Find the value of the variable. If your answer is not an integer, leave it in simplest radical form.
[tex]5\sqrt{2}[/tex]
[tex]\frac{5\sqrt{2} }{2}[/tex]
[tex]5\sqrt{3}[/tex]
[tex]\frac{5\sqrt{3}}{2}[/tex]
Answers
Answer:
[tex]$\frac{5\sqrt{2} }{2}$[/tex]
Step-by-step explanation:
[tex]x: \text{opposite side of the angle of 45\º}[/tex]
[tex]5: \text{hypotenuse of the right triangle}[/tex]
[tex]$\sin(\theta)=\frac{\text{opp}}{\text{hyp}} \Rightarrow \sin(45\º)=\frac{x}{5} $[/tex]
[tex]$\text{Once }\sin(45\º)=\frac{\sqrt{2} }{2} $[/tex]
[tex]$\frac{\sqrt{2} }{2} =\frac{x}{5} \Rightarrow 2x=5\sqrt{2} \Rightarrow x=\frac{5\sqrt{2} }{2} $[/tex]
You can just remember that 5 is the diagonal of a square of side length x.
[tex]$5=x\sqrt{2} \Rightarrow x=\frac{5}{\sqrt{2} } \Rightarrow x=\frac{5}{\sqrt{2} } \cdot \frac{\sqrt{2} }{\sqrt{2} } = \frac{5\sqrt{2} }{2} $[/tex]
Related Questions
at the movie theatre admission is $6.30 an adult admission is $9.60. on thursday twice as many adult tickets as child tickets were sold for a total sale of $535.50 how many child tickets were solf that day
Answers
Answer:
number of child tickets sold on saturday is 21
number of adult tickets sold on saturday is 42
Step-by-step explanation:
Let's assume
number of child tickets sold on saturday is x
number of adult tickets sold on saturday is y
On saturday, twice as many adult tickets as child tickets were sold
so, we get
child admission is $6.30 and adult admission is $9.60
a total sales of $535.50
we get
now, we can plug y=2x
now, we can solve for x
now, we can find y
so,
number of child tickets sold on saturday is 21
number of adult tickets sold on saturday is 42.........Answer
Which equation has roots of –3 and 5?
(x+3)(x-5)=0
(x+3)(x+5)=0
O
(x-3)(x+5)=0
(x-3)(x-5)=0
C
Answers
Answer:
(x + 3)(x - 5)
Step-by-step explanation:
The Yogurt Packaging company is now re-designing their factory. They are going to construct a building in
the shape of a square box. Their contractor has told them that the diagonal braces needed to make the roof
are 150 feet long.(please help)
1. What would be the floor plan of the building? Label the diagonal braces
2. Find the dimensions of the new factory
3.Find the perimeter of the new factory
4.the yogurt machines will be placed along the wall of the new factory . Each machine is 10 feet wide.
Find the company fit 40 of the machines in the building Why or Why not ?
Answers
Answer:
1. see attached diagram
2. The dimensions are 75 sqrt(2) by 75 sqrt(2) ft
3. The perimeter is 300 sqrt(2) ft
4. cannot fit 40 machines along the walls
Step-by-step explanation:
We are using a top down view. We have a square building with side length s. The diagonal is 150 ft
Using the Pythagorean theorem
s^2 + s^2 = 150^2
2s^2 = 22500
s^2 =11250
Taking the square root of each side
sqrt(s^2) = sqrt(11250)
s = sqrt(6225*2)
s = 75 sqrt(2)
The dimensions are 75 sqrt(2) by 75 sqrt(2) ft
The perimeter of a square is given by
P = 4s = 4(75 sqrt(2)) =300 sqrt(2) ft
The perimeter is 300 sqrt(2) ft
Assuming the machines are square ( that they are as wide as they are long) 75 sqrt(2) is approximately 106 ft so you can fit 10 along the wall
Putting them along the top and bottom walls = 20 machines
We are only left with 86 ft along the side walls
86/10 = 8 machines
machines * 2 walls = 16
We can fit 20+16 machines = 36 machines not 40
Reduce 102/126 to its lowest terms
Answers
Answer:
17/21
Step-by-step explanation:
102/126
Divide the top and bottom by 6
17/21
Answer:
17/21
Step-by-step explanation:
102/2=51 126/2=63
51/3=17 63/3=21
17/21
Find the indicated side of the right triangle
Answers
Answer:
Step-by-step explanation:
tan30°=3/x
xtan30°=3
x=3/tan30°
x= 5.2
Help anyone can help me do this question 3,I will mark brainlest.
Answers
Answer:
see explanation
Step-by-step explanation:
Calculate the slopes between pairs of the 3 points using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 9, 3) and (x₂, y₂ ) = (- 3, 9)
m = [tex]\frac{9-3}{-3-(-9)}[/tex] = [tex]\frac{6}{-3+9}[/tex] = [tex]\frac{6}{6}[/tex] = 1
Repeat with (x₁, y₁ ) = (5, 1) and (x₂, y₂ ) = (- 3, 9)
m = [tex]\frac{9-1}{-3-5}[/tex] = [tex]\frac{8}{-8}[/tex] = - 1
If lines are perpendicular then the product of their slopes = - 1 , then
1 × - 1 = -1
Thus there is a right angle between the 2 lines
Then triangle is right- angled
traders fix the price of cosmetic items 30% above the cost price when he sold an item at 25% discount there was a loss of Rs 15 find the cost price and marked price of the item
Answers
Cost price is Rs600 and marked price is Rs780.
Must click thanks and mark brainliest
Can someone please help meee
Answers
Answer:
b
basically 5/8 goes to 1/2 0.8 times which is 4/5
Which products result in a difference of squares? Select three options. A. (x minus y)(y minus x) B. (6 minus y)(6 minus y) C. (3 + x z)(negative 3 + x z) D. (y squared minus x y)(y squared + x y) E. (64 y squared + x squared)(negative x squared + 64 y squared)
Answers
Answer:
C D E
Step-by-step explanation:
Edg
Out of the given options, options C, D and E are a difference of squares.
What is the difference of squares?Difference of Squares, two terms that are squared and separated by a subtraction sign.
Given are, options,
D) (y squared minus x y)(y squared + x y) = (y²-xy)(y²+xy) = y⁴-(xy)²
E) (64 y squared + x squared)(negative x squared + 64 y squared) = (64y²+x²)(64y²-x²) = (64y)⁴-x⁴
C) (3 + x z)(negative 3 + x z) = (3+xz)(3-xz) = 3²-(xz)²
Hence, out of the given options, options C, D and E are a difference of squares.
For more references on difference of squares, click;
https://brainly.com/question/11801811
#SPJ6
Which of the following is a rational number?
square root 97
square root 98
square root 99
square root 100
Answers
Answer:
[tex]\sqrt{100}[/tex] is a rational number
Step-by-step explanation:
[tex]\sqrt{97}=9.848857.....\\\\\sqrt{98}=\sqrt{2*7*2}=2\sqrt{7}\\\\\sqrt{99}=\sqrt{3*3*11}=3\sqrt{11}[/tex]
Square root of all prime numbers are irrational numbers
HELP ASAP WILL MARK BRAINLIEST!!! Add or subtract. Write your answer in scientific notation. 4.2 x 10^6 − 1.2 x 10^5 − 2.5 x 10^5 3.3 x 10^9 + 2.6 x 10^9 + 7.7 x 10^8 8.0 x 10^4 − 3.4 x 10^4 − 1.2 x 10^3
Answers
Answer:
see below
Step-by-step explanation:
4.2 x 10^6 − 1.2 x 10^5 − 2.5 x 10^5
All exponent have to have the same number
42 x 10^5 − 1.2 x 10^5 − 2.5 x 10^5
Subtract the number
42 - 1.2 - 2.5 = 38.3
Add back the exponent
38.3 * 10 ^5
This is not in scientific notation
Move the decimal one place to the left and add one to the exponent
3.83 * 10^6
3.3 x 10^9 + 2.6 x 10^9 + 7.7 x 10^8
All exponent have to have the same number
3.3 x 10^9 + 2.6 x 10^9 + .77 x 10^9
Add the numbers
3.3+2.6+.77 =6.67
Add back the exponent
6.67*10^9
This is in scientific notation
8.0 x 10^4 − 3.4 x 10^4 − 1.2 x 10^3
All exponent have to have the same number
8.0 x 10^4 − 3.4 x 10^4 − .12 x 10^4
Subtract
8.0 - 3.4 - .12 = 4.48
Add back the exponent
4.48* 10^4
This is in scientific notation
PLEASE ELP ME ITS URGENT!!! 25 POINTS!!!!!
Write 2.4 × 1012 in standard notation.
Answers
Answer:
2,400,000,000,000
Step-by-step explanation:
2.4 x 10^12 means that the decimal point is moved 12 places to the right (hence the power of 12)
So by moving the decimal point 12 times you get this: 2,400,000,000,000
The reason why there are only 11 zeroes is because the 4 was a decimal place to the right of 2, thus losing a zero.
Will Mark Brainlest Help pls
Answers
Answer:
2 2
1 -3
Step-by-step explanation:
2b=[4 4]
2 -6
b=[4/2 4/2]
2/2 -6/2
b=[2 2]
1 -3
Can anyone help me with this
Answers
Answer:
x=0, - 9
Step-by-step explanation:
x^2+9x=0
x(x+9)=0
x=0 or x=-9
Answer:
x =0 x= -9
Step-by-step explanation:
x^2 + 9x = 0
Factor out x
x(x+9) =0
Using the zero product property
x =0 x+9 =0
x =0 x= -9
Three people are standing on a Cartesian coordinate plane. Robert is standing at point $(4,3)$, Lucy at point $(6,1)$, and Liz at point $(1,7)$. How many units away is the farther person from Robert?
Answers
Answer: Liz, she is 5 units away from Robbert.
Step-by-step explanation:
Ok, the data that we have is:
Robert is at (4,3 )
Lucy is at (6, 1)
Liz is at (1, 7)
We want to find the units between Robert and the person that is farther away from him.
The distance between Robert and Lucy can be calculated as:
First we calculate the difference in the point or in the position vector:
(4, 3) - (6, 1) = (4 - 6, 3 - 1) = (-2, 2)
To calculate the exact distance, we need to calculate the magnitude of this point, this is:
For a point (x, y), the magnitude is M = √(x^2 + y^2)
Then we have:
D = √( (-2)^2 + 2^2) = √8
Now, the distance between Robert and Liz can be calculated in the same way:
(4, 3) - (1, 7) = (4 - 1, 3 - 7) = (3, -4)
The magnitude is:
D = √(3^2 + (-4)^2) = √(9 + 16) = √25 = 5
Now, we know that 5 > √8
Then the person that is farthest away from Robert is Liz, and she is 5 units away.
A water park has 28 water attractions: pools, game areas, and water slides. There are P pools and P +2 games areas. If 50% of the attractions are water slides, how many games areas are there?
Answers
Answer:
8
Step-by-step explanation:
total: 28 water attractions
pools: p
game areas: p + 2
water slides: 50% of 28 = 14
14 + p + p + 2 = 28
2p = 12
p = 6
game areas:
p + 2 = 6 + 2 = 8
Which of the following is a solution of y > |x| - 6? A(-1, -5) B(-5, 1) C(5, -1)
Answers
Answer:
B(-5, 1)
Step-by-step explanation:
We can test each value in the equation and see if the equation works out.
[tex]y > |x| - 6[/tex]
Let’s try A - (-1, -5).
[tex]-5 > |-1|-6\\\\-5 > 1-6\\-5>-5[/tex]
-5 is NOT greater than -5, it is equal so A doesn’t work.
Let’s try B, (-5, 1).
[tex]1 > |-5| -6\\1 > 5-6\\1 > -1[/tex]
1 IS greater than -1, so B works.
Let’s try C for fun.
[tex]-1 > |5| -6\\-1 > 5-6\\-1 > -1[/tex]
-1 is NOT greater than -1, it is equal, so it doesn’t work.
Hope this helped!
Answer:
B(-5,1)
Let us simply just write this in all scenarios.
A(-1,-5)
-5>|-1|-6
-5>-5
(False)
B(-5,1)
1>|-5|-6
1>-1
(True)
C(5, -1)
-1>|5|-6
-1>-1
False
You want to build supports at each end of a table in the shape of a triangle. What type of triangle would you use to act as the supports: acute, right, or obtuse? Why?
Answers
Answer:
obtuse
Step-by-step explanation:
because obtuse triangle would provide more support that acute or right as its bigger.
if the first step of the equation -x + 6 = 5 - 3x is "subtract 5" then what should the next step be
Answers
Answer:
The next step is add x to each side
Step-by-step explanation:
-x + 6 = 5 - 3x
Subtract 5 from each side
-x + 6-5 = 5-5 - 3x
-x+1 = -3x
Add x to each side
-x+1 = -3x+x
1 = -2x
Answer:
Step-by-step explanation:
all you need to do is solve for x right? so in that case when you subtract 5 from both sides you get -x+1=-3x
then you will add x on each side
you should now have 1=-2x
divide each side by -2 and then you will have
-1/2=x
Circle experts...help! will give brainly to most detailed answer
Answers
Answer:
IU=161
Step-by-step explanation:
Angle Formed by Two Secants= 1/2 (difference of Intercepted Arcs)
42 = 1/2 (7m+5 - (3m-1))
Distribute the minus sign
42 = 1/2 (7m+5 - 3m+1))
Combine like terms
42 = 1/2 ( 4m+6)
Distribute the 1/2
42 = 2m+3
Subtract 3 from each side
42-3 = 2m+3-3
39 = 2m
Divide by 2
19.5 = m
The sum of the arcs = 360
IU+ 3m-1 + 7m+5 = 360
IU +10m+4 = 360
IU +10(19.5) +4 = 360
IU +195+4 = 360
IU = 360 - 199
IU=161
can you make a triangle with 1. 2cm 3cm and 4cm 2. 2cm 3 cm 6 cm 3. 90 degrees 45 degrees 45 degrees 4. 90 degrees 60 degrees 60 degrees?
Answers
Answer:
1. 2cm 3cm and 4cm
yes, because 2+3>4
2. 2cm 3 cm 6 cm
no, 2+3<6
3. 90 degrees 45 degrees 45 degrees
yes, 90+45+45 = 180
4. 90 degrees 60 degrees 60 degrees?
no, 90+60+60=210!=180
Find the coordinates of the image of Z(−3,−1) after the translation (x,y)→(x−2,y−7).
Answers
======================================================
Explanation:
We get this point by doing two things.
Subtract 2 from the x coordinate, due to the x-2Subtract 7 from the y coordinate, because of the y-7If we started with x = -3, then x-2 = -3-2 = -5. Also, if we had y = -1 then y-7 = -1-7 = -8
So that's how we end up with Z(-3,-1) moving to Z ' (-5, -8)
You could also show your work like this
[tex](x,y) \to (x-2, y-7)\\\\(-3,-1) \to (-3-2, -1-7)\\\\(-3,-1) \to (-5, -8)\\\\[/tex]
Combine f(x) =(x)(2x + 5) and g(x) = 2x2 - 13x + 6
Addition
Answers
Answer:
f(x) + g(x) is 2(2x² - 4x - 3)
Step-by-step explanation:
[tex]f(x) + g(x) = (x)(2x + 5) + ( {2x}^{2} - 13x + 6) \\ = (2 {x}^{2} + 5x) + (2 {x}^{2} - 13x + 6) \\ = 4 {x}^{2} - 8x - 6 \\ = 2(2 {x}^{2} - 4x - 3)[/tex]
PLEASE HELP ASAP! Alayna is hanging a picture frame in the center of a wall that is 8 feet wide. If the picture frame is 22 1/4 inches wide, how far will each side of the picture frame be from the edge of the wall (in inches)? First, estimate the amount and then find the exact measurement. In two or more complete sentences, explain how you solved the problem. You may include a diagram in your explanation if you wish.
Answers
Answer:
See below.
Step-by-step explanation:
Approximation:
The wall is 8 ft wide.
The frame is 22 1/4 inches wide. 22 1/4 inches is close to 2 ft since 2 ft = 24 inches.
8 ft - 2 ft = 6 ft
There will be approximately 6 ft of space tot he sides of the frame.
6 ft/2 = 3 ft
3 ft * 12 in./ft = 36 in.
There will be approximately 36 in. on each side of the frame.
Exact:
8 ft - 22 1/4 in. = 8 * 12 in. - 22 1/4 in. =
= 96 in. - 22 1/4 in.
= 95 4/4 in. - 22 1/4 in.
= 73 3/4 in.
The total amount of width of the wall not occupied by the frame is 73 3/4 in.
Half of that amount is on each side of the frame.
(73 3/4 in.)/2 = (73 3/4 in.) * 1/2 = (73 * 1/2 + 3/4 * 1/2) in. =
= 36 1/2 in. + 3/8 in.
= 36 4/8 in. + 3/8 in.
= 36 + 7/8 in.
= 36 7/8 in.
-1/2 divided by 1/19
Answers
Answer:
-19/2 or
-9 1/2
Step-by-step explanation:
-1/2 ÷ 1/19
Copy dot flip
-1/2 * 19/1
-19/2
-9 1/2
NEED HELP!!! Please Write the quotient
as a mixed number.
93 divided by 5 = 18 R 3
Answers
Answer:
Hey there!
93 ÷ 5 can be written as 93/5.
5 goes into 93, 18 times, so we have [tex]18\frac{3}{5}[/tex]
Let me know if this helps :)
7. solve for x!
please help
Answers
(3x/6) + 2 = 8
=> 3x/6 = 8 - 2
=> 3x/6 = 6
=> 3x = 6 × 6
=> 3x = 36
=> x = 36/3
=> x = 12
Answer:
x=12
Step-by-step explanation:
3x/6+2=8
3x/6=8-2
=6
3x/6(6)=6(6)
3x=36
x=12
Use the Law of Sines to find the missing angle of the triangle.
Find m < C to the nearest tenth if the c= 102, a = 71 and m < A=40
Answers
Answer:
66.9 degrees
Step-by-step explanation:
The Law of Sines states that a/sinA = c/sinC. Plugging in the values for c, a, and M < A, we get:
71/sin40 = 102/sinC
Cross multiplying, we get:
102(sin40deg) = 71(sinC)
Now, we simplify the left side and get:
65.56 = 71(sinC)
Next, we divide 65.56 by 71 to get:
0.92 = sinC
Taking the inverse sign we get:
C = 66.9 degrees
x^5+x-1
x^5+x-1
x^5+x-1
Answers
Step-by-step explanation:
x⁵+x-1
(2x-x+1) ( x³+x²-1 )
Is 3.18 a real number