If each side of an equilateral triangle is 2 inches long, then what is the area of the triangle?
Answers
Solution:
The image below represents the equilateral triangle of 2 inches long
From the triangle above, the given values include
[tex]\begin{gathered} a=2in \\ b=2in \\ c=2in \end{gathered}[/tex]Concept:
To calculate the area of the triangle, we will use Heron's formula below
[tex]\begin{gathered} A=\sqrt[]{s(s-a)(s-b)(s-c)} \\ \text{where,s = semi perimter} \\ s=\frac{a+b+c}{2} \end{gathered}[/tex]Step 1:
Calculate the semi perimeter s
[tex]\begin{gathered} s=\frac{a+b+c}{2} \\ s=\frac{2in+2in+2in}{2} \\ s=\frac{6in}{2} \\ s=3in \end{gathered}[/tex]Step 2:
Substitute the value of s,a,b,c in the heron's formula
[tex]\begin{gathered} A=\sqrt[]{s(s-a)(s-b)(s-c)} \\ A=\sqrt[]{3(3-2)(3-2)(3-2)} \\ A=\sqrt[]{3\times1\times1\times1} \\ A=\sqrt[]{3} \\ A=1.73in^2 \end{gathered}[/tex]Hence,
The area of the triangle = 1.73 squared inches
Related Questions
find the values of the variables X and Y in the given parallelogram
Answers
In the given parallelogram
From the property of diagonals of Parallelogram
The diagonals are bisect each other into equal parts
So, according to the figure
length 2x= length of y
2x=y
Similarly for the second diagonal,
length y+4=length3x
y+4=3x
Simplify the both equation by substitution method,
In substitution method, substitute the value of any one varibale and put into the another equation and simplify
[tex]\begin{gathered} 2x=y \\ y=2x \\ \text{Substitute the value of y into the other equation} \\ y+4=3x \\ 2x+4=3x \\ 3x-2x=4 \\ x=4 \end{gathered}[/tex]Now substitute the value of x=4 into the first equation and simplify for y
[tex]\begin{gathered} x=4 \\ 2x=y \\ 2(4)=y \\ y=8 \end{gathered}[/tex]So the value of varriables x = 4 and y=8
Answer : A) x=4, y=8
#1 An airplane rises at an angle of 14° with the ground. Find, to the nearest 10 feet, the distance it has flown when it has covered a horizontal distance of 1500 feet.
Answers
The airplane rises at an angle of 14° with respect to the ground.
You have to find the distances (diagonal) that it frew if it covered a horizontal distance of 1500 feet.
The distance flew by the place with respect to the horizontal ground and the height the plane is at after traveling 1500 feet form a right triangle. Where x represents the hypothenuse of the triangle. To determine its measure, you have to use the trigonometric relations
[tex]\begin{gathered} \sin \theta=\frac{opposite}{hypohtenuse} \\ \cos \theta=\frac{adjacent}{hypothenuse} \\ \tan \theta=\frac{opposite}{adjacent} \end{gathered}[/tex]Given that θ=14° and we know that the adjacent side to the angle measures 1500 feet, using the cosine we can determine the length of x as:
[tex]\begin{gathered} \cos 14=\frac{1500}{x} \\ x\cos 14=1500 \\ x=\frac{1500}{\cos 14} \\ x=1545.92ft \end{gathered}[/tex]The distance flew by the airplane is 1545.92ft
уA 5-digit PIN number is selected. What it the probability that there are no repeated digits?hoThe probability that no numbers are repeated isWrite your answer in decimal form, rounded to the nearest thousandth.Check Answer
Answers
Since there are 5 choices and there are 10 possible digits for each digit of the PIN( 0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
The total value possible 5 pins are 10⁵ = 100000
Using permutation, since 5 numbers are selected without repetition:
[tex]\frac{n!}{(n-k)!}=\frac{10!}{(10-5)!}=30240[/tex]The probability that no numbers are repeated is= 30240/ 100000
≈ 0.302
Given that U = (a, b, c, d, e, f, g} and A = {c,d, e, f], B = (a, c, e, g}, and C = (e, f, 9 }. Find the following sets.a.AU(BNC)b.A'n(BUC)c. A n(B'nc')
Answers
a) A U (B ∩ C)
In order to obtain the result for the previous set, first find (B ∩ C)
∩ is the intersection operation (the result is a set with common elements in the implied sets) Based on the given sets, for interection operation, you get:
(B ∩ C) = {e , g}
Next, the union operation with A results (union operation results in a set with all values of both sets but without repeating elements):
A U (B ∩ C) = {c , d , e , f , g}
b) A' ∩ (B U C)
A' is the complement of A (all values of the universe not present in A). In this case:
A' = {a , b , g}
B U C = {a , c , e , f , g}
Then:
A' ∩ (B U C) = {a , g}
c) A i (B' ∩ C')
B' = {b , d , f}
C' = {a , b , c , d}
B' ∩ C' = {b , d}
Then:
A ∩ (B' ∩ C') = {d}
takes Kim 11 hours to proof a chapter of Hawkes Learning SystemsIntroductory Algebra book and it takes Bethany 6 hours. How long would it take them working together? (Round your answer to two decimal places)
Answers
3.88 hours
Explanation:
If it takes Kim 11 hours to proof a chapter of Hawkes Learning Systems Introductory Algebra book, this shows that she will prove 1/11 of the chapter in 1 hour.
Similarly, if it took Bethany 6hrs to proof the same chapter, she will prove 1/6 of the chapter in 1hour
If x is the time take to read a chapter if the work together, the time it will take them working together is given as
[tex]\begin{gathered} \frac{1}{x}=\frac{1}{11}+\frac{1}{6} \\ \frac{1}{x}=\frac{6+11}{66} \\ \frac{1}{x}=\frac{17}{66} \end{gathered}[/tex]Cross multiply
[tex]\begin{gathered} 17x=66\times1 \\ 17x=66 \\ x=\frac{66}{17}=3\frac{15}{17}=3.88hours \end{gathered}[/tex]Hence the time it will take them to work together is 3.88 hours
Given: triangle ABC is an equilateral triangle. L, M, and N are the midpoints of AC, CB, and AB respectively. Prove: LMNB is a rhombus
Answers
Given:
∆ABC is an equilateral triangle, hence, all the three sides have the same length.
L, M, N are the midpoints of AC, CB, and AB. Hence, for instance, the distance between segment CM and MB are equal, by definition of midpoint.
Prove: LMNB is a rhombus.
Statement → Proof
1. ∆ABC is an equilateral triangle. → Given
2. Segment AB ≅ Segment AC ≅ Segment BC → Definition of an Equilateral Triangle
3. 1/2AB ≅ 1/2AC ≅ 1/2BC → Division Property of Equality
4. M and L are midpoints of BC and AC respectively. → Given
5. 1/2AB = Segment ML. → Midpoint Theorem
6. 1/2BC = Segment MB → Definition of Midpoint
7. Segment ML = Segment MB → Transitive Property of Equality using Statement 5 and 6
8. L and N are midpoints of AC and AB respectively. → Given
9. 1/2BC = Segment LN → Midpoint Theorem
10. 1/2AB = Segment BN → Definition of Midpoint
11. Segment LN = Segment BN → Transitive Property of Equality using Statement 9 and 10
12. Segment ML = Segment BN → Transitive Property of Equality using Statement 5 and 10
11. Segment MB = Segment LN → Transitive Property of Equality using Statement 6 and 9
13. Segment LN = Segment BN = Segment ML = Segment MB → Substitution Property of Equality using Statement 11 and 12
14. LMNB is a rhombus. → Definition of a rhombus.
One of the properties of a rhombus is that all 4 sides are equal in length.
Questions 12-14: The box below shows some of the steps of multiplying twopolynomials. Use this picture for the next THREE questions.+8x26x46x2-8x+3x18x3-24x2-64x16+22x2
Answers
In the red block will be the product of 6x^2 times +8 so:
[tex]6x^2\cdot8=48x^2[/tex]In the blue block will be the product of -8x and x^2
[tex]x^2\cdot(-8x)=-8x^3[/tex]and in the yellow block will be the product of 2 and 3x so:
[tex]3x\cdot2=6x[/tex]Draw a sketch of f(x)= (x+4)^2-5. Plot the point for the vertex, and label the coordinate as a maximum or minimum, and draw & write the equation for the axis of symmetry.
Answers
Answer: The vertex is (-4,-5) and the axis of symmetry is x=-4.
Explanation:
Given:
f(x)=(x+4)^2-5
The graph for the given equation is:
The point for the vertex is at (-4,-5) and it is also the minimum coordinate.
To find the axis of symmetry, we rewrite first the equation y=(x+4)^2-5 in the form y=ax^2 +bx +c.
So,
[tex]\begin{gathered} y=(x+4)^2-5 \\ y=x^2+8x\text{ +16 -5} \\ y=x^2+8x\text{ +1}1 \end{gathered}[/tex]Let:
a=1, b=8, c =11
The formula for the axis of symmetry is:
[tex]x=\frac{-b}{2a}[/tex]We plug in what we know.
[tex]\begin{gathered} x=\frac{-b}{2a} \\ =\frac{-8}{2(1)} \\ =\frac{-8}{2} \\ x=-4 \end{gathered}[/tex]The axis of symmetry is x=-4.
Therefore, the vertex is (-4,-5) and the axis of symmetry is x=-4.
Sam is collecting pennies. On the first day of the month, Sam is given 16 pennies Each day after than he gets 4 more pennies. Which of the following equations defines how many pennies he has after the nth day
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ANSWER:
[tex]d_n=4n+16_{}[/tex]STEP-BY-STEP EXPLANATION:
If n is the number of days that pass.
So each day Sam gets 4 more, which means that he would multiply the number of days by 4, before adding that number to the original number of pennies, which was 16.
Therefore, the equation would be:
[tex]d_n=4n+16_{}[/tex]5) . Write theequation of a line in slope-intercept form.
Answers
Explanation
Given the two points
[tex]\begin{gathered} (x_1,y_1)=(-2,4) \\ (x_2,y_2)=(-1,1) \end{gathered}[/tex]The rise and run of the line is given as;
[tex]m=\frac{\text{rise}}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{1-4}{-1-(-2)}=-\frac{3}{1}=-3^{}_{}[/tex]Recall, the equation of a line in slope-intercept form is given as;
[tex]y=mx+c[/tex]Since we know the value of m, we can find the value of c by using one of the points above.
When x=-2, y= 4. Therefore;
[tex]\begin{gathered} 4=-3(-2)+c \\ 4=6+c \\ c=4-6 \\ c=-2 \end{gathered}[/tex]We then insert m and c into the slope-intercept equation.
Answer:
[tex]y=-3x-2[/tex]I went from my house to a playground, 300metres away in 10 minutes. I ran back andreached in 2 minutes. What was my averagespeed?
Answers
Average speed= total distance / total time
Distance 1 = 300 meters
Distance 2 = 300 meters (back)
Total distance = 300m+300m = 600 meters
Time 1= 10 minutes
Time 2 = 2 minutes
Total Time = 10min+2min=12 minutes
Average speed= 600 meters / 12 minutes = 50 meters/minute
Question 2: 14 ptsOut of the 10,000 people who took their driving test for the first time, it was found that 6500 passed the test onthe first attempt. Estimate the probability that a randomly selected person would pass the driving test on thefirst attempt.A0 0.5, or 50%O 0.65, or 65%O 0.8. or 80%• 0.35, or 35%
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To calculate the probability of an event we would use the probability formula as follows;
[tex]P\lbrack E\rbrack=\frac{\text{Number of required outcomes}}{Number\text{ of possible outcomes}}[/tex]From the experiment conducted, 10,000 people took the driving test and 6500 passed the test on the first attempt. Therefore, to find the probability that a person randomly selected would pass the driving test on first attempt;
[tex]\begin{gathered} P\lbrack\text{first attempt\rbrack=}\frac{Number\text{ of required outcomes}}{Number\text{ of all possible outcomes}} \\ P\lbrack\text{first attempt\rbrack=}\frac{6500}{10000} \\ P\lbrack\text{first attempt\rbrack=}\frac{65}{100} \\ P\lbrack\text{first attempt\rbrack=0.65 or 65\%} \end{gathered}[/tex]ANSWER:
The second option is the correct answer.
solutions to 2y-3x=5
Answers
The equation 2y - 3x = 5 has infinitely many solutions.
In this question, we have been given an equation 2y-3x=5
We need to solutions to given equation.
for x = -1,
2y -3(-1) = 5
y = 1
for x = 0,
2y - 3(0) = 5
y = 5/2
y = 2.5
for x = 1,
2y - 3(1) = 5
y = 4
In this way for any real value of x we can find infinitely many values of y.
Therefore, the equation 2y - 3x = 5 has infinitely many solutions.
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What is the equation of the line that is perpendicular tothe given line and passes through the point (2, 6)?108(2.6)6x = 2O x = 62-10 -8 6 -22O y = 2O y = 62468 10X1-8-4)(8.4)68-10Oh
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The line in the graph is horzontal and slope of a horizontal line is 0.
Determine the slope of perpendicular line as product of slope of perpendicular line is -1.
[tex]\begin{gathered} m=-\frac{1}{0} \\ =\text{undefined} \end{gathered}[/tex]The slope is undefined means line is vertical and passing through the point (2,6). So equation of line is,
[tex]x=2[/tex]Answer: x = 2
Let Fx= x^3 + 2^x2 - 18 For what values of x is f(x) = 9 Enter your answers as a comma-separated list.
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We have the following function f(x) = x^3+2x^2 -18. We want to solve the following equation
[tex]x^3+2x^2-18=9[/tex]By subtracting 9 on both sides, we get the equivalent equation
[tex]x^3+2x^2-27=0[/tex]The function h(x)=0.4+2 models the height of the water level in a pool, in feet after x hours. Part A: After 1 hour, the height of the water level is:
Answers
Answer:
Need help myself
Step-by-step explanation:
The height of the water level after 1 hour is 2.4 units.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given function is h(x)=0.4x+2.
Given input value is x=1
So, the height of the water level is
h(1)=0.4(1)+2
= 0.4+2
= 2.4 units
Therefore, the height of the water level after 1 hour is 2.4 units.
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What are the first five terms of the arithmetic sequence defined explicitly by the formula an=1/8+2/3n
Answers
Answer:
D
Step-by-step explanation:
Given the formula of the arithmetic sequence, to find the first 5 terms, you just have to substitute n=1, n=2, n=2, n=4, and n=5.
Then, for the 1st term:
[tex]\begin{gathered} a_n=\frac{1}{8}+\frac{2}{3}n \\ a_1=\frac{1}{8}+\frac{2}{3}(1) \\ a_1=\frac{19}{24} \end{gathered}[/tex]2nd term:
[tex]\begin{gathered} a_2=\frac{1}{8}+\frac{2}{3}(2) \\ a_2=\frac{35}{24} \end{gathered}[/tex]There is no need to find the other 3 because there is no other sequence that has the first two terms as D.
a country with an area of 326 square miles has a population of 6846 residents which rate best represents the relationship between the population of the country in the area of the country
Answers
To answer this question, we need to remember the concept of rate. A rate is a result of comparing two different quantities, numbers. It is also a ratio - the result of dividing two numbers. In this case, we have two different quantities (or numbers):
1. Square miles that indicate the measurement of area. In this case, 326 square miles or 326 mi².
2. Population. In this case, we have 6846 residents.
In general, we can express the relationship if we divide the population by the area of the county, as the question suggests. Then, we have:
[tex]rate=\frac{Population}{Area}\Rightarrow rate=\frac{6846\text{residents}}{326mi^2}\Rightarrow rate=21\frac{residents}{mi^2}[/tex]Therefore, the rate that best represents the relationship between the population of the county and the area of the county is 21 residents per square mile (option C).
Find the surface area of a cylinder with a base diameter of 6 in and a height of 9 in. Write your answer in terms of II, and be sure to include the correct unit.
Answers
The surface area of a cylinder (S) with radius "r" and height "h" is:
[tex]S=2*\pi *r^2+2*\pi *r*h[/tex]Also, radius = diameter/2
Given:
r = 6/2 = 3 in
h = 9 in
Substitute the values in the equation and find S:
[tex]\begin{gathered} S=2\pi *3^2+2\pi *3*9 \\ S=2\pi *9+2\pi *27 \\ S=18\pi+54\pi \\ S=72\pi\text{ in}^2 \end{gathered}[/tex]Answer: The surface area is 72π in².
Can someone pls help me with my homework I have to go to sleep so pls be fast
Answers
Okay, here we have this:
Let's calculate the slope (using the points: (2, 58.5) and (4, 107.5)):
m=(107.5-58.5)/(4-2)=49/2=24.5
Finally we obtain that the slope is 24.5, so this means that option III is incorrect.
And considering that the y intercept represents the value of y when x equals 0 (0 tickets sold), If a person does not buy any ticket, they should not pay anything, this means that the option IV isn't right.
So, finally we are only left with option I and II let's check them:
Replacing in function:
Total value = (number of tickets * cost per ticket) + service charge
2 Tickets:
58.5=(2*24.5)+9.5
58.5=49+9.5
58.5=58.5
4 Tickets:
107.5=(4*24.5)+9.5
107.5=98+9.5
107.5=107.5
8 Tickets:
205.5=(8*24.5)+9.5
205.5=196+9.5
205.5=205.5
12 Tickets:
303.5=(12*24.5)+9.5
303.5=294+9.5
303.5=303.5
20 Tickets:
499.5=(20*24.5)+9.5
499.5=490+9.5
499.5=499.5
Finally we obtain that the correct answer is the option A. Statements I and III.
in the right triangle ABC, if m < C = 90 and sun A = 3/5, cos B is
Answers
Given a right angle triangle ABC:
[tex]\begin{gathered} m\angle C=90 \\ \sin A=\frac{3}{5} \end{gathered}[/tex]As the measure of angle C = 90
so, the sum of the angles A and B = 90
So, angles A and B are complementary angles
so,
[tex]\begin{gathered} \sin A=\cos B \\ \\ \cos B=\sin A=\frac{3}{5} \end{gathered}[/tex]so, the answer will be cos B = 3/5
AISD estimates that it will need 280000 in 8 years to replace the computers in the computer labs at their high schools. if AISD establishes a sinking fund by making fixed monthly payments in to an account paying 6% compounded monthly how much should each payment be
Answers
The initial amount of money that must be spend to replace the computers is P = $280,000. The period of time expected to replace all the computers is t = 8 years = 96 months. The interest rate is r = 6%.
Then, the monthly payment A is given by the formula:
[tex]\begin{gathered} A=P\frac{r(1+r)^t}{(1+r)^t-1} \\ A=280,000\cdot\frac{0.06\cdot(1+0.06)^{96}}{(1+0.06)^{96}-1} \\ A=\text{ \$16,862.74} \end{gathered}[/tex]Craig earns $2.50 per hour plus $3.50 for each haircut he gives.He worked 7 hours and gave 4 haircuts. How much did he earn?a. $31.50b. $168c. $46d. $17.50
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Craig earns $2.50 per hour plus $3.50 for each hair cut he gives.
He worked for 7 hours.
In hour basis, he earned
[tex]2.50\times7=17.5[/tex]He gave 4 hair cuts.
For 4 haircuts, he earned
[tex]3.50\times4=14[/tex]So, he total earned
[tex]17.5+14=31.5[/tex]Hence, the correct option is (A).
A triangle is formed by three roads that connect Shelbyville, Springfield, and Capitol City together. These roads are 19, 21, and 24 miles long. This forms a(n) _______ triangle.
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Given:
A triangle is formed by three roads that connect Shelbyville, Springfield, and Capitol City together.
These roads are 19, 21, and 24 miles long.
So, as we can see the three sides are different in lengths
So, the answer will be:
This forms a scalene triangle.
[tex]y = 3x + 19 \\ y = 5x + 33[/tex]how do you solve this with substitution?
Answers
We have the next system of equations:
[tex]\begin{gathered} y=3x+19\text{ (eq. 1)} \\ y=5x+33\text{ (eq. 2) } \end{gathered}[/tex]Substituting y = 3x + 19 into the second equation, and solving for x:
[tex]\begin{gathered} 3x+19=5x+33 \\ 3x+19-3x-33=5x+33-3x-33 \\ -14=2x \\ \frac{-14}{2}=\frac{2x}{2} \\ -7=x \end{gathered}[/tex]Substituting x = -7 into the first equation:
[tex]\begin{gathered} y=3(-7)+19 \\ y=-21+19 \\ y=-2 \end{gathered}[/tex]The solution is (-7, -2)
Type the correct answer in each box. Use numerals instead of wordsFind the value of each decimal model and then find the sum
Answers
To find the decimal values you have to count the number of shaded squares and divide it by the total number of squares in the grid.
Left value:
The grid is 10 x 10, which means that it is divided into 100 squares.
There are 23 shaded squares in the grid, so you can determine the decimal value as follows:
[tex]\frac{nº\text{shaded squares}}{total\text{ number of squares}}=\frac{23}{100}=0.23[/tex]Right value:
The grid is 10 x 10, so it is divided into 100 squares.
The number of shaded squares is 62. Divide 62 by 100 to determine the decimal value:
[tex]\frac{nº\text{shaded squares}}{total\text{ number of sqaures}}=\frac{62}{100}=0.62[/tex]Now what is left to do is to add both decimal values:
[tex]0.23+0.62=0.85[/tex]Which fraction has a value greater than 0.4? A 1/3 B 4/10 C 3/8 D 5/9
Answers
Answer:
D 5/9
Step-by-step explanation:
This fraction equates to over 0.5
Answer:
1/2, 5/8, 3/4
Step-by-step explanation:
1/2 is 0.5 5/8 is .625 and 3/4 is .75
Kyle is a secretory. She earns $12.38 per hout. She worked 2 hours last week. What is her straight fine pay
Answers
Answer:
Her pay is;
[tex]\text{ \$24.7}6[/tex]Explanation:
Given that;
She earns $12.38 per hour
and She worked 2 hours last week.
Her pay can be calculated as;
[tex]\text{Total pay}=Rate\times time[/tex]Substituting the given values;
[tex]\begin{gathered} \text{Pay}=\text{ \$12.38}\times2 \\ \text{Pay}=\text{ \$24.76} \end{gathered}[/tex]Her pay is;
[tex]\text{ \$24.7}6[/tex]Write a quadratic equation that has two imaginary solutions
Answers
We are asked to determine a quadratic equation that has two imaginary solutions. Let's suppose that the solution of the equation is the following:
[tex]x=\pm i[/tex]This means that the two imaginary solutions are "i" and "-i". Now, we use the following:
[tex]\pm i=\sqrt[]{-1}[/tex]Substituting we get:
[tex]x=\sqrt[]{-1}[/tex]Squaring both sides:
[tex]x^2=-1[/tex]Now, we add 1 to both sides:
[tex]x^2+1=0[/tex]And thus we have obtained a quadratic equation with two imaginary solutions.
Write an expression for the sequence of operations described below.multiply p by q, then multiply 10 by the resultDo not simplify any part of the expression.
Answers
Answer:
p x q x 10
Explanation:
First, we interpret the statement: multiply p by q
[tex]=p\times q[/tex]The result is: p x q
So if we then multiply 10 by the result, we have:
[tex]=p\times q\times10[/tex]This is the required expression.