Find the vector equation for the line of intersection of the planes 3x + 3y + z = 4 and 3x + 5z = -3 r= (________,________,0) + t(15,________,________)

The required step that is not usually a problem-solving step that use to help to find the right answer is to write the question (given data).

Given that,
When tackling a difficult question, which is NOT usually a problem-solving step that you use to help you find the right answer is to be justified.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
Step of the solution,
Step 1 = To write given data
Step 2 = approch
Step 3 = calculation
Step 4 = answer

Thus, The required step that is not usually a problem-solving step that use to htp to find the right answer is to write the question (given data).

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Answer:

c. Write a definition

Step-by-step explanation:

Jessica gets more rocks to skip across the surface of the pond than Henry.

To determine who gets more rocks to skip across the surface of the pond, we will take the ratio of rocks that skip to rocks that are thrown for each person.

For Henry, the ratio is 5 rocks that skip to 9 rocks thrown i.e 5/9.

For Jessica, the ratio is 7 rocks that skip to 12 rocks thrown i.e 7/12.

Now to compare the ratios, we need to convert them into like fractions. We will do this by making the denominations of both the fractions same.

We will multiply the numerator and denominator of Henry's ratio by 12 to get -

5/9 x 12/12 = 60/108

Also, we will multiply the numerator and denominator of Jessica's ratio by 9 to get -

7/12 x 9/9 = 63/108

Comparing the numerators we get 60<63.

This implies that 60/108 < 63/108.

Therefore, Jessica gets more rocks to skip across the surface of the pond.

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The complete question is -

Henry and Jessica skipping rocks across the surface of a pond. For every nine rocks Henry throws he got five of them to skip across the pond. For every twelve rocks

Jessica throws she got seven of them to skip across the pond. Who gets more rocks to skip across the surface of the pond​?

The number of people died from aids in U.S. in 2005 are 2,30,68,96,671

Given, diseases tend to spread according to the exponential growth model.

In the early days of aids, the growth factor (i.e. common ratio; growth multiplier) was around 1.9.

In 1983, about 1700 people in the U.S. died of aids.

we have to find the number of people died from aids in 2005.

Let the exponential function, be

P(x) = AB^x

where, A is the initial population of people died of aids in U.S.

B is the growth factor of aids in U.S.

as, B = 1.9

In 1983, x = 0

P(0) = AB^0

1700 = A

Now, P(x) = 1700(1.9)^x

and the number of years from 1983 to 2005 are, 22 years

The number of people died from aids in 2005 be,

P(22) = 1700(1.9)^22

P(22) = 2,30,68,96,671

So, 2,30,68,96,671 people died from aids in 2005.

Hence, 2,30,68,96,671 people died from aids in 2005.

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Answer:

y=½x-6

Step-by-step explanation:

m= ½

equation of the line: y-y1=m(x-x1)

y+5=½(x-2)

y=½x-6

Answer:

\(y =\dfrac{1}{2}x-6\)

Step-by-step explanation:

Point-slope formula

\(y-y_1=m(x-x_1)\)

where:

Given:

Substitute the given values into the formula:

\(\begin{aligned}y-y_1 & =m(x-x_1)\\\\\implies y-(-5) & =\dfrac{1}{2}(x-2)\\\\y+5 & =\dfrac{1}{2}x-1\\\\y & =\dfrac{1}{2}x-1-5\\\\y & =\dfrac{1}{2}x-6\end{aligned}\)

The missing number of points scored in the last basketball game is 13.

What is the meaning of the data set?

A data set is a grouping of data. A data set refers to one or more database tables in the case of tabular data, where each column of a table represents a specific variable and each row corresponds to a specific record of the data set in question.

Given that,

the number of points scored in the last basketball game by each player on the Dragons basketball team are 7, 5,8,11,7,5,?.

Assume that the missing point is x.

The sum of points is 7+5+8+11+7+5+x = 43 + x.

The number of points is 7.

The mean is the sum of points/number of points

= (43+x)/7

Given that the mean of the data set is 8 points.

Therefore,

(43+x)/7 = 8

Multiply both sides by 7:

43+x = 8×7

43 + x = 56

x = 56 - 43

x = 13

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A customer can select the meal in 960 ways

Permutations: The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a permutation is a term that refers to a variety of possible arrangements or orders. With permutations, the arrangement's sequence is important. Permutations come in three varieties, one without repetition and two with repetition. In contrast to combinations, where data is selected from a group and the order is irrelevant, permutations choose data from a group.

Number of appetizers offered = 6

Number of salads offered = 4

Number of entrees offered = 8

Number of desserts offered = 5

Total number of choices = 6*4*8*5 = 960 ways

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Answer:

I dont know what letter but its 12i^2+i+6

Step-by-step explanation:

cross multiply

The first derivatives for the given functions are:

For \(y = 3x^2 + 5x + 10,\) the first derivative is dy/dx = 6x + 5.

For  \(y = 100200x + 7x,\) the first derivative is dy/dx = 100207.

For \(y = ln(9x^4),\) the first derivative is dy/dx = 4/x.

To find the first derivative for each of the given functions, we'll use the power rule, constant rule, and chain rule as needed.

For the function\(y = 3x^2 + 5x + 10:\)

Taking the derivative term by term:

\(d/dx (3x^2) = 6x\)

d/dx (5x) = 5

d/dx (10) = 0

Therefore, the first derivative is:

dy/dx = 6x + 5

For the function y = 100200x + 7x:

Taking the derivative term by term:

d/dx (100200x) = 100200

d/dx (7x) = 7

Therefore, the first derivative is:

dy/dx = 100200 + 7 = 100207

For the function \(y = ln(9x^4):\)

Using the chain rule, the derivative of ln(u) is du/dx divided by u:

dy/dx = (1/u) \(\times\) du/dx

Let's differentiate the function using the chain rule:

\(u = 9x^4\)

\(du/dx = d/dx (9x^4) = 36x^3\)

Now, substitute the values back into the derivative formula:

\(dy/dx = (1/u) \times du/dx = (1/(9x^4)) \times (36x^3) = 36x^3 / (9x^4) = 4/x\)

Therefore, the first derivative is:

dy/dx = 4/x

To summarize:

For \(y = 3x^2 + 5x + 10,\) the first derivative is dy/dx = 6x + 5.

For y = 100200x + 7x, the first derivative is dy/dx = 100207.

For\(y = ln(9x^4),\) the first derivative is dy/dx = 4/x.

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Step-by-step explanation:

121630....................................

Answer:

there isn't any pictur

Step-by-step explanation:

Answer:

a. 5.6

b. 38.4

c. 8.25

d. 24

Step-by-step explanation:

To calculate the probability that at least two people in a class of 30 share the same birthday, we can use the complement rule, which states that the probability of an event happening is equal to one minus the probability of the event not happening.

If we assume that birthdays are uniformly distributed throughout the year (i.e., each day is equally likely to be someone's birthday), then the probability that no two people in the class share the same birthday is:

365/365 * 364/365 * 363/365 * ... * 336/365

This is because the first person can have any birthday (probability of 365/365), the second person must have a different birthday (probability of 364/365), the third person must have a different birthday than the first two (probability of 363/365), and so on, up to the 30th person, who must have a different birthday than the first 29 (probability of 336/365).

Calculating this probability gives us:

(365/365) * (364/365) * (363/365) * ... * (336/365) ≈ 0.2937

So the probability that no two people in the class share the same birthday is approximately 0.2937.

Using the complement rule, the probability that at least two people in the class share the same birthday is:

1 - 0.2937 = 0.7063

Therefore, the probability that at least two people in a class of 30 share the same birthday is approximately 0.7063, or 70.63%.

Answer:

c/sin(60°) = 14/sin(25°)

c = 14sin(60°)/sin(25°) = 28.7

Answer:

Bus 18 is more consistent than Bus 47 based on the IQR, which is smaller for Bus 18 (16) compared to Bus 47 (24), indicating less spread of data between the 25th and 75th percentiles.

Step-by-step explanation:

Answer: The correct option regarding which bus has the least spread among the travel times is given as follows:

Bus 14, with an IQR of 6.

How to obtain the measures of spread?

First, we consider the dot plot, which shows the number of times that each observation appears in the data set.

Then we consider the interquartile range, which gives the difference between the third quartile and the first quartile of the data set.

The interquartile range is a better measure of spread compared to the range of a data set, as it does not consider outliers.

For groups of 15 students, we have that:

The first half is composed of the first seven students, hence the first quartile is the fourth dot, which is the median of the first half.

The second half is composed of the last seven students, hence the first quartile is the eleventh dot, which is the median of the first half.

The quartiles for Bus 14 are given as follows:

Q1 = 12.

Q3 = 18.

Hence the IQR is of:

IQR = Q3 - Q1 = 18 - 12 = 6.

The quartiles for Bus 18 are given as follows:

Q1 = 9.

Q3 = 16.

Hence the IQR is of:

IQR = Q3 - Q1 = 16 - 9 = 7.

Step-by-step explanation:

Step-by-step explanation:

it is given r=s

then, t =100.

2s+t=180°

2s=180-100

2s=80°

s=40° = r

hope this helps you.

Correct option is B, The only quadrilateral that satisfies the requirements for a kite is quadrilateral EFGH. A kite has opposed sides that are not congruent and two sets of adjacent sides that are.

One quadrilateral is a closed figure with four sides. These geometric shapes are quadrilaterals: a quadrilateral form. There is just one set of parallel sides to the shape, and there are no right angles.

Each quadrilateral has four sides, four angles, and four vertices. Its inner angles add up to 360 degrees.

4 angles

The four sides of a quadrilateral also create four angles. Here are a few quadrilateral instances. Each figure has four straight sides and four angles, as you can see. Any quadrilateral's interior angles add up to 360°.

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Complete question -

Answer:

Joe makes 5 dollars a week

Step-by-step explanation:

Joe started with 173 so you will subtract that from the total

208-173=35

You will then divide that number by the number of weeks he has worked

35÷7=5

Therefore joe makes 5 dollars a week

The amount of money that he earns each week will be $5 per week.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Joe has $173 he earns the same amount of money each week for seven weeks and put this money in the bank now Joe has $208 in the bank.

Let 'm' be the amount of money that he earns each week. Then the equation is written as,

208 = 7m + 173

Simplify the equation, then we have

208 = 7m + 173

35 = 7m

m = $5

The amount of money that he earns each week will be $5 per week.

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Answer:

The answer is 8.......!!

Answer:

option B

Step-by-step explanation:

Given :

\(y = \frac{2}{3}x + 3\\\\y = \frac{5}{2}x + \frac{7}{2}\\\\\)

Step 1 : simplify the equation :

\(3y = 2x + 9\\\\2y = 5x + 7\\\)

Step 2: Arrange the terms :

\(2x - 3y = - 9\\\\5x -2 y = -7\)

Step 3 : Solve for x and y :

                                2x - 3y = - 9 ------ ( 1 )

                                5x - 2y = - 7 --------- ( 2 )

                              _____________________

              ( 1 ) x 5 => 10x - 15y = - 45    ---------- (3 )

              ( 2) x 2 => 10x - 4y = - 14    ----------- (4 )

                             _______________________              

           ( 3 ) - ( 4 ) =>  0x - 11y = - 31

                                    - 11 y = - 31

                                        \(y = \frac{31}{11}\)

              Substitute y in ( 1 ) :

                     2x - 3y = - 9

                     \(2x - 3 (\frac{31}{11}) = - 9\\\\2x = -9 + 3(\frac{31}{11})\\\\2x = - 9 + \frac{93}{11}\\\\2x = \frac{-99 + 93}{11} \\\\2x = \frac{-6}{11} \\\\x = \frac{-6}{2 \times 11} = -\frac{3}{11}\)

Therefore the solution to the sytem is \(( - \frac{3}{11} , \frac{31}{11})\)

The solution of the system of equation is a point which lies

on the both the lines.

Option A : False ,  It says the solution lies above one of the given line.

               But the solution of the system of equation always lies on

                both the line.

Option B : True , says the solution is a point on the coordinate plane.

Option C : False, because if the solution is on the x-axis , then

                  the y coordinate in the solution would be zero.

                   But it  is not zero.

Option D : False , the solution is the point where both the lines intersect.

Answer:

-8

Step-by-step explanation:

Answer: D

f(x) > 0 over the interval

Step-by-step explanation:

If f(x) is a continuous function and all of the critical points of behavior change are described by the given information, we can say that the function crossed the x axis to reach a minimum value of -12 at x=-2.5, then as x increases it ascends to a maximum value of -3 for x = 0 (which is also its y-axis crossing) and is thus most likely a local maximum.

The function was then above the x axis (greater than zero) from till it crossed the x axis (becoming negative) at x = -4. As a result, the function was positive (greater than zero) in this period.

There is no such thing as a unique declaration about the function's positive or negative value when The interval is extended from -4 to -3, because the function takes negative values between -4 and -3.

Answer:

f=2

Step-by-step explanation:

First, you move the variables to the left side of the equation and change its sign.

After doing so, you  have 4f -5f =2.

Now, combine like terms. 4f-5f = -f, or -1f. Either way is fine.

Your equation looks like this now: -f = -2

Now remove the negative symbols due to their being one on both side.

f=2

Mark brainliest if possible please! Have a nice day.

Answer:  

I would think 15c+5= 35 because it is the one answer that makes the most sense.  If you get this wrong I am so sorry.

Answer:its the last choice

Step-by-step explanation: im sorry if i get this wrong lol

The equation allows us to chart the tree's development over time and forecast its ultimate height.

A function is a mathematical formula that allots each input from one set, known as the domain, to precisely one output from another set, known as the range. A function can be used to model relationships between variables, answer issues, and make predictions. It can be represented by an equation, a graph, a table, or a verbal description. Numerous branches of mathematics, as well as disciplines like physics, engineering, finance, and computer science, make extensive use of functions. Typical instances of functions include: When a function is graphed, it always changes at the same rate and forms a straight line. They are frequently used to simulate relationships between two variables that are related linearly, such as time and location.

given

After d days, Alani created the following algorithm to measure the height of the banana tree:

h = d + 8

Since this function is linear, the banana tree's development will remain constant over time. According to the calculation, the tree starts out at a height of 8 units, and it increases by 1 unit per day after that.

We can enter a figure for d (the number of days) and solve for h using this equation (the height of the tree after d days). For instance, we can enter d = 10 into the calculation to get the height of the tree after 10 days:

h = 10 + 8

h = 18

Therefore, the altitude of the banana plant after 10 days would just be 18 units. This equation allows us to chart the tree's development over time and forecast its ultimate height.

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\(2 - \sqrt{1} \\ = 2 - 1 \\ = 1\)

The largest value that f(4) can possibly be is 29.

The mean value theorem states that for a function f(x) that is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), there exists a number c in the open interval (a, b) such that:

f(b) - f(a) = f'(c)(b - a)

In this case, we are given that f(0) = -3 and that f'(x) ≤ 8 for all values of x. To determine how large f(4) can possibly be, we can use the mean value theorem with a = 0 and b = 4:

f(4) - f(0) = f'(c)(4 - 0)

Substituting the given values:

f(4) - (-3) = f'(c)(4)

f(4) + 3 = 4f'(c)

Since f'(x) ≤ 8 for all values of x, we can say that f'(c) ≤ 8. Therefore:

f(4) + 3 ≤ 4f'(c) ≤ 4(8) = 32

Therefore, we have:

f(4) ≤ 32 - 3 = 29

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