Answers
we know that
sin(30°)=0.5 cos(30°)=√3/2
sin(60°)=√3/2 cos(60°)=0.5
sin(60)=BC/AC=5√3/10=√3/2-------------- is ok
cos (60)=AB/AC=5/10=0.5---- is ok
sin(30)=BA/AC=5/10=0.5-------------- is ok
cos (30)=BC/AC=5√3/10=√3/2-------------- is ok
if angle B is 90°
then
AB²+BC²=AC²------------> 5²+(5√3)²=10²=(25+75)=100------------- > is ok
the solution in the attached figure
Related Questions
if m ABC = 116 degrees what is ABC
Answers
Given: KLMN is a parallelogram, KA − angle bisector of ∠K LA − angle bisector of ∠L Prove: m∠KAL = 90°
Answers
Final answer:
This answer explains how to prove that angle KAL is 90 degrees in a parallelogram using angle bisectors.
Explanation:
To prove: m∠KAL = 90°
Given: KLMN is a parallelogram, KA - angle bisector of ∠K, LA - angle bisector of ∠L.
Proof:
Since KA and LA are angle bisectors in parallelogram KLMN, m∠K = m∠L.In a parallelogram, consecutive angles are supplementary, so m∠K + m∠L = 180°.Substitute m∠K for m∠L in the above equation: m∠K + m∠K = 180°, which simplifies to 2m∠K = 180°, giving m∠K = 90°.Proved that the measure of angle KAL is 90 degrees, which means that angle KAL is a right angle.
To prove that [tex]\( m\angle KAL = 90^\circ \)[/tex], we need to use the properties of angle bisectors and parallelograms.
Step 1: Identify the properties of a parallelogram.
In a parallelogram, opposite sides are equal in length, and opposite angles are equal. Also, adjacent angles are supplementary, meaning they add up to 180 degrees.
Step 2: Apply the properties to parallelogram KLMN.
Since KLMN is a parallelogram, we have:
[tex]\[ m\angle K + m\angle L = 180^\circ \][/tex]
[tex]\[ m\angle K = m\angle M \][/tex]
[tex]\[ m\angle L = m\angle N \][/tex]
Step 3: Use the properties of angle bisectors.
An angle bisector divides an angle into two equal parts. Therefore, we have:
[tex]\[ m\angle KAK = m\angle KAA \][/tex]
[tex]\[ m\angle LAL = m\angle LAA \][/tex]
Step 4: Express the angles in terms of the bisected angles.
Since KA is the angle bisector of [tex]\( \angle K \)[/tex], we can express [tex]\( m\angle KAK \)[/tex]and [tex]\( m\angle KAA \)[/tex] as half of [tex]\( m\angle K \)[/tex]:
[tex]\[ m\angle KAK = m\angle KAA = \frac{1}{2}m\angle K \][/tex]
Similarly, since LA is the angle bisector of [tex]\( \angle L \)[/tex], we can express [tex]\( m\angle LAL \)[/tex] and [tex]\( m\angle LAA \)[/tex] as half of [tex]\( m\angle L \)[/tex]:
[tex]\[ m\angle LAL = m\angle LAA = \frac{1}{2}m\angle L \][/tex]
Step 5: Use the supplementary angle relationship.
Since [tex]\( \angle K \)[/tex] and [tex]\( \angle L \)[/tex] are supplementary, we have:
[tex]\[ m\angle K + m\angle L = 180^\circ \][/tex]
Dividing both sides by 2, we get:
[tex]\[ \frac{1}{2}m\angle K + \frac{1}{2}m\angle L = 90^\circ \][/tex]
Step 6: Substitute the expressions for the bisected angles.
[tex]\[ m\angle KAK + m\angle LAL = 90^\circ \][/tex]
[tex]\[ \frac{1}{2}m\angle K + \frac{1}{2}m\angle L = 90^\circ \][/tex]
Step 7: Recognize that [tex]\( m\angle KAL \)[/tex] is the sum of [tex]\( m\angle KAK \)[/tex]and[tex]\( m\angle LAL \)[/tex].
[tex]\[ m\angle KAL = m\angle KAK + m\angle LAL \][/tex]
Step 8: Substitute the values from Step 6 into the equation from Step 7.
[tex]\[ m\angle KAL = \frac{1}{2}m\angle K + \frac{1}{2}m\angle L \][/tex]
[tex]\[ m\angle KAL = 90^\circ \][/tex]
A certain lottery has 3434 numbers. in how many different ways can 44 of the numbers beâ selected? (assume that order of selection is notâ important.)
Answers
A certain lottery has 34 numbers. in how many different ways can 4 of the numbers be selected? (assume that order of selection is not important.)
we know that
C=n!/[(n-r)!*r!]
n=34
r=4
then
C=34!/[(34-4)!*4!]=34*33*32*31/[4*3*2*1]=46376
the answer is 46376
It takes 212121 minutes for 555 people to paint 777 walls. How many minutes does it take 333 people to paint 555 walls?
Answers
Solution: We are given that:
5 people can paint 7 walls in 21 minutes
Therefore, 1 person can paint 7 walls in [tex] 21 \times 5=105 [/tex] minutes
Which means 1 person can paint 1 wall in [tex] \frac{105}{7} =15 [/tex] minutes
Now, 3 people can paint 1 wall in [tex] \frac{15}{3} =5 [/tex] minutes
Therefore, 3 people can paint 5 walls in [tex] 5 \times 5=25 [/tex] minutes
Answer:
25 :)
Step-by-step explanation:
Solve for X.
x - 7.9 = 2.23
Answers
add 7.9 to both sides
x - 7.9 (+7.9) = 2.23 (+7.9)
x = 2.23 + 7.9
x = 10.13
hope this helps
The mean of people in the sample of households of 7th-grade students is 4.3. The mean of people in the sample of households for 8th-grade students is 4.5. What might Principal Coleman infer or predict about the entire population based on the data?
Answers
Answer:
The mean of something is the "average"
For example, if the mean of people in the households of 7th-grade students is 4.3, this means that if you go to a random house of a 7th-grade student, you can expect around 4 people in there.
Now, for the 7th-grade students, the mean is 4.5, just a 0.2 bigger. (This means that, on average, there is more people in the 8th-grade student's households)
So Principal Coleman can infer that the amount of people in the households of 7th-grade students and 8th-grade students is almost the same, wherein the 8th-grade students there is a small chance of finding more people, but this difference is almost depreciable.
glenn raced his motorcycle 30 times last season. he finished first 12 times, second 5 times and crashed in 9 races. what percent of races did he crash? set up a proportion and solve.
Answers
Final answer:
Glenn crashed in 30% of the races.
Explanation:
To find the percentage of races Glenn crashed, you can set up a proportion. A proportion is an equation that states that two ratios are equivalent. Since Glenn raced 30 times and crashed 9 times, the ratio of crashes to total races is 9 crashes out of 30 races.
You can set up the proportion as follows:
Crashes / Total Races = Percentage of Crashes / 100
Plugging in the known values gives us this:
9 / 30 = Percentage of Crashes / 100
To solve for the percentage of crashes, you multiply both sides of the equation by 100:
(9 / 30)
100 = Percentage of Crashes
Simplifying gives us:
(9/3) 10 = Percentage of Crashes
Hence, the percentage of races that Glenn crashed is 30%.
Find f '(0.3) for f of x equals the integral from 0 to x of the arccosine of t, dt
Answers
By the fundamental theorem of calculus,
[tex]\displaystyle\frac{\mathrm d}{\mathrm dx}\int_0^x\cos^{-1}t\,\mathrm dt=\cos^{-1}x[/tex]
so that
[tex]f'(0.3)=\cos^{-1}0.3\approx1.266[/tex]
Ava bought a rectangular rug for her hallway. The rug is 23 yards wide and 234 yards long. What is the area of the rug as a mixed number in simplest form?
Answers
5,382 is in the simplest form
this is not a fraction, so i don't see where the simplest form comes in
The area of Ava's rectangular rug is 5382 square yards, calculated by multiplying the width (23 yards) and the length (234 yards).
To find the area of Ava's rectangular rug, we need to multiply its length and width:
Area = length × width
Using the given dimensions: 23 yards wide and 234 yards long:
Area = 23 × 234
First, let's perform the multiplication:
23 × 234 = 5382 square yards
Thus, the area of the rug is 5382 square yards as an improper fraction, which cannot be simplified further as a mixed number. Since the measurements are whole numbers, converting to a mixed number doesn't apply in this case.
How many possible outcomes exist when Louisa spins the spinner below twice? The spinner is numbered from 1-8.
Answers
So for two spins there are 8*8=64 possible outcomes, order counts, i.e. 5-3 is different from 3-5.
Answer:
The total number of possible outcomes are:
64
Step-by-step explanation:
It is given that:
Louisa spins the spinner below twice.
The spinner is numbered from 1-8.
Now, on spinning the spinner twice we obtain the sample space as:
(1,1) (1,2)....................(1,8)
(2,1) (2,2)...................(2,8)
(3,1) (3,2)..................(3,8)
(4,1) (4,2)..................(4,8)
(5,1) (5,2)..................(5,8)
(6,1) (6,2)..................(6,8)
(7,1) (7,2)..................(7,8)
(8,1) (8,2)..................(8,8)
Hence, the total number of outcomes is equal to the number of elements in sample space.
Hence, the total number of possible outcomes are:
64
What are the solutions of the system? Solve by graphing. y=x2-2x-1 y = -2
Answers
1. Rewrite the equations:
y=x²-2x-1 (i)
y=-2 (ii)
2. Then:
(i)=(ii)
-2=x²-2x-1
3. Now, you must order the terms and and factorize, as below:
(x-1)(x-1)=0
(x-1)²=0
4. The solution is:
x=1
You can see that the graphs attached touch each other in x=1. Therefore, the solution is x=1
Which describes the slope of this line?
Number graph ranging from negative five to five on the x and y axes. A line is drawn on the graph that passes through (zero, negative three) and (two, one).
negative slope
positive slope
undefined slope
zero slope
Answers
The slope coefficient is S= (yb-ya)/(xb-xa)
S= (1-(-3))/(2-0) => S= (1+3)/2 = 4/2= +2 => S= +2
The correct answer is positive slope
Good luck!!!
A biologist studied the populations of common guppies and Endler's guppies over a 6-year period. the biologist modeled the populations, in tens of thousands, with the following polynomials where x is time, in years.
common guppies: 3.1x^2+6x+0.3
Endler's guppies: 4.2x^2-5.2x+1
what polynomial models the total number of common and Endler's guppies
Answers
To get our answers we need to add those two polynomials. We add polynomials by adding their like terms. Like terms are those that have the same exponent.
[tex]3.1x^2+6x+0.3+4.2x^2-5.2x+1=\\=(3.1x^2+4.2x^2)+(6x-5.2x)+(0.3+1)=\\ =7.3x^2+0.8x+1.3[/tex]
So the total amount of guppies would be modeled using this polynomial:
[tex]7.3x^2+0.8x+1.3[/tex]
what polynomial models the total number of common and Endler's guppies
your answer will be:
7.3x^2+0.8+1.3
Step-by-step explanation:
this answer correct for 2022
Deposit $400 into an account that pays simple interest at rate of 4% per year how much interest will she be paid in the first 6 years
Answers
Simple interest = 4%
Simple interest for one year = 4% of $400 = 0.04 x 400 = $16
Simple interest for 6 years = 16 x 6 = $96
Total interest for 6 years is $96
Juno deposited $750 in a savings account that earns 4% interest compounded annually. If she does not deposit or withdraw any more money, how much money will there be in the account after 13 years? Round your answer to the nearest dollar. A. $1249 B. $1360 C. $1427 D. $1140
Answers
Explanation:
The amount of interest is calculated using the formula
[tex]A=p(1+\frac{r}{n})^{nt}[/tex],
where a is the amount of principal, r is the interest rate as a decimal number, n is the number of times per year the interest is compounded, and t is the number of years.
Our principal is $750, the interest rate is 4%=4/100=0.04, n is 1, and t is 13:
[tex]A=750(1+\frac{0.04}{1})^{13\times1}=750(1+0.04)^{13}=750(1.04)^{13}=1248.81[/tex],
which rounds to 1249.
Answer:
A. $1249.
Step-by-step explanation:
We have been given that Juno deposited $750 in a savings account that earns 4% interest compounded annually. We are asked to find the amount of money in the account after 13 years.
To solve our given problem, we will use compound interest formula. [tex]A=P(1+\frac{r}{n})^{nt}[/tex], where,
A = Amount after t years,
P = Principal amount,
r = Interest rate in decimal form,
n = Number of times interest is compounded per year,
t = Time in years.
Let us convert our given interest rate in decimal form.
[tex]4\%=\frac{4}{100}=0.04[/tex]
Upon substituting our given values in compound interest formula we will get,
[tex]A=\$750(1+\frac{0.04}{1})^{1\cdot 13}[/tex]
[tex]A=\$750(1+0.04)^{13}[/tex]
[tex]A=\$750(1.04)^{13}[/tex]
[tex]A=\$750\times 1.665073507310388[/tex]
[tex]A=\$1248.805130482791\approx \$1249[/tex]
Therefore, there will be $1249 in Juno's account after 13 years and option A is the correct choice.
What fraction is equivalent to the fraction 0/6
Answers
Since this is equal to zero, the answer could actually be any number in the demoninator and zero in the numerator.
Hope this helps!
In a circle with a radius of 26.9 m, an arc is intercepted by a central angle of 9π5 radians.
What is the arc length?
Use 3.14 for π and round your final answer to the nearest hundredth.
Make sure to show your calculations.
Answers
find the length of a circumference
L=2*pi*r-------------> 2*pi*26.9=53.8*pi m
Step 2
find the arc length
if 2*pi radians --------------> 53.8*pi m
(9/5)*pi radians------------> X
X=[(9/5)*pi*53.8*pi]/[2*pi]-------------> [9*53.8*pi]/[5*2]=152.04 m
the answer is 152.04 m
152.04 is right i just took the test
your welcome ;)
Make a comparison between the government’s roles in a capitalist economic system versus a socialist or communist economic system.
Answers
In a Capitalist Economic System, the government is expected to guarantee the respect to private property, promulgate laws that defend economic freedom, and is an intermediary between the private sector and society. In this economic system, the government is reduced an doesn't intervene in the free market.
In a Socialist or Communist Economic System, the government redistributes goods and services, takes the means of production (private property) from their owners to put them in service of the working class, promulgate laws that limit economic freedom and heavily intervenes in the market and economy.
Have a nice day!
A capitalist economic system is built on the respect of private property and competition. Hard work and free enterprise benefit citizens more than the government can. For the most part, government intervention is reduced. However, the government does provide security and some basic services, like infrastructure, to its citizens.
Socialist and communist systems endure more government control. Citizens of these economies have a limited amount of freedom by law. The government controls the market place and the production of most goods and services.
^ My answer from Edge
How many sequences of length 5 can be made when each component of the sequence can take 3 different values?
Answers
[tex]3^5=243[/tex]
what is the gcf of the numerator and denominator of the rational expression
3x-15/x^2-x-20
A: x-5
B: x+4
C: 4
D: 5
Answers
The only common factor is (x -5).
Selection A is appropriate.
find d for the arithmetic series with S17=-170 and a1=2
Answers
[tex]\bf \textit{ sum of a finite arithmetic sequence}\\\\ S_n=\cfrac{n(a_1+a_n)}{2}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ ----------\\ n=17\\ S_{17}=-170\\ a_1=2 \end{cases} \\\\\\ -170=\cfrac{17(2+a_{17})}{2}\implies \cfrac{-170}{17}=\cfrac{(2+a_{17})}{2} \\\\\\ -10=\cfrac{(2+a_{17})}{2}\implies -20=2+a_{17}\implies -22=a_{17}[/tex]
well, since the 17th term is that much, let's check what "d" is then anyway,
[tex]\bf n^{th}\textit{ term of an arithmetic sequence}\\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\ ----------\\ n=17\\ a_{17}=-22\\ a_1=2 \end{cases} \\\\\\ -22=2+(17-1)d\implies -22=2+16d\implies -24=16d \\\\\\ \cfrac{-24}{16}=d\implies -\cfrac{3}{2}=d[/tex]
share 747 pound in the ratio 2:7 betwen tom and ben
Answers
9p = 747 divded by 9 = 83
2 * 83 = 166 7 * 83 = 581
Hope it helps
a square has 4 right angle corners. give another shape with 4 right angle corners
Answers
Action wheels manufacturers models of antique cars for collectors. In August , it manufactured 300 model cars. In September, action wheels manufactured 5% fewer model cars than in August . What is the difference in the numbers of cars manufactured in August and September?
Answers
The difference in the number of cars manufactured in August and September is 15 cars.
The difference in the number of cars manufactured in August and September can be calculated as follows:
In August, Action Wheels manufactured 300 model cars.In September, they manufactured 5% fewer cars than in August, which means they made 95% of the cars they made in August.Calculating the number of cars manufactured in September: 300 * 0.95 = 285 cars.Therefore, the difference in the numbers of cars manufactured in August and September is 300 - 285 = 15 cars.Complete the factorization of 3x2 – 5x + 2.
Which two factors can be multiplied together to make this trinomial?
(x – 2)
(x – 1)
(x + 1)
(3x – 2)
(3x + 2)
Answers
= 3x² - 3x - 2x + 2
= 3x(x-1) - 2(x-1)
= (x-1)(3x-2)
the answers are (x-1) and (3x-2)
Suppose p(x1) = .75 and p(y2 | x1) = .40. what is the joint probability of x1 and y2?
Answers
[tex]\mathbb P(Y_2\mid X_1)=\dfrac{\mathbb P(Y_2\cap X_1)}{\mathbb P(X_1)}[/tex]
so
[tex]\mathbb P(Y_2\cap X_1)=0.40\times0.75=0.3[/tex]
The joint probability of x1 and y2 is P (Y₂/X₁ ) = P(Y₂ ∩ X₁ )/ P (X₁) will be 0.3.
What is the probability about?In the joint probability of x1 and y2 is P (Y₂/X₁ )= P(Y₂ ∩ X₁ )/ P (X₁).
Therefore:
P(Y₂ ∩ X₁ )
=0.40 x 0.75
= 0.3
Therefore by following the law of conditional probability, the outcome of the The joint probability of x1 and y2 is P (Y₂/X₁ ) = P(Y₂ ∩ X₁ )/ P (X₁) will be 0.3.
Learn more about probability from
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for this job , Hayden earns an hourly rate of $30. For each hour he works over 40 hours, he earns 1.5 times his regular hourly rate. In a two-week period, Hayden earns $2175 by working 40 regular hours, plus overtime. How many overtime hours did Hayden work?
Answers
Extra hour rate is 1.5×30=$45
given that he earned $2175 by working 40 regular hours, the number of overtime hours he worked will be given as follows;
let the number of overtime be x
hence total amount earned will be:
(40×30)+(45×x)=2175
1200+45x=2175
45x=2175-1200
45x=975
solving for x we get
x=975/45
x=65/3=21 2/3 hours
You borrow $6,730 to buy a car. the terms of the loan call for monthly payments for 5 years a rate of interest of 6 percent. what is the amount of each payment?
Answers
interest, i = 0.06/12 = 0.005 per month
term, n=5 years = 60 months
Monthly payment,
A=[tex]\frac{P(i*(1+i)^n)}{(1+i)^n-1}[/tex]
[tex]=\frac{6730(.005*(1+.005)^{60})}{(1+.005)^{60}-1}[/tex]
=130.11 [to the nearest cent]
4j-2/2=4j+5
4j minus 2 divided by 2 equals 4j plus 5 ?
Answers
[tex] \frac{4j - 2}{2} = 4j + 5[/tex]
then this is the answer:
[tex] \frac{4j - 2}{2} \times 2 = 2 \times (4j + 5)[/tex]
[tex]4j - 2 = 8j + 10[/tex]
4j - 2 - 4j = 8j + 10 - 4j
-2 = 4j + 10
-2 - 10 = 4j + 10 - 10
-12 = 4j
[tex] \frac{ - 12}{4} = \frac{4j}{4} [/tex]
-3 = j
j = -3
The solution to the equation (4j - 2) / 2 = 4j + 5 is j = -3. The equation was simplified by eliminating fractions and isolating the variable j through algebraic steps.
To solve the equation (4j - 2) / 2 = 4j + 5 for the variable j, you can follow these steps:
1. First, simplify both sides of the equation:
(4j - 2) / 2 = 4j + 5
2. Multiply both sides of the equation by 2 to eliminate the fraction:
4j - 2 = 2 * (4j + 5)
3. Distribute the 2 on the right side:
4j - 2 = 8j + 10
4. Move the variable terms to one side of the equation and the constants to the other side. You can do this by subtracting 8j from both sides:
4j - 8j - 2 = 10
5. Combine like terms:
-4j - 2 = 10
6. Add 2 to both sides to isolate the variable term:
-4j = 10 + 2
-4j = 12
7. Finally, divide both sides by -4 to solve for j:
j = 12 / -4
j = -3
So, the solution to the equation is j = -3.
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Identify the pair of alternate interior angles.
Question options:
A.) 2 and 8
B.) 1 and 8
C.)2 and 7
D.) 4 and 6