Answers
Answer:
Options (1), (3) and (4)
Step-by-step explanation:
From ΔABC given in the picture,
By Pythagoras theorem
Hypotenuse² = (Leg 1)² + (Leg 2)²
BC² = AB² + AC²
(18)² = 9² + AC²
AC = [tex]\sqrt{324-81}[/tex]
AC = [tex]9\sqrt{3}[/tex] cm
sin(C) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{AB}{BC}[/tex]
= [tex]\frac{9\sqrt{3}}{18}[/tex]
sin(C) = [tex]\frac{\sqrt{3} }{2}[/tex]
sin(B) = [tex]\frac{AC}{BC}[/tex]
= [tex]\frac{9}{18}[/tex]
= [tex]\frac{1}{2}[/tex]
cos(B) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{9\sqrt{3}}{18}[/tex]
= [tex]\frac{\sqrt{3} }{2}[/tex]
tan(B) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
= [tex]\frac{AC}{AB}[/tex]
= [tex]\frac{9}{9\sqrt{3} }[/tex]
= [tex]\frac{1}{\sqrt{3} }[/tex]
tan(C) = [tex]\frac{AB}{AC}[/tex]
= [tex]\frac{9\sqrt{3}}{9}[/tex]
= [tex]\sqrt{3}[/tex]
Therefore, Options (1), (3) and (4) are the correct options.
Answer:
Options (1), (3) and (4)
Step-by-step explanation:
From ΔABC given in the picture,
By Pythagoras theorem
Hypotenuse² = (Leg 1)² + (Leg 2)²
BC² = AB² + AC²
(18)² = 9² + AC²
AC =
AC = cm
sin(C) =
=
=
sin(C) =
sin(B) =
=
=
cos(B) =
=
=
tan(B) =
=
=
=
tan(C) =
=
=
Therefore, Options (1), (3) and (4) are the correct options.Step-by-step explanation:
Related Questions
From a collection of 52 store customers, 3 are to be chosen to receive a special gift. How many groups of 3 customers are possible?
Answers
Answer:
132,600 possibilities
Step-by-step explanation:
The first one chosen can be 1 of 52
The 2nd one chosen is 1 out 51
And the 3rd chosen is 1 out 50
So...
52 x 51 x 50 = 132,600
There are 22,100 groups of 3 customers that are possible from the given collection of 52 store customers.
What is a combination?It is an arrangement of a set of numbers from a total set where the order of the set is not relevant.
We have,
The number of groups of 3 customers that can be chosen from a collection of 52 store customers can be calculated using the combination formula:
nCr = n! / r!(n - r)!
where n is the total number of customers (52) and r is the number of customers chosen (3).
Substituting the values, we get:
52C3 = 52! / 3!(52 - 3)!
52C3 = 52! / 3!49!
52C3 = (52 × 51 × 50) / (3 × 2 × 1)
52C3 = 22,100
Therefore,
There are 22,100 groups of 3 customers that are possible from the given collection of 52 store customers.
Learn more about combination here:
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In Exercises 45–48, let f(x) = (x - 2)2 + 1. Match the
function with its graph
Answers
Answer:
45) The function corresponds to graph A
46) The function corresponds to graph C
47) The function corresponds to graph B
48) The function corresponds to graph D
Step-by-step explanation:
We know that the function f(x) is:
[tex]f(x)=(x-2)^{2}+1[/tex]
45)
The function g(x) is given by:
[tex]g(x)=f(x-1)[/tex]
using f(x) we can find f(x-1)
[tex]g(x)=((x-1)-2)^{2}+1=(x-3)^{2}+1[/tex]
If we take the derivative and equal to zero we will find the minimum value of the parabolla (x,y) and then find the correct graph.
[tex]g(x)'=2(x-3)[/tex]
[tex]2(x-3)=0[/tex]
[tex]x=3[/tex]
Puting it on g(x) we will get y value.
[tex]y=g(3)=(3-3)^{2}+1[/tex]
[tex]y=g(3)=1[/tex]
Then, the minimum point of this function is (3,1) and it corresponds to (A)
46)
Let's use the same method here.
[tex]g(x)=f(x+2)[/tex]
[tex]g(x)=((x+2)-2)^{2}+1[/tex]
[tex]g(x)=(x)^{2}+1[/tex]
Let's find the first derivative and equal to zero to find x and y minimum value.
[tex]g'(x)=2x[/tex]
[tex]0=2x[/tex]
[tex]x=0[/tex]
Evaluatinf g(x) at this value of x we have:
[tex]g(0)=(x)^{2}+1[/tex]
[tex]g(0)=1[/tex]
Then, the minimum point of this function is (0,1) and it corresponds to (C)
47)
Let's use the same method here.
[tex]g(x)=f(x)+2[/tex]
[tex]g(x)=(x-2)^{2}+1+2[/tex]
[tex]g(x)=(x-2)^{2}+3[/tex]
Let's find the first derivative and equal to zero to find x and y minimum value.
[tex]g'(x)=2(x-2)[/tex]
[tex]0=2(x-2)[/tex]
[tex]x=2[/tex]
Evaluatinf g(x) at this value of x we have:
[tex]g(2)=(2-2)^{2}+3[/tex]
[tex]g(2)=3[/tex]
Then, the minimum point of this function is (2,3) and it corresponds to (B)
48)
Let's use the same method here.
[tex]g(x)=f(x)-3[/tex]
[tex]g(x)=(x-2)^{2}+1-3[/tex]
[tex]g(x)=(x-2)^{2}-2[/tex]
Let's find the first derivative and equal to zero to find x and y minimum value.
[tex]g'(x)=2(x-2)[/tex]
[tex]0=2(x-2)[/tex]
[tex]x=2[/tex]
Evaluatinf g(x) at this value of x we have:
[tex]g(2)=(2-2)^{2}-2[/tex]
[tex]g(2)=-2[/tex]
Then, the minimum point of this function is (2,-2) and it corresponds to (D)
I hope it helps you!
In a survey a bunch of students were asked to name their favorite elective class. There were 15 students who chose "other". How many students participated?
Answers
Without performing the calculations, which expression equals the greatest value?
A)
2x (3-5)
B)
3x (
3-5)
)
5x (3-5)
D)
7x (3-5)
Answers
due to pemdas whatever is inside the parentheses goes first. it’s going to be a negative. if you make the outside number greater, the value of the overall number will become less because negative numbers are less in value the higher they are
Question
what's 10÷0=_
Answer please
Answers
Answer:
Undefined
Step-by-step explanation:
Answer:
you cant divide by 0
Step-by-step explanation:
no solution
please help solve for the area
Answers
Answer:
The area of the shape is 126 cm.
Step-by-step explanation:
6 + 3 + 3 = 12 cm, all sides
12 * 12 = 144
3 * 3 = 9 / 2 = 4.5
4.5 * 4 = 18
144 - 18 = 126cm
Can someone explain to me why I should have used the point (-2, 4) for this equation instead of (-7. -3)?
Answers
3.14 x 6.25 step by step
Answers
Answer:
Step-by-step explanation:
3.14x6.25
19.625
Answer:
19.625
Step-by-step explanation:
THIS IS SO BAD RN SMH HELP ME WITH ANOTHER MATH SOLVING
4 x 3 x 4 x 9 + 3 - 20
Answers
Answer:
=415
Step-by-step explanation:
The girl in that picture is so pretty oml so if its you then you pretty a.ff
Determine whether the two expressions are equivalent.If so,tell that property is applied. (37) and (2.3). 7*
O Yes; Identity Property
O Yes; Associative Property
O Yes; Commutative Property
O Yes; Inverse Property
O Expressions are not equal
Answers
Answer:
Yes; Inverse Property...
I hope it helps..
This is for geometry and I need help!
Answers
Answer:
B, C, E, and F
Step-by-step explanation:
Recall the acronym for trigonometric functions: SOHCAHTOA
Thus:
B = 180 - (48 + 90) = 42°
Let's find the trigonometric functions using 42° as the reference angle:
Opp = b
Hyp = c
Adj = a
Applying SOH:
Sin 42 = opp/hyp
✅Sin 42 = b/c (option C is correct)
Applying CAH:
Cos 42 = adj/hyp
✅Cos 42 = a/c (option A is incorrect)
Applying TOA:
Tan 42 = opp/adj
✅Tan 42 = b/a (option E is correct)
Using 48° as reference angle:
Opp = a
Hyp = c
Adj = b
Applying SOH:
Sin 48 = opp/hyp
✅Sin 48 = a/c (option D is incorrect)
Applying CAH:
Cos 48 = adj/hyp
✅Cos 48 = b/c (option B is correct)
Applying TOA:
Tan 48 = opp/adj
✅Tan 48 = a/b (option F is correct)
which of the following is correct statement about this relation?
Answers
Given:
The relation is:
(-3,1),(-2,3),(-1,5),(0,7),(1,9),(2,11)
To find:
The slope and y-intercept for the given relation.
Solution:
Consider any two points from the given relation.
Let the two points are (0,7) and (1,9). So, the slope of the given relation is:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{9-7}{1-0}[/tex]
[tex]m=\dfrac{2}{1}[/tex]
[tex]m=2[/tex]
The slope of the given relation is 2.
A point of relation is (0,7). It means the value of relation is 7 at x=0.
So, the y-intercept is 7.
Therefore, the correct option is D.
Ms. Gallegos burns 236 calories riding her bike each hour. She wants to burn more than 590 calories riding her bike at the same rate.
Which inequlity represents all possible values for t, the number of hours Ms. Gallegos must ride her bike to burn more than 590 calories?
A.
t > 2.5
B.
t < 2.5
C.
t > 0.4
D.
t < 0.4
Answers
Answer:
Bro the answer is A
Step-by-step explanation:
trust me straight 100% brain dead person
Help pls and thank you ..
Answers
Answer:
i think this is the anwer 100
two packages of rice cost the same amount. Which is the better buy? 12 ounce or 400 grams
Answers
Answer:
400 grams
Step-by-step explanation:
12ounce= 340.19 grams approximately
So,its best to buy the package that weighs 400 grams
Help please !!! Thanks guys
Answers
(b+4) and (b-1)
Explanation:
do a generic rectangle
b times b is b^2
b times 4 = 4b
-1 times b = -1b
-1 times 4 = -4
b^2+4b-1b-4
simplify
b^2+3b-4
Could someone please help me, I have to turn this in, in 30 minutes, only answer if you know how to do it
Answers
9514 1404 393
Answer:
a. The value of A₀ changes from 10 to 20
b. t is replaced by (t-5)
Step-by-step explanation:
a. The given formula comes with a description that says A₀ is the initial dose in mg. If the initial dose changes from 10 mg to 20 mg, then A₀ changes from 10 to 20. The function becomes ...
A = 20·0.97^t
__
b. Shifting the graph of the function to the right by 5 minutes is accomplished by replacing t with (t-5). At the same time, the domain changes from t ≥ 0 to t ≥ 5. The function becomes ...
A = A₀·0.97^(t-5) . . . . . . . . for t ≥ 5
A random sample of 50 students at a large high school resulted in a 95 percent confidence interval for the mean number of hours of sleep per day of (6.73, 7.67). Which of the following statements best summarizes the meaning of this confidence interval?
A . About 95% of all random samples of 50 students from this population would result in a 95% confidence interval that covered the population mean number of hours of sleep per day.
B. 95% of the students in the survey reported sleeping between 6.73 and 7.67 hours per day.
C. 95% of the students in this high school sleep between 6.73 and 7.67 hours per day.
D. A student selected at random from this population sleeps between 6.73 and 7.67 hours per day for 95% of the time.
Answers
Answer:
A . About 95% of all random samples of 50 students from this population would result in a 95% confidence interval that covered the population mean number of hours of sleep per day.
Step-by-step explanation:
x% confidence interval:
A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.
In this question:
95% CI from a sample of 50 students is (6.73, 7.67).
This means that we are 95% sure that the population mean is in this interval, that is, about 95% samples of 50 would contain the population mean, which is given by option A.
By using basic definition of confidence interval we can say that option A " About 95% of all random samples of 50 students from this population would result in a 95% confidence interval that covered the population mean number of hours of sleep per day." is correct.
What is confidence interval ?confidence interval tells us the degree of certainty or uncertainty that is existent in a sampling method. It gives us a range of values, telling us we are fairly sure that our true value or parameter lies within the range.
Here given that 95% confidence interval from a sample of 50 students is (6.73,7.67). so we can say that there are 95% chance that the population mean is in this interval (6.73,7.67) , that is, about 95% samples of 50 would contain the population mean, so option A is correct
By using basic definition of confidence interval we can say that option A " About 95% of all random samples of 50 students from this population would result in a 95% confidence interval that covered the population mean number of hours of sleep per day." is correct.
To learn more about confidence interval visit :
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Write the equation that is parallel to the question: y = -2/3x - 5 and goes through point: (6,-1)
Answers
Answer:
y = -2/3x + 3
Step-by-step explanation:
Parallel lines have the same slope so we already know
y = -2/3x + b
Solve for b using the point given
-1=-2/3(6)+b
-1+4=b
b=3
y = -2/3x + 3
In AOPQ, the measure of angle Q=90°, the measure of angle O=66°, and QO = 4.5 feet. Find the length of OP to the nearest tenth of a fo
Answers
Answer:11.1 feet
Step-by-step explanation:
(30, points)
A right triangle is shown. Which is closest to the value of an x
Answers
Answer:
I think the answer might be 13. I don't know it is wrong or not
The height of a cuboid whose volume is 385 cu cm and base area is 35 sq cm is
Answers
Answer:
11cm
Step-by-step explanation:
Given data
Volume of cuboid =385 cm^3
Base area= 35cm^2
We know that
Volume = Area* Height
substitute and solve for Height
385=35*H
H= 385/35
H= 11cm
Hence, the height is 11cm
How many miles will Mrs. Garcia drive in eight hours if she is traveling 65 mph? _ miles
Answers
Answer:
520 miles
Step-by-step explanation:
65 mph * 8 hours = 520 miles
I hope this helps :)
A triangle has side lengths of 4cm, 6cm, and 11cm. Is the triangle acute, obtuse, or right?
Answers
Answer:
No
Step-by-step explanation:
Three segments 4cm, 6cm, and 11cm cannot form a right triangle because if they could, then by Pythagorean theorem, 4^2 + 6^2 = 11^2, which is not true.
Moreover, the three segments cannot form an acute or obtuse triangle because by Triangle Inequality Theorem, the sum of two sides has to be greater than the third side. Here, (4cm + 6cm) is NOT larger than 11cm, and thus you cannot form a triangle.
Hope it helps,
Please mark me as the brainliest
Thank you
Science (from the Latin word Scientia, meaning "knowledge") is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe.
The earliest roots of science can be traced to Ancient Egypt and Mesopotamia in around 3500 to 3000 BCE
Answers
Answer:
?
Step-by-step explanation:
What are you even asking-
If F(x) = 5x - 7 and G(X) = x2 - 41, what is G(F(x))?
O A. 5(x2 - 41) -7
O B. -5x +7x2 + 205x – 287
O C. (5-7 - 41
O D. 5x2 - 7x2 - 205x+287
Answers
A number divided by negative three is greater than negative three Write the inequality and solve 50 points i need the correct answer asap !!!! Will mark brainiliest !!!
Answers
Answer:
No clue, but i would recommend using desmos, mathpapa, quizlet,
Step-by-step explanation:
A parachutist's rate during a free fall reaches 90 miles per hour. What is this rate in feet per second? At this rate, how many feet will the parachutist fall during 5 seconds of free fall? In your computations, use the fact that 1 mile is equal to 5 feet. Do not round your answers
Answers
Answer:
The parachutist's rate of fall is 132 feet per second. In turn, in 5 seconds, the parachutist will drop 660 feet.
Step-by-step explanation:
Given that a parachutist's rate during a free fall reaches 90 miles per hour, to determine what is this rate in feet per second and, at this rate, how many feet will the parachutist fall during 5 seconds of free fall, knowing that 1 mile is equal to 5280 feet, the following calculations must be performed:
90 x 5280 = 475,200
475,200 / 60/60 = X
7,920 / 60 = X
132 = X
Thus, the parachutist's rate of fall is 132 feet per second.
132 x 5 = 660
In turn, in 5 seconds, the parachutist will drop 660 feet.
Which equation has a slope: 3/2, y-intercept: –4
Answers
Answer:
The equation of the line that has a slope of 3/2 and a y-intercept of -4 is:
y=3/2x-4.
Step-by-step explanation:
You want to find the equation for a line that has a slope of 3/2 and a y-intercept of -4. First of all, remember what the equation of a line is:
y = mx+b Where: m is the slope, and b is the y-intercept
All you really have to do here is replace m with 3/2, which is the slope you gave, and replace b with -4, the y-intercept you gave, in the equation y=mx+b.
there are 60 sixth graders at wilson middle school. only 50% of the sixth graders will attend the morning assembly. how many sixth graders will be at the morning assembly?
Answers
Answer:
30 sixth graders
Step-by-step explanation:
50% = 0.50
multiply 60 by the decimal fraction of the percentage:
60 x 0.50 = 30
you can also just take 60 and divide by 2 since 50% means half