Y = 3x(x -4) how many solutions

Answer:

0.125

Step-by-step explanation:

to get the reciprocal of a number we divide the number by 1

in this case it would be 1 divide by 8

1/8 = 0.125

Answer:

\(L + \frac{5}{8} = 1\)

Step-by-step explanation:

Given

A cup of coffee

Kelly drank 5/8 of the coffee

Required

Determine how much is left

Start by representing the amount of coffee left with L

Because the amount of coffee Kelly drank is in fraction (5/8), the total cup of coffee will equate to 1;

Hence, the addition equation as requested in the question to represent the scenario is

\(L + \frac{5}{8} = 1\)

Answer:

Option (A)

Step-by-step explanation:

By the characteristics of a quadrilateral given in the question,

1). All four sides are congruent.

It may be Square, Rhombus

2). Both the pairs of opposite sides are parallel.

It may be Parallelogram, Rhombus.

3). Diagonals are perpendicular.

It may be Rhombus, Rectangle, Square.

Since all three characteristics define the properties of a Rhombus,

The given quadrilateral matches with a rhombus.

Therefore, Option (A) will be the answer.

Answer:

Choice C

\(\frac{\sqrt{186}+\sqrt{15}}{18}\)

Step-by-step explanation:

The quadrant in which an angle lies determines the signs of the trigonometric functions sin, cos and tan

If an angle Θ lies in quadrant IV, cos(Θ) is positive and both sin(Θ) and tan(Θ) are negative

Two of the trigonometric identities we can use are

1. \(\sin^2(\theta) + cos^2(\theta) = 1\)  and

2. \(\cos(A-B) = \cos A\cos B - \sin A\sin B\)

Using identity 1, we can solve for cos(s) and cos(t)

\(sin(s)=-\frac{\sqrt{3}}{3}, sin^{2}(s)=\frac{3}{9}=\frac{1}{3}\\cos^{2}(s)=1-sin^{2}(s)=1-\frac{1}{3}=\frac{2}{3}; cos(s)=\pm\sqrt{\frac{2}{3}}\\\\\)

\(sin(t)=-\frac{\sqrt{5}}{6}, sin^{2}(t)=\frac{5}{36}cos^{2}(t)=1-sin^{2}(t)=1-\frac{5}{36}=\frac{31}{36};cos(t)=\pm\frac{\sqrt{31}}{6}\)

Since both angles lie in quadrant IV, both cos(s) and cos(t) must be positive so we only consider the positive signs of both values

Using identity 2, we can solve for cos(s-t)

\(cos(s-t)=cos(s)cos(t)+sin(s)sin(t)=\frac{\sqrt{2}}{\sqrt{3}}.\frac{\sqrt{31}}{6}+(-\frac{\sqrt{3}}{3})(-\frac{\sqrt{5}}{6})\)

Multiplying numerator and denominator of the first term by \(\sqrt{3}\) gives us the final expression as

\(\frac{\sqrt{3}}{\sqrt{3}}\frac{\sqrt{2}}{\sqrt{3}}.\frac{\sqrt{31}}{6}+(-\frac{\sqrt{3}}{3})(-\frac{\sqrt{5}}{6})=\frac{\sqrt{186}}{18}+\frac{\sqrt{15}}{18}= \frac{\sqrt{186}+\sqrt{15}}{18}\)

Using the concept of the word problem and utilizing the provided conditions and values, The answer is 18, 20, and 22.

A word problem in mathematics is a problem or exercise that is expressed in a natural language, rather than in mathematical notation. These types of problems often present a real-world situation that involves mathematical concepts, such as numbers, operations, or measurements. They typically require the use of mathematical reasoning and problem-solving skills to understand the problem and find a solution. Examples of word problems include: "If a train travels 60 miles per hour and you want to know how far it will travel in 4 hours", "If a rectangle is 6 meters long and 4 meters wide, what is its area?", "If a bag contains 3 red balls and 4 blue balls, what is the probability of picking a blue ball?"

In a mathematical problem, the conditions refer to the specific information or constraints provided in the problem statement that must be taken into account in order to find a solution. These conditions can include information about the quantities involved in the problem, the operations that need to be performed, or the specific requirements that the solution must meet.

Let x be the smallest of the three consecutive even integers. Then the next two integers are x+2 and x+4. We know that:

x + (x+4) * 3 = 84

Expanding and solving for x:

x + 3x + 12 = 84

4x = 72

x = 18

So the three consecutive even integers are 18, 20, and 22.

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a) To re-express the given differential equation as a first-order differential equation using matrix and vector notation, we can rewrite it in the form:

\(x' = Ax\)

where x is a vector and A is a square matrix.

b) To determine the stability of the system obtained in part (a), we need to analyze the eigenvalues of matrix A.

If all eigenvalues have negative real parts, the system is stable.

If at least one eigenvalue has a zero real part, the system is neutrally stable.

If at least one eigenvalue has a positive real part, the system is unstable.

c) To compute the eigenvalues and eigenvectors of matrix A, we solve the characteristic equation

\(det(A - \lambda I) = 0\),

where λ is the eigenvalue and I is the identity matrix.

By solving this equation, we obtain the eigenvalues.

Substituting each eigenvalue into the equation

\((A - \lambda I)v = 0\),

where v is the eigenvector, we can solve for the eigenvectors.

d) Once we have computed the eigenvalues and eigenvectors of matrix A, we can construct the diagonalization relationship as follows:

\(A = PDP^{(-1)}\)

where P is a matrix whose columns are the eigenvectors of A, and D is a diagonal matrix whose diagonal elements are the eigenvalues of A.

To show that this relationship is valid, we can compute \(PDP^{(-1)}\) and verify that it equals A.

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Answer:

To calculate the future value of an investment compounded annually, we can use the formula:

Future Value = Principal Amount * (1 + Interest Rate)^(Number of Periods)

In this case, the principal amount is $3200, the interest rate is 2.4% (or 0.024), and the investment is compounded annually for 4 years.

Plugging these values into the formula, we get:

Future Value = $3200 * (1 + 0.024)^4

Calculating the exponent first:

(1 + 0.024)^4 = 1.024^4 = 1.09985925696

Multiplying the principal amount by the exponent:

Future Value = $3200 * 1.09985925696

Future Value ≈ $3,519.47

Therefore, the investment will be worth approximately $3,519.47 after 4 years when compounded annually at a rate of 2.4%.

Step-by-step explanation:

Answer:

The answer to this question can be defined as follows:

Step-by-step explanation:

In the question equation is missing so, the equation and its solution can be defined as follows:

\(B={b_1,b_2}\\\\b_1= \left[\begin{array}{c}5&5\end{array}\right] \ \ \ \ \b_2= \left[\begin{array}{c}2&-5\end{array}\right] \ \ \ \ \x= \left[\begin{array}{c}-7&-35\end{array}\right]\)

\(\left[\begin{array}{c}a&c\end{array}\right] =?\)

\(\to \left[\begin{array}{c}-7&-35\end{array}\right]= a\left[\begin{array}{c}5&5\end{array}\right]+c \left[\begin{array}{c}2&-5\end{array}\right] \\\)

\(\to \left[\begin{array}{c}-7&-35\end{array}\right]= \left[\begin{array}{c}5a+2c&5a-5c\end{array}\right]\\\\\to 5a+2c=-7....(1)\\\\\to 5a-5c=-35....(2)\\\\\)

subtract equation 1 from equation 2:

\(\to 7c=28\\\\\to c=\frac{28}{7}\\\\\to c= 4\\\\\)

put the value of c in equation 1

\(\to 5a+2(4)=-7\\\to 5a+8=-7\\\to 5a=-7-8\\\to 5a=-15\\\to a= -3\)

coordinate  value is [-3,4].

The equivalent quadratic function in vertex form is:

y = (x + 9.97)² - 19.95.

We have,

A quadratic equation is modeled by:

y = ax^2 + bx + c

The vertex is given by: x_v, y_v

In which:

x_v = -b/2a

y_v = - b² -4ac/2a

Considering the coefficient a, we have that:

If a < 0, the vertex is a maximum point.

If a > 0, the vertex is a minimum point.

In this problem, the function is:

f(x) = x² + bx + 118.

The coefficients are of a = 1 and c = 118. The minimum is of y_v = 37, hence we use it to solve for b.

37 =  - (b² -4ac)/2a

b² - 472 = -74

b² = 398

b = sqrt(398)

b = 19.95

The x-value of the vertex is:

x_v = -b/2a = - 9.97

What is the equation of a parabola given it’s vertex?

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

For this problem, we have that a = 1, h = - 9.97 and k = 19.95, hence:

y = (x + 9.97)² - 19.95.

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Answer:

2 and 16/25

Step-by-step explanation:

first: change 0.64 into a fraction which is 64/100

second: simplify by dividing by four which is:

64/4 = 16

100/4 = 25

so...

2.64 = 2 16/25

HOPE THIS HELPS :)

Answer:

2 and 16/25 OR 66/25

Step-by-step explanation:

As a mixed fraction, 2.64 is 2 and 64/100 because you have 2 whole 100s and a 64/100. Simplify 64/100 to 16/25 (divide both 64 and 100 by 4) and you're left with 2 and 16/25.

In improper form, you have 264/100. Simplify that (divide 264 and 100 by 4) and you're left with 66/25.

Answer:

HI

Step-by-step explanation:

HI HI HI HI HI HI HI HI HI HI HI HI

Answer:

Your slope is -3/2 and your y-intercept is -3/2

Step-by-step explanation:

Let's solve for x.

2x−y=−3

Step 1: Add y to both sides.

2x−y+y=−3+y

2x=y−3

Step 2: Divide both sides by 2.

2x/2=y−3/2

x=1/2y+−3/2

Domain: (-∞, ∞)

Range: [0, ∞)

Domain and range help describe the values that the function covers.

Domain

The domain of a function describes the x-values covered by a function. This means that any x-value that can be input into the function is part of the domain. The domain of this function is all real numbers. This is because any x-value could be input into the function and give an output. Additionally, the graph will continue for infinity and cover all x-values. In interval notation, the domain is (-∞, ∞). The domain for all quadratic functions is all real numbers, also written as (-∞, ∞).

Range

The range of a function describes the y-values covered by a function. Any y-values that are possible outputs are a part of the range. In this function, we can see that the parabola does not cover the positive y-values. So, the only possible outputs for the function are negative values. This means that our range will only be the negative values. In interval notation, the range is  [0, ∞). We use brackets to show that the 0 is included in the range. Since infinity cannot be included in a domain or range, we use parentheses.

Bank account with an interest rate of r% per year = 2.5%

Simple Interest :

Simple interest paid or received over a certain period is a fixed percentage of the principal amount.

Simple Interest=P×\(\frac{r}{100} }\)×T

where:

P=Principal

r= interest rate on a certain period

T= Time

Given :

Principal(P)=  £1000

Time (T)= 1 Year

Find :

the interest rate per year = r%

Now,  

Interest earned on account =  £1025 - £1000

Simple Interest= £ 25

Simple Interest=P×\(\frac{r}{100}\)×T

25= 1000×\(\frac{r}{100}\)×1

25×100=1000r

2500=1000r

\(\frac{2500}{1000} =r\\\frac{25}{10} =r\\\frac{5}{2} =r\\2.5=r\)

r= 2.5%

the interest rate of r% per year. after one year the value of the account=2.5%

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​

The unknown measures in similar triangles in which x is 24 in.

What is a similar triangle?

Two triangles are similar if their corresponding angles are equal and their corresponding sides are within the same ratio (or proportion). Similar triangles will have the same shape, but not necessarily the same size.

We have given,

ΔABC ≈ ΔXYZ

In ΔABC

AC = 36 in, BC = 18 in and AB = x in

In ΔXYZ

XY = 16in, ZY = 12in and  XZ = 24in

We know that,

the side and angles of a similar triangle are in proportion to each other.

AC / XZ = 36 / 24 = 3/2

BC / ZY = 18 / 12 = 3/2

AB / XY = x / 16

AC / XZ = BC / ZY = AB / XY   --------(similar triangle)

x / 16 = 3/2

x  = 3/2 * 16

x = 3 * 8

x = 24

hence, the unknown measures in similar triangles in which x is 24 in.

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Answer:

m=54/5=104/5=10.8

Step-by-step explanation:

3.6=m×(1.2/3.6)

3.6=m×(12/36)

3.6=m×(1/3)=3.6

m=3.6×3

m=10.8

Done!

Answer:

838.89, simplified 840

Step-by-step explanation:

Answer:

A. (1/2)(4+i)= 2+ (1/2)i

Step-by-step explanation:

The equation 1/2(4+i) = 2+(1/2)i is the transformation if we multiply the complex number 4 + i with 1/2 option first is correct.

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have a complex number:

= 4+i

Multiply it by 1/2

\(= \rm \dfrac{1}{2}(4+i)\\\\\rm =2+ \dfrac{1}{2}i\)

\(\rm \dfrac{1}{2}(4+i) =2+ \dfrac{1}{2}i\)

Thus, the equation 1/2(4+i) = 2+(1/2)i is the transformation if we multiply the complex number 4 + i with 1/2 option first is correct.

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Answer:

208.16 miles

Step-by-step explanation:

421.06 - 212.9 =208.16

Answer:

208.16

Step-by-step explanation:

if you subtract 421.06-212.9 you get 208.16

Answer:

Dessert 1 is 10 million

Step-by-step explanation:

Do 12 million divided by six and you get 2 million. Then do 2 million times 5 and you get 10 million and this works because 10 million is five times more than 2 million and they add up to get 12 million.

Please give me brainliest

Answer:

The product of 3 and 10√28, in its simplest radical form is: 60√7.

Step-by-step explanation:

hope it helps

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Answer:

x = 0, 4/5

Step-by-step explanation:

The zero-product property states that if the product of a and b is zero, then either a = 0, b = 0, or both terms equal zero

Answer:

Explained below.

Step-by-step explanation:

In this case we need to determine if there has been an increase in the proportion of rooms occupied over the one-year period.

(a)

The hypothesis can be defined as follows:  

H₀: The proportion of rooms occupied over the one-year period has not increased, i.e. p₁ - p₂ ≤ 0.  

Hₐ: The proportion of rooms occupied over the one-year period has increased, i.e. p₁ - p₂ > 0.  

(b)

The information provided is:

n₁ = 1750

n₂ = 1800

X₁ = 1470

X₂ = 1458

Compute the sample proportions and total proportions as follows:

 \(\hat p_{1}=\frac{X_{1}}{n_{1}}=\frac{1470}{1750}=0.84\\\\\hat p_{2}=\frac{X_{2}}{n_{2}}=\frac{1458}{1800}=0.81\\\\\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{1470+1458}{1750+1800}=0.825\)

(c)

Compute the test statistic value as follows:

\(Z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat p(1-\hat p)\times [\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}\)

   \(=\frac{0.84-0.81}{\sqrt{0.825(1-0.825)\times [\frac{1}{1750}+\frac{1}{1800}]}}\\\\=2.352\)

The test statistic value is 2.352.

(d)

The decision rule is:

The null hypothesis will be rejected if the p-value of the test is less than the significance level.

Compute the p-value as follows:

 \(p-value=P(Z>2.352)=1-P(Z<2.352)=1-0.99061=0.00939\)

The p-value of the test is very small. The null hypothesis will be rejected at any significance level.

Thus, there enough evidence suggesting that there has been an increase in the proportion of rooms occupied over the one-year period.

Peter left Town A around 10 a.m., traveling at an average speed of 84 km/h. William would reach Town B at 1:23 PM.

Firstly, we need to find the distance between Town A and Town B which can be calculated by calculating the distance travelled by Peter

Time taken by Peter = 2PM - 10AM

= 4 hrs

Speed of Peter = 84 km/h

Distance travelled by Peter = speed × time

= 84 × 4

= 336 km

So, the distance between Town A and Town B  = distance travelled by Peter = 336 km.

Now, we will calculate time taken by William.

Speed of William = 70 km / hr

Distance travelled by William = distance between Town A and town B = 336 km

Time taken by William = distance / speed

= 336 / 70 hr

= 4.8 hr

This can b converted into hrs and minutes

4.8 hr = 4 hr + 0.8 × 60

= 4 hr 48 mins

Time William took off = 10 AM - 1hr 25 mins

= 8:35 AM

Now, we will calculate the time William would reach town B.

Time = 8:35 + 4hr 48 mins

= 1:23 PM

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Answer.

8.4>6.9

Step-by-step explanation:

because 8.4 is greater than 6.9

Answer:

8.4 >6.9

Step-by-step explanation:

The ship is 88.8 miles far from the port at 4 pm.

Given,

The displacement from 1 to 3 in the afternoon.

D1 = 30 miles/hr × 2 hr

     = 60 miles to the north

The displacement from 3 till 4 in the afternoon.The ship changes its course 20 degrees eastward at 3 o'clock.

Therefore, D2 = 30 miles/hr × 1 hr

                       = 30 miles to the 20° north eastward

By combining two vectors, the resulting displacement:

D = √((D1 ₊ D2 × cos(20°))² ₊ (D2 × sin(20°))²

D = √((60 ₊ 30 × cos (20°))² ₊ (30 × sin(20°))²

D = 88.8 miles

Hence the ship is 88.8 miles far away from the port at 4 pm.

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Answer:

The radical cannot be simplified, but it can be approximated.

Exact Form:

24

√

30

Decimal Form:

131.45341380

Step-by-step explanation:

cannot show steps right now

Answer:

7 years

Step-by-step explanation:

27370 - 26986.82 = 383.18ft

0.2% = 0.2/100 = 0.002

27370*0.002 = 54.74

each year the montain reduce your elevation

54.74ft

then:

383.18/54.74 = 7

Answer:

7 years