find the lateral area, surface area, and volume of the following figure. leave answer in simplest radical form or in terms of pi. round to the nearest tenth. Solve for the lateral surface area

Let x be the larger number and y be the smaller number.

Given the difference between two numbers is 16.

Given larger number is five less than four times the smaller number.

Now, solve the equation (1)

Put x in the 2nd equation.

Further solved as,

Now, put the value of y in equation (1)

Thus,

Therefore, the two numbers are 23 and 7.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

If 3x + 2y = 72 and 2y = 3z then 3x + 3z = 72.

This is due to the property of substitution.

Option E is the correct answer.

None of the above.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

3x + 2y = 72 _____(1)

2y = 3z ______(2)

Substitute (2) in (1) we get,

3x + 3z = 72

We got 3x + 3x = 72 using the property of substitution.

Thus,

If 3x + 2y = 72 and 2y = 3z then 3x + 3z = 72.

This is due to the property of substitution.

Option E is the correct answer.

None of the above.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ1

Answer:

33

Step-by-step explanation:

3

Regular decagon.

The same decagon can be obtained by rotating the figure by 36 degrees, it is mapped onto itself every time it is rotated by 36 degrees.

To learn more about decagon refer to :

https://brainly.com/question/27596718

#SPJ9

In the equation f(x) = -3(2), reflected about x - axis is : f(x) = 3.2

According to the question, given that

equation f(x) = -3(2)

the equation reflected x - axis is f(x) = 3.2

Therefore, Reflected about the x-axis in the equation f(x) = -3(2) is f(x) = 3.2

The graph of the parent function is either "moved," "resized," or "reflected" by a function transformation. The three primary categories of function transformations are as follows:

- Translation

- Dilation

- Reflection

The only one of these transformations, dilation, alters the size of the original shape; the other two, however, just affect the shape's location.

By comparing the original and converted graphs, you can quickly determine which one has changed because you can tell by by glancing at the graph that it has moved up 2 units, left 3 units, etc. However, it can be challenging to graph the function transformation when a graph is provided. The next few steps make it much simpler to graph transformations. Here, the function y = f(x) is changed to y = a f(b (x + c)) + d.

Step 1: Write down some of the original curve's defining coordinates. Thus, we are aware of the previous x and y coordinates.

Step 2: Simply put "b (x + c) = old x-coordinate" and solve for x to determine the new x-coordinate of each location.

Step 3: Simply apply all outside operations (of brackets) on the old y-coordinate to determine the new y-coordinate of each point. To determine each new y-coordinate, find ay + d, where 'y' is the old y-coordinate.

To learn more about graph transformations visit here : brainly.com/question/10059147

#SPJ1

The correct answer is option C.

With this, we can already rule out option A.

Next, we can see a slanted dashed line, that when x = 0, y = 2. The solution set is below this line. The inequality that represnts this is:

Thus, option C is the correct one.

The probability P10 for a data with mean of 198 and standard deviation of 74.5 is P10 = 25.15%

As per the question statement, a distribution of values is normal with a mean of 198 and a standard deviation of 74.5 and we are supposed to find P(10), which is the score separating the bottom 10% from the top 90%.

Given mean (µ) = 48.5 , SD(σ) = 18.2

z = (X - μ) / σ, where X = data

X = 216.74

z = (216.74 - 198) / 74.5 = 0.2515 or 25.15%

Hence the probability P10 for a data with mean of 198 and standard deviation of 74.5 is P10 = 25.15%

To learn more about Probability, click on the link given below:

https://brainly.com/question/11234923

#SPJ1

Solution

Step 1:

Write the systems of equations

Step 2

To find the value of y, add both equations

82

1) Since Tanner is going to write a number with 8 tens and 2 ones

Then we can write:

2) Tanner writes the number 82

Answer:

The amount of time it would take 160 workers to build 16 miles of Highway is;

Explanation:

Given that the amount of time it takes to build a highway varies directly with the length of the highway and inversely with the number of workers.

Let t represent the time in weeks, l represents the length of the highway in miles, and n represent the number of workers;

So, we have;

Given;

it takes 100 workers 6 weeks to build 4 miles of Highway

so, for 160 workers to build 16 miles of Highway the time it will take is;

Therefore, the amount of time it would take 160 workers to build 16 miles of Highway is;

Answer:

If the complement of an angle is 62°, then its supplement is 152°.

hope it helps u

branliest?

We are given that the rate of growth is:

Now, recall that the growth factor is:

Therefore, the growth factor is:

Solving for x :

EXPLANATION

Since we have 3 1/2 slices of cake, and we need to distribute a half of slice by each friend, we need to divide 3 1/2 by 2, as follows:

Therefore, since each friend gets a half slice of cake, we can affirm that each whole slice of cake can be divided into two halves.

Now, adding from half to half to obtain 3 1/2 slices of cake, give us:

1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 = 7 slices

So, 3 1/2 slices of cake is a total of 7 halves.

Because each friend gets half of a slice of cake, we can affirm there are 7 friends.

Answer:

See below

Step-by-step explanation:

3  +  one half     slices      each whole (3 of them ) can be cut into two halves

6  halves  + 1 half = 7 halfves

   if everyone gets a a half, there are 7 people

We have the following system of functions:

The second equation gives us an expression for y. We can replace y with these expression in the first equation:

We can substract 3x from both sides:

The x is a factor of both terms on the left. Then we can rewrite this equation:

So we have that the product of two terms is equal to 0. This happens when any of them is equal to 0 so we have two equations:

From the first we have x=0 and we can add 3 to both sides of the second equation:

Then we divide both sides by 49:

So we have the two x-values of the solutions: x=0 and x=3/49. In order to find their respective y-values we can use any of the two original functions:

We have two solutions: (0,0) and (3/49,21/49). We can round the values of the second solution:

Then the solutions are (0,0) and (0.06,0.43). Then the answer is the fourth option.

Answer:

2.50 + 1.50m = c

Step-by-step explanation:

Since he pays a fee of 2.50 when he enters the taxi were going to start with:
2.50 +

Now after its 1.50 for each mile so were going to do :

2.50 + 1.50m

Since we want to find the cost the equation will be:

2.50 + 1.50m = c

Answer:

[tex]2^1[/tex]

Step-by-step explanation:

Hello! So, to tackle this problem let's start off with writing out the formula as such! [tex]\frac{2^2 * 2^3}{2^4}[/tex]

To solve this, what we can do is start off by isolating [tex]\frac{2^2}{2^4}[/tex] (we can worry about [tex]2^3[/tex] later). To evaluate [tex]\frac{2^2}{2^4}[/tex], we're essentially just simplifying the fraction and reducing the exponents. In this case, we can reduce the power of 2 from both the numerator and denominator to get [tex]\frac{1}{2^2}[/tex] (this is obtained by dividing both numerator and denominator by [tex]2^2[/tex])

Once we have that, we are now essentially left with [tex]\frac{2^3}{2^2}[/tex]! From here, we can apply exponent rule, which allows us to get rid of the denominator entirely and now it becomes 2^(3-2). We can subtract the numbers to then simplify it into our answer, [tex]2^1[/tex] or in other words just 2!

The range of the function will be equal to [-1, 27].

Function may be defined as an expression in which for every input variable there is only one output variable. The input variable is the variable x and also called as independent variable and output variable is the y variable and is also called as dependent variable. Domain of a function may be defined as the set of values of all the input values. Range of a function may be defined as the set of values of all the output values. For the domain -5 ≤ x < 3 we have function x² + 2. So, if we put -5 as x, we get the value equal to 27. Also, for the domain 3 ≤ x < 7 we have the function x - 4 and if we put the value 3 as x, we get the value equal to -1. Now, the range will be equal to [-1. 27].

Learn more about Range at:

brainly.com/question/4206663

#SPJ1

To find the y-intercept, replace x=0:

Therefore, the y-intercept of the given equation is 1.

From the function, we can conclude:

Answer:

Zero(s) of multiplicity one: 6

Zero(s) of multiplicity two: 9

Zero(s) of multiplicity three: -6, -4

The endpoints are (1,4) and (-9,-6). The equation for the perpendicular bisector of the line segments with given end points is x-y+3=0.

Given that,

The endpoints are (1,4) and (-9,-6).

We have to find the equation of the perpendicular bisector of the line segments with given end points.

First we have to find

The slope of the line m= [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

m=(-6-4)/(-9-1)

m=-10/-10

m=1

Now,

The equation of the line is y-y₁=m(x-x₁)

Taking point (1,4)

y-4=1(x-1)

y-4=x-1

x-y+4-1=0

x-y+3=0

Therefore, the equation for the perpendicular bisector of the line segments with given end points is x-y+3=0.

To learn more about equation visit: https://brainly.com/question/10413253

#SPJ1

Answer:

105 degrees

Elias' mistake was that he added m

Explanation:

To be able to determine the measure of AFB, we have to 1st of all find the value of x.

Let's go ahead and solve for x as shown below;

Since we know the value of x, let's go ahead and solve for [tex]\begin{gathered} (3x+3)+m\angle\text{AFB}=180\text{ (sum of angles on a straight line)} \\ 3(24)+3+m\angle AFB=180 \\ 75+m\angle AFB=180 \\ m\angle AFB=180-75 \\ m\angle AFB=105^{\circ} \end{gathered}[/tex]

The inverse of the function is 1/64x², for x≥0

What is a function?

Al-Biruni and Sharaf al-Din al-Tusi, two Persian mathematicians, are responsible for the first documented treatment of the concept of function. Initially, functions expressed the idealized interaction of two changing quantities. A planet's location, for instance, depends on time. In the past, the idea was developed with the infinitesimal calculus at the end of the 17th century, and the functions that were taken into consideration until the 19th century were differentiable (that is, they had a high degree of regularity). The realms of application of the idea of a function were substantially expanded at the conclusion of the 19th century when it was defined in terms of set theory.

The inverse of the function is given by option (D) 1/64x², for x≥0

To know more about function, click on the link

https://brainly.com/question/11624077

#SPJ9

The slope of the line is 125.

The meaning of the slope in this context is the change in prices with respect to the change in sizes of the houses in square feet.

Using the slope intercept equation the line won't pass through (5, 650)

The graph is a relationship between the cost of a home and the size of the houses in square.

Therefore, the slope can be found as follows:

The slope is the change in y with respect to the change in x.

The slope is rise over run.

Therefore,

slope of the line(m) = y₂ - y₁ / x₂ - x₁

using (1, 125)(2, 250)

m = 250 - 125 / 2 - 1

slope = 125

The slope in this context is the change in price with respect to the change in sizes of the house.

Let's check if the line will pass through (5, 650) using slope intercept equation.

y = mx + b

where

y = 125x + 0

625 = 125(5)

Therefore, the lines won't pass through (5, 650) instead it will pass through (5, 625)

learn more on slope here:https://brainly.com/question/12203383

#SPJ1

hello

to solve this question we should simply express this in percentage

from the calculation above, the percentage of houses painted yellow are 28%

Solution

- The question tells us to find the % change from $250 to $303.

- To calculate the percentage change, we use the formula given below:

- The New is $303 and the Old is $250. Thus, we can calculate the percentage change as follows:

Final Answer

The percentage change from $250 to $303 is 21.2%

Given the information, we have the following right triangle:

notice that x represents the distance from the base of the ladder to the house.

Then, using the trigonometric function sine we have the following:

thus, the base of the ladder is 1.35m from the house

Let's call X the number of pounds of cashews and Y the number of pounds of Brazil nuts.

Now, we want to make 33 pounds of the mixture, so:

X + Y = 33

Adittionally, every pound mixture will be sell for $5.64 per pound. It means that:

7X + 4Y = 5.64*33

7X + 4Y = 186.12

Because every pound of cashews cost $7 and every pound of Brazil nuts cost $4

Then, we can solve for X on the first equation and replace it on the second as:

So, we can solve for Y as:

Now, we can calculate X as:

Therefore, we need to use 18.04 pounds of cashews and 14.96 pounds of Brazil nuts to make a 33 pounds mixture that sells for $5.64 per pound

Answer 18.04 pounds of cashews and 14.96 pounds of Brazil nuts