(2+5root7)/(2-5root7) = a+b root7
class 9

with complete explanation pls

Initial value of the linear function through A and B is 3.

The starting output value, or the y-value when x = 0, is the initial value. The rate of change is the rate at which the input or, in the case of a graph, the rate at which y changes in relation to x. A function's starting value in mathematics denotes the function's y-intercept. The constant in an equation can also be used to determine initial values. In graph functions, understanding the y-intercept is beneficial. By substituting 0 0 for x x and finding y y, you may verify the starting value.

Given,

Points

A (1,3)

B (6,13)

Linear function,

f(x) = ax + b

Equating,

f(x) = x + 3

Let x = 0

f(x) = 3

As we know,

The graph of a linear function is a straight line. The following is the form of a linear function. a + bx = y = f(x). One independent variable and one dependent variable make up a linear function. X and Y are the independent and dependent variables, respectively.

Initial value of the linear function through A and B is 3.

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Equal sides are the paragraph's omission.

Common Side BA is the Missing Piece of the Proof.

The reasons given in the evidence are sufficient to demonstrate that BCA and BFA are similar.

ΔBFA≅ ΔBCA, but not sufficiently to demonstrate that BCA is compatible with BFA.

To demonstrate congruent triangles, we must demonstrate that the corresponding sides are likewise equal, so we must demonstrate that BA = BA (common side) before the Proof is complete.

Hence, Equal sides are the paragraph's omission.

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Answer:

in picture

Step-by-step explanation:

Answer:

22/17

Step-by-step explanation:

If a/b = 3/4, then a = 3 and b = 4.

6a + b/3a + 2b

Substitute the variables.

6(3) + 4/3(3) + 2(4)

Multiply 6 and 3, 3 and 3, and 2 and 4.

18 + 4/9 + 8

Add 18 and 4, 9 and 8.

22/17.

Once mona returns to her starting point, swam a total of 132 yards.

It states that in any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs).

We can use the Pythagorean theorem to find the distance that Mona has swum. Let's call the diagonal distance between the northwest and southeast corners of the swimming pool "d".

Using the Pythagorean theorem, we have:

d² = 44² + 33²

d² = 1936 + 1089

d² = 3025

d = 55

Therefore, the diagonal distance that Mona has swum is 55 yards. However, since she swam along the width and length of the pool as well, we need to add those distances to the diagonal distance to get the total distance she swam.

Mona swam 44 yards along the width and 33 yards along the length, so her total distance swum is:

55 + 44 + 33 = 132 yards

Therefore, Mona swam a total of 132 yards.

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Answer: 0.640

Step-by-step explanation:

Multiply in your calculator

Step-by-step explanation:

let gold fish= X

let Plecos fish= Y

X +Y = 17................(I)

13.49X + 3.25Y =198.61........(II)

solve simuteniously to get

X = 14

Y = 3.....therefore

she bought 14 gold fish and 3 plecos fish

Answer:

Step-by-step explanation:

For equation-x²4x+11

x=-b+_√b²-4ac/2a

 = -4+-√16-44/2

 =-2+-√-7

 =-2+-√7i

hence correct option is

Answer:

i help to solve the problem

Answer:

$52.50

Step-by-step explanation:

Divide to find the unit rate.

84 / 8 = $10.50 per lawn

Multiply.

10.5 * 5 = $52.50 for 5 lawns

Best of Luck!

Answer:

52.50

Step-by-step explanation:

Answer: 12 days

Step-by-step explanation:

3.87/3=1.29 liters of jam in 1 day

1.29*12=15.48 liters in 12 days

Answer:

12 days

Step-by-step explanation:

Answer:

  544 units²

Step-by-step explanation:

The surface area is the sum of the areas of the three rectangular faces and the two triangular bases.

  SA = 10×14 +10×14 +12×14 + 2(1/2)(12)(8)

  = 14×(10+10+12) +12×8

  = 448 +96

  = 544 . . . . square units

_____

The area of a rectangle is the product of its dimensions:

  A = LW

The area of a triangle is half the product of its base and height:

  A = (1/2)bh

Here, both triangles have the same area, so we multiplied the area of one of them by 2 to get the area of both of them.

Yes, the forester was justified in using a Normal model to analyze the woods, because the histogram is unimodal and symmetric. So option A is correct.

A histogram is a type of graph that uses vertical bars to show the distribution of a set of data. This particular histogram is unimodal, meaning that it has one peak which is an indication that the data is distributed normally. Additionally, the histogram is symmetric, which is another indication that the data is normally distributed.
Using a Normal model to analyze the woods is a valid approach because it allows the forester to identify the average diameter of the trees, as well as the spread of the data. It also allows him to check for any outliers, or points that fall outside the normal range. With this information, the forester can determine if the woods is suitable for sale, or if the buyer should be aware of any unexpected features.
Overall, the histogram is an effective way for the forester to analyze the data and determine if a Normal model is appropriate. By noting the unimodal and symmetric nature of the histogram, the forester can be sure that a Normal model will accurately represent the data, allowing him to make an informed decision about the woods.

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The probability that a randomly chosen person will test positive is given by 0.1704.

The Bayes Theorem and the rule of total probability are used to calculate conditional probabilities. These fundamental theorems are crucial for determining the likelihood of occurrences that rely on other events in the same experimental setting or study domain.

How sensitive and precise a test is can tell us how accurate our forecasts of a certain occurrence are.

Let D represent the occurrence of a disease in a person and O represent the occurrence of the person testing positive for the disease.

P(O|D) = 0.98

P(O'|D') = 0.90

P(D) = 0.08

In this instance, we must determine the probability, P, that a randomly selected individual would test positive (O).

Using law of total probability:

P(O) = P(O|D) x P(D) + P(O|D') x P(D')

= 0.98 x 0.08 + 0.10 x 0.92

= 0.1704

As a result, 0.1704 percent of randomly selected individuals will test positive.

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Answer:

Yeah, that's happening to me right now.. :/

Im not sure how to fix it either :c

Answer:

I just need popints

Step-by-step explanation:

I just need points

Answer: R=3 Bracelets per HR

O=2 Bracelets per HR

Step-by-step explanation: She can go faster

Answer:

a = 6, b = 1, c = -6

Step-by-step explanation:

Quadratic equations can be written as ax² + bx + c. In this case, a = 6, b = 1, c = -6.

Answer:

\(b= \frac{-4}{7} a - \frac{52}{7}\)

Step-by-step explanation:

1st, isolate b.

7b=-4a-52

Next, divide both sides by 7.

b=(-4a/7)-(52/7)

Sigma notation to write the Taylor series about x=x0 for the function. e−3x, x0=(−1/3) is e^-3x = ∑k=0[infinity] (-3e)^k/ (k!) (x+1/3). Sigma notation is a way to represent series of numbers using the summation symbol, Σ.

To write the Taylor series about x=x0=(-1/3) for the function e^-3x, we first need to find the derivatives of the function at x=x0.
f(x) = e^-3x
f(0) = e^0 = 1
f'(x) = -3e^-3x
f'(-1/3) = -3e^1 = -3e
f''(x) = 9e^-3x
f''(-1/3) = 9e^1 = 9e
f'''(x) = -27e^-3x
f'''(-1/3) = -27e^1 = -27e
And so n.
Using the Taylor series formula, we can write the Taylor series as:
e^-3x = ∑k=0[infinity] (f^(k)(-1/3)/k!)(x+1/3)^k
Substituting the values we calculated above, we get:
e^-3x = ∑k=0[infinity] (-3e)^k/ (k!) (x+1/3)^k
Sigma notation is a way to represent series of numbers using the summation symbol, Σ. In this problem, we used sigma notation to write the Taylor series for the function e^-3x about the point x=x0=(-1/3). The notation allows us to express the terms of the series in a compact and concise manner, making it easier to manipulate and work with. The formula for the Taylor series allows us to approximate a function as a sum of its derivatives at a particular point. By finding the derivatives of the function and substituting them into the formula, we obtain the Taylor series in sigma notation. This series can be used to approximate the value of the function at a point near x=x0, given that the function is analytic at that point.

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Hence , equation of the line that is perpendicular to the line y = 6 and passes through the point (-4,-3) is x = -4 which is option (a) .

The line y = 6 could be a horizontal line through the purpose (0,6) on the coordinate axis. A line perpendicular thereto are vertical and thru the coordinate axis. this suggests its equation are x = a wherever a is that the x-coordinate. Since it should experience the purpose (-4,-3) then the equation is x =  -4.

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Answer:

m∠QRS = 52°

Step-by-step explanation:

From the given figure,

In right triangles ΔRQT and ΔRST,

QT = TS = 7.5 units [Given]

RT ≅ RT [Reflexive property]

ΔRQT ≅ ΔRST [By HL theorem of congruence]

Therefore, m(∠QRT) = m(∠SRT) = 26° [CPCTC]

m(∠QRS) = 2m(∠QRT)

               = 2×(26°)

               = 52°

Answer:

d. y ≤ 3/4x -6

Step-by-step explanation:

3x -4y ≥ 24

-4y ≥ -3x +24  subtraction property

y ≤ 3/4x -6 division property (change the direction of the symbol)

Answer:

Part A

y ≤ 3/4x – 6

the last option

Part B

answer is in the attachment

Part C

(-2,-8)

(8,0)

(4,-4)

Step-by-step explanation:

Part A

Use the properties of inequalities to rewrite the inequality:

3x − 4y ≥ 24  

-4y ≥ -3x + 24 subtraction property

y ≤ x – 6 division property (change the direction of the symbol)

Part B

Plot the boundary line, which will be solid because the inequality is non-strict. Use either the equation 3x − 4y = 24  or y=3/4x-6

Next, use a test point, such as (0,0), to determine where to shade:

3(0) − 4(0) ≥ 24

0 ≥ 24

The result is false, so shade on the opposite side of the boundary line.

Part C

Use the graph of the inequality to determine whether each point lies in the solution set.

For this non-strict inequality, any point in the shaded region or on the line is a solution. So (8,0), (4,-4), and (-2,-8) are all solutions to the inequality.

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The total amount to be paid at the end of the 10-year period is $24,465. The correct answer is option d. To calculate the total amount to be paid, we need to consider the compounded interest on the borrowed amount.

The nominal interest rate of 12% compounded quarterly means that interest is added to the principal four times a year. Using the formula for compound interest, we can calculate the future value of the loan. The formula is given as:

Future Value = Principal * (1 + (Nominal Interest Rate / Number of Compounding Periods))^Number of Compounding Periods * Number of Years

In this case, the principal is $7,500, the nominal interest rate is 12% (or 0.12), the number of compounding periods per year is 4 (quarterly), and the number of years is 10.

Plugging in these values into the formula, we get:

Future Value = $7,500 * (1 + (0.12 / 4))^(4 * 10) = $24,465

Therefore, the total amount to be paid at the end of the 10-year period is $24,465. The correct answer is option d.

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The equation to find the cost of each pair of shorts is 175 = 75 + 5x where each short cost $20

Cost of jackets= $75

Number of shorts= 5

Cost of each short = x

Total amount Jim spent= $175

Total amount Jim spent = Cost of jackets + (Number of shorts × Cost of each short)

175 = 75 + 5x

subtract 75 from both sides

175 - 75 = 5x

100 = 5x

divide both sides by 5

x = 100/5

x = $20

Ultimately, each pair of shorts cost $20

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The equation that represents this direct variation is  (7/4)x flowers planted in x minutes.

Given,

Caroline planted first 7 flowers in 4 minutes.

After 12 minutes, she had planted 21 different flowers.

We have to find the equation that represents this direct variation;

Here,

We can use Unitary method;

Unitary Method;

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

That is,

4 minute ⇒ 7 flowers

1 minute ⇒ 7/4 flowers

Therefore,

x minute ⇒ (7/4)x flowers

Therefore,

The equation that represents this direct variation is  (7/4)x flowers planted in x minutes.

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The equation of the line that is parallel to 2y = 3x - 1 and passes through the point (4, 2) is: y = (3/2)x - 4

To find the equation of a straight line that is parallel to the line 2y = 3x - 1, we need to remember that parallel lines have the same slope.

First, let's rearrange the given equation into slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept:

2y = 3x - 1

y = (3/2)x - 1/2

So the slope of this line is 3/2.

Now, if we want to find the equation of a line that is parallel to this line, we just need to use the same slope. Let's call the new line y = mx + b, where m is the slope we just found and b is the y-intercept we need to find.

So the equation of the parallel line is:

y = (3/2)x + b

To find the value of b, we need to use a point on the line. Let's say we want the line to go through the point (4, 2):

2 = (3/2)(4) + b

2 = 6 + b

b = -4

So the equation of the line that is parallel to 2y = 3x - 1 and passes through the point (4, 2) is: y = (3/2)x - 4

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The probability of having, at most, 9 girls, is 0.9515

The probability that a random baby is a girl is:

p = 0.5

And the probability that a random baby is a boy is:

q = 0.5

Then the probability that, at most, 9 out of 11 babys are girls, is given by:

1 - p(10) - p(11)

Where P(10) is the probability that 10 of the babies are girls and p(11) is the probability that the 11 babies are girls.

p(10) = C(11, 10)*(0.5)^10*(0.5)^1 = C(11, 9)*(0.5)^11

Where C(11, 10) is the combinations of 10 elements that we can make with a set of 11 elements, such that:

C(11, 10)=  11!/(11 - 10)!*10! = 11

Replacing that, we get:

P = 11*(0.5)^11 = 0.0054

p(11) = C(11, 11)*0.5^11 = 1*0.5^11 = 0.0005

Then the probability is:

P = 1 - 0.0054 - 0.0005 = 0.9515

The probability of having, at most, 9 girls, is 0.9515

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Answer:

10 cm

Step-by-step explanation:

Step-by-step explanation:

It is given that, Katie walks 2 ft forward and 5 ft backwards. We need to find her displacement traveled.

The difference between final position and the initial position is equal to displacement. It is the shorted path covered.

Let forward is +x and backward is -x

Initial position of Katie = +2 ft

Final position of Katie = -5 ft

Displacement = final position - initial position

= -5 - 2

Displacement = -7 ft

So, her displacement is 7 feet in backward direction.

Step-by-step explanation:

There are 500 little squares covered....each square is 2 mice

 there are 60 squares that are less than 10 gm

   so that would be 120 mice <10 gm