Find the slope of the line through each pair of points.
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The expression of the solution of the given quadratic equation is gotten as; x = 5 ± 2√3

We want to find the solution to the quadratic equation given as;

x² - 10x + 13 = 0

We will use the quadratic formula to get;

x = [-b ± √b² - 4ac]/2a

x = [-(-10) ± √(-10)² - 4(1 × 13)]/2(1)

x = 5 ± (√48)/2

x = 5 ± (4√3)/2

x = 5 ± 2√3

Thus, the solution is x = 5 ± 2√3

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Answer:

96.023 is the answer yeah

The Project Triangle is also known as the triple constraints model and consists of three elements: cost, time and scope.

The Project Triangle is also known as the Iron Triangle or Triple Constraints and is a graphical representation of the connection between project costs, schedule, and scope. It is one of the key principles of project management, and it is utilized to help organizations and project managers understand and handle trade-offs between different objectives of a project.

The three elements of the Project Triangle are:

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There were about 204 principals in attendance.

The correct option is (A).

The mathematical branch known as arithmetic deals with the study and application of numbers, their relationships, and mathematical observations.

As per the given data:

The total number of people in the recent conference = 875

The total number of people in one exhibit room = 60

Number of teachers in one exhibit room = 46

Number of principals in one exhibit room = 14

To find out the total number of exhibit rooms:

= Total number of people in the conference / total people in one room

= 875 ÷ 60

= 14.58 = 15 {rounding off to the nearest integer}

Number of principals in one exhibit room = 14

Total number of principals in the conference:

= Number of rooms × Principals in one room

= 15 × 14 = 210 which is equal to 204 {approximate answer}

There were about 204 principals in attendance.

Hence, There were about 204 principals in attendance.

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Answer:

9/3+4=

4+3=

7

Step-by-step explanation:

Because of order of operations, we have to divide first. Then we will add the quotient with 4. If m=3, then we will replace m with 3.

9/3 is 3. Now we add.

3+4=7.

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sorry if this doesn't help

The vector (1,5) could be in E5, and option(a) there is not enough information to determine whether any other vector from the given options could be in E5.

In the given , we are told that the eigenvalues of the 2x2 symmetric matrix A are 3 and 5. We are also given that E3 spans the vector (1,5). This means that (1,5) is an eigenvector corresponding to the eigenvalue 3.

To determine which of the given vectors could be in E5, we need to find the eigenvector(s) corresponding to the eigenvalue 5. However, this information is not provided. The eigenvectors corresponding to the eigenvalue 5 could be any vector(s) that satisfy the equation Av = 5v, where v is the eigenvector.

Given this lack of information, we cannot determine whether any of the vectors (5,-1), (-5,1), (10,-2), or (1,1) are in E5. The only vector we can confidently say is in E5 is (1,5) based on the given information that E3 spans it.

In conclusion, (1,5) could be in E5, but there is not enough information to determine whether any of the other given vectors are in E5.

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Answer:

x=150

y=240

Step-by-step explanation:

*Use simultaneous equation solving

1.Label your equations

x+y=390......1

2x+4y=1260......2

*make one of the unknowns subject of formula, to form equation 2

x=390-y.....3

*sub.3 into 2

2(390-y)+4y=1260

780-2y+4y=1260

2y+780=1260

y=240

sub. y into 3

x=390-y

x=390-240

x=150

Answer:

b= 20.8

Step-by-step explanation:

Pythagorean Theorem: a²+b²=c²

a= 12

b= ?

c= 24

Equation: 12²+b²=24²

12²= 144

24²= 576

New equation: 144+b²=576

Find b: 576-144=432

\(\sqrt432\)= 20.7846097

Round to nearest tenths: 20.8

b= 20.8

Check answer:

144+432=576

Correct!

The equilibrium level of real GDP can be determined by equating aggregate demand (AD) with aggregate supply (AS). At this level, there is no tendency for output to change, and the economy is operating at full employment.

