Find the length of side x in the simplest radical form with a rational denominator.
Answers
Answer:
[tex]\sqrt{2}[/tex]
Step-by-step explanation:
We can use either angle, but I'm going to use the one on the bottom. So, in order to find x, we need to use tangent. One side we know is the adjacent, and the side we don't know is the opposite, therefore we need tangent. Here's the equation:
[tex]tan(45)=\frac{x}{\sqrt{2}}[/tex]
Obviously, we can't have a root in our denominator, so we need to get rid of it somehow. Here's how:
We multiply the denominator of the fraction by [tex]\sqrt{2}[/tex]. [tex]\sqrt{2}[/tex] multiplied by itself is simply 2. Try it! We also want to multiply the numerator by [tex]\sqrt{2}[/tex], but there isn't really a number we can use with that, so we'll just add it to the side. The equation you have now is:
[tex]tan(45)=\frac{x\sqrt{2} }{2}[/tex]
Let's try to work this out now. Since the denominator is 2, we have to multiply both sides by it to find x.
[tex]\frac{x\sqrt{2} }{2*2} =x\sqrt{2}[/tex]
[tex]tan(45)*2=2[/tex]
We can plug 2 in for the x in the numerator now:
[tex]\frac{2\sqrt{2} }{2}[/tex]
2 and 2 cancel out, so you get 1 in both the numerator and denominator. That's how we get our answer of [tex]x=\sqrt{2}[/tex]
Also, because this is a 45-45-90 triangle, you don't really have to do all that work. If it's a 45-45-90 triangle, both legs should be the same length. :)
Related Questions
The heights of a large population of ostriches are normally distributed. Which is the closest to the percentage of these heights that is within 3 standard deviations of the mean?
a. 95%
b. 99.7%
c. 0.3%
d. 5%
Answers
The value of 99.7% is the closest to the percentage of these heights that is within 3 standard deviations of the mean.
What is the empirical rule?If your distribution follows a normal distribution, the standard deviation and mean can tell you where the majority of the data are.
It is given that:
The heights of a large population of ostriches are normally distributed.
The percentage of these heights that is within 3 standard deviations of the mean
As we know from the empirical rule:
It is the rule of 68-95-99.7.
From the data given in the question:
The height of a large population of ostriches is normally distributed.
So,
X ~ (u, б²)
Normal distribution.
P{u - 3б < X < u + 3б}
From the distribution table:
P{u - 3б < X < u + 3б} = 99.7%
Thus, the value of 99.7% is the closest to the percentage of these heights that is within 3 standard deviations of the mean.
Learn more about the empirical rule here:
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A triangle has sides with lengths of 44 meters, 55 meters, and 77 meters. Is it a right triangle?
Answers
Answer:
no it is not a right triangle because the lengths add up to 176 and a right triangle should add up to 190.
Step-by-step explanation:
The side measures of the triangle does not form a right triangle.
What is a triangle?A triangle is a flat geometric figure that has three sides and three angles. The sum of the interior angles of a triangle is equal to 180°. The exterior angles sum up to 360°.
For the given situation,
The side lengths of the triangle are 44 meters, 55 meters, 77 meters.
For the triangle to be a right triangle, one interior angle should be 90°.
Based on the sides, by Pythagoras theorem,
Square of long side = sum of square of other two sides
⇒ [tex]77^{2}=44^{2} +55^{2}[/tex]
⇒ [tex]5929=1936+3025[/tex]
⇒ [tex]5929\neq 4961[/tex]
Hence we can conclude that the side measures of the triangle does not form a right triangle.
Learn more about triangles here
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What is 90\%90%90, percent of 202020?
Answers
Answer:
90 Percent of 20 is 18
Step-by-step explanation:
multiply 90 x 100 then divide by 20
The possibility of an event happening is its ______.
Answers
Answer:
Probability
Step-by-step explanation:
Answer:
Probability.
Step-by-step explanation: This is the chance of an event or something happening. Like one green, blue, yellow, and a red square have a1/4 chance of happening since there are four. This can go to 1/6 if we add white and purple to the spinner.
What are the center and the radius of the circle 4x2 + 4y2 - 4x + 16y + 1 = 0?
Answers
Answer:
Center of circle: (1, -2)
Radius: √6
Step-by-step explanation:
First, we need to isolate the constant:
Then, we can divide the whole equation by 4:
Then, we can complete the square(reminder: (a+b)^2 = a^2 + 2ab + b^2)
Now that we got the standard equation of the circle, we can find the center and radius by using the equation , where (h, k) is the coordinate of the center, and r is the radius.
Therefore, the center of the circle is (1, -2), and the radius of the circle is √6.
Step-by-step explanation:
The center and radius of the circle 4x² + 4y² - 4x + 16y + 1 = 0 are (1/2, -2) and 2 respectively.
To solve the question, we need to know the standard equation of a circle.
What is the standard equation of a circle?The standard equation of a circle with center (h,k) and radius, r is
(x - h)² + (y - k)² = r² (1)
Now, to find the center and radius of 4x² + 4y² - 4x + 16y + 1 = 0, we convert it to standard form by completing the square method.
What is completing the square method?This is a mathematical operation in which we convert a mathematical expression into a perfect square.
So, 4x² + 4y² - 4x + 16y + 1 = 0
Subtracting 1 from both sides, we have
4x² + 4y² - 4x + 16y + 1 - 1 = 0 - 1
4x² + 4y² - 4x + 16y = - 1
Divding through by 4, we have
x² + y² - x + 4y = -1/4
Adding half the square of the coefficient of x and y to both sides, we have
x² + y² - x + 4y + (-1/2)² + 2² = -1/4 + (-1/2)² + 2²
x² - x + (-1/2)² + y² + 4y + 2² = -1/4 + 1/4 + 2²
(x - 1/2)² + (y + 2)² = 0 + 2²
(x - 1/2)² + (y + 2)² = 2² (2)
Comparing equations (1) and (2), we have h = 1/2, k = -2 and r = 2.
So, the center and radius of the circle 4x² + 4y² - 4x + 16y + 1 = 0 are (1/2, -2) and 2 respectively.
Learn more about standard equation of a circle here:
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Find the median of the data set below:
3,5,7,10,10,4,7,5,8,10,6
Answers
Answer:
7
Step-by-step explanation:
First put them in order. I got 3, 4, 5, 5, 6, 7, 7, 8, 10, 10, 10. The middle is the sixth, because (1+11)/2 is 6. So the median is 7.
please help meee!
If the points (-9, ) and (-8, -9) fall on a line with a slope of -5. What is the value of f?
Answers
Answer:
the value of f is -9
Step-by-step explanation:
hii please help i’ll give brainliest
Answers
Answer:
X>3
Step-by-step explanation:
Shaan’s math homework scores for the semester are 90, 85, 98, 60, 84, and 78. Shaan’s teacher said she would drop the lowest homework score when calculating grades. How does the mean of Shaan’s actual math scores compare to the mean of the scores when the lowest one is dropped?
a. The relationship cannot be determined.
b. The final mean is the same as the original.
c. The final mean is lower than the original.
d. The final mean is higher than the original.
Answers
Answer:
The final mean is higher
Step-by-step explanation:
The mean of all the scores = [tex]\frac{90 + 85 + 98 + 60 + 84 + 78}{6\\} = \frac{495}{6} = 82.5\\[/tex]
The mean of the scores with the 60 dropped = [tex]\frac{435}{5} = 87[/tex]
The final mean is higher
That will always happen when you drop the lowest score. I worked it out for you so that you would see that it happened in your case.
Answer:
lol i have this question too
Step-by-step explanation:
btw is yall really in highschool, cuz this is a middle school question......
Solve and write equation in Slope intercept
form (y=mxth) ! Label Slope and y intercept
1) -3x +y = 8
2) -2x + 3y = 1
3)5y +3X = 10
Answers
Answer:
Step-by-step explanation:
1. is y= 3 x +8
-3 x + y - 8= 0
y = 3x+ 8
2. is in the pictures
3.
3 X + 5 y - 10 = 0
Real solution:
y = 2 - (3 X)/5
Solution:
y = 2 - (3 X)/5
Integer solution:
X = 5 n, y = 2 - 3 n, n element Z
Solution for the variable y:
y = 1/5 (10 - 3 X)
Can anyone find d-bar (the d with the line over it) and explain it to me? For this problem five trials are done at eight am and then twelve am. The eight am trials are 98.4, 98.6, 97.8, 97.1, and 97.5. The 12am ones are 98.9, 99, 97.9, 96.6, and 97.7. The correct answer is -0.14 but I can't get that answer.
Answers
Answer:
d-bar= ∑d/n= -0.7/ 5= -0.14
Step-by-step explanation:
Eight am 12 am difference (8:00am- 12:00 am)= d
98.4 98.9 (98.4-98.9=) -0.5
98.6 99 (98.6-99=) -0.4
97.8 97.9 (97.8-97.9=) - 0.1
97.1 96.6 (97.1-96.6=)+0.5
97.5 97.7 (97.5-97.7=)-0.2
∑ -0.7
d= difference between 8 am and 12 am
First we subtract the 12.00 am times from 8:00 am times.
Then we add all the differences to get the total difference ∑d.
∑d= -0.7= total of the difference between two times.
n= number of observations=5
Putting the values in the formula would give the answer.
d-bar= d`= ∑d/n= -0.7/ 5= -0.14
please help! need answers today!!
Answers
Answer:
Step-by-step explanation:
log 31.3= 1.49554433755 (round to 1.496)
ln square root of 7= 0.97295507452 (round to .973)
what quadrilateral can you draw that has exactly one pair of parallel sides
Answers
Answer:
trapezoid
Step-by-step explanation:
prove that 15-7 root 3 is irrational
Answers
Answer:
Step-by-step explanation:
[tex]\text{Did you mean}\\ \\ \sqrt[3]{15-7}\\ \\ \sqrt[3]{8}=2\text{ which IS a rational number}[/tex]
Rewrite the point-slope equation in slope-intercept form: y - 3 = 2(x + 4)
A) y = 2x + 5C
B) y = 2x + 7
C) y = 2x + 9
D) y = 2x + 11
Answers
Answer:
y = 2x + 11
Step-by-step explanation:
y - 3 = 2(x + 4)
y - 3 = 2*x + 2*4
y -3 = 2x + 8
y = 2x + 8 +3
y = 2x + 11
Wich hotel costs the least per night ? :)
Answers
Answer:
answer b
step - by - step explanation
Hotel A. per night charge is 64 $Hotel B. per night charge is 60$ Hotel c. per night charge is 65$b(-3)=-12
Find the solution
Answers
Answer:
b =4
Step-by-step explanation:
Remove parentheses.[tex]b * -3 =-12[/tex]
2. Regroup terms
[tex]-3b=-12[/tex]
3. Divide both sides by -3.
[tex]b=\frac{-12}{-3}[/tex]
4. Two negatives make a positive.
[tex]b=\frac{12}{3}[/tex]
5. Simplify [tex]\frac{12}{3}[/tex] to 4.
b = 4
Ilk defa buraya giriş yapıyorum sırf deneme için bir soru paylaşıyorum. 23*11= yukarıdaki soruyu yaparsanız sevinirim
Answers
Cevap:
253
Adım adım açıklama:
23 ve 11'in çarpımı;
_____2 ___ 3
___ * _ 1 ____1
_________
_____2____3
_ + _ 2_3
____________
__2__5____3
____________
Dolayısıyla 23 * 11'in çarpımı 253'tür.
Hesap makinesi problemi çözmekte zorlanırsa aynı sonuç.
What value for x makes the following sentence true?
x+ 4 = 3(x - 2)
'A 5
B 40
C 20
D3
Answers
Answer:
Value of x = 5
Step-by-step explanation:
Given:
x + 4 = 3(x - 2)
Find:
Value of x
Computation:
x + 4 = 3(x - 2)
⇒ x + 4 = 3x - 6
⇒ x = 3x -6 - 4
⇒ x - 3x = -10
⇒-2x = - 10
⇒ x = -10 / - 2
Value of x = 5
15 points! whats value of q?
Answers
Answer:
30 degrees
Step-by-step explanation:
Good luck fam
A set cards has the numbers 1 through 25 on each card. Each numbers appears on exactly one card. What is P (less than8)?
Answers
Answer:
7/25
Step-by-step explanation:
A store pays $45 for a video game. The percent of markup is 35%. What is the selling price of the video game?
Answers
Steps:
45 * 35%
45 * 0.35 = $15.75
45 + 15.75 = $60.75
what ur fav ainme :)
Answers
The figure below is reflected over y-axis and then rotated 180° counterclockwise.
What are the coordinates of the image of point Y after these transformations?
Answers
Answer:
The coordinates of point y after the transformation is (-6,5)
Step-by-step explanation:
Firstly , we need to get the coordinates of the point y before the transformation
The coordinates are
(-6,-5)
By reflecting over the y-axis, we have the following change;
(x,y) becomes (-x,y)
So we have;
(6,-5)
Then we are to rotate at an angle of 180 degrees counterclockwise
The operation here will be;
(x,y) to (-x,-y)
So we have;
(6,-5) to (-6,5)
Find the first term of a sequence x+1,2x-18,2x-1,if this sequence is an arithmetic progression
Answers
Answer:
a₁ = 37
Step-by-step explanation:
In an arithmetic progression the common difference d is
d = a₂ - a₁ = a₃ - a₂ , that is
2x - 18 - (x + 1) = 2x - 1 - (2x - 18) ← distribute and simplify both sides
2x - 18 - x - 1 = 2x - 1 - 2x + 18
x - 19 = 17 ( add 19 to both sides )
x = 36
Thus
a₁ = x + 1 = 36 + 1 = 37
What is the number lateral faces, bases, edges and vertices? Pls I need this ASAP
Answers
Answer:
4 lateral faces
1 base
8 edges
5 vertices
simplest form of ratio 24:36:60
Answers
Answer:
2:3:5
Step-by-step explanation:
24:36:60
1) Find the greatest common factor
24 ⇒ 1, 2, 3, 4, 6, 8, 12, 24
36 ⇒ 1, 2, 3, 4, 6, 9, 12, 18, 36
60 ⇒ 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Therefore, the greatest common factor is 12.
2) Divide all values by 12
24 ÷ 12 = 2
36 ÷ 12 = 3
60 ÷ 12 = 5
Therefore, the simplified form of the ratio is 2:3:5.
I hope this helps!
If p : q = 2/3 : 3 and p : r = 3/4 : 1/2 , calculate the ratio p : q : r Giving your answer in its simplest form.
Answers
Answer:
Step-by-step explanation:
p:q = ⅔:3 = 2:9 = 6:27
p:r = ¾:½ = 3:2 = 6:4
p:q:r = 6:27:4
I need help with my home work please
Answers
Genise is making cookies. She needs 1 2/3 cups of flour for one batch, but she wants to make 2 1/2batches. Write an equation that can be used to find how many cups of flour Genise will need. I need help with my math quiz thanks
Answers
Answer:
(1 2 ÷ 3) (2 1 ÷ 2) = x
Step-by-step explanation:
The equation is
Let us assume x be the amount of flour she will need in cups.
Now
1 2 ÷ 3 becomes 5 ÷ 3
2 1 ÷ 3 becomes 5 ÷ 2
Now multiply each number
(5 ÷ 3)(5 ÷ 2) = x
25 ÷ 6 = x
Hence, (1 2 ÷ 3) (2 1 ÷ 2) = x this would be the equation