3. What is f-3) if f(x) = 2x – 11 – 5? (​

The equation for the plane passing through Q and perpendicular to line PQ is r (2 i + 3 j + 6 k) + 28 = 0.

Let position vector of point P be:

p = 3 i + j + 2 k

Let position vector of point Q be:

q = i - 2 j - 4 k

So, PQ = Q - P

PQ = n = i - 2 j - 4 k - (3 i + j + 2 k)

n = i - 2 j - 4 k - 3 i - j - 2 k

n = - 2 i - 3 j - 6 k

The Equation of plane passing through point Q and perpendicular to PQ will be:

(r - q).n = 0

r n = q n

q n = (i - 2 j - 4 k) . (- 2 i - 3 j - 6 k)

q n = - 2 + 6 + 24

q n = 28

r n = 28

r (- 2 i - 3 j - 6 k) = 28

r (2 i + 3 j + 6 k) + 28 = 0

Therefore the equation for the plane passing through Q and perpendicular to line PQ is r (2 i + 3 j + 6 k) + 28 = 0.

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The solution to the equation given by M * M * M = 729 is 9

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

Given the equation:

M.M.M = 729

This gives:

M * M * M = 729

M³ = 729

Taking the cube root of both sides:

∛M³ = ∛729

M = 9

The solution to the equation is 9

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Answer:

x = (2√6)/3

Step-by-step explanation:

Reference angle = 30°

Hypotenuse = x

Adjacent = √2

Thus, applying trigonometric ratio, we have:

Cos(30) = adj/hyp = √2/x

x*cos(30) = √2

x = √2/cos(30)

x = √2/(√3/2) (cos 30 = √3/2)

x = √2 × 2/√3

x = (2√2)/√3

Rationalize

x = (2√2 × √3)/(√3 × √3)

x = (2√6)/3

Answer:This would be option letter C

Step-by-step explanation:The diagram is a gram of external geofram so the position Is fFX(4) ^N

Answer:

D

Step-by-step explanation:

f(x)= -x^2+4

Draw graph of -x^2 and shift it 4 units above

Answer:

Given the information you provided, we can model cellular phone usage over time with an exponential growth model. An exponential growth model follows the equation:

`y = a * b^(x - h) + k`

where:

- `y` is the quantity you're interested in (cell phone usage),

- `a` is the initial quantity (34 million in 1995),

- `b` is the growth factor (1.22, representing 22% growth per year),

- `x` is the time (the year),

- `h` is the time at which the initial quantity `a` is given (1995), and

- `k` is the vertical shift of the graph (0 in this case, as we're assuming growth starts from the initial quantity).

So, our specific model becomes:

`y = 34 * 1.22^(x - 1995)`

To find the cellular usage in 2003, we plug 2003 in for x:

`y = 34 * 1.22^(2003 - 1995)`

Calculating this out will give us the cellular usage in 2003.

Let's calculate this:

`y = 34 * 1.22^(2003 - 1995)`

So,

`y = 34 * 1.22^8`

Calculating the above expression gives us:

`y ≈ 97.97` million.

So, the cellular phone usage in 2003, according to this model, is approximately 98 million.

Answer:

B) \(4i\sqrt{2}\)

Step-by-step explanation:

\(\sqrt{-2}=i\sqrt{2}\\\sqrt{-18}=i\sqrt{18}=i\sqrt{9*2}=3i\sqrt{2}\\\\\sqrt{-2}+\sqrt{-18}=i\sqrt{2}+3i\sqrt{2}=4i\sqrt{2}\)

Answer:

10 - 3x

Step-by-step explanation:

Note the term, "decreased BY". This means that we have to remove 3x from 10.

If it says, "decreased TO", it means that from 10, there are only 3x remaining.

The "if statement" to show that  increases pay by 3% if score is greater than 90, otherwise increases pay by 1% ; is written below .

The if statement in that implements the conditions that increases pay by 3% if score is greater than 90, otherwise increases pay by 1% is written as :

⇒ if (score > 90)

⇒  pay *= 1.03;

⇒  else

⇒  pay *=1.01;

In the above mentioned  code, the "score" is a variable that represents the value to be tested, and "pay" is a variable that represents the current pay.

