A cabin was built in the shape of a rectangle. It is 15 meters (m) long and 10 m wide. How far is it all the way around the outside of the cabin?
Which of these shows a way to solve the problem?

The equation of the line perpendicular to y=1/2x-1 and passing through the point (5,6) is y = -2x + 16.

To find the equation of the line perpendicular to y=1/2x-1, we need to determine its slope. We can recall that the slope of a line in slope-intercept form, y = mx + b, is given by m, the coefficient of x. So in the given equation y=1/2x-1, the slope is 1/2.

The slope of a line perpendicular to this line will be the negative reciprocal of the slope, which means it will be -2. To see why this is true, remember that the product of the slopes of two perpendicular lines is always -1. So if the slope of the original line is m, the slope of the perpendicular line will be -1/m.

Now that we know the slope of the perpendicular line is -2, we can use the point-slope form of the equation of a line to find its equation. The point-slope form is:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line.

We are given a point on the perpendicular line, (5, 6), so we can substitute that into the equation and also substitute in the slope, -2:

y - 6 = -2(x - 5)

y - 6 = -2x + 10

y = -2x + 16

Hence, the equation of the line perpendicular to y=1/2x-1 and passing through the point (5,6) is y = -2x + 16.

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Answer:

It Is!

Step-by-step explanation:

"For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students' ages."

There is no real Value of k that will satisfy the equation 2x² - x + 8k = 0 if a and 1/a are the roots of the polynomial.

(i) Zeroes of the polynomial:

In the graph, we have two points where the curve intersects the x-axis: one is at (-1,0), and the other is at (2,0).The corresponding values of x are -1 and 2, and they are the zeros of the polynomial. Therefore, the zeros of the polynomial are -1 and 2.(ii) Forming the quadratic polynomial:

From the graph, we can observe that the curve intersects the y-axis at the point (0,5), implying that the constant term of the polynomial is 5.

We can use the formula to find the quadratic polynomial if we have two zeros and one constant term. Thus, the quadratic polynomial is given by:(x + 1)(x - 2) = x² - x - 2x + 2 = x² - 3x + 2. Therefore, the quadratic polynomial is x² - 3x + 2.(iii) Value of k if a, 1/a are the zeroes of the polynomial 2x² - x + 8k:

We know that a and 1/a are the zeroes of the polynomial 2x² - x + 8k. Therefore, we can find the sum and product of the roots and use them to determine the value of k.

The sum of the roots is a + 1/a, and their product is a(1/a) = 1. Using the sum and product of the roots, we can write: a + 1/a = 1/2 (1/2 is the coefficient of x)Substituting a with 1/a in the above equation, we get: 1/a + a = 1/2Multiplying both sides of the equation by 2a, we get: 2 + 2a² = a

Simplifying the equation, we get: 2a² - a + 2 = 0Multiplying both sides by 2,

we get: 4a² - 2a + 4 = 0Dividing both sides by 2, we get: 2a² - a + 2 = 0

Using the quadratic formula, we get: a = [1 ± √(1 - 4(2)(2))]/(2(2))

Simplifying, we get: a = [1 ± √(-31)]/4Since the discriminant of the quadratic formula is negative, the roots are imaginary. Therefore, there is no real value of k that will satisfy the equation 2x² - x + 8k = 0 if a and 1/a are the roots of the polynomial.

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Answer:

18/7

Step-by-step explanation:

Since m<2 includes 1, m<2 = m<1

9x = 2x + 2 ⇒ 7x = 2 ⇒ x = 2/7

m<1  = 2(2/7) + 2 = 4/7 + 14/7 = 18/7

Answer:

Option 2.

Step-by-step explanation:

Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.

Domain: \((- \infty} ,0)\) ∪ \((0, \infty} )\)

Range: \((- \infty} ,0)\)∪\((0, \infty} )\)

Check the picture below.

so hmmm let's find the length of the slanted side, namely the hypotenuse of the triangle with sides of 9 and 7(half of 14).

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{9}\\ o=\stackrel{opposite}{7} \end{cases} \\\\\\ c=\sqrt{ 9^2 + 7^2}\implies c=\sqrt{ 81 + 49 } \implies c=\sqrt{ 130 }\)

so now let's get the areas of those triangles and those rectangles.

\(\stackrel{\textit{two triangles}}{2\left[\cfrac{1}{2}(14)(9) \right]}~~ + ~~\stackrel{\textit{left and right rectangles}}{2(\sqrt{130})(20)}~~ + ~~\stackrel{\textit{bottom rectangle}}{(20)(14)} \\\\\\ 126+40\sqrt{130}+280\implies 406+40\sqrt{130} ~~ \approx ~~ \text{\LARGE 862.07}~cm^2\)

just give the other kid brainiest

Step-by-step explanation:

Step-by-step explanation:

\(5. {x}^{3} - xy + {y}^{2} = 4\)

\( \frac{dy}{dx} ( {x}^{3} - xy + {y}^{2} ) = \frac{dy}{dx} (4)\)

\(3 {x}^{2} - x(1) \frac{dy}{dx} + 1(y) + 2y \frac{dy}{dx} \)

Combine the dy/dx.

\( \frac{dy}{dx} ( - x + 2y) + y + 3 {x}^{2} \)

\( \frac{dy}{dx} ( - x + 2y) = - 3 {x}^{2} - y\)

\( \frac{dy}{dx} = \frac{ - 3 {x}^{2} - y}{ - x + 2y} \)

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

Answer:

\(\frac{dy}{dx}\) = \(\frac{y-3x^2}{2y-x}\)

Step-by-step explanation:

using the product rule to differentiate - xy then

3x² - (x\(\frac{dy}{dx}\) + y(1) ) + 2y\(\frac{dy}{dx}\) = 0

3x² - x\(\frac{dy}{dx}\) - y + 2y\(\frac{dy}{dx}\) = 0

3x² + \(\frac{dy}{dx}\) (2y - x) - y = 0 (subtract 3x² - y from both sides )

\(\frac{dy}{dx}\) (2y - x) = y - 3x² ← divide both sides by (2y - x)

\(\frac{dy}{dx}\) = \(\frac{y-3x^2}{2y-x}\)

Answer:

A fancy way of saying "solutions" of the equation

Answer:

20

Step-by-step explanation:

4 + \((m-n)^{4}\) ← substitute m = 7 and n = 5 into the expression

= 4 + \(7-5)^{4}\)

= 4 + \(2^{4}\)

= 4 + 16

= 20

Answer:

12

Step-by-step explanation:

edge 1045

Answer:obtuse angle

Step-by-step explanation:

An obtuse angle is an angle of greater than 90° and less than 180°. It is bigger than an acute angle. It is smaller than a straight angle, which measures 180°. Angles are measured with a protractor obtuse angle is specifically present in hexagon and pentagon and others.

Answer:

12(a+b+c)

Step-by-step explanation:

how to verify:

Distribute 12 and you'll get the original expression

I hope my answer was helpful!

It's Letter C. 1 3 and 5

that's the domain

(i) The first term (a) is 24 and the common difference (d) is -2.

(ii) The sum of the progression is 2520.

i) Finding the first term and common difference:

Given that the number of terms in the arithmetic progression is 40 and the last term is -54, we can use the formula for the nth term of an arithmetic progression to find the first term (a) and the common difference (d).

The nth term formula is: An = a + (n-1)d

Using the given information, we can substitute the values:

-54 = a + (40-1)d

-54 = a + 39d

We also know that the sum of the first 15 terms added to the sum of the first 30 terms is zero:

S15 + S30 = 0

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values for S15 and S30:

[(15/2)(2a + (15-1)d)] + [(30/2)(2a + (30-1)d)] = 0

Simplifying the equation:

15(2a + 14d) + 30(2a + 29d) = 0

30a + 210d + 60a + 870d = 0

90a + 1080d = 0

a + 12d = 0

a = -12d

Substituting this value into the equation -54 = a + 39d:

-54 = -12d + 39d

-54 = 27d

d = -2

Now we can find the value of a by substituting d = -2 into the equation a = -12d:

a = -12(-2)

a = 24

Therefore, the first term (a) is 24 and the common difference (d) is -2.

ii) Finding the sum of the progression:

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values:

S40 = (40/2)(2(24) + (40-1)(-2))

S40 = 20(48 - 39(-2))

S40 = 20(48 + 78)

S40 = 20(126)

S40 = 2520

Therefore, the sum of the arithmetic progression is 2520.

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37

Hope it helps

Good luck

Answer:

(63 ÷ 9) + 5 x 2 x 3 we use BODMAS

7 + 10 X 3

7 + 30=37

Step-by-step explanation:

In June, A.B.C company invested $20,000, purchased equipment, paid insurance premium, bought office supplies, billed students for tutorial services, received cash, paid for supplies, withdrew personal funds.

Accounting Cycles:

1. June 1:

  - A.B.C company invests $20,000 in the business.

  - Prepare the journal entry:

    - Debit: Cash ($20,000)

    - Credit: Capital ($20,000)

2. June 3:

  - Purchased equipment for $12,100.

  - Prepare the journal entry:

    - Debit: Equipment ($12,100)

    - Credit: Cash ($12,100)

3. June 4:

  - Paid $220 premium for an insurance policy.

  - Prepare the journal entry:

    - Debit: Insurance Expense ($220)

    - Credit: Cash ($220)

4. June 6:

  - Purchased office supplies on account for $140.

  - Prepare the journal entry:

    - Debit: Office Supplies ($140)

    - Credit: Accounts Payable ($140)

5. June 9:

  - Purchased a new computer for $9,000. Paid 40% in cash and agreed to pay the remainder later.

  - Prepare the journal entry for the cash payment:

    - Debit: Computer ($3,600) [40% of $9,000]

    - Credit: Cash ($3,600)

  - Prepare the journal entry for the remaining amount:

    - Debit: Computer ($5,400)

    - Credit: Accounts Payable ($5,400)

6. June 10:

  - Billed student Omar $58 for tutorial services performed.

  - Prepare the journal entry:

    - Debit: Accounts Receivable ($58)

    - Credit: Tutorial Services Revenue ($58)

7. June 14:

  - Paid for the supplies purchased on June 6th ($140).

  - Prepare the journal entry:

    - Debit: Accounts Payable ($140)

    - Credit: Cash ($140)

8. June 15:

  - The owner suggested purchasing a new building for the company for $22,000.

  - No journal entry is required at this point. It is a decision made by the owner.

9. June 25:

  - Received $85 cash from student Salim Ali for tutorial services performed.

  - Prepare the journal entry:

    - Debit: Cash ($85)

    - Credit: Accounts Receivable ($85)

10. June 30:

   - Student billed on June 10 pays the amount due ($58).

   - Prepare the journal entry:

     - Debit: Cash ($58)

     - Credit: Accounts Receivable ($58)

11. June 30:

   - A.B.C company withdraws $60 for personal use.

   - Prepare the journal entry:

     - Debit: Withdrawals ($60)

     - Credit: Cash ($60)

These transactions represent the accounting cycles for the given period.

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Answer:

To solve the problems in this lesson, students use the slope formula, which states that m = (y2 -- y1) / (x2 -- x1). The slope formula can be read as "slope equals the second y coordinate minus the first y-coordinate over the second x-coordinate minus the first x-coordinate".

Hope helps

The factorized form of \(x^3 - (y - z)^3\ is \ (x - y + z)(x^2 - xy + 2xz + yz - 2z^2).\)

The Factorization is derived from the application of a mathematical identity. As an AI language model, the information provided is generated based on existing knowledge and formulas.

The given expression is \(x^3 - (y - z)^3.\)To factorize it,  the difference of cubes, which states that a^3 - b^3 can be factorized as\((a - b)(a^2 + ab + b^2).\)

Applying this identity to our expression, we have:

\(x^3 - (y - z)^3 = (x - (y - z))((x - (y - z))^2 + (x - (y - z))(y - z) + (y - z)^2)\)

Simplifying further, we get:

\(= (x - y + z)(x^2 - 2xy + 2xz - y^2 + 2yz - z^2 + xy - y^2 + yz - z^2 + y^2 - 2yz + z^2)\\= (x - y + z)(x^2 - 2xy + xy + 2xz + yz - 2yz - y^2 + y^2 - y^2 + 2yz - 2z^2 + y^2 - z^2 + z^2)\\= (x - y + z)(x^2 - xy + 2xz + yz - 2z^2)\)

So, the factorized form of \(x^3 - (y - z)^3 \ is\ (x - y + z)(x^2 - xy + 2xz + yz - 2z^2).\)

the above factorization is derived from the application of a mathematical identity.

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If only 2,836 students were admitted into the Ateneo among 27,813 students, who took the ACET this year, the Ateneo’s acceptance rate is b. 10.2%.

The rate is the ratio of one value, expression, measurement, or quantity compared to another.

The rate represents the quotient of the numerator and the denominator.

The rate is expressed as a percentage by multiplication with 100.

The number of students who took the ACET this year = 27,813

The number of students who were admitted into the Ateneo = 2,836

The percentage or rate admitted = 10.19667% (2,836 ÷ 27,813 × 100)

= 10.2%

Thus, we can conclude that the acceptance rate or percentage is Option B.

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Answer:

Yes. The vertical line never touches the graph at more than one point at the same time.

Step-by-step explanation:

this is the plato and edmentum answer

(make sure this is the right question)

As the vertical line touches the graph of the equation y = 2x - 3 it is a function.

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

Given, An equation y = 2x - 3.

Now, If we draw a vertical line and it touches the graph at only one point

the equation is a function but if the vertical line touches the graph at more than two points the equation is not a function.

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Answer:

386.75

Step-by-step explanation:

added in the picture

The cost of joining the gym for 6 months is 386.75.

Given,

The function G(m) = 49.5m + 89.75 represents the cost of joining the gym in addition to the one-time membership fee.

The cost, G, is measured in dollars for m months.

We need to find the value of G(6).​

Here,

The one-time membership = 89.75.

Now,

Putting m = 6 months in:

G(m) = 49.5m + 89.75

G(6) = 49.5 x 6 + 89.75

       = 297 + 89.75

       = 386.75

Thus the cost of joining the gym for 6 months is G(6) = 386.75.

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Answer:

f(2) = 9

Step-by-step explanation:

It's give in the question,

Two different functions are,

f(x) = 4x + 1

g(x) = -2x

Then we have to find the output value of function 'f' for the input value x = 2.

By substituting the value of x in the function 'f',

f(2) = 4(2) + 1

     = 9

f(2) = 9

Answer: 0.0228

Step-by-step explanation:

Let x be the weight of a product.

The probability that a randomly selected unit from a recently manufactured batch weighs more than 5 ounces:

\(P(X>5)\\\\=P(\dfrac{X-Mean}{\sqrt{Variance}}>\dfrac{5-4}{\sqrt{0.25}})\\\\=P(Z>\dfrac{1}{0.5}) \ \ \ [z=\dfrac{X-Mean}{\sqrt{Variance}}]\\\\=P(z>2)\\\\=1-P(Z<2)\\\\=1-0.9772\ \ [\text{Using p value table}]\\\\=0.0228\)

Hence, the required probability = 0.0228

Based on the graph, we can see that the line passes through the point (0,3) as the line is horizontal, therefore the y-intercept is (0,3).

Answer:

(0,4)

Step-by-step explanation:

its where it intersects with the y axis

Answer:

Step-by-step explanation:

we know this is a 2 dimensional shape so m*3 out, its m not ft so only answer is

24 m*2

The equation that represents the cost, c, of n sets is c = 63.74n

from the question, we have the following parameters that can be used in our computation:

Each volleyball set costs $63.74.

Let the total number of sets be n

So we have

Cost of n = 63.74 * n

This gives

c = 63.74n

Hence, the equation is c = 63.74n

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Answer:

Step-by-step explanation:

Let the number of quarters be x and nickels be y.

Given:

We have equations:

Solve the system by elimination, subtract 5 times the first equation from the second one:

Find the value of y:

Verify: