A regular hexagon has sides of 5 feet. What is the area of the hexagon? 12.5 ft 2 37.5 ft 2 25 ft 2 50 ft 2
Answer: [tex]37.5\sqrt{3}[/tex]
This value is exact. We can write this as 37.5*sqrt(3)
This approximates to roughly 64.9519
The units for the area are in square feet.
==========================================
Explanation:
Split the regular hexagon into 6 identical equilateral triangles.
Each equilateral triangle has side length x = 5 ft.
The exact area of one of the equilateral triangles is
A = 0.25*sqrt(3)*x^2
A = 0.25*sqrt(3)*5^2
A = 0.25*sqrt(3)*25
A = 0.25*25*sqrt(3)
A = 6.25*sqrt(3)
Multiply this by 6 to get the exact area of the regular hexagon.
6*A = 6*6.25*sqrt(3) = 37.5*sqrt(3) which is the exact area in terms of radicals or square roots.
If your teacher meant to say choice B is 37.5*sqrt(3), then that would be the final answer. If your teacher only said 37.5 without the sqrt(3) term, then there's a typo.
Help me or ill fail plz
Answer:
1,108 in²
Step-by-step explanation:
SA = (12×20) + (2×20×5 + 2×12×5) + (2×½×12×9)
+ (2×20×11)
= 240+320+108+440
= 1,108 in²
True or false: If you are changing a larger unit into a smaller unit, like cm into mm, the decimal is moved to the right because you are multiplying by a power of ten
Answer:true
Step-by-step explanation:
i dont know
write the following numbers in scientific notation. 0.0009. 12. 1000. 0.03. 1.12. 120
Answer:
Step-by-step explanation:
Take the first real number and keep a decimal point to the right of it. Write the number after it.
Put a multiplication symbol and then 10.
Now count the number places to the right of the first real number and the number of place will be the power of 10.
If , number of place are before the first real number, then the power of 10 will be negative.
0.0009 = 9 * 10⁻⁴
12 = 1.2 *10
1000 = 1* 10³
0.03 = 3 *10⁻²
120 = 1.2 * 10²
1.12 = 1.12 *10⁰
Could you help me and answer a couple questions for me?
Answer:
I think no. D is the answer
Question 9 of 10
What is the area of the polygon given below?
3
3
19
14
2
12
Answer:
Please could you add an image, maybe I could answer then
Step-by-step explanation:
271 unit² is the area of the polygon. The correct option is option B among all the given options.
What is area?The size of a patch on a surface is determined by its area. Surface area is defined as the circumference of an open surface or indeed the boundaries of a three-dimensional object, whereas the area of a plane region and plane area relates to the area of a form or planar lamina.
Area can be interpreted as the quantity of material with such a specific thickness required to create a replica of the shape or as the quantity of paint required to completely cover a surface in a single coat. This is the two-dimensional equivalent of the volume of a solid or the length of a curve.
The area is the sum of 3 rectangles are:
First 12 × 19 = 228
Second 3 × 3 = 9
Third 2 × 17 = 34
total area = 228 + 34 + 9 = 271 unit²
Therefore, 271 unit² is the area of the polygon. The correct option is option B.
To know more about area, here:
https://brainly.com/question/12187609
#SPJ7
Your question is incomplete but most probably your full question was,
What is the area of the polygon given below
Solve the system by substitution.
y + 4 = x
10x + 2y = 16
Answer:
(2, -2)Step-by-step explanation:
Given system:
y + 4 = x 10x + 2y = 16Substitute x into the second equation:
10(y + 4) + 2y = 1610y + 40 + 2y = 1612y = -24y = -2Find x:
x = -2 + 4x = 2Answer:
x = 2 and y = -2
Step-by-step explanation:
Given system :-
y + 4 = x
10x + 2y = 16
Solve the system by substitution:-
Let,
y + 4 = x ...(1)
10x + 2y = 16 ...(2)
Solve for y;
Substitute y + 4 as x in the eq.(2)
10( y + 4 ) + 2y = 16
Distribute 10.10y + 40 + 2y = 16
Combine like terms.12y + 40 = 16
Move constant to the right-hand side and change their sign.12y = 16 - 40
Subtract 16 from -40.12y = -24
Divide both side by 12.12y / 12 = -24/12
Hence, y = -2
Solve for x.
Substitute the value of y in eq.(1)-2 + 4 = x
Add -2 and 4.Hence, 2 = x
For any number n>1, is
|(.5 +.2i)^n|
A. greater than 1?
B. less than 1?
C. equal to 1?
PLZ HELP
Answer:
B. Less than 1
Step-by-step explanation:
You could plug in values of n greater than 1 and see what happens....
Example n=2 gives |(.5+.2i)^2|
Simplifying inside gives |(.5)^2+2(.5)(.2i)+(.2i)^2|
=|.25+.2i+.04i^2|=|.25+.2i-.04|=|.21+.2i|.
Applying the absolute value part gives sqrt(.21^2+.2^2)=sqrt(.0441+.04)=sqrt(.0841)=.29
This value is less than 1.
We should also be able to do the absolute value first then the power.
|.5+.2i|=sqrt(.25+.04)=sqrt(.29)
So |.5+.2i|^2=.29 which is what we got long way around.
Anyways (sqrt(.29))^n where n is greater than 1 will result in a number greater than 0 but less than 1.
Which System of inequalities has this graph as its solution?
A. y<2x-3
y<1/3x+4
B. y>2x-3
y>1/3x+4
C. y>2x-3
y<1/3x+4
D. y<2x-3
y>1/3x+4
Answer: B
Step-by-step explanation:
The line [tex]y=2x+3[/tex] is dotted and shaded above.
Eliminate A and D.Similarly, the line [tex]y=\frac{1}{3}x+4[/tex] is also shaded above.
Eliminate C.This leaves B as the correct answer.
Solve the formula for t
Answer:
Step-by-step explanation:
S - 4πc^2 = 6πct
t = (S - 4πc^2)/6πc
t = S/(6πc) - 2/3 c
assuming c ≠ 0
Emily drove to town with an average speed of 32 miles per hour, and then back home with an average speed of 38 miles per hour. If her total traveling time was 42 minutes, how far is it from home to town?
Answer:
12.16 milesStep-by-step explanation:
Speed - s, Distance - d, Time - t
Equation of time is:
t = d/sGiven,
s1 = 32 m/h, s2 = 38 m/h, t1 + t2 = 42 min = 42/60 h = 7/10 hTotal time is the sum of time values to and from the town:
d/32 + d/38 = 7/10d/16 + d/19 = 7/5d(1/16 + 1/19) = 7/5d(16 + 19) = 7(16*19)/535d = 425.6d = 425.6/35d = 12.16It is given that,
→ s1= 32 miles/h
→ s2 = 38 miles/h
Now t1 + t2 is,
→ 42 min
→ 42/60 hours
→ 7/10 hours
The formula we use,
→ Time = Distance/Speed
→ t = d/s
Then the total time is the,
Sum of time values to and from the town.
→ d/32 + d/38 = 7/10
→ d/16 + d/19 = 7/5
→ d{(1/16) + (1/19)} = 7/5
→ d(16 + 19) = (7/5) × (16 × 19)
→ 35d = 425.6
→ d = 425.6/35
→ d = 12.16
Hence, the distance is 12.16 miles.
One number is 2/3 of another number. The sum of the two numbers is 40. Find
the two numbers.
Answer:
5353454
Step-by-step explanation:
Answer: 16 and 24
Step-by-step explanation:
2x+3x= 40
5x = 40
x=8
that means 2x8 equal 16 and 3x8 equals 24 which leads us to the answer
Find dy/dx of the function y = √x sec*-1 (√x)
Hi there!
[tex]\large\boxed{\frac{dy}{dx} = \frac{1}{2\sqrt{x}}sec^{-1}(\sqrt{x}) + \frac{1}{2|\sqrt{x}|\sqrt{{x} - 1}}}[/tex]
[tex]y = \sqrt{x} * sec^{-1}(-\sqrt{x}})[/tex]
Use the chain rule and multiplication rules to solve:
g(x) * f(x) = f'(x)g(x) + g'(x)f(x)
g(f(x)) = g'(f(x)) * 'f(x))
Thus:
f(x) = √x
g(x) = sec⁻¹ (√x)
[tex]\frac{dy}{dx} = \frac{1}{2\sqrt{x}}sec^{-1}(\sqrt{x}) + \sqrt{x} * \frac{1}{\sqrt{x}\sqrt{\sqrt{x}^{2} - 1}} * \frac{1}{2\sqrt{x}}[/tex]
Simplify:
[tex]\frac{dy}{dx} = \frac{1}{2\sqrt{x}}sec^{-1}(\sqrt{x}) + \sqrt{x} * \frac{1}{2|x|\sqrt{{x} - 1}}[/tex]
[tex]\frac{dy}{dx} = \frac{1}{2\sqrt{x}}sec^{-1}(\sqrt{x}) + \frac{1}{2|\sqrt{x}|\sqrt{{x} - 1}}[/tex]
Answer:
[tex]\displaystyle y' = \frac{arcsec(\sqrt{x})}{2\sqrt{x}} + \frac{1}{2|\sqrt{x}|\sqrt{x - 1}}[/tex]
General Formulas and Concepts:
Algebra I
Exponential Rule [Rewrite]: [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex]Exponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Calculus
Derivatives
Derivative Notation
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Arctrig Derivative: [tex]\displaystyle \frac{d}{dx}[arcsec(u)] = \frac{u'}{|u|\sqrt{u^2 - 1}}[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = \sqrt{x}sec^{-1}(\sqrt{x})[/tex]
Step 2: Differentiate
Rewrite: [tex]\displaystyle y = \sqrt{x}arcsec(\sqrt{x})[/tex]Product Rule: [tex]\displaystyle y' = \frac{d}{dx}[\sqrt{x}]arcsec(\sqrt{x}) + \sqrt{x}\frac{d}{dx}[arcsec(\sqrt{x})][/tex]Chain Rule: [tex]\displaystyle y' = \frac{d}{dx}[\sqrt{x}]arcsec(\sqrt{x}) + \bigg[ \sqrt{x}\frac{d}{dx}[arcsec(\sqrt{x})] \cdot \frac{d}{dx}[\sqrt{x}] \bigg][/tex]Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle y' = \frac{d}{dx}[x^\bigg{\frac{1}{2}}]arcsec(\sqrt{x}) + \bigg[ \sqrt{x}\frac{d}{dx}[arcsec(\sqrt{x})] \cdot \frac{d}{dx}[x^\bigg{\frac{1}{2}}] \bigg][/tex]Basic Power Rule: [tex]\displaystyle y' = \frac{1}{2}x^\bigg{\frac{1}{2} - 1}arcsec(\sqrt{x}) + \bigg[ \sqrt{x}\frac{d}{dx}[arcsec(\sqrt{x})] \cdot \frac{1}{2}x^\bigg{\frac{1}{2} - 1} \bigg][/tex]Simplify: [tex]\displaystyle y' = \frac{1}{2}x^\bigg{\frac{-1}{2}}arcsec(\sqrt{x}) + \bigg[ \sqrt{x}\frac{d}{dx}[arcsec(\sqrt{x})] \cdot \frac{1}{2}x^\bigg{\frac{-1}{2}} \bigg][/tex]Rewrite [Exponential Rule - Rewrite]: [tex]\displaystyle y' = \frac{1}{2x^\bigg{\frac{1}{2}}}arcsec(\sqrt{x}) + \bigg[ \sqrt{x}\frac{d}{dx}[arcsec(\sqrt{x})] \cdot \frac{1}{2x^\bigg{\frac{1}{2}}} \bigg][/tex]Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle y' = \frac{1}{2\sqrt{x}}arcsec(\sqrt{x}) + \bigg[ \sqrt{x}\frac{d}{dx}[arcsec(\sqrt{x})] \cdot \frac{1}{2\sqrt{x}} \bigg][/tex]Arctrig Derivative: [tex]\displaystyle y' = \frac{1}{2\sqrt{x}}arcsec(\sqrt{x}) + \bigg[ \sqrt{x}\frac{1}{|\sqrt{x}|\sqrt{(\sqrt{x})^2 - 1}} \cdot \frac{1}{2\sqrt{x}} \bigg][/tex]Simplify: [tex]\displaystyle y' = \frac{arcsec(\sqrt{x})}{2\sqrt{x}} + \frac{1}{2|\sqrt{x}|\sqrt{x - 1}}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
Roulette is a casino game that involves spinning a ball on a wheel that is marked with numbered squares that are red, black, or green. Half of the numbers 1 - 36 are colored red and half are black and the numbers 0 and 00 are green. Each number occurs only once on the wheel. What is the probability of landing on an even number and a number greater than 17? (A number is even if it is divisible by 2. 0 and 00 are considered even as well.)
Answer:
the wording (punctuation) of the question can lead to different interpretations....
I assume that the question was >17 & even which is "5/19",
BUT... it can also be read as two questions
first >17 which is "10/19"
and second an even number which is "9/19"
BUT !!! I think that the question answer is 5/19
Step-by-step explanation:
Even Number = 18/38 = 9/19
greater 17 = 20/38 = 10/19
Even & greater 17 = 10/38 = 5/19
Plss help!!! Image included
Answer:
(-5,2)
Step-by-step explanation:
A function is a relation where each y-value has a unique x-value. That means that x's can never repeat. Therefore, to solve find the ordered pair that does not have the same x-value as one of the points on the graph. The x-values currently represented on the graph are -4, -2, 2, 3. So, the only coordinate pair that does not repeat an x-value is the last option, (-5, 2).
please help me now I need it please this is calculuse
Answer:
none of these
Step-by-step explanation:
Assume the random variable X is normally distributed, with mean = 54 and standard deviation o = 8. Find the 15th percentile.
Answer:
45.712
Step-by-step explanation:
We need to find the Zscore of the area of 15 percent of the distribution ; using a Z table or calculator ;
Zscore of 15% of the distribution is : - 1.036
Using the Zscore formula :
Zscore = (x - mean) / standard deviation
Where, x = score
-1.036 = (x - 54) / 8
Cross multiply
-1.036 * 8 = x - 54
-1.288 = x - 54
x = - 8.288 + 54
x = 45.712
An air conditioning system can circulate 310 cubic feet of air per minute. How many cubic yards of air can it circulate per minute? The air conditioning system can circulate about cubic yards of air per minute.
Answer:
310/[tex]3^{3}[/tex] = 310/27 =11.48
Step-by-step explanation:
Answer:
310/ = 310/27 =11.48
Step-by-step explanation:
Mai drives a truck for a soft drink company. Her truck is filled with 15-ounce cans and 70-ounce bottles. Let c be the number of 15-ounce cans the
truck is carrying, and let b be the number of 70-ounce bottles.
The truck must be carrying less than 4000 pounds (64,000 ounces). Using the values and variables given, write an inequality describing this.
Answer:
15c + 70b < 64,000
Step-by-step explanation:
15c will represent the amount of ounces in the truck from the 15 ounce cans.
70b will represent the amount of ounces in the truck from the 70 ounce bottles.
These need to be added together in the inequality to represent the total weight in the truck.
Then, a less than inequality sign needs to be used, since the truck has to be carrying less than 64,000 ounces.
Put this all together:
15c + 70b < 64,000
So, the inequality is 15c + 70b < 64,000
Andrew wants to build a square garden and needs to determine how much area he has for planting the perimeter of the garden is between 12 and 14 feet what is the range if the possible areas
Answer:
9 ft^2 and 12.25 ft^2
Step-by-step explanation:
We need to figure out the area for a square with a perimeter of 12 feet and 14 feet.
A square has four sides that are all equal in length, therefore:
12/4 = 3
14/4 = 3.5
3 and 3.5 are the individual side lengths of the garden, so to find the area, we just multiply those numbers by themselves (since it is a square garden).
3*3 = 9
3.5*3.5 = 12.25
Therefore, the answer is 9 ft^2 and 12.25 ft^2
8. The point in a distribution below which 75% of the cases lie in the?
A 3rd decile
B. 7th percentile C. 3rd quartile D. 1st quartile
Answer:
C. 3rd quartile
Step-by-step explanation:
Percentile:
A data belonging to the xth percentile means that the data is greater than x% of the values of the data-set, and smaller than (100 - x)%.
Point below 75% of the cases lie:
This is the 75th percentile, which is the 3rd quartile, as 75 = 3*100/4. Thus, the correct answer is given by option c.
answer it correctly:)
can anyone help me?:)
Answer:
JAR WITH MARBLES.
There's
5 Blue Marbles
3 Red Marbles
2 Yellow Marbles
Pr = No of desired outcome/No of Possible Outcomes
No of Possible Outcomes = 10.
1. Pr(yellow) = 2/10 = 1/5.
2. Pr(Red) = 3/10
3. Pr(Blue) = 5/10 = 1/2
4. Pr(Yellow and Red) = 2/10 x 3/10 = 6/100 = 3/50.
5.Pr(Blue and Red)= 5/10 x 3/10 = 15/100 = 3/20.
6.Pr( Yellow and Blue) = 2/10 x 5/10 = 10/100 = 1/10.
THE CHIPS ARE PLACED IN A JAR AND MIXED.
No of Possible Outcomes = 8.
The Numbers are 1,2,3,4,5,6,7,8.
There's
4 Even Numbers
4 Odd Numbers
1. Pr(Even) = 4/8 = 1/2
2. Pr(Odd) = 4/8 = 1/2
3. Pr(Chip with Biggest No) = 1/8.
Reason. There can only be one Number which Is the biggest amongst all. So the Probability of picking it is 1.
4.Pr(Smallest Number) = 1/8 (Same concept).
5.Pr(Prime Number)
The prime Numbers above are 2,3,5,7
Pr(Prime) = 4/8 = 1/2.
Hope this helps!.
Express 20% as a decimal number
Answer:
.20
Step-by-step explanation:
take the two digit % and move the decimal two places to the left
Answer: 0.2
Step-by-step explanation: 20/100 is 1/5 and 1/5 means 1 divided by 5 so the answer is 0.2
find the slope of the line graphed above
Answer:
The slope of the line is -6.
Instructions: Solve the following literal
equation.
Solve 4x – 2y = 18 for y.
y =
Answer:
[tex]y = - 9 + 2x[/tex]
Step-by-step explanation:
Objective: Use the rules of Algebra to isolate y.
[tex]4x - 2y = 18[/tex]
[tex] - 2y = 18 - 4x[/tex]
[tex]y = \frac{18 - 4x}{ - 2} [/tex]
[tex]y = - 9 + 2x[/tex]
help with this please !!
Answer:
B
Step-by-step explanation:
The coeffecients (I totally didn't spell that right) and variables match up.
Calculate 20% of 15,998
Answer:
3,199 approximately
Step-by-step explanation:
to find how much 20% of 15,998 does we multiply 15,998 with 20 and then divide it by 100
15,998 x 20 / 100 = 3,199
What is the surface area of this rectangular prism
Answer:
3*7 = 21*2=42
13*3=39*2=78
7*13=91*2=182
42+78+182=302
So the answer is D
Hope This Helps!!!
Answer:
D. 302
Step-by-step explanation:
This is how I did it:
First multiply 7 by 3, 21
Multiply that by 2 because there are 2 of those faces. 42.
Then multiply 3 by 13, and again by 2. 78.
And 13 by 7 by 2. 182.
Add. 302.
Or do an equation and use a calculator: 7(3)(2)+3(13)(2)+13(7)(2)=302
PLESE HELp ANYONE. SOLVE ABC. ROUND YOUR ANSWERS TO THE NEAREST HUNDREDTH IF NECESSARY
Answer:
C=25°
a=11
b=12
Step-by-step explanation:
Find angle c,since angles in a triangle add up to 180 and we know angleA andB angle C will be
65+90+C=180
C=180-155
C=25°
To find a
use trig ratios
tanA=opposite/adjacent
tan65=a/5
a=tan65×5
a=10.72 round off to 11
To find b
sinC=opposite/hypotenuse
sin25=5/b
sin25 b=5
b=11.8 or rather 12
Answer:
Step-by-step explanation:
First find side a and to find this calculate tan 65
Tan 65 = [tex]\frac{opposite \ side}{adjacent\ side}=\frac{a}{5}\\\\[/tex]
2.144 = a/5
a = 2.144 * 5
b² = a² + c²
= 121+25
= 146.
b = √146 = 12.08 = 12
a = 10.72 = 11
Now find Tan C
[tex]Tan \ C = \frac{5}{10.72}\\\\Tan \ C = 0.4664\\[/tex]
C = tan⁻¹ 0.4664
C = 25°
Consider this linear function:
y = 1/2x + 1
Plot all ordered pairs for the values in the domain.
D: {-8, -4,0, 2, 6)
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The attachment shows the ordered pairs (x, f(x)) and their graph.
