Find the equation of a line perpendicular to 2x – 3y = 21 that passes through the point (2,8).​

the answer for this question is  i don't know

So , bye

(a) This differential equation can be written in the form (*) with P(x) = 1, Q(x) = 2x, and n = 2.

(b) The substitution u = 1/y will transform it into the linear equation Du/dx +  0u = -2x

(c)Using the substitution in part (b), we rewrite the initial condition in part  u(1) = 1/y(1) = 1/4.

(d) the linear equation in part (b) is y = 1/(C - x) and  the solution that satisfies the initial condition in part (c) U(x) = -y⁻¹ = -x + C,

(e) Finally, solve for y(x) = 1/(1/4 + 1 - x) = 4/(5 - x).

What is  Bernoulli differential equation?

A Bernoulli differential equation is a type of non-linear ordinary differential equation of the form:

dy/dx + P(x)y = Q(x)yⁿ

where P(x) and Q(x) are functions of x and n is a constant. The equation is named after the Swiss mathematician Jakob Bernoulli.

These types of differential equations are important in various fields of science, such as physics, engineering, and economics. They are non-linear, meaning that the dependent variable y appears in both linear and non-linear terms, making them difficult to solve in general.

a) This differential equation can be written in the form (*) with P(x) = x, Q(x) = 2x, and n = 2.

b) The substitution u = y⁻¹ will transform it into the linear equation du/dx - xu = -2x.

c) Using the substitution in part (b), we rewrite the initial condition as u(1) = 1/4.

d) Now we solve the linear equation in part (b). The characteristic equation is given by d/dx(e\(\mathrm{(\int -xdx))}\) = -xe\(\mathrm{(\int -xdx))}\) which has the general solution u(x) = Ce\((-x^2/2)\).

Using the initial condition, we find C = 1/4, so u(x) = 1/4e\((-x^2/2)\).

e) Finally, we solve for y. From u = y⁻¹, we have y = 1/u = 4e\((-x^2/2)\).

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The given expression \(g^2/3h\) is equivalent to the option (c) \(8g^2/24h\)as we have multiplied 8 in both numerator and denominator.

The given expression is \(g^2/3h\).

Now, to further simplify the expression, we can multiply both numerator and denominator by 8. This gives us:

\((g^2/3h) * (8/8)\)

Simplifying further, we get:

\((8g^2)/(24h)\)

Therefore, the expression equivalent to \(g^2/3h\) is \((8g^2)/(24h)\).

Thus, the given expression \(g^2/3h\) is equivalent to the option (c) \(8g^2/24h\) as we have multiplied 8 in both numerator and denominator.

The numerator is the top part of a fraction, which represents the number of equal parts being considered. It is the value that is above the fraction bar and represents the quantity being divided into equal parts.

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The complete question is :

Which expression is equivalent to \(g^2/3h\)?

Click on the correct answer.

(A) \(g^2+5/3h+5\)

(B) \(6g^2/15h\)

(C) \(8g^2/24h\)

Answer:

y = 3

x = - 3

Step-by-step explanation:

First we represent "x" through "y"

y = x + 6

x = y - 6

Then we substatute this value instead of "x" in the other formula, and so we get...

y = - 2x - 3

y = - 2(y - 6) - 3

y = - 2y + 12 - 3

3y = 9

y = 3

Now that we know "y" we can find out "x" by doing...

x = y -6

x = 3 - 6

x = - 3

The values of x for the tangent segments to the circles are: (25). x = 2 and (26). x = 4

A theorem of tangents to a circle states that if from one exterior point, two tangents are drawn to a circle then they have equal tangent segments.

(25). 2x - 1 = x + 1 {equal tangent segments}

2x - x = 1 + 1 {collect like terms}

x = 2

(26). 2x - 4 = x {equal tangent segments}

2x - x = 4 {collect like terms}

x = 4

Therefore, the values of x for the tangent segments to the circles are: (25). x = 2 and (26). x = 4

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Answer:

I think its C

Step-by-step explanation:

Answer:

700,000

Step-by-step explanation:

Answer:

700,000

Step-by-step explanation:

It's closer to 700,000 than 800,000. Hope this helps! Have a nice day :)

Answer:

Step-by-step explanation:

Step-by-step explanation:

area of rectangle= l*b

2and 2/3  * 7 and 3/4

8/3 * 31/4

62/3 sq . feet

20 and 2/3 feet

La edad actual de José es de 30 años.

Para resolver este problema, primero debemos establecer ecuaciones basadas en la información proporcionada. Llamemos "x" a la edad actual de José y "y" a la edad actual de Ana. Según la primera condición, la edad de Ana es la mitad de la edad de José, por lo que podemos escribir la ecuación: y = (1/2)x.

La segunda condición nos dice que dentro de 10 años, sus edades serán dos tercios de sus edades actuales. Esto se puede expresar como: (x + 10) * (2/3) = y + 10.

Reemplazando el valor de y en la segunda ecuación con la primera ecuación, obtenemos: (x + 10) * (2/3) = (1/2)x + 10.

Resolviendo esta ecuación, podemos simplificarla y llegar a: 2(x + 10) = 3[(1/2)x + 10].

Al resolver la ecuación resultante, encontramos que x = 30.

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Answer: C

Step-by-step explanation:

The image of the resulting figure (quadrilateral A'B'C'D') is presented below as attachment.

How to graph a dilated quadrilateral

According to geometry and linear algebra, a dilation of a point \(P(x,y)\) with respect to another point \(G(x,y)\) is determined by the following expression:

\(P'(x,y) = P(x,y) +k\cdot [P(x,y) - G(x,y)]\) (1)

Where:

Now we proceed to make the corresponding operations (\(A(x,y) = (-1, 3)\), \(B(x,y) = (2,0)\), \(C(x,y) = (2, -1)\), \(D(x,y) = (-3, -1)\)):

\(A'(x,y) = (-1,3)+(-0.5)\cdot [(-1,3)-(2,1)]\)

\(A'(x,y) = (-1, 3) + (-0.5)\cdot (-3, 2)\)

\(A'(x,y) = (-1, 3) + (1.5, -1)\)

\(A'(x,y) = (0.5, 2)\)

\(B'(x,y) = (2,0) + (-0.5)\cdot [(2,0)-(2,1)]\)

\(B'(x,y) = (2,0) + (-0.5)\cdot (0, -1)\)

\(B'(x,y) = (2,0) + (0, 0.5)\)

\(B'(x,y) = (2, 0.5)\)

\(C'(x,y) = (2, -1) + (-0.5)\cdot [(2,-1)-(2,1)]\)

\(C'(x,y) = (2, -1) + (-0.5)\cdot (0,-2)\)

\(C'(x,y) = (2,-1) + (0, 1)\)

\(C'(x,y) = (2, 0)\)

\(D'(x,y) = (-3,-1) + (-0.5)\cdot [(-3, -1)-(2,1)]\)

\(D'(x,y) = (-3,-1) + (-0.5)\cdot (-5, -2)\)

\(D'(x,y) = (-3, -1) + (2.5, 1)\)

\(D'(x,y) = (-0.5, 0)\)

Lastly, we proceed to graph both the original and resulting figure. \(\blacksquare\)

The statement is incomplete. Complete description is shown below:

Draw the image of quadrilateral ABCD (\(A(x,y) = (-1, 3)\), \(B(x,y) = (2,0)\), \(C(x,y) = (2, -1)\), \(D(x,y) = (-3, -1)\)) under the dilation with scale factor -0.5 and center of dilation \(G(x,y) = (2, 1)\).

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Answer:

A.

Step-by-step explanation:

The solution to the inequality would the shaded area. The shaded area stretches from negative infinity all the way until x equals -2 (but does not include -2).

Therefore, the solution set would be:

\((-\infty,2)\)

Note that parentheses instead of brackets are used because (1), you can only approach infinity and (2), the solution set does not include 2.

Answer:

-0.5. is 5

Step-by-step explanation:

i need the poits

for KW 1 calculation output are 15,17,19,21,23for KW 2 calculation output are 61,63,65  for KW 3 calculation are   16,23,30,37,114,121,128,  just by substituting to equation we can get answer

what is equation ?

An equation is a mathematical statement that asserts that two expressions are equal. It is typically written using an equal sign (=) between the two expressions. An equation can contain variables, which are symbols that represent unknown values.

In the given question,

for table 1 calculation is as below

output x=0 is  15+2x=15+2*0=15

output x=1 is  15+2x=15+2*1=17

output x=2 is  15+2x=15+2*2=19

output x=3 is  15+2x=15+2*3=21

output x=4 is  15+2x=15+2*4=23

for table 2 calculation is as below

output x=1 is  60+2x=60+2*1=61

output x=2 is   60+2x=60+2*2=63

output x=3 is   60+2x=60+2*3=65

for table 3 calculation is as below

output x=0 is 16+7x=16+7*0=16

output x=1 is  16+7x=16+7*1=23

output x=2 is 16+7x=16+7*2=30

output x=3 is  16+7x=16+7*3=37

output x=14 is 16+7x=16+7*14=114

output x=15 is 16+7x=16+7*15=121

output x=16 is 16+7x=16+7*0=128

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for KW 1 calculation output are 15,17,19,21,23for KW 2 calculation output are 61,63,65  for KW 3 calculation are   16,23,30,37,114,121,128,  just by substituting to equation we can get answer

what is equation ?

An equation is a mathematical statement that asserts that two expressions are equal. It is typically written using an equal sign (=) between the two expressions. An equation can contain variables, which are symbols that represent unknown values.

In the given question,

for table 1 calculation is as below

output x=0 is  15+2x=15+2*0=15

output x=1 is  15+2x=15+2*1=17

output x=2 is  15+2x=15+2*2=19

output x=3 is  15+2x=15+2*3=21

output x=4 is  15+2x=15+2*4=23

for table 2 calculation is as below

output x=1 is  60+2x=60+2*1=61

output x=2 is   60+2x=60+2*2=63

output x=3 is   60+2x=60+2*3=65

for table 3 calculation is as below

output x=0 is 16+7x=16+7*0=16

output x=1 is  16+7x=16+7*1=23

output x=2 is 16+7x=16+7*2=30

output x=3 is  16+7x=16+7*3=37

output x=14 is 16+7x=16+7*14=114

output x=15 is 16+7x=16+7*15=121

output x=16 is 16+7x=16+7*0=128

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These two triangles must be congruent because they both have the same side lengths and angles.

Answer:

The ticks on the sides of the triangles tell us that the sides are congruent.

Step-by-step explanation:

Whenever you see ticks, they represent congruence. We can observe the paired ticks on both triangles.

Answer:

Age difference between oldest the  youngest = 48 years

Step-by-step explanation:

Given: Ratio of ages of Kissi and Esinam is 3:5, ratios of ages of Esinam and Lariba is 3:5 and sum of the ages of all 3 is 147 years

To find: age difference between oldest the  youngest

Solution:

Let age of Lariba be x years

As ratios of ages of Esinam and Lariba is 3:5,

Age of Esinam = \(\frac{3}{5}x\)  years

As ratio of ages of Kissi and Esinam is 3:5,

Age of Kissi = \((\frac{3}{5}) (\frac{3}{5}x)=\frac{9}{25}x\) years

Sum of the ages of all 3 = 147 years

\(x+\frac{3}{5}x+\frac{9}{25}x=147\\ \frac{25x+15x+9x}{25}=147\\ x=\frac{147(25)}{49}=75\)

Age of Lariba = x = 75 years

Age of Esinam = \(\frac{3}{5}(75)=45\,\,years\)

Age of Kissi = \(\frac{9}{25}(75)=27\,\,years\)

So,

Age difference between oldest the  youngest = 75 - 27 = 48 years

Answer:

83 kilometres per hour =

51.574 miles per hour

\(x^2-8x+10=x^2-8x+16-6=(x-4)^2-6\)

Answer:

x=(y+81)/7

Step-by-step explanation:

y=7x-72-9

y=7x-81

y+81=7x

7x=y+81

x=(y+81)/7

x=(y+81)/7

\( \frac{12}{16} = \frac{x}{13} \)

\(16x = 12 \times 13\)

\(x = \frac{12 \times 13}{16} \)

\(x = \frac{156}{16} = 9.75\)

Absolute error and relative error for a) will be 0.0012645 and 4.0250 × 10−4 And the Absolute error and relative error of b) will be 7.3464 × 10−6 and 2.3384 × 10−6.

Use calculator for calculations.

a) Absolute error: |p − p∗| = |π − 22/7| = 0.0012645.

Relative error: |p−p∗|

|p| = |π−22/7|

π = 4.0250 × 10−4.

b) Absolute error: |p − p∗| = |π − 3.1416| = 7.3464 × 10−6.

Relative error: |p−p∗|

|p| = |π−3.1416|

π = 2.3384 × 10−6.

mistakes, in applied arithmetic, the difference between a real fee and an estimate, or approximation, of that value. In information, a commonplace instance is the difference among the mean of a whole populace and the suggest of a sample drawn from that population.

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The inverse statement is false.

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Answer:

Step-by-step explanation:

50% of 366 is 183, therefore your answer is 366.

Answer:

D

Step-by-step explanation:

a. It will take 7 months to pay off the credit card.

b. it will take 4 months to pay off the credit card.

Since, APR stands for Annual Percentage Rate. It is the interest rate charged on a loan or credit card, expressed as a yearly percentage rate. The APR takes into account not only the interest rate, but also any fees or charges associated with the loan or credit card.

a. If you put half of the available money each month toward the credit card, then you are paying $150.00 per month towards the credit card balance.

We can use the formula for the present value of an annuity to find how many months it will take to pay off the credit card:

PV = PMT × ((1 - (1 + r)⁻ⁿ) / r)

where:

PV is the present value of the debt

PMT is the payment amount per period

r is the monthly interest rate

n is the number of periods

Substituting the values, we get:

754.43 = 150 × ((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)

Simplifying and solving for n, we get:

n = log(1 + (PV ×r / PMT)) / log(1 + r)

n = log(1 + (754.43×0.011333 / 150)) / log(1 + 0.011333)

n = 6.18

Therefore, it will take 7 months to pay off the credit card if you put half of the available money each month toward the credit card.

b. If you put all of the available money each month toward the credit card, then you are paying $300.00 per month towards the credit card balance.

754.43 = 300 ×((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)

Simplifying and solving for n, we get:

n = log(1 + (PV × r / PMT)) / log(1 + r)

n = log(1 + (754.43× 0.011333 / 300)) / log(1 + 0.011333)

n = 3.43

Therefore, it will take 4 months to pay off the credit card if you put all of the available money each month toward the credit card.

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Yes the  expressions b³ and a³, can be written in radical form as; ∛b⁹

or ∛a⁹ respectively

Radical form is defined as the expression that involves radical signs such as square root, cube root, etc rather than using exponents to describe the same entity. We can make use of laws of exponents to convert the exponential form to radical form as;

(a)^(2/3) =∛a²

Thus, from the given expressions as b³ and a³, we can write them in radical form as;

b^(9/3) = ∛b⁹

or ∛a⁹

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Let

x and y -----< two complementary angles

so

x+y=90 -----> equation 1

x-y=60 -----> equation 2

Solve the system of equations

Solve by elimination

Adds equation 1 and equation 2

x+y=90

x-y=60

------------

2x=150

x=75 deg

Find out the value of y

75+y=90

y=15 deg

therefore

Answer:

c

Step-by-step explanation:

Answer:

the answer is 5

Step-by-step explanation:

Answer:

17.7 inches

Step-by-step explanation:

Use the Pythagorean Theorem.

length² + width² = diagonal²

width² = diagonal² - length² = 19² - 7² = 312

width = √312 ≅ 17.7 inches

Answer:

17.7

Step-by-step explanation:

got it right at k12 :)

Answer:

103288

Step-by-step explanation:

1 mile is equal to 63360 inches. 98 times 63360 is 6209280 inches per hour

divide by 60 to get 103288 inches per minute.