The equilibrium level of real GDP is determined by the intersection of the aggregate demand (AD) and aggregate supply (AS) curves. At this point, the total spending in the economy matches the total production, resulting in no unplanned inventory changes. In the given problem, we need to consider the consumption function, tax function, planned investment, and planned government expenditures to calculate the equilibrium level of real GDP.

In a closed economy, the equilibrium level of real GDP is determined by the intersection of the aggregate demand (AD) and aggregate supply (AS) curves. The consumption function represents the relationship between disposable income (y - t) and consumption (c). In this case, the consumption function is given as c = 3.5 + 0.6(y - t) billions of 2020 dollars. The tax function shows the relationship between national income (y) and taxes (t), given as t = 0.15y + 0.4 billions of 2020 dollars. Planned investment is $2.5 billion, and planned government expenditures are $2 billion.

To calculate the equilibrium level of real GDP, we need to equate aggregate demand (AD) with aggregate supply (AS). Aggregate demand (AD) is the sum of consumption (C), planned investment (I), and government expenditures (G), represented as AD = C + I + G. In this case, AD = [3.5 + 0.6(y - t)] + 2.5 + 2. By substituting the tax function into the consumption function and simplifying, we can rewrite the aggregate demand equation as AD = [3.5 + 0.6(y - (0.15y + 0.4))] + 2.5 + 2.

The aggregate supply (AS) curve represents the relationship between the price level and the quantity of real GDP supplied. Since the problem does not provide information about the AS curve, we assume that it is upward sloping. At the equilibrium level of real GDP, AD equals AS. By equating AD and AS, we can solve for the value of y, which represents the equilibrium level of real GDP.

To summarize, the equilibrium level of real GDP in this closed economy can be calculated by equating aggregate demand (AD) with aggregate supply (AS). We need to consider the consumption function, tax function, planned investment, and planned government expenditures to determine the equilibrium level of real GDP. By solving the equations and finding the intersection point, we can find the value of y, representing the equilibrium level of real GDP.

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Answer:

42 sheet of paper

Step-by-step explanation:

$7.84 divided by $0.16

This equals 42

After spending 7 dollars and 84 cents, 42 sheets of paper will be sold.

D(t)= 6sin (pi/5t) + 10

General form:

y = A sin (Bx +C) +D

Where:

A = amplitude

D= vertical shift

C = phase shift B= period

For the given function:

Amplitude = 6

Phase shift = 10

The bottom graphs are Cosine functions, so they are not.

Among the top ones, The first one has an amplitude of 6 and the second one has an amplitude of 3 .

Correct answer:

Answer: B) as x→-∞, f(x) →∞ as x→∞, f(x) →-∞

Step-by-step explanation:

Answer:

It is daytime for me

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

Answer:

nth term = 7+(n-1)4

Step-by-step explanation:

Answer:

We conclude that:

\(-4k+5\le \:21\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:k\ge \:-4\:\\ \:\mathrm{Interval\:Notation:}&\:[-4,\:\infty \:)\end{bmatrix}\)

The number line graph of the solution is also attached below.

Step-by-step explanation:

Given the equation

\(-4k+5\le \:21\)

Subtract 5 from both sides

\(-4k+5-5\le \:21-5\)

Simplify

\(-4k\le \:16\)

Multiply both sides by -1 (reverse the inequality)

\(\left(-4k\right)\left(-1\right)\ge \:16\left(-1\right)\)

Simplify

\(4k\ge \:-16\)

Divide both sides by 4

\(\frac{4k}{4}\ge \frac{-16}{4}\)

Simplify

\(k\ge \:-4\)

Therefore, we conclude that:

\(-4k+5\le \:21\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:k\ge \:-4\:\\ \:\mathrm{Interval\:Notation:}&\:[-4,\:\infty \:)\end{bmatrix}\)

The number line graph of the solution is also attached below.

The algebraic expression for this problem is given as follows:

2C - D = -2x² + 2x + 11.

The definition for C in this problem is given as follows:

C = x + 3.

We applying the distributive property to multiply by 2 as follows:

2C = 2(x + 3) = 2x + 6.

The definition for D in this problem is given as follows:

D = 2x² - 5.

The subtraction is then obtained as follows:

2C - D = 2x + 6 - (2x² - 5)

2C - D = 2x + 6 - 2x² + 5

2C - D = -2x² + 2x + 11.

Meaning that the second option is correct.

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Hey there! I'm happy to help!

Sum means to add. Let's call our number n.

n+6

We multiply this whole thing by 5.

5(n+6)

And this is 48.

5(n+6)=48

Have a wonderful day! :D

Answer:

-6 +2 = -4

Step-by-step explanation:

Its simple. Whenever you see two negative signs next to each other, they merge into an addition sign "positive".

-6+2 = -4

The answer is option (C), that is, the events of rolling a fair die two times are independent. The events are neither disjoint nor exclusive.

When rolling a fair die two times, one can get any one of the 36 possible outcomes equally likely. Let A be the event of obtaining an even number on the first roll and let B be the event of getting a number greater than 3 on the second roll. Let’s see how the outcomes of A and B are related:

There are three even numbers on the die, i.e. A={2, 4, 6}. There are four numbers greater than 3 on the die, i.e. B={4, 5, 6}. So the intersection of A and B is the set {4, 6}, which is not empty. Thus, the events A and B are not disjoint. So option (A) is incorrect.

There is only one outcome that belongs to both A and B, i.e. the outcome of 6. Since there are 36 equally likely outcomes, the probability of the outcome 6 is 1/36. Now, if we know that the outcome of the first roll is an even number, does it affect the probability of getting a number greater than 3 on the second roll? Clearly not, since A∩B = {4, 6} and P(B|A) = P(A∩B)/P(A) = (2/36)/(18/36) = 1/9 = P(B). So the events A and B are independent. Thus, option (C) is correct. Neither option (A) nor option (C) can be correct, so we can eliminate options (D) and (E).

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to hi hello how to help you out front of your house at the

The required amount in the account is given as $878.48.

Given that,
On February 1, the balance is your account is $516.81. On July 1, you deposit $310.90. Your bank pays 6.25% interest.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan.

Here,
According to the question,
Total money in the account = 516.81 + 310 = 775.81
Total money in the account after interest = 775.81 [1 + 0.0625] = 878.48

Thus, the required amount in the account is given as $878.48.

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Answer:

Step-by-step explanation:

-4x+7y=20

y=3x+15

sol

7y/7=20/7+4x7

y=2.857+4/7x

y=3x+15

Answer:

8.7%

Step-by-step explanation:

Well the net sales of Quarter 1 = 115 whilst the net sales of Quarter 2 = 125.

So the difference in the 2 numbers is 125-115 = 10

To find percentage change, you do 10/115 = 0.0869565217

Then, 0.0869565217 x 100 = 8.7% change to 1 decimal point.

So your percentage change is 8.7%.

Answer:

Step 1

Formulate a recursive sequence modeling the number of grams after n  minutes.

we have that

100%-17.1%-------------- > 82.9%------------> 0.829

a(n) = 780*[0.829^n]

for n=19 minutes

a(19)=780*[0.829^(19)]=22.1121 g---------------> 22.1 g

the answer is 22.1 g

Step-by-step explanation:

Answer:

4   5

Step-by-step explanation:

I got it right here.

The factored form of (20x² – 12x) + (25x– 15) is (4x+ 5)( 5x- 3).

The process of breaking or decomposing an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorisation or factoring.

Given:

(20x² – 12x) + (25x– 15)

or, 4x(5x – 3) + 5(5x – 3)

or, (4x+ 5)( 5x- 3)

Hence, the factored form of (20x² – 12x) + (25x– 15) is (4x+ 5)( 5x- 3).

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Answer:

(4x)^2-49

Step-by-step explanation: hoped I helped

The picture represents isosceles triangle theorem.

From the figure :

It is represented that two sides are equal.

And the angles opposite to this two equal sides are equal.

So it is a isosceles triangle.

Isosceles triangle:

If two sides of a triangle are congruent , then the angles opposite to these sides are congruent.

Therefore the picture represents isosceles triangle theorem.

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