Given f(x)=ln x, evaluate
a) f (e⁴)
b) f (e ㏑ 5)
c) f (e³ ㏑ 5)

191 of adult plates and 81 child plates were sold.

Two or more expressions with an Equal sign is called as Equation.

Given,

Adult plate costs A= $8

Child plate costs C=$5

Total plates sold is 272

A+C=272..(1)

8A+5C=1,933..(2)

C=272-A

Substitute in equation 2

8A+5(272-A)=1933

8A+1360-5A=1933

1360+3A=1933

Subtract 1360 on both sides

3A=1933-1360

3A=573

Divide both sides by 3

A=191

Now substitute A value in 1

191+C=272

Subtract 191 on both sides

C=272-191

C=81

Hence, 191 of adult plates and 81 child plates were sold.

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The value of the ratio of the perimeters of the rectangles PQTU and PRSU is 30:36, that is 5:6.

The perimeter of a form is the space surrounding its edge. Find the perimeter of various forms by summing the lengths of their sides.

Equation for perimeter of a rectangle (P) =2 (l + w), where l is the length and w is the width.

In the question, length of rectangle PQTU= 11cm

Width of rectangle PQTU= 4 cm

Perimeter of rectangle PQTU= 2( 11+4)

                                                = 2 x 15

                                                = 30 cm

The length of the rectangle PRSU= 11cm

The width of the rectangle PRSU= PQ + QR

                                                      = 4+3 = 7

The perimeter of the rectangle PRSU= 2(11+7)

                                                              = 36 cm

Therefore, perimeter of PQTU: perimeter of PRSU = 30:36

Dividing by 6 on both= 30/6 :36/6 = 5:6

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The values of the objective function obtained for the given set of equation is 7.

For the stated question-

Objective function z = x1+2x2

Constraints

Subtract equation 2 from 1.

x1 = 8 - 5

x1 = 3

Put value if x1 in eq 2

x1 + x2 = 5  

x2 = 5 - 3

x2 = 2

Put the values of x1 and x2 in Objective function

z = x1 + 2x2

z = 3 + 2x2

z = 7

Thus, the values of the objective function obtained for the given set of equation is 7.

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Answer:17

Step-by-step explanation:

Substitute: 25-4x2

Calculate the product or quotient: 25-8

Calculate the sum or difference: 17

Answer: 17

The required sum of the series sum from n equals 1 to infinity is -9/5

geometric series, in science, a  infinite series of the structure a + ar + ar^2 + ar^3+⋯, where r is known as the common ratio. A basic model is the mathematical series for a = 1 and r = 1/2, or 1 + 1/2 + 1/4 + 1/8 +⋯, which joins to an amount of 2 (or 1 on the off chance that the initial term is barred).

We have,

GP; -3(3/8), -3(3/8)^2,................ -3(3/8)^∞

Common ratio(r) = 3/8, a = -9/8

S(1 to ∞) = a/(1 - r)

S(1 to ∞) = -9/8(1 - 3/8)

S(1 to ∞) = -9/8/5/8

S(1 to ∞) = -9/5

Thus, sum of geometric series is -9/5.

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The equation of the line in slope-intercept form that passes through (3, 4) and (4, 9) is: y = 5x - 11.

The equation of a line can be written in point-slope form as y - b = m(x - a), if we know the slope (m) and a point (a, b) on the line. It can be rewritten to the slope-intercept form as y = mx + b.

Given the points on a line:

(3, 4) and (4, 9)

Slope of the line (m) = change in y / change in x = (9 - 4)/(4 - 3)

Slope of the line (m) = 5/1

m = 5

To write the equation of the line, substitute m = 5 and (a, b) = (3, 4) into y - b = m(x - a):

y - 4 = 5(x - 3)

Rewrite in slope-intercept form:

y - 4 = 5x - 15

y = 5x - 15 + 4

y = 5x - 11 [equation of the line]

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Answer:

Step-by-step explanation:

[tex]\frac{3}{n}[/tex] - 10.

The quotient of 3 and a number translates to [tex]\frac{3}{n}[/tex], then, all you have to do is subtract 10 from that value, giving the expression above.

Set up your equation

4q + q = 315                      Add                                  (q = amount of quarters)

5q = 315                            Divide

q = 63                              

Therefore he has 63 quarters.

To find the amount of nickels, multiply 4 and 63

4 x 63 = 252

Therefore he has 63 quarters and 252 nickels.

I hope this helps! :)

By the definition of the vertex form of the quadratic equation x - 1 = 6 · (y + 6)² has its vertex at (h, k) = (- 6, 1) and opens to the right. (Correct choices: A, B)

In this problem we find the definition of a quadratic equation in vertex form, whose axis of symmetry is parallel to the x-axis. This form of quadratic equation is described below:

x - h = C · (y - k)²

Where:

Please notice that the parabola opens to the right (+ x direction) when the vertex constant is greater than 0. By direct inspection, we have the following conclusions:

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Answer: y=-x

Step-by-step explanation:

Choose 2 coordinates: (-2,2) and (2,-2)

Let us find the slope m:

[tex]\displaystyle\\m=\frac{y_2-y_1}{x_2-x_1} \\\\x_1=-2\ \ \ \ \ x_2=2\ \ \ \ \ y_1=2\ \ \ \ \ y_2=-2\\\\m=\frac{-2-2}{2-(-2)} \\\\m=\frac{-4}{2+2} \\\\m=\frac{-4}{4} \\\\m=-1\\[/tex]

Hence,

y=-x+b

To find the coefficient b, choose any coordinate belonging to the given line, for example (-2,2):

2=-(-2)+b

2=2+b

0=b

Hence, b=0

Thus, y=-x

The solution to the given linear inequality, r - 6 > -11, is r > -5

From the question, we are to determine the solution of the given inequality

The given inequality is

r - 6 > -11

To determine the solution of the inequality, we will solve the inequality for the unknown variable.

In the inequality, the unknown variable is r.

Solving the inequality for r

r - 6 > -11

Add 6 to both sides

r - 6 + 6 > -11 + 6

r > -5

Hence, the solution is r > -5

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Answer: 27/70

the area of the shaded rectangle

Step-by-step explanation:

9/10 and 3/7 of the rectangle are shaded on top and bttom. So you multiple this together and you will get 27/70

9/10 x 3/7 = 27/70

Answer: 0.75 inches per hour

Step-by-step explanation:

9/12=0.75
0.75 x 12 = 9
0.75 inches per hour

Answer:  4.5 hours.

Step-by-step explanation:

Use a proportion.

3 3/8 = 3.375

9 inch is to 12 hours as 3.75 inches is to x hours.

9/12 = 3.375/x

3/4 = 3.375/x

3x = 4 * 3.375

x = 4 * 1.125

x = 4.5

Answer: 4.5 hours

Answer:

Step-by-step explanation:

To fill the table using the expression

you have to replace each value with x and solve the expression

Answer:

Step-by-step explanation:

Expression : 9x - 5

To fill the table using the expression, you have to replace each value with x and solve the expression.

The answer is attached to the picture.

The acceleration of the car is 6m/s²

Acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities. Acceleration is measured in meter per second squared

It can also be defined as the ratio of the change in velocity to the time

Therefore acceleration is given as (v-u)/t

where v is the final velocity and u is the initial velocity, t is the time

therefore a= 30-0/5

a= 30/5

a= 6m/s²

therefore the acceleration of the car is 6m/s²

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Answer:

$85

Step-by-step explanation:

x=0     p= 85 => (0,85) {y-intercept}

p=0     x= -3400 => (-3400,0) {x-intercept}

y-intercept means Isaiah sells $0, then the company will pay him $85.

The number of solution of the equation x + 2 = 3y will be infinite for the infinite value of 'x'. The solution is (1, 1).

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given below.

x + 2 = 3y

There is only one equation, so we have to assume 'x'.

If x = 1, then the value of the variable 'y' is given as,

3y = 1 + 2

3y = 3

y = 3 / 3

y = 1

Similarly, the number of solution of the equation x + 2 = 3y will be infinite for the infinite value of 'x'.

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Answer:

B

Step-by-step explanation:

x² + 3x + 3 = 4 ( subtract 3 from both sides )

x² + 3x = 1

to complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2( [tex]\frac{3}{2}[/tex] )x + ([tex]\frac{3}{2}[/tex] )² = 1 + ( [tex]\frac{3}{2}[/tex] )²

(x + [tex]\frac{3}{2}[/tex] )² + [tex]\frac{9}{4}[/tex] = 1 + [tex]\frac{9}{4}[/tex]

that is [tex]\frac{9}{4}[/tex] is added to both sides

Answer:

None of the values.

Step-by-step explanation:

Simplify the given equation.

First, simplify by combining like terms. Like terms are terms that share the same amount of the same variables:

4 = m + 5 - 2m

4 = (m - 2m) + 5

4 = -m + 5

Next, isolate the variable, m. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

-

First, subtract 5 from both sides of the equation:

4 = -m + 5

4 (-5) = -m + 5 (-5)

4 - 5 = -m

-1 = -m

Next, isolate the variable m. Remove the negative sign by dividing -1 from both sides of the equation:

(-1)/-1 = (-m)/-1

m = -1/-1 = 1

None of the values will make the equation true, as 1 is not a given value.

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https://brainly.com/question/2466865 - Defining variables.

a) The net for the sale is: $4,500

b) The capital gain is $2,200

We know that you had 100 shares, now the value of each of these is $45.00, then the amount that you make if you sell the 100 shares is:

S = 100*$45.00 = $4,500

The capital gain is the difference between the amount we found above and the amount you paid for the shares.

The price of the shares was $23.00, then the amount you paid is:

C = $23.00*100 = $2,300

Then the capital gain is:

g = $4,500 - $2,300 = $2,200

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Answer:

59

Step-by-step explanation:

31+4 × [11-(1+3)]

31+4*[11-4]

31+4*(7)

31+28

59

The easy Answer is 59. When doing these types of questions remember:

Parentheses

Exponents

Multiplication

Divionsion

Add

Subtract

Answer:

D'(-6, -9)

Step-by-step explanation:

When a point is reflected over the x-axis, the x-coordinate remains the same. The reflected point is the same distance from the x-axis as the original point, but it's on the other side of the x-axis, so the y-coordinate changes sign.

In general, point (x, y) reflected over the x-axis becomes point (x, -y).

Here, point D(-6, 9) becomes point D'(-6, -9).

Answer:

y = 4x - 22

Step-by-step explanation:

y = 4x + b

-2 = 4(5) + b

-2 = 20 + b

b = -22

y = 4x - 22

The converse, inverse, contrapositive and biconditional for the given sentences has been written down for a better understanding.

Two assertions that are logically opposed to one another are referred to be inverse statements. An inverted statement would be "It is raining" and "It is not raining."Biconditional statements can be both true and untrue depending on the veracity or falsity of each of its component elements. For instance, "If it is raining, then the ground is wet" is a biconditional statement because if it is raining, the ground will be wet, and if it is not raining, the ground won't be wet. In other words, the truth or falsehood of the first part (it is raining) determines the truth or falsehood of the second part.

How to solve?

Converse: If studying hurts your grade, then studying also helps your grade.

Inverse: If studying does not help your grade, then studying does not hurt your grade.

Contrapositive: If studying does not hurt your grade, then studying does not help your grade.

Bi-conditional: Studying helps your grade if and only if studying also hurts your grade.

The conditional is false.

The converse is false.

The bi-conditional is false.

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Answer: $279.40

Step-by-step explanation:

To find how much he is paying in property taxes, you have to multiply the maintenance fee by the percentage you are given, so

1,397×20%=279.40

Answer:

$3,352.80

Step-by-step explanation:

This is the correct answer

Answer: [tex]C. \frac{125}{7}[/tex]

Step-by-step explanation:

1. Find the sum of the infinite geometric sequence:

[tex]S = \frac{125}{7}[/tex]

2. Find the correct option:

C

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Required percentage value = a

total value = b

Percentage = a/b x 100

The percentage error of the measurement is 47.8%.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

The actual length of the line = 2.3 inches

The measured length of the line = 2.2 inches

The error length of the line.

= 2.3 - 2.2

= 1.1 inches

The percentage error of the measurement.

= 1.1/2.3 x 100

= 47.8%

Thus,

The percentage error of the measurement is 47.8%.

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