Mathematics College

amy is building a house. the basement floor is at -15 feet. the roof of the house is above the ground 25 feet. write an inequality to compare the heights. explain the meaning of the inequality.

BONUS: what is an inequality.

Answers

Answer 1
An inequation is a mathematical expression that is used to make constraints given a problem.
 For example, this is a problem of heights.
 There is a minimum height and a maximum height.
 We can use the following inequation to describe the problem:
 Let
 x = height in feet.
 The inequation is:
 -15 <= x <= 25
 answer:
 -15 <= x <= 25

Related Questions

In an office, the number of chairs, c , is equal to five more than twice the number of desks, d. Which equation matches the information?

Answers

c (unknown)
d (unknown)
chair is 5 more than twice the number of desks
So if I'm not wrong
The answer should be

c = 5+2d

Please correct me if I'm wrong :D

Final answer:

The algebraic equation that represents the relationship between the number of chairs, c, and the number of desks, d, in an office, where the number of chairs is five more than twice the number of desks, is c = 2d + 5.

Explanation:

The student's question pertains to creating an algebraic equation based on a given word problem describing the relationship between the number of chairs (c) and desks (d) in an office. The problem states that 'the number of chairs, c, is equal to five more than twice the number of desks, d'.

To formulate the equation that illustrates this relationship, we apply the information provided:

Identify the number of chairs as c.Determine that c is 'five more than' something, which suggests addition.Recognize that 'twice the number of desks' means 2 times d, or 2d.Combine the above to conclude that the 'five more than' is added to the 'twice the number of desks', which gives us the equation c = 2d + 5.

A bond is a small, interest-bearing loan made by an individual to a corporate or government entity.


Please select the best answer from the choices provided

T
F

Answers

the answer to this question is T

Answer: TRUE

Step-by-step explanation:

A radar gun used to determine the speed of passing cars must be within 7 mph of the actual speed of a selected car. If a highway patrol officer reads a speed of 59 mph for a car, does he have irrefutable evidence that the car was speeding in a 55 mph zone?

Answers

No. if it has a 7mph range the highest and lowest possible values would be 66mph to 52mph.  The radar gun would have to measure 63 to cover the 14mph range for accuracy to claim the person was speeding.

Rearrange the formula A = P + Prt for t.

Answers

Given that: 
A=P+Prt
Solving for t.
Factor out P from the right side of the equation.
A=P(1+rt)
Divide both sides by P.
A/P= 1+rt
Subtract 1 from both sides
A/P-1=rt
Divide both sides by r.
(A/P) / r - 1/r= t
or
t= (A/P) / r - 1/r
t= A/Pr - 1/r
t= (A-P)/r

Answer: t= (A-P)/rP
Divide both side by p+pr . And T should be t= A over p+pr

how to solve -2x+y=7, 3y=6x+4

Answers

Consider, pls, this option.
To the additional, see the attached graph for this system.

Elijah is going to spin a spinner that goes to 4 180 times.He predicts that 60 of those spins will result in the spinner landing on the section labeled 3. Based on the theoretical probability, which best describes Elijah’s prediction?

Answers

The spinner will probably land on 3

Answer:

A. Elijah’s prediction is exact because 180 divided by 3 = 60.

Step-by-step explanation:

HELP ME PLEASE! How is the graph of mc027-1.jpg related to its parent function, mc027-2.jpg?

Answers

We will try to approach it generally. If we have a function y=f(x) and we have then y=f(2x), then the graph of the function will be horizontally compressed. If we take f(x/2), the graph of the function will be dilated. (To get horizontal shifts, we need f(x+a), which is not the case here; for example [tex] \sqrt{x+4} [/tex] is horizontally shifted relative to its parent function). If we consider -y=f(x), then the graph of this new function is the graph of the parent function flipped along the x-axis. If we consider y=f(-x) (which is the case here, since [tex] \sqrt{-x} = \sqrt{(-x)} [/tex]) we have that the graph of the new function is the same as the old graph, just flipped along the y-axis. Each of those transformations is independent; combining our observations we see that the last answer is the correct one.

The graph of [tex]y = \sqrt{-2x[/tex] relates to its parent function as a result of (d) horizontal compression by a factor of 2, and a reflection across the y-axis

What is a function transformation?

A function transformation involves changing the form or equation of a function to another through reflection, dilation, translation or rotation

How to determine the function transformation

The parent function is given as:

[tex]y = \sqrt x[/tex]

Compress the function horizontally by a factor of 2, using the following rule

[tex](x,y) \to (2x,y)[/tex]

So, we have:

[tex]y = \sqrt {2x[/tex]

Next, reflect the function over the y-axis, using the following rule

[tex](x,y) \to (-x,y)[/tex]

So, we have:

[tex]y = \sqrt {-2x[/tex]

Hence, the function transformation is (d)

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The scale on a map is 1 cm for every 400 km. If Maine and Japan are 22 cm apart on the map, what is the distance between Maine and Japan?

Answers

Essentially, you must multiply 22 by 400. You get 8800 km apart for your answer.

Please help me with questions 24

Answers

Answer: B) quadrant IV; no

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

After the translation, the triangle stays in quadrant IV. It then reflects over to quadrant I, only to rotate back to quadrant IV again. The size and shape does not change. These transformations are known as "rigid transformations" which preserve segment lengths (aka keep them the same). So the final triangle is congruent to the original triangle. All that has happened is that it has moved around.

△ABC is reflected to form​​ ​ △A′B′C′ ​. The vertices of △ABC are A(3, 1) , B(1, 5) , and C(6, 9) . The vertices of △A′B′C′ are A′(−1, −3) , B′(−5, −1) , and C′(−9, −6) . Which reflection results in the transformation of ​ △ABC ​​ to ​ △A′B′C′ ​​?

Answers

The reflection of the triangle across  y = -x is the new triangle.

Answer:

that would be a reflection across the y axis resulting in a -x

Step-by-step explanation:

Find the sum of the geometric series with a1 = 7, r = 2, And n = 14

Answers

Final answer:

The sum of the geometric series with a1 = 7, r = 2, and n = 14 is -327661.

Explanation:

The question is asking for the sum of a geometric series. In mathematics, the sum (S) of a geometric series is determined using the formula S = a1 * (1 - r^n) / (1 - r), where a1 is the first term, r is the common ratio, and n is the number of terms.

In the provided geometric series, a1 = 7, r = 2, and n = 14. Substituting these values into the formula gives us S = 7 * (1 - 2^14) / (1 - 2). After performing the calculations, the sum of the geometric series is -327661.

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Final answer:

The sum of the first 14 terms of the geometric series with the first term (a1) = 7, common ratio (r) = 2, is 114,691.

Explanation:

Given the first term of the geometric series (a1) = 7, the common ratio (r) = 2, and the number of terms (n) = 14, we would like to find the sum of this series.  Using the formula for the sum of a geometric series, S = a1 * (1 - r^n) / (1 - r), substituting the given values, we get:

S = 7 * (1 - 2^14) / (1 - 2)

This simplifies to S = 7 * ( -16383) / -1, which results in S = 114,691. So, the sum of the first 14 terms of this geometric series is 114,691.

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1/6 of 3 yards=______feet

I know I just ask one but u get 17 points so plz help I'm stuck

Answers

In this question, first we have to see how many feets are in 1 yard .

And there are 3 feets in 1 yard.

So in 3 yards, there are 9 feets

Therefore we will get

[tex] \frac{1}{6}*3 yards= \frac{1}{6} * 9 feet = 1.5 feet [/tex]

Therefore the answer of the given question is 1.5 feet.

Final answer:

To find the equivalent feet for 1/6 of 3 yards, multiply 1/6 by 3 feet per yard to get 1.5 feet.

Explanation:

1/6 of 3 yards=_____feet

Step 1: 1 yard is equal to 3 feet.

Step 2: To find the equivalent feet for 1/6 of 3 yards, calculate 1/6 x 3 = 0.5 x 3 = 1.5 feet.

Patrick ate 2/3 of a fruit bar write an equivalent fraction for the amount of fruit bar Patrick ate

Answers

To get an equivalent fraction, multiply the fraction by a whole number. For example, you can do 2/3 times 2 to both sides which is 4/6.

A bucket is put under a leaking ceiling. the amount of water in the bucket doubles every minute. after 8 minutes, the bucket is full. after how many minutes is the bucket half full? show work

Answers

This question is more of an Intelligence Question rather than a Mathematics Question.

The water in the bucket doubles every minute. After 8 minutes the bucket is full. This means a minute earlier (i.e. at 7th minute) the water in bucket was half as compared to water in bucket after 8 minute.

So, if after 8 minutes bucket is full, after 7 minutes bucket will be half full. So the answer is 7 minutes.

Let u = <6, -9>, v = <1, -4>. Find u - v.

A) <5, -5>
B) <10, -10>
C) <15, 5>
D) <7, -13>

Answers

To subtract vectors, subtract the x coordinates together. Do the same for the y coordinates as well.

In terms of a formula if we had the vectors u and v such that
u = <a,b>
v = <c,d>
then 
u - v = <a-c, b-d>

Let's use that to get...
u - v = <6,-9> - <1,-4>
u - v = <6-1,-9-(-4)>
u - v = <6-1,-9+4>
u - v = <5,-5>
----------------------
Answer: A) <5,-5>

Final answer:

To find the difference between vectors u and v, subtract the components of v from the corresponding components of u, resulting in the vector A) <5, -5>.

Explanation:

The question involves finding the difference of two vectors u and v. To find the vector u - v, you subtract each corresponding component of vector v from vector u.

For the first component, subtract the x-component of v (1) from the x-component of u (6), which equals 5.For the second component, subtract the y-component of v (-4) from the y-component of u (-9), which equals -5.

Thus, the vector u - v is A) <5, -5>.

Point R is located at (11,5).point S is located at (-1,5). what is the distance between point R and point S

Answers

We can solve this using the distance formula:

d=√(x2-x1)² + (y2-y1)²
d=√(-1-11)² + (5-5)²
d=√(-12)² + 0
d=12

Use Cavalieri’s Principle to calculate the exact volume of an oblique cylinder with a radius of 10 meters and a height of 11 meters

Answers

recall that Cavalieri's Principle only says that if an oblique cylinder, like in this case, has the same cross-section all the way up, it has the same volume as a non-oblique cylinder.

so, the volume of a cylinder is V = πr²h.

now, we know the radius is 10, and the height is 11, so then V = π10²*11 is its volume.

The exact volume of the oblique cylinder with a radius of 10 meters and a height of 11 meters is 110π cubic meters.

To calculate the exact volume of an oblique cylinder using Cavalieri's Principle, follow these steps:

1. Consider a right cylinder with the same base and height as the oblique cylinder. The volume of the right cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.

2. Since the oblique cylinder and the right cylinder have the same base and height, their volumes are equal according to Cavalieri's Principle.

3. The formula for the volume of a right cylinder can be applied to the oblique cylinder, giving the volume as V = πr^2h.

4. Substituting the values of the radius (r = 10 meters) and height (h = 11 meters) into the formula gives V = π(10)^2(11) = 110π cubic meters.

5. Therefore, the exact volume of the oblique cylinder with a radius of 10 meters and a height of 11 meters is 110π cubic meters.

a kittens heartbeat can be as fast as 240 beats per minute . to find the number of times a kittens heart beats in 30 seconds , Aiden says divide 240 ny 30 . do you agree with him why or why not

Answers

I do not agree. If you divide 240 by 30, it would be 8 heartbeats, which is absurd. It's impossible for something to survive with 8 heartbeats per 30 seconds.
In order to get the CORRECT answer, divide 240 by 60 seconds.
This would give you 4 heartbeats per second.
Then, multiply it by 30 seconds, which would give you 120 heartbeats.

CORRECT answer: 120

Ruben has two congruent wooden dowels. He cuts one dowel in two in order to have three pieces to make a triangle. Explain why, despite having three sides, Ruben will not be able to make a triangle with his three pieces.

Answers

Let the two original dowels be of length x.
After cutting one of the dowels, the lengths will then be
x/2, x/2,x.

He cannot form a triangle using the three dowels because the triangle inequality requires that the sum of the two shorter sides of a triangle must be greater than the third side.  Here x/2+x/2=x equals the third side, so a triangle cannot be formed.

By the way, if he cuts the long dowel a little shorter, he will then be able to make a triangle.

Answer:

The dowels are congruent, so they have the same length. If one is cut, the sum of the lengths of the two cut pieces will equal the length of the longer piece. If the pieces are to make a triangle, the sum of the lengths of the two cut pieces must be greater than the length of the third piece.

Step-by-step explanation:

how many radians are in a semicircle? a.2π, b.π, c.π/2, d.3π/2

Answers

Final answer:

A semicircle, which is half of a full circle, consists of half the total amount of radians in a full circle. Since a full circle has 2π radians, a semicircle contains π radians. Therefore, the correct answer is b.π.

Explanation:

To answer your question, let's review the structure of a circle.It is divided by its radius into 360 degrees or by its diameter into a full rotation of 2π radians. Therefore, a semicircle, which is half of a circle, must consist of half the total amount of radians in a full circle.

In a full circle, there are 2π radians. Hence, in a semicircle, which is exactly half of the full circle, there would be 2π/2. This simplifies to π radians.

So, the correct answer to your question 'How many radians are in a semicircle?' is b.π.

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A rectangular prism has a length of 4 1/2 millimeters, a width of 4 1/2 millimeters, and a height of 6 millimeters.

Sally has a storage container for the prism that has a volume of 143 cubic millimeters.

What is the difference between the volume of the prism and the volume of the storage container?

Help Please?

Answers

Volume of a rectangular prism is found by multiplying the length by the width by the height.  The volume of our given prism would be
V = (4 1/2)(4 1/2)(6)
Converting the fractions to mixed numbers we have
V = (9/2)(9/2)(6/1) = 486/4 = 121.5

The storage container has a volume of 143, so the difference is 143 - 121.5 = 21.5 cubic mm.

Answer:

21 1/2

Step-by-step explanation:

Which statement best compares -1/2 and -2 1/2

Answers

From the Iready New York CCLS Question 18, The answer is B. If you count the spaces between -1 1/2 and -2 1/2 you get -2.

The Comparison between -1/2 and -2 1/2 is -1/2 is -2 more than -5/2.

What are fraction?

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.

Given:

-1/2 and -2 1/2

So, -1/2 and -5/2.  

So, the quantity -1/2 > -5/2

Also, -1/2 is -2 more than -5/2.

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If f(x)=7+4x and g(x)=1/2x What is the value of (f/g)(5)?

Answers

If im not mistaken the answer is D 270

Answer:

[tex]\bigg(\displaystyle\frac{f}{g}\bigg)(5) = 270[/tex]

Step-by-step explanation:

We are given the following information in the question:

[tex]f(x) = 7 +4x\\\\g(x) = \displaystyle\frac{1}{2x}[/tex]

We have to find the values of [tex]\displaystyle\frac{f}{g}(x)[/tex]

[tex]\bigg(\displaystyle\frac{f}{g}\bigg)(x) = \frac{f(x)}{g(x)} = \frac{7 + 4x}{\frac{1}{2x}} = 2x(7+4x)[/tex]

Putting x = 5, we have:

[tex]\bigg(\displaystyle\frac{f}{g}\bigg)(x) = 2x(7+4x)\\\\\bigg(\displaystyle\frac{f}{g}\bigg)(5) = 2(5)(7+20)=270[/tex]

270 is the required value of [tex]\bigg(\displaystyle\frac{f}{g}\bigg)(5)[/tex].

Which expression represents the sixth term in the binomial expansion of (5y+3)^10

Answers

[tex]\bf \textit{the coefficient and values of an expanded term}\\\\ (5y-3)^{10} \qquad \qquad \begin{array}{llll} expansion\\ for\\ 6^{th}~term \end{array} \quad \begin{cases} \stackrel{term}{k}=0..10\\ \stackrel{exponent}{10}\\ -----\\ k=\stackrel{6^{th}~term}{5}\\ n=10 \end{cases}[/tex]

[tex]\bf \stackrel{coefficient}{\left(\frac{n!}{k!(n-k)!}\right)} \qquad \stackrel{\stackrel{first~term}{factor}}{\left( a^{n-k} \right)} \qquad \stackrel{\stackrel{second~term}{factor}}{\left( b^k \right)}[/tex]

[tex]\bf \stackrel{coefficient}{\left(\frac{10!}{5!(10-5)!}\right)} \qquad \stackrel{\stackrel{first~term}{factor}}{\left( (5y)^{10-5} \right)} \qquad \stackrel{\stackrel{second~term}{factor}}{\left( (-3)^5 \right)} \\\\\\ 252(5y)^5(-3)^5\implies 252(5^5y^5)(-3)^5\implies -252(3125y^5)(243) \\\\\\ -191362500y^5[/tex]

Answer:

bb

Step-by-step explanation:

What is the solution to 2log9(x)=log^9(8)+log9(x-2)

Answers

2log9(x)=log^9(8)+log9(x-2)

Log₉x² = log₉8 + log₉(x-2)


Log₉x² = log₉(8×(x-2))

Log₉x² = log₉8x-16

Log₉x² - log₉8x-16 = 0

Log₉(x²/(8x-16)) = 0

x²/(8x-16) = 9°

x² = 1 × 8x-16

x²-8x+16 = 0

x²-4x-4x+16 = 0

x(x-4)-4(x-4) = 0

(x-4)(x-4) =0

Therefore x = 4.....

Answer:

C. x=4

Step-by-step explanation:

After losing 30 pounds, an individual weigh 110 pound more than one-third his previous weight

Answers

Write an equation based on the problem
For an instance, x is the previous weight
"After losing 30 pounds" could be written as (x - 30)
"110 pounds more than one-third his previous" could be written as (110 + [tex] \frac{1}{3} [/tex]x)

Join the expression and solve for x
x - 30 = 110 + [tex] \frac{1}{3} [/tex]x

Move 1/3 x to the left side, and the constant of 30 to the right side, so like terms will be on equal side
x - [tex] \frac{1}{3} [/tex]x = 110 + 30

Equalize the denominators of the fractions
[tex] \frac{3}{3} [/tex]x - [tex] \frac{1}{3} [/tex]x = 140
[tex] \frac{2}{3} [/tex] = 140
x = 140 × [tex] \frac{3}{2} [/tex]
x = 420/2
x = 210

The previous weight was 210 pounds
The new weight is 210 - 30 = 180 pounds

The measure of angle E, the angle of elevation from point A to point B, is 5(x-2). The measure of angle D, the angle of depression from point B to point A, is (x+14). Find the measure of each angle.

Answers

The angle of elevation and the angle of depression are the same. (They are alternate interior angles between the parallel lines of the ground and "horizontal.")
  5(x -2) = x +14
  5x -10 = x +14 . . . . . . . eliminate parentheses
  4x = 24 . . . . . . . . . . . . add 10-x
  x = 6

The angles of elevation and depression are both (6+14)° = 20°.

Answer:

measure of angle E equals 20 degrees, measure of angle D equals 20 degrees

What is the slope of a line that is parallel to to the one shown? (-3, 2) (0, -2)

Answers

(-3, 2) (0, -2)
slope = (2 + 2)/(-3 - 0) = -4/3
parallel lines have same slope

so answer is -4/3

Which is a disadvantage of withdrawing more money than is available in a checking account?

Answers

One disadvantage is most banks charge an overdraft fee once you take out more money than what is available.

A disadvantage of withdrawing more than you have in your account is you will be charged an overdraft fee.

What is an Overdraft Fee?

An overdraft fee can be described as the fee your bank charges you when you make a withdrawal from your account beyond what you have in it.

An overdraft fee is one of the disadvantages of withdrawing more money than you have in your account..

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Translated these questions to a equation:
6 more than 9 times a number x is -12
the quotient of a number t and 7, plus 2, is -4

Answers

6 more than 9 times a number x is -12...
6 + 9x = -12

the quotient of a number t and 7, plus 2, is -4 ...
(t/7)+ 2 = -4

Hope this helps :)
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