The statement checks that if score is greater than 90.  pay is increased by 3% (multiplying by 1.03). If score is not greater than 90, pay is increased by 1% (multiplying by 1.01).

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Answer:

6.9%.

Step-by-step explanation:

Given that a university class has 26 students: 12 are art majors, 9 are history majors, 5 and are nursing majors, and the professor is planning to select two of the students for a demonstration, where the first student will be selected at random, and then the second student will be selected at random from the remaining students, to determine what is the probability that the first student selected is a history major and the second student is a nursing major the following calculations must be performed:

26 = 100

9 = X

9 x 100/26 = X

900/26 = X

34.61 = X

25 = 100

5 = X

500/25 = X

20 = X

0.2 x 0.3461 = X

0.069 = X

Thus, the probability that the first student selected is a history major and the second student is a nursing major is 6.9%.

Answer:

6.9%

Step-by-step explanation:

Hope this will help

The company should produce 235 units of Metakeb, 96 units of Mewesson, and 17 units of Metekem per month to use up all the available resources.

What is the Gaussian method?

The Gaussian method, also known as Gaussian elimination or row reduction, is a technique for solving systems of linear equations. It involves performing a sequence of operations on the rows of a matrix to transform it into an equivalent matrix that is in row echelon form or reduced row echelon form.

To use the Gaussian method, we need to set up a system of linear equations based on the given information. Let x, y, and z be the number of units of Metakeb, Mewesson, and Metekem produced per month, respectively. Then we have:

Machining department: 1200x + 1800y + 3000z = 1050(60)

Inspection department: 2400x + 1200y = 1160(60)

Assembly department: 600x + 3000y = 830(60)

Simplifying these equations, we get:

Machining department: 20x + 30y + 50z = 3150

Inspection department: 8x + 4y = 232

Assembly department: x + 5y = 139

Now we can use the Gaussian method to solve for x, y, and z:

Step 1: Write the augmented matrix:

| 20 30 50 | 3150 |

| 8 4 0 | 232 |

| 1 5 0 | 139 |

Step 2: Use row operations to get the matrix in row echelon form:

R2 → R2 - 4/5 R3

R1 → R1 - 20R3

| 0 -2 50 | 850 |

| 0 2 -4   | -28 |

| 1 5 0     | 139 |

R2→ -1/2 R2

R1 → R1 + R2

| 0 1 -25 | 407 |

| 0 1 -2 | 14 |

| 1 5 0 | 139 |

R1→ R1 - R2

| 0 0 -23 | 393 |

| 0 1 -2 | 14 |

| 1 5 0 | 139 |

R3→ R3 - 5R2

| 0 0 -23 | 393 |

| 0 1 -2 | 14 |

| 1 0 10 | 65 |

R1→ -1/23 R1

| 0 0 1 | -17 |

| 0 1 -2 | 14 |

| 1 0 10 | 65 |

R2 → R2 + 2R3

| 0 0 1 | -17 |

| 0 1 0 | 96 |

| 1 0 10 | 65 |

R3 → R3 - 10R1

| 0 0 1 | -17 |

| 0 1 0 | 96 |

| 1 0 0 | 235 |

Step 3: Read off the solution from the row echelon form:

z = -17

y = 96

x = 235

Therefore, the company should produce 235 units of Metakeb, 96 units of Mewesson, and 17 units of Metekem per month to use up all the available resources.

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Given:

Find-:

A possible degree for the following graph.

A factor of the polynomial

relative maximum

Sol:

(a)The degree of function is:

The function has the most n x-intercept

The function has most (n-1) turns

Here, x - the intercept is 5 then the degree is 5.

(c)The relative maximum is:

(b)

Factor of polynomial is:

Answer:

y = - 3x + 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (0, 7) and (x₂, y₂ ) = (2, 1) ← 2 points on the line

m = \(\frac{1-7}{2-0}\) = \(\frac{-6}{2}\) = - 3

the line crosses the y- axis at (0, 7 ) ⇒ c = 7

y = - 3x + 7 ← equation of line

The equation of the line in fully simplified slope-intercept form is y = -2.8x + 7

The linear graph represents the given parameter

For the graph, we have the points

(0, 7) and (25, 0)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 7

Using the point (2.5, 0) on y = mx + 7, we have

m(2.5) + 7 = 0

2.5m + 7 = 0

Evaluate

m = -2.8

So, we have

y = -2.8x + 7

Hence, the equation of the line in fully simplified slope-intercept form is y = -2.8x + 7

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To make the fractions equivalent, we need to find the missing numerators that would make them equal. Let's fill in the missing numerators:

1/2 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

1/2 and 4/8

Now, the fractions are equivalent.

