(b) Find the value of k such that point (3,-2) lies on the locus 2x²-3y² + 2k-6y + 2 = 0

The equation of line which passes through (1, -4) and whose slope is 0 is y = -4.

According to the given question.

A line passes throught the point (1, -4) and its slope is 0.

Let the equation of the line be y = mx + b.

Where,

m is the slope of the line

and b is the y intercept.

Since, the line is passing through (1, -4) and slope is 0 i.e. m = 0.

Therefore, m = 0 and (x, y) = (1, -4) must statisfy y = mx + b.

-4 = 1(0) + b

⇒ -4 = b

⇒ b = -4

Therefore, the equation of line which passes through (1, -4) and whose slope is 0 is y = -4.

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The linear model tells you about the rental cost of apartments in the complex that is $410.6

A linear equation is an equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = MX + c. Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.

A linear equation is given as y = MX + b

where m is the rate of change, b is the initial value of y, and, x are variables.

Assume that y represents the monthly rental price and x represents the square footage.

Given the equation:

Predicted Rental Price = 391+0.98· Area

For the rental price versus area (in square feet) for 20 apartments.

Predicted Rental Price = 391+0.98· Area

Predicted Rental Price = 391 +0.98· (20)

= 410.6

The  linear model tells you about the rental cost of apartments in the complex that is $410.6

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Answer: C, F

Step-by-step explanation: this is a form of distribution meaning you have to distribute -10 to the numbers inside the parenthesis. -10x4= -40x and -10 x -5= 50 therefor it is -40x+50. This answer can work as commutative meaning -40x+50 can also be written as 50-40x

Answer:

1/2

Step-by-step explanation:

5/8 students of the 4/5 students have rodents. The word "of" tells us to multiply. 5/8 * 4/5 is equal to 5*4/8*5, which is 20/40 and therefore simplifies to 1/2.

2.35(2)+1.85+1.60= $8.15 total before gift card

8.15-5.00= $3.15 because the gift card was $5

now you do

20.00-3.15 to get the total change which is $16.85

Thanks hope you see this susususususususususuusususususuusususus

Answer:

[tex] \large{ \boxed{ \tt{3 {x}^{2} - 12x - 1 }}}[/tex]

Please see the attached picture for full solution!

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The equation of line that is perpendicular to the given equation and passes through the given point is y = -3x - 2.

Given the equation of line and point;

First, find the slope intercept form ( y = mx + b )of the given equation to determine the slope.

−2x + 6y = −1

Solve for y

6y = 2x - 1

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

y = (1/3)x - 1/6

Hence, the slope m =  1/3

Now, the equation of a perpendicular line must have a slope that is the negative reciprocal of the original slope.

Slope of the perpendicular will be;

m_perpendicular = -3

Next, find the equation of the perpendicular line using the point slope formula y - y₁ = m( x - x₁ ).

Plug in the slope m = -3 and the point (-2,4).

y - y₁ = m( x - x₁ )

y - 4 = -3( x - (-2) )

y - 4 = -3( x + 2 )

y - 4 = -3x - 6

y = -3x - 6 + 4

y = -3x - 2

Therefore, the equation of line that is perpendicular to the given equation and passes through the given point is y = -3x - 2.

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[tex]\left( \cfrac{-5x^2}{y^3} \right)^{\underline{2}}\implies \left( \cfrac{(-5)^{\underline{2}}x^{2\cdot \underline{2}}}{y^{3\cdot \underline{2}}} \right)\implies \cfrac{(-5)(-5)x^4}{y^6}\implies \cfrac{25 x^4}{y^6}[/tex]

The amount in the bank account at the end of 4 years will be = $6540

The amount deposited by Michas in the savings account = $6000

Interest rate = 2.25% annually

No. of years principal is invested = 4 years

Calculating the amount in the bank account after 4 years, using the formula:

Simple interest = P*R*T/100

where P = principal invested

R = rate of interest annually

T = number of years amount is invested

So, Simple interest on the principal invested for 4 years= 6000*2.25*4/100 = 540

The amount in the bank account at the end of 4 years will be = 540 + 6000 = $6540

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Answer:

0,48

Step-by-step explanation:

whenever we convert a fraction to a decimal, it is easier to convert the denominator to a power of 10 and then move the comma the amt of zeros left of the number

Answer:

37 subsets

Step-by-step explanation:

yeah just copy that and that's all

The common difference and the first four terms are - 12 and 3, -9, -21 , -33 respectively

Given that the sum of an arithmetic sequence is  6n-3n²

S1  = a1 = 6(1) - 3(1)² = 6 - 3 = 3

S4 = a1 + a2 + a3 + a4 = 6(4) - 3(4)² = -24

a1 + a2+ a3 + a4 + d = -24

4(a1) + d = -24

4(3) + d = -24

12 + d = -24

d = -24 + 12

d = -12

The first four terms are;

T2 = 3 + (2-1) -12

T2 = 3 -12

T2 = -9

T3 = 3 + 2(-12)

T3 = 3 - 24

T3 = -21

T4 = 3 + 3(-12)

T4 = 3 - 36

T4 = -33

Thus, the common difference and the first four terms are - 12 and 3, -9, -21 , -33 respectively

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Answer:

6003-457= 5546

Step-by-step explanation:

because when is second 603 - 457 when you subtract 7 from 3 it can't be possible so here is very tools so we will say so you go and borrow one from the 6 today's 0 nearest sex making it 10 and you borrow long from the time we

Answer: graph 'y=16-8x'

Step-by-step explanation:

First, alter the equation by making it a 'y=...' statement (y=-8x+16).

Secondly, plot your first point at positive 16.

Third, make sure that your slope is going down 8 from positive 16, so you plot your second point at positive 8, and move that second point to the right by 1.

Let me know if this helps!

Answer: 19

Step-by-step explanation: 13+6=19

Answer:

qfgggghbvvcccvvv kknnbvvvvvvvvvvvbhg

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

According to given information,

when, x is not equal to -2, that means g(x) = 4 for all values of x except " - 2 "

Therefore,

[tex]\qquad \sf  \dashrightarrow \: g( - 5) = 4[/tex]

and

[tex]\qquad \sf  \dashrightarrow \: g(3) = 4[/tex]

And, when x = -2, it's value is 2, hence :

[tex]\qquad \sf  \dashrightarrow \: g( - 2) = 2[/tex]

Answer:

[tex] \sf \large \: x<19 \: or \: x>−5[/tex]

Step-by-step explanation:

Let's solve your inequality step-by-step.

|x−7|<12

Solve Absolute Value.

|x−7|<12

We knowx−7<12andx−7>−12

x−7<12(Condition 1)

x−7+7<12+7(Add 7 to both sides)

x<19

x−7>−12(Condition 2)

x−7+7>−12+7(Add 7 to both sides)

x>−5

Answer:

x<19 and x>−5

Answer:

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "q2" was replaced by "q^2". 1 more similar replacement(s).

STEP

1

:

Equation at the end of step 1

(9 • (p2)) - (23•5q2)

STEP

2

:

Equation at the end of step

2

:

32p2 - (23•5q2)

STEP

3

:

Trying to factor as a Difference of Squares:

3.1 Factoring: 9p2-40q2

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 9 is the square of 3

Check : 40 is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares.

Rachel and her sister Fran together can paint the living room in [tex]\frac{10}{7}[/tex] hours

Given that

Rachel can paint half of the living room in 1 hour

Fran can paint [tex]\frac{1}{5}[/tex]th part of the living room in 1 hour

Let's assume together they paint the living room in x hours

⇒ together they can paint [tex]\frac{1}{x}[/tex]th part of the living room in 1 hour

By proportions,

⇒[tex]\frac{1}{2}[/tex]+[tex]\frac{1}{5}[/tex]= [tex]\frac{1}{x}[/tex] {using operation proportions and addition}

⇒[tex]\frac{7}{10}[/tex]=[tex]\frac{1}{x}[/tex]

⇒x=[tex]\frac{10}{7}[/tex]        

⇒ together they can paint [tex]\frac{7}{10}[/tex]th part of the living room in 1 hour

It means, Rachel and her sister Fran together can paint the living room in [tex]\frac{10}{7}[/tex] hours

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Answer:

y = 2x -9

Step-by-step explanation:

Amount of sludge dispose per minutes is 100 lb.

What is Rate of change?

A rate is anything that can be measured over time. Common rates include velocity (which is the rate of distance traveled), power (rate of work being done), etc. All these have one thing in common which is that they are all divided by the amount of time it took to obtain a certain measurement.

