The area of the base of a rectangular prism is 4 3/4 and the height is 2 1/3 Determine the volume of the rectangular prism

Therefore, the final answer with two significant digits is:Combined length = 110 cm

The combined length of the two rods can be found by adding the length of the first rod and the length of the second rod. The length of the first rod is given as 31.4 cm and the length of the second rod is given as 82.25 cm. Therefore, the combined length of the two rods can be found as follows:Combined length = length of first rod + length of second rod= 31.4 cm + 82.25 cm= 113.65 cm

However, we need to report our answer with the correct number of significant digits. The least number of significant digits in the given values is two, which is the number of significant digits in 31.4 cm. Therefore, we must round our answer to two significant digits. Since the digit in the hundredth place is 5, which is greater than or equal to 5, we must round up the digit in the tenth place.

To know more about significant digits:

https://brainly.com/question/28993414

#SPJ11

The graph that represents the ordered pairs of the first five terms of the patterns from the table is the line graph.

The graph that represents the ordered pairs of the first five terms of the patterns from the table is the **line graph**.

The x-values in the table are increasing by 3 each time, while the y-values are increasing by 6 each time. This means that the ordered pairs are forming a straight line. The line graph is the only graph that shows a straight line.

The other graphs are either curves or not straight lines. The **scatter plot** shows a cloud of points that are not evenly distributed. The **bar graph** shows a series of vertical bars that are not evenly spaced. The **histogram** shows a series of horizontal bars that are not evenly spaced.

Here is a table of the first five terms of the patterns from the table, along with the corresponding ordered pairs:

X | Y | Ordered Pair

-- | -- | --

0 | 0 | (0, 0)

3 | 6 | (3, 6)

6 | 12 | (6, 12)

9 | 18 | (9, 18)

12 | 24 | (12, 24)

As you can see, the ordered pairs form a straight line.

For such more questions on line graph

https://brainly.com/question/19040584

#SPJ8

The slope of the equation y = 7x^2 is 14x, not one of the given options.

The slope of a quadratic equation can be determined by finding its derivative with respect to x. In this case, we have y = 7x^2. To find the derivative, we apply the power rule of differentiation. The power rule states that if we have a term of the form ax^n, the derivative is given by nx^(n-1).

Applying the power rule to y = 7x^2, we get dy/dx = 2 * 7x^(2-1) = 14x. The slope of the equation is represented by the derivative, which in this case is 14x. It is important to note that the slope of a quadratic equation varies depending on the value of x. Therefore, the slope is not a constant value like the options given (-7, -5, 2, or 7). Instead, the slope is expressed as a function of x, which is 14x in this case.

Learn more about slope here:

https://brainly.com/question/3605446

#SPJ11

The presents are divided as follows:

Let us assume that there are x, y and z purses in the yellow, red and green sacks respectively.

Then, we have the following cases:

Case I: Yellow and Red sacks

There are 20 presents, therefore,x+y must be a multiple of 5.

However, it is not possible to satisfy this constraint if y = 0 or y = 5.

Since x+y = 20, the possibilities are:

xy155

10x10

15x+20-x25

x=20

Therefore, there are 10 yellow and 10 red sacks.

Case II: Yellow and Green sacksThere are 35 presents, therefore,x+z must be a multiple of 5.

However, it is not possible to satisfy this constraint if z = 0 or z = 5.

Since x+z = 35, the possibilities are:

xz3055

25z=35-x

Therefore, there are 10 yellow and 25 green sacks.

Case III: Red and Green sacksThere are 25 presents, therefore,y+z must be a multiple of 5.

However, it is not possible to satisfy this constraint if z = 0 or z = 5.

Since y+z = 25, the possibilities are:

yz201515

z=25-y

Therefore, there are 15 red and 10 green sacks.

The presents are divided as follows:Yellow: 10 sacks with x purses each Red: 10 sacks with y purses each Green: 25 sacks with z purses each.

To know more about constraint, visit:

https://brainly.com/question/32636996

#SPJ11

The cost of a call of m minutes duration, given the cost of the calls would be c = 0. 05 + 0. 99m

If you have $ 12 to spend, the time you can spend is 10.15 minutes.

The cost per minute would be :

= Difference between 5 and 10 minute call / Number of minutes

= ( 10. 86 - 5. 91 ) / 5

= $ 0.99

The cost per minute is therefore:

= 0. 99 x number of minutes

= 0. 99m

The initial cost is :

=  5 - 0. 99 x 5

= $ 0. 05

The number of minutes with $12 is:

= ( 12 - 0.05 ) / 0. 99

= 12. 1 minutes

Find out more on cost of call at https://brainly.com/question/12637165

#SPJ4

The value of the given expression is approximately 71.31.

[tex]$$75 - 12(20 ÷ 2.5) ÷ 26$$[/tex]

The Order of Operations states that the sequence of steps in which we carry out the operations of a given problem.

So, we follow the Order of Operations to solve this expression.

Firstly, we will evaluate the parentheses:

[tex]$$20 ÷ 2.5 = 8$$[/tex]

Now, the given expression becomes:

[tex]$$75 - 12 × 8 ÷ 26$$[/tex]

Then, we will evaluate multiplication and division in order from left to right.

12 × 8 = 96

So, the given expression becomes:

[tex]$$75 - 96 ÷ 26$$[/tex]

Evaluating division, we get:

[tex]$$75 - 3.6923$$[/tex]

Now, we will add and subtract from left to right.

[tex]75 − 3.6923 ≈ 71.31[/tex]

Therefore, the value of the given expression is approximately 71.31.

So, the required  is approximately 71.31.

To know more about expression visit:

https://brainly.com/question/28170201

#SPJ11

The System Of Inequalities are : $3s + $12p ≤ $120

Let's represent the number of bags of soil as 's' and the number of plants as 'p'.

The given information can be translated into the following system of inequalities:

1. Cost inequality: $3s + $12p ≤ $120

  (The total cost of soil bags and plants should be less than or equal to $120.)

2. Plant requirement: p ≥ 5

  (Tre's mom wants at least 5 plants in her garden.)

Now, let's find two possible solutions that satisfy the given conditions:

Solution 1:

- Let's consider Tre purchasing 8 bags of soil (s = 8).

- Then, he can buy 5 plants (p = 5).

  (8 bags of soil cost $24, and 5 plants cost $60, which sums up to $84.)

Solution 2:

- Let's consider Tre purchasing 10 bags of soil (s = 10).

- Then, he can buy 6 plants (p = 6).

  (10 bags of soil cost $30, and 6 plants cost $72, which sums up to $102.)

These two solutions satisfy the conditions of at least 5 plants and a total cost of $120 or less.

Learn more about Inequalities at https://brainly.com/question/24372553

#SPJ4

To make the theoretical and experimental probabilities closer, Jonas can increase the sample size by conducting more rolls of the 10-sided die. This will provide a more accurate representation of the theoretical probability.

By increasing the sample size, Jonas can gather more data points, which can help to reduce the impact of random variations and provide a more accurate representation of the theoretical probability. As the number of rolls increases, the experimental probability is more likely to approach the theoretical probability.

In this case, Jonas can conduct more rolls of the 10-sided die beyond the initial 20 rolls. The larger the number of rolls, the better the experimental probability will reflect the theoretical probability of rolling a 3. By increasing the sample size, Jonas can minimize the impact of outliers or chance occurrences that may have influenced the results in the initial 20 rolls, resulting in a closer alignment between the theoretical and experimental probabilities.

Learn more about experimental probability here:

https://brainly.com/question/3733849

#SPJ11

The plastic coating would be needed to coat the surface of the chain is 345.4 cm². Hence option 3 is true.

A cylinder's surface area is the overall area or region that the shape's surface covers. A cylinder's total surface area comprises both the area of the curved surface and the area of the two flat surfaces since there are two flat surfaces and one curved surface.

The formula for a particular cylinder's total surface area is as follows:

TSA = 2πr (h + r)

Given that;

One link in a chain was made from a cylinder that has a radius of 2.5 cm and a height of 22 cm.

Hence, The plastic coating would be needed to coat the surface of the chain is,

2 × 3.14 × 2.5 × 22

= 345.4 cm²

So, The plastic coating would be needed to coat the surface of the chain is 345.4 cm². Hence option 3 is true.

To learn more about surface area refer to:

brainly.com/question/20771646

#SPJ12

The cost of painting all the cones is ₹ 384.34 (approx.)

Here, we have,

Given: The base diameter of the cone is 40 cm and its height is 1m.

