The exact value of sin(11π/12) is (√6 - √2)/4.
Explanation:To find the exact value of sin(11π/12), we can use trigonometric identities to determine the value of an equivalent angle in the first quadrant. Since π/12 is the reference angle of 11π/12, which is in the second quadrant, we can find the sine of the equivalent angle in the first quadrant. The reference angle in the first quadrant is π/12. Therefore, the exact value of sin(11π/12) is the same as the exact value of the sine of π/12. Using a trigonometric identity, we find that sin(π/12) = (√6 - √2)/4.
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The city sales and use tax collected on taxable items in falles, Texas is 8.25%. The tax you must Pay depends on the price of the item you are purchasing. Determine the sales tax you must Pay on the following items.
sales tax alone = 0.99, 2.06, 16.5, 1237.5 for the items
which expression is equivalent to (2^1/2 2^3/4)^2
Answer:
[tex]\sqrt{2^5}[/tex]
Step-by-step explanation:
[tex]2^{1/2}[/tex] × [tex]2^{3/4}[/tex] = [tex]2^{5/4}[/tex]
([tex]2^{5/4}[/tex])² = [tex]2^{5/2}[/tex] = [tex]\sqrt{2^5}[/tex]
Answer:
[tex]\large\boxed{\sqrt{2^5}}[/tex]
Step-by-step explanation:
[tex]\bigg(2^\frac{1}{2}\cdot2^\frac{3}{4}\bigg)^2\qquad\text{use}\ a^n\cdot a^m\\\\=\bigg(2^{\frac{1}{2}+\frac{3}{4}}\bigg)^2\qquad\left/\dfrac{1}{2}+\dfrac{3}{4}=\dfrac{1\cdot2}{2\cdot2}+\dfrac{3}{4}=\dfrac{2}{4}+\dfrac{3}{4}=\dfrac{5}{4}\right/\\\\=\bigg(2^\frac{5}{4}\bigg)^2\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=2^{\frac{5}{4}\cdot2}\\\\=2^{\frac{5}{2}}\qquad\text{use}\ a^\frac{m}{n}=\sqrt[n]{a^m}\\\\=\sqrt{2^5}[/tex]
What is the greatest common factor of 28 and 60
Answer:
4 is your answer.
Step-by-step explanation:
You would break down both numbers into their factors.
28 is divisible by 1,2,4,7,14,and 28
60 is divisible by 1,2,3,4,5,6,10,12,15,20,30, and 60
find the common pairs: (1,1), (2,2), (4,4) Both numbers have these as factors, so find the largest one.
The greatest common factor (GCF) of 28 and 60 is 4.
To find the Greatest Common Factor GCF of two numbers, we need to determine the largest number that divides both numbers without leaving a remainder. One way to find the GCF of 28 and 60 is to list the factors of each number and identify the largest factor that they have in common.
The factors of 28 are 1, 2, 4, 7, 14, and 28.
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
The largest factor that 28 and 60 have in common is 4.
Therefore, the GCF of 28 and 60 is 4.
Another way to find the GCF of two numbers is to use prime factorization. To do this, we need to express each number as a product of its prime factors.
The prime factorization of 28 is 2² x 7, and the prime factorization of 60 is 2² x 3 x 5. To find the GCF, we take the product of the common prime factors with the smallest exponents, which in this case is 2². Therefore, the GCF of 28 and 60 is 2², which is equal to 4.
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Solve for x. Round your answer to the nearest hundredth.
15.56x - 200 < 758.92
Answer: x<61.63
Step-by-step explanation: Add 200 to both sides, giving you 15.56x<958.92 .
Than divide by 15.56 giving you x< x<61.627249
Round to the nearest hundredth giving you x<61.63
Answer: 61.63
Step-by-step explanation:
The given inequality : [tex]15.56x - 200 < 758.92[/tex]
Adding 200 on both the sides , we get
[tex]15.56x < 758.92+ 200\\\\\Rightarrow\ 15.56x <958.92 [/tex]
Dividing 15.56 on both the sides , we get
[tex]\dfrac{15.56x}{15.56}<\dfrac{958.92}{15.56}\\\\\Rightarrow\ x<61.6272493573\approx61.63[/tex]
Hence, the value of x (to the nearest hundredth) = 61.63
At a certain store, apples are packed in equal quantities. Mary bought 3 packs of apples and she checked that she got a total of 45 apples. If Sam bought 7 packs of apples from the same store, how many apples did he get?
Answer:
315 apples
Step-by-step explanation:
45 divided by 3 = 15 then time's that by 7
An energy drink company claims that its product increases students' memory levels. To support its claims, the company issues advertisements claiming that 8 out of 10 people (chosen randomly from across the country) who tried their product reported improved memory. The missing component in this study is a .
The missing component is a Control Group
Answer:
Control group
Step-by-step explanation:
A control group is necessary in all experiments that require a comparison. A control group and an experimental group are both included in an experiment. These two need to be identical in every way with the exception of the fact that the experimental group will be subjected to a treatment that is believed to have a particular outcome. In this case, it is difficult to know whether the drink really has the desired effects or not, as we are not aware of the results of a control group.
Which recursive formula can be used to generate the sequence below, where f(1) = 3 and n ≥ 1?
3, –6, 12, –24, 48, …
f (n + 1) = –3 f(n )
f (n + 1) = 3 f(n )
f (n + 1) = –2 f(n )
f (n + 1) = 2 f(n)
Answer:
[tex]f(n)=-2\cdot f(n-1)[/tex], where f(1)=3
Step-by-step explanation:
The given sequence is; 3, –6, 12, –24, 48, …
The first term of this sequence is
[tex]f(1)=3[/tex]
There is a common ratio of [tex]r=\frac{-6}{3}=-2[/tex]
We can actually use any other two consecutive terms in the sequence to obtain the common ratio.
The recursive formula is given by:
[tex]f(n)=r\cdot f(n-1)[/tex]
We plug in the common ratio to get:
[tex]f(n)=-2\cdot f(n-1)[/tex], where f(1)=3
Answer:
The answer is C
Step-by-step explanation:
a line segment AD, contains B&C such that C is between A and D, and B is between A and C. if AB=6, BD=23, and AB=CD, find the length of segment AD.
Answer:
AD = 29
Step-by-step explanation:
Note that
AD = AB + BD = 6 + 23 = 29
Describe the relationship between the variables .
Answer:
B) As the age increases, the height increases.
Step-by-step explanation:
There is a clear trend that is shown with a positive slope. That means that the the variables, here, the age and the height, are directly proportionate to each other. That means our answer is B or D.
Another note is that in a situation like this, the y-variable is dependent on the x-variable. So, here, that means that the height depends on the age. So, the answer is B, since in a sentence structure like so indicates that the second variable is dependent on the first.
Answer: the answer is b
Step-by-step explanation:
can you rate me good
which graph represents the solutions for x^2+x-12>0
To find the answer, we can use the method of finding x- intercepts by solving the equation.
To solve the equation:
x^2 + x -12> 0
by using cross method,
we can find that 3 x -4 = -12
(x-3)(x+4) = 0
Therefore, x = 3 or x=-4
Hope it helps!
graph C represents the solutions for x^2+x-12>0
What are inequalities?Inequality is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
How to find which graph represents the solution ?The given inequality is :
x^2+x-12>0
Now factorizing the expression we get,
(x-3)(x+4)>0
⇒ x>3 and x<-4
Clearly graph C represents the solutions.
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which of the following is a point-slope (-2,4) and a slope of 3
Answer:
y - 4 = 3(x + 2)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
here m = 3 and (a, b) = (- 2, 4), hence
y - 4 = 3(x - (- 2)), that is
y - 4 = 3(x + 2) ← in point- slope form
An object in geometry with no width, length or height is a(n):
O A. ray
O B. angle
O
c. line
O
D. point
SUBMIT
Answer: D
Step-by-step explanation:
I would say the answer is a point, points are theoretically a
zero-dimensional idea
Answer:
D. point
Step-by-step explanation:
A point is an undefined term in Geometry. It represents a position in space. It has no length, width, or height.
x^2 + mx + n = 0, m and n are integers. The only possible value for x is -3. What is the value of m?
plz the solution is necessary
Thanks
Answer:
The value of m is 3
Step-by-step explanation:
we have
[tex]x^{2}+mx+n=0[/tex]
step 1
Find the value of n
For x=0
[tex]0^{2}+m(0)+n=0[/tex]
[tex]n=0[/tex]
step 2
Find the value of m
For x=-3
substitute
[tex]x^{2}+mx=0[/tex]
[tex](-3)^{2}+m(-3)=0[/tex]
[tex]9-3m=0[/tex]
[tex]3m=9[/tex]
[tex]m=3[/tex]
simplify root45 - root20 +4root5
Answer:
( -3√5)
Step-by-step explanation:
√45 - √20 - 4√5 = √5*3*3 - √2*2*5 - 4√5
= 3√5 - 2√5 - 4√5
= √5 (3 - 2 - 4)
= ( -3√5)
The intensity, or loudness, of a sound can be measured in decibels (dB), according to the equation I(dB)=10log[1/10], where I is the intensity of a given sound and I0 is the threshold of a hearing intensity. What is the intensity, in decibles, [I(dB)], when I=10^32(I0)? Round to the nearest whole number.
Answer:
C. 320
Step-by-step explanation:
According to it's formula, the intensity when [tex]l = 10^{32}[/tex] is of 440 db.
What is the formula for the intensity of a sound?The intensity of a sound l is given by:
[tex]L(l) = 10\log{\left(\frac{l}{l_0}\right)}[/tex]
In which [tex]l_0 = 10^{-12}[/tex] is the threshold of a hearing intensity.
In this problem, we have that the sound is of [tex]l = 10^{32}[/tex], hence:
[tex]L(l) = 10\log{\left(\frac{10^{32}}{10^{-12}}\right)} = 10\log{10^{44}} = 10 \times 44 = 440[/tex]
Hence, the intensity of the sound is of 440 db.
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in parallelogram abcd angle b is a right angle determine whether the parallelogram is a rectangle if so by what property
Answer:
If a parallelogram has at least one 90 degree angle then its opposite angle is equal and also = 90 degrees.
The 2 remaining opposite angles add up to 180 degrees and since they must be equal, they must be 90 degrees each.
So, we have a quadrilateral with four 90 degree angles and is therefore a rectangle OR it could possibly be a square.
Step-by-step explanation:
Answer: one right angle property
Line l passes through the points (1, 3) and (2, 5), and
line m passes through point (1, 4) and has a slope of 1.
If lines l and m intersect at point (a, b), then what is the
value of a – b ?
Answer:
-3
Step-by-step explanation:
I'm going to find both equations first.
Slope for line l can be found by doing
(1 , 3)
- (2 , 5)
-------------
-1 -2 so slope is -2/-1 or just 2
y=mx+b is a linear equation with slope m and y-intercept b
y=2x+b now we need b
3=2(1)+b plug in a point on the line
3=2+b
so b=1
The equation for line l is y=2x+1
The other equation line m has the slope given which is 1 so this equation will be of the form y=1x+b
to find this b (this y-intercept) use the point that you know is on the line
4=1(1)+b
so b=3
so line m is y=1x+3 or y=x+3
So we want to find when y=2x+1 and y=x+3 intersect
Replace first y with the 2nd y which is x+3
x+3=2x+1
subtract x on both sides
3= x+1
subract 1 on both sides
2=x
x=2
y=2x+1
y=2(2)+1
y=4+1
y=5
So the intersection is (2,5)
So a=2 and b=5
a-b =2-5=-3
Lines l and m intersect at point (2, 5)
The equation of a straight line is given by:
y = mx + b;
where y,x are variables, m is the slope of the line and b is the y intercept.
Line l passes through the points (1, 3) and (2, 5), hence its equation is:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1 )\\\\y-3=\frac{5-3}{2-1}(x-1)\\\\y-3=2x-2\\\\2x-y=-1[/tex]
2x - y = -1 (1)
Line m passes through point (1, 4) and has a slope of 1, hence:
[tex]y-y_1=m(x-x_1)\\\\y-4=1(x-1)\\\\x-y=-3[/tex]
x - y = -3 (2)
To determine point (a, b) we solve equation 1 and 2 simultaneously to get:
x = 2, y = 5
Hence lines l and m intersect at point (2, 5)
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Solve 9x + 4 = 11 for x using the change of base formula log base b of y equals log y over log b.
Answer:
[tex]x = \frac{7}{9} [/tex]
Step-by-step explanation:
[tex]9x + 4 = 11 \\ \\ 1. \: 9x = 11 - 4 \\ 2. \: 9x = 7 \\ x = \frac{7}{9} [/tex]
Answer with explanation:
The given equation in one variable is:
→ 9 x +4 =11
Subtracting 4 from both sides
→9 x +4 -4=11 -4
→ 9 x=7
Taking log on both sides
→log ( 9 x)= log 7-----log having base 10 is considered.
→ log 9 + log x= log 7
→ 0.95424 + log x= 0.8450
→ log x=0.8450 - 0.9542
→ log x= -0.1092
[tex]\rightarrow\frac{\log x}{\log 10}=-0.1092\\\\\rightarrow \log x=-0.1092 \times \log 10\\\\\rightarrow \log x=\log 10^{-0.1092}\\\\\rightarrow x=10^{-0.1092}\\\\\rightarrow x=0.77767\\\\x=0.778[/tex]
The double number line shows that Toni can type 180 words in 2 minutes.
Based on the ratio shown in the double number line, how many words can Toni type in 3
minutes
Answer:
270 words per minute
Step-by-step explanation:
It is given 180 words in 2 minutes, this means Toni can type 180/2 = 90 words per minute (90wpm).
Thus, in the same ratio/rate, Toni would be able to type:
90 * 3 = 270 words per minute.
Correct answer 270 wpm
Answer:
270
Step-by-step explanation:
hello
Choose the triangle that seems to be congruent to the given one
The triangle that seems to be congruent to the given one is triangle EFA.
Here's why:
Both triangles have three straight sides.
Both triangles have the same angles at corresponding vertices. For example, the angle at vertex E in triangle EFA is congruent to the angle at vertex A in the given triangle, and the angle at vertex F in triangle EFA is congruent to the angle at vertex C in the given triangle.
The corresponding sides of the triangles have the same lengths. For example, side EF in triangle EFA is congruent to side AC in the given triangle, and side FA in triangle EFA is congruent to side CB in the given triangle.
Therefore, based on the properties of congruence, triangle EFA is congruent to the given triangle.
Combine the following expressions.
3\sqrt{27x^3}-2\sqrt{12x^3}
A) 19x
B) 5x
C) 13x
The correct answer is: B) 5x √3x
I just did the test, trust me it is B.
The solution for the following expression is,[tex]5x\sqrt{3x}[/tex].None of the options are correct.
What exactly is simplification?Simplifying is making something easier to do or comprehend, as well as making something less difficult.
The following expression is given ;
[tex]3\sqrt{27x^3}-2\sqrt{12x^3}[/tex]
Simplify the given expression;
[tex]3\sqrt{27x^3}-2\sqrt{12x^3} \\\\ 3 \times 3x \sqrt {3x} -2 \times 2x \sqrt{3x}\\\\ 9x \sqrt {3x}-4x\sqrt{3x}\\\\\ 5x\sqrt{3x}[/tex]
The solution for the following expression is,[tex]5x\sqrt{3x}[/tex].
Hence one of the options is correct.
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Triangle WXY is isosceles. ∠YWX and ∠YXW are the base angles. YZ bisects ∠WYX. m∠XYZ = (15x)°. m∠YXZ = (2x + 5)°. What is the measure of ∠WYX?
Step-by-step explanation:
angle YWX = angle YXW ...eqn 1
angle XYZ = angle WYX (0.5) = 15x...eqn 2
angle YXZ = angle YXW = 2x + 5...eqn 3
=> from eqn 1 and 3 we get...
angle YWX = 2x + 5 ...eqn 4
=> from eqn 2 we get
angle WYX = 2 × angle XYZ = 30x...eqn 5
a triangle has a total of 180deg,
=>angle WYX + angle YWX + angle YXW = 180deg
=> 30x + 2x +5 + 2x +5 = 180deg
=> 34x +10 =180deg
=> x = 5deg
subst x = 5deg in eqn 5, we get
angle WYX = 30 × 5 = 150deg
Answer:
D = 150 degrees
Step-by-step explanation:
Just got it correct on Edg, 2021!
Figure ABCD is a parallelogram.
What are the lengths of line segments AB and BC?
A
3y - 2
B
AB = 4; BC = 16
OAB = 4; BC = 8
AB = 10; BC = 20
OAB = 10; BC = 28
2x - 4
x + 12
y + 6
First you need know that AB = DC and AD = BC.
So,
3y - 2 = y + 6
2y = 8
y = 4
AB = 3(4) - 2 = 12 - 2 = 10
2x - 4 = x + 12
x = 12 + 4
x = 16
BC = 16 + 12 = 28
So your answer is:
AB = 10; BC = 28
The lengths of line segments AB = 10 and BC = 28.
How to estimate the lengths of line segments?The opposite sides of a parallelogram are congruent,
AB = DC,
3y - 2 = y + 6
subtract y from both sides, then we get
2y - 2 = 6
adding 2 to both sides
2y = 8
Dividing both sides by 2, then we get
y = 4
Hence AB = 3y - 2 = (3 × 4) - 2 = 12 - 2 = 10
and AD = BC, that exists
2x - 4 = x + 12
subtract x from both sides
x - 4 = 12
adding 4 to both sides
x = 16
BC = x + 12 = 16 + 12 = 28
The lengths of line segments AB = 10 and BC = 28.
Therefore, the correct answer is AB = 10 and BC = 28.
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If f(x) = 4x - 3 and g(x) = x + 4, find (f - g) (x)
[tex](f-g)(x)=4x-3-(x+4)=4x-3-x-4=3x-7[/tex]
What is the true solution to 2 In 4x= 2 In 8?
Answer:
1
Step-by-step explanation:
[tex] ln4x = 2 ln8 \div 2 \\ ln4x = ln4 \\ x = 1[/tex]
Hope it helps you...☺
Answer:
x = 2
Step-by-step explanation:
Using the rules of logarithms
• log [tex]x^{n}[/tex] ⇔ n logx
• log x = log y ⇒ x = y
Given
2 ln 4x = 2 ln 8
ln (4x)² = ln 8²
ln 16x² = ln 64, hence
16x² = 64 ( divide both sides by 16 )
x² = 4 ( take the square root of both sides )
x = [tex]\sqrt{4}[/tex] = 2
1) Irene places a mirror on the ground 24ft from base of an oak tree.she walks backward until she can see the top of the tree in the middle of the mirror. At that point, Irene’s eyes are 5.5 above the ground, and her feet are 4 ft from the mirror.How tall is the oak tree?
Answer:
Oak tree is 33 ft tall.
Step-by-step explanation:
We know that Irene places a mirror on the ground and walks backwards such that the mirror is in between her and the oak tree (as shown in the attached picture).
Given the distance of Irene's eyes from ground, distance between oak tree and mirror and distance between mirror and Irene, we are to find the height of the tree.
For this, we will use the ratio method:
[tex]\frac{T}{24} =\frac{5.5}{4}[/tex]
T = 33 ft
Y= -(x-1)(x+3) has how many roots
Answer:
two
Step-by-step explanation:
Two
x - 1 = 0
x = 1
x + 3 = 0
x = - 3
You can see them for your self. The roots are the points where the graph cuts the x axis.
(1,0) and
(-3,0)
One solution of x^2-25=0 is 5. What is the
other solution?
Enter the correct answer.
Answer:
The other solution: x = -5Step-by-step explanation:
[tex]x^2-25=x^2-5^2\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(x-5)(x+5)\\\\x^2-25=0\to(x-5)(x+5)=0\iff x-5=0\ \vee\ x+5=0\\\\x-5=0\qquad\text{add 5 to both sides}\\x=5\\\\x+5=0\qquad\text{subtract 5 from both sides}\\x=-5[/tex]
What is 3x^2-3x+2 divided by x+2
For this case, we must build a quotient that, when multiplied by the divisor, eliminates the terms of the dividend until it reaches the remainder. In this case we have to:
Remainder: 20
Quotient: 3x-9
It must be fulfilled that:
Dividend = Quotient * Divider + Remainder
Answer:
See attached image
The perimeter of a rectangle is 18 feet, and the area of the rectangle is 20 square feet. What is the width of the rectangle?
4 ft or 5 ft
i think thats right
Answer:
The width can be 5 ft or the width can be 4 ft
Step-by-step explanation:
Perimeter = 2 (l+w) for a rectangle
Area = l*w for a rectangle
Using perimeter
18 = 2(l+w)
Divide by 2
18/2 = 2/2 (l+w)
9 = l+w
Solving for l
9-w = l
Using area
20 = l*w
Substituing for l
20 = (9-w) * w
20 = 9w - w^2
Subtract 20 from each side
20-20 =-w^2 +9w -20
0 = -w^2 +9w -20
Multiply by -1
0 = w^2 -9w+20
Factor
0 = (w-5) (w-4)
Using the zero product property
w-5 = 0 w-4 = 0
w= 5 w=4
The width can be 5 ft or the width can be 4 ft