Here it is given that :

A pump can dispose of sludge at the rate of 6,000 lb/h, that is in one hour pump dispose 6000 lb of sludge.

it is known that 1 hour = 60 minutes

Therefore, to find the amount of sludge dispose by pump in ome minute we divide 6000 with 60 :

amount of sludge dispose in one hour = 6000 lb

amount of sludge dispose in 60 minutes = 6000 lb

amount of sludge dispose in 1 minutes = 6000 lb/60 = 100 lb

Therefore, amount of sludge dispose per minutes is 100 lb

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Answer:

3

Step-by-step explanation:

and the answer is 17

Answer:

1. The total cost of movie and the total cost of refreshments purchased and the total  cost of video games played cannot exceed 40

2. 14.50 + 7.75x + 0.75y ≤  40

3. y ≤ 34 - 10.333x

4. See attached graph

5.

one  refreshment means you can play 23 times
two refreshments means you can play 13 times
three refreshments means you can play 3 times

Step-by-step explanation

We have to assume that you can see one movie but but buy multiple refreshments and play multiple video games. A refreshment is considered to be one drink and one popcorn.

If not we have a situation where we have three unknowns and it will be difficult to solve in a 2D context

1. Verbal inequality model
The total cost of one movie and the total cost of refreshments purchased and the total  cost of video games played cannot exceed 40

2. Algebraic Inequality Model
Since the cost of a movie is 14.50 and you are seeing only 1 movie, the cost is 14.50(1) = 14.50

Assume you are going to buy x refreshments. Total cost of refreshments = 7.75x

Assume you are going to play y video games. Total cost of video games played = 0.75y

This cannot be greater than 40 i.e ≤ 40

So the algebraic inequality is
14.50 + 7.75x + 0.75y ≤  40

3. Solving the inequality

Subtracting 14.50 from both sides we get
7.75x + 0.75y ≤  25.50

Subtracting 14.50 from both sides we get
7.75x + 0.75y ≤  25.50

Subtract 7.75x from both sides:
0.75y ≤ 25.50- 7.75x

Divide both sides by 0.75
y ≤ 25.50/0.75 - 7.75x/0.75

which is
y ≤ 34 - 10.333x

3. Graph of Inequality

This is an inequality in 2 variables and can be graphed.
See attached graph. The shaded portion represents the inequality
y ≤ 34 - 10.333x

Note that since neither x nor y can be < 0, we should not consider any portion of the shaded area which would mean two more constraints x ≥ 0 and y ≥ 0 but in this case I have stuck to only the above one inequality

5. Possible number of times you can play the same video game

Again we consider only 1 movie and multiple refreshments and video games

Using the inequality y ≤ 34 - 10.33x

If x = 1 refreshment,
y ≤ 34 - 10.33 x 1
y ≤ 23.67 or max 23 times you can play the video game max

If x = 2,
y ≤ 34 - 10.33 x 2
y ≤ 13.34 or maximum 13 times

If x = 3
y ≤ 34 - 30.99
y ≤ 3.01 or maximum 3 times

By free fall motion, the ball will take a time of 3.252 seconds to hit the ground.

The ball experiments a free fall motion, that is an uniform accelerated motion due to gravity, in which effects from Earth's rotation and air viscosity are neglected. The height of the ball (h), in feet, is modelled by a quadratic equation:

h = 205 - 11 · t - 16 · t²

Where t is the time, in seconds.

If we know that h = 0 ft, then the time needed for the ball to hit the ground is:

205 - 11 · t - 16 · t² = 0

16 · t² + 11 · t - 205 = 0

16 · [t² + (11 / 16) · t - 205 / 16] = 0

16 · (t - 3.252) · (t + 3.940) = 0

For time is a whole number, only the first root offers a reasonable answer.  

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The intercepts of the graph (0, 6) (0, -6) is symmetry on x-axis, y-axis and it is graphically shown.

A symmetry of a function is a transformation that leaves the graph unchanged. Symmetric function is a function having several variables which remain unchanged for any type of permutation of the variable.

For the given situation, Symmetry with respect to x-axis

The point becomes (x, -y) as the point flips by itself up or down which changes its y coordinate to negative of whatever it was. And there is no motion is done horizontally so no change in x coordinate.

The interecpets are; (0, 6) (0, -6)

Thus this intercepts is symmetric to y-axis. this intercepts is not symmetric about origin.

Hence we can conclude that the intercepts is symmetric about x - axis.

Therefore, The intercepts of the graph (0, 6) (0, -6) is symmetry on x-axis and it is graphically shown.

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Answer:

d

Step-by-step explanation: