To find the height of a display in a museum, a person place a mirror on the ground 35ft from the display. Then he stepped back 5ft so he could see the top of the display. His eyes were about 5'4" from the ground. What is the height of the display?(ill send the image because it was to big)
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Now let's calculate the angle of the first triangle. We will use the tangent function because we have information from the opposite side and the adjacent side.
[tex]\begin{gathered} \tan \theta=\frac{5\text{ ft 4''}}{5\text{ ft}} \\ \end{gathered}[/tex][tex]\begin{gathered} \theta=\tan ^{-1}(1.0666) \\ \theta=46.84\text{ degree} \end{gathered}[/tex]With this angle we can calculate the height of the display. Again we will use the tangent function.
[tex]\begin{gathered} \tan (46.84)=\frac{x}{35} \\ x=35\cdot\tan (46.84) \end{gathered}[/tex][tex]x=37.33\text{ ft}[/tex]The answer would be 37.33 ft the height of the display
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ANSWER QUESTION 3 PHOTO ATTACHEDFAST REPLY = BETTER RATINGTHANK YOU!
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Given
[tex]f(x)=xe^{7x}[/tex]Calculate the second derivative of f(x), as shown below
[tex]\begin{gathered} \Rightarrow f^{\prime}(x)=e^{7x}+7xe^{7x} \\ and \\ \Rightarrow f^{\prime}^{\prime}(x)=7e^{7x}+7(e^{7x}+7xe^{7x}) \\ \Rightarrow f^{\prime}^{\prime}(x)=14e^{7x}+49xe^{7x} \end{gathered}[/tex]Then, find the interval such that f''(x)>0 in order to find where f(x) is concave up,
[tex]\begin{gathered} 14e^{7x}+49xe^{7x}>0 \\ \Rightarrow2e^{7x}+7x*e^{7x}>0 \\ and \\ e{}^{7x}>0,x\in\Re \end{gathered}[/tex]Then,
[tex]\begin{gathered} 2e^{7x}>-7xe^{7x} \\ \Rightarrow2>-7x \\ \Rightarrow x>-\frac{2}{7} \end{gathered}[/tex]Therefore, f(x) is concave up when x in (-2/7, +infinite).
In the case of concavity down,
[tex]\begin{gathered} f^{\prime}^{\prime}(x)<0 \\ \Rightarrow2e^{7x}+7x*e^{7x}<0 \\ \Rightarrow2+7x<0 \\ \Rightarrow-\frac{2}{7}>x \end{gathered}[/tex]Thus, f(x) is concave down when x in (-infinite, -2/7).
The answer is the fifth and last option (top to bottom).
u= ak - b solve for a
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To solve it for "a" is to isolate "a' in one side, by doing some algebraic operations.
U =ak -b
1) Let's rewrite it
-b+ak=u
2) Add b to both sides
-b +b +ak = u +b
ak = u+b
3) Divide both sides by k
[tex]\frac{ak}{k}=\frac{u+b}{k}[/tex]4) Finally, we have it for 'a':
[tex]a\text{ =}\frac{u}{k}\text{ + }\frac{b}{k}[/tex]Hi so some of the problems I don't know like I can't but I did do some problem by myself you can tell me whether it's correct
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The symmetric property of equality, if AB = YU. then YU = AB
As per the symmetric property of equality,
if AB = YU. then YU = AB
As per the symmetric property of congurence,
∠H ≅ ∠K then ∠K ≅ ∠H
As per the reflexive property of congurence,
∠PQR ≅ ∠PQR
As per the distibutive property, multiplying the sum of two or more term by a number produces the same result as when each term is multiplied individually by the number and the products are added together.
3(x - 1) = 3x - 3
As per the substitution property one value can replace another value in an expression or equation and the value will remain the same.
If LM = 7, EF + LM = NP
Then EF + 7 = NP
Therefore, the above bits are done as per the property mentioned.
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For the following set of data, find the percentage of data within population standarddeviations of the mean, to the nearest percent.88, 92, 57, 62, 57, 56, 58, 57Copy Values for CalculatorOpen Statistics Calculator
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Answer: 100 %
Explanation:
The first step is to rearrange the numbes in ascending order. It becomes
56, 57, 57, 57, 58, 62, 88, 92
The next step is to calculate the population μ, mean.
μ = sum of terms/number of terms
From the information given
n = number of terms = 8
μ = (56 + 57 + 57 + 57 + 58 + 62 + 88 + 92)/8 = 65.875
μ = 65.875
The formula for calculating the population standard deviation, σ is
σ = √[Σ(x - μ)^2]/n
Σ(x - μ)^2/n = [(56 - 65.875)^2 + (57 - 65.875)^2 + (57 - 65.875)^2 + (57 - 65.875)^2 + (58 - 65.875)^2 + (62 - 65.875)^2 + (88 - 65.875)^2 + (92 - 65.875)^2)]/8 = 197.859375
σ = √197.859375
σ = 14.1
2 population standard deviations to the left of the mean = 65.875 - 2(14.1) = 37.675
2 population standard deviations to the rig tof the mean = 685875 -+2(14.1) == 94.075
Number of terms between 37.675 and 94.075 = 8
Thus,
the percentage of data within 2 population standard deviations of the mean
= 8/8 x 100 = 100%
A cylinder has a height of 10 ft and a volume of 25,456 ft^3.The radius of the cylinder is approximately ___ feet.Round your answer to the nearest whole number.
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From the question given, they provided us with the height,h = 10ft, and volume, V=25,456 cubic feet.
Thus, we have:
[tex]\begin{gathered} V=\pi\times r^2\times h \\ 25,456=\pi\times r^2\times10 \\ \frac{25,456}{10\pi}=r^2 \\ \text{Taking the value of }\pi\text{ as 3.142, we have:} \\ r^2=\frac{25,456}{10\times3.142} \\ r^2=810.1846 \\ r=\sqrt[]{810.1846} \\ r=28.46ft \end{gathered}[/tex]Hence, the radius of the cylinder is 28.46ft
The sum of the two numbers is 133. Four times the smaller of the two numbers equals three times the greater number find the numbers using one variable.
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The Solution:
Let the two number be x and y133-x (
Such that:
[tex]\begin{gathered} x<133-x \\ x=small\text{ number} \\ 133-x=larger\text{ number} \end{gathered}[/tex]So,
[tex]\begin{gathered} 4x=3(133-x) \\ \end{gathered}[/tex]Solve for x:
[tex]\begin{gathered} 4x=399-3x \\ \text{ Collect the like terms.} \\ 4x+3x=399 \\ 7x=399 \end{gathered}[/tex]Divide both sides by 7.
[tex]x=\frac{399}{7}=57[/tex]Therefore, the correct nswers are:
57 and 76
Find the standard deviation for the following wroup of data Hems, Round your answer to the nearest tenth for one decimal place), 7,9,11,14,15,16
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The standard deviation of the groups of data is 3.3 .
The standard deviation is calculated using the formula [tex]{\displaystyle \sigma={\sqrt {{\frac {1}{N}}\sum _{i=1}^{N}\left(x_{i}-{\mu }\right)^{2}}}}[/tex]
Where σ is the standard deviation.
x denotes the data of the population.
N is the size of the population.
μ is the mean of the population.
The given population is 7,9,11,14,15,16
Here N= 6
Mean (μ) = (7+9+11+14+15+16)÷6 = 72/6=12
Now we will put the values in the above equation to calculate the sd.
[tex]{\displaystyle \sigma={\sqrt {{\frac {1}{6}}\sum _{i=1}^{6}\left(x_{i}-{12 }\right)^{2}}}}[/tex]
Simplifying we get:
σ = √(64/6)
σ = 3.2659..
σ = 3.3
The standard deviation is a statistic that indicates the degree of volatility or dispersion in a set of numerical values.
A low standard deviation shows that possibly the values tend toward being close to the mean, sometimes referred to as the expected value of the set, whereas a large standard deviation suggests that the values are distributed over a wider range.
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please answer quickly I'm just trying to confirm my answer
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Given the following vector:
[tex]v=<-\sqrt{3},2\sqrt{3}>[/tex]The magnitude of the vector will be as follows:
[tex]||v||=\sqrt{(-\sqrt{3})^2+(2\sqrt{3})^2}=\sqrt{3+12}=\sqrt{15}[/tex]So, the answer will be option 2) ||v|| = √15
If $4,780 is deposited in an account that pays 1.25% interest compounded annually, how much interest is in the account at the end of 8 years? A $5,279.44 B $500.44 C$ 478.00 D $499.44
Answers
We can calculate the interest as the difference between the future and the present value of the investment:
[tex]I=FV-PV[/tex]The present value is $4780.
The annual interest rate is r=1.25/100=0.0125.
The number of years is 8, so n=8.
We can calculate the future value as:
[tex]\begin{gathered} FV=PV(1+r)^n \\ FV=4780\cdot(1+0.0125)^8 \\ FV=4780\cdot1.0125^8 \\ FV\approx4780\cdot1.1045 \\ FV\approx5279.44 \end{gathered}[/tex]Then, we can calculate the interest as:
[tex]I=FV-PV=5279.44-4780=499.44[/tex]Answer: D. $499.44
If V1 = (2,4) and V2 = (-1,5), then V1*V2is equal to which of the following? A. (-2,20) , B. 18 , C. 22 , D. (8,-5)
Answers
B. 18
Explanation
The dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number
it is given by.
[tex]\begin{gathered} u=(u_x,u_y) \\ v=(v_{_x},v_y) \\ u\cdot v=(u_xv_x+u_yv_y) \end{gathered}[/tex]so, we can find the dot product by multiplying the corresponding values in each vector and adding them together
Step 1
get the dot product
let
[tex]\begin{gathered} v_1=(2,4) \\ v_2=(-1,5) \end{gathered}[/tex]then
[tex]\begin{gathered} v_1\cdot v_2=(2\cdot-1)+(4\cdot5) \\ v_1\cdot v_2=-2+20 \\ v_1\cdot v_2=18 \end{gathered}[/tex]therefore, the answer is
B. 18
I hope this helps you
Suppose 2' is a normally distributed random variable with ft = 10.3 and 0 = 3.8. For the following probability,draw an appropriate diagram, shade the appropriate region and then determine the value:P(9 <2 ≤ 14) = Note: Enter your answer up to 4 decimal places.
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GIVEN
The following values are given:
[tex]\begin{gathered} \mu=10.3 \\ \sigma=3.8 \end{gathered}[/tex]SOLUTION
The z-score for the x values 9 and 14 can be calculated using the formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]For x = 9:
[tex]\begin{gathered} z=\frac{9-10.3}{3.8} \\ z=-0.34 \end{gathered}[/tex]For x = 14:
[tex]\begin{gathered} z=\frac{14-10.3}{3.8} \\ z=0.97 \end{gathered}[/tex]The probability can be calculated as follows:
[tex]P(9\le x\le14)=Pr(-0.34The region that represents the solution is shown below:Therefore, the probability is given to be:
[tex]P(9\le x\le14)=0.4671[/tex]The probability is 0.4671.
1.) twenty-five and five hundred seventy-eight thousandths
2.) Six thousand one and one hundreadths
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Answer:
Here are the numbers:
1) 25.578
2) 6,001.01
r-9<-25. on a graph bar
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r-9<-25 is equal to solution: [tex]$\quad R < -16$[/tex], Interval Notation: [tex]$\quad(-\infty,-16)$[/tex]. The graph is shown in attachement.