---

4/12 and __/60

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 5:

4/12 and 20/60

Now, the fractions are equivalent.

---

2/3 and __/12

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

2/3 and 8/12

Now, the fractions are equivalent.

---

4/4 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 2:

4/4 and 8/8

Now, the fractions are equivalent.

\({ \qquad\qquad\huge\underline{{\sf Answer}}} \)

Here we go ~

\(\qquad \sf  \dashrightarrow \: \dfrac{((243 {)}^{2n/5} ) \sdot( {3}^{2n + 1}) }{ ({9}^{n + 1}) \sdot( {3}^{2(n - 2)} )}\)

\(\qquad \sf  \dashrightarrow \: \dfrac{(3{)}^{5(2n/5)} ) \sdot( {3}^{2n + 1}) }{ ({3 }^{2(n + 1)}) \sdot( {3}^{2(n - 2)} )}\)

\(\qquad \sf  \dashrightarrow \: \dfrac{(3{)}^{2n} \sdot( {3}^{2n + 1}) }{ ({3 }^{(2n + 2)}) \sdot( {3}^{(2n - 4)} )}\)

let's break it up :

now let's take \({ \sf {3}^{(2n-4)}} \) common here ~

\(\qquad \sf  \dashrightarrow \: \dfrac{(3{)}^{(2n - 4)} (3 {}^{4} \sdot{3}^{5}) }{ {(3 )}^{(2n - 4)}(3 {}^{6} \sdot1)}\)

\(\qquad \sf  \dashrightarrow \: \dfrac{{} (3 {}^{4} \sdot{3}^{5}) }{ (3 {}^{6} \sdot1)}\)

\(\qquad \sf  \dashrightarrow \: \dfrac{{} 3 {}^{9} }{ 3 {}^{6} }\)

\(\qquad \sf  \dashrightarrow \: 3 {}^{3} \)

\(\qquad \sf  \dashrightarrow \: 27\)

Answer:

Step-by-step explanation:

\(\sf \cfrac{243^{\frac{2n}{5}}\cdot \:3^{2n+1}}{9^{n+1}\cdot \:3^{2\left(n-2\right)}}\)

\(\sf 9^{n+1}\cdot \:3^{2\left(n-2\right)}\)

Simplify:-

\(\sf \cfrac{3^{2n}\cdot \:3^{2n+1}}{\boxed{\bf 3^{4n-2}}}\)

Now, Factor:-

\(\sf \cfrac{3^{2n}\cdot \:3^{2n+1}}{3^{4n-2}}\)

Now, let's simplify:-

Simplify:-

Apply the exponent rule:-

Therefore, your answer is 27.

______________________

Hope this helps!

Have a great day!

Answer: 803.84cm3

Step-by-step explanation:
The formula for finding the volume of a cylinder is πr2h.
In other words, the area of the top face's circle times the height.

To find the circle's area, we first find the radius of the circle. Since the diameter is 8cm, we divide by 2 to get the radius, which is 4cm.

4cm squared is 4cm x 4cm, which is 16cm. 16cm times 3.14 is 50.24cm squared.

Now, we have the area of the circle. 50.24cm squared!

The height is 16cm, so to find the cylinder, we times the area of the circle by the height of the cylinder! So,

16cm x 50.24cm squared = 803.84cm cubed.

The volume of the can of soup is 803.84cm cubed.

Answer:

Step-by-step explanation:

In order to find two unknown values, length and width of a rectangle, you must have two independent relations between those values. One relation is given in the problem statement:

  L = 2W -65 . . . . . length is 65 ft less than twice the width

Another relation is given by the formula for the perimeter of a rectangle:

  P = 2(L +W) . . . . with P = 770 given in the problem statement

__

Using the first relation for L, we can substitute into the relation for perimeter to get ...

