The perimeter of the hexagon is the sum of its side lengths
The perimeter of the hexagon is 48.5 ft
The given parameters are:
[tex]\mathbf{Area = 169.74}[/tex] --- the area of the hexagon
[tex]\mathbf{a = 7}[/tex] -- the apothem
Let the perimeter of the hexagon be p.
So, the area is calculated as:
[tex]\mathbf{Area = \frac 12 pa}[/tex]
Substitute values for Area and (a)
[tex]\mathbf{169.74 = \frac 12 \times p \times 7}[/tex]
Multiply both sides by 2
[tex]\mathbf{339.48= p \times 7}[/tex]
Divide both sides by 7
[tex]\mathbf{48.5= p }[/tex]
Rewrite as:
[tex]\mathbf{p = 48.5}[/tex]
Hence, the perimeter of the hexagon is 48.5 ft
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Three of six people are to be selected and given sinall prizes. One will be
given a book, one will be given a cal cul ator, and one will be given an iTunes
card. In how many different ways can these prizes be awarded?
Answer:
The three prizes can be awarded in 6 different ways
Step-by-step explanation:
1. P1 - Book; P2 - Calc; P3 - Card
2. P1 - Book; P2 - Card; P3 - Calc
3. P1 - Calc; P2 - Card; P3 - Book
4. P1 - Calc; P2 - Book; P3 - Card
5. P1 - Card; P2 - Book; P3 - Calc
6. P1 - Card; P2 - Calc; P3 - Book
For what value of k does the equation 6(x+1)+2 = 3(k/5x + 1) +3 have no solution
This one is an interesting question.
Lets solve first the equation by isolation of the unknown x:
6x + 6 +2 = (3k / 5x )+3 +3
6x = (3k/5x) + 6 -6-2
6x = (3k/5x) -2
6x = (3k / 5x) - (10x / 5x)
6x = (3k-10x)/5x
6x*5x = 3k - 10x
30x² = 3k - 10x
30x² + 10x = 3k
30x² + 10x - 3k = 0
This is really interesting because this looks exactly like a polynomial function. So we know that there is no solution for a polynomial once the discriminant delta is strictly less than 0.
But delta = b² - 4ac where b = 10, a = 30 and c = -3k
So we need to solve delta < 0
100 - 4*30* (-3k) < 0
100 - 120*(-3)*k < 0
100 - (-360)k < 0
100 + 360k < 0
360k < -100
k < -100/360= -10/36
So there is no solution for all k strictly less than -10/36
Good luck
find the slope of the line
Answer:
-2
Step-by-step explanation:
[tex]\frac{(-5-1)}{(3-0)}[/tex] = [tex]\frac{-6}{3}[/tex] = -2
If x= 4, find 6x- x^2.
Answer: 8
Step-by-step explanation: (6)(4)-4^2 24−4^2 24−16 8
For which values of x does each expression make sense? √(-2x)^2
We want to see for which values of x does the rational expression make sense. We will see that the expression makes sense for x ≤ 0
We know that the argument of a square root can only be a real number equal to or larger than zero.
In this case, we have the expression:
[tex]\sqrt{(-2x)^2} = (\sqrt{-2x} )^2[/tex]
One would want to directly cancel the square root with the 2 exponent, but we can't do that, because in the right-side expression we would have a complex number if the argument is smaller than zero.
The first thing we need to do is to make the argument equal or larger than zero:
-2x ≥ 0
x ≤ 0/-2
x ≤ 0
So the given expression only makes sense for x ≤ 0
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Answer: No, the answer is All Real Numbers
Step-by-step explanation: e
Which of the following is the difference of two squares

4g-16h
16a^2-4y^2
2x^2-4y^2
25m^3+100n^2
Answer:
2nd option
Step-by-step explanation:
A difference of squares has the general form
a² - b²
where the terms on either side of the subtraction ( the difference ) are both perfect squares.
The only one fitting this description is
16a² - 4y²
= (4a)² - (2y)² ← difference of squares
What trig function and angle is equivalent to sin(270°)?
Answer:
θradians sin(θ)
3π/2 -1
Step-by-step explanation:
leave a thanks if helped pls <3
The trigonometric function gives the ratio of different sides of a right-angle triangle. The trigonometric function and angle are equivalent to sin(270°).
What are Trigonometric functions?The trigonometric function gives the ratio of different sides of a right-angle triangle.
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\[/tex]
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.
Given the trigonometric function sin(270°) which can be written in the form of radian angle. So that the value of the angle is the same. Therefore, the trigonometric function and angle that is equivalent to sin(270°) can be written as,
sin(270°) = sin(3π/2) = -1
Also, if the trigonometric function is needed to be changed then we can write,
sin(3π/2) = cos(π) = cos(180°) = -1
Hence, the trigonometric function and angle are equivalent to sin(270°).
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Which equation can be solved to find x, the measure of BD in the diagram
below?
C
53
AB
D
E
2330
O A. *- 53 = 233
B. }(233 + x) = 53
C. (233 - x) = 53
D. x+ 53 = 233
=
The value of x is equal to 127 degrees.
Data;
Outer angle = 233Inner angle = 53unknown angle = xAngle tangent to a circleTo find the angle x which is related to angle 233 to form the outer angle 53, the equation
[tex]\frac{1}{2} (233 - x) = 53[/tex]
We can proceed to solve for x by simplifying the equation which will give us
[tex]\frac{1}{2}(233-x) = 53\\2 * 53 = 233 - x\\106 = 233 - x\\x = 233 - 106\\x = 127^0[/tex]
The value of x is equal to 127 degrees.
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Answer:
Step-by-step explanation:
just took the quiz
Hello please help with this question.
Answer:
77.32°Step-by-step explanation:
Use sine to find the measure of ∠A:
sine = opposite / hypotenusesin A = 80/82m∠A = arcsin (80/82) = 77.32°look at the image, i need help with b mostly and please also answer a so i can check my answer
Answer:
a) 10 per for 4 min means 150 per hour. so more hamburgers are sold per hour.
b) see attachment
HELP ASAP 100 POINTS RIGHT ANSWER GETS BRAINLSIT
Solve for x.
14(x−12)=−235
Enter your answer as a mixed number in simplest form by filling in the boxes.
x =
Answer:
Hell your answer for x is 4 11/14 ( that is what i got)
Step-by-step explanation: K12
4 1/4-2 3/5 what is the answer to this.
Answer:
1.65
Step-by-step explanation:
What is the easy way to do fractions to decimals.
The easiest way to convert a fraction to a decimal is to divide the numerator (the top of the fraction) by the denominator (the bottom of the fraction) by using a calculator. The resulting answer will be the value of the fraction expressed as a decimal number.
What is the product?
Enter your answer as a fraction, in simplified form, in the box.
3/8*(-36)
Answer:
-27/2
Step-by-step explanation:
3/8 × -36
(3×-36)/8
-108/8
-27/2
A binomial experiment has 4 trials in which p=0. 35. What is the probability of 1 success?.
Answer: 5798
Step-by-step explanation:
Probability of [tex]1[/tex] success as per given condition is equals to [tex]0.384475[/tex] ≈ [tex]0.4[/tex].
What is probability?" Probability is defined as the ratio of number of favourable outcomes to the total number of outcomes.Probability is always less than or equals to one."
Formula used
For binomial experiment
Probability = [tex]^n C_r p^{r} q^{n-r}[/tex]
[tex]p =[/tex]success rate
[tex]q=[/tex] failure rate
[tex]p+q=1[/tex]
[tex]n=[/tex]Number of trials
[tex]r=[/tex] number of success
According to the question,
Total number of trials [tex]'n' =4[/tex]
Number of success [tex]'r' =1[/tex]
[tex]p = 0.35\\\\q = 1-0.35\\ \\\implies q = 0.65[/tex]
Substitute the value to get the required probability,
Probability [tex]= ^4C_1 (0.35)^{1}(0.65)^{4-1}[/tex]
[tex]=\frac{4!}{(4-1)!1!} \times\frac{35}{100}\times(\frac{65}{100})^{3} \\\\= 4 \times \frac{35}{100}\times \frac{274625}{1000000} \\\\= 0.384475[/tex]
≈ [tex]0.4[/tex]
Hence, probability of [tex]1[/tex] success as per given condition is equals to [tex]0.384475[/tex] ≈ [tex]0.4[/tex].
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Given: △ABC, m∠A=60°,
m∠C=45°, AB=9
Find: Perimeter of △ABC,
Area of △ABC
Pleas be sure to answer BOTH PARTS ... thank you!
Answer:
p = 32.317
A = 47.911
Step-by-step explanation:
given ∠A = 60
∠C = 45
AB = 9
From sum of all angles in triangle is 180
∠A + ∠B + ∠C = 180
60 + ∠B + 45 = 180
∠B = 180 - 105 = 75
∠B = 75
from sine rule in ΔABC
AB / sin C = BC / sin A
=> 9 / sin 45 = BC / sin 60
=> 9 / 1/[tex]\sqrt{2}[/tex] = BC / [tex]\sqrt{3} / 2[/tex]
=> [tex]9\sqrt{2} = BC * 2 / \sqrt{3}[/tex]
BC = [tex]9\sqrt{2} * \sqrt{3} / 2\\[/tex]
BC = 11.023
length of AC is
AC / sin B = AB / sin C
AC / sin 75 = 9 / sin 45
AC = 9 / 1/[tex]\sqrt{2} * sin 75[/tex]
= [tex]9\sqrt{2} * sin 75\\12.294[/tex]
perimeter of ΔABC
AB + BC + CA
= 9 + 11.023 + 12.294
= 32.317
Area of ΔABC is
= 1/2 * AB * AC * sin A
= 1/2 * 9 * 12.294 * sin 60
= 1/2 * 9 * 12.294 * √3/2
= 47.911
A baseball tournament begins with 128 teams. After each round of games, only half of the teams are left. How many teams will be left after three rounds of games?
Answer:
End of round 1:
128 ÷ 2 = 64
End of round 2:
64 ÷ 2 = 32
End of round 3:
32 ÷ 2 = 16
Step-by-step explanation:
Answer: 16
Step-by-step explanation: i think :)
which number sentence can be used to find 42 divied by 7
Answer: isn't it 42÷7=6?
Answer:
42 / 7 = 6
Step-by-step explanation:
Just use a multiplication table.
Find the perimeter. Simplify your answer.
Answer:
Step-by-step explanation:
p = 10x + 2 + 7x - 6 + 8x
p = 25x - 4
Answer:
To Find the perimeter we add all the sides,perimeter = 10x + 2 + 7x - 6 + 8x
= 25x - 4...ans
Step-by-step explanation:
Hope it Helps you!!How to simplify and multiply fractions.
Answer:
*Find a number on top of the fractions and a number on the bottom of the fractions that can both be divided by the same number.
*Divide both numbers in the fractions by this number.
*Write the answers to this division in the place of the original numbers in the fraction.
Is this a function?
Answer:
Yes
Step-by-step explanation:
Yes, the graph represents a function because it passes the vertical line test: Any vertical line drawn through this graph intersects this graph only once.
What goes up as soon as the rain comes down?
Answer:
Umbrella goes up when rain comes down.
WILL GIVE BRAINLIEST! Consider the graph at right and answer the following questions.
Answer:
a.)A and B are the intersection between the two curves. The x coordinate is the equation
[tex]f(x) = g(x)[/tex]
Let's solve it
[tex]\frac12 (x-2)^3 +1 = 2x^2-6x-3\\x^3-6x^2+12x-8+2=4x^2-12x-6\\x^3-10x^2+24x=0\\x(x^2-10x+24)=0\\x(x-4)(x-6)=0[/tex]
We can see that if we substitute x= 0 or x= 4 the equation is verified.
b. The equation has a third solution, x = 6, that is too far to the right to be visible in the graph.
c. the x coordinate of C is the solution of [tex]f(x)=0[/tex] or [tex]\frac 12 (x-2)^3 +1=0\\(x-2)^3 = -2\\(x-2) = -\sqrt[3]2[/tex]
At this point let's guesstimate the cubic root of 2 -let's say the cubic root of 2 is equal to 1plus an error e, and since we know how to calculate the cube of a binomial, let's build it.
[tex](1+e)^3 = 2 \rightarrow 1+3e+3e^2+e^3 = 2[/tex] Now, assuming the error is small enough, it's square and its cube gets even smaller. (if the error is 0.1, it's square becomes 0.01 and the cube 0.01), let's ignore them. [tex]1+3e=2 \rightarrow 3e=1 e= \frac13[/tex] So, going back to our equation, we can tell that the right hand side is [[tex]\mathbb{R}[/tex]]-(1+\frac13)[/tex] Not perfect, but good enough. Let's solve it now.
[tex]x-2= -1-\frac13 \rightarrow x=1-\frac13 = \frac23[/tex]
Which seems close enough from the photo.
c. Domain of both function are the whole Real set, since they're polynomials. Range of f(x) is again the whole real set, since it's an odd degree polynomial. g(x) is a parabula and its range is for y above the vertex y-coord, which is [tex]y>g(\frac32) = 2(\frac94)-6(\frac32)-3 = \frac92 -3(\frac62) -\frac62 = \frac92-4\frac62= -\frac{24-9}2 = -\frac{15}2[/tex]
Practice: Find the value of the variable(s) in each figure explain your reasoning.
Answer:
I'm assuming you know how to solve first degree equations, in particular how to move terms from one side to the other.
Top figure. The two angles measuring 3x and 5x-20 are congruent (they are alternate angles related to the two parallels and the transversal closing the triangle.. Now, if 3x = 5x-20 a simple solution is x=10. Now into the triangle, the sum of the internal angles has to be 180, and we already know how much x measures. 2y+4y+30 =180. Solve for y =25
Middle figure. From the bottom right corner, you can already tell that 2y+106= 180, or y=37. But 2y and x are congruent (corresponding angles), so x= 74. Pick the method you prefer to say that either 4z+6=106 (both angles are congruent to the one in the bottom corner since they're corresponding, thus they have to be equal to each other) OR 4z+6+x = 180 (they're conjugate angles to x, so their sum is 180). To get z=25
Bottom row in both cases, the two angles sum up to 90°
Left one: 4x-20+2x-16 = 90 so x = 21
Right one: 2x-30 +x+15= 90 so x = 35
4800 persons run a marathon, 1200 reach the finish line. What is the percent of people reach the finish line at the marathon?
Answer: 25%
Step-by-step explanation: So first make the number of people who ran the marathon and the number of people who finished the marathon into a ratio
1200:4800
then make that into a fraction, 1200/4800
then make the percent of people who reached the marathon into a fraction, using 100 as the denominator and a variable as the numerator.
for example. p/100 (p, represents the percent)
then cross multiply.
1200x100=1200000
Last divide 1200000 by 4800 to get 25%.
Find the slope from points (9,-13), (7,-11)?
That’s what my question is
Answer:
Step-by-step explanation:
The entered points belong to an increasing, linear function.
Equation: y = 1x + 4.
3. After a study was completed at a local college, it was found that 386 in 1,112 students live
with their parents. What percent of the students lives with their parents? Round to the nearest
hundredth of a percent where necessary.
O 3.44%
O 34.71%
49.36%
065.28%
Answer:
34.71%
Step-by-step explanation:
1112-100 percent
386-x percent
x=386*100/1112≈34.71
The percentage of students living with their parents is 34.44%. The correct option is B.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that after a study was completed at a local college, it was found that 386 in 1,112 students live with their parents.
The percentage of the students who live with their parents will be calculated as,
Percentage = ( 386 / 1120 ) x 100
Percentage = 0.3471 x 100
Percentage = 34.71%
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Determine if the table represents a linear function, quadratic function, or exponential function.
Answer:
Quadratic
Step-by-step explanation:
Formula: ax^2+bx+c
50 ptssss
what is 2+2
Answer:
4!!!
Step-by-step explanation:
brainliest please?
Answer:
4
Step-by-step explanation:
I hope this helps!
I got 8 green crayons for the a part just confused for the b part
Answer:
Just apply the same method to part B
x:24
5:8
x3 x3
15:24
Answer:
8
7
Step-by-step explanation:
24 purple
green : purple = 1 : 3
g / p = 1/3
g / 24 = 1/3
g = 24/3
g = 8
now abbi put x green crayons into box
now green : purple = 5 : 8
(8 + x) / 24 = 5/8
8 + x = 5/8 * 24
8 + x = 5 * 3
8 + x = 15
x = 15 - 8
x = 7