The functions log10 x and log2 x are of the same order, which is the logarithmic order.

In each case, we determine the limit of the ratio of the two functions as the input approaches infinity. If the limit is a constant value, then the functions are of the same order. The order represents the growth rate or complexity of the functions as the input size increases.

To know more about logarithmic click here

brainly.com/question/31117877

#SPJ11

Around 1950, family sociologists described a standard marriage pattern at about age 20 for women and age a) 22 for men.

The standard marriage pattern today, based on the time a couple marries, is mid-to-late twenties.  Some marriages are contracted very late, with some in the forties.

Sociologists have pointed out that the current delay in marriages is caused by the higher priority placed on education and career by youths.

However, marriage patterns based on the type of arrangement include:

Traditionally, marriages have served two societal purposes:

Thus, around 1950, family sociologists described a standard marriage pattern at about age 20 for women and age  22 for men.

Learn more about marriages at https://brainly.com/question/15522379

#SPJ4

Answer:

LET ME KNOW WHEN U GET THE ANSWERR

Step-by-step explanation:

Answer:

Scale Factor = 0.75

Step-by-step explanation:

The dilated object (image) has coordinates given as:

X' (-6, -1.5)

Y' (0, -4.5)

Z' (-9, -9)

The coordinates of the object (the initial) as read from the graph are given by:

X (-8, -2)

Y(0, -6)

Z (-12, -12)

To get the scale factor, we will compare the coordinates of the image to the initial object.

Kindly note that the image is the triangle in red

while the object is the triangle in black

Comparing the X' and X coordinates

\(for \: the \: x - coordinte \\ \\ \frac{ - 6}{ - 8} = \frac{3}{4} \\ \\ for \: the \: y - \:coordinate \\ \\ \frac{ - 1.5}{ - 2} = \frac{3}{4} \)

Similarly, if we compare Y' and Y and also Z' and Z

The scale factor is:

\(scale \: factor \: = \frac{3}{4} = 0.75\)

Given:

Total number of people surveyed = 205

a) Percentage of the survey respondents that do not like both hamburgers and burritos.

Number of people that do not like both = 54

To find the percentage of the respondents that do not like both, we have:

Therefore, the percentage of the survey respondents that do not like both hamburgers and burritos is 26.3%

b) Marginal relative frequency of all customers that like hambugers.

Given:

Number of customers that like hamburgers = 110

To find the marginal relative frequency, we have:

The marginal relative frequency of all customers that like hambugers is 54%

c) Conditional relative frequencies:

i) Conditional relative frequency that a person likes hamburgers given that the person does not like burritos:

ii) Conditional relative frequency that a person likes burritos, given that the person does not like hamburgers:

Answer:

Step-by-step explanation:

5x +2.57=25.92

5x=23.35

23.35/5

x=4.67

The ordered pairs for the system of equations f(x) = x^2 -2x + 3 and f(x) = -2x + 12 are (3, 6) and (-3, 18)

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term. The first condition for an equation to be a quadratic equation is the coefficient of x2 is a non-zero term(a ≠ 0)

f(x) = x^2 -2x +3 and f(x) = -2x + 12

which means

x^2 -2x +3  = -2x + 12

x^2 -2x +3  + 2x - 12 = 0

x^2 -9 = 0

by factorizing we have

(x-3)(x+3) = 0

x = 3 or -3

when x = 3

f(x) = -2x + 12

f(3) = -2(3) + 12 which is 6

when x = -3

f(-3) = -2(-3) + 12 which is 18

ordered pairs are (3, 6) and (-3, 18)

In conclusion, (3, 6) and (-3, 18) are the ordered pairs

Learn more about Quadratic equation: https://brainly.com/24334139

#SPJ1

Answer:

thats tough

Step-by-step explanation:

Answer:

3rd one

Step-by-step explanation:

12

The term "element" refers to a well-defined group of objects or substances that share common characteristics.

In the context of chemistry, elements are the fundamental building blocks of matter, consisting of atoms that possess a specific number of protons in their nucleus. Each element is unique, with distinct physical and chemical properties that distinguish it from other elements.

The periodic table of elements is a widely recognized tool for organizing elements based on their atomic structure and properties. The periodic table displays the elements in order of increasing atomic number, with elements that share similar properties arranged in the same vertical column, or group.

The properties of elements can be studied and manipulated in various ways, leading to their use in a wide range of applications, from medicine to electronics to energy production. By understanding the unique characteristics of each element, scientists can better understand the natural world and develop new technologies that benefit society.

To learn more about element

https://brainly.com/question/13025901

#SPJ4

Step-by-step explanation:

Principal Amount = $150,000

Rate of appreciation per year = 6%

Appreciated amount = $150,000×6/100

= 6×1500 = $9,000 per year

in 7 years(2020) , the appreciated amount becomes = $9000×7yrs

= $63,000

Thus the value in 2020 = $150,000+$63,000

= $213,000