Answer:
Step-by-step explanation:
Given 3 positive integers x, y and z, if their product is 125, then;
xyz = 125 .......... 1
Sum of the integers S(x, y, z) = x+y+z ........... 2
From equation 1; x = 125/yz ........3
Substitute equation 3 into 2
S(x, y, z) = 125/yz+y+z
Sy = -125/y²z + 1
Sz = -125/z²y + 1
For the sum to be minimum, Sy = Sz = 0
-125/y²z + 1 = 0
-125/y²z = -1
-125 = -y²z
125 = y²z
Also; is Sz = 0
-125/z²y + 1 = 0
-125/z²y = -1
-125 = -z²y
125 = z²y
Hence y²z = z²y = 125
From y²z = 125, z = 125/y²
Substitute z = 125/y² into the equation 125 = z²y
125 = (125/y²)²× y
125 = 125²/y⁴ × y
125 = 125²/y³
1 = 125/y³
y³ = 125.
y = 5
Since 125 = y²z
5²z = 125
25z = 125
z = 5
From the product xyz = 125
x(5)(5) = 125
25x = 125.
x = 5
Hence x = y = z = 5
A rectangle has a perimeter of 60 inches. The length of the rectangle is 3 inches less than twice the width
What is the length of the rectangle?
Answer:
length = 19 units
Step-by-step explanation:
width = x
length = 2x-3
width = 11 units
length = 2(11)-3
length = 22-3
length = 19 units
perimeter = 11 + 11 + 19 + 19 = 60 units
The perimeter of a shape is the sum of the side lengths of the shape. The length of the rectangle is 19 units.
Given that:
[tex]Perimeter = 60[/tex]
[tex]Length = 2 \times Width -3[/tex]
The perimeter of a rectangle is:
[tex]Perimeter = 2 \times (Length + Width)[/tex]
So, we have:
[tex]60= 2 \times (2\times Width - 3+ Width)[/tex]
Divide both sides by 2
[tex]30= 2\times Width - 3+ Width[/tex]
Collect like terms
[tex]3 + 30= 2\times Width + Width[/tex]
[tex]33= 3Width[/tex]
Divide both sides by 3
[tex]11= Width[/tex]
Rewrite as:
[tex]Width = 11[/tex]
Recall that: [tex]Length = 2 \times Width -3[/tex]
[tex]Length = 2 \times 11 - 3[/tex]
[tex]Length = 22- 3[/tex]
[tex]Length = 19[/tex]
Hence, the length of the rectangle is 19 units.
Read more about perimeters at:
https://brainly.com/question/6465134
A pizza stand offers hand-tossed, pan, and thin crust pizza. How many outcomes
are there?
Don't quite understand the question so I'm gonna provide 2 answers
The simplest one being 3
If you're making combinations then 7
hand-tossed(1), thin(2), pan(3), hand-tossed and thin(4), hand-tossed and pan(5), thin and pan(6), all 3(7)
8/2=6/n+4 Solve for n
Answer:
No solution (because the n's cancel out!)
Step-by-step explanation:
Let's solve your equation step-by-step.
8
2
=
6
n
+4
Multiply all terms by n and cancel:
8n
2
=6+4n
4n=4n+6(Simplify both sides of the equation)
4n−4n=4n+6−4n(Subtract 4n from both sides)
0=6
Answer:
No solutions.
Help me with this question plz thx!!
Answer:
9x² - 9y + 9
Step-by-step explanation:
Step 1: Write out expression
3 - 2y - 1 + 5x² - 7y + 7 + 4x²
Step 2: Combine like terms (x²)
9x² + 3 - 2y - 1 - 7y + 7
Step 3: Combine like terms (y)
9x² - 9y + 3 - 1 + 7
Step 4: Combine like terms (constants)
9x² - 9y + 9
What are some methods for finding the distance between points A and B? You can use the pen tool to explore different options on the number line?
Answer:
Ok, the straightforward thing you can do, when you have a number line like in this situation, you can just "count" the number of units that are between A and B.
Now, a more correct way:
First, A is located at the value -3, then we can write:
A = -3.
And B is located at the value 5, then:
B = 5.
Now, the distance between A and B is equivalent to the difference between A and B:
D = B - A = 5 - (-3) = 8
The distance between A and B is 8 units.
someone please help me with this question !!
Find the distance between each pair of points.
Answer: the distance is 9,
Step-by-step explanation: If you count the blocks you will see it's nine! Hope this helped you!
Write g(x) = 4x2 + 88x in vertex form. The function written in vertex form is g(x) = (x +11)2 + .
Answer:
y = 4(x + 11)² - 484
Step-by-step explanation:
y = 4x² + 88x
factor the expression
y = 4(x² + 22x)
complete the square
y + ? = 4(x² + 22x + ?)
y + ? = 4(x² + 22x + 121)
add 4 • 121 to the left side
y + 4 • 121 = 4(x² + 22x + 121)
multiply
y + 484 = 4(x² + 22x + 121)
y + 484 = 4(x + 11)²
subtract both sides by 484
y = 4(x + 11)² - 484
Answer:
y = 4(x + 11)² - 484
Step-by-step explanation:
Plzzzzzzzzzzzzzzzzzzz
Answer:
Complementary
Step-by-step explanation:
Complementary Angles add up to 90°
Supplementary Angles add up to 180°
60 + 30 = 90
14 + (-12)-8-5
FAST PLEASE ALSO PLEASE SHOW THE STEPS!!!
Answer:
-11
Step-by-step explanation:
start with PEMDAS (parenthesis, exponents, multiplication, division, addition, subtraction)
so you would first start with 14 + (-12) so the + and - become a negative so it becomes 14 - 12 which is 2
so then do -8-5 which is -13
so then you combine them and get 2-13 which is -11
16-2v+3 what is the answer pls help
Answer:
the answer is 19-2v combine like terms if not that then try this....
19-2y=0
-2y=-19
Then divide by -2
y=-19/-2
=9.5
there are 16 circles and 20 squares. What is the simplest ratio of circles to total shapes
Answer:
4 : 9
Step-by-step explanation:
Step 1: Find total amount of shapes
16 circles + 20 squares = 36 total shapes
Step 2: Write out ratio of circles to total shapes
16 : 36
Step 3: Simplify by dividing both numbers by 4
16/4 : 36/4
4 : 9
A group of 8 children and 8 adults are going to a movie. Child tickets cost $2, and adult tickets cost $6. How much will the movie tickets cost in all?
Answer:
Hey there!
8(2)+8(6)
16+48=64
The total price is 64 dollars.
Let me know if this helps :)
Does anyone know this? Needed ASAP
Answer:
50 square units
Step-by-step explanation:
Using the formula provided, [tex]a = \frac{1}{2}h(b_1+b_2)[/tex], substituting the height (5), b1 (8) and b2 (12), we can solve for the formula.
[tex]a = \frac{1}{2}\cdot5(8+12)\\\\a = \frac{1}{2}\cdot5(20)\\\\a = \frac{1}{2}100\\\\a = 50[/tex]
Hope this helped!
Answer:
50 units²
Step-by-step explanation:
The area of a trapezoid can be found using the following formula.
[tex]A=\frac{1}{2}h(b_{1} +b_{2} )[/tex]
The height of the trapezoid is 5 units. The bases are 8 units and 12 units.
[tex]h= 5 \\b_{1} = 8\\b_{2} = 12[/tex]
Substitute the values into the formula.
[tex]A=\frac{1}{2}*5(8+12)[/tex]
Solve inside the parentheses. Add 8 and 12.
8+12=20
[tex]A=\frac{1}{2}*5(20)[/tex]
Multiply 5 and 20.
5*20= 100
[tex]A=\frac{1}{2}*100[/tex]
Multiply 1/2 and 100 or divide 100 by 2.
100 * 1/2= 50 or 100/2= 50
[tex]A= 50[/tex]
Add appropriate units. For this problem, the units are units².
[tex]A= 50 units^2[/tex]
The area of the trapezoid is 50 square units.
Add 2 x 2 + 5 x + 6 to − 4 x 2 − x + 7
Add 2 x 2 + 5 x + 6 to − 4 x 2 − x + 7
Add the expressions.
13
Sena determines the remainder of 4x32−14x16+2x3−8x−1, using the remainder theorem. How does she proceed to the correct answer? Drag a value into each box to correctly complete the statements.
The acceleration of an object due to gravity is 32 feet per second. What is acceleration due to gravity in inches per second?
Answer:
384 inches per second.
Step-by-step explanation:
We are given that the acceleration of an object due to gravity is 32 feet per second.
And we want to find the acceleration in inches per second.
The acceleration can be represented as a ratio of 32 feet : second. This can be written as a fraction:
[tex]\displaystyle \frac{32\text{ feet}}{\text{second}}[/tex]
Use dimensional analysis. It is known that there is 12 inches in a feet. So, multiply by 12in/feet:
[tex]\displaystyle = \frac{32\text{ feet}}{\text{second}}\cdot\frac{12\text{ inches}}{\text{feet}}[/tex]
Cancel like units:
[tex]\displaystyle =\frac{32\cdot 12\text{ inches}}{\text{second}}[/tex]
Multiply:
[tex]\displaystyle =\frac{384\text{ inches}}{\text{second}}[/tex]
In conclusion, our answer is 384 inches per second.
Solve the two-step equation.
- 2/3 x - 21/4 = 27/4
Answer:
x = -18
I hope this helps!
Answer:
X- (-18)
Step-by-step explanation:
Hope this helps:)
somebody plz help this is algebra ll I need help fast plz anyone?
Answer:
the answer is A.
Step-by-step explanation:
1800 people attended the National Day dinner in a certain constituency Given that 35.5 of them were. men, 40 % of them were women and the rest were children, find the number of children who attended the dinner
children
25.5 %
so 25.5% of 100
495
Quadrilateral A'B'C'D'A
′
B
′
C
′
D
′
A, prime, B, prime, C, prime, D, prime is the result of translating quadrilateral ABCDABCDA, B, C, D by 555 units to the left and 555 units down.
Answer:
14.2
Step-by-step explanation:
= AB+BC+CD+DA
= 2.2+4.5+6.1+1.4
= 14.2
Answer: 14.2
Step-by-step explanation:
Khan Academy
Find the exact trigonometric ratios for the angle x whose radian measure is given. (If an answer is undefined, enter UNDEFINED.) −7π
Answer:
sin(x) = tan(x) = 0
cos(x) = sec(x) = -1
cot(x) = csc(x) = UNDEFINED
Step-by-step explanation:
An angle of -7π is co-terminal with an angle of π (or 180°). Its trig ratios are ...
sin(x) = tan(x) = 0
cos(x) = sec(x) = -1
cot(x) = csc(x) = UNDEFINED
Solve each of the following equations. Be sure to check your solutions.
3x-5=2.5x+3-(x-4)
Answer: x=8
Step-by-step explanation:
3x - 5= 2.5x + 3 -(x-4) apply the distributive property
3x -5 = 2.5x + 3 - x + 4 combine like terms on the right side
3x - 5 = 1.5x + 7 Add 5 to both sides
+5 +5
3x = 1.5x + 12 subtract 1.5x from both sides
-1.5x -15.x
1.5x = 12 Now divide both sides by 1.5
x = 8
7-(5t - 13)= -12 need help!!!
Answer:
t = 32/5
Step-by-step explanation:
7 - (5t - 13) = -12
7 - (5t - (-13) = -12
7 - 5t + 13 = -12
-5t = -12 - 13 - 7
-5t = -32
t = -32 / -5
t = 32/5
A goniometer may be used to measure the range of motion of a joint. A health professional is measuring the angle of a person's back and elevated leg. The symbol theta is used to represent the angle measurement. In the picture, the angle made by the goniometer is classified as a(n) angle. ° < θ < °
Answer:
Step-by-step explanation:
Answer:
obtuse , 90 , 180 .
Step-by-step explanation:
Evaluate the expression 2(8 − 4)2 − 10 ÷ 2.
Thanks for the help!
Answer:
A
Step-by-step explanation:
So we have the piecewise function:
[tex]f(x)= \begin{cases}\sqrt{2x} & \text{if }x<3 \\2x+10 & \text{if }3\leq x<8\\42&\text{if } x\geq 8\end{cases}[/tex]
And we want to find f(8).
Since our input value is 8, choose the equation that fits our input.
The first equation demand x to be less than 3. 8 is not less than 3, so we won't use that.
The second equation demand x to e greater than or equal to 3 and less than 8. 8 is not less than 8. So, we won't use that.
The third equation demands x to be greater than or equal to 8. 8 is greater than or equal to 8, so we'll use the third equation.
So:
[tex]f(x)=42\text{ if }x\geq 8[/tex]
[tex]f(8)=42[/tex]
There're nothing more to do, we're done :)
The answer is A.
Edit: Improved Format
Identify whether each of the datasets is quantitative or qualitative a. Types of computer software used in a database management system. b. Life-lengths of laser printers c. Brands of calculators used by 100 engineering students on campus d. Mileage attained by 12 automobiles powered by alcohol
Answer:
a. Types of computer software used in a database management system. =Qualitative
b. Life-lengths of laser printers =Quantitative
c. Brands of calculators used by 100 engineering students on campus =Qualitative
d. Mileage attained by 12 automobiles powered by alcohol= Quantitative
Step-by-step explanation:
Data is described as quantitative when it deals with numeric values whereas qualitative data is categorical in nature. Quantitative data tells us how much, how many, or the frequency of occurrence of certain variables. Qualitative data provides answers to the what, why, which, and where questions.
1. Types of computer software are not numeric variables as they answer the 'what' question.
2. Length deals with numbers, so the life-lengths of laser printers is a quantitative variable.
3. Brands of calculators are categorical data and are thus qualitative.
4. Mileage is a numerical variable and is thus quantitative.
(1 point) Find the volume of the parallelepiped with one vertex at (4,2,4), and adjacent vertices at (6,3,8), (6,1,10), and (0,6,3)
Answer:
8 cubic units
Step-by-step explanation:
Let he vertices of the parallelepiped be A = (4,2,4), B= (6,3,8), C = (6,1,10) and D = (0,6,3)
The edges of the parallelepiped are
AB = (6,3,8) - (4,2,4) = (2,1,4)
AC = (6,1,10) - (4,2,4) = (2,-1,6)
AD = (0,6,3) - (4,2,4) = (-4,4,-1)
Therefore the volume of the parallelopiped is = |[AB,AC,AD]|
= [tex]$ \begin{vmatrix}\ 2\ \ \ 1\ \ \ \ 4\ \\2\ -1\ \ \ 6 \\-4\ \ \ 4\ -1 \end{vmatrix}$[/tex]
= |2(1-24)+1(-2+24)+4(8-4)|
= |2(-23) + 1(22) + 4(4)|
= |8|
=8 cubic units
For each of the following questions, solve for the unknown quantity by rearranging the given equation.For numerical answers, make sure to express all answers in scientific notation with the proper number ofsignificant figures. Be careful to write out all units and convert if necessary.a. F=GMm/r^2a. M =b. r =b. M=kxa^3/p^2a. P =b. a =
Answer:
a. F=GMm/r^2; a. M =
[tex]M = \frac{Fr^{2} }{Gm}[/tex]
a. F=GMm/r^2; b. r =
[tex]r = \sqrt{\frac{GMm}{F} \\}[/tex]
b. M=kxa^3/p^2; a. P =
[tex]p = \sqrt{\frac{kxa^{3}}{M}}[/tex]
b. M=kxa^3/p^2; b. a =
[tex]a = \sqrt[3]{\frac{Mp^{2}}{kx} }[/tex]
Step-by-step explanation:
For a. F=GMm/r^2; a. M =
To solve for M, we will rearrange the given equation F=GMm/r^2 such that M is the subject of the formula
From
F=GMm/r^2
[tex]F = \frac{GMm}{r^{2} }[/tex]
First, Cross multiplication, we then get
[tex]Fr^{2} = GMm[/tex]
Now, divide both sides by [tex]Gm[/tex]
[tex]\frac{Fr^{2} }{Gm} = \frac{GMm}{Gm} \\[/tex]
The equation becomes
[tex]\frac{Fr^{2} }{Gm} = M[/tex]
∴ [tex]M = \frac{Fr^{2} }{Gm}[/tex]
For a. F=GMm/r^2; b. r =
Also, to solve for r, we will rearrange the given equation F=GMm/r^2 such that r is the subject of the formula
From
F=GMm/r^2
[tex]F = \frac{GMm}{r^{2} }[/tex]
First, Cross multiplication, we then get
[tex]Fr^{2} = GMm[/tex]
Now, divide both sides by [tex]F[/tex], Such that we have
[tex]\frac{Fr^{2} }{F} = \frac{GMm}{F} \\[/tex]
Then, [tex]r^{2} = \frac{GMm}{F} \\[/tex]
∴ [tex]r = \sqrt{\frac{GMm}{F} \\}[/tex]
For b. M=kxa^3/p^2; a. P =
To solve for P, we will rearrange the given equation M=kxa^3/p^2 such that P becomes the subject of the formula
From
M=kxa^3/p^2
[tex]M = \frac{kxa^{3}}{p^{2} } \\[/tex]
First, Cross multiply, we then get
[tex]Mp^{2} = kxa^{3}[/tex]
Divide both sides by [tex]M[/tex], such that the equation becomes
[tex]\frac{Mp^{2} }{M} = \frac{kxa^{3}}{M}[/tex]
Then, [tex]p^{2} = \frac{kxa^{3}}{M}[/tex]
∴ [tex]p = \sqrt{\frac{kxa^{3}}{M}}[/tex]
For b. M=kxa^3/p^2; b. a =
To solve for a, we will rearrange the given equation M=kxa^3/p^2 such that a becomes the subject of the formula
From
M=kxa^3/p^2
[tex]M = \frac{kxa^{3}}{p^{2} } \\[/tex]
First, Cross multiply, we then get
[tex]Mp^{2} = kxa^{3}[/tex]
Now, Divide both sides by [tex]kx[/tex], such that the equation gives
[tex]\frac{Mp^{2}}{kx} = \frac{ kxa^{3}}{kx}[/tex]
Then, [tex]\frac{Mp^{2}}{kx} = a^{3}[/tex]
[tex]a^{3} = \frac{Mp^{2}}{kx}[/tex]
∴ [tex]a = \sqrt[3]{\frac{Mp^{2}}{kx} }[/tex]