Find the length of side x in the simplest radical form with a rational denominator
Answers
Answer:
The value of x = 1
Step-by-step explanation:
Given
hypotenuse = √2 angle Ф = 45°To determine
x = ?
Using the trigonometric ratio
cos Ф = adjacent / hypotenuse
here
Ф = 45°
adjacent of 45° = x
hypotenuse = √2
so substituting Ф = 45° adjacent = x and hypotenuse = √2 in the equation
cos Ф = adjacent / hypotenuse
[tex]\cos \left(45^{\circ \:}\right)=\frac{x}{\sqrt{2}}[/tex]
switch sides
[tex]\frac{x}{\sqrt{2}}=\cos \left(45^{\circ \:}\right)[/tex]
Multiply both sides by 2
[tex]\frac{2x}{\sqrt{2}}=2\cos \left(45^{\circ \:}\right)[/tex]
[tex]\sqrt{2}x=\sqrt{2}[/tex] ∵ [tex]\cos \left(45^{\circ \:}\right)=\frac{\sqrt{2}}{2}[/tex]
Divide both sides by √2
[tex]\frac{\sqrt{2}x}{\sqrt{2}}=\frac{\sqrt{2}}{\sqrt{2}}[/tex]
[tex]x=1[/tex]
Therefore, the value of x = 1
Related Questions
HELP PLZ DUE IN 30 MIN
x =
Answers
Answer:
x=4
Step-by-step explanation:
20x+5+24x-1=180
44x+4=180
- 4 -4
44x=176
/44 /44
x=4
9514 1404 393
Answer:
x = 4
Step-by-step explanation:
The two marked angles are supplementary when the lines are parallel.
(20x +5)° +(24x -1)° = 180°
44x +4 = 180 . . . . . . simplify
44x = 176 . . . . . . . . . subtract 4
x = 4 . . . . . . . divide by 44
__
The two angles are ...
(20·4 +5)° = 85°
(24·4 -1)° = 95°
Jade has 100 to spend on shoes and socks. She buys a pair of shoes for 75 and wants to wants to spend the rest of the money on socks. Each of socks cost $3.50. let n represent the number of the pair of socks that jade can buy. Which inequality represents her situation?
Answers
Answer:
75 + 3.5n ≤ 100
Step-by-step explanation:
Given that:
Total amount = $100
Cost of shoe = $75
Cost per socks = $3.50
n = number of socks pairs
Cost of shoe + (cost per pair of socks * number of socks) ≤ total amount
75 + (3.50 * n) ≤ 100
75 + 3.5n ≤ 100
what is the image point of (8,-7) after a translation right 1 unit and up 4 units?
Answers
Answer:
It is (9,-3) because x increased by 1 unit and y increased by 4 units.
Answer:
[tex](9,-3)[/tex]
Step-by-step explanation:
[tex](8,-7)[/tex]
If it moves right, add the value to the x-coordinate. If it moves left, subtract the value from the x-coordinate. In this case, because the point was translated 1 unit right, we add 1 to the x-coordinate 8.
[tex](9,-7)[/tex]
If it moves up, add the value to the y-coordinate. If it moves down, subtract the value from the y-coordinate. In this case, because the point was translated 4 units up, we add 4 to the y-coordinate.
[tex](9,-3)[/tex]
I hope this helps!
Help me out I will gave Brainliest
Answers
Step-by-step explanation:
(3x-2y=-16)first put in standard form y=mx+b
(-2y=-3x-16) divide both sides by -2
y=3/2x+8
Answer:
C
Step-by-step explanation:
By opposite I'm going to assume they mean the perpindicular line
To do this you first need to convert the function into linear form
So we have 3x-2y=-16
and so we can add 2y and 16 to both sides to get
3x+16=2y
then divide by 2 to get
3/2x+8=y
This is our function in linear form but now we need the opposite by taking the negative reciprocal of the slope
This means our near equation is now -2/3x+8 while none of them give that as an option directly if you simplify C it will match
1.5:4=9:(2y+5)
Solve for y
Answers
Answer:
y = 9.5
Step-by-step explanation:
Express the ratios in fractional form, that is
[tex]\frac{1.5}{4}[/tex] = [tex]\frac{9}{2y+5}[/tex] ( cross- multiply )
1.5(2y + 5) = 36 ( divide both sides by 1.5 )
2y + 5 = 24 ( subtract 5 from both sides )
2y = 19 ( divide both sides by 2 )
y = [tex]\frac{19}{2}[/tex] = 9.5
Please help!
Write the sum, and then write an equivalent expression by collecting like terms and removing parentheses whenever possible.
Answers
Answer:
The opposite of -10·t and t - 10·t is t
Step-by-step explanation:
1) The opposite of 4·x and -5 + 4·x is given as follows;
-4·x + (-5 + 4·x) = -4·x -5 + 4·x = -4·x + 4·x - 5 = 0 - 5 = -5
2) The opposite of -10·t and t - 10·t is given as follows;
-(-10·t) + (t - 10·t) = 10·t + t - 10·t = 10·t - 10·t + t = 0 + t = t
3) The opposite of (-7 - 4·v) and -4·v is given as follows;
-(-7 - 4·v) + (-4·v) = -1 × (-7 - 4·v) - 4·v = 7 + 4·v - 4·v = 7 + 0 = 7
The absolute value of -12 is
Answers
Answer:
12
Step-by-step explanation:
If the original number is zero or positive, then the absolute value of the number is simply the original number. If the number is negative, then the absolute value is the original number with the negative sign stripped away. For example: Notice that an equation with an absolute value represents two possibilities. could i get brainliest please
The line AB is shown on the grid.
a) Find the gradient of a line
perpendicular to AB.
b) Find the equation of the line
perpendicular to AB and passing
through the midpoint of AB.
Answers
Answer:a=-2
Step-by-step explanation:
4(4y - 3x) Need help
Answers
Answer:
4(4y - 3x)
16y -12x
you can't simplify this any further
I hope this helps
1/4 as a decimal rounded to one significant figure
Answers
Answer:
0.2
Step-by-step explanation:
Answer:
The correct answer is 0.25
Convert the fraction to a decimal by dividing the numerator by the denominator.
0.25
slope and y intercept of 5x + 8y = 8
Answers
Answer:
Slope: -5/8
y intercept: (0,1)
Step-by-step explanation:
The slope of the line will be {m} = -5/8 and the y - intercept will be 1.
What is direct variation?Direct variation of a quantity {y} with respect quantity {x} means that the value of {y} increases as the the value of {x} increases. Mathematically -
y = Kx
K = y/x
where -
{K} is scale factor. It also tells by how many times is {y} greater than {x}.
Given is the equation of a straight line as -
5x + 8y = 8
We can rewrite the equation as -
5x + 8y = 8
8y = - 5x + 8
y = -(5/8)x + 1
So the slope will be -
m = -(5/8)
c = 1
Therefore, the slope of the line will be {m} = -5/8 and the y - intercept will be 1.
To solve more questions on direct variation, visit the link below -
brainly.com/question/14254277
#SPJ2
Use the figures to complete the statements proving the converse of the Pythagorean theorem.
Drag and drop a phrase, value, or equation into the box to correctly complete the proof.
To prove the converse of the Pythagorean theorem, we must show that if △ABC has sides of a, b, and c such that a² + b² = c² , then △ABC is a right triangle.
Define △DEF so that it is a right triangle with sides a, b, and hypotenuse x. By the Pythagorean theorem, a² + b² = x² .
Since a² + b² = c² and a² + b² = x², it must be true that c² = x². Since sides of triangles are positive, then we can conclude that Response area. Thus, the two triangles have congruent sides and are congruent.
Finally, if △ABC is congruent to a right triangle, then it must also be a right triangle.
Two right triangles with points labeled in capital letters and sides labeled in lower case letters.
Answers
Answer:
def
Step-by-step explanation:
trust meh
took quiz
Answer:
it is DEF
Step-by-step explanation:
i did the k12 quiz
HELP PLS ILL MARK BRAINLIEST PLEASEEEEEEEEE
Answers
Answer: A
Step-by-step explanation: because I had that same test last year
Plzzzzzzzzzzz helpp ASAP
Answers
Answer:
the answer a
Step-by-step explanation:
i had it
Because zero cannot be in the denominator of a fraction ...if u plu zero in as x u get zero in the last expression which is undefined....hope this helps
✨LOTS OF POINTS✨
For each sequence write an explicit formula: 7. 1,5, 25, ... a_1:___ r/d:___ a_n:___
8. 29, 35, 41, ... a_1:___ r/d:___ a_n:___
For this sequence, write a recursive formula 9. 7,49,343, ... r/d:___ a_n:___
Answers
Answer:
Q7. a₁ = 1 , r = 5, aₙ = 5ⁿ⁻¹Q8. a₁ = 29, d = 6, aₙ = 6n + 23Q9. a₁ = 7, r = 7, aₙ = 7aₙ₋₁Step-by-step explanation:
Q7.
Given sequence
1, 5, 25, ...This is a GP with the first term of a₁ = 1 and common ratio r = 5
Explicit formula is:
aₙ = 1*5ⁿ⁻¹= 5ⁿ⁻¹Q8.
Given sequence
29, 35, 41, ...This is an AP with the first term of a₁ = 29 and common difference d = 6
Explicit formula:
aₙ = 29 + 6(n - 1) = 29 + 6n - 6 = 6n + 23Q9.
Given sequence
7, 49, 343, ...This is a GP with the first term a₁ = 7 and common ratio r = 7
Recursive formula is:
aₙ = aₙ₋₁*7 = 7aₙ₋₁Determine whether the function f(x) = -9.5 + 6 + x² is even, odd or neither.
Answers
Answer:
The function f(x) = -9.5 + 6 + x² is neither odd or even.
Step-by-step explanation:
We know that a function is termed as 'even' when
f(-x) = f(x) for all x
We know that a function is termed as 'odd' when
f(-x) = -f(x) for all x
Given the function
f(x) = -9.5x⁵ + 6 + x²
substitute x with -x
f(-x) = -9.5(-x)⁵ + 6 + (-x)²
as (-x)⁵ = -x⁵, so
f(-x) = -(-9.5x)⁵ + 6 + (-x)²
Apply exponent rule: (-a)ⁿ = aⁿ, if n is even
f(-x) = -(-9.5x)⁵ + 6 + x²
Apply rule: -(-a) = a
f(-x) = 9x⁵ + 6 + x²
As
f(-x) ≠ f(x) ≠ -f(x)
Therefore, the function f(x) = -9.5 + 6 + x² is neither odd or even.
This my question on the photo can you help me
Answers
Answer:
45 degree..................................
Write a linear equation with a slope of -9/5 and passes through the point (10,-2).
Answers + explanations please!
Answers
Y +2 = -9/5(x -10)
URGENT FOR MY FINAL GRADE DEPENDS IF I PASS THIS CLASS PLEASE HELP
Answers
Answer:
The Answer is B
Step-by-step explanation:
PEMDAS
4 to the power of 3 is 64
100/5 = 20
20 * 4 = 80
80 + 64 = 144
find the base of a parallelogram when the area is 180 feet squared and the height is 15 feet
Answers
Answer:
The base is 12ft
Solve the equation
2x^2 + 8x - 1 = 0
by completing the square.
Give your answers correct to 2 decimal places.
Answers
Step-by-step explanation:
2x² + 8x - 1 = 0
2(x + 2)² - 9 = 0
2(x + 2)² = 9
(x + 2)² = 4.5
x = √4.5 - 2 or x = -√4.5 - 2
x = 0.12 or x = -4.12.
Laura walked 612 laps of a circular path in 2 hours. At that rate, how many laps of the path did she walk in one hour? PLz help
Answers
Answer:
The answer is 3 1/4
Step-by-step explanation:
I hope this helps! :)
Answer:
3 1/4
Step-by-step explanation:
Find the sum.
(3/8x-8)+(3/8x-3)
Step by step explain please!
Answers
first calculate the sum
3/4x - 8 - 3
then calculate the difference
3/4x - 11
Answer: 3/4x + -11
Step-by-step explanation:
3/8x -8 + 3/8x - 3
= 3/8x + - 8 + 3/8x + -3
Combine like terms
3/8x + -8 + 3/8x + -3
=(3/8x + 3/8x) + ( -8 + -3)
Answer: 3/4x + -11
"The difference between four-fifths of
a number and 11 is -46."
Answers
Answer:
The number is -43.75.
Step-by-step explanation:
4x/5 - 11 = -46
4x/5 = -35
x = -43.75
Answer:
-43.75
Step-by-step explanation:
This is the answer because:
1) We know that 4/5 of a number has to equal -35 since -46 + 11 = -35.
2) 4/5x = -35 (solve for x): -35 ÷ 4/5 = -43.75
3) 4/5 x -43.75 = -35, I got this by solving for x (look at step 2)
Therefore, the answer is -43.75
Hope this helps! :D
Which equation shows one way to find the value of 45 × 4? 45 × 4 = (9 × 5) × (2 × 2) = (9 × 2) × (5 × 2) = 18 × 10 = ? 45 × 4 = (9 × 5) × (2 × 2) = (9 + 5) × (2 + 2) = 14 × 4 = ? 45 × 4 = (9 × 5) × (2 × 2) = (9 + 2) × (5 + 2) = 11 × 7 = ? 45 × 4 = (9 × 5) × (2 × 2) = (18 × 2) × (10 × 9) = 36 × 90 = ?
Answers
Answer:
45 × 4 = (9 × 5) × (2 × 2) = (9 × 2) × (5 × 2) = 18 × 10 = ?
Step-by-step explanation:
Which equation shows one way to find the value of 45 × 4?
45 × 4
Splitting each number into factors of each other
45 = 9 × 5
4 = 2 × 2
45 × 4 = (9 × 5) × (2 × 2)
45 × 4 = (9 × 2) × (5 × 2)
45 × 4 = 18 × 10
Option A is the correct option
A rectangular soccer field may have a width between 50 and 100 yards and a length
between 100 and 130 yards. One particular soccer field has a perimeter of 320 yards. Its
length measures 40 yards more than its width. What are the dimensions of this field?
The length is___yards.
The width is____yards.
Answers
Answer:
[tex]perimeter = 2(l + w) \\ but \: length = 40 \times width \\ perimeter = 2(40w + w) \\ p = 2(41w) \\ 320 = 2(41w) \\ w = \frac{320}{(2 \times 41)} \\ w = 3.902 \: yards \\ length = 40 \times w \\ = 40 \times 3.902 \\ l = 156.08 \: yards[/tex]
9514 1404 393
Answer:
length: 100 yardswidth: 60 yardsStep-by-step explanation:
Let w represent the width of the field. Then the length is (w+40), and the perimeter is ...
P = 2(L +W)
320 = 2((w+40) +w) . . . . fill in values
160 = 2W +40 . . . . . . . . . divide by 2, collect terms
80 = w +20 . . . . . . . . . . . divide by 2
60 = w . . . . . . . . subtract 20
w+40 = 100
The length is 100 yards; the width is 60 yards.
Grayson bought snacks for his team's practice. He bought a bag of oranges for $3.11
and a 24-pack of juice bottles. The total cost before tax was $50.15. How much was
each bottle of juice?
Answers
Answer:
so he bought oranges of 3.11 and a 24 pack of juice bottles the total cost before tax was 50.15 how much was each bottle of juice what you have to do is....
2
Step-by-step
its 2 dollars each or 2.10 dollars each
A number is squared, then doubled and then 4 is subtracted. The result is the original number. What could the number be?
(Give answers to 2 d.p)
Answers
Answer:
umm its B cause i got it right hope this helped :)
Step-by-step explanation:
Jason agreed to make 12 payments of $38.50 to buy a new TV so far he has made Seven payments how much more money does Jason owe
Answers
Answer:
$192.50
Step-by-step explanation:
12*38.50=462
7*38.50=269.5
462-269.50=192.50
Evaluate 6x - 3, when x = 2 1/4
Answers
Answer:
10.5
Step-by-step explanation:
Plug in 2 1/4
10.5 or 10 1/2
Answer:
21/2 in fractions or 10.5 in decimals
Step-by-step explanation:
6(2 1/4)-3 multiply the denominator with the whole number 2 and add 1
6x 9/4-3 reduce the number with the gratest common factor 2
3 x 9/2-3 when dealing with fraction just multiply denominator
27/2-3 the denominator will stay the same always
21/2 Calculate the difference