In ΔABC, ∡A is a right angle, and m∡B = 45°. What is the length of BC? If the answer is not an integer, leave it in simplest radical form. The diagram is not drawn to scale.
Answers
BC² = 121 + 121
BC² = 242
BC = √242
BC = 11√2
Answer: 11√2
Answer:
The length of BC is 11√2 ft.
Step-by-step explanation:
Given,
A right angled triangle ABC,
In which,
AC = 11 ft ( By diagram ),
∠A = 90°,
∠B = 45°,
By the law of sine,
[tex]\frac{sin B}{AC}=\frac{sin A}{BC}[/tex]
[tex]\implies BC\times sin B = AC\times sin A[/tex] ( By cross multiplication )
[tex]\implies BC = \frac{AC\times sin A}{sin B}[/tex]
By substituting the values,
[tex]BC=\frac{11\times sin 90^{\circ}}{sin 45^{\circ}}[/tex]
[tex]=\frac{11}{\frac{1}{\sqrt{2}}}[/tex]
[tex]=11\sqrt{2}[/tex]
Hence, the length of BC is 11√2 ft.
Related Questions
The height of a tree in feet over x years is modeled by the function f(x). f(x)=301+29e−0.5x which statements are true about the growth of the tree? select each correct answer. the tree's maximum height is limited to 30 ft. the tree is initially 2 ft tall. between the 5th and 7th years, the tree grows approximately 7 ft. after growing 15 ft, the tree's rate of growth decreases.
Answers
Final answer:
The tree's maximum height is not limited to 30 ft but approaches 301 ft. Initially, the tree is 30 ft tall, not 2 ft. To verify the growth between the 5th and 7th years, one must calculate f(5) and f(7). The rate of growth indeed decreases over time.
Explanation:
When analyzing the function f(x) = 301 + 29e^{-0.5x} to understand the growth pattern of a tree, it is apparent that some statements about the tree's growth can be identified as true or false.
The tree's maximum height is not limited to 30 ft; instead, the model suggests that the height approaches 301 ft as x increases indefinitely, because the exponential term decreases towards zero.The tree is initially 30 ft tall, not 2 ft tall, since f(0) = 301 + 29 × 1 = 330 ft.Between the 5th and 7th years, the growth can be calculated using f(5) and f(7) to determine if it grows approximately 7 ft during that period.After growing 15 ft, the rate of growth would decrease since the exponential function's growth rate decreases as x increases.What is the surface area of the prism? Include steps.
Answers
Area of a rectangle: Area = Length x Height
- Rectangular Prism Dimensions:
Length: 3m
Width: 4m
Height: 2m
To calculate the surface area of a rectangular prism we first need to realize that he has 3 pairs of equal rectangles.
- The first pair (Photo 1):
Two rectangles with the same measure, so we can say that the area of this pair is: (L x H) x (L x H) or 2 x (L x H).
-> Area (Pair 1) = 2 x (3 x 2) = 2 x 6 = 12m^2
But if we will do the same thing to 3 different pairs, we can describe that:
- Total Surface Area (At):
At = 2 x (L x H) + 2 x (L x H) + 2 x (L x H)
-> At = 2 x ((L x H) + (L x H) + (L x H))
So now, just put the values inside de formula,
- Pair 1: Length = 3m ; Height = 2m
- Pair 2: Length = 4m ; Height = 2m
- Pair 3: Length = 4m ; Height = 3m
*I know that this pair doesn't have a "real Height" but this doesn't change anything when solving, you can consider the 4m as height and the 3m as length or vice versa, the order of the factors doesn't change the product.
-> At = 2 x ((3 x 2) + (4 x 2) + (4 x 3))
-> At = 2 x (6 + 8 + 12)
-> At = 2 x (26)
-> At = 52 m^2
A bus covered the 400-km distance between points a and b at a certain speed. on the way back the bus traveled at the same speed for 2 hours and then increased the speed by 10 km/hour until it reached a, thus spending 20 fewer minutes on the return trip. how long did the return trip take?
Answers
xt=400,
On the way back, the 2x+(x+10)(t-7/3), where it was total time minus 2 hours already driven minus 1/3 of hour, the 20 minutes.
