please help me it's for tomorrow

The equation 3x² - 12x - 15 = 0 when solved by factoring has the solutions x = 5 and x = -1

The equation 3x² - 12x - 15 = 0, is a representation of the equation in the question.

The aforementioned problem is a quadratic equation, and factoring is one way to solve this kind of issue.

Divide 3 from the equation.

As a result, we have the following

x² - 4x - 5 = 0.

Expanding the equation, we get

x² + x - 5x - 5 = 0.

Factoring the equation, we get

x(x + 1) - 5(x + 1) = 0

The result is

(x - 5)(x + 1) = 0.

We can solve for x by getting

x = 5 and x = -1.

Thus, the equation's answers are 5 and -1.

And it means that there are actually two solutions to the equation.

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Answer:

C

Step-by-step explanation:

I believe this is the best answer.

Answer:

1

Step-by-step explanation:

GCF of 343 and 477 is 1, because no number can multiply and get both of them.

The greatest common factor of 343 and 477 is 1, indicating that the two numbers have no common factors other than 1.

To find the greatest common factor (GCF) of 343 and 477, we can determine the common factors of both numbers and identify the largest one.

First, let's list the factors of each number:

The factors of 343 are: 1, 7, 49, 343.

The factors of 477 are: 1, 3, 9, 53, 159, 477.

Now, we identify the common factors from both lists: 1.

Therefore, the greatest common factor of 343 and 477 is 1.

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By using unitary method, we found that the cost of 5m cloth is Rs. 1050.

According to the unitary method, the cost of 1 meter of cloth is equal to the total cost of 7 meters of cloth divided by 7. That is,

Cost of 1m cloth = Total cost of 7m cloth/7

We know that the total cost of 7m cloth is Rs. 1470. Therefore,

Cost of 1m cloth = 1470/7

Cost of 1m cloth = Rs. 210

This means that the cost of 1 meter of cloth is Rs. 210. Now, we need to find the cost of 5m cloth. To do that, we can use the unitary method again.

Cost of 5m cloth = Cost of 1m cloth x 5

Cost of 5m cloth = Rs. 210 x 5

Cost of 5m cloth = Rs. 1050

Therefore, the cost of 5m cloth is Rs. 1050.

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Answer:

pronoun

Step-by-step explanation:

Answer:

I replaced alpha by A and bitta by B. Sorry for this mistake

Answer:

Step-by-step explanation:

Given

Then the sum and product of the roots are:

(i) Roots are α + 1 and β + 1, then we have:

(ii) Roots are 2 - α and 2 - β, then we have:

(iii) Roots are α² and β², then:

(iv) Roots are 1/α and 1/β, then:

(v) Roots are 2/α² and 2/β², then:

Therefore, the probability that more than 35% of the 30 Americans in the sample concur that climate change is a serious threat to humanity is 0.5 or 50%.

The main goal of the mathematical branch known as statistical inference is to estimate the likelihood that a statement is accurate or that a particular event will take place. Any number among 0 and 1, where 1 typically denotes confidence and 0 typically denotes possibility, can be used to symbolise chance.A probability diagram illustrates the likelihood that a particular occurrence will take place.

Here,

The problem specifies a sample size of n = 30 and a success chance of p = 0.35.

We want to determine the likelihood that the percentage of the 30 Americans sampled who believe that climate change poses an immediate danger to humanity exceeds 35%.

P(p-hat > 0.35)

where p-hat is really the percentage of sample respondents who concur that climate change poses a direct danger to humanity.

The sample proportion P-hat has a standard variation of and a mean of 0.35, both of which are within the normal distribution.

√(p*(1-p)/n) = √(0.35*(1-0.35)/30) = 0.089 is the formula for standard deviation.

As a result, the sample percentage can be standardised as follows:

Standard deviation = (p-hat -0.35) / 0.089 and z = (p-hat - p)

We can also determine the chance as follows:

P(z > (0.35 - 0.35) / 0.089) = P(z > 0) = P(p-hat > 0.35)

Therefore, the likelihood that more than 35% of the 30 Americans in the sample concur that climate change is a serious threat to humanity is 0.5 or 50%.

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Answer:

No

Step-by-step explanation:

x=(b-5)/c≠(5-b)/c

supposedly

b=6

c=1

x=6-5/1=1

x=5-6/1= -1

1≠ -1

Answer:

No

Step-by-step explanation:

x = b - 5 / L equal to - (5 - b) / L

Answer:

X > 4

Step-by-step explanation:

X – 1.5 > 2.5

X  > 2.5 + 1.5

X > 4.0

The value of the double integral (4x − 9y) dA over the region D bounded by the circle with center at the origin and radius 2 is -48.

To evaluate the double integral (4x − 9y) dA over the region D bounded by the circle with center at the origin and radius 2, we need to use polar coordinates.

In polar coordinates, the equation of the circle with center at the origin and radius 2 is given by r = 2. Therefore, the limits of integration for r are 0 and 2, and the limits of integration for θ are 0 and 2π.

The element of area in polar coordinates is given by dA = r dr dθ. Therefore, we can rewrite the double integral in terms of polar coordinates as follows

∬D (4x − 9y) dA = ∫₀² ∫₀²π (4r cosθ - 9r sinθ) r dθ dr

= ∫₀² r² (4cosθ - 9sinθ) dθ dr [Using the properties of integrals]

The integral with respect to θ is zero for sinθ and cosθ over a full period. Therefore, we have

∬D (4x − 9y) dA = ∫₀² r² (4cosθ - 9sinθ) dθ dr

= 4∫₀² r² cosθ dθ dr - 9∫₀² r² sinθ dθ dr

Integrating with respect to θ, we get

∫₀² r² cosθ dθ = [2r² sinθ]₀²π = 0

∫₀² r² sinθ dθ = [-2r² cosθ]₀²π = 4r²

Substituting these values in the original equation, we get

∬D (4x − 9y) dA = 4∫₀² r² cosθ dθ dr - 9∫₀² r² sinθ dθ dr

= 4(0) - 9(4r²) dr

= - 36 ∫₀² r² dr

= -36 [r³/3]₀² = -48

Therefore, the value of the double integral is -48.

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The given question is incomplete, the complete question is:

Evaluate the double integral. (4x − 9y) dA, D is bounded by the circle with center the origin and radius 2

Answer: \(x=13, y=132\)

Step-by-step explanation:

Using the same-side interior angles theorem, \(y=132\).

Using the alternate interior angles theorem, \(5x-17=48 \implies x=13\)

10 maybe? I don't really know but maybe 10 will be right?????

Answer:

\(r = \sqrt{ {(6 - 2)}^{2} + {(1 - ( - 3))}^{2} } \)

\(r = \sqrt{ {4}^{2} + {4}^{2} } = \sqrt{16 + 16} = \sqrt{32} \)

So the equation of the circle is

\( {(x - 2)}^{2} + {(y + 3)}^{2} = 32\)

To find the value of z such that 0.03 (3%) of the area lies to the left of z, we need to use a standard normal distribution table or a calculator that can perform normal distribution calculations.

In a standard normal distribution, the area to the left of a particular z-score represents the cumulative probability up to that point. We need to find the z-score that corresponds to a cumulative probability of 0.03.

Using a standard normal distribution table or a calculator, we find that the z-score corresponding to a cumulative probability of 0.03 is approximately -1.88 (rounded to two decimal places).

Therefore, the value of z such that 0.03 of the area lies to the left of z is approximately -1.88.

The value of z such that 0.03 of the area lies to the left of it is approximately -1.88.

In statistics, the area under a normal distribution curve represents the probability of an event occurring. To find the value of z, we need to refer to the standard normal distribution table or use statistical software.

The given question specifies that 0.03 of the area lies to the left of z. This means we need to find the z-score associated with the cumulative probability of 0.03.

By referring to the standard normal distribution table or using statistical software, we find that the z-score corresponding to 0.03 is approximately -1.88 when rounded to two decimal places.

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The Area of Trapezium is 50, 267 mm².

We have,

base 1 = 224 mm

base 2 = 77 mm

Height = 334 mm

Now, Area of Trapezium

= 1/2 (Sum of parallel side) x height

= 1/2 (224 + 77) x 334

= 1/2 x 301 x 334

= 50, 267 mm²

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Janelle will earn approximately 729.19 more with the compound interest option compared to the simple interest option over a period of 7 years.

The amount Janelle will earn with the compound interest option can be calculated using the formula for compound interest:

\(A = P(1 + r/n)^{(nt)}\)

Where:
A is the total amount after interest has been compounded
P is the principal amount (the initial deposit)
r is the annual interest rate (expressed as a decimal)
n is the number of times interest is compounded per year
t is the number of years

In this case, Janelle deposits 3,000 at an interest rate of 3% for 7 years. We'll compare the simple interest and compound interest options.

For the simple interest option, the interest is calculated using the formula:

I = P * r * t

Where:

I is the total interest earned

Using the given values, we can calculate the interest earned with simple interest:

I = 3000 * 0.03 * 7
I = 630

Now, let's calculate the total amount earned with the compound interest option.

Since the interest is compounded monthly, the interest rate needs to be divided by 12 and the number of years needs to be multiplied by 12:

r = 0.03/12

t = 7 * 12

Using these values, we can calculate the total amount with compound interest:

\(A = 3000 * (1 + 0.03/12)^{(7*12)}\)

A ≈ 3,729.19

To find out how much more Janelle will earn with the compound interest option, we subtract the initial deposit from the total amount with compound interest:

Difference = A - P
Difference = 3,729.19 - 3,000
Difference ≈ 729.19

Therefore, Janelle will earn approximately 729.19 more with the compound interest option compared to the simple interest option over a period of 7 years.

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Probability all three drawn cards have numbers on them = 32.3%

Out of 52 total cards, there are 36 numbered cards.

In the first attempt probability of numbered cards being drawn

= 36 / 52

=0.692

After the first draw, total numbered cards remaining = 35

Total cards remaining = 51

Probability of numbered card in second attempt = 35 / 51

= 0.686

Probability of numbered card in third attempt = 34 / 50

= 0.68

Total probability of all cards being numbers = (36 / 52) x (35 / 51) x (34/50)

= 0.692 x 0.686 x 0.68

=0.323 x 100%

=32.3%

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To identify and calculate the perimeter:

a)

Since, it has 3 sides.

Therefore, it is a triangle.

Perimeter is,

Hence, perimeter of the triange is 35 ft.

b)

It is a trapezium.

Perimeter of trapezium is,

Hence, perimeter of the trapezium is 20 ft.

c)

It is a rhombus.

Perimeter of rhombus is,

Hence, perimeter of the rhombus is 56 ft.

d)

It is a regular hexagon.

Perimeter of regular hexagon is,

Hence, perimeter of the regular hexagon is 48 ft.

\(\sf \large \boldsymbol {} 1) \ (4^0)^6= 4^{0\cdot 6}= 4^0\neq 4^6 \ False \\\\\\ 2) \ \dfrac{3^8}{3^{-2}} =3^{8-(-2)}=3^{8+2}=3^{10} \ \ True \\\\\\ 3) \ 2^{-5}\cdot 2^3=2^{-5+3}=2^{-2}=\dfrac{1}{2^2} \ \ True \\\\\\ 4) \ 6^4\cdot 3^4=(6\cdot 3)^4=18^4\neq 18^8 \ \ False\)

Answer:

false, true, true, false

Step-by-step explanation:

(4^0)^6=1 is not equal to 4^6=4096

3^8/3^-2=59049 is equal to 3^10=59049

2^-5*2^3=0.25 is equal to 1/2^2=1/4=0.25

6^4*3^4=104976 is not equal to 18^8=11019960576

hope this helps!

9. The third derivative of f(x) if f(x)=2x-x+4x-2x +5x-8 is 24 - 48x + 300x². 10. Using implicit differentiation, he derivative dy/dx for the equation 2x^3y^2 + 5y^3 = 4x - 1 is (-6x^2y^2 - 4) / (8xy + 15y^2).

Question 9: Determine the third derivative of f(x) if f(x) = 2x - x² + 4x³ - 2x⁴ + 5x⁵ - 8

We know that the derivative of a function gives us the slope of the curve at any point. If we take a second derivative of a function, we get the rate of change of the slope. Similarly, if we take a third derivative, we get the rate of change of the rate of change of the slope. Therefore, if we take the third derivative of f(x), we will get the rate of change of the rate of change of the slope, or the rate of change of the curvature of the function f(x).

Now let's find the third derivative of f(x).f(x) = 2x - x² + 4x³ - 2x⁴ + 5x⁵ - 8

The first derivative of f(x) = d/dx(2x - x² + 4x³ - 2x⁴ + 5x⁵ - 8) = 2 - 2x + 12x² - 8x³ + 25x⁴

The second derivative of f(x) = d²/dx²(2x - x² + 4x³ - 2x⁴ + 5x⁵ - 8) = -2 + 24x - 24x² + 100x³

The third derivative of f(x) = d³/dx³(2x - x² + 4x³ - 2x⁴ + 5x⁵ - 8) = 24 - 48x + 300x²

Therefore, the third derivative of f(x) is 24 - 48x + 300x².

Question 10.

Now let's solve the implicit differentiation problem.

a. 4x + 2y = 3y

To find dy/dx, we differentiate both sides of the equation with respect to x, treating y as a function of x.

Differentiating 4x + 2y = 3y:

4 + 2(dy/dx) = 3(dy/dx)

Now, solve for dy/dx:

2(dy/dx) - 3(dy/dx) = -4

-1(dy/dx) = -4

dy/dx = 4

Therefore, the derivative dy/dx for the equation 4x + 2y = 3y is 4.

b. 2x^3y^2 + 5y^3 = 4x - 1

To find dy/dx, we differentiate both sides of the equation with respect to x, treating y as a function of x.

Differentiating 2x^3y^2 + 5y^3 = 4x - 1:

6x^2y^2 + 4x(2y)(dy/dx) + 15y^2(dy/dx) = 4

Now, solve for dy/dx:

4x(2y)(dy/dx) + 15y^2(dy/dx) = -6x^2y^2 - 4

(dy/dx)(8xy + 15y^2) = -6x^2y^2 - 4

dy/dx = (-6x^2y^2 - 4) / (8xy + 15y^2)

Therefore, the derivative dy/dx for the equation 2x^3y^2 + 5y^3 = 4x - 1 is (-6x^2y^2 - 4) / (8xy + 15y^2).

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Complete question is:

"Determine the third derivative of f(x) if f(x)=2x-x+4x-2x +5x-8. Use positive exponents in your final answer. (3 marks) 10. Determine using implicit differentiation. dy dx a. 4x+2y=3y VVS: 31 A2 Summer 22- b. 2x³y² +5y³ = 4x-1 "

Answer:

88 yards

Step-by-step explanation:

because the park is 11 inches wide in the drawling, and the scale of it is 1:8

so the actual width of the park is

\(11/1/8=11*8=88 yards\)

11 divided by 1/8

Answer:

-8x + 12

Step-by-step explanation:

It is asking us to simplify.  Therefore, we multiply the terms. -4(2x - 3) =

- 8x + 12

Answer:

-8× + 12

Step-by-step explanation:

-4x (2x - 3) simplify

Apply the distributive property

-4 (2x) - 4 × -3

multiply 2 by -4

-8x -4 × -3

multiply -4 by -3

= -8x + 12

Difference between the fees of Ahab and his sister is \(2.8*10^{3} -1.15*10^{3}=1.65*10^{3}\)

Review the following subtraction rules and properties:

Given: Ahab pays dollars for one year's tuition fees and his sister pays dollars fees in tuition for the first year

To find: Difference in tuition fees paid by Ahab and his sister?

Solution:

To find the difference in their fees we have to perform simply normal subtraction

Subtract the fees of his sister from Ahab's fees which is as follows:

\(2.8*10^{3} -1.15*10^{3}=1.65*10^{3}\)

Hence the difference between the fees of Ahab and his sister is \(2.8*10^{3} -1.15*10^{3}=1.65*10^{3}\)

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With a credit card balance of $17,426, a minimum monthly payment of $461, and an interest rate of 15.5%, we need to calculate the number of years it will take to pay off the card without adding any additional debt.

To determine the time required to pay off the credit card, we consider the monthly payment and the interest rate. Each month, a portion of the payment goes towards reducing the balance, while the remaining balance accrues interest.

To calculate the time needed for repayment, we track the decreasing balance each month. First, we determine the interest accrued on the remaining balance by multiplying it by the monthly interest rate (15.5% divided by 12).

We continue making monthly payments until the remaining balance reaches zero. By dividing the initial balance by the monthly payment minus the portion allocated to interest, we obtain the number of months needed for repayment. Finally, we divide the result by 12 to convert it into years.

In this scenario, it will take approximately 3.81 years to pay off the credit card (17,426 / (461 - (17,426 * (15.5% / 12))) / 12).

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The length of the QR is 16 cm when PQR ~MNO

In the given question, it is given that two similar triangles as PQR ~MNO

Then, the corresponding sides will be in equal proportion to each other as follows

PQ / MN = PR / MO = QR / NO

We need to find the length of the side QR

As above relations are given,

\(\frac{PQ}{MN}\) = \(\frac{PR}{MO}\) = \(\frac{QR}{NO}\)

\(\frac{30}{10}\) = \(\frac{5x + 7}{x+5}\) = \(\frac{4x}{\frac{16}{3} }\)

Equating all the fractions, equal to each we'll find

\(\frac{5x + 7}{x+5}\) = \(\frac{30}{10}\)

5x + 7 = 3(x +5)

5x + 7 = 3x + 15

2x = 8

x = 4

We know that, the length of the QR = 4x cm = 4 x 4 cm = 16 cm

Therefore, the length of the QR is 16 cm when PQR ~MNO

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the probability that the next 3 cards are also spades is 0.0156.

There are 13 spades in a deck of 52 cards. The probability of each card being a spade is 13/52 or 0.25. The probability that the next 3 cards are also spades is 0.25 x 0.25 x 0.25 = 0.016. Therefore, the probability that the next 3 cards are also spades is 0.0156.

1. Calculate the probability of one card being a spade: 13/52 or 0.25

2. Calculate the probability of the next 3 cards being spades: 0.25 x 0.25 x 0.25 = 0.016

3. Round the answer to four decimal places: 0.0156

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To find the dimensions of the expanded rectangular garden, we'll start by considering the original square garden. Let's assume the side length of the square garden is x feet.

After expanding one side by 12 feet, the new length becomes x + 12 feet. Similarly, after expanding the other side by 15 feet, the new width becomes x + 15 feet.

The area of a rectangle is calculated by multiplying its length and width. According to the given information, the expanded rectangular garden will have an area of no more than 2,000 square feet.

Therefore, we can form the inequality: (x + 12)(x + 15) ≤ 2,000.

Simplifying the inequality - brainly.com/question/30228778

x^2 + 27x + 180 ≤ 2,000,

x^2 + 27x - 1,820 ≤ 0.

To find the values of x that satisfy the inequality, we can either solve the quadratic equation or use a graphing calculator. The solutions for x will give the maximum possible side length for the original square garden.

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The total number of items purchased during the accounting period was 53 items, and the total cost of the purchases was $217.00.

During the last accounting period, purchases of an inventory item were made in varying quantities and at different unit prices.

The total number of items purchased can be calculated by an expression obtained by summing the quantities, and the total cost of the purchases can be found by multiplying the quantity of each item by its corresponding unit price and summing the results.

To determine the total number of items purchased, we add up the quantities: 5 + 3 + 7 + 11 + 27 = 53 items.

To calculate the total cost of the purchases, we multiply the quantity of each item by its unit price and sum the results.

For the first purchase of 5 items at $4.00 per item, the cost is 5 * $4.00 = $20.00.

The second purchase of 3 items at $6.00 per item has a cost of 3 * $6.00 = $18.00.

The third purchase of 1 item at $9.00, the fourth purchase of 7 items at $7.00 per item, and the fifth purchase of 11 items at $11.00 per item have costs of $9.00, 7 * $7.00 = $49.00, and 11 * $11.00 = $121.00, respectively.

Adding up all the costs, we have $20.00 + $18.00 + $9.00 + $49.00 + $121.00 = $217.00.

Therefore, the total number of items purchased during the accounting period was 53 items, and the total cost of the purchases was $217.00.

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