  770 = 2((2W -65) +W)

  770 = 6W -130 . . . . . . . . simplify

  900 = 6W . . . . . . . . . add 130 to both sides

  150 = W . . . . . . . . divide both sides by 6

  L = 2(150) -65 = 235 . . . . . use the equation for L to find the length

The base is 235 feet long and 150 feet wide.

Answer:

The input is zero, the output is -1

Step-by-step explanation:

We want to know the y value when the x value is zero

When x =0, y = -1

The input is zero, the output is -1

Answer:

D

Step-by-step explanation:DV

By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.

To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.

Let's start by graphing the constraints:

1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.

2. Plot the line -x + 3y = 6 using a similar process.

3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.

Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.

Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.

Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.

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Answer:

think it's about 5 feet and 4 inches more.

Answer:

300

Step-by-step explanation:

A=wl=10·30=300

multiply the length of the rectangle by the width of the rectangle.

The area is measurement of the surface of a shape. To find the area of a rectangle or a square you need to multiply the length and the width of a rectangle or a square. Area, A, is x times y.

Answer:

Area = 378.5 ft²

Step-by-step explanation:

The figure is having two semi circles and one rectangle.

\({ \sf{area = area \: of \: semicircles + area \: of \: rectangle}} \\ \\ { \sf{area = 2( \frac{1}{2} \pi {r}^{2}) + (l \times w) }} \\ \\ { \sf{area = \pi {r}^{2} + (l \times w) }} \\ \\ { \sf{area = 3.14 \times {5}^{2} + (30 \times 10)}} \\ \\ { \sf{area = 378.5 \: {ft}^{2} }}\)

Answer:

Step-by-step explanation:

As given system of linear equations,

Hence taking 1st equation ,

-3x+3y=12    

-3(x-y)=12   ( common -3 )

now take 2nd equation ,

y=x+4

Now add these two equations, we get

x-y+ y- x=-4+4

0x+0y=0

Answer:

y = 2x-7

Step-by-step explanation:

I'm not really sure this is the slope-intercept form, as I've never called it like that before, but if it is, there you go.

Answer:

\(\huge\boxed{\sf y = 2x - 7}\)

Step-by-step explanation:

Given equation is:

2x - y = 7

Add y to both sides

2x = 7 + y

Invert the equation

7 + y = 2x

Subtract 7 to both sides

y = 2x - 7

This is the required equation in slope-intercept form y = mx + b where m is slope and b is y-intercept.

\(\rule[225]{225}{2}\)

Hope this helped!

Answer:

The answer is 0.5

Answer:

rhe answer is r= .50

Step-by-step explanation:

125-75=50

Answer:

5^x

Step-by-step explanation:

Each level of the question is multiplied by 5 every time x increases by 1.

The exponential function represents the data in the table is f(x) = \(5^{x}\) .

An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.

The exponential function is an important mathematical function which is of the form

f(x) = \(a^{x}\)

Where a>0 and a is not equal to 1.

x is any real number.

If the variable is negative, the function is undefined for -1 < x < 1.

Here,

“x” is a variable

“a” is a constant, which is the base of the function.

According to the question

Exponential function represents the data in the table

x   f(x)

2     25

3     125

4     625

Now,

Putting values in Exponential function equation at :

x   f(x)

2     25

f(x) = \(a^{x}\)  

25 = \(a^{2}\)

a =  ± 5

Now

x   f(x)

3   125  

f(x) = \(a^{x}\)  

125 = \(a^{3}\)

a =   5

Therefore ,

a = 5 which will satisfy all the values of x for f(x)

Hence, exponential function represents the data in the table is f(x) = \(5^{x}\) .

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Answer:

Maria is 58 inches tall and Juan is 42 inches

Step-by-step explanation:

Answer:

\(f(x) = {x}^{2} - 2x + 17 \\ completing \: squares \\ divide \: the \: sum \: by \: 2 \: and \: the \: result \: to \: the \: {x}^{2} and \: subtract \: it \: from \: the \: product \\ in \: this \: case. \: our \: sum \: is \: 2 \\ f(x) = ({x}^{2} \times \frac{2}{2} ) + (17 - \frac{2}{2} ) \\ f(x) = {(x + 1)}^{2} + (17 - 1) \\ f(x) = {(x + 1)}^{2} + 16\)

Answer:

Because knowledge is beautyyyy

Step-by-step explanation: