one of the roots of the equation x^2+kx-6=0 is 3 and k is a constant

To calculate the time it takes to triple your money at a 12.5 percent interest rate, we can use the formula for compound interest and we obtain the answer as 9.33(Approximately)

FV = PV * (1 + r)^n

Where FV is the future value, PV is the present value, r is the interest rate, and n is the number of compounding periods.

In this case, we want to find the value of n when the future value (FV) is three times the present value (PV). Let's assume the initial amount is $1.

3 * 1 = 1 * (1 + 0.125)^n

Simplifying the equation, we have:

3 = 1.125^n

To solve for n, we need to take the logarithm of both sides of the equation:

log(3) = n * log(1.125)

n = log(3) / log(1.125)

Using a calculator, we find that n is approximately 9.33 years.

Therefore, the correct answer is: 9.33 years.

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think sometimes prob 4x5 i don't know

The volume of water in the tank before the valve is opened can be found by plugging in t = 0 into the given equation V = 62(151 - t), which gives the initial volume.

To find the volume of water in the tank before the valve is opened, we plug in t = 0 into the given equation: V = 62(151 - t). Substituting t = 0 gives V = 62(151), which simplifies to V = 9338 cubic meters.

To find how long it takes the tank to fully empty, we set V = 0 in the equation V = 62(151 - t) and solve for t. This gives 0 = 62(151 - t), which simplifies to 151 - t = 0. Solving for t gives t = 151 hours.

The equation dv/dt represents the rate at which the volume of water is changing with respect to time. To find the flow rate after 23 hours, we substitute t = 23 into the derivative equation dv/dt. This gives dv/dt = 62.

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Answer:

translation . translation. rotation

Answer:

it hard too

Step-by-step explanation:

it's hard also so

Answer:   180

an = a1 + (n - 1)d

a1 = 6 [1st term]

d = 4 [common difference]

n = 30 [30th term]

a30 = 6 + (30 - 1)*6 = 180

Answer:

The cost of the necklace would be 7 dollars.

5*3 = 15

40-4=36

36-15=21

21/3= 7 dollar necklaces.

I didn't round to the nearest integer you have to do that yourself.

Answer:

The maximum height of the rocket is about 391.1 feet.

Step-by-step explanation:

The height of the rocket y in feet x seconds after launch is modeled by the equation:

\(y=-16x^2+125x+147\)

We want to find the maximum height reached by the rocket.

Since this is a quadratic equation, the maximum height occurs at the vertex. The vertex of a quadratic is given by:

\(\displaystyle \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)\)

In this case, a = -16, b = 125, and c = 147.

Thus, the x-coordinate of our vertex is:

\(\displaystyle x=-\frac{125}{2(-16)}=\frac{125}{32}\)

To find the maximum height, we will substitute this value back in. So:

\(\displaystyle y_{\text{max}}=-16\left(\frac{125}{35}\right)^2+125\left(\frac{125}{32}\right)+147\approx391.1\text{ feet}\)

The maximum height of the rocket is about 391.1 feet.

Answer:

6.7 per unit

Step-by-step explanation:

The probability of getting all tails when flipping a coin three times can be calculated using the multiplication rule of probability. For each flip of the coin, there are two possible outcomes: heads or tails.

Assuming the coin is fair, both outcomes are equally likely, so the probability of getting tails on any one flip is 1/2.

P(all tails) = P(tails on first flip) x P(tails on second flip) x P(tails on third flip)

= (1/2) x (1/2) x (1/2)

= 1/8

Therefore, the probability of getting all tails when flipping a coin three times is 1/8 or 0.125 when expressed as a decimal rounded to four decimal places.

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Answer: Margo does 48 activities in 4 weeks.

Step-by-step explanation:

In the calendar,

Red dots represent homework, yellow dots represent work, and green dots represent practice.

On a typical week , she uses 5 red dots, 3 yellow dots, and 4 green dots.

That means , total activity he does in a week = 5+3+4=12

Then, total activities in 4 weeks = 4 x 12 = 48

Hence, Margo does 48 activities in 4 weeks.

There are infinite solutions for the given homogenous system of linear equations.

To solve the following homogeneous system of linear equations: 3x1​−6x2​+9x3​=0−3x1​+6x2​−8x3​=0.

We can begin by using the augmented matrix. The augmented matrix is obtained by appending the vector of constants (i.e., the right-hand side) to the matrix that represents the coefficients of the system of equations. This yields the matrix equation Ax=b where x is the vector of variables, A is the matrix of coefficients, and b is the vector of constants. The augmented matrix for the given system of equations is given by `[[3,-6,9,0],[-3,6,-8,0]]`.We can solve the system by using row operations. We can add the first row to the second row and divide the first row by 3.

The resulting row-echelon form of the augmented matrix is given by:\($$\begin{pmatrix} 1 & -2 & 3 & 0 \\ 0 & 0 & -5 & 0 \end{pmatrix}$$\).

Since there are only two pivots (the first and the third columns), there is only one leading variable (i.e., x1) and two free variables (i.e., x2 and x3). We can express the solution set in parametric form as follows:\($$x_1=2x_2-3x_3$$$$x_3=t$$$$x_2=s$$\)

Where t and s are arbitrary constants. Since there are free variables, the system has an infinite number of solutions.

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Considering the area of the rectangular lot, the width of the walkway is of 3.9 feet.

Considering a rectangle of length l and width w, we have that the area and the perimeter are given as follows:

In the context of this problem, for the garden and the walkway, the dimensions are given as follows:

Considering that the area is of 238 square feet, we can solve for the width of the walkway as follows:

15(12 + w) = 238

12 + w = 238/15

12 + w = 15.9.

w = 15.9 - 12

w = 3.9 feet, which is the width of the walkway.

Since the area is in square feet, the length and the width are in feet.

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Answer:

Solution

here,

X=?

now,

X+90+42=180 (Sum of angles of Triangle)

or, X=180-132

or, X=48

Hence the value of X is 48 degrees

The values of the variables and numbers in radical form are presented as follows;

43a) x > -5

40a) a > 0

44b) x < 0

47e) x > 0

43b) x = The set of all real numbers

44a) The set of all numbers

45 a) x = 14

45 b) x = 0

45 c) x = -1

45 d) x = -4

45 e) x = 1

42 d)x = 5/196

9 e) x = 4

9 f) x = 8

9 a) √(0.6/36) ≈ 0.13

9 h) √((4 - 10)/(0.01)) = i·10·√6

A radical also known as a root is represented using the square root or nth root symbol and is the opposite of an exponent.

43 a) \(\sqrt{x + 5}\)

x + 5 > 0

Therefore, x > -5

40a) ∛a

a > 0

44b) √(-5·x)³

-5·x < 0

x < 0

47e) √(13 - (13 - 2·x))

(13 - (13 - 2·x)) > 0

13 > (13 - 2·x)

0 > -2·x

x > 0

43b) √|x| + 1

x = All real numbers

44 a) √(-2·x)²

√(-2·x)² = -2·x

x = Set of all numbers

45 a) √(x - 5) = 3

(x - 5) = 3² = 9

x = 9 + 5 = 14

45b) √(2·x + 4) = 2

2·x + 4 = 2²

2·x = 2² - 4 = 0

x = 0/2 = 0

45c) √(x·(x + 1)) = 0

(x·(x + 1)) = 0

(x + 1) = 0

x = -1

45 d) √(x + 5) = -1

(x + 5) = (-1)²

x + 5 = 1

x + 5 = 1

x = 1 - 5 = -4

x = -4

45e) √x + x² = 0

√x = -x²

(√x)² = (-x²)² = x⁴

x  = x⁴

1 = x⁴ ÷ x = x³

x = ∛1 = 1

x = 1

42d) \(\sqrt{\dfrac{5}{x} } +3= 17\)

\(\sqrt{\dfrac{5}{x} }= 17-3 =14\)

\(\dfrac{5}{x} }=14^2=196\)

\(x = \dfrac{5}{196}\)

9e) \(\sqrt{\dfrac{4}{x} } = 1\)

\(\dfrac{4}{x} } = 1^2\)

x × 1² = 4

x = 4

19f) ∛x - 2 = 0

∛x = 2

x = 2³ = 8

9a) \(\sqrt{\dfrac{0.6}{36} }\)

\(\sqrt{\dfrac{0.6}{36} }\) = \(\sqrt{\dfrac{1}{60} }= \dfrac{\sqrt{15}}{30} \approx 0.13\)

9h) \(\sqrt{\dfrac{4-10}{0.01} }\)

\(\sqrt{\dfrac{4-10}{0.01} }\)= √(-600) = √(-1)·√(600) = i·10·√6

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Step-by-step explanation:

hope it helps u.........

Answer:

206

Step-by-step explanation:

The formula for this problem would be -310 + 13(8) which = 206

Answer:

a) $520

b) $580

c) Interest amount is same each year

Step-by-step explanation:

Given - Georgie put $500 in her savings account, earning interest at a rate of 4% each year. She did not make any more deposits or withdrawals.

To find - a) How much money was in the account after one year?

              b) How much money was in the account after 4 years?

              c) Was the amount of money earned in interest the same or different each year?

Proof -

Here given that,

Principal amount = $500

rate of interest = 4% = 4/100 = 0.04

Now,

a)

Amount =  P [ 1 + RT ]

             = 500 [ 1 + 0.04(1)]

             = 500 [ 1 + 0.04] = 520

⇒Amount = $520

b)

Amount =  P [ 1 + RT ]

             = 500 [ 1 + 0.04(4)]

             = 500 [ 1 + 0.16] = 580

⇒Amount = $580

c)

In 2nd year,

Amount =  P [ 1 + RT ]

             = 500 [ 1 + 0.04(2)]

             = 500 [ 1 + 0.08] = 540

⇒Amount = $540

Now,

Interest in 1st year = 520 - 500 = 20

Interest in 2nd year = 540 - 520 = 20

So,

The interest amount  is same each year

Answer:

574

Step-by-step explanation:

I drew a picture of this situation

I am going to assume you know SOH CAH TOA (if you don't just ask)

We have the adjacent side and need to solve for the opposite so I will be using TOA

tan(68.17)=x/230

230tan68.17=x

x=574

There are 13 diamonds in the deck (as well as other colors). Since there are 52 cards, the probability of getting a diamond on the first draw is 13/52. After the first card is drawn, all that's left are his 12 diamonds. Therefore, the probability of drawing a diamond is 12/51 (note that he has only 51 cards left after pulling/removing the first card since there are no replacement cards). The overall probability is the product of two possibilities. The odds of drawing diamonds from the original deck are 13/52 times the odds of drawing diamonds from his remaining 51 cards. Assuming the first card drawn is a diamond, 12/51.

P=13/52*12/51=1/4*4/17=1/17.

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(a) Recall the definition of the step function,

\(\theta(t) = \begin{cases} 1 & \text{if } t \ge 0 \\ 0 & \text{if } t < 0 \end{cases}\)

Then we have

• \(\theta(t-2) = 1\) if \(t-2\ge0\), or \(t\ge2\)

• \(\theta(t-3) = 1\) if \(t-3\ge0\), or \(t\ge3\)

and we can combine these to get

\(\theta(t-2) - \theta(t-3) = \begin{cases} 1 & \text{if }2\le t < 3 \\ 0 & \text{if }t<2 \text{ or } t\ge3 \end{cases}\)

then scale up by 4 to get the value we want over [2, 3].

\(f(t) = \boxed{4\bigg(\theta(t-2) - \theta(t-3)\bigg)}\)

At least that's what I get using the aforementioned definition of "step function". I don't see a way to have both \(f(2)=4\) and \(f(3)=4\) with this definition...

(b) No function was given...

Answer:

y=-2.5-5/4x and no it doesn't pass through (4,12)

Step-by-step explanation:

5x-4y=10

-5x     +5x

-4y=10+5x

/-4     /-4

y=-2.5-5/4x

The solution is the set of all points (x,y) that satisfy the inequalities:

y < 2x + 4,  y < x/4 - 3, x + 3 = y, and 2x - 6 + 2 = y.

What is the graph of a function?

The graph of a function is a visual representation of the relationship between the input values (x-coordinates) and the output values (y-coordinates) of the function. In other words, it is a visual representation of the function's rule.

The graph of a function can take many different forms, depending on the function's rule. Linear functions, for example, will produce a straight line on the graph.

i) 2y - 4x < 8 can be solved by adding 4x to both sides and then dividing by 2, giving:

y < 2x + 4.

ii) -4y > -x + 12 can be solved by adding x to both sides and then dividing by -4, giving: y < x/4 - 3.

iii) | x + 3 | = y, you can split this into two cases:

i. x + 3 = y

ii. -(x + 3) = y

iv) |2x – 6| + 2 = y, you can split this into two cases:

i. 2x - 6 + 2 = y

ii. -(2x - 6) + 2 = y

We can use these equations to plot the graph on a coordinate plane.

Hence, the solution is the set of all points (x,y) that satisfy the inequalities:

y < 2x + 4,  y < x/4 - 3, x + 3 = y, and 2x - 6 + 2 = y.

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Answer:

x=24

Step-by-step explanation:

Step 1: Add 3 to both sides: 1/2x-3+3=9+3

Simplify that: 1/2x=12

Step 2: Multiply both sides by 2: 1/2x*2=2*12

Simplify: x=24

Hope this helped! :)

Answer:

A =576 pi in ^2

Step-by-step explanation:

Circumference  is given by

C = 2 * pi *r

48 pi = 2 * pi *r

divide by 2 pi

48 pi /2 pi = 2 * pi * r / 2 pi

24 = r

We can find the area by

A = pi r^2

A = pi (24)^2

A =576 pi in ^2

Answer:

576π in^2

Step-by-step explanation:

Circumference of circle (C) = 2πr = 48π in

2πr = 48 π

r = 48π/2π = 24 in

Area of circle (A) = πr^2

r (radius of circle) = 24 in

A = π(24 in)^2 = 576π in^2

Step-by-step explanation:

An economy is made up of every single activity that has to do with production, consumption, and the buying and selling of goods or rendering services.

In an economy there are combinations of market transactions and decisions made collectively or in hierarchy. Individuals, families, businesses, governments make up the decision-making process.

Money is the legal tender of an economy. It is the medium of exchange that an economy uses for transactions.

Answer: x = 20

5 x 1 - (3x/5) = -7

5 - (3x/5)= -7

5 + 7 = 3x/5

12 = 3x/5

12 x 5 = 3x

60 = 3x

60/3 = 3x/3

20 = x

Answer:

80*

80*

75*

120*

Step-by-step explanation:

both angle 1 and 2 for the first image have the same value as  the other angle of 80* because it is a set of parallel lines and one line going through it.

1 on the next set of images is 75* because is is an alternate exterior angle.

2 of the last set of images is 120* because it is same side interior angles.

Answer:

(g + h)(x) = x² + 7x + 1

Step-by-step explanation:

(g + h)(x)

= g(x) + h(x)

= x² + 4x + 5 + 3x - 4 ← collect like terms

= x² + 7x + 1

Answer:

the answer is y = x-5

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

= 2x - 8 + 2x - 6 =

= 2x + 2x - 8 - 6 = 4x - 14 ← the end