Calculate the size of angle x.
Give your answer to 1 decimal place.
8 cm
11 cm
х
15 cm
Answers
Given:
Consider the below figure attaches with this question.
To find:
The size of angle x.
Solution:
Law of Cosines:
[tex]\cos A=\dfrac{b^2+c^2-a^2}{2bc}[/tex]
Three sides of the triangle are 11 cm, 8 cm, 15 cm. Since 11 cm is the opposite side of the angle x, therefore [tex]a=11[/tex].
Let [tex]A=x,a=11,b=8,c=15[/tex]. Substitute these values in the above formula.
[tex]\cos x=\dfrac{8^2+15^2-11^2}{2(8)(15)}[/tex]
[tex]\cos x=\dfrac{64+225-121}{240}[/tex]
[tex]\cos x=\dfrac{168}{240}[/tex]
[tex]\cos x=0.7[/tex]
Taking cos inverse on both sides, we get
[tex]x=\cos^{-1} 0.7[/tex]
[tex]x=45.572996^\circ[/tex]
[tex]x\approx 45.6^\circ[/tex]
Therefore, the measure of angle x is 45.6°.
Related Questions
Frisco ISD had a student enrollment of approximately 46,000 students in 2013 and is growing at an average rate of about 6% annually. If this rate continues the enrollment growth can be modeled using the equation 46000(1.06)t = y where t represents time in years and y represents number students. How many years will pass until the population of Frisco ISD is at 100,000 students? ≈ 13.33 years ≈ 85.91 years ≈ 5.62 years ≈ 2.05 years
Answers
Answer:
≈ 13.33 years
Step-by-step explanation:
The population of Frisco ISD after t years is given by the following equation:
[tex]y(t) = 46000(1.06)^{t}[/tex]
How many years will pass until the population of Frisco ISD is at 100,000 students?
This is t for which [tex]y(t) = 100000[/tex]. So
[tex]y(t) = 46000(1.06)^{t}[/tex]
[tex]46000(1.06)^{t} = 100000[/tex]
[tex](1.06)^{t} = \frac{100000}{46000}[/tex]
[tex]\log{(1.06)^{t}} = \log{\frac{100000}{46000}}[/tex]
[tex]t\log{1.06} = \log{\frac{100000}{46000}}[/tex]
[tex]t = \frac{\log{\frac{100000}{46000}}}{\log{1.06}}[/tex]
[tex]t = 13.33[/tex]
So the answer is ≈ 13.33 years
Use the Binomial Theorem to expand (x + 1)^6
Answers
Answer:
Here is what i got x^2+6x^5+15x^4+6x+1
Step-by-step explanation:
^ that mark is for exponents btw. For anyone that is new to this
The Binomial Expansion of [tex](x+ 1)^6[/tex] is [tex]x^6[/tex] + 6[tex]x^5[/tex]y + 15[tex]x^4[/tex]y² + 20x³y³ + 15x²[tex]y^4[/tex] + 6x[tex]y^5[/tex] + [tex]y^6[/tex].
What is Binomial Expansion?An expression that has been raised to any finite power can be expanded using the binomial theorem. A useful expansion technique with applications in probability, probability theory, and algebra is the binomial theorem. A binomial expression is an algebraic expression with two terms that are not the same.
Given:
We have to expand [tex](x+ 1)^6[/tex]
We know the general form of Binomial Expansion
(x + y[tex])^n[/tex] = C(n, 0) [tex]x^ny^0[/tex] + C(n, 1) [tex]x^{n-1}y^1[/tex] +.........+ C(n, n) [tex]x^0y^n[/tex]
Here n= 6
So, the expansion of [tex](x+ 1)^6[/tex] is
= C(6, 0) [tex]x^6y^0[/tex] + C(6, 1)[tex]x^5y^1[/tex] + C(6, 2) [tex]x^4y^2[/tex] + C(6, 3) x³y³ + C(6, 4) x²[tex]y^4[/tex] +
C(6, 5) x[tex]y^6[/tex] + C(6, 6) [tex]x^0y^6[/tex]
= [tex]x^6[/tex] + 6[tex]x^5[/tex]y + 15[tex]x^4[/tex]y² + 20x³y³ + 15x²[tex]y^4[/tex] + 6x[tex]y^5[/tex] + [tex]y^6[/tex]
Learn more about Binomial Expansion here:
https://brainly.com/question/28983418
#SPJ5
A figure was translated 4 units down and 3 to the left then reflected over the y-axis. The figures are
Answers
Answer:
Congruent and similar
Step-by-step explanation:
because you did not change anything about the shape that shape is still the same size and shape just in a different spot
GIVING BRAINIEST!!!!!!!!!!!! 3 times the difference of 4g and 4 is less than -6 times the sum of -3g and 4!
Answers
Answer:
3(4g-4)<-6(-3g+4)
18. Let f(x) = ax? + bx-6 and 0 (x) = bx2 + ax.
If x-2 divides f(x) completely but leaves
the remainder -12 when it divides $(x),
then factorise f (x) + 0 (x) + 2x2.
Answers
Step-by-step explanation:
the number of members in A municipal corporation depends upon the _______ city
The distance in New York is 3 hours ahead of the distance in LA. The miles between the cities is 7,120. A plane left New York at 6:25a.m. and arrived at 8:25a.m. local time. At what speed did the plane travel?
Answers
What is the answer to 2.5 divided by 5
Answers
2.5/5=0.5
0.5 is the value of 2.5 by 5.
What is Division?A division is a process of splitting a specific amount into equal parts.
We need to find the solution when 2.5 divided by 5.
2.5/5
2.5 is the numerator and 5 is the denominator.
5 is the divisor and 2.5 is the dividend.
Zero point five is the value of 2.5 by 5.
0.5 is the value of 2.5 by 5.
Hence, 0.5 is the value of 2.5 by 5.
To learn more on Division click:
https://brainly.com/question/21416852
#SPJ5
please help:) i would appreciate it lol
Answers
Answer:
subtotal: $65.00
8% sales tax: $5.20
total: $70.20
Step-by-step explanation:
Triangle Theorems please!!!!!!
Answers
Answer:
x = 8
Step-by-step explanation:
GIVING BRAINIEST!!!! I NEED THE INEQUALITY SENTENCE FOR IT!!!
Answers
find the measure of each given angle
Answers
9514 1404 393
Answer:
∠2 = 19°
Step-by-step explanation:
Angles that are equal to 161° are vertical and corresponding angles: 1, 4, 5.
Angles that are equal to the supplement of 161° are the remaining angles: 2, 3, 6, 7.
Angle 2 is the supplement of 161°:
∠2 = 180° -161°
∠2 = 19°
(10 POINTS) answer ASAP if you can
Answers
Lines that appear to be tangent are tangent. O is the center of the circle. What is the value of x?
Answers
Answer:
28
Step-by-step explanation:
Neat Question.
Thanks for posting.
The straign line (horizontal) makes an isosceles triangle inside the circle. So the bottom angle of the triangle is also 59 degrees. The central angle of the interior triangle is
180 - 59 - 59 = 62.
x and the 62 degree angle are complementary -- both are in the 90 degree angle triangle made by the tangent. x + 62 = 90
x = 90 - 62 = 28
Answer:
x = 28°
Step-by-step explanation:
PQ is tangent to circle O, ∠OPQ = 90°
∠QPR = 90-59 = 31°
mOP = mOR (radius) ∠PRO = ∠OPR = 59° (isosceles triangle)
∠PRO = ∠QPR + x° (triangle exterior angle)
x = 59° - 31° = 28°
Kevin is reading a 295-page book. On Friday, he read 73 pages. On Saturday, he read
89 pages. Which equation most closely estimates how many pages Kevin has
remaining to read?
Answers
The equation most closely estimates the number of pages Kevin has remaining to read will be x + 73 + 89 = 295.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less complicated.
Kevin is reading a 295-page book. On Friday, he read 73 pages. On Saturday, he read 89 pages.
Let 'x' be the number of pages to be read. Then the equation is given as,
x + 73 + 89 = 295
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ2
look at the picture for the question 10 points will mark brainilest
Answers
Answer:
you want to have an answer to the question do you, i wish i could help but im only here for my answers
Step-by-step explanation:
sorry
Answer:
B
Step-by-step explanation:
accidentally commented
Which of these is an exponential parent function?
A. f(x) = x
B. f(x) = x
C. f(x) = 2x
D. f(x) = 1x1
SMIT
Answers
Option B is correct, f(x) = 2ˣ is an exponential parent function.
What is a function?A relation is a function if it has only One y-value for each x-value.
The exponential parent function is of the form:
f(x) = aˣ
where a is a positive constant (the base of the exponential function).
Among the given options, the exponential parent function is,
⇒ f(x) = 2ˣ,
Because it has the form of an exponential function, where the base is 2.
f(x) = x is a linear function, not an exponential function.
f(x) = |x| is an absolute value function, not an exponential function.
f(x) = x² is a quadratic function, not an exponential function.
Hence, f(x) = 2ˣ is an exponential parent function, Option B is correct.
To learn more on Functions click:
brainly.com/question/30721594
#SPJ5
Find the slope of a line perpendicular to the equation: 3x – 2y = 6
Answers
Answer:
3/2x
Step-by-step explanation:
so
y=mx+c
-2y=-3x+6
2y=3x-6
y=3/2x-3
So the gradient of the perpendicular would be
m= -2/3
find the x and y
y=3/2(0)-3
=-3
(0)=3/2x-3
x=2
So
Substitute them all into
y=mx+c
-3=-2/3(2)+c
c=-5/3
So
y=-2/3x-5/3
I might have made mistakes since I typed this so recheck if you can
PLEASE JUST GIVE EXPRESSION. WILL GIVE BRAINLIEST
Samantha works part-time at a store where she earns $462.30 each month. Write an expression that could be used to find the amount Samantha earns working any number of months, m.
Answers
Answer:
like a month she earns $462.30
so if you want like how many she earns in 4 years then,
just do $462.30×4
after calculation answer will come.
The measure of c is
.
Answers
Answer:
10
Step-by-step explanation:
6^2=36
8^2=64
64+36=100
The square root of 100 is 10
What is m Angle Q B O? 5° 9° 12° 24°
Answers
Answer:
12
Step-by-step explanation:
Martha ran 2 miles in 15 minutes.
At this rate, how many miles
would she run in 2 hours?
Answers
Help me ! This is due today
Answers
Answer:
y = 1/4 x + 1
The slope is 1/4, and the y intercept is 1.
Let me know if this helps!
The principal of a high school e-mails a survey to all parents asking them to vote on the best time to have the PTA meeting. She only receives responses from 56% of the parents. Describe how the design of the survey leads to bias.
A. A nonresponse error was made in this design. This type of sampling only represents those who answered the survey; it does not represent the entire population.
B. A nonresponse error was made in this design. This type of sampling only represents the parents at this school and not the entire population.
C. A convenience sample error was made in this design. This type of sampling only represents the parents with e-mail addresses and not the entire population.
D. An undercoverage error was made in this design. This type of sampling only represents the parents in the city and not the entire population.
E. There are no potential areas of bias.
Answers
Answer:
A
Step-by-step explanation:
The design of the survey leads to bias because a nonresponse error was made in this design. This type of sampling only represents those who answered the survey; it does not represent the entire population.
Only 56% of response were received this means the entire population did not participate in the survey only a chuck of them answered the survey. This can lead to a biased result, an assumption.
A party rental company has chairs and tables for rent. The total cost to rent 5 chairs and 3 tables is $31.the total cost to rent 2 chairs and 6 tables is $22.what is the cost to rent each chairs and each table?
Answers
Answer:
$1.25 & $10.25
Step-by-step explanation:
Let c be the cost of renting one chair and t be the cost of renting table. We're given two equations:
#1. 5c + 3t = 37
#2. 2c + 6t =64
We have a system of equations. Using our system of equations calculator, we can solve this problem any of 3 ways below:
Chairs (c) cost $1.25Tables (t) cost $10.25The sum of 8 and t
help anyone??
Answers
Not sure if I’m wrong but I am also learning this.
Answer:
8 + tStep-by-step explanation:
The sum of 8 and t ⇒ 8 + t
An independent research firm conducted a study of 100 randomly selected children who were participating in a program advertised to improve mathematics skills. The results showed no statistically significant improvement in mathematical skills, using a significance level of 0.05. The program is effective, which of the following would be an appropriate method for increasing power in this context?
a. Increase the sample size to 200 children.
b. Use a two-sided test instead of a one sided test.
c. Decrease the sample size.
d. Use alpha-0.01 instead of a-alpha.
e. Use a one sided test instead of a two-sided test.
Answers
Answer:
b) use a two-sided test instead of a one sided test.
Step-by-step explanation:
If we are using a significance level of 0.05, then the two-tailed test assigns half alpha to test for statistical significance in one direction and half alpha to test statistical significance in the other direction. This implies that .025 is present in each tail of the test statistical distribution. When using the two-tailed test, regardless of the direction of the relationship you assume, we test the possibility of the relationship in both directions.
(10p+10)+(8p−1) factored?
anyone know, please, i need this for school..
Answers
Answer:
the answer is
9(2p+1)
Answer:
18p +9
Step-by-step explanation:
Because you add the numbers in front of the p's (10+8) and then you add 10 plus -1, which is 9.
Hope this helps! Have a good day and remember to be tiger fierce!! :)
Which is the largest interval over which the function shown in the table is decreasing?
Answers
Answer:
c
Step-by-step explanation:
Because to make the same we have to have x as 1 which is x>0
When x = 2.5 and y = 5, which of the expressions below will be greater than 75? Select all that apply.
A) 8x+12y
B) 10xy
C) 4y^2–8x
D) y^3/2x
Answers
Answer:
C is may answer
Step-by-step explanation:
I HOPE IS HELPS
Carlos, Julio and Ricky were born in consecutive years Carlos was the oldest of the three and Ricky was the youngest. In 1990, after their birthday, the sum of their ages was 129. In what years were they born?
Answers
Answer:
Carlos born in 1944
Julio born in 1945
Ricky born in 1946
Step-by-step explanation:
x = Carlos age
x+1 = Julio age
x+2 = Ricky age
x + x+1 + x+2 = 129
3x + 3 = 129
3x = 126
x = 42 (Carlos age)
x+1 = 43 (Julio age)
x+2 = 44 (Ricky age)
1990 - 42 = 1944 (year Carlos born)
1990 - 43 = 1945 (year Julio born)
1990 - 44 = 1946 (year Ricky born)