The volume of a rectangular prism is given by the formula V = lwh, where l is the length of the prism, w is the width, and h is the height. Suppose a box in the shape of a rectangular prism has length (2a + 11), width (5a – 12), and height (a + 6). Which expression represents the volume of the box?
answer choices in pics
Answer:
[tex]V = (10a^3+91a^2+54a-792)[/tex]
Step-by-step explanation:
We have
[tex]V = lwh[/tex] (I), and
[tex]l=2a+11[/tex] (II)
[tex]w=5a-12[/tex] (III)
[tex]h=a+6[/tex] (IV)
We substitute the expression (II),(III) and (IV) in (I), that is
V= (2a+11)(5a-12)(a+6), solve the first one terms
[tex]V = (10a^2-24a+55a-132)(a+6)[/tex]
[tex]V = (10a^2+31a-132)(a+6)[/tex]
[tex]V = (10a^3+31a^2-132a+60a^2+186a-792)[/tex], simplifying
[tex]V = (10a^3+91a^2+54a-792)[/tex]
You are ordering pizzas for a birthday party and getting them delivered to your house. you order 12 pepperoni pizzas, 8 cheese pizzas, and 4 hawaiian pizzas. there is a delivery fee of $5.50 if your total comes to 184.54. how much was each pizza
The answer would be $7.46. If you subtract the delivery fee then divide by how much pizzas there are you would find the amount per each pizza.
What is the radius of a circle whose equation is x2 + y2 + 8x – 6y + 21 = 0?
Answer: The required center of the given circle is 2 units.
Step-by-step explanation: We are given to find the radius of a circle with the following equation:
[tex]x^2+y^2+8x-6y+21=0~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
The standard equation of a CIRCLE with radius 'r' units and center at the point (h, k) is given by
[tex](x-h)^2+(y-k)^2=r^2.[/tex]
From equation (i), we have
[tex]x^2+y^2+8x-6y+21=0\\\\\Rightarrow (x^2+8x+16)+(y^2-6y+9)-16-9+21=0\\\\\Rightarrow (x^2+2\times x\times 4+4^2)+(y^2-2\times x\times 3+3^2)-4=0\\\\\Rightarrow (x+4)^2+(y-3)^2=4\\\\\Rightarrow (x-(-4))^2+(y-3)^2=2^2.[/tex]
Comparing the above equation with the standard equation (i), we get
radius, r = 2 units and center, (h, k) = (-4, 3).
Thus, the required center of the given circle is 2 units.
Write an equation for the line parallel to line AB that contains point C (0,3)
AB: y=-2x+1
does this set of ordered pairs represent a function?why or why not? (-5,-5),(-1,-2),(0,-2),(3,7),(8,9)
The set of ordered pairs (-5,-5),(-1,-2),(0,-2),(3,7),(8,9) represent the function.
What is a function?A function is a relationship between a number of inputs and outputs. A function is an association of inputs where each input is coupled with exactly one output. There is a range, co-domain, and domain for every function.
As per the information provided:
Let's list the x-coordinates and y-coordinates of the ordered pairs:
x: -5, -1, 0, 3, 8
y: -5, -2, -2, 7, 9
There is no x-coordinate that appears more than once in the list, so there are no two or more ordered pairs with the same x-coordinate.
Therefore, the set of ordered pairs represents a function.
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Question 3 e and f are sets of real numbers defined as follows.
Euler's formula, V – E + F = 2 relates the number of vertices V, the number of edges E, and the number of faces F of a polyhedron. How many faces does a polyhedron with 4 vertices and 6 edges have?
7
4
6
5
Please Help!
A polyhedron with 4 vertices and 6 edges would have 4 faces, according to Euler's formula.
Explanation:This question involves the understanding of Euler's formula applied on polygons. Euler's formula, as given in the question is V – E + F = 2, where V is the number of vertices, E is the number of edges, and F is the number of faces. To answer your question, we need to solve the formula for F. Let's replace V and E with the given numbers, which are 4 for vertices and 6 for edges.
So the formula becomes 4 – 6 + F = 2. Simplifying this, we get -2 + F = 2. Solving for F, we find F = 1 + 2, which means F = 4. So, a polyhedron with 4 vertices and 6 edges would have 4 faces.
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The expression V = 2x3 + 6x2 can be used to find the volume of the trapezoidal prism below. If x = 12 cm, what is the volume of the prism?
The volume of the prism is 4320 cubic units
The expression for the volume is given as:
V = 2x^3 + 6x^2
When x = 12, the expression becomes
V = 2 * 12 ^3 + 6 * 12^2
Evaluate the exponent
V = 2 * 1728 + 6 * 144
Evaluate the products
V = 3456 + 864
Evaluate the sum
V = 4320
Hence, the volume of the prism is 4320 cubic units
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Which is true of a melting point and a boiling point?
A. The melting point is a higher temperature than the boiling point.
B. The melting point is a lower temperature than the boiling point.
C. The melting point and the boiling point depend on the size of the sample.
Answer:
B - The melting point is a lower temperature than the boiling point.
Step-by-step explanation:
Melting point is the temperature at which any given solid will melt. The state of the solid changes from solid to liquid.
Boiling point is the temperature at which a given liquid boils and changes to vapor state. Like water starts to boil at 100 degrees Celsius.
The boiling point of a substance cannot be lower than its melting point.
So, the answer here is - The melting point is a lower temperature than the boiling point.
In a couple of sentences and your own words describe how to re-write an expression that's in radical form into an expression with rational exponents?
What is the expression in radical form?
(5x^4y^3)2/9
Enter your answer, in simplest form, in the box.
if the problem is (5x^4y^3)^2 divided by 9
5^2 = 25
4*2 =8
3*2 =6
so you get (25x^8y^6)/9
if that isn't how the equation was supposed to be written let me know and I will edit my answer.
The given algebraic expression expressed in the simplest radical form is;
25x⁸y⁶/9
The algebraic expression we are given is;(5x⁴y³)²/9
Now, simplifying to a radical form simply means eliminating general square roots, cube roots, squares, cubes e.t.c where possible.Now, from the algebraic expression given, we can see that expanding the bracket gives us;[5² × (x⁴)² × (y³)²]/9
According to laws of indices we will multiply the external exponent by the internal one for the x and y variable. This gives us;
25x⁸y⁶/9
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What is the equation of a circle with center (-3, -1) that contains the point (1, 2)?
Answer:
(x + 3)^2 + (y + 1^)2 = 25
Step-by-step explanation:
The distance formula gives the length of the radius:
r = √(-3-1)^2 + (- 1-2)^2 = √25 = 5
Substituting h = -3, k = -1, and r = 5 into the standard form (x - h)2 + (y - k)2 = r2, you get (x + 3)2 + (y + 1)2 = 52 = 25.
edmentum :)
N a trip to his grandparents, donny drove 60 miles per hour for 45 minutes and 50 miles per hour for 30 minutes. how many miles did donny drive?
The solution is, donny drove 70 miles.
What is speed?Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).
Speed = Distance/ Time.
here, we have,
we know that,
Speed: The ratio of distance to time.
To find the distance we use the following formula.
Given that
donny drove 60 miles per hour for 45 minutes and 50 miles per hour for 30 minutes.
so, we get,
In 45 minutes, she traveled = ( 60/60 * 45)
= (1 * 45)
=45 miles.
again, we have,
The she drove 50 miles per hour for 30 minutes.
so, we get,
In 30 minutes, she traveled = ( 50/60 * 30 )
=50/2
= 25 miles
Therefore donny drove (45+25) miles= 70 miles.
Hence, The solution is, donny drove 70 miles.
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Select all that apply. If p is a statement, which of the statements is the negation of p. not p. and p. p is false. or p. p is true.
The base of the triangle is seven less than twice its height. If the area of a triangle is 102cm², find the length of the base.
Answer:
The length of the base is [tex]b=17cm[/tex]
Step-by-step explanation:
We start by writing the equation of the base :
Given that the base of the triangle is seven less than twice its height we can write that
[tex]b=2h-7[/tex] (I)
Where ''b'' is the base and ''h'' is the height.
Now, the area of a triangle is [tex]\frac{bh}{2}[/tex]
We know that the area is [tex]102(cm^{2})[/tex] ⇒
[tex]\frac{bh}{2}=102(cm^{2})[/tex]
Now we can replace ''b'' by the expression in (I) ⇒
[tex]\frac{bh}{2}=102(cm^{2})[/tex]
[tex]\frac{(2h-7)(h)}{2}=102(cm^{2})[/tex]
Rearraging the expression :
[tex]\frac{(2h-7)(h)}{2}=102(cm^{2})[/tex]
[tex](2h-7)(h)=204(cm^{2})[/tex]
[tex]2(h^{2})-7h=204(cm^{2})[/tex]
[tex]2(h^{2})-7h-204(cm^{2})=0[/tex]
We need the values of ''h'' that satisfy the equation.
We can use the quadratic formula with
[tex]a=2\\b=-7\\c=-204[/tex]
The quadratic formula will be
[tex]h1=\frac{-b+\sqrt{b^{2}-4ac}}{2a}[/tex]
and [tex]h2=\frac{-b-\sqrt{b^{2}-4ac}}{2a}[/tex]
Using [tex]a=2\\b=-7\\c=-204[/tex] in the expression of h1 and h2 we find that
[tex]h1=12\\h2=-8.5[/tex]
Given that ''h'' is a length ⇒ [tex]h\geq 0[/tex]
We conclude that h1 = 12 cm is the correct value of ''h''
With this value of ''h'' we go to the expression of ''b'' ⇒
[tex]b=2h-7\\b=2(12)-7\\b=24-7\\b=17[/tex]
The value of the base ''b'' that satisfies the problem is [tex]b=17cm[/tex]
Find the equation of a line parallel to y - 5x = 10 that passes through the point (3, 10). (answer in slope-intercept form)
The equation of the required line is [tex]y=5x-5[/tex].
Given:
The eqation of paralle line is [tex]y-5x=10[/tex]. The required line passes through the point [tex](3,10)[/tex].To find:
The equation of the required line in slope-intercept form.
Explanation:
The given equation can be rewritten as:
[tex]y=5x+10[/tex]
On comparing this equation with [tex]y=mx+b[/tex], we get
[tex]m=5[/tex]
Slopes of parallel lines are always equal.
The slope of reqired line is [tex]m=5[/tex] and it passing through the point [tex](3,10)[/tex]. Using the point slope form, the equation of the line is:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-10=5(x-3)[/tex]
[tex]y=5x-15+10[/tex]
[tex]y=5x-5[/tex]
Therefore, the equation of the required line is [tex]y=5x-5[/tex].
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I need help with this question.
Ezra works two summer jobs to save for a laptop that costs at least $1100. He charges $15/hr to mow lawns and $10/hr to walk dogs. Recall the inequality that represents this situation: 15x + 10y ≥ 1100
Is (60, 20) a solution? How do you know? What does this point represent?
The coordinate pair (60, 20) is a solution because it satisfies the inequality. The coordinate pair (60, 20) is a solution because Ezra earns 60 x $15 = $900 mowing lawns and 20 x $10 = $200 walking dogs, for a total of $1100. Ezra can spend 60 hours mowing lawns and 20 hours walking dogs to earn enough money for the laptop.
A bread recipe calls for 1/3 cup of white flour and 2 3/4 cups of whole wheat flour. What is the total amount of flour needed?
Kevin has a box of cereal that contains 10 1/2 cups of cereal. A serving size of the cereal is 3/4 cup. How many servings are in the box of cereal? Enter your answer in the box
The number of servings in the box of cereal is:
14
Step-by-step explanation:It is given that:
Kevin has a box of cereal that contains 10 1/2 cups of cereal.
i.e. the number of cups of cereal= 21/2 cups
Also,
A serving size of the cereal is 3/4 cup.
This means that:
The number of servings in the box are:
Ratio of number of cups of cereal in box to the number of cups of cereal in one serving
which is calculated as:
[tex]\text{Number of servings}=\dfrac{\dfrac{21}{2}}{\dfrac{3}{4}}\\\\\\\text{Number of servings}=\dfrac{21\times 4}{3\times 2}\\\\\\\text{Number of servings}=14[/tex]
Michael, a freelance editor, charges the rates shown in the table below to edit manuscripts. The cost per page increases as the quality of editing improves. Michael also gives a 5% discount if the entire amount is paid up front. A 2 column table with Type of Editing and Cost per page as the column headings. Express Proofreading costs 2.20 dollars, Basic Proofreading 2.80 dollars, Extended Proofreading 3.90 dollars, and Deep Editing 12 dollars Maria has a 25-page manuscript. The equation below shows the relationship between the total cost of editing 25 pages, T, and the cost per page, c, if she gets the 5% discount: 25c − 0.05(25c) = T Using the equation, what is the best quality of editing that Maria can get done for a maximum of $66.50?
What is the maturity value of a 3-month, 14% note for $50,000? (round your answer to the nearest dollar.)
a.$57,000
b.$51,750
c.$50,000
d.$52,000?
The maturity value of a 3-month, 14% note for $50,000 is calculated by first determining the interest over the 3-month period and then adding it to the principal. The interest is $1,750, resulting in a maturity value of b) $51,750.
The maturity value of a 3-month, 14% note for $50,000 can be calculated using the formula for simple interest: M = P + (P × r × t), where M is the maturity value, P is the principal amount, r is the annual interest rate (as a decimal), and t is the time in years. Let's calculate the interest first and then add it to the principal to find the maturity value.
First, convert the annual interest rate to decimal: 14% = 0.14.
Then, because the note is for 3 months (which is 3/12 or 0.25 of a year), the time period t is 0.25.
Now, calculate the interest: I = P × r × t = $50,000 × 0.14 × 0.25 = $1,750.
Finally, add the interest to the principal to get the maturity value: M = P + I = $50,000 + $1,750 = $51,750.
So, the correct answer is b. $51,750.
The length of a rectangle is 55 meters longer than the width. if the area is 2929 square meters, find the rectangle's dimensions. round to the nearest tenth of a meter.
Several people form groups with four people in each group. Write an expression for the number of groups from doing by p people. How many groups are formed if there are 28 people?
Answer: 28/p; 7
Step-by-step explanation:
Hope it helps
Translate the variable expression into a word phase
2 x (3 - x)
A plumber charges $70 per hour plus $40 for the call. What does he charge for 4 hours of work? What's the dependent, solution, independent, and function
Kate has some dimes and quarters. if she has 1919 coins worth a total of $2.95, how many of each type of coin does she have?
For what value of b does
The yearbook club had a meeting. the meeting had 20 people, which is four-fifths of the club. how many people are in the club? answer
what is 0.81% written as a decimal
I need help on how to figure out this question! A track coach made a two way table to show his runners gender and running category. Male: Sprints- 16 Middle distance- 11 Long distance- 9 Female: Sprints- 12 Middle distance- 14 Long distance- 5 To the nearest hundredth, what is the probability that a randomly chosen female runs sprints? This obviously says that order doesn't matter as they mention "randomly chosen". I am just having trouble figuring out how to solve this.
Answer: Approx 0.39 will be the required probability.
Step-by-step explanation:
Here,Number of,
Male: Sprints=16, Middle distance=11, Long distance= 9
So, total males=36
And, Female: Sprints= 12, Middle distance=14, Long distance=5
So, total females=31
Thus, If one female randomly chosen,
Then, The probability that female runs sprint= Number of females who run sprint / total number of females
⇒ The probability that female runs sprint=12/31= 0.38709677419≈0.39