Since the outer side of each cone is to be painted, the area to be painted will be equal to the curved surface area of the cone.

The curved surface area of a right circular cone with base radius(r) and slant height(l) is πrl

Slant height, l = √(r² + h²) where h is the height of the cone.

Diameter, d = 40cm = 40/100 m = 0.4m

Radius, r = 0.4/2m = 0.2m

Height, h = 1 m

Slant height, l = √(0.2)² + (1)²

= √0.04m² + 1m²

= √1.04 = 1.02m (given)

The curved surface area = πrl

= 3.14 × 0.2m × 1.02m

= 0.64056 m2

Curved surface area of 50 cones = 50 × 0.64056 m2 = 32.028 m2

Cost of painting of 50 cones at ₹ 12 per m2 = 32.028 × 12

= ₹ 384.34 (approx.)

Thus, the cost of painting all the cones is ₹ 384.34 (approx.)

To learn more on Area click:

brainly.com/question/20693059

#SPJ4

complete question:

A bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled cardboard. Each cone has a base diameter of 40 cm and height 1 m. If the outer side of each of the cones is to be painted and the cost of painting is ₹ 12 per m2, what will be the cost of painting all these cones? (Use π = 3.14 and take √1.04 = 1.02)

Therefore, the measure of the angle BDK is 62.5°.

Given: Steve determines that sides DK and BC are congruent. Therefore, DK ≅ BC.

He also measures the angle DBK to be 55°. Therefore, ∠DBK = 55°.

To find the measure of the angle BDK, we can use the fact that the sum of the angles in a triangle is 180°.

∠BDK = 180° - ∠DBK - ∠BKD

Since DK ≅ BC, ∠BDK = ∠BCD.

∴ ∠BDK = ∠BCD = (125° - ∠BCD)

Simplifying the equation, we get:

2∠BCD = 125°

∠BCD = 62.5°

Therefore, the measure of the angle BDK is 62.5°.

Hence, option D is correct.

To know more about words,equation Visit :

https://brainly.com/question/29657983

#SPJ11

Yes, In order to determine the measure of EC, we need a proportion that relates the corresponding sides of similar triangles. we can use the proportion 9/10 = 8.75/EC to determine the measure of EC

The proportion is,

To solve for EC, we can cross-multiply and then solve for EC.

9/10 = 8.75/EC

9×EC=10×8.75

Simplifying we get,

EC = 9.72

Therefore, the measure of EC is approximately 9.72 units.

Please provide the correct proportion relating the corresponding sides of

ΔABC and ΔDEC, and I'll be happy to help you solve for EC.

Hence, the correct answer is:Yes, EC ≈ 9.7222.

To know more about proportion visit:

https://brainly.com/question/30657439

#SLJ11

It is not possible to determine the area of the shape from the given information as the measurements of the sides and angles are not provided.

However, we can identify the shape as a trapezoid because it has one pair of parallel sides. A trapezoid is a quadrilateral with one pair of parallel sides. To calculate the area of a trapezoid, we can use the formula:Area of trapezoid = 1/2 × (sum of parallel sides) × (distance between parallel sides)If we have the measurements of the parallel sides and the distance between them, we can substitute them into the formula to find the area of the trapezoid.

If the measurements are not provided, we cannot find the area of the trapezoid. Thus, it is not possible to determine the area of the shape from the given information, which only tells us that it has one pair of parallel sides.

To know more about parallel visit:

brainly.com/question/22746827

#SPJ11

The given figure has only one pair of parallel sides. The opposite sides of the trapezium are not parallel. The formula to calculate the area of the trapezium is given as:

A = (a+b)/2 * h, where 'a' and 'b' are the parallel sides of the trapezium and 'h' is the distance between these parallel sides.

We can clearly see that the parallel sides 'a' and 'b' are 6 cm and 10 cm, respectively, and the height 'h' of the trapezium is 4 cm.

Therefore, substituting these values in the above formula, we have:

A = (6 + 10)/2 * 4A = 16/2 * 4A = 8 * 4A

= 32The area of the trapezium is 32 sq cm.

Thus, the area of the given shape is 32 square centimeters.

To know more about trapezium visit:

https://brainly.com/question/22607187

#SPJ11

Jordan's pet grooming business has a monthly cost function of C - $12p+ $2100. The monthly cost function for Jordan's pet-grooming company is C - $12p+ $2100.

His Revenue is given by the function R - $62p, where C is the total costper month, R is the total revenue he receives each month and x is the number of pets he grooms in a month. We need to find out how many pets must he groom each month to break even.Let's set revenue equal to costs, and solve for p.R = C62p = 12p + 2100p = (12p + 2100) / 62p = 0.1935p ≈ 19.35 petsJordan must groom approximately 19.35 pets each month to break even. The nearest whole number is 19.

To know more about  revenue, visit ;

https://brainly.com/question/16232387

#SPJ11

Nicholas scooped a few gumballs into his bag and found that it weighed 0.76 pounds.

Nicholas's bag of gumballs weighs 0.76 pounds. This weight includes the combined mass of the gumballs and the bag itself. The weight measurement indicates the force exerted by the bag due to the gravitational pull of the Earth. To determine the weight of just the gumballs, Nicholas would need to subtract the weight of the bag from the total weight.

To find the weight of the bag, Nicholas could use a scale or balance to measure an empty bag of the same type. Once he knows the weight of the empty bag, he can subtract that weight from the total weight of the bag with the gumballs. The result will give him the weight of the gumballs alone.

It's important to note that the weight of the gumballs may vary depending on their size, density, and the material of the bag. Different types of gumballs may have different weights. To get an accurate measurement, Nicholas should use a precise weighing instrument and account for any external factors that could affect the weight, such as moisture or contaminants.

Learn more about weighing instrument:

https://brainly.com/question/32535722

#SPJ11

The answer is C. 400 times more likely. The more likely is a manual filer to make an error than an electronic filer if 20% of all manually filed returns contain %-errors, and 0.05% of all electronically filed returns contain errors is 400 times using percentages.

It's important to note that percentages are ratios of numbers in relation to 100.

So, we must first convert 20% and 0.05% to decimals.

20% = 20/100

       = 0.200.0

5% = 0.05/100

     = 0.0005

Therefore, we know that if 20% of all manually filed returns contain errors, then 0.2 of every 1 return contains errors. Similarly, if 0.05% of all electronically filed returns contain errors, then 0.0005 of every 1 return contains errors.

To determine how much more likely a manual filer is to make an error than an electronic filer, we need to divide the probability of a manual filer making an error by the probability of an electronic filer making an error:(Probability of manual filer making an error) / (Probability of electronic filer making an error)= 0.2/0.0005= 400

Therefore, a manual filer is 400 times more likely to make an error than an electronic filer.

To know more about %-errors, visit:

brainly.com/question/30760250

#SPJ11

Nadia has £5 to buy pencils and rulers. She says,"I will buy 15 pencils. Then I will buy as many rulers as possible. With my change, I will buy more pencils.

"Let the price of each pencil be p and the price of each ruler be r. Presenting the above scenario into the equation,15p + (x × r) = 5Here, x is the number of rulers to be bought. To minimize the number of pencils Nadia will buy with the change, we have to calculate the maximum number of rulers she can buy with the given £5.Let's assume Nadia buys a maximum of y rulers with all of her money, thus the number of pencils she will be left to buy will be,15p + (y × r) ≤ 5Therefore, Nadia can purchase 15 pencils and 2 rulers with £5 as shown below,15p + (2 × r) = 5Nadia can then buy more pencils with the remaining money, which is,£5 − [(15 × p) + (2 × r)] = Remaining money£5 − [(15 × 0.20) + (2 × 0.35)] = 0.40Hence, Nadia can buy 2 rulers and 15 pencils. She can buy only 2 rulers as many rulers she can buy with £5 is only 2.

Learn more about rulers as possible here:

https://brainly.com/question/4894198

#SPJ11

The logarithm base 12 can be expressed as log12 or in exponential form as 12^x = y, where x is the exponent and y is the result.

The logarithm function is the inverse of exponentiation. It represents the exponent to which a given base (in this case, 12) must be raised to obtain a certain value. There are four different ways to express log12:

Logarithmic form: log12(y) - This notation indicates that the logarithm base 12 is being applied to a value y.

Exponential form: 12^x = y - In this form, the base 12 is raised to an exponent x to produce a value y.

Fractional exponent form: y^(1/12) - The fractional exponent represents the root of y with a base of 12. It is equivalent to log12(y).