2x+xt-(7/3)x+10t-70/3=400
2x+400-(7/3)x+10t-70/3=400
thus
-(1/3)x+4000/x=70/3
multiplying through by x we get:
-(1/3)x^2-(70/3)x+4000=0
x^2+70x-12000=0
x=(1/2)(-70+/-sqrt52900)
x=80 kmp
thus:
it took 5 hours to make the first trip
on way back 2 hours at 80 kph which means he traveled for 160 km at this speed
2 h 40 min at 90 k/h=90*8/3=240 km
The speed going to B is x, the time t and the distance, 400 km.
xt=400, x kph and t in hours
on the way back, the 2x+(x+10)(t-7/3), where it was total time minus 2 hours already driven minus 1/3 of an hour, the 20 minutes.
2x+xt-(7/3)x+10t-70/3=400
2x+400-(7/3)x+10t-70/3=400, 400 cancels, t=400/x
-(1/3)x+4000/x=70/3
multiply by x
-(1/3)x^2-(70/3)x+4000=0
x^2+70x-12000=0
x=(1/2)(-70+/- sqrt 52900); sqrt term=230
x=80 kph
took 5 hours to go there
on way back 2 hours at 80 kph=160 km
2h40m at 90kph=90*8/3=240 km
They add to 400 km.
The return trip took 4h40m
Rewrite 0.85 as a fraction in lowest terms.
Answers
well, 0.85 has two decimals, so we use two zeros,00, at the bottom of the fraction and lose the dot, let's do so,
[tex]\bf 0.\underline{85}\implies \cfrac{085}{1\underline{00}}\implies \cfrac{85}{100}\implies \stackrel{simplified}{\cfrac{17}{20}}[/tex]
sabendo que x2 + y2=74 e que xy=35, calcule valor de (x - y2)2
Answers
1. You have the following information given in the problem above:
- x²+y²=74
xy=35
2. Therefore, you have that (x-y)² is:
=(x-y)²
=x²-2xy+y²
=(x²+y²)-2xy
3. When you substitute the values given in the problem, you obtain:
=74-2(35)
=74-70
=4
4. Therefore, as you can see, the correct answer is: 4
In circle H, HJ¯¯¯¯¯ is a radius and JK¯¯¯¯¯ is a tangent segment. Which statement must be true?
A) HJ=JK
B) ∠HJK is an obtuse angle.
C) HJ=HK
D) ∠HJK is a right angle.
Answers
D) ∠HJK is a right angle.
Which box plot represents the data?
135, 149, 156, 112, 134, 141, 154, 116, 134, 156
Answers
135, 149, 156, 112, 134, 141, 154, 116, 134, 156
rearranging we get:
112,116, 134, 134, 135, 141, 149, 154, 156, 156
then:
Lower value=112
Q1=134
Median=(135+141)/2=138
Q3=154
Largest value=156
The second figure is the correct figure.
The box plot that represents the data is option B.
What is a box plot?A box plot is known to be a method that is employed to demonstrate the locality and skewness of numerical data. This is carried out graphically and done through the quartiles of the given numerical data.
Rearranging the given data, we have:
112,116, 134, 134, 135, 141, 149, 154, 156, 156
The minimum value after rearranging = 112.
First Quartile, Q1 = 134.
Second Quartile, Q2 or Median = 135+141/2 = 276/2 = 138
Third Quartile, Q3 = 154
Largest figure = 156
The answer is the second figure.
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Simplify i to the power 41
Answers
Answer:
It should be just "i"
The function f(x)=35+15x represents the amount of money, in dollars, mr. lewis earns for working x hours. how much money does mr. lewis earn for working 25 hours?
Answers
You can get this by plugging in the 25 for x in the above equation.
By substituting x with 25 in the equation f(x)=35+15x, we find out that Mr. Lewis would earn $410 for working 25 hours.
Explanation:The function provided is f(x)=35+15x, which represents the amount of money Mr. Lewis earns for working x hours. In the case of Mr. Lewis working for 25 hours, we substitute the value of x with 25 in the equation to calculate his earnings. Therefore, f(25)=35+15(25)=35+375=$410. Hence, Mr. Lewis would earn $410 for working 25 hours.
