solve for x using common denominators f/6(x+4)=x/(x+4)

Answer:

The area of the piece of paper is 466 cm²

Step-by-step explanation:

First you would want to find the area of the rectangle

39x20=780 cm²

Both semi-circles are the same, so you can just find the area of the whole circle

The diameter is 20 cm so you would use 10 as the radius

A=πr²

A=3.14x10²

A=3.14x100

A=314

Then you have to subtract the area of the circle from the area of the rectangle.

780-314=466

The area of the piece of paper is 466 cm²

Let the unit price for pencil be x

Let the unit price for pack be y

If the students bought 3 packs of pencil and 2 packs of pen for $8.25, then;

\(2x+3y=8.25.... 1\)

Similarly;

If her friend bought 5 packs of pencil and 2 packs of pen for $11, then ;

\(5x+2y=11 .... 2\)

We will have to solve both equations simultaneously as shown;

\(2x+3y=8.25... 1...*5 \\5x+2y=11 ... 2 ... *2 \\\)

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

\(10x+15y=41.25\\10x=4y=22 \\\)

Subtract the resulting equations;

\(15y-4y=41.25-22\\11y=19.25\\y=19.25/11\\y= $ 1.75 \\\)

Hence 1 pack of pen costs %1.75

To get x, you will substitute y= 1.75 into equation 2;

\(2;5x+2y=11\\5x+2(1.75)=11\\5x+3.5=11\\5x=11-3.5\\5x=7.5\\x=\frac{7.5}{5} \\x=1.5\)

Hence 1 pack of pencil will cost costs $1.5

From the above solution, we can conclude that there are enough information to find the cost of each pack of pen and pencil.

PLEASE MARK ME AS BRAINLIEST

Let the unit price for pencil be x

Let the unit price for pack be y

If the students bought 3 packs of pencil and 2 packs of pen for $8.25, then;

Similarly;

If her friend bought 5 packs of pencil and 2 packs of pen for $11, then ;

We will have to solve both equations simultaneously as shown;

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

Subtract the resulting equations;

Hence 1 pack of pen costs %1.75

To get x, you will substitute y= 1.75 into equation 2;

Hence 1 pack of pencil will cost costs $1.5

From the above solution, we can conclude that there are enough information to find the cost of each pack of pen and pencil.

Answer:

\(y=|\frac{1}{4}x|\)

Step-by-step explanation:

Given that

transformed graph of the parent graph y=|x|

The transformed function is shown below:-

We see the graph at y=1 x reaches to 4 i.e, x=4

In the Same manner at y = 1

and x reaches to -4

that is

x=-4

Now, as per the options that are given in the question

The graph would be satisfied these two points would become transformation

\(y=|\frac{1}{4}x|\)

Now,

At x=4

\(y=|\frac{1}{4}x|\)

\(y=|\frac{1}{4}(4)|\)

y = 1

we can say that the point totally satisfied the equation.

So, Option 1 is right that is

\(y=|\frac{1}{4}x|\)

With the help of a diagram we can go through as attached.

The Function for given graph will be \(y=|\frac{1}{4} x|\)

If the graph of f(x) is given, then the graph of \(f(\frac{1}{k} x)\) is stretch by a factor of k.

Here function is given that,   y=|x|

From given graph it is observed that, graph is stretched by a factor of 4.

So that function for given graph will be,

                            \(y=|\frac{1}{4} x|\)

Graph is attached below,

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Therefore, it will take approximately 13.7 years for the population to double.

a. To determine the growth rate, you need to calculate the percentage increase in population. The formula for growth rate is:

Growth Rate = (New Value - Old Value) / Old Value * 100

Using the given values, we have:

Growth Rate = (1577 - 1500) / 1500 * 100
Growth Rate = 77 / 1500 * 100
Growth Rate ≈ 5.13%

b. To write a general equation for the population, you can use the formula:

p(t) = p(0) * (1 + r/100)^t

where p(t) is the population at time t, p(0) is the initial population, r is the growth rate, and t is the number of years.

c. To estimate the population in 2010, we need to find the population at time t = 2010 - 2000 = 10 years. Using the general equation from part b, and substituting the given values:

p(10) = 1500 * (1 + 5.13/100)^10
p(10) ≈ 1500 * (1.0513)^10
p(10) ≈ 1500 * 1.6436
p(10) ≈ 2465.4

Therefore, the estimated population in 2010 is approximately 2465.

d. To find out how many years it will take for the population to double, we need to solve the equation:

2 * p(0) = p(0) * (1 + r/100)^t

Simplifying the equation, we have:

2 = (1 + r/100)^t

Taking the logarithm of both sides, we get:

log(2) = t * log(1 + r/100)

Finally, solving for t, we have:

t = log(2) / log(1 + r/100)

Substituting the growth rate from part a, we have:

t = log(2) / log(1 + 5.13/100)
t ≈ log(2) / log(1.0513)
t ≈ 13.7 years

Therefore, it will take approximately 13.7 years for the population to double.

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Answer:

ur m=4/3 as an improper fraction it's 1 and 1 over 3

The linear function is:f(x) = mx + c

where, m = slope = 6and,

f(0) = c = 3

So, the equation of the linear function is:f(x) = 6x + 3Hence, and option (b) is correct.

1. The equivalent capacitance across AB in the given circuit is:  C = (0.1) + (0.1) = 0.2 F

The equivalent capacitance across AB is 0.2F. So, the equivalent capacitance across AC is given by:

C_eq = C1+C2

= 0.2+0.1

= 0.3F

So, we can use the formula, C = 2π/(ln(b/a))

Where,b = distance from A to C= 3.2 cm

= 0.032 m

and a = distance from A to B= 1.8 cm= 0.018 m

Thus,C= 2π/(ln(0.032/0.018))= 0.098 F

So, the answer is option (b) -(0.1)C.2. Given, f(0)=3 and slope = 6.

So, the linear function is:f(x) = mx + c

where, m = slope = 6and,

f(0) = c = 3

So, the equation of the linear function is:f(x) = 6x + 3

Hence, option (b) is correct.

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Answer:

The answer is 77

Answer:

x=1

Step-by-step explanation:

Its x=1 because if we put the 1 as in x then it will be like 2(1)+3(4(1)-3)= 8-3(1)

2(1)+3(4(1)-3) is equal to 5

8-3(1) is equal to 5

5=5

so x is 1

Answer:

x=1

Step-by-step explanation:

Answer:

Expressions with fractional or negative exponents can be factored by pulling out a GCF. Look for the variable or exponent that is common to each term of the expression and pull out that variable or exponent raised to the lowest power. These expressions follow the same factoring rules as those with integer exponents.

Step-by-step explanation:

Answer:

y = 2x + 7

Step-by-step explanation:

The sum of squares of the residuals (SSR) is 3.25.

To answer part 2 of the question, we need to find the sum of squares of the residuals.

The residuals are the differences between the observed values of the dependent variable (y) and the predicted values obtained from the regression model.

In this case, the residuals are given as: 0.2, 0.3, -0.8, -0.8, -0.3, 0.4, 0.1, -0.1, -0.4, -0.7, 0.6, -0.1, -0.1, 0.3, 0.

To calculate the sum of squares of the residuals (SSR), we square each residual value and sum them up.

\(SSR = (0.2^2) + (0.3^2) + (-0.8^2) + (-0.8^2) + (-0.3^2) + (0.4^2) + (0.1^2) + (-0.1^2) + (-0.4^2) + (-0.7^2) + (0.6^2) + (-0.1^2) + (-0.1^2) + (0.3^2) + (0^2)\)

SSR = 0.04 + 0.09 + 0.64 + 0.64 + 0.09 + 0.16 + 0.01 + 0.01 + 0.16 + 0.49 + 0.36 + 0.01 + 0.01 + 0.09 + 0

SSR = 3.25.

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Answer:

2 5/12

Step-by-step explanation:

(5 + 1/4) - (2 - 5/6)

5 - 2 = 3

(1/4 x 3/3) - (5/6 x 2/2) = 3/12 - 10/12 = -7/12

3 - 7/12 = 2 5/12

The number of vats to be used is 8

Given: Weight of material used per day = 196 pounds

Weight of each vat = 26 pounds

Cycle time for each vat = 2.5 hours

Inefficiency factor assigned by manager = 25%

Time available for each day = 8 hours

To calculate the number of vats to be used, we need to calculate the time required to transport the total material by the available vats.

So, the number of vats required = Total material weight / Weight of each vat

To calculate the total material weight transported in 8 hours, we need to calculate the time required to transport the weight of one vat.

Total time to transport one vat = Cycle time for each vat / Inefficiency factor

Time to transport one vat = 2.5 / 1.25

(25% inefficiency = 1 - 0.25 = 0.75 efficiency factor)

Time to transport one vat = 2 hours

Total number of vats required = Total material weight / Weight of each vat

Total number of vats required = 196 / 26 = 7.54 (approximately)

Therefore, the number of vats to be used is 8 (rounded up to the next whole number).

Answer: 8 vats will be used.

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Answer:

B.) 25 dollars times 0.20

Step-by-step explanation:

0.20 = 20%.

Answer: Cost= 25 +0.2*25

Step-by-step explanation:

Thus, the equations of the required lines are:

\($$y = \frac{7}{3}x - \frac{19}{3}$$$$y = -\frac{3}{7}x + \frac{29}{7}$$\)

Given: Equation of a line:

y = (7/3) x + 2

Point on the line: (2, 5) Let's find the slope of the given line. Slope of the given line is same as slope of the line parallel to it.

Therefore, slope of the new line is:

\($$m = \frac{7}{3}$$.\)

The equation of the line passing through (2,5) with slope

m = 7/3

can be written using the point-slope formula:

\($$y - y_1 = m(x - x_1)$$where (x1, y1)\\ = (2, 5) and m\\ = 7/3.$$y - 5 \\= \frac{7}{3}(x - 2)$$$$y \\= \frac{7}{3}x - \frac{19}{3}$$\)

Now, let's find the equation of the line passing through (2,5) that is perpendicular to the given line. The slope of a line perpendicular to the given line is the negative reciprocal of its slope.

Therefore, the slope of the new line is:

\($$m = -\frac{3}{7}$$.\)

The equation of the line passing through (2,5) with slope

m = -3/7

can be written using the point-slope formula:

\($$y - y_1 = m(x - x_1)$$\\where\\ (x1, y1) \\= (2, 5) and m \\= -3/7.$$y - 5 = -\frac{3}{7}(x - 2)$$$$y \\= -\frac{3}{7}x + \frac{29}{7}$$\)

Thus, the equations of the required lines are:

\($$y = \frac{7}{3}x - \frac{19}{3}$$$$y = -\frac{3}{7}x + \frac{29}{7}$$\)

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Answer:

b

Step-by-step explanation:

Since the parabola opens upwards and the vertex is the minimum point, f(x) is greater than 0 (positive) for all x values except at x = 3, where it is equal to 0.

To determine where the quadratic function f(x) = x^2 - 6x + 9 is equal to 0, we need to find the x-values that satisfy the equation f(x) = 0.

We can solve this quadratic equation by factoring, completing the square, or using the quadratic formula.

Using factoring:

x^2 - 6x + 9 = 0

(x - 3)(x - 3) = 0

(x - 3)^2 = 0

By factoring, we see that the equation is a perfect square trinomial, and the factor (x - 3) is repeated. Therefore, the only solution is x = 3.

So, f(x) = 0 at x = 3.

To determine where f(x) is greater than 0 or less than 0, we can analyze the shape of the quadratic curve. Since the coefficient of x^2 is positive, the parabola opens upwards, and the vertex represents the minimum point.

The vertex of the quadratic function f(x) = x^2 - 6x + 9 can be found using the formula x = -b/2a. In this case, a = 1 and b = -6.

x = -(-6) / 2(1)

x = 6/2

x = 3

The vertex is located at (3, f(3)).

Since the parabola opens upwards and the vertex is the minimum point, f(x) is greater than 0 (positive) for all x values except at x = 3, where it is equal to 0.

Therefore:

- f(x) > 0 for x ≠ 3

- f(x) = 0 at x = 3

Please note that I have assumed that the given quadratic function is f(x) = x^2 - 6x + 9, as the question does not specify the signs of the quadratic terms. If the signs are different, the results may vary.

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To find the critical points at which profit is maximized given the total revenue TR = 4700 - 302 and total cost TC = 320/10,500, we need to compute the marginal revenue and marginal cost, equate MR = MC to find the optimal quantity Q∗, verify if Q∗ is a relative maximum point, and compute the maximum profit level (π) by evaluating π∗ = 9(π(Q∗)).

Marginal Revenue (MR) is the derivative of the total revenue function with respect to quantity (Q). In this case, MR = dTR/dQ. By taking the derivative of TR = 4700 - 302 with respect to Q, we can find the expression for MR.

Marginal Cost (MC) is the derivative of the total cost function with respect to quantity (Q). In this case, MC = dTC/dQ. By taking the derivative of TC = 320/10,500 with respect to Q, we can find the expression for MC.

To find the optimal quantity Q∗, we equate MR and MC by setting MR = MC and solve for Q. This is because profit is maximized when MR equals MC.

Once we have found Q∗, we need to verify if it is a relative maximum point. This can be done by checking the second derivative of the profit function and determining if it is negative at Q∗. If the second derivative is negative, it confirms that Q∗ is a relative maximum point.

Finally, to compute the maximum profit level (π∗), we evaluate π(Q∗) by substituting Q∗ into the profit function. In this case, we can multiply the value of π(Q∗) by 9 to obtain the maximum profit level (π∗).

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Answer:

1,500

Step-by-step explanation:

hope this helped!

Answer:

1500.

Step-by-step explanation:

The hundreds digit is the 5.

A the next digit ( the tens) is 0  ( < 5) it remains as 0 and the 8 becomes 0.

The factor of the expression will be (x + 1) and (x + 1). Then the product of two binomials will be (x + 1) and (x + 1).

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The expression is given below.

⇒ x² + 2x + 1

Factorize the expression, then the factor of the expression will be

⇒ x² + x +  x + 1

⇒ x(x + 1)x + 1(x + 1)

⇒ (x + 1)(x + 1)

⇒ (x + 1)²

The product of two binomials will be (x + 1) and (x + 1).

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Answer:

Bat Araw pa sa Inyo? ay oo nga Pala hshshs

The way that increasing the amount of charge on an object affects the electric force it exerts on another charged object is; The electric force increases because the amount of charge has a direct relationship to the force

The amount of charge on an object due to the effect of the force that is exerted on it can be calculated by using the formula :

F = E × q

Where;

F is the electric force.

E is the energy.

q is the charge.

The electric force between charged particles at rest is known as electrostatic force.

The magnitude of the electric force between point charges is directly proportional to the multiplication of the charges and inversely proportional to the distance between them.

Therefore, we conclude that increasing the amount of charge on an object would increase the electric force because the amount of charge has a direct relationship with the force.

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the formula of the kinet

The general solution to the given differential equation is:

y = 7x³+ C

To solve the given differential equation \(\(\frac{dy}{dx} = 21x^2\)\), we can integrate both sides with respect to their respective variables.

\(\[\int dy = \int 21x^2 dx\]\)

Integrating the left side with respect to y yields y, and integrating the right side with respect to x gives us:

\(\[y = \int 21x^2 dx\]\)

To integrate \(\(x^2\)\), we can use the power rule of integration. For any constant n, the integral of \(\(x^n\)\) with respect to\(\(x\) is \(\frac{x^{n+1}}{n+1}\)\). Applying this rule, we have:

\(\[y = \frac{21}{3}x^3 + C\]\)

where C is the constant of integration. Thus, the general solution to the given differential equation is:

y = 7x³+ C

where C can be any constant.

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Answer:

$254.40

Step-by-step explanation:

Find the total bill by multiplying 212 by 1.2, which will calculate the cost included with the 20% tip:

212(1.2)

= 254.4

So, the total bill will be $254.40

Answer:

\(\$254.40\)

Step-by-step explanation:

Since 20% as a decimal is 0.2, the total bill including tax is 1.2 times larger than the original bill.

Original bill of $212.00:

Final bill: \(212.00\cdot 1.2=\boxed{\$254.40}\)

Answer:

A- 1/2K-1

Step-by-step explanation:

Answer:

1/2K-1

Step-by-step explanation:

Step-by-step explanation:

x= 10 sin 60° = 10×½√3 = 5√3

y= 10 cos 60° = 10×½ = 5

Answer:

I think it might be 13 or 14 I'm not completely sure though.

Step-by-step explanation: