Step-by-step explanation:
Cavalieri's Principle. A method, with formula given below, of finding the volume of any solid for which cross-sections by parallel planes have equal areas. This includes, but is not limited to, cylinders and prisms.
If f(a) =11, then use the table above to find f(a-2)
Answer:
7Step-by-step explanation:
From the table
f(a) = 11 → a = 7
a - 2 = 5
f(a - 2) = f(5) = 7
Find the coordinates of P so that P partitions the segment AB in the ratio 1:3 if A(5,8) and B(−1,4).
A. (-6.5, -9)
B. (-1.5, -1)
C. (3.5, 7)
D. (-4, -6)
Answer:
The coordinates of point P are (3.5 , 7) ⇒ answer C
Step-by-step explanation:
* Lets explain how to solve the problem
- If the point (x , y) divide a line whose endpoints are (x1 , y1) , (x2 , y2)
at ratio m1 : m2 from the point (x1 , y1), then the coordinates of the
point (x , y) are [tex]x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}},y=\frac{y_{1}m_{2}+y_{2}m_{1}}{m_{1}+m_{2}}[/tex]
* Lets solve the problem
∵ A is (5 , 8) and B is (-1 , 4)
∵ P divides AB in the ratio 1 : 3
∴ m1 = 1 and m2 = 3
- Let A = (x1 , y1) and B = (x2 , y2)
∴ x1 = 5 , x2 = -1 and y1 = 8 , y2 = 4
- Let P = (x , y)
∴ [tex]x=\frac{(5)(3)+(-1)(1)}{1+3}=\frac{15+(-1)}{4}=\frac{14}{4}=3.5[/tex]
∴ [tex]y=\frac{(8)(3)+(4)(1)}{1+3}=\frac{24+4}{4}=\frac{28}{4}=7[/tex]
∴ The coordinates of point P are (3.5 , 7)
Use row reduction to solve the system of equations. x-2y+z=4, 3x-5y-17z=3, 2x-6y+43z=-5
Answer:
x = -1223, y = -629, and z = -31.
Step-by-step explanation:
This question can be solved using multiple ways. I will use the Gauss Jordan Method.
Step 1: Convert the system into the augmented matrix form:
• 1 -2 1 | 4
• 3 -5 -17 | 3
• 2 -6 43 | -5
Step 2: Multiply row 1 with -3 and add it in row 2:
• 1 -2 1 | 4
• 0 1 -20 | -9
• 2 -6 43 | -5
Step 3: Multiply row 1 with -2 and add it in row 3:
• 1 -2 1 | 4
• 0 1 -20 | -9
• 0 -2 41 | -13
Step 4: Multiply row 2 with 2 and add it in row 3:
0 2 -40 -18
• 1 -2 1 | 4
• 0 1 -20 | -9
• 0 0 1 | -31
Step 5: It can be seen that when this updated augmented matrix is converted into a system, it comes out to be:
• x - 2y + z = 4
• y - 20z = -9
• z = -31
Step 6: Since we have calculated z = -31, put this value in equation 2:
• y - 20(-31) = -9
• y = -9 - 620
• y = -629.
Step 8: Put z = -31 and y = -629 in equation 1:
• x - 2(-629) - 31 = 4
• x + 1258 - 31 = 4
• x = 35 - 1258.
• x = -1223
So final answer is x = -1223, y = -629, and z = -31!!!
Tickets to the college basketball game are $2.50 for students and $3 for general admission. If 58 people attended the last game and the box office collected $162, how many of each type of ticket did they sell?
The box office sold _____ general admission tickets and _____ student tickets.
Answer:
The box office sold 34 general admission tickets and 24 student tickets.
Step-by-step explanation:
2.5 dollars for students and 3 dollars for general admission.
58 people attended and 162 dollars was collected.
We are asked to find the number of general admission tickets and number of student tickets sold. Let's call the number of general admission tickets sold g and the number of student tickets sold s.
So we are going to make a money equation and a how many equation.
Let's being the money equation: 2.5 per student means you have 2.5*s
and 3 dollars per general admission ticket means you have 3*g. You are given total collected was 162 dollars so 162 is the sum of whatever 2.5s and 3g is. That setup as an equation in symbol form is 162=2.5s+3g
Let's do the how many equation: There are only 2 kinds of tickets, s and g. And we know that the sum of these should be 58 since that is how many people attended. So the equation in symbol form is 58=s+g.
This is our system of equations:
162=2.5s+3g
58= s+ g
------------------I'm going to set this up for elimination by multiplying both equation by -3 which gives:
162=2.5s+ 3g
-174= -3s+-3g
------------------------Now I'm going to add.
-12=-0.5s+0
-12=-0.5s
Divide both sides by -0.5
24=s
Or s=24.
Now we know that s+g=58 and s=24 so g=58-24=34.
The box office sold 34 general admission tickets and 24 student tickets.
Answer:
24 tickets for students
34 tickets for general admission
Step-by-step explanation:
Let's call x the number of students admitted and call z the number of Tickets for general admission
Then we know that:
[tex]x + z = 58[/tex]
We also know that:
[tex]2.50x + 3z = 162[/tex]
We want to find the value of x and z. Then we solve the system of equations:
-Multiplay the first equation by -3 and add it to the second equation:
[tex]-3x - 3z = -174[/tex]
[tex]2.50x + 3z = 162[/tex]
----------------------------------
[tex]-0.50x = -12[/tex]
[tex]x =\frac{-12}{-0.50}\\\\x=24[/tex]
Now we substitute the value of x in the first equation and solve for the variable z
[tex]24 + z = 58[/tex]
[tex]z = 58-24[/tex]
[tex]z = 34[/tex]
What is the coefficient of xy^4 in the expansion of (2x+y)^5
Answer:
The coefficient of xy^4 is 10
Step-by-step explanation:
to solve the questions we proceed as follows:
(2x+y)^5
=(2x+y)²(2x+y)²(2x+y)
We will solve the brackets by whole square formula:
=(4x²+4xy+y²)(4x²+4xy+y²)(2x+y)
By multiplying the brackets we get:
=32x^5+32x^4y+8x³y²+32x^4y+32x³y²+8x²y³+8x³y²+4x²y³+2xy^4+16x^4y+
16x³y²+4x²y³+16x³y²+16x²y³+4xy^4+4x²y³+4xy^4+y^5
=32x^5+80x^4y+80x³y²+40x²y³+10xy^4+y^5
Therefore the coefficient of xy^4 is 10
The answer is 10....
Answer: 10
Step-by-step explanation: a p e x
Which of the following relations shows a function?
A.{(5, -7), (6, -7), (-8, -1), (0, -1)}
B.{(4, -1), (4, -2), (3, -1), (2, 4)}
C.{(4, 5), (3, -2), (-2, 5), (4, 7)}
D.{(1, 4), (4, 1), (1, -4), (-4, 1)}
I believe it should be A
The sum of three consecutive numbers is 60. What are these three numbers?
Answer:
The numbers are 19,20 and 21
Step-by-step explanation:
Let
x -----> the first consecutive number
x+1 ---> the second consecutive number
x+2 --> the third consecutive number
we know that
x+(x+1)+(x+2)=60
Solve for x
3x+3=60
3x=57
x=19
so
x+1=19+1=20
x+2=19+2=21
therefore
The numbers are 19,20 and 21
Answer:
The numbers are 1, 20, and 21
Step-by-step explanation:
Let n, n+1 and n+2 be the three consecutive numbers.
To find the numbers
It is given that, the sum of 3 consecutive numbers is 60
n + (n + 1) + (n + 2) = 60
n + n + 1 + n + 2 = 60
3n + 3 = 60
3n = 60 - 3 = 57
n = 57/3 = 19
Therefore the numbers are 1, 20, and 21
If the slope of two lines are negative reciprocals,the lines are perpendicular
Answer:
Step-by-step explanation:
Yes, "If the slopes of two lines are negative reciprocals,the lines are perpendicular" is correct.
Answer:
True
Step-by-step explanation:
a p e x
Find the greatest common factor of 4c and 18c
Answer:
2c
Step-by-step explanation:
c is a common factor of both terms
Consider the factors of the coefficients 4 and 18
factors of 4 : 1, 2, 4
factors of 18 : 1, 2, 3, 6, 9, 18
The common factors are 1, 2
The greatest common factor is 2
Combining with c gives
Greatest common factor of 2c
To find the greatest common factor of 4c and 18c, the common factor is 2c.
To find the greatest common factor of 4c and 18c, you need to identify the largest factor that both numbers share. In this case, the common factor is 2c. Here's how you can determine it:
Write the numbers as a product of their prime factors: 4c = 2 * 2 * c and 18c = 2 * 3 * 3 * c.
Identify the common factors: The common factors are 2 and c.
Multiply the common factors together: 2 * c = 2c.
which simplified equation is equivalent to the equation below
15x-5+x=-47
The equation 15x-5+x=-47 simplifies to x=-2.625.
The student has provided the equation 15x - 5 + x = -47 and is looking to simplify it. To simplify this equation, we can combine like terms by adding 15x and x together, resulting in 16x - 5 = -47. The next step is to isolate the variable x by adding 5 to both sides of the equation, which gives us 16x = -42. Finally, we divide both sides by 16 to solve for x: x = -42 / 16.
It seems that there might be confusion with the typos and irrelevant parts in the question; the solution presented does not result in x = 3 or x = -7, as suggested by the incorrect context provided. The proper solution using the equation given leads to x = -42 / 16, which simplifies to x = -2.625. This is the correct solution for the presented equation.
As a check, we can substitute the value of x back into the original equation and confirm that the left side equals the right side, thus verifying our solution.
Problem Solving
ercises: Solve each problem.
CW ALL WORK. Use a separate sheet of paper (if necessary) and staple to this page.
The Acme Supply Store sells a security system for $2150,00 excluding tax. They
sold 12 systems. If the total profit on these sales was $4824.36, how much did
each system cost Acme Supply? Show your work.
I think the answer is $1,747.97
you're absolutely correct.
each system is sold for $2150, that includes cost + markup, namely the markup is the surplus amount otherwise called "profit".
they sold 12 of those, 2150 * 12 = 25800
they had $4824.36 in profits from it, so if we subtract that from the sale price, we'll be left with the cost of all 12 systems
25800 - 4824.36 = 20975.64
that's the cost for all 12 systems sold, how many times does 12 go into 20975.64? 20975.64 ÷ 12 = 1747.97.
I need help to solve this problem Simplify (6^7)^3
Answer:
C.
Step-by-step explanation:
(6^7)^3 means (6^7)(6^7)(6^7).
When multiply numbers with same base, add the exponents.
6^(7+7+7)=6^(3*7)=6^(21).
In the beginning you could have just multiply 7 and 3 so the answer is 6^(21).
Answer: The Answer to this question is C bc of the brackets it multiplies the exponents if that makes sense, hope this helps
Step-by-step explanation:
4^-2 x 7^-2 equivalent expression
Answer:
Not sure exactly which equivalent expression you are looking for but my goal would be to write it without the negative exponent.
[tex]\frac{1}{28^2}[/tex]
Step-by-step explanation:
They have the same exponent and it is multiplication.
There is a law of exponent that says [tex](a \cdot b)^x=a^x \cdot b^x[/tex] .
So we have [tex]4^{-2} \cdot 7^{-2}[/tex] equals [tex](4 \cdot 7)^{-2}[/tex].
Let's simplify (4*7)^(-2).
Since 4*7=28, we can say [tex](4*7)^{-2}=(28)^{-2}[/tex].
Some people really hate that negative exponent. All that - in the exponent means is reciprocal. So [tex]28^{-2}=\frac{1}{28^2}[/tex].
segment DB is a median of ΔADC. Which statement best describes the relationship between triangles ABD and CBD?
A. Triangles ABD and CBD are congruent by the SSS Congruence Postulate.
B. Triangles ABD and CBD are similar by the SSS Similarity Postulate.
C. Triangles ABD and CBD are congruent by the SAS Congruence Postulate.
D. Triangles ABD and CBD are similar by the SAS Similarity Postulate.
Answer:
Triangles ABD and CBD are congruent by the SSS Congruence Postulate
⇒ Answer A is the best answer
Step-by-step explanation:
* Lets revise the cases of congruence
- SSS ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ
- SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and
including angle in the 2nd Δ
- ASA ⇒ 2 angles and the side whose joining them in the 1st Δ
≅ 2 angles and the side whose joining them in the 2nd Δ
- AAS ⇒ 2 angles and one side in the first triangle ≅ 2 angles
and one side in the 2ndΔ
- HL ⇒ hypotenuse leg of the first right angle triangle ≅ hypotenuse
leg of the 2nd right angle Δ
* Lets solve the problem
- In ΔADC
∵ DA = DC
∵ DB is a median
- The median of a triangle is a segment drawn from a vertex to the
mid-point of the opposite side of this vertex
∴ B is the mid-point of side AC
∴ AB = BC
- In the two triangles ABD and CBD
∵ AD = CD ⇒ given
∵ AB = CB ⇒ proved
∵ BD = BD ⇒ common side in the two triangles
∴ The two triangles are congruent by SSS
* Triangles ABD and CBD are congruent by the SSS Congruence
Postulate.
HELLO :)
Triangles ABD and CBD are congruent by the SSS Congruence Postulate, this is because both of the triangles have the same angle and the have the same sides. Therefore they are congruent by the SSS Congruence Postulate.
Prove that sin^2A/cos^2A + cos^2A/sin^2A = 1/cos^2A*sin^2A - 2
Answer:
prove that:
Sin²A/Cos²A + Cos²A/Sin²A = 1/Cos²A Sin²A - 2
LHS = \frac{Sin^2A}{Cos^2A} + \frac{Cos^2A}{Sin^2A}
Cos
2
A
Sin
2
A
+
Sin
2
A
Cos
2
A
= \begin{lgathered}= \frac{Sin^4A + Cos^4A}{Cos^2A . Sin^2A}\\\\Using\: a^2 + b^2 = (a+b)^2 - 2ab\\\\a = Cos^2A \: \& \:b = Sin^2A\\\\= \frac{(Sin^2A + Cos^2A)^2 - 2Sin^2A Cos^2A}{Cos^2A Sin^2A} \\\\Sin^2A + Cos^2A = 1\\\\= \frac{1 -2Sin^2A Cos^2A}{Cos^2A Sin^2A}\end{lgathered}
=
Cos
2
A.Sin
2
A
Sin
4
A+Cos
4
A
Usinga
2
+b
2
=(a+b)
2
−2ab
a=Cos
2
A&b=Sin
2
A
=
Cos
2
ASin
2
A
(Sin
2
A+Cos
2
A)
2
−2Sin
2
ACos
2
A
Sin
2
A+Cos
2
A=1
=
Cos
2
ASin
2
A
1−2Sin
2
ACos
2
A
\begin{lgathered}= \frac{1}{Cos^2A Sin^2A} - 2\\\\= RHS\end{lgathered}
=
Cos
2
ASin
2
A
1
−2
=RHS
LHS=RHS
Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identity
sin²A + cos²A = 1
Consider the left side
[tex]\frac{sin^2A}{cos^2A}[/tex] + [tex]\frac{cos^2A}{sin^2A}[/tex]
= [tex]\frac{sin^2A}{1-sin^2A}[/tex] + [tex]\frac{cos^2A}{1-cos^2A}[/tex]
= [tex]\frac{sin^2A(1-cos^2A)+cos^2A(1-sin^2A)}{(1-sin^2A)(1-cos^2A)\\}[/tex]
= [tex]\frac{sin^2A-sin^2Acos^2A+cos^2A-sin^2Acos^2A}{1-sin^2A-cos^2A+sin^2Acos^2A}[/tex]
= [tex]\frac{sin^2A+cos^2A-2sin^2Acos^2A}{1-(sin^2A+cos^2A)+sin^2Acos^2A}[/tex]
= [tex]\frac{1-2sin^2Acos^2A}{sin^2Acos^2A}[/tex]
= [tex]\frac{1}{sin^2Acos^2A}[/tex] - [tex]\frac{2sin^2Acos^2A}{sin^2Acos^2A}[/tex]
= [tex]\frac{1}{sin^2Acos^2A}[/tex] - 2 = right side ⇒ proven
Please help, I'm stuck
Answer: Option B
[tex]k> 0[/tex]
Step-by-step explanation:
The graph shows a radical function of the form [tex]f(x)=a(x+k)^{\frac{1}{n}}+c[/tex]
Where n is a even number.
This type of function has its vertex at the origin when [tex]k = 0[/tex] and [tex]c = 0[/tex]
If [tex]k> 0[/tex] the graph moves horizontally k units to the left
If [tex]k <0[/tex] the graph moves horizontally k units to the right.
Note that in this case the vertex of the function is horizontally shifted 5 units to the left. Therefore we know that [tex]k = 5> 0[/tex]
The correct answer is option B
Need Help with this. 4(v+4)-7v
Answer:16-3v
Step-by-step explanation:
Take off the brackets by multiplying the terms inside the bracket by 4,
4v+16-7v
Simplify
16-3v
Answer:
16-11v
Step-by-step explanation:
4(v+4)-7v - Question
4v+16-7v - Distribute the 4 with the digits inside the parenthesis
-4v - Subtract 4 from both sides
16 -11v - Answer
To stretch a spring by 2.5 cm from its equilibrium position requires 8J of work what was the maximum force required to stretch it that distance?
•160N
•640N
•800N
•550N
Answer:
640
Step-by-step explanation:
The maximum force required to stretch the spring that distance is 640N. This is calculated by dividing the work done (8J) by the distance (0.025m) to find the force, and then doubling this figure because the maximum force is needed at maximum extension of the spring.
Explanation:In this question, we are asked to find the maximum force required to stretch a spring by a certain amount. The work done on an object, in this case, the spring, is equal to the force applied times the distance over which the force is applied. This is expressed in the formula Work = Force x Distance. We are given that the work done is 8 Joules and the distance is 2.5 cm (or 0.025 m, converting centimeters to meters).
So, to find the force, we re-arrange the formula to be Force = Work/Distance. Plugging in the given values, we find Force = 8J/0.025m = 320N. However, the maximum force required to stretch it that distance happens at the maximum extension of the spring, so we have to double that force (because for a spring, force is linear with displacement until it reaches maximum extension). Hence, the maximum force is 2 x 320N = 640N, thus making the correct option the second one.
Learn more about Spring Force here:https://brainly.com/question/35436312
#SPJ3
What is the value of cosC AB=8 BC=15 CA=17
Answer:
The value of cos C = 15/17
Step-by-step explanation:
* Lets revise the cosine rule
- In Δ ABC
# AB opposite to angle C
# BC opposite to angle A
# AC opposite to angle B
# ∠A between AB and AC
# ∠B between BA and BC
# ∠C between CA and CB
- Cosine rule is:
# AB² = AC² + BC² - 2(AC)(BC) cos∠C
# BC² = AC² + AB² - 2(AC)(AB) cos∠A
# AC² = AB² + BC² - 2(AB)(BC) cos∠B
* Lets solve the problem
∵ AB = 8 units
∵ BC = 15 units
∵ CA = 17 units
∵ AB² = AC² + BC² - 2(AC)(BC) cos∠C
- Add 2(AC)(BC) cos∠C to both sides
∴ AB² + 2(AC)(BC) cos∠C = AC² + BC²
- Subtract AB² from both sides
∴ 2(AC)(BC) cos∠C = AC² + BC² - AB²
- Divide two sides by 2(AC)(BC)
∴ cos∠C = (AC² + BC² - AB²)/2(AC)(BC)
- Substitute the values of AB , BC , AC to find cos∠C
∴ cos∠C = (17)² + (15)² - (8)²/2(17)(15)
∴ cos∠C = (289 + 225 - 64)/510
∴ cos∠C = 450/510 = 15/17
* The value of cos C = 15/17
What is the value of y?
Answer:
Shii ion kno... Ong I don't
*25 BRAINLIEST FOR WHOEVER ANSWERS FIRST*
Lara and Tim took different routes to travel from Point A to Point C. Lara took the route along A, B, and C. Tim took the route along A, E, D, and C. Their routes with distances and times are shown.
A 5 sided figure ABCDE is shown. Point A is labeled Start and Point E is labeled End. AB is 6 miles and 1.5 hours, BC is 2 miles and 1 hour, CD is 6 miles and 1.5 hours, DE is 4 miles and 1.5 hours, and AE is 2 miles and 0.5 hour
Which person's average speed is greater?
Answer:
Lara's average speed :
average speed = total distance / total time
=> 8 miles / 2.5 hours
=> 3.2 mph
Tim's average speed :
= total distance / total time
= 12 miles / 3.5 hours
= 3.43 mph
therefore,
Tim's average speed (3.43 mph) is greater.
After calculating the average speeds for Lara (3.2 mph) and Tim (3.43 mph), it is evident that Tim's average speed is greater than Lara's on their respective routes from Point A to Point C.
Explanation:To answer the question of which person's average speed is greater, we need to calculate the speeds of Lara and Tim on their respective routes from Point A to Point C.
Lara's route from A to B is 6 miles taking 1.5 hours, and from B to C is 2 miles taking 1 hour. To find her average speed, we sum up the distances and times, which gives us 8 miles over 2.5 hours, resulting in:
Average speed of Lara = Total Distance / Total Time = 8 miles / 2.5 hours = 3.2 miles per hour.
Tim's route from A to E is 2 miles taking 0.5 hours, from E to D is 4 miles taking 1.5 hours, and from D to C is 6 miles taking 1.5 hours. Summing Tim's distances and times, we have 12 miles over 3.5 hours, which means:
Average speed of Tim = Total Distance / Total Time = 12 miles / 3.5 hours = 3.43 miles per hour.
Comparing both average speeds, Tim's average speed is greater than Lara's.
Learn more about Average Speed here:https://brainly.com/question/12322912
#SPJ2
Two poles, AB and ED, are fixed to the ground with the help of ropes AC and EC, as shown
What is the approximate distance, in feet, between the two poles?
A. 7.14
B. 7.21
C. 14.35
D. 15.59
Answer:
14.35 ft.
Step-by-step explanation:
We have 2 right-angled triangles so we can apply the Pythagoras theorem to each one:
14^2 = 12^2 + BC^2
BC^2 = 14^2 - 12^2 = 52
BC = √52 = 7.21.
10^2 = 7^2 + CD^2
CD^2 = 100 - 49 = 51
CD = √51 = 7.14.
So the distance between the 2 poles = BC + CD
= 14.35 ft.
The distance between B and D is 14.35 ft if two poles, AB and ED, are fixed to the ground with the help of ropes AC and EC option (C) is correct.
What is a right-angle triangle?It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
From the right angle triangle ABC:
14² = 12² + BC²
BC = √52 = 7.21 feet
In right angle triangle DCE
10² = 7² + CD²
CD = √51 = 7.14 feet
BD = BC + CD = 7.21 + 7.14
BD = 14.35 ft
Thus, the distance between B and D is 14.35 ft if two poles, AB and ED, are fixed to the ground with the help of ropes AC and EC option (C) is correct.
Learn more about the right angle triangle here:
brainly.com/question/3770177
#SPJ2
Which size random sample is likely to provide the most trustworthy results?
a) 50
b) 20
c) 10
d) There is no difference
Apply the distributive property to create an equivalent expression.
\dfrac12(10x + 20y +10z) =
2
1
(10x+20y+10z
Step-by-step explanation:
[tex]\text{The distributive property:}\ a(b+c)=ab+ac\\\\\dfrac{1}{2}(10x+20y+10z)=\dfrac{1}{2\!\!\!\!\diagup_1}\cdot10\!\!\!\!\!\diagup^5x+\dfrac{1}{2\!\!\!\!\diagup_1}\cdot20\!\!\!\!\!\diagup^{10}y+\dfrac{1}{2\!\!\!\!\diagup_1}\cdot10\!\!\!\!\!\diagup^5z\\\\=5x+10y+5z[/tex]
Answer:
5x+10y+5z
Step-by-step explanation:
I did it on Khan Academy :)
An Information Services Manager is purchasing a large number of word processing software licenses at a cost of $125 each. the software company gives a volume discount of 3.5% for large purchases. If the department manager has a budget of $17,300 to purchase the licenses, approximately how many licenses can she purchase.
Answer:
143
Step-by-step explanation:
17300=.965(125X)
17927.46=125X
143.41=X
To calculate the number of software licenses the department manager can purchase, we first find the discounted price of a single license, then divide the total budget by this single license price. In this case, the manager can purchase approximately 143 licenses with a budget of $17,300.
Explanation:The subject of this question is a typical real-life application of Mathematics, specifically in percentages and budgeting. Given the scenario, the Information Services Manager plans to buy word-processing software licenses for each cost of $125. However, a volume discount of 3.5% is offered for large purchases.
Firstly, we need to figure out the discounted price of one license, which can be calculated as 96.5% (100% - the 3.5% discount) of $125, leading to $120.63 approximately (rounding the number to two decimal places).
With a total budget of $17,300, the number of licenses she can purchase can be found by dividing the total budget by the price of a single license after the discount: $ 17,300 divided by $120.63, which gives us approximately 143.
Therefore, the department manager can buy approximately 143 licenses when considering the volume discount.
Learn more about Budgeting and Purchasing here:https://brainly.com/question/34872170
#SPJ3
Which of the following functions gives the length of the base edge, a(V), of a right square pyramid that is 8 inches tall as a function of its volume, v, in cubic inches?
Answer:
s = √(3V/[8 in])
Step-by-step explanation:
Where are "the following functions" that were mentioned in this problem statement? Please share them. Thanks.
The volume of a right square pyramid is V = (1/3)(area of base)(height). In more depth, V = (1/3)(s²)(h). We want to solve this for s.
Multiplying both sides by 3 to eliminate the fractional coefficient, we get:
3V = s²(h), and so s² = 3V/h.
Taking the square root of this, we get:
s = √(3V/h).
Now let's substitute the given numerical value for the height:
s = √(3V/[8 in]). We could also label this as a(V) as is done in the problem statement.
For the function y=x^5+1x^3-30x, find all real zeros.
Answer:
The real zeroes are -√5 , 0 , √5
Step-by-step explanation:
* Lets explain how to solve the problem
- The function is y = x^5 + x³ - 30x
- Zeros of any equation is the values of x when y = 0
- To find the zeroes of the function equate y by zero
∴ x^5 + x³ - 30x = 0
- To solve this equation factorize it
∵ x^5 + x³ - 30x = 0
- There is a common factor x in all the terms of the equation
- Take x as a common factor from each term and divide the terms by x
∴ x(x^5/x + x³/x - 30x/x) = 0
∴ x(x^4 + x² - 30) = 0
- Equate x by 0 and (x^4 + x² - 30) by 0
∴ x = 0
∴ (x^4 + x² - 30) = 0
* Now lets factorize (x^4 + x² - 30)
- Let x² = h and x^4 = h² and replace x by h in the equation
∴ (x^4 + x² - 30) = (h² + h - 30)
∵ (x^4 + x² - 30) = 0
∴ (h² + h - 30) = 0
- Factorize the trinomial into two brackets
- In trinomial h² + h - 30, the last term is negative then the brackets
have different signs ( + )( - )
∵ h² = h × h ⇒ the 1st terms in the two brackets
∵ 30 = 5 × 6 ⇒ the second terms of the brackets
∵ h × 6 = 6h
∵ h × 5 = 5h
∵ 6h - 5h = h ⇒ the middle term in the trinomial, then 6 will be with
(+ ve) and 5 will be with (- ve)
∴ h² + h - 30 = (h + 6)(h - 5)
- Lets find the values of h
∵ h² + h - 30 = 0
∴ (h + 6)(h - 5) = 0
∵ h + 6 = 0 ⇒ subtract 6 from both sides
∴ h = -6
∵ h - 5 = 0 ⇒ add 5 to both sides
∴ h = 5
* Lets replace h by x
∵ h = x²
∴ x² = -6 and x² = 5
∵ x² = -6 has no value (no square root for negative values)
∵ x² = 5 ⇒ take √ for both sides
∴ x = ± √5
- There are three values of x ⇒ x = 0 , x = √5 , x = -√5
∴ The real zeroes are -√5 , 0 , √5
Find a linear equation satisfying the conditions:
x-intercept at (-2,0) and y-intercept at (0, -3).
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 2, 0 ) and (x₂, y₂ ) = (0, - 3)
m = [tex]\frac{-3-0}{0+2}[/tex] = - [tex]\frac{3}{2}[/tex]
Note the line crosses the y- axis at (0, - 3) ⇒ c = - 3
y = - [tex]\frac{3}{2}[/tex] x - 3 ← equation in slope- intercept form
what the slope of the line perpendicular to y=-1/2x+5
Answer:
slope = 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - [tex]\frac{1}{2}[/tex] x + 5 ← is in slope- intercept form
with slope m = - [tex]\frac{1}{2}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{2} }[/tex] = 2
celest
Guided Practice
4. Find the next three terms in the sequence.
etric Sequences
-3, 6, -12, 24, ...
A - 48,96, -1923
hential Growth and
B 48, -96, 192
stest
C -36, 72, -144
mials
mials and Factoring
nic Equations and
Answer:
A - 48,96, -192
Step-by-step explanation:
Given:
geometric sequence:
-3, 6, -12, 24,
geometric sequence has a constant ratio r and is given by
an=a1(r)^(n-1)
where
an=nth term
r=common ratio
n=number of term
a1=first term
In given series:
a1=-3
r= a(n+1)/an
r=6/-3
r=-2
Now computing next term a5
a5=a1(r)^(n-1)
= -3(-2)^(4)
= -48
a6=a1(r)^(n-1)
= -3(-2)^(5)
= 96
a7=a1(r)^(n-1)
= -3(-2)^(9)
= -192
So the sequence now is -3, 6, -12, 24,-48,96,-192
correct option is A!