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Which number would it be if rounded to the nearest foot
7191.51
A. 7191 FT
OR
B. 7192 FT
Answers
Cam rode her bike 5 times as far as Dante did. Dante rode 187 meters farther than Michael did. Cam rode 15.25 Kilometers. How many meters did Michael ride? Explain how you know you got your answer
Answers
Given that Cam rode 15.25 km
then
5x=15.25
x=3.05 km
thus Dante rod 3.05 km
but
1 km=1000m
thus
3.05 km=3050 m
But Dante rod 187 m more than Michael, the distance Michael will ride then will be:
3050-187
=2863 m
It was found that Michael rode 2863 meters.
To find out how many meters Michael rode, we first need to establish the relationship between the distances Cam, Dante, and Michael rode. According to the problem, Cam rode 5 times as far as Dante did. If Cam rode 15.25 kilometers, we first convert this to meters by multiplying by 1000 (since there are 1000 meters in a kilometer):
15.25 km × 1000 = 15250 meters.
Now that we know Cam rode 15250 meters and that this is 5 times the distance Dante rode, we can find Dante’s distance:
15250 meters / 5 = 3050 meters.
Dante rode 3050 meters, which is 187 meters farther than Michael did. To find the distance Michael rode, we subtract 187 meters from Dante’s distance:
3050 meters - 187 meters = 2863 meters.
Therefore, Michael rode 2863 meters.
Stan's cookie recipe makes 242424 cookies and calls for exactly 384384384 sprinkles. He is wondering how many sprinkles (p)(p)left parenthesis, p, right parenthesis he will need to make 606060 cookies. He assumes each cookie will have the same number of sprinkles. How many sprinkles does Stan need to make 606060 cookies?
Answers
For every 242,424 cookies he needs 384,384,384 sprinkles. So how many sprinkles does he need for 606,060 cookies?
242,424/384,384,384 = 606,060/x
384,384,384 * 606,060 = 242,424 * x
232,959,999,767,040 = 242,424 * x
960,960,960 = x
To find the number of sprinkles needed for 60 cookies, determine the number of sprinkles per cookie by dividing 384 by 24, which is 16. Then multiply 16 by 60 to get 960 sprinkles.
The question asks us to calculate the number of sprinkles (p) needed for 60 cookies when a recipe for 24 cookies calls for 384 sprinkles.
To solve this, we start by finding the number of sprinkles per cookie:
Divide the total number of sprinkles (384) by the number of cookies in the recipe (24).Multiply the result by the number of cookies we want to make (60).Therefore:
384 sprinkles ÷ 24 cookies = 16 sprinkles per cookie 16 sprinkles per cookie × 60 cookies = 960 sprinkles for 60 cookiesStan would need 960 sprinkles to make 60 cookies.
24 inches is 250% of what length
Answers
________________________________________________________
Explanation:
________________________________________________________
24 = 250/100 * x ;
24 = 2.5 x ;
↔ 2.5 x = 24 ;
2.5 x / 2.5 = 24/ 2.5 ;
x = 9.6 ;
The answer is: " 9.6 inches " .
_________________________________________________________
Using the discriminant, how many real number solutions does this equation have? 3x^2 – 2 = 5x
Answers
I hope that helps.
Find the value of the lesser root of x^2-6x+8=0
Answers
[tex]x= \frac{-b+/- \sqrt{b^{2}-4ac} }{2a} a=1, b=-6, c=8 [/tex]
[tex]x= \frac{6+/- \sqrt{36-4*1*8} }{2*1} x=(6+/- \sqrt{36-32} )/2 x=(6+/-2)/2 x_{1} =4, x_{2}=2[/tex]
Answer:
The value of lesser root is:
x=2
Step-by-step explanation:
We are given a quadratic equation in terms of variable " x " as:
[tex]x^2-6x+8=0[/tex]
We know that for any quadratic equation of the type:
[tex]ax^2+bx+c=0[/tex]
The roots of x are calculated as:
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Here we have:
a=1 , b=-6 and c=8
Hence, on solving for roots:
[tex]x=\dfrac{-(-6)\pm \sqrt{(-6)^2-4\times 1\times 8}}{2\times 1}\\\\\\x=\dfrac{6\pm \sqrt{36-32}}{2}\\\\\\x=\dfrac{6\pm \sqrt{4}}{2}\\\\\\x=\dfrac{6\pm 2}{2}[/tex]
Hence, we have:
[tex]x=\dfrac{6+2}{2}\ or\ x=\dfrac{6-2}{2}\\\\x=\dfrac{8}{2}\ or\ x=\dfrac{4}{2}\\\\\\x=4\ or\ x=2[/tex]
Hence, the value of lesser root is:
x=2
Use the table to determine the following probabilities. The probability that a randomly chosen person from this group has type B is . The probability that a randomly chosen person from this group has type AB is . The probability that a randomly chosen person from this group has type B or type AB blood is .
Answers
Use the table to determine the following probabilities.
The probability that a randomly chosen person from this group has type B is 3/25
The probability that a randomly chosen person from this group has type AB is 1/25
The probability that a randomly chosen person from this group has type B or type AB blood is 4/25
The probability that a randomly chosen person is:
first person: 3/25
second person: 1/25
third person: 4/25
ProbabilityUse the table to determine the following probabilities.
The probability that a randomly chosen person from this group has type B is 3/25.
The probability that a randomly chosen person from this group has type AB is 1/25.
The probability that a randomly chosen person from this group has type B or type AB blood is 4/25.
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Which transformation is a rotation?
Answers
Answer:
the answer is c.
Step-by-step explanation:
Stephanie rdes her bike 2 miles to the post office, and then another 50 yards to the train station. How many yards long was her trip?
Answers
Multiply 1,760 by 2 = 3,520
Add 50 to 3,520 = 3,570
Stephanie's trip was 3,570 yards long.
Factor this trinomial completely.
10x2 + 7x – 12
A. (2x + 3)(5x – 4)
B. (x + 4)(10x – 3)
C. (x + 3)(10x – 4)
D. (2x + 4)(5x – 3)
Answers
Now, the expression would look like this: 10x^2+15x-8x-12
Next, factor out the 5x and -4 from the expression: 5x(2x+3)-4(2x+3)
Now, factor out the 2x+3 from the expression and you have your answer:
(2x+3)(5x-4)
The trinomial "10[tex]x^2[/tex] + 7x - 12" is factored by finding two numbers that multiply to -120 and add up to 7, which are 15 and -8. Split the middle term, group, and factor by grouping to get (2x + 3)(5x - 4), which is option A.
Explanation:To factor the trinomial "10x2 + 7x − 12" completely, you want to find two binomials that, when multiplied together, will give you the original trinomial. To do this, you will need two numbers that multiply to give you the product of the coefficient of the x2 term (which is 10) and the constant term (which is −12), which equals −120, and also add up to the coefficient of the x term (which is 7).
The two numbers that meet these criteria are 15 and −8, since (15)(−8) = −120 and 15 + (−8) = 7. Next, split the middle term of the trinomial using these two numbers:
10x2 + 15x − 8x − 12
Now, group the terms:
(10x2 + 15x) − (8x + 12)
Factor out the greatest common factor from each group:
5x(2x + 3) − 4(2x + 3)
Finally, factor out the common binomial factor:
(2x + 3)(5x − 4)
Therefore, the correct factorization of the trinomial 10x2 + 7x − 12 is (2x + 3)(5x − 4), which corresponds to option A.
Write an equation and solve: Twice a number, increased by 3 is 7.
Answers
2x +3=7
-3 -3
2x=4
divide both sides by 2
x=2
the answer is 2
i need help!!!!!!!!!!!!!!?!!!
Answers
The appropriate choice is
B. [tex]\dfrac{\sqrt{3}}{2}[/tex]
PLZ HELP ME!! You will earn 15 POINTS and BRAINLIEST!!!!
What is the average rate of change of the function over the interval x = 0 to x = 6? f(x)=2x−1
____
3x+5
Answers
[tex]\bf \cfrac{\left[ \frac{2(6)-1}{3(6)+5} \right]~~-~~\left[ \frac{2(0)-1}{3(0)+5} \right]}{6}\implies \cfrac{\left[ \frac{11}{23}\right]~~-~~\left[-\frac{1}{5} \right]}{6} \\\\\\ \cfrac{\frac{11}{23}+\frac{1}{5}}{6}\implies \cfrac{\quad \frac{78}{115}\quad }{\frac{6}{1}}\implies \cfrac{78}{115}\cdot \cfrac{1}{6}\implies \cfrac{13}{115}[/tex]
On average, Scott drinks ½ of a 6-ounce glass of water in ⅔ hour. How much water does he drink in an hour?
a) 0.75 ounces b) 2 ounces c) 4.5 ounces d) 9 ounces
Answers
3/2 = 1.5. He drinks 1.5 ounces in one third of an hour. 1.5 * 3 = 4.5
C. 4.5 ounces in one hour
Please help!!!
Use DeMoivre's theorem to evaluate the expression
[sqrt 3( cos 5pi/3 + i sin 5pi/3)]^4 ? write the answer in rectangular form
a. 9sqrt3/2 + 9/2 i
b. 9sqrt3/2 - 9/2 i
c. -9/2 - 9sqrt3/2 i
d. -9/2 + 9sqrt3/2 i
Answers
if z = a ( cos θ + i sin θ)
∴ z^n = a^n ( cos nθ + i sin nθ)
For the given complex number ⇒⇒⇒ [ √3 ( cos 5π/3 + i sin 5π/3 ) ]⁴
[ √3 ( cos 5π/3 + i sin 5π/3 ) ]⁴ = (√3)⁴ ( cos 4*5π/3 + i sin 4*5π/3 )
= 9 ( cos 20π/3 + i sin 20π/3 )
= 9 ( cos 2π/3 + i sin 2π/3 )
= 9 ( -1/2 + i √3 /2 )
= -9/2 + 9√3 /2 i
note: 20π/3 = 2π/3 + 6π = 2π/3 + 3 *2π = 2π/3
∴ The correct answer is option d
d. -9/2 + 9sqrt3/2 i
Answer:
Option d - [tex]\sqrt3(\cos (\frac{5\pi}{3})+i\sin(\frac{5\pi}{3}))^4=-\frac{9}{2}+\frac{9\sqrt3}{2}i[/tex]
Step-by-step explanation:
Given : [tex]\sqrt3(\cos (\frac{5\pi}{3})+i\sin(\frac{5\pi}{3}))^4[/tex]
To find : Use DeMoivre's theorem to evaluate the expression?
Solution :
DeMoivre's theorem state that, for complex number
If [tex]z = r(\cos\theta+ i\sin \theta)[/tex] then [tex]z^n = r^n(\cos n\theta+ i\sin n\theta)[/tex]
We have given,
[tex]\sqrt3(\cos (\frac{5\pi}{3})+i\sin(\frac{5\pi}{3}))^4[/tex]
On comparing [tex]r=\sqrt3[/tex] and n=4
Applying DeMoivre's theorem,
[tex]=(\sqrt3)^4(\cos 4(\frac{5\pi}{3})+i\sin4(\frac{5\pi}{3}))[/tex]
[tex]=9(\cos (\frac{20\pi}{3})+i\sin(\frac{20\pi}{3}))[/tex]
[tex]=9(\cos (6\pi+\frac{2\pi}{3})+i\sin(6\pi+\frac{2\pi}{3}))[/tex]
[tex]=9(\cos (\frac{2\pi}{3})+i\sin(\frac{2\pi}{3}))[/tex]
We know, the value of
[tex]\cos (\frac{2\pi}{3})=-\frac{1}{2},\sin (\frac{2\pi}{3})=\frac{\sqrt3}{2}[/tex]
[tex]=9(-\frac{1}{2}+i\frac{\sqrt3}{2})[/tex]
[tex]=-\frac{9}{2}+i\frac{9\sqrt3}{2}[/tex]
Therefore, Option d is correct.
[tex]\sqrt3(\cos (\frac{5\pi}{3})+i\sin(\frac{5\pi}{3}))^4=-\frac{9}{2}+\frac{9\sqrt3}{2}i[/tex]
Factor each polynomial. Check your answer by distributing. 2x^2+5x+2
Answers
(X+2)(2x+1)
Plz help!!!! Will mark brainliest!!
Ratios
Ms. Grande brought 24 apples and 18 oranges for a party after a class play. Find the ratio of the number of apples to the total number of fruits Ms. Grande bought.
There are 44 chicken and fish filets altogether in a freezer. There are 12 chicken filets. Which is the ratio of the number of chicken filets to the number of fish filets in the freezer?
There were 12 boys and 18 girls in a class. Then, 3 more boys joined the class and 2 girls left. What is the ratio of the number of boys to the number of girls in the class now?
Monica had $42 and Naomi had $18 at first. Monica then gave $6 to Naomi. What is the ratio of the amount of money Monica has to the amount of money Naomi has in the end?
Answers
2) 11:3
3) 15:16
4) 3:2
To find the ratio of the number of apples to the total number of fruits, divide the number of apples by the total number of fruits. Simplify the ratio by dividing both numbers by their greatest common factor. For the ratio of chicken filets to fish filets, divide the number of chicken filets by the total number of filets. Simplify the ratio if possible. To find the ratio of boys to girls, determine the new number of boys and girls after some changes. For the ratio of money, calculate the amounts each person has and simplify the ratio.
Explanation:To find the ratio of the number of apples to the total number of fruits, we divide the number of apples (24) by the total number of fruits (24 apples + 18 oranges = 42). This gives us a ratio of 24:42. We can simplify this ratio by dividing both numbers by their greatest common factor, which is 6. So the simplified ratio is 4:7.
For the second question, we need to find the ratio of the number of chicken filets to the number of fish filets. There are 12 chicken filets and a total of 44 filets in the freezer. So the ratio is 12:44. This can also be simplified by dividing both numbers by 4, giving us a simplified ratio of 3:11.
In the third question, we start with 12 boys and 18 girls. Then, 3 more boys join and 2 girls leave. So the new number of boys is 12 + 3 = 15, and the new number of girls is 18 - 2 = 16. The ratio of boys to girls is therefore 15:16.
In the fourth question, Monica has $42 and Naomi has $18. When Monica gives $6 to Naomi, Monica will have $42 - $6 = $36 left, and Naomi will have $18 + $6 = $24. The ratio of the amount of money Monica has to the amount of money Naomi has is 36:24, which can be simplified to 3:2.
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Find the first six terms of the sequence. a1 = -3, an = 2 ● an-1
Answers
According to the formula each next term will be obtained by multiplying the previous term by 2.
So, next terms will be:
Second term = 2 x First Term = 2 x (-3) = - 6
Third term = 2 x (-6) = -12
Fourth term = -24
Fifth term = -48
Sixth term = -96
So, the sequence will be:
-3, -6, -12, -24, -48, -96 ...
The center of a circle is at (2, -5) and it's radius is 12. What is the equation of the circle?
A.) (x+2)^2 + (y-5)^2 =24
B.) (x-2)^2 + (y+5)^2 = 24
C.) (x+2)^2 + (y-2)^2 = 144
D.) (x-2)^2 + (y+5)^2 = 144
Answers
You just have to plug in your coordinates h is the x and k is the y.
The r is radius squared.
so, (x-2)^2+(y-(-5)^2=144
You have to be careful of those tricky negative values. When you distribute the y-(-5) it turns into y+5.
So your answer is D.
Answer:
The answer is D
Step-by-step explanation:
It is D
If you shift the linear parent function, f(x)=x, down 7 units what is the equation of the new function
Answers
1- You have that following parent function (the most basic function of the linear functions) given in the problem above:
f(x)=x
2- When you graph this parent function, you obtain the graph shown in the figure attached.
3- If you shift the linear parent function 7 units down, you have the following new function:
f(x)=x-7
4- The graph of the new function is shown in the second figure attached.
The answer is: f(x)=x-7
f(x)=x-7 is indeed the correct answer.just got it right
students have 40 minuets to complete 50 questions on the aspire ___ test
A) math
B) reading
C) english
D) writing
Answers
Answer:
english C)
Step-by-step explanation: