One of the legs of a right triangle is twice as long as the other, and the perimeter of the triangle is 28. Find the length of the hypotenuse.
In a right triangle, the 58-cm hypotenuse makes a 51-degree angle with one of the legs. To the nearesttenth of a cm, how long is that leg?
Evaluate: sin (Arccos(5/13))
Evaluate: tan(Arctan(π/6))
Answers
1) If we let the lengths of the legs be x and 2x, then by the Pythagorean theorem,
[tex]x+2x+\sqrt{x^{2}+(2x)^{2}}=28\\3x+x\sqrt{5}=28\\x(3+\sqrt{5})=28\\x=\frac{28}{3+\sqrt{5}} \cdot \frac{3-\sqrt{5}}{3-\sqrt{5}}=21-7\sqrt{5}[/tex]
This means that the length of the hypotenuse is:
[tex]\sqrt{5}(21-7\sqrt{5})=\boxed{21\sqrt{5}-35}[/tex]
2) (Diagram attached) We know that
[tex]\cos 51^{\circ}=\frac{x}{58}\\x=58 \cos 51^{\circ} \approx \boxed{36.5}[/tex] (in cm)
3) From the Pythagorean identity,
[tex]\sin^{2}\left (\arccos \frac{5}{13} \right)+\cos^{2} \left (\arccos \frac{5}{13} \right)=1\\\left(\frac{5}{13} \right)^{2}+\sin^{2} \left (\arccos \frac{5}{13} \right)=1\\\frac{25}{169}+\sin^{2} \left (\arccos \frac{5}{13} \right)=1\\\sin^{2} \left (\arccos \frac{5}{13} \right)=\frac{144}{169}\\\sin \left (\arccos \frac{5}{13} \right)=\boxed{\frac{12}{13}}[/tex]
4) [tex]\frac{\pi}{6}[/tex]
Related Questions
Which combined inequality has the same solution set shown in the graph of x?
Number line ranging from negative four to four, with a line beginning with an open point at negative three and ending with a closed point at negative one
–3 > x ≥ –1
–3 < x ≤ –1
–3 ≤ x < –1
–3 ≤ x > –1
Answers
Step-by-step explanation:
an open (empty) point means the point itself is not included.
a closed (filled) point means the point itself is included.
the x values going from -3 (not included) to -1 (included) means
-3 < x <= -1
so, the second answer is correct.
[tex]2\frac{2}{5}[/tex]
Answers
A fraction is a way to describe a part of a whole. The decimal form of 2 2/5 is 2.4.
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
The decimal form of 2 2/5 can be written as,
2 2/5 = 2 + 2/5 = 2 + 0.4 = 2.4
Hence, the decimal form of 2 2/5 is 2.4.
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Tempest graphs a function that has a maximum located at (-4, 2). Which could be her graph?
Answers
The width of a rectangle is 32 inches shorter than twice its length. The area of the rectangle is 72 square inches. What is the length of the rectangle?
Answers
Answer:
18 inches
Step-by-step explanation:
Equation is (2x-32)(x)=72, where x represents length and (2x-32) represents the width. When you simplify the equation, it ends up as 2x^2-32x-72=0. After factoring, you get 2(x-18)(x+2). Since x cannot be negative, it would therefore be 18. If you plug it back into the equation, you can see that it is right :)
It’s been a while since I did Math but, in most scenarios, when you solve for an equation with only 1 x variable and you substitute it back in, it should always be true and equal the answer in the original equation(?).
For this equation, the answer was x=7, but when I substitute it back in, I was unable to get the original solution back, which means it is “no solution” after all.
Why is that?
Answers
Let's replace every copy of x with 7 and simplify.
[tex]\sqrt{5x+1}+9 = 3\\\\\sqrt{5*7+1}+9 = 3\\\\\sqrt{35+1}+9 = 3\\\\\sqrt{36}+9 = 3\\\\6+9 = 3 \ \text{ .... note the 6 on the left isn't negative}\\\\15 = 3\\\\[/tex]
Which is clearly false. This is probably the set of steps you followed to get "no solution".
Why is there no solution? Well let's subtract 9 from both sides to isolate the square root
[tex]\sqrt{5x+1}+9 = 3\\\\\sqrt{5x+1}+9-9 = 3-9\\\\\sqrt{5x+1} = -6\\\\[/tex]
Recall that the result of a square root operation is never negative. The range of [tex]y = \sqrt{x}[/tex] and [tex]y = \sqrt{5x+1}[/tex] is the set of nonnegative numbers. There is no way we can have the left hand side result in -6
If there was a negative sign out front the square root and we have this instead
[tex]-\sqrt{5x+1}+9 = 3\\\\[/tex]
then the answer would be x = 7
Unfortunately, there isn't such a negative sign, so we stick with "no solutions".
A cafeteria manager can choose from among six side dishes for the lunch menu: applesauce, broccoli, corn, dumplings, egg rolls, or French fries. He uses a computer program to randomly select three dishes for Monday’s lunch.
What is the theoretical probability that applesauce and broccoli will both be offered on Monday?
10%
20%
50%
80%
Answers
Answer:
20%
Step-by-step explanation:
The theoretical probability that applesauce and broccoli will both offered on monday is 20%.
What is combination?A combination is a way of selecting items from a collection where the order of selection does not matter. It is calculated by
[tex]^{n} C_{r} = \frac{n!}{(n-r)!}[/tex]
Where,
[tex]^{n} C_{r}[/tex] is the total number of combinations.
n is the total number of objects
r is the number of objects selected.
What is theoretical probability?The theoretical probability is defined as the ratio of the number of favourable outcomes to the number of possible outcomes.
According to the question.
There are total 6 dishes.
Manger have to choose three dishes for monday.
Now the total number of combination of selecting 3 dishes from 6 dishes
[tex]=^{6} C_{3}[/tex]
[tex]= \frac{6!}{3!(6-3)!}[/tex]
[tex]= \frac{6\times5\times4\times3!}{3\times2\times1\times3!}[/tex]
[tex]=20[/tex]
So, the manager has total 20 choices to select three dishes randomly out or 6 dishes.
Also, it is given that for monday applesauce and broccolli will both offered so the number of choices or combination or the three dishes will be
Applesauce, broccoli, and cornapplesauce, brocolli, and dumplingsapplesauce, brocolli, and egg rollsapplesauce, brocolli, and french friesTherefore, the theoretical probability that applesauce and brocoli will both be offered on monday
[tex]= \frac{4}{20}\times100[/tex]
[tex]= \frac{1}{5} \times 100\\= 20\%[/tex]
Hence, the theoretical probability that applesauce and broccoli will both offered on monday is 20%.
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Find the sum of the interior angles for the polygon that has twice the number of sides as an octagon.
Answers
Answer:
The sum of the interior and exterior angles = 8640+360 = 9000 deg. So, the regular polygon has 9000/180 = 50 sides. Its name is pentacontagon
Step-by-step explanation:
A bag contains 2 red, 5 blue, and 3 green marbles. A marble is chosen at random. What is the probability of NOT choosing a red marble
Answers
Step-by-step explanation:
Number of red = 2Number of blue = 5Number of green = 3total number of marbles = 10probability of not choosing a red marble = 1--choosing a red marble.Because probability is always one(1).
Probability =
[tex]1 - \frac{2}{10} [/tex]
[tex] \frac{8}{10} [/tex]
[tex] \frac{4}{5} [/tex]
Is the probability of not choosing a red marble.
) Find the domain of definition
a) f(x)=3x-1/√1-5x
Answers
Answer:
(-∞, 1/5)
Step-by-step explanation:
[tex]f\left( x\right) =\frac{3x-1}{\sqrt{1-5x} }[/tex]
f is defined ,if and only if ,
1 - 5x > 0
⇔ 1 > 5x
⇔ 1/5 > x
⇔ x < 1/5
Which measure of central tendency is the most affected by outliers
Median
Mean
Midrange
Mode
(Is it the mean or midrange?)
Answers
Mean measure of central tendency is the most affected by outliers. Then the correct option is B.
What is Mean?The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean. The normal is alluded to as the number-crunching mean. It's the proportion of the number of genuine perceptions to the absolute number of perceptions.
Mean measure of central tendency is the most affected by outliers.
Then the correct option is B.
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What are the coordinates of the turning point of the parabola whose equation is
y = x² - 4x + 48
(1) (2.0) (2) (-2, 16)
(3) (2,-4)
(4) (-2,0)
What is the equation for the axis of symmetry for: y = -x² - 2x-1
(1) x= 1 (2) X=-1
(3) y = 1
(4) y = -1
If the roots of a quadratic equation are -2 and 3, the equation can be written as:
1) (x-2)(x+3) = 0
3) (x + 2)(x + 3) = 0
2) (x + 2)(x-3) = 0
4) (x-2)(x-3) = 0
The equation of the axis of symmetry of the graph of y=2x2-3x+7 is
3
3
3
3
(1) X
(2) y=-
(3) X=-
(4) y=-
4
2
2
Ex7: What are the vertex and axis of symmetry of the parabola shown in the graph below?
(1) Vertex (1. 6); axis of symmetry: y=1
(2) Vertex (1, 6); axis of symmetry: x = 1
(3) Vertex (6, 1); axis of symmetry: y = 1
(4) Vertex (6, 1); axis of symmetry: x = 1
Answers
i really hope this helps :))))
What is the square root of 121 ?
Answers
Answer:
√121 = 11
Explanation:
11 × 11 = 121
Answer:
11
Step-by-step explanation:
The square root of 121 is 11.
= 11*11 = √(121)
= 121 = 11
done
What fraction is equal to 5
Answers
Answer:
5/1
Step-by-step explanation:
because 1 in the denominator means the number has no denominator
A group of 31 friends gets together to pay a sport. First, people must be divided into teams. Each team has to have exactly 3 players, and no one can be on more than one team. How many teams can they make?(It is possible that not everyone can be on a team)
Answers
Answer:
10 teams (1 remainder)
Step-by-step explanation:
if each team has 3 players and there are 30 friends, divide that and youll end up with 10 teams. you will also have 1 remaining player
Please I need help ASAP
Answers
Answer: 50 mg
Step-by-step explanation:
Substituting into the half-life formula, we get that
[tex]N(t)=800\left(\frac{1}{2} \right)^{t/25}[/tex]
So, after 100 years,
[tex]N(100)=800\left(\frac{1}{2} \right)^{100/25}=\boxed{50 \text{ mg}}[/tex]
The polynomial 40p + 50f + 90 represents the amount of ink, in milliliters, of printing "p" poster and f flyers in
colour. The polynomial 15p+20f + 45 represents the amount of ink, in milliliters, of printing "p" poster and f flyers
in black and white.
How much ink is saved (HINT: use subtraction) if someone prints 26 posters and 45 flyers in black and white rather
than in colour?
ongle below. Then determine the area when
Answers
color : 40p + 50f + 90
b&w : 15p+20f + 45
p = 26
f = 45
[substitute the values given]
color : 40(26) + 50(45) + 90
b&w : 15(26)+20(45) + 45
[solve the equation]
color : 3380
b&w : 1335
[subtract to see how much ink is saved]
3380 - 1335 = 2045
5 more than n is the quotient of n and 4
Answers
Help asap I DONT KNOW THIS QUESTION!!!
Answers
Answer:
a and b is ur answer
Step-by-step explanation:
what is the perimeter of the square ABCD?
Answers
Answer:
P= 4a would be the answer
How is the graph of the parent function y=x² transformed to produce the graph of y=3(x+1)²?
a) It is translated 1 unit right and compressed vertically by a factor of 3.
b) It is translated 1 unit left and compressed vertically by a factor of 3.
c) It is translated 1 unit right and stretched vertically by a factor of 3.
d) It is translated 1 unit left and stretched vertically by a factor of 3.
Answers
Answer:
Step-by-step explanation:
Remark
Always the easiest way to study these questions is to get a graph. The one below shows
Red: y = x^2
Blue: y= 3(x + 1)^2
You will notice that (x+1)^2 shifts the graph Left -- the opposite to what you might think.
The 3 is a little harder. It narrows the red mother graph. Which choice says that?
The choice is between b and d. Why. Because the blue graph is to the left of the red one.
You have to learn the meaning of compressed. A better word might be narrows.
Answer
B
Cost of Bikes ($) at Bike Shop
312, 352, 480, 392, 368, 352, 416, 640
b. median
The median is?
Answers
Answer:380
Step-by-step explanation:sort the list, take center value or mean of center values if even number of items in list
e) 35-12 + 6 x 36 /4
Answers
[tex]35 - 12 + \frac{6 - 36}{4 } \\ 35 - 12 + \frac{216}{4} [/tex]
2. Divide the number[tex] 35 - 12 + \frac{216}{4} \\ 35 - 12 + 54[/tex]
3. Add the numbers[tex]35 - 12 + 54 \\ 77[/tex]
Solution : 77Which number produces an irrational number when added to 1/3 ?
A. -1/7
B. 2.4494897
C. 0.464646
D. Square root 9
Answers
Question 17
Consider the equation y = 15 - 4x.
Which of the following is a graph of this equation?
Answers
The graph of the given linear equation is the one that you can see below.
How to get the graph of the linear equation?
To graph lines, we need to get two points on the line. To get the points, we can evaluate the line in two different values of x. Here I will use x = 1 and x = 0.
For x = 0 we have:
y = 15 - 4*0 = 15
So we have the point (0, 15).
For x = 1 we have the point:
y = 15 - 4*1 = 11
So we have the point (1, 11).
Now we need to graph these two points and connect them with a line, you will get the graph that you can see below.
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9,10,12,x,20,25 find x the median is 14
Answers
Answer:
16
Step-by-step explanation:
Answer:
16
Step-by-step explanation:
12+16=28
28/2=14
please give brainliest!
hope this helps :)
At her sisters birthday party Cheyenne thought it would be funny to drink lemonade from a party hat if the radius is 4.8 cm and the height of a hat is 12 cm how many cubic centimeters of lemonade can Cheyenne pour into the hat
Answers
92.16 pi cm^3.
Step-by-step explanation:
Shape of a party hat : conical
Volume of a cone = (1/3)(pi)(r^2)(h)
(pi(1/3)(23.04)(12))cm^3
Therefore, approximately
92.16 pi cm^3.
sin A tan A/ 1 - cos A = 1+ sec A
Answers
[tex]\text{L.H.S}\\\\=\dfrac{\sin A \tan A}{1- \cos A}\\\\\\=\dfrac{\sin A \cdot \tfrac{\sin A}{\cos A} }{ 1- \cos A}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;\left[\tan A = \dfrac{\sin A }{\cos A}\right]\\\\\\=\dfrac{\tfrac{\sin^2 A}{ \cos A}}{1- \cos A}\\\\\\=\dfrac{\sin^2 A}{\cos A(1-\cos A)}\\\\\\=\dfrac{1-\cos^2 A}{\cos A( 1- \cos A)}~~~~~~~~~~~~~~~~~~~~~~~~;[\sin^2 A + \cos^2 A = 1]\\\\\\[/tex]
[tex]=\dfrac{(1+ \cos A)(1 - \cos A)}{\cos A(1 - \cos A)}\\\\\\=\dfrac{1+ \cos A}{ \cos A}\\\\\\=\dfrac{1}{\cos A} + \dfrac{\cos A}{ \cos A}\\\\\\=\sec A + 1 \\\\\\=1+ \sec A\\\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]
Dayshawn can choose two of his four t-shirts to take on a weekend trip.
If the t-shirts are labeled A, B, C, and D, which choice represents the sample space, S, for the event?
S = {ABCD}
S = {ABCD, DCBA}
S = {AB, AC, AD, BC, BD, CD}
S = {AB, BA, AC, CA, AD, DA, BC, CB, BD, DB, CD, DC}
Answers
Answer:
it is C S = {AB, AC, AD, BC, BD, CD}
Step-by-step explanation:
i just took it edge 2022 good luck
The solution is: C is the right answer. Sample space of the given event is given by S= {AB, AC, AD, BC, BD, CD}
What is probability?
Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
Here, we have,
Given :
Total T-shirts =4
He chose T-shirt to take on weekend trip = 2
In an random trial or experiment , the set of all possible outcomes or results of that experiment is called the sample space of it.
If the t-shirts are labeled A, B, C, and D,
then its sample space of the event is given by
S= {AB, AC, AD, BC, BD, CD}
Hence, The solution is: C is the right answer. Sample space of the given event is given by S= {AB, AC, AD, BC, BD, CD}
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Kindly solve all the questions below .
I'll give the brainliest
Answers
(4)
1. 11.444 repeater
2. 0.58333 repeater
3. 6.7333 repeater
4. 27.5454 repeater (on both 5 and 4)
5. 1.482517482517 (482517 repeater)
6. 2.285714285714 (285714 repeater)
7. 7.5666 repeater
8. 60.60606060 (60 repeater)
(5)
1. 0.666 (repeater)
2. 0.3666 (repeater)
3. 1.1818181818 (18 repeater)
4. 0.418181818 (18 repeater)
Riley took tests in science.
Each test had a different score.
The mean score of the tests was .
The median score of the tests was .
Based on this information, select the two statements that must be true.
A. At least one score was exactly 85%
B. At least one score was exactly 90%
C. More than half of the scores were 85% or greater.
D. More than half of the scores were 90% or greater.
E. There were no scores less than 90%
F. There were no scores less than 85%
Answers
Answer:c
Step-by-step explanation:heheh
Answer: C
Step-by-step explanation: