Answer:
3.2
Step-by-step explanation:
Any number raised to the zero power is one. 3.2 x 1 = 3.2
a wire of length 38 m is divided into two pieces and each piece is bent into a square. how should this be done in order to minimize the sum of the areas of the two squares? (give your answer in the form of a comma separated list of the lengths of the two pieces.)
The lengths of the two pieces of a wire will be 19,19.
Define square.A square is a closed, two-dimensional object with four equal sides and four vertices. On either side, it has parallel sides.
The square of a square's side determines its area.
Given data -
Length of a wire = 38 m
As the wire is divided into two pieces,
Let the length of two pieces of wire be x and y m respectively.
As per given data, x + y = 38
Therefore, y = 38 - x
As each piece is bent into a square, area of squares will be
[tex](x/4)^{2}[/tex] and [tex](y/4)^{2}[/tex]
Therefore, the sum of areas of two squares will be A = [tex](x/4)^{2}[/tex] + [tex](y/4)^{2}[/tex]
A = [tex]x^{2}[/tex]/16 + [tex]y^{2}[/tex]/16
A = [tex]x^{2}[/tex]/16 + [tex](38-x)^{2}[/tex]/16
By differentiating, we will get
A' = [tex]\frac{2x}{16}[/tex] - [tex]\frac{2(38-x)}{16}[/tex]
In order to minimize the the sum of the areas of the two squares, we will take A' = 0
0 = x - (38 - x)
2x = 38
x = 19
Therefore y = 19
The length of two pieces of a wire should be 19 m each.
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Find the LCM of 6, 24 and 32
Answer:
96
Step-by-step explanation:
Write an expression equivalent to \frac{9^5}{9^3} in the form of b^n.
The expression that is equivalent to \frac{9^5}{9^3} is 9^2.
What is an expression?It should be noted that an expression is simply used to shoe the relationship between the variables that are illustrated.
In this case the given expression is 9^5 / 9^3. It should be noted that when dividing powers, we have to subtract them. Therefore, 5 - 3 = 2.
The value will be:
= 9^5 / 9^3
9^2
The expression is 9^2.
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Sam counted 12 liters of hand sanitizer in the storage cabinet . He fills the seven of the examination rooms as follows : 350 mL , 600 mL , 475 mL, 580 720 , and 500 mL .a)How many total milliliters did sam use to fill the dispensers?B) After filling the dispensers, how many liters of sanitizer remain in the storage cabinet?
a) To know the total millilites that sam use to fil the dispenser, we will have to add all the seven amount filled as shown;
Total (in milliliters) = 350 mL + 600 mL + 475 mL + 580mL + 720mL + 500 mL
Total (in milliliters) = 3225mL
Hence the total milliliters that sam use to fill the dispensers is 3225millilitres
b) The amount liters of sanitizer remaining will be 12litres - 3225mL
Convert 3225mL to litres
3225mL = 3225/1000 Litres
3225mL = 3.225litres
The amount liters of sanitizer remaining = 12 - 3.225
The amount liters of sanitizer remaining = 8.775litres
Which is more 15% or 1/4
Answer: 1/4 is more
Step-by-step explanation:
1/4=25%
25%>15%
1/4>15%
1/4 is more than 15%
◄) Add.
8/11+6/11+6/11+7/15
Answer:
[tex]\frac{377}{165}[/tex] or 2 [tex]\frac{47}{165}[/tex]
Step-by-step explanation:
Find the slope of the line that contains the given point
Answer:
(2, 1) and (4, 2): [tex]\frac{1}{2}[/tex]
(-4, 5) and (-3, -7): [tex]-12[/tex]
Step-by-step explanation:
Hello! Let's help you with that problem there!
So we know that in a slope intercept form, it is depicted as [tex]y=mx+b[/tex]. There are two ways to essentially find m, which is slope in this case. The first method is the [tex]\frac{rise}{run}[/tex] method. This is typically used when you have a graph to look off from and it's just a matter of counting the displacement from one point to another.
However, there is another way to find the slope given 2 points and that is what we are going to do here, since we have no graph to reference and have all the relevant information to find the slope using this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
With this formula, we can plug in the coordinate values and solve for the slope!
(2, 1) and (4, 2):
[tex]m=\frac{2-1}{4-2}[/tex]
[tex]m=\frac{1}{2}[/tex]
Therefore, the slope of these points is [tex]m=\frac{1}{2}[/tex]
(-4, 5) and (-3, -7):
[tex]m=\frac{-7-5}{-3-(-4)}[/tex]
[tex]m=\frac{-12}{1}[/tex]
[tex]m=-12[/tex]
Therefore, the slope of these points is [tex]m=\frac{-12}{1}[/tex] or [tex]m=-12[/tex]
A pet store clerk suggested 4 small fish for a 5-gallon fish tank. What size tank would be suggested to hold 60 small fish?
12-gallon tank
48-gallon tank
75-gallon tank
240-gallon tank
The size of the tank would be suggested to hold 60 small fish is 75 gallon-tank option (C) is 75 gallon-tank.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.
It is given that:
A pet store clerk suggested 4 small fish for a 5-gallon fish tank.
4 small fish = 5-gallon
60 small fish = x gallon
x = (5)(60)/4
x = 75 gallon-tank
Thus, the size of the tank would be suggested to hold 60 small fish is 75 gallon-tank option (C) is 75 gallon-tank.
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How many toys would Patricia build in 10 hours if she built 5 toys
every 6 minutes?
Answer:
500
Step-by-step explanation:
she can build 5 in 6 minutes. 6 × 10 is 1 hour
so you would do 5 × 10 = 50
then multiply 50 × 10 hours = 500 toys
Answer:
Patricia will build 500 toys in 10 hours
Step-by-step explanation:
5 toys ? toys
--------- = ----------
6 minutes 10 hours
so we would turn the hours into minutes which would be
600 minutes.
5 toys ? toys
--------- = ----------
6 minutes 600 mins
Then we would cross multiply and that will give us how many toys she can build in 10 hours, which is 500 toys.
What is the area of a triangle whose vertices are R(3, 4), S(6, 2), and T(7, 10)?
Enter your answer in the box.
[ ] units²
The area of the triangle is 13 square units.
We are given the coordinates of the vertices of a triangle.The coordinates of the vertices of the triangle are R(3, 4), S(6, 2), and T(7, 10).We need to find the area of the triangle.We know the coordinates of all the vertices.We will use the formula in coordinate geometry.Let the area of the triangle be "A".The equation can be written as given below :A = (1/2)[x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)]A = (1/2)[3(2 - 10) + 6(10 - 4) + 7(4 - 2)]A = (1/2)[3(-8) + 6(6) + 7(2)]A = (1/2)[-24 + 36 + 14]A = (1/2)(26)A = 13The area of the triangle is 13 square units.To learn more about equations, visit :
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Please please help! :)
Answer:
∠ 2 = 140°
Step-by-step explanation:
the left base angle in the triangle and 110° are a linear pair and sum to 180°
base angle + 110° = 180° ( subtract 110° from both sides )
base angle = 70°
the 2 sides of the triangle are congruent so Δ is isosceles with base angles congruent.
the vertex of the Δ is then
(180 - 70 - 70)° = 180° - 140° = 40°
the vertex and ∠ 2 are a linear pair and sum to 180° , that is
∠ 2 + 40° = 180° ( subtract 40° from both sides )
∠ 2 = 140°
24 students in a class took an algebra test
If 18 students passed the test, what percent passed
Answer:
only 75% of the class or students passed the algebra test
Answer: 75%
Step-by-step explanation: The equation for percentages is: part = percent • whole.
We can use our given values and plug them into the equation to solve for our percent.
In this problem, the “part” is 18, and our “whole” is 24, since the whole class has 24 people, and part of the class (18) passed.
P = % • W
18 = % • 24
(to solve for %, we have to get isolate it, or get rid of the • 24. We use division, the opposite operation, to cancel our • 24.)
18 = % • 24
÷24 ÷24
0.75 = %
Since percents are out of 100, we have to multiply 0.75 by 100.
0.75 • 100 = 75%
I hope this helped!
Michael is going on a 3150 mile drive. He needs to stop for gas every 320 miles. How many times will he need to stop?
Is this a valid argument?
Given: If two points lie on the same plane, then they are coplanar.
Points X and Y both lie on plane R.
Conclusion: Points X and Y are coplanar.
Yes, this is a valid argument. This argument uses the Law of Detachment.
What is the Law of Detachment in logic?The Law of Detachment states that if the hypothesis of a true conditional statement is true, then the conclusion must be true as well. The Law of Detachment is the most often employed deductive reasoning theory.
Given:
Points X and Y both lie on plane R.
Conclusion: Points X and Y are coplanar.
The argument is true because,
The term "coplanar" refers to "being on the same plane." Coplanar points are points that are on the same plane. A group of points in space is said to be coplanar if there is a geometric plane that contains all of them.
Hence, the Conclusion is Points X and Y are coplanar.
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8. the floor of a rectangular meeting room has raised platform that is the same length as the room. the whole room has an area of 46 14/15, ( 7 1 /3 yards )
Part B Suppose there are of the platform is 7 34/45 square yards. what fraction of the entire floor is the raised platform. P.s make sure to show your work
Answer:The width of the room is .
Step-by-step explanation:
Consider the provided information.
It is given that the whole room has an area 46 14/15 sq yd.
This can be written as:
yd.
Now consider the figure shown below:
From the figure we know that the length of the rectangular meeting room is yd.
The area of rectangle is
Let width of the rectangle is w yard.
Hence, the width of the room is .
active attachment
Step-by-step explanation:
The width of the room is .
Step-by-step explanation:
Consider the provided information.
It is given that the whole room has an area 46 14/15 sq yd.
This can be written as:
yd.
Now consider the figure shown below:
From the figure we know that the length of the rectangular meeting room is yd.
The area of rectangle is
Let width of the rectangle is w yard.
Hence, the width of the room is .
active attachment
is 0.49 a rational or irrational number?
(please explain how you know this)
Answer:
Rational
Step-by-step explanation:
there are very few irrational numbers, such as
[tex] \sqrt{2} [/tex]
or π
most of irrational numbers have a lot of decimal digits. And also numbers with 2 decimal digits are all rational because you can write them as
[tex] \frac{49}{100} [/tex]
Graph the line with slope -3/4 and y-intercept 9.
The equation of the line with slope -3/4 and y intercept 9 is y=-3/4x+9.
Based on the conditions formulate:
m=-3/4
and b = 9
Write the equation of the linear function:
y=mx+b
substitute m=-3/4 and b=9 into y=mx+b:
y = -3/4x+9
A line's equation must be in the Slope-Intercept Form, y = mx + b, in order to be graphed using its slope and y-intercept.
This format makes it simple to read off the slope and y-intercept values. The y-intercept is the constant term b, whereas the slope is just the m coefficient of the variable x.
plot the y intercept (0,9) in the xy axis.
Use the slope to locate a different point beginning at the y-intercept. The direction you travel from one point to another is contained in the slope.
Hence the required graph is plotted.
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Claire drove 204 miles in 4 hours. If she continued at the same rate, how far would she travel in 13 hours?
Answer:
15 hours
Step-by-step explanation:Easy math
Answer:
663
Step-by-step explanation:
Good luck on this
What is The sum of two consecutive even integers divided by four is 1895
Answer:
I don't understand what the question is asking, so just see if you can get something from what I wrote below.
Step-by-step explanation:
Call the first number x and the next one x+2.
(x+ (x+2))/4 = 1895
Multiply by 4 on both sides...
x+(x+2) = 7580
Simplify on the left side...
2x+2 = 7580
2x = 7578
Divide by 2...
x = 3,789
x+2 = 3791
Nerissa has 5 pink bows, 1 blue bow, and 4 purple bows in a box. She will randomly choose 1 bow from the box.
What is the probability Nerissa will choose a purple bow?
1/2
2/5
1/10
3/5
Answer: 2/5 is
Step-by-step explanation: 2/5 is equal to 40% and there is 10 bows
Pls, Help Right Now For 10!!!!!!!
Answer:
9
01000101010101010101011101010110110101011010
10101010101010110101101010101011011001010101
10101010100101010101010101101101101010101010
What is a x? Show your work
Answer:
a value that is not yet shown
Step-by-step explanation:
Mark me as branlist to help
Determined whether the relation is a function. If it is not a function, circle the ordered pairs that cause it not to be a function.
To be a function, each input can only go to one output
A. The input 1 goes to two different output values
(1,6) (1,7) causes it not to be a function
B. This is a function. Each input has only one output value
C. The input 0 goes to two different output values
(0,-5) snf (0,4) causes it not to be a function
Directions: Write the slope form of the equation with the given information.
13) through (3,4) and (5,-2)
Answer:
y=-3x+13
Step-by-step explanation:
step one you will need to find the slope by the Y2 minus y1 all over x2 minus X1 formula. so you would have -2 - 4 all over 5 - 3 . you will get -6 over 2 which is equal to -3 . that means that -3 is the slope .
Step 2 you can find the equation with the point slope form formula . the point slope form formula is y-y1=m(x-x1). by substituting your values into these equation you can find the equation of this line . you can substitute any point into it as long as it is on the line . let's use (3,4) where 3=x1 and 4=y1.
step 3. simplify. you will get y-4=-3(x-3). keep in mind I substituted -3 into the equation because -3 is the slope.
you can simplify this if you want to . you will get y=-3(x-3)+4. it becomes through foiling, y=-3x+9+4. it simplifies to y=-3x+13.
in a sale , normal prices are reduced by 17%. the normal price of a washing machine is reduced by £42.50. work out the sales price of the washing machine
The sales price of washing machine is 250.
What is sales price?The price at which something sells or is offered for sale after having its price lowered is known as sales price.
A sale price is the reduced cost at which goods or services are offered for sale. Typically, this price is provided for a brief period of time in an effort to boost sales during a slow period or get rid of extra inventory.
The promotional price is indicated as a percentage off of the standard list price.
Let x be the sales price of washing machine, then as per given
17% of x = 42.5
(17/100) * x =42.5
x = 250
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izzes
The radius of a circle is 4 centimeters. What is the area of a sector bounded by a 45° arc?
45⁰
The area of the sector is 6.28 cm².
What is a sector?A sector is referred to as a component of a circle made up of the circle's arc and its two radii. It is a section of the circle made up of the arc's circumference and the radii of the circle at its ends. A slice of pizza or a pie can be used as an analogy for the shape of a circle's sector.So, the area of the sector:
The formula for the area of the sector: θ/360 πr²Where θ is 45° and r is 4cm.Now, substitute the values in the formula as follows:
θ/360 πr²45/360 π4²1/8 π16π2(Let π be 3.14)
π2 = 6.28Therefore, the area of the sector is 6.28 cm².
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Aislinn bought a new car. After 8 months, the odometer read 14,010 miles. How many miles did
Aislinn average per month on her car?
OA. Aislinn drove an average of 876 miles per month.
OB. Aislinn drove an average of 1,168 miles per month.
OC. Aislinn drove an average of 1,401 miles per month.
D. Aislinn drove an average of 1,751 miles per month.
When
out their o
19 milon
4
if their
d) Aislinn's average per month on her car is 1,751 miles per month.
How to find the average speed?The average speed is calculated by dividing the total distance traveled by the total time it took to travel that distance. Speed is the rate at which something moves at any given time.
Average speed is the average rate of speed over the course of a journey. Velocity exists as the directional speed of a moving object as an indication of its rate of change in position as observed from a specific frame of reference and measured by a specific time standard.
Given,
After 8 months, the odometer read 14,010 miles.
Solution:
t = 8,
d = 14,010 miles,
s = ?
s = d/t
s = 14,010/8
s = 1751 miles/month.
Aislinn drove an average of 1,751 miles per month.
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Victoria is studying the population of the town of Oak Hills for a class project. Based on census data, she found that the equation p = 660n + 14,400 can be used to estimate the population, p, of Oak Hills n years after the year 1900. What will be the estimated population of Oak Hills in the year 2100?
A. 3,012,000
B. 146,400
C. 15,300
D. 132,000
Answer:
Step-by-step explanation:
2100 - 1900 = 200
660(200) + 14,400
p = 146400
146,400 people
The answer is B
Look at the pic tell me what’s correct
Answer:
B
Step-by-step explanation:
V = 27(0.8)^1
V = 21.6
V = 27(0.8)^2
V = 17.28
And more
show me the standard algorithm for 546 divided by 13
The value of the quotient expression 546 ÷ 13 is 42
How to evaluate the expressions?The expression is given as
546 divided by 13
Rewrite the expression as
546 ÷ 13
By the standard algorithm, we have
The expression can be solved using a calculator and with the use of standard algorithm i.e. partial decomposition
By the rule of partial decomposition, we have
a ÷ b = (c ÷ d) ÷ b
Where
a = c + d
Next, we expand the expression as follows:
546 ÷ 13 = (520 + 26) ÷ 13
Remove the brackets
So, we have
546 ÷ 13 = 520 ÷ 13 + 26 ÷ 13
Evaluate the quotients
So, we have
546 ÷ 13 = 40 + 2
Evaluate the sum
So, we have
546 ÷ 13 = 42
Hence, the solution of 546 ÷ 13 is 42
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