Find the exact value of cos 45º in simplest form with a rational denominator.
Answers
Answer:
[tex]\frac{\sqrt{2} }{2}[/tex]
Step-by-step explanation:
Cos is Adjacent over Hypotenuse, (see picture below)
x/xsqrt(2)
1/sqrt(2)
sqrt(2)/2
Related Questions
Which equation for a line with a slope of -3 and a y intercept of 4? Multiple Choice Answer: y=-4+3, y= - 3/4x+4, y=-3x+4, y= - 4\3x-3. HElP QUICKLY
Answers
y=-3x+4
dedont be suspicoes
A MOP TO CLEAN CULO
c
c
c
c
c
Solving Logarithmic Equations
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Identify the solution set of 3 In 4 = 2 In x.
o {6}
O {-8, 8}
o {8}
DONE
(8)
Answers
Answer:
Step-by-step explanation:
3ln(4) = 2ln(x)
ln(4³) = ln(x²)
4³ = x²
(2²)³ = x²
2⁶ = x²
x = ±√2⁶ = ±2³ = ±8
However, the argument of a logarithm must be positive, so x=8.
The solution set of the equation is {8, -8}, but we can discard the negative solution as it is not physically meaningful in this context. So, the final solution set is {8}. Option D is correct.
To solve the equation, we can use the logarithmic identity that states:
n * log(a) = log(aⁿ)
Using this identity, we can rewrite the equation as:
In(4³) = In(x²)
Simplifying both sides using the natural logarithm properties, we get:
In(64) = In(x²)
Taking the exponential of both sides, we have:
[tex]e^{In 64} = e^{In x^2}\\64 = x^2[/tex]
Taking the square root of both sides, we get:
x = ±8
However, we must check if either of these solutions makes the argument of the natural logarithm negative, which is not allowed. Since the argument of the natural logarithm is positive for both x = 8 and x = -8, both solutions are valid.
Therefore, the solution set of the equation is {8, -8}, but we can discard the negative solution as it is not physically meaningful in this context. So, the final solution set is {8}.
Learn more about logarithmic function here:
https://brainly.com/question/3181916
#SPJ7
Wayne is hanging a string of lights 45 feet long around the three sides of his patio, which is adjacent to his house. The length of his patio, the side along the house, is five feet longer than twice its width. Find the length and width of the patio.
Answers
Answer:
The length and width of the patio are 18¹/₃ feet and 6²/₃ feet respectively.
Step-by-step explanation:
Let L and W be the length and width of the patio respectively. Since the patio is a rectangle, its perimeter, P = 2(L + W). This perimeter equals the length of string of lights which is 45 ft.
Now, the length of his patio, the side along the house, is five feet longer than twice its width implies that L = 2W + 5.
Substituting L into P, we have
P = 2(L + W)
= 2(2W + 5 + W)
= 2(3W + 5)
= 6W + 5
Since P = 45 feet,
6W + 5 = 45
6W = 45 - 5
6W = 40
W = 40/6
W = 20/3 feet
W = 6²/₃ feet
Since L = 2W + 5, substituting W = 20/3 into L, we have
L = 2W + 5
= 2(20/3) + 5
= 40/3 + 5
taking the L.C.M, we have
= (40 + 15)/3
= 55/3 feet
= 18¹/₃ feet
So, the length and width of the patio are 18¹/₃ feet and 6²/₃ feet respectively.
A sports tournament has d teams. Each team has 15 players. Using d, write an expression for the total number of players in the tournament.
Answers
Answer:
d x 15=total players.
Step-by-step explanation:
dx15=total number of players in the tournament.
Answer:
15d
Step-by-step explanation:
If there are d teams and 15 people in each team d x 15 = 15d
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Cylender A has a radius of 4 inches and height of 2 inches. Cylinder B has a radius of 2 inches. What is the height of cylinder B if both cylinders have the same volume?
Answers
Answer:
Cylinder B: The height would be 8 inches.
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
V = A * h
CA = 4² = 16 * 2 = 32π
CB = 2² = 4 * 8 = 32π
Write the equation of a circle that has a diameter of 12 units if its center is at (4,7).
PLZ HELP ASAP! I will give you BRAINLIEST
Answers
9514 1404 393
Answer:
(x -4)^2 +(y -7)^2 = 36
Step-by-step explanation:
The equation of a circle with radius r and center at (h, k) is ...
(x -h)^2 +(y -k)^2 = r^2
When the diameter is 12, the radius is 6 (half the diameter). Then for your center point, the equation is ...
(x -4)^2 +(y -7)^2 = 36
please help me with this and explain. It’s due in a bit :/
Answers
Answer:
choice D
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
they have similar angles and similar sides, and the description choice D gives is also correct
ITS A ANGLE QUESTON PLS HELP
Answers
This is a right angles triangle
(6x6)/2
18
Hope this helps :>From CambridgePlease give brainliestAnswer:
18 cm²
Step-by-step explanation:
The area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
Here b = 6 and h = 6 , then
A = [tex]\frac{1}{2}[/tex] × 6 × 6 = 3 × 6 = 18 cm²
find the mean of the given data. 147 141 120 124 128
Answers
660/4 =132
hope that helps xo
I divided by 5 because there are 5 items in the set of data.
Hope this helped!!
What is the area of the image below?
I will mark brainliest!!!
Answers
Answer:
116 square cm
Step-by-step explanation:
Find the area of each shape
7*10=70
4*4=16
1/2(15)*4=30
70+16+30=116
A rectangle has a length of 7 cm and a width of (3x+4)cm. Which expression represents the perimeter?
Answers
Answer:
2{7 + (3x + 4)} represents the perimeter of the rectangle
12. The base angles of an isosceles triangle are represented by (5x + 10) and 50°. Find x.
Answers
Answer:
x = 8
Step-by-step explanation:
Base angles of isoceles triangle are equal
5x + 10 = 50
5x = 40
x = 8
Your friend Mel says he has an easier way to solve this problem. Here are the first steps in his method.
First, isolate all of the x-terms on the left side. This leaves a constant on the right that isn't equal to 0.
Factor the GCF out of the terms on the left side.
If there's a whole-number factor on the left side, divide both sides by that number. Notice that after you do this, one factor on the left is just x.
Apply Mel's steps to your equation in question 1. (5 points)
The original equation is 2x^2 +6x+4=24 ft.^2
Answers
Simplifying
2x2 + 6x + 4 = 24
Reorder the terms:
4 + 6x + 2x2 = 24
Solving
4 + 6x + 2x2 = 24
Solving for variable 'x'.
Reorder the terms:
4 + -24 + 6x + 2x2 = 24 + -24
Combine like terms: 4 + -24 = -20
-20 + 6x + 2x2 = 24 + -24
Combine like terms: 24 + -24 = 0
-20 + 6x + 2x2 = 0
Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + 3x + x2) = 0
Factor a trinomial.
2((-5 + -1x)(2 + -1x)) = 0
Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:
Simplifying
-5 + -1x = 0
Solving
-5 + -1x = 0
Move all terms containing x to the left, all other terms to the right.
Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5
Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5
Combine like terms: 0 + 5 = 5
-1x = 5
Divide each side by '-1'.
x = -5
Simplifying
x = -5
Answer:
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:
-5 + -1x = 0
-5 + -1x = 0
Move all terms containing x to the left, all other terms to the right.
-5 + 5 + -1x = 0 + 5
Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5
Combine like terms: 0 + 5 = 5
-1x = 5
x = -5
Step-by-step explanation:
PLEASE HELP WILL GIVE BRAINLIEST!!!
Answers
Answer:
angle U ( the third option down)
Step-by-step explanation:
Ted has the following triangle dimensions.
side length of 8
side length of 14
side length of 23
How many triangles can he construct?
He can construct only one triangle.
He can construct two triangles.
He can construct three triangles.
He cannot construct a triangle.
Answers
Answer:
He cannot construct a triangle
Step-by-step explanation:
In order to construct a triangle the two shorter sides added together have to be greater than the longest side if that makes sense
So basically 8+14 has to be greater than 23 in order for it to be side lengths of a triangle
8+14=22
22 is not greater than 23 therefore he cannot create a triangle
AnsweFREE 50 POINTS FOR MEEE
Step-by-step explanation:
its D :)
find the value of x3-1 if x= 0, 1,-1
Answers
Step-by-step explanation:
Given
x³ - 1
When x = 0
0³ - 1 = - 1When x = 1
1³ - 1 = 0when x = - 1
( -1)³ - 1 = - 2Hope it will help :)❤
Roland bought 6 tickets for him and his family to attend the high school basketball game. He bought a combination of student tickets for $3 each and adult tickets for $5 each. If he spent a total of $24 on the tickets, which system of equations could be used to find the number of student tickets, x, and the number of adult tickets, y, he bought?
Answers
Answer:
RM 21 for student and for adults
Find the volume of a pyramid with a square base, where the perimeter of the base is
17 cm and the height of the pyramid is 15 cm. Round your answer to the nearest
tenth of a cubic centimeter.
Answers
Answer:
90.3125 cm³
Step-by-step explanation:
Since the perimeter of the bottom square is 17, you can divide by four to find out what the lenght of each side is.
17/4=4.25 cm
We know the height of pyramid is 15 cm
The formula for the volume of a square pyramid is
V=a²(h/3)
V=a2(h/3)=4.252·15/3=90.3125 cm³
4 points
4.) How could we determine who has the greater total change in the
amount of juice in their carton?
Felicia pours juice from a carton into a glass. Every time she fills the glass, the
amount of juice in the carton changes by -0.44 L. She fills her glass 2 times in
all. Bernadette has a different carton of juice that is the same size. Every time she
fills her glass, the amount of juice in her carton changes by -0.42 L. She fills her
glass 2 times in all. Who has
the greater total change in the amount of juice in
their carton?
A. 2 3/4 multiplied by (-0.44) and 2 2/3 multiplied by (-0.42)
B. 2 3/4 divided by -0.44 and 2 2/3 divided by -0.42
Answers
Answer:
A is the answer you sent on the question on carton
how do you prove something as a parallelogram?
Answers
need help again... asap
Answers
Answer:
9/41
Step-by-step explanation:
cos=adjacent/hypotenuse
adjacent=9
hypotenuse=41
−2x+y=0, −7x+3y=2 adding
Answers
Answer:
X= -2, y=-4
Step-by-step explanation:
hard to explain it
Ruben adds some water to a glass of juice. The ratio of water to juice in his glass in now 4:6. Which fraction below represents this ratio? A 3/5 C 2/3 B 3/2 D 2/5
Answers
Answer:
C
Step-by-step explanation:
since we're being told to convert the ratio to fraction then it is C. note that 4 ratio is also the same as dividing 4 by 6
complete the square to solve 3x^2+12x=9
A. x=3+√6
B. x=2+√7
C. x=-2+√7
D. x=-2+√13
Answers
(
b
2
)
2
(
b
2
)
2
in order to create a new term. Solve for
x
x
by using this term to complete the square.
Exact Form:
x
=
±
√
7
−
2
x
=
±
7
-
2
Decimal Form:
x
=
0.64575131
…
,
−
4.64575131
…
Step-by-step explanation:
3 {x}^{2} + 12x - 9 = 0
[tex] \frac{ - (12) \binom{ + }{ - } \sqrt{ {12}^{2} - 4(3)( - 9)} }{2(3)} [/tex]
Explain how you would find 90% of 120 will give brainliest if correct
Answers
12
Explanation:
Turn 90% into a decimal , 0.9
Multiple it by 120, 120x0.9=108
Now that we know 108 is 90% of 120
subtract it to see the remaining amount, 120-108=12
Hope this helps!
50 points
Help if you know.
Thanks.
Answers
Answer:
RhombusStep-by-step explanation:
Refer to attached
You can easily calculate that each of the sides have the length:
AB= BC = CD = AD = [tex]\sqrt{1^2+4^2} = \sqrt{17}[/tex]Parallel sides have equal slopes:
m = - 4 for AB and CDm = - 1/4 for AD and BCDiagonals are perpendicular as their slopes are negative reciprocal:
m = 1 for ACm = -1 for BDSo we see the quadrilateral ABCD has two pairs of parallel sides, all sides are equal and the diagonals are perpendicular.
This is the definition of the rhombus.
Kim was sitting in row 5, seat 8 at a soccer game when she discovered her ticket was for row 2, seat 3. Write a rule to describe the translation needed to put her in the proper seat.
Answers
Answer:
Step-by-step explanation:
We can assume we are seeing these seats as points on a graph with her current position being (8, 5) and her destination being (3, 2). Using these values Kim would need to follow the following rules...
Move 3 positions down to point/seat (8, 2)
Move 5 positions to the left to point/seat (3,2)
Following these instructions, she would correctly transition to the correct seat.
hi what’s the answer to this question
Answers
Answer:
yes, x and y are in a proportional relationship
Step-by-step explanation:
The relationship is proportional if the graph is a straight line through the origin. This graph is, so the relationship is proportional.
make p the subject of the formula A=p+prt÷100
Answers
Answer:
p = a - prt x 100
Step-by-step explanation:
a = p + prt ÷ 100
a - prt = p ÷ 100
a - prt x 100 = p
Hope this helps. :)
What is the area of rectangle CDEF?ILL GIVE BRAINLIEST
Answers
Answer:
180 is the answer
Step-by-step explanation:
To find out areas of rectangles, you have to count the left side of the rectangle which is (12) and then count the bottom of the rectangle which is (15)
Then multiply 12 times 15 to find out the area
15 x 12= 180
what do you mean CDEF
and can I get brainliest?