Convert y+2=-3(x-7) to standard form​

Answer:

IM SLOWWWWWWWWWWWWWWWWWWWWWw

Step-by-step explanation:

Answer:

1044 cm²

Step-by-step explanation:

Split the shape up into two

Area of shape A:

Area = length × width

To calculate the width = 46 - 21 = 25 cm

Area = 30 cm × 25 cm = 750cm²

Area of shape B

Area = length × width

Area = 14 cm × 21 cm = 294 cm²

Add up both of the areas:

750 cm² + 294 cm² = 1044 cm²

The volume of the solid the region defined by the given curves must be rotated about the x-axis is V = \(\frac{384\pi }{5}\).

Given that,

The region defined by the given curves must be rotated about the x-axis to determine the solid's volume, which is y =6 -x², y =2.

We know that,

Take the equation of the curves about the x- axis

y =6 -x², y =2.

Substitute y = 2 in equation y = 6 - x²

2 = 6 - x²

-x² = 2-6

x² = 4

Taking square root on both sides

x = ±2

Now, volume formula is define by using washer method

V =  \(\pi \int\limits^a_b {[f(x)]^2 - [g(x)]^2} \, dx\)

V = \(\pi \int\limits^2_{-2} {[6-x^2]^2 - [2]^2} \, dx\)

V = \(\pi \int\limits^2_{-2} {(36 + x^4 - 12x^2 - 4}) \, dx\)

V = \(\pi \int\limits^2_{-2} {(x^4 - 12x^2 - 32)} \, dx\)

V = \(\pi( [\frac{x^5}{5}] - 12\times\frac{x^3}{3} -32x)^2_{-2}\)

V = \(\pi[( [\frac{2^5}{5}] - 12\times\frac{2^3}{3} -32(2))-([\frac{-2^5}{5}] - 12\times\frac{-2^3}{3} -32(-2))]\)

V = \(\pi[( [\frac{32}{5}] - 4 \times 8 -64)-( [\frac{-32}{5}] - 4\times(-8) +64)]\)

V = \(\pi[( [\frac{32}{5}] - 32 -64)-( [\frac{-32}{5}] +32 +64)]\)

V = \(\pi( [\frac{384}{5}] )\)

V = \(\frac{384\pi }{5}\)

Therefore, The volume of the solid is V = \(\frac{384\pi }{5}\)

To know more about volume visit:

https://brainly.com/question/32615476

#SPJ4

Answer:

arc HK = 60

Step-by-step explanation:

angle HLK is an inscribed angle and arc HK is the arc it intercepts

an inscribed angle is equal to half the measure of the arc it intercepts

this can also be said as the intercepted arc is equal to twice the measure of the inscribed angle

Hence arc HK = 30 * 2 = 60

Hope this help!!!

Have a nice day!!!

Given 2y + 14y = 5xIf y(0) = 0.5, we want to find y(3) using the midpoint method and step size of h = 15.

The midpoint method is given as follows:yi+1 = yi + hf(xi + h/2, yi + h/2f(xi, yi))where f(xi, yi) is the derivative of the given function at (xi, yi).To apply the midpoint method to the given differential equation, we need to rewrite it in the form y' = f(x, y). To do this, we first isolate y' on one side:2y + 1 = 5x - 4yy' = (5x - 4y)/2

Now we can substitute this expression for y' into the midpoint formula and simplify: y1 = 0.5,

h = 15

y2 = y1 + hf(x1 + h/2, y1 + h/2f(x1, y1))

= 0.5 + 15(5(0) - 4(0.5)/2)

= 0.5 - 15

= -14.5

y3 = y2 + hf(x2 + h/2, y2 + h/2f(x2, y2))

= -14.5 + 15(5(15/2) - 4(-14.5)/2)

= -14.5 + 137.25

= 122.75

Therefore, y(3) = 122.75.

To know more about midpoint method visit:

https://brainly.com/question/30242985

#SPJ11

The equation for the area of the trapezoid (A) can be expressed as:

A = r + 2t

A trapezoid is a four-sided polygon with two parallel sides.

The area of a trapezoid can be calculated by adding the areas of the two triangles formed by the height of the trapezoid and the lengths of the parallel sides, and the area of the rectangle formed by the base of the trapezoid and the height.

The equation for the area of the trapezoid (A) can be expressed as:

A = r + 2t

Here, r represents the area of the rectangle, and 2t represents the sum of the areas of the two triangles. By adding these components together, we obtain the total area of the trapezoid.

Learn more about Area of Trapezoid here:

https://brainly.com/question/12221769

#SPJ1

Answer:

0.48 feets

Step-by-step explanation:

Given that :

Length of stone = x

Number of stones used = 25

Length of path made from the stones = 12 feets

Hence. The length of each stone could be obtained by dividing the length of path by the number of stones used :

length of path / number of stones

= 12 feets / 25

= 0.48 feets

Hence length of each stone = 0.48 feets

1) General solution for second order differential equation, y" – 2y' + y = 0, is y = (c₁x + c₂)eˣ .

2) General solution for differential equation, 9y" + 6y' + y = 0, is y =(c₁x + c₂)e⁻³ˣ.

3) General solution for differential equation, 4y"- 4y'- 3y = 0, is y = c₁ e⁶ˣ+ c₂e⁻⁴ˣ.

4) General solution for differential equation, 4y" + 12y' +9y = 0, is y = (c₁x + c₂)e⁻⁶ˣ.

5) General solution for differential equation, y" – 2y' + 10y = 0, is y = eˣ (c₁cos(6x) + c₂sin(6x)).

6) General solution for differential equation, y" – 6y' +9y = 0 is y = (c₁x + c₂)e³ˣ.

7) General solution for differential equation, 4y" + 17y' + 4y = 0, is y = c₁e⁻ˣ + c₂e⁻¹⁶ˣ.

8) General solution for differential equation, 16y" + 24y' +9y = 0, is y = (c₁x + c₂)e⁻¹²ˣ.

9) General solution for differential equation, 25y" – 20y' + 4y = 0, is y = (c₁x + c₂)e¹⁰ˣ.

10) General solution for differential equation, 2y" + 2y' + y = 0, is y = e⁻ˣ (c₁cos(2x) + c₂sin(2x)).

General solution is also called complete solution and complete solution = complemantory function + particular Solution

Here right hand side is zero so particular solution is equals to zero. Therefore, evaluating the complementary function will be sufficient to determine the general solution to the differential equation.

1) y"-2y' + y = 0, --(1)

put D = d/dx, so (D² - 2D + 1)y =0

Auxiliary equation for (1) can be written as, m² - 2m + 1 = 0 , a quadratic equation solving it by using quadratic formula,

\(m =\frac{-(- 2) ± \sqrt { 4 - 4}}{2}\)

=> m = 1 , 1

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)eˣ .

2) 9y" + 6y' + y = 0 or (9D² + 6D + 1)y =0 Auxiliary equation can be written as, 9m² + 6m + 1 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{ - (6) ± \sqrt {36 - 4×4}}{2}\)

=> m = - 6/2

=> m = -3 , -3

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)e⁻³ˣ.

3) 4y"- 4y'- 3y = 0

put D = d/dx, so (4D² - 4D - 3)y = 0

Auxiliary equation can be written as, 4m² - 4m - 3 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{-(-4) ± \sqrt {16 - 4×4×(-3)}}{2}\)

=> m = (4 ± 8)/2

=> m = -4 , 6

The roots of equation are real and equal. So, general solution is y = c₁ e⁶ˣ + c₂e⁻⁴ˣ.

4) 4y" + 12y' +9y = 0 or (4D² + 12D + 9)y= 0

Auxiliary equation can be written as, 4m² + 12m + 9= 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{-(12) ± \sqrt{144 - 4×4×9}}{2}\)

=> m = -12/2

=> m = -6 , -6

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)e⁻⁶ˣ.

5) y" – 2y' + 10y = 0 or (D² - 2D + 10)y = 0 Auxiliary equation can be written as, m² - 2m + 10 = 0 , a quadratic equation

solving it by using quadratic formula,

\(m =\frac{ - (-2) ± \sqrt {4 - 4×1×10}}{2}\)

=> m = (2 ± 6i)/2 ( since, √-1 = i)

=> m = 1 + 6i , 1-6i

The roots of equation are imaginary and unequal. So, general solution is y =eˣ (c₁cos(6x) + c₂sin(6x)).

6) y" – 6y' +9y = 0 or (D²- 6D + 9)y =0

Auxiliary equation can be written as, m² - 6m + 9 = 0 , a quadratic equation

solving it by using quadratic formula,

\(m =\frac{ - (-6) ± \sqrt {36 - 4×1×9}}{2}\)

=> m = 6/2 = 3,3

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)e³ˣ.

7) 4y" + 17y' + 4y = 0 or (4D²+ 17D + 4)y=0

Auxiliary equation can be written as, 4m² + 17m + 4 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{- (-17) ± \sqrt {16 - 4×4×17}}{2}\)

=> m = ( -17 ± 15)/2

=> m = (-17 + 15)/2, (- 17 - 15)/2= -1, -16

The roots of equation are real and unequal. So, general solution is y = c₁e⁻ˣ + c₂e⁻¹⁶ˣ.

8) 16y"+24y'+9y =0 or (16D²+ 24D + 9)y= 0

Auxiliary equation can be written as, 16m² + 24m + 9 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{ - (24) ± \sqrt {576 - 4×9×16}}{2}\)

=> m = (-24 ± 0)/2

=> m = -12,-12

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)e⁻¹²ˣ.

9) 25y"- 20y' +4y =0 or (25D²-20D + 4)y = 0

Auxiliary equation can be written as, 25m²- 20m + 4 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{ - (-20) ± \sqrt {400 - 4×4×25}}{2}\)

=> m = 20/2

=> m = 10 , 10

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)e¹⁰ˣ.

10) 2y" + 2y' + y = 0 or (2D²+ 2D + 1)y =0

Auxiliary equation can be written as, 2m² + 2m + 1 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{ - (2) ± \sqrt {4 - 4×1×2}}{2}\)

=> m = (- 2 ± 4i)/2 ( since, √-1 = i)

=> m = -1 + 2i , -1 - 2i

The roots of equation are imaginary and unequal. So, general solution is y = e⁻ˣ (c₁cos(2x) + c₂sin(2x)). Hence, required solution of differential equation is y = e⁻ˣ (c₁cos(2x) + c₂sin(2x)).

For more information about general solution of differential equation, visit:

https://brainly.com/question/30078609

#SPJ4

Answer:

4900

Step-by-step explanation:

because it is square root of 70 and it means

sol?

square of 70 =70²=70×70=4900

Answer:

22.  30

prime factorization of 30

2 × 3 × 5

so there is no simplification needed here

23. 126

2 × 3 × 3 × 7

simplification

2 × \(3^{2}\) × 7

24.  4900

2 ×2 × 5 × 5 × 7 ×7

simplification

\(2^{2}\) × \(5^{2}\) × \(7^{2}\)

25.  39204

2 × 2 × 3 × 3 × 3 × 3 × 11 × 11

simplification

\(2^{2}\) × \(3^{4}\) × \(11^{2}\)

26 .  

Yes 4900 is a square number it's square root is 70

you can even cross-check

70 × 70

= 4900

and even 39204 is a square number it's square root is 198

you can even cross-check

198 × 198

= 39204

Hence 2 numbers 4900 and 39204 are square numbers

27 .

i. highest common factor of 30 and 126

factors of 30 are 2 × 3 × 5

factors of 126 are 2 × 3 × 3 × 7

now find common between them

common factors are 2 and 3

so multiply 2 and 3

2 × 3

= 6

6 is the highest common factor

ii. 126 and 39204

factors of 126 are 2 × 3 × 3 × 7

factors of 39204 are 2 × 2 × 3 × 3 × 3 × 3 × 11 × 11

now find common between them

common factors are 2 × 3 × 3

= 18

18 is the highest common factor

28 .

1 .  126 and 4900

factors of 126 are 2 × 3 × 3 × 7

factors of 4900 are 2 ×2 × 5 × 5 × 7 ×7

make the pairs of the numbers

2 ×2 × 5 × 5 × 3 × 3 × 7 ×7

= 44100   least common multiple

ii. 4900 and 39204

factors of 39204 are 2 × 2 × 3 × 3 × 3 × 3 × 11 × 11

factors of 4900 are 2 ×2 × 5 × 5 × 7 ×7

make the pairs of the numbers  

2 ×2 × 3 x 3 x 3 x 3 x 5 x 5 x 7 x 7 x 11 x 11

= 48024900 least common multiple

The roots of the equation 2x - 3 = -5x² are x = -1 and x = 3/5. Therefore, the correct options are (B) and (D).

To find the roots of the equation 2x - 3 = -5x², we need to solve the equation and determine the values of x that satisfy it.

Rearranging the equation, we have -5x² - 2x + 3 = 0.

To solve this quadratic equation, we can either factor it or use the quadratic formula. Let's use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

For the equation -5x² - 2x + 3 = 0, the coefficients are:

a = -5, b = -2, c = 3.

Plugging these values into the quadratic formula, we get:

x = (-(-2) ± √((-2)² - 4(-5)(3))) / (2(-5))

x = (2 ± √(4 + 60)) / (-10)

x = (2 ± √64) / (-10)

x = (2 ± 8) / (-10)

Simplifying further:

x = (2 + 8) / (-10) or x = (2 - 8) / (-10)

x = 10 / (-10) or x = -6 / (-10)

x = -1 or x = 3/5

Therefore, the roots of the equation 2x - 3 = -5x² are x = -1 and x = 3/5.

Among the given options, the correct answers are:

D. x = -1

B. x = 3/5

For more such questions on roots , Visit:

https://brainly.com/question/428672

#SPJ11

From the given data of room ,ceiling , windows and door , the area of the four walls and ceiling to be painted is equal to 783.75 ft².

As given in the question,

Room is 14ft by 20 ft

Height of the room = 8ft

Two windows are of 3ft by 4ft

Door is 2.5ft by 6.5ft

Area of the four walls = 2 (14 × 8) + 2(20×8)

                                  = 224 +320

                                  = 544ft²

Area of the ceiling = 14 × 20

                             = 280ft²

Area of two windows = 2(3×4)

                                  =24ft²

Area of the door= 2.5 ×6.5

                         =16.25ft²

Total area to be painted = ( 544 + 280 -24-16.25 )

                                      = 783.75 ft²

Therefore, the total area of the four walls and ceiling to be painted is equal to 783.75 ft².

The complete question is :

A room is 14ft by 20ft. It needs to be painted. The ceiling is 8ft above the floor. There are two windows in the room, each one is 3ft by 4ft. The door is 2.5ft by 6.5ft.

a. find the total area of the four walls and ceiling to be painted?

Learn more about area here

brainly.com/question/27683633

#SPJ1

Answer:

-2x-10=-2(x+5)

Step-by-step explanation:

Answer:

it's the third one

Step-by-step explanation:

I believe on doing homework to good luck with your work hope this helps

Step-by-step explanation:

refer to the picture.. hope this helps :)

Answer:

the answer is 10 the other dude is right

Step-by-step explanation:

Answer:

10

Step-by-step explanation:i just took the test and got it right :)

Answer:

x=10°

Step-by-step explanation:

(5x+7)°+(4x+16)°+(5x+17)°=180° (a triangle contains 180°)

5x+7+4x+16+5x+17=180

14x+40=180

14x=180-40

14x=140

x=140/14

x=10

x=10°

note:to avoid writing ° always. I made it implicit.

Answer:

x=3

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

The solution is:

Work/explanation:

For now I am going to focus on the left side.

I use the distributive property and "distribute" 5:

\(\bf{5(x+2)+1=26}\)

\(\bf{5x+10+1=26}\)

\(\bf{5x+11=26}\)

Subtract 11 on each side

\(\bf{5x=15}\)

Divide each side by 5

\(\bf{x=3}\)

Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

To know more about interest visit:

https://brainly.com/question/30393144

#SPJ11

The first model of inequality satisfy the problem i.e 2w + 2* 4w ≤ 106

A rectangle is a four-sided, two-dimensional flat shape. The opposite sides of a rectangle's four sides are parallel and equal to one another. It belongs to a category of quadrilaterals where each of the four angles is a straight angle or measures 90 degrees. A particular kind of parallelogram that has all of its angles equal is the rectangle. A square is a rectangle with four equally sized sides. Let's now explore the characteristics of the rectangle in this essay.

Rectangles' essential characteristics are as follows:

A rectangle is a parallelogram.

The Perimeter of the rectangle is 2a + 2b where a and b are the two sides

Now , if w is the width of the rectangle then, the length is 4w given in problem.

Perimeter,

2w + 2* 4w

As it is given in the problem

2w + 2* 4w ≤ 106

The first model of inequality satisfy the problem.

To learn more about inequatity refer to :

brainly.com/question/2456006

#SPJ1

The simplified expression for (f ∘ g)(x) is 2 + x (option d).

To find and simplify (f ∘ g)(x), we need to substitute the expression for g(x) into f(x) and simplify.

Given:

f(x) = log₃(9x)

g(x) = \(3^x\)

Substituting g(x) into f(x):

(f ∘ g)(x) = f(g(x)) = log₃\((9 * 3^x)\)

Now, we simplify the expression:

log₃\((9 * 3^x)\) = log₃(9) + log₃\((3^x)\)

Since logₓ(a * b) = logₓ(a) + logₓ(b), we have:

log₃(9) + log₃\((3^x)\) = log₃\((3^2)\) + x

Using the property logₓ\((x^a)\) = a * logₓ(x), we get:

log₃\((3^2)\) + x = 2 * log₃(3) + x

Since logₓ\((x^a)\) = a, where x is the base, we have:

2 * log₃(3) + x = 2 + x

Therefore, (f ∘ g)(x) simplifies to:

(f ∘ g)(x) = 2 + x

So, the correct answer is (d) 2 + x.

To know more about expression, refer here:

https://brainly.com/question/31800038

#SPJ4

Complete Question:

Given f(x)=log₃(9x) and g(x)=\(3^x\). Find and simplify (f ∘ g)(x)

(a) 2x

(b) x

(c) \(27^x\)

(d) 2+x

(e) None of these.

The equation that can be used to model the total cost is y = 18x

The given parameters are:

Cost = $72

Time = 4 hours

The hourly rate is calculated as:

k = Cost/Time

So, we have

k = 72/4

Evaluate

k = 18

The form of the equation is given as
y = kx

Substitute k = 18 in y = kx

y = 18x

Hence, the equation that can be used to model the total cost is y = 18x

Read more about proportional equations at:

https://brainly.com/question/12242745

#SPJ1

Answer:

100, percentage increased by 85% (percent) of its value = 185 Jan 16 02:56 UTC (GMT

Answer:

=100+85%

=100.85.......

Step-by-step explanation:

Sam's Income = ₹9000

Lisa's Income = ₹6000

Total earning = Sam's Income + Lisa's Income = ₹15000

Now,

Ratio of Sam's Income to the Total earning = ₹9000/₹15000 = 3:5

Ratio of Lisa's Income to Sam's earning = ₹6000/₹9000 = 2:3

The statistical test that compares the distribution of mean differences between two groups to the mean difference between two groups is independent-sample t test.

Given that,

We have to find the statistical test that compares the distribution of mean differences between two groups to the mean difference between two groups.

We know that,

The independent Samples t take a look at analyzes the manner of two separate organizations to see if there's statistical guide that the populace imply values are statistically extensively distinctive. A parametric take a look at is the unbiased Samples t take a look at.

since, the two agencies are independent and we're checking if difference is good sized is independent-samples t test.

consequently, the statistical test that compares the distribution of imply differences between two companies to the imply difference among  corporations is unbiased-pattern t check.

To learn more about statistic visit: https://brainly.com/question/23091366

#SPJ4

Answer:

C

Step-by-step explanation:

The result of the given algebraic simplification is 8x^2 - 10xy + 12y^2.

To simplify the expression 3x^2 - 4xy + 5y^2 - (-5x^2 + 6xy - 7y^2), we need to distribute the negative sign to the terms inside the parentheses. This yields: 3x^2 - 4xy + 5y^2 + 5x^2 - 6xy + 7y^2.

Next, we combine like terms, grouping the x^2 terms, the xy terms, and the y^2 terms: (3x^2 + 5x^2) + (-4xy - 6xy) + (5y^2 + 7y^2). Simplifying each group gives us: 8x^2 - 10xy + 12y^2.

Therefore, the simplified form of the given expression is 8x^2 - 10xy + 12y^2.

To learn more about algebraic simplification click here:

brainly.com/question/31478689

#SPJ11

Answer:

C.12

Step-by-step explanation:

Just took the quiz

The margin of error will be larger for a 99% confidence interval than for a 95% confidence interval, assuming the same sample size and level of variability in the data.

The margin of error is the range of values above and below the point estimate within which the true population parameter is likely to fall.

A higher level of confidence requires a larger margin of error. This is because as the level of confidence increases, the range of values that contains the true population parameter becomes wider.

For example, a 95% confidence interval has a margin of error of plus or minus two standard errors of the point estimate.

Increasing the confidence level to 99% would require a wider range of values, and therefore a larger margin of error, such as plus or minus three standard errors of the point estimate.

Learn more about confidence interval.

brainly.com/question/24131141

#SPJ11