ANSWER
[tex]\tan(\sin^{ - 1}( \frac{x}{2} )) = \frac{x}{ \sqrt{4 - {x}^{2} } } \: \:where \: \: x \ne \pm2[/tex]
EXPLANATION
We want to find the exact value of
[tex] \tan( \sin^{ - 1}( \frac{x}{2} ) ) [/tex]
Let
[tex]y = \sin^{ - 1}( \frac{x}{2} )[/tex]
This implies that
[tex] \sin(y) = \frac{x}{2} [/tex]
This implies that,
The opposite is x units and the hypotenuse is 2 units.
The adjacent side is found using Pythagoras Theorem.
[tex] {a}^{2} + {x}^{2} = {2}^{2} [/tex]
[tex]{a}^{2} + {x}^{2} = 4[/tex]
[tex]{a}^{2} = 4 - {x}^{2}[/tex]
[tex]a= \sqrt{4 - {x}^{2}} [/tex]
This implies that,
[tex] \tan(y) = \frac{opposite}{adjacent} [/tex]
[tex]\tan(y) = \frac{x}{ \sqrt{4 - {x}^{2} } } [/tex]
But
[tex]y = \sin^{ - 1}( \frac{x}{2} )[/tex]
This implies that,
[tex]\tan(\sin^{ - 1}( \frac{x}{2} )) = \frac{x}{ \sqrt{4 - {x}^{2} } } \: \:where \: \: x \ne \pm2[/tex]
At the beginning of year 1, Lisa invests $500 at an annual compound interest
rate of 3%. She makes no deposits to or withdrawals from the account.
Which explicit formula can be used to find the account's balance at the
beginning of year 6? What is the balance?
O A. A(n) = 500 (1 + 0.03)(n = 1); $579.64
O B. A(n) = 500 + (0.03+500) -1); $584.50
O C. A(n) = 500 + (n - 1)(0.03 . 500); $575.00
O D. A(n) = 500 - (1 +0.03), $597.03
Answer:
the actual answer is a(n)= 500 * ( 1 + 0.03) ^(n - 1) ;$579.64
Step-by-step explanation:
Will mark BRAINLIEST!! — Point H is the circumcenter of triangle DEF. Which must be true? Check ALL that apply. See image.
Answer:
A, C, F
Step-by-step explanation:
Definition: The circumcenter is the center of the triangle's circumcircle - the circle that passes through all three of the triangle's vertices. If point H is the circumcenter of the triangle DEF, then the circumcircle passes through its vertices D, E and F (option A is true).
Option B is false, the circumcircle doesn't pass through the points L, M and N. This option is true for inscribed circle, not for circumcircle.
Option C is true, because HD and HE are the radii of the circumcircle.
Option D is false. This option is true for inscribed circle, not for circumcircle.
Option E is false. This option is true for inscribed circle, not for circumcircle.
Option F is true, because both these angles are right angles.
27.) FEMALE LAWYERS There are 1,094,751 active lawyers living
in the United States. If 71.4% of these lawyers are male, find
(a) the percent of the lawyers who are female and (b) the number
of lawyers who are female. Round to the nearest whole number.
Answer:
28.6%; 313,099
Step-by-step explanation:
Lawyers are either male or female, so if 71.4% are male, then 100% minus that are female.
100% - 71.4% = 28.6%
28.6% of 1,094,751 is:
0.286 × 1094751 = 313098.786
Rounded to the nearest whole number, there are 313,099 female lawyers.
What is the period of the function?
Answer:
2pi
Step-by-step explanation:
Jeremy, Sue, and Holly are siblings. Sue was born three years before Holly, and Jeremy was born five years before Sue. The product of Sue's age and Jeremy's age is at most 150.
If x represents the age of Holly, which inequality can be used to find the age of each sibling?
A.
x2 - 11x + 24 ≤ 150
B.
x2 + 8x + 15 ≤ 150
C.
x2 + 8x ≤ 150
D.
x2 + 11x + 24 ≤ 150
Answer:
D is the correct answer
Step-by-step explanation:
Let the age of Holly is x years. Now from the statements of the question we will form the equations.
Sue was born three years before Holly.
Sue = Holly + 3 = x + 3------(1)
Jeremy = Sue + 5
From equation (1)
Jeremy = (x + 3) + 5 = x + 8------(2)
Now statement says the product of Sue's age and Jeremy's age is at most 150.
Sue × Jeremy ≤ 150
(x + 3)(x + 8) ≤ 150
x² + 11x + 24 ≤ 150
Therefore inequality x² + 11x + 24 ≤ 150 can be used to find the age of each sibling.
HAVE AN AMAZING DAY, GLAD TO HELP. ^.^
Solve For X
A: 10
B:10.5
C:20
D:6[tex]\sqrt{3}[/tex]
The answer is gonna be (B)
Evaluate sin(Arcos(-9/√145)).
Use the fact that [tex]\sin x = \sqrt{1-\cos^2 x}[/tex] to solve it.
[tex]\sin(\arccos(-\frac{9}{\sqrt{145}}))=\sqrt{1-\cos^2(\arccos(-\frac{9}{\sqrt{145}}))} =\\= \sqrt{1-(-\frac{9}{\sqrt{145}})^2}=\frac{8}{\sqrt{145}}[/tex]
Answer:
a
Step-by-step explanation:
If pizzas cost $9.83 per pizza, estimate how much money you would need to buy 18 of them.
Your answer does not need to be exact, so please do NOT use a calculator and please do not put a $ sign in your answer.
Answer:
180
Step-by-step explanation:
because it doesn't has to be exact you can do: 10 × 18 = 180
Answer:
180
Step-by-step explanation:
This is a good question to keep in mind. When you do use a calculator the answer to this estimate will tell you if your work on the calculator is correct.
round the cost of the pizza to 10
18 * 10 = 180 dollars. So you should get an answer that is under 180 dollars -- about 3 dollars short. (0.17 * 18 which is another guess).
Now pick up your calculator and do the math. It comes to 176.94
If you do any grocery shopping, this is a good skill to have.
Find the value of x. Round the length to the nearest tenth
A.) 9.0 yd
B.) 15.6 yd
C.) 31.2 yd
D.) 10.4 yd
the answer will be B
Answer:
D.) 10.4 yd
Step-by-step explanation:
In the given figure the alternate angles are equal and hence a right angle triangle with one of its angle as 30 degree is formed .
For angle 30 degrees adjacent side is 18 yard and opposite side is x.
Tan of an angle is equal to [tex]\frac{opposite}{adjacent}[/tex]
[tex]Tan 30=\frac{x}{18}[/tex]
x=Tan 30 (18)
x= 10.39
x= 10.4 yard (rounded to tenth place)
Option D is the right answer.
The equation y = 4x + 4 describes the relationship between the quantities x and y. Are the quantities in a proportional relationship?
Answer:
Yes, because as x grows larger so does y, that means to be in a proportional relationship.
Step-by-step explanation:
Answer: For this to be a proportional relationship, the function would have to be y=4x. Since y=mx+b, this is not a proportional relationship because each time the value of x increases, the value for figure 0 is added on.
So, no. This is not proportional.
Hope this helps!
Solve 2x2 + 5x = 12.
A. x= three over two and x = −4
B. x = 2 and x = −3
C. x = −6 and x = 5
D. x = one over two and x = one over three
Answer:
A. x= three over two and x = −4
Step-by-step explanation:
2x^2 + 5x = 12
I will use complete the square
Divide each side by 2
2x^2 /2 + 5/2 x = 12/2
x^2 +5/2 x =6
Take 5/2 , divide by 2 and then square it
5/2 ÷2 = 5/2 (5/4) ^2 = 25/16
Add this to both sides
x^2 + 5/2 x + 25/16 = 6 + 25/16
(x+5/4)^2 = 6 *16/16 + 25/16
(x+5/4)^2 = 96/16 +25/16
(x+5/4)^2 = 121/16
Take the square root of each side
sqrt((x+5/4)^2) = sqrt(121/16)
x+5/4 = ±11/4
Subtract 5/4 from each side
x+5/4-5/4 = ±11/4 -5/4
x = ±11/4 -5/4
x = -11/4 - 5/4 and x = 11/4 - 5/4
x = -16/4 = -4 and x = 6/4 = 3/2
When all three points are connected, triangle PQR will be a right triangle. At which coordinates must R be located?
A) (-6,3)
B) (-3,3)
C) (0,3)
D) (5,3)
b) u gotta each R point w p & q and see which one would give u a right triangle, which is b
Answer:
your answer should be (-3,3)
Step-by-step explanation:
brainliest pls
Find the circumference or distance around a circus ring (circle) with a diameter of 100 feel. Use 3.14 for pi
Use Formula C= pi(d) so that would be 3.14 x 100 = 314
Answer:
the circumference is 314.16
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
Use the probability distribution table to answer the question.
What is P(X ≥ 2)?
Enter your answer, as a decimal, in the box.
Answer: 0.88
Step-by-step explanation:
P(X ≥ 2) = P(X = 2) + P(X = 3) + P(x = 4) + P(X = 5) + P(X = 6)
= 0.21 + 0.35 + 0.21 + 0.06 + 0.05
= 0.88
If x < 5, then which of the following must be true?
-x < -5
-x > -5
-x < 5
-x > 5
Answer:
B
Step-by-step explanation:
x<5
When we multiply by negative number sign of inequality should be changed also.
x*(-1) > 5*(-1)
-x>-5
For this case we have the following expression:
[tex]x <5[/tex]
By definition we have to:
Let [tex]c <0[/tex]. If [tex]a <b,[/tex] then [tex]ac> bc[/tex]
That is to say:
If we multilate on both sides of the inequality by -1, the sign automatically changes direction.
[tex](-1) (x) <(- 1) (5)\\-x> -5[/tex]
ANswer:
Option B
A banquet that costs $3,000 at Luci’s serves how many people?
Answer:
the answer will be 125 people
A mechanic gives a survey to all of his customers asking them to rate the quality of the service they received. He then keeps track of how many customers return to the shop for additional services during the next six months. Last year, the results showed that of the customers who reported high quality service, 20% returned for additional services. What conclusion can be drawn from this study?
Answer:
Some customers who rate their service as high quality return for additional services.
Step-by-step explanation:
Last year, the results showed that of the customers who reported high quality service, 20% returned for additional services.
This shows than some customers are satisfied overall and return back for additional services.
What is the maximum number of possible solutions for the system shown below?
[tex]x^2+4y^2=64\\x+y=5[/tex]
Answer:
2
Step-by-step explanation:
The first equation is that of a an ellipse. The second equation is that of a line.
Attached is the graphs of both of these equations.
If you think about it, there can only be 2 possible ways of solutions (intersection points) of an ellipse and a line.
1. The line will not intersect the ellipse at all, so no solution
2. The line will intersect the ellipse at 2 points maximum
So, we can clearly see from the reasoning that the maximum number of possible solutions would be 2. The graph attached confirms this as well.
Answer:
The maximum number of solutions that the system can have are 2
Step-by-step explanation:
We have a system of equations composed of an ellipse of equation [tex]x ^ 2 + 4y ^ 2 = 64[/tex] and a line of equation [tex]x + y = 5.[/tex]
The solution to the system of equations gives information about when the values of both equations coincide. In other words, the solutions of the system of equations give information about the number of times that the line [tex]x + y = 5[/tex]. touch or intercept the graph of the ellipse [tex]x ^ 2 + 4y ^ 2 = 64[/tex]
Graphically you can verify that a line can only touch an ellipse once or can intercept an ellipse a maximum of two times, or never touch it
Therefore, the maximum number of solutions that the system can have are 2.
What is the maximum number of possible solutions for the system shown below?
[tex]x^2-4y^2=16[/tex]
[tex]x^2+y^2=36[/tex]
A. 1
B. 4
C. 3
D. 2
Answer:
4
Step-by-step explanation:
Match each property with the appropriate example.
1.
4(x - 2) = 4x - 8
2.
(4+2) + 8 = 4 + (2+8)
3.
4 * 2 = 2 * 4
4.
4 * 1 = 4
a.
Commutative property
b.
Distributive property
c.
Associative property
d.
Identity property
Answer:
1. Distrubutive 2. Associative 3. Commutative 4. Identity
Step-by-step explanation:
1. Distributive property 2. Associative property
3. Identity property 4. Commutative property
For this case we have that by definition:
the distributive property establishes that:[tex]a (b + c) = ab + ac[/tex]
So:
[tex]4 (x-2) = 4x-8[/tex]
State the distributive property.
The associative property states:[tex]a + (b + c) = (a + b) + c[/tex]
So:
[tex](4 + 2) + 8 = 4 + (2 + 8)[/tex]
Enunciates the associative property
The commutative property establishes that the order of the factors does not alter the product.[tex]a * b = b * a[/tex]
So:
[tex]4 * 2 = 2 * 4[/tex]
Enunciates the commutative property
The Identity property establishes that every number multiplied by 1 gives the same number. So:[tex]4 * 1 = 4[/tex]
State identity property
Answer:
Distributive property
Associative property
Commutative property
Identity property
1. A triangle has a side length of 450mm.The scale factor is 1/25.What is the side length of the scale drawing.
Answer:
18 mm
Step-by-step explanation:
To find the side length of the scale drawing, multiply the length of the side by the scale factor
450 * 1/25 =18
The side length in the drawing is 18 mm
Please please help me please
I believe the answer is 70 degrees. If you divide 360 by 9 (amount of degrees divided by amount of sides) you get 40 and we know that the three angles in a triangle add up to 180 degrees. So if we subtract the 40 we got for the top angle we get 140 degrees. We know the other two angles in the triangle are congruent so we can divide 140 by 2 to get the degree of both angles which is 70. Hope this helps!
When two six-sided dice are rolled, there are 36 possible outcomes. a. Find the probability that the sum is not 4. Express your first answer as a fraction in simplest form, and round your percent answer to the nearest whole percent. b. Find the probability that the sum is greater than 5. Express your first answer as a fraction in simplest form, and round your percent answer to the nearest whole percent. Round the fraction
The probability of not getting a sum of 4 when rolling two six-sided dice is 33/36 or 92%. The probability of getting a sum greater than 5 when rolling two six-sided dice is 13/18 or approximately 72%.
Explanation:The subject area for this question is in Mathematics, specifically probability. The question asks to determine the probability of a sum not being 4, and of a sum being greater than 5 when two six-sided dice are rolled.
(a) The possibilities of getting a sum of 4 are (1,3), (2,2), and (3,1). That's 3 possibilities out of a total of 36, therefore the probability of not getting a sum of 4 is 1 - (3/36) = 33/36 (in simplified form) and as a percentage that's approximately 92%.
(b) The possibilities of getting a sum greater than 5 are (2,4),(3,3),(3,4),(4,2),(4,3),(4,4),(1,5),(2,5),(3,5),(4,5),(5,1),(5,2),(5,3),(5,4),(5,5),(1,6),(2,6),(3,6),(4,6),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5), and (6,6). That's 26 possibilities out of 36, therefore the probability of getting a sum greater than 5 is 26/36 or 13/18 in simplest form, and as a percentage that's approximately 72%.
In this way, understanding of probability and how to calculate it properly can help in accurately determining outcomes in different scenarios.
Learn more about Probability here:https://brainly.com/question/32117953
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The probability of the sum not being 4 is (36 - 3) / 36, and the probability of the sum being greater than 5 is 21 / 36.
Explanation:When two six-sided dice are rolled, there are 36 possible outcomes. To find the probability that the sum is not 4, we need to calculate the number of outcomes where the sum is not 4 and divide it by the total number of outcomes.
There are 3 outcomes with a sum of 4, so the probability is (36 - 3) / 36.
To find the probability that the sum is greater than 5, we need to calculate the number of outcomes where the sum is greater than 5 and divide it by the total number of outcomes.
There are 21 outcomes with a sum greater than 5, so the probability is 21 / 36.
Learn more about probability here:https://brainly.com/question/32117953
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Math Question please help
Answer:
Step-by-step explanation:a+b
ANSWER
B. y=8x +1200
EXPLANATION
If the family's well pumps on average 8 gallons of water per minute, then the unit rate of change is 8.
This implies that, the slope of the linear equation that models this situation is
[tex]m = 8[/tex]
It was also given that, the well's tank had 1200 gallons of water in the morning.
This implies that the y-intercept of the straight line is
[tex]b = 1200[/tex]
The equation is given by:
[tex]y = mx + b[/tex]
We substitute the values to obtain:
[tex]y = 8x + 1200[/tex]
The amount of water in the tank, y after it has been pumping for x minutes is
[tex]y = 8x + 1200[/tex]
Compute the following linear combination.
(79.4, 58.1) + 3(-0.8, 6.3)
Answer:
(77, 77)
Step-by-step explanation:
Carry out the indicated multiplication:
3(-0.8, 6.3) → (-2.4, 18.9)
Next, combine like terms:
(79.4, 58.1) + (-2.4, 18.9). In other words, combine the x terms 79.4 and -2.4 separately and then the y terms 58.1 and 18.9 separately:
(79.4, 58.1) + (-2.4, 18.9) → (77, 77)
The resultant of the following linear combination is:
(77,77)
Step-by-step explanation:We are asked to find the linear combination of the expression:
(79.4, 58.1) + 3(-0.8, 6.3)
We multiply each of the term in the second coordinate by 3 .
i.e. this could also be given by:
(79.4, 58.1) + (3×-0.8, 3×6.3)
= (79.4, 58.1) + (-2.4, 18.9)
Now as there is a addition sign in between the two coordinates i.e. each of the first and the second coordinate will get added
i.e.
= (79.4+(-2.4),58.1+18.9)
= (79.4-2.4,58.1+18.9)
= (77,77)
i.e.
(79.4, 58.1) + 3(-0.8, 6.3)=(77,77)
Haya , curra , and Brooke are waiting in line. Brooke is not first in line. Haya is being the oldest in line. Brooke is behind haya. List the girls in order from first to last
haya, brooke, curra is the order, i believe
To line up alphabetically by name, Brooke comes first followed by Curra, and Haya is last.
The question requires organizing the names of three girls in alphabetical order without speaking and within a time limit. Given the names are Haya, Curra, and Brooke, we can determine the alphabetical order by looking at the first letter of each name.
Brooke
Curra
Haya
To line up alphabetically by name, Brooke would be first because 'B' comes before 'C' and 'H' in the alphabet. Curra would be second since 'C' comes after 'B' but before 'H'. Finally, Haya would be last because 'H' comes after both 'B' and 'C'.
( Help Please )
A farmer is searching his farmland, looking for a missing horse that went grazing in the field of newly cut hay. He finds himself on the opposite corner of where he started and wants to return to his truck as soon as possible. The field is 450 yd by 600 yd. How far will he walk if he walks diagonally across the field, and how much distance will he save instead of walking around the field? Explain your answer. Make sure to use the Pythagorean Theorem when solving this word problem.
Answer:
750 yards
Step-by-step explanation:
I entered the area of the field into a Pythagorean Theorem Calculator and it concluded that the diagonal length of the field would be approximately 750 yard.
Answer:
300 yd saved
Step-by-step explanation:
The length of the diagonal of the field is found using the Pythagorean Theorem and is
d = √( 450 yd)² + ( 600 yd)² ) = √562500 yd² = 750 yd is the diagonal distance. If, on the other hand, the farmer walks the length and width of the perimeter of the field, that would be 450 yd + 600 yd, or 1050 yd.
The farmer could spare himself 1050 - 750, or 300 yd, of walking if he crosses the field along a diagonal.
35 less than seven times a certain number is fifty-three more than 3 times that number. What is the number?
Answer:
70
Step-by-step explanation:
The equation derived from the problem is 7x - 35 = 3x + 53. Solving this equation by combining like terms and isolating the variable x gives us the certain number, which is 22.
We need to find the certain number mentioned in the problem. According to the problem, '35 less than seven times a certain number is fifty-three more than 3 times that number.' We can translate this into an equation:
7x - 35 = 3x + 53
Where 'x' represents the certain number. Now, let's solve the equation step by step:
First, subtract 3x from both sides to move the variable terms to one side of the equation. 7x - 3x - 35 = 3x - 3x + 53 4x - 35 = 53
Next, add 35 to both sides to isolate the variable term. 4x - 35 + 35 = 53 + 35 4x = 88
Finally, divide by 4 to solve for x. 4x / 4 = 88 / 4 x = 22
So, the certain number we are looking for is 22.
What is the mean absolute deviation of the data set?
{12, 10, 10, 8, 6, 7, 7, 12}
.1
.2
.6
.9
Answer:
the mean absolute deviation of the data set is 2.
Step-by-step explanation:
To calculate the mean absolute deviation of a data set, we need to follow the following steps:
Step 1: Calculate the mean.
Step 2: Calculate how far away each data point is from the mean (always keeping a possitive distance).
Step 3: Calculate the mean of the deviations.
Step 1: The mean of the data set is:
Mean = (12 + 10 + 10 + 8 + 6+ 7 + 7 + 12)/8 = 72/8 = 9
Step 2:
{12 -9, 10-9, 10-9, 9-8, 9-6, 9-7, 9-7, 12-9} = {3, 1, 1, 1, 3, 2, 2, 3}
Step 3: (3 + 1 + 1 + 1 + 3 + 2 + 2 + 3)/8 = 2
In conclusion, the mean absolute deviation of the data set is 2. Which corresponds to the option B.
What is the value of a in the equation , when ?
3
15
21
39
Answer:
15
Step-by-step explanation:
5 times 15 is 75
10 times 3 is 30
75 -30 = 45
Answer:
The value of a is 15
Step-by-step explanation:
Given the equation
[tex]5a-10b=45[/tex]
we have to find the value of a when b is 3
[tex]5a-10b=45[/tex]
Substitute b=3, we get
[tex]5a-10(3)=45[/tex]
[tex]5a-30=45[/tex]
[tex]5a=45+30=75[/tex]
[tex]a=\frac{75}{5}=15[/tex]
Hence, the value of a is 15