Common logarithm form: log(y) / log(12) - If the logarithm base 12 function is not directly available, we can use the common logarithm (base 10) or any other logarithmic base and apply the change of base formula. The result is the logarithm of y divided by the logarithm of 12.

Learn more about logarithm function here: brainly.com/question/29287497

#SPJ11

Mrs. Hynes gave 8 students 3 pieces of candy each and an additional 2 pieces to one student for good behavior. So Mrs. Hynes gave away 26 pieces of candy.

Mrs. Hynes gave 3 pieces of candy to each of the 8 students, resulting in 3 x 8 = 24 pieces of candy distributed to the class.

In addition, one student received an extra 2 pieces of candy for good behavior. Therefore, we need to add 2 to the total candy count.

Adding the candy pieces given to the class (24) and the extra candy pieces (2), we find that Mrs. Hynes gave away a total of 24 + 2 = 26 pieces of candy.

Thus, Mrs. Hynes gave away 26 pieces of candy in total when distributing 3 pieces to each of her 8 students and rewarding 2 extra pieces to one student for good behavior.

Learn more about Distribution click here :brainly.com/question/29375938

#SPJ1

The quadrilateral formed by the given vertices is a parallelogram based on the congruence of sides and angles.To determine the type of quadrilateral formed by the vertices W(-1,4), X(3,5), Y(4,1), and Z(0,0).

we can examine the properties and characteristics of the quadrilateral.

To identify the type of quadrilateral, we can consider its sides and angles.

1. Sides: We can calculate the lengths of the sides using the distance formula.

- Side WX = √[(3 - (-1))^2 + (5 - 4)^2] = √(16 + 1) = √17

- Side XY = √[(4 - 3)^2 + (1 - 5)^2] = √(1 + 16) = √17

- Side YZ = √[(0 - 4)^2 + (0 - 1)^2] = √(16 + 1) = √17

- Side ZW = √[(-1 - 0)^2 + (4 - 0)^2] = √(1 + 16) = √17

2. Angles: We can calculate the measures of the angles using the slopes of the sides.

- Angle WXY = arctan((5 - 4)/(3 - (-1))) ≈ 45.96°

- Angle XYZ = arctan((1 - 5)/(4 - 3)) ≈ -63.43° (Note: negative due to slope)

- Angle YZW = arctan((0 - 4)/(0 - (-1))) ≈ -75.96° (Note: negative due to slope)

- Angle ZWX = arctan((4 - 0)/(-1 - 0)) ≈ -90°

Based on the information above, we can conclude that the quadrilateral WXYZ is a parallelogram. This is because opposite sides are congruent (WX ≈ YZ and XY ≈ ZW), and opposite angles are congruent (WXY ≈ XYZ and YZW ≈ ZWX).

Therefore, the quadrilateral formed by the given vertices is a parallelogram based on the congruence of sides and angles.

To learn more about quadrilateral click here:

/brainly.com/question/31866616

#SPJ11

The solution to the linear system of equations in terms of a, b, and c is given by the values of x and y obtained from the determinants.

To solve the linear system of equations using determinants, we can use Cramer's Rule, which relies on the concept of determinants. The determinants involved in Cramer's Rule are the coefficient determinant (D), the x-determinant (Dx), and the y-determinant (Dy).

The general form of the linear system of equations is:

a1x + b1y = c1

a2x + b2y = c2

To find the solution using determinants, we first calculate the coefficient determinant (D):

D = | a1 b1 |

| a2 b2 |

The coefficient determinant D represents the determinant of the matrix formed by the coefficients of x and y.

Next, we calculate the x-determinant (Dx):

Dx = | c1 b1 |

| c2 b2 |

The x-determinant Dx is obtained by replacing the x-coefficients in the coefficient determinant D with the constants c1 and c2.

Similarly, we calculate the y-determinant (Dy):

Dy = | a1 c1 |

| a2 c2 |

The y-determinant Dy is obtained by replacing the y-coefficients in the coefficient determinant D with the constants c1 and c2.

Now, we can find the values of x and y using the determinants:

x = Dx / D

y = Dy / D

It's important to note that this method using determinants applies specifically to linear systems with two variables. For larger systems, the method becomes more complex and involves calculating determinants for higher-order matrices.

In summary, to find the solution using determinants, we calculate the coefficient determinant (D), the x-determinant (Dx), and the y-determinant (Dy) based on the given linear system of equations. Then, we find the values of x and y using the determinants. The solution is expressed in terms of a, b, and c.

Learn more about linear system at: brainly.com/question/26544018

#SPJ11

1. At atmospheric pressure, a sample of Cl2 gas has a volume of 3.45 L at 51.0ºC. What volume, in liters, will the Cl2 gas occupy if the temperature is decreased to -55.0ºC.

The gas laws state that the volume of a gas is directly proportional to its temperature, provided that the pressure and quantity of gas are constant. The equation for this is as follows:V1 / T1 = V2 / T2V1 = initial volume = 3.45 LT1 = initial temperature = 51.0ºCV2 = final volumeT2 = final temperature = -55.0ºCUsing the formula above and substituting the given values:V2 = (V1 x T2) / T1= (3.45 L x -55.0ºC) / 51.0ºC= -3.71 LThe volume of the Cl2 gas will occupy -3.71 L if the temperature is decreased to -55.0ºC.2. At constant temperature, a sample of 3.75 L of N2 at 775 mmHg pressure is compressed until the volume decreases to 3.15 L.

Follows:P1 x V1 = P2 x V2P1 = initial pressure = 775 mmHgV1 = initial volume = 3.75 LP2 = final pressureV2 = final volume = 3.15 LUsing the formula above and substituting the given values:P2 = (P1 x V1) / V2= (775 mmHg x 3.75 L) / 3.15 L= 922 mmHgThe new pressure of N2 is 922 mmHg, which can be converted to atmospheres using the conversion factor: 1 atm = 760 mmHgP2 = 922 mmHg x (1 atm / 760 mmHg) = 1.21 , the new pressure of N2 is 1.21 atm.

To know more about temperature  visit:

https://brainly.com/question/7510619

#SPJ11

The approximate radius of the bike wheel is 11.0 inches.

If a bike wheel covers a total of 69.08 inches after one complete rotation, we can use the formula for the circumference of a circle to find the approximate radius of the bike wheel.

Circumference = 2piradius

where pi is approximately 3.14.

We are given that the circumference is 69.08 inches, so we can plug in these values and solve for the radius:

69.08 = 23.14radius

Dividing both sides by 2*pi, we get:

radius = 69.08 / (2*3.14) ≈ 11.0 inches

Therefore, the approximate radius of the bike wheel is 11.0 inches.

learn more about radius here

https://brainly.com/question/12923242

#SPJ11

The weight in Newtons that the scale reads when the elevator is in different scenarios can be calculated using the formula W = mg, where W = weight, m=  mass, and g = the acceleration due to gravity.

a. When the elevator is at rest, there is no acceleration, so the weight will be equal to the gravitational force acting on the person. The weight can be calculated as W = mg, where m is the mass of the person (85 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2). Thus, the weight is W = 85 kg * 9.8 m/s^2.

b. the weight will remain the same as the gravitational force, which is calculated using the formula W = mg.  c. The acceleration is still zero, and the weight will be the same as the gravitational force, calculated using the formula W = mg.

d. We need to consider the net force acting on the person. The net force will be the sum of the gravitational force and the force due to the acceleration. The weight can be calculated as W = mg + ma, where m is the mass of the person (85 kg), g is the acceleration due to gravity (approximately 9.8 m/s^2), and a is the upward acceleration (3 m/s^2).

e. We calculate the weight similarly to case d. The weight is W = mg + ma, where m is the mass of the person (85 kg), g is the acceleration due to gravity (approximately 9.8 m/s^2), and a is the downward acceleration (-4 m/s^2) since it acts in the opposite direction.

Learn more about Newtons here: https://brainly.com/question/4128948

#SPJ11

In the function f(x) = 1/x, when x is close to zero, the value of f(x) approaches positive or negative infinity. As x approaches zero from the positive side (x → 0+).

The function f(x) = 1/x becomes increasingly large and approaches positive infinity. This is because dividing a positive number by a very small positive number yields a very large positive result.

On the other hand, as x approaches zero from the negative side (x → 0-), the function f(x) = 1/x also becomes increasingly large but in the negative direction, approaching negative infinity. Dividing a negative number by a very small negative number yields a very large negative result.

However, it is important to note that the function f(x) = 1/x is undefined at x = 0 since division by zero is undefined in mathematics. Therefore, we say that the function has a vertical asymptote at x = 0, meaning that the function gets arbitrarily close to positive or negative infinity as x approaches zero, but it never actually reaches zero. In conclusion, when x is close to zero in the function f(x) = 1/x, the value of f(x) could be positive or negative infinity depending on whether x approaches zero from the positive or negative side, respectively.

Learn more about negative infinity here:- brainly.com/question/24224719

#SPJ11

The distance that Benjamin travels in 100 seconds is 1400 meters.

Given that :

Benjamin is riding a unicycle.

Circumference of the tire = 2.8 meters

The number of times the tire revolves in 1 second = 5 times.

Distance travelled when revolved one time is :

Distance = 2.8 meters

Distance travelled in 1 second = 5 × 2.8 meters

                                                  = 14 meters

Distance travelled in 100 seconds is :

D = 14 × 100 = 1400 meters

Hence the distance is 1400 meters.

Learn more about Circumference here :

https://brainly.com/question/28757341

#SPJ4

The solutions to the equation f(x) = g(x) are x = 1/65. Hence, this is our final answer.

We have the following functions to graph:f(x)=−32x and ​g(x)=(12)x−1.Similarly, to graph the above functions we would require a table of values. For this we set x = −2, −1, 0, 1, 2 and solve for f(x) and g(x):x -2 -1 0 1 2f(x) 192 96 0 −32 −64g(x) 0.25 0.5 1 2 4Once we get the table of values, we can then graph the functions on the same coordinate plane.

We have the graph as below:Graph of f(x) = −32x and g(x) = (1/2)x−1Now to get the solutions to the equation f(x) = g(x), we equate the two expressions:−32x = (1/2)x−1Multiplying both sides by 2, we get:-64x = x - 1Collecting like terms, we get:-65x = -1Dividing both sides by -65, we get:x = 1/65

To know more about equation  visit:-

https://brainly.com/question/29657983

#SPJ11

The lengths of the sides of the triangle are approximately:

The two equal sides: 61/45 cm

The third side: 1089/405 cm

Let's assume that the two equal sides of the triangle are represented by "x" cm each. According to the given information, the third side is 1 1/3 cm longer than the other two sides.

So, the length of the third side can be represented as "x + 1 1/3" cm.

The perimeter of a triangle is the sum of all its sides. In this case, the perimeter is given as 5 2/5 cm.

Using this information, we can write the equation:

2x + (x + 1 1/3) = 5 2/5

To solve this equation, let's convert the mixed number 1 1/3 to an improper fraction.

1 1/3 = (3× 1 + 1) / 3 = 4/3

Substituting the value, we have:

2x + (x + 4/3) = 5 2/5

To simplify the equation, let's convert the mixed number 5 2/5 to an improper fraction.

5 2/5 = (5 ×5 + 2) / 5 = 27/5

Now, the equation becomes:

2x + (x + 4/3) = 27/5

Combining like terms, we have:

3x + 4/3 = 27/5

To eliminate the fractions, let's multiply both sides of the equation by the least common multiple (LCM) of the denominators, which is 15:

15 × (3x + 4/3) = 15 ×(27/5)

45x + 20 = 81

Subtracting 20 from both sides:

45x = 61

Dividing both sides by 45:

x = 61/45

So, the value of x is 61/45 cm. This represents the length of the two equal sides of the triangle.

Now, to find the length of the third side, we substitute x back into the expression:

x + 1 1/3 = (61/45) + 4/3

To add these fractions, we need to find a common denominator. The LCM of 45 and 3 is 45:

[(61/45) × (3/3)] + (4/3) = (183/135) + (4/3)

Now, we can add the fractions:

(183/135) + (4/3) = (549/405) + (540/405) = 1089/405

So, the length of the third side is 1089/405 cm.

Therefore, the lengths of the sides of the triangle are approximately:

The two equal sides: 61/45 cm

The third side: 1089/405 cm

Learn more about improper fraction here:

https://brainly.com/question/21449807

#SPJ11

Answer:

y = 1.5x + 4

The slope is 1.5, and the y-intercept is 4.

Answer

there's 120 members in total

84 not pensioners

Explaination

36÷30% = 120

70% are not pensioners

so 70% × 120 = 84

or you could minus the pensioners from the total 120-36=84