R-9<-25
Add 9 to both sides
R-9+9<-25+9
Simplify
R<-16
A graph is simply an orderly representation of data. It aids us in comprehending the info. The numerical information gathered through observation is referred to as data.
Data is derived from the Latin term Datum, which meaning "anything supplied."
Data is collected continuously through observation when a research question is formulated. It is then organized, summarized, categorised, and graphically shown.
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The graph of g consists of two straight lines and a semi circle. Evaluate each
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Given:
a)
[tex]\int ^1_0g(x)dx[/tex]Consider the shape included in the region from 0 to 1 of g(x).
The area is,
[tex]\int ^1_0g(x)dx=\frac{1}{2}\times1\times4=2[/tex]b) From x = to x = 6 includes the semi-circle. Its area is calculated as,
[tex]\int ^6_2g(x)dx=-\frac{1}{2}(\pi\times r^2)=-\frac{1}{2}(\pi\times2^2)=-2\pi=-6.28[/tex]Select all of the constraints that apply to this situation $1.25x when x <12$12.00 + $0.75(x-12) when X_>12$1.25x when x _>120.75x when x >12$12.00 + $0.75x when x >12
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We want to write expressions that describe the cost of the cookies. Let say we sell x cookies. If x is less than 12, then the cost per cookie is 1.25. So the cost of x cookies would be the product of this numbers, so it would be
[tex]1.25x,x<12[/tex]Note that when x=12 the cost should be 12. Also note that for each extra cookie, starting at 12, each cookie costs 0.75. If we buy x cookies , to calculate the extra cookies, with respect to 12, we simply substract 12 from x and we multiply it by 0.75. This would be
[tex]0.75\cdot(x\text{ -12)}[/tex]as this is an additional cost to the 12, we add 12 to this expression. THen we get
[tex]12+0.75\cdot(x\text{ -12)}[/tex]Note that for this expression, when x=12, we get that the expression becomes
[tex]12+0.75\cdot(12\text{ -12)=12}[/tex]THis means that the expression applies from 12 and on, so we have the followin inequality12
[tex]12+0.75\cdot(x\text{ -12), x}\ge12[/tex]Number 3.Light travels 1.9x10^5 kilometers per second.there are 6.4 x 10^5 seconds in one week .About how many kilometers does light travel.
Answers
helloo
from the question given, we have some variables
[tex]\begin{gathered} \text{speed}=1.9\times10^5\operatorname{km}\text{ /s} \\ \text{time}=6.4\times10^5s \\ \text{distance}=x \end{gathered}[/tex]now the formula for speed is given as
[tex]\begin{gathered} \text{speed}=\frac{\text{distance}}{\text{time}} \\ 1.9\times10^5=\frac{x}{6.4\times10^5} \\ x=(1.9\times10^5)\times(6.4\times10^5) \\ x=1.22\times10^{11}\operatorname{km} \end{gathered}[/tex]find the area of the circle with a diameter of 8.6 ft
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Given:
Diameter of the circle, d = 8.6 ft
To find the area of a circle, use the formula below:
[tex]undefined[/tex]Diameter of the circle, d
Two cards are drawn from a deck of 52 cards. The first card is replaced before drawing the second card. Find the probability that the first card is red and the second card is a 7
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The probability that the first card is red and the second card is a 7 is 1/26.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
Probability that the first card is a red and the second is a 7 = (number of red cards / total number of cards) x (number of 7 / total number of card)
Probability that the first card is a red and the second is a 7 = (26 / 52) x (4/52) = 1/26
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Type the correct answer in each box. Use numerals instead of words.The exterior of a solid cone is painted. The height of the cone is 11.4 centimeters, and the diameter of its opening is 5 centimeters.What is the surface area of the solid cone requiring paint to the nearest square centimeter?The surface area of the solid cone requiring paint rounded to the nearest whole number is square centimeters.
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The surface area of a cone with diameter d and height h is given by:
[tex]A=\pi(\frac{d}{2})^2+\pi\cdot\frac{d}{2}\cdot\sqrt[]{h^2+(\frac{d}{2})^2}[/tex]For d = 5 cm and h = 11.4 cm, we have:
[tex]\begin{gathered} A=\pi(\frac{5}{2})^2+\pi\frac{5}{2}\sqrt[]{11.4^2+(\frac{5}{2})^2} \\ A=\frac{25}{2}\pi+\pi\frac{25}{2}\sqrt[]{129.96+\frac{25}{2}} \\ A=12.5\pi+12.5\cdot\pi\cdot\sqrt[]{142.46} \\ A\approx12.5\pi+12.5\cdot11.94\cdot\pi \\ A\approx508cm^2 \end{gathered}[/tex]Please help me I don’t know how to do this
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Translations
One point located at (x,y), translated to the point (h,k) has been applied the rule:
T(x,y) -> (h,k)
And the translation changed the coordinates by ( h-x, k-y).
The point (4,-9) is mapped to (9,-14). The change is:
(9 - 4, -14 - (-9 ) = (5 , -5)
The rule of translation is:
T(x,y) -> (x + 5 , y -5)
If we translated the point (-9,-8) under the same rule:
T(-9,-8) -> (-9 + 5 , -8 -5)
T(-9,-8) -> ( -4 , -13)
The image of the point (-9,-8) is ( -4 , -13)
Express - 345 asin simplest form, where m and n are integers.Enter the correct answer in the box.-345 =
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As -345 is an integer, the simplest fraction form is:
[tex]\frac{-345}{1}[/tex]or -345/1 (m=-345, n=1).
Mariah needs to randomly select one of three groups of students to make their presentation first. Which simulation tools could she use in thissituation?O a bag containing 12 chips in three different colors, with four of each coloro a six-sided number cubea full standard deck of cardsa spinner divided evenly into four sections, with each section a different colorO two coins
Answers
the correct answer is a bag containing 12 chips in three different colors, with four of each color (option A)
Explanation:
number of groups of student = 3
We need to select one out of the three.
The option that can be used to simulate this choice is having 12 chips in three different colours. Each colour will have 4 each.
The 3 different colours represent the 3 different groups. While each 4 number of a colour represent the number of students in each group.
Hence, the correct answer is a bag containing 12 chips in three different colors, with four of each color (option A)
Rational and Irrational Numbers make up the____ system.
Answers
We have the following:
Therefore, the answer is real numbers
express 0.004 in scientific notation
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We are asked to express 0.004 in scientific notation
The number 0.004 has the decimal point at the start, so we move this decimal point to the right until there is only one non-zero digit is left (4 in this case) and then count the number of times we moved.
[tex]0.0004=4\times10^{-3}[/tex]In this case, we moved 3 times so the exponent (power) is -3
The sign of exponent is negative when we move to the right (like in this case)
The sign of exponent is positive when we move to the left.
Find the vbalie If K, and then write an equation to describee the direct variation.
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Given:
x = 9 and y = 6
Use the equation:
y = kx
Where y varies directly as x
K is the constant of proportionality.
Let's find the value of k:
[tex]\begin{gathered} y\text{ = kx} \\ \\ 6\text{ = 9k} \\ \\ \text{Divide both sides by 9:} \\ \frac{6}{9}=\frac{9k}{9} \\ \\ \frac{2}{3}=k \end{gathered}[/tex]k = ⅔
An equation to describe the direct variation is:
[tex]y\text{ = }\frac{2}{3}x[/tex]ANSWER:
[tex]undefined[/tex]46 = -6t - 8 what is t
Answers
t=9,
1) Solving for t we have:
46 = -6t - 8 Add 8 to both sides
46+8 = -6t
54 = -6t Divide both sides by -6
9 = t Flipping it
t=9
2) So the Solution Set is S={9} for this equation.
6(__+x)-8(-3+8x) = 30-58xfill in the blank
Answers
In this expression, we have the same value on the left side is equal to the same amount on the right side.
So, let's start operating it to simplify it
6(_+x) -8(-3+8x)=30-58x
6(_+x)+24-64x=30-58x
6( ) +6x +24 -64x =30 -58x
6( ) -58x+24=30-58x
6( )-58x +58x=30-24
6( ) =14 DIviding both sides by six
( ) =7/3
Testing:
6(7/3 +x) -8(-3+8x)=30-58x
14+6x +24 -64x =30-58x
38
Find each probability of the events and place them in order
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Considering Box A,
Total number of pens = 3 + 5 = 8 pens
Probability of picking a purple (P) and black (B) pen is given below as,
[tex]\begin{gathered} P(P)=\frac{3}{8} \\ P(B)=\frac{5}{8} \end{gathered}[/tex]Considering Box B,
Total number of pens = 15 + 5 = 20 pens
Probability of picking a purple and black pen is given below as,
[tex]\begin{gathered} P(P)=\frac{15}{20} \\ P(B)=\frac{5}{20} \end{gathered}[/tex]For event 1, probability of choosing a red (R) pen from Box B is zero because there is no red pen in the Box.
Event 1 P(R) = 0
For event 2, probability of choosing a purple or black pen from Box A is,
[tex]P(P\text{ or B)=}\frac{3}{8}+\frac{5}{8}=\frac{3+5}{8}=\frac{8}{8}=1[/tex]Event 2 P(P or B) = 1
For event 3, probability of choosing a purple pen from Box A is,
[tex]P(P)=\frac{3}{8}[/tex]Event 3 (P) = 3/8
For event 4, probability of choosing a black pen from Box B is given below as,
[tex]P(B)=\frac{5}{20}=\frac{1}{4}[/tex]Event 4 P(B) = 1/4
Arranging each events from the least likely to the most likely is in the order below
[tex]\text{Event 1, Event 4, Event 3, Event 2}[/tex]Answer deduced above.
CAN SOMEONE HELP WITH THIS QUESTION?✨
Answers
The given function's f(t) = (t - 4)(t + 1)(t - 7), f-intercept is f(t) = 28 and the t-intercepts are t = - 1, 4, 7.
What are intercepts?A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the y-axis of the coordinate system in analytic geometry using the widely used convention that the horizontal axis represents a variable x and the vertical axis represents a variable y. Therefore, x = 0 is satisfied at these sites. The x-intercept and y-intercept are the points where a line crosses each axis.
An intercept is a location where an axis and a graph intersect. The x-intercept is the name given to this particular one.
Put t = 0 in the function f(t) = (t - 4)(t + 1)(t - 7)
f(t)= (0-4)(0+1)(0-7)
f(t) = (-4)(1)(-7)
f(t) = 28
So, the f-intercept is (0,28)
Put f(t) = 0 to find t- intercepts
0 = (t-4)(t+1)(t-7)
So, t - 4 = 0
t = 4
For t + 1 = 0
t = -1
For (t - 7) = 0
t = 7
So, the t intercepts are t = -1, 4, 7.
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An equilateral triangle is folded in half.IN60° 60°14 cm-4What is x, the height of the equilateral triangle?O 14V301407307
Answers
An equilateral triangle is a triangle that has the same length on all its three sides. Therefore, we can say that:
Since the triangle is folded in half, then we can say that:
From this, we can solve "x" using the Pythagorean Theorem.
[tex]c^2=a^{2^{}}+b^2[/tex]where "c" = hypotenuse and "a" and "b" can be either of the remaining sides.
[tex]\begin{gathered} 14^2=7^2+x^2 \\ 196=49+x^2 \\ 196-49=49+x^2-49 \\ 147=x^2 \\ \sqrt[]{147}=\sqrt[]{x^2} \\ 7\sqrt[]{3}=x \end{gathered}[/tex]Therefore, the height of our equilateral triangle is 7√3. This is found in the third option.