solving sin ( 4x ) = √3 / 2 , the value of x is 15°
What is trigonometry?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
For angle of 30° and 60°
sin 30° = 1/2
cos 60° = √3/2
tan60° = √3
for angle 60 °
sin60° = √3/2
cos 60° = 1/2
tan60° = 1/√3
since sin(4x) = √3/2
and sin 60° = √3/2
sin60° = sin(4x)
this means 60° = 4x
divide both sides 4
x = 60/4
x = 15°
therefore the value of x is 15°
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What is the AAA equation?
If any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other.
Consider two triangles ABC and XYZ, if ∠ A = ∠X and ∠C = ∠Z then
ΔABC ~ΔXYZ.
If, two triangles ΔABC and ΔXYZ are similar only if,
i)∠A =∠X, ∠B =∠Y and ∠C=∠Z
ii)AB/XY=BC/YZ=AC/XZ
"AAA" means "Angle, Angle, Angle" when we know all three angles of a triangle, but no sides.
If two triangles have their corresponding angles equal if and only if their corresponding sides are proportional.
An AAA triangle is a triangle where only the three angles are defined:
α + β + γ = 180°
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(PLEASE HELP AS SOON AS POSSIBLE)
Answer:
you answer would be F: Point W
What is the volume of the composite shape to the nearest whole number? (Pls answer, due today!)
A. 1,178 in^3
B. 1,035 in^3
C. 960 in^3
D. 2,138 in^3
Answer:
2,138 in^3
Step-by-step explanation:
I know this is old but other people can find this helpful
•18 POINTS• don’t explain
a.) neither
b.)SAS
c.)HL
SAS congruence theorem should be used.
Option (B) is correct.
What is the SAS congruence theorem?
In Euclidean geometry, the SAS congruence theorem states that if two triangles have two sides of one triangle congruent (equal in length) to two sides of the other triangle, and the included angle is congruent, then the triangles are congruent. This theorem is often abbreviated as SAS, and is used in combination with other congruence theorems, such as ASA and SSS, to prove that triangles are congruent.
In the given picture, we can say both triangles has the same side of length 7 and along with it, one more side is of equal length.
and both triangles are having the right-angle,
so we can say that we can prove these triangles congruent by using SAS congruence theorem.
Hence, SAS congruence theorem should be used.
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Luke and Seth each need to buy the same amount of fencing for their gardens. While Seth's garden is square in shape, Luke's garden is rectangular with the length 3 feet longer than Seth's. Luke's width is half of the length of his own garden.
How much fencing did each buy? Need this asap please and thank you.
option
40. 5 feet
81 feet
72 feet
36 feet
Fencing that Luke and Seth did each buy is 72 feet
Using the information given, you can set up and solve the system of equations. Let x be the length of Seth's garden.
Seth's garden is square, so it has four times the perimeter.
The perimeter of Luke's garden is a rectangle of length x + 3 feet and width x/2 feet, so 2(x + 3) + 2(x/2).
We also know that Luke and Seth should buy the same amount of fences. So:
4x = 2(x + 3) + 2(x/2)
Solving this equation for x gives x = 6 feet.
So Seth's yardage is 6 feet and Luke's yardage is 9 feet.
So the fence required for Seth's garden is 46 = 24 feet
and the fence required for Luke's garden is 2(9) + 2(9/2) = 29 + 2*4.5 = 36 + 9 = 45 It's feet.
So the total fencing required is 24 + 45 = 72 feet.
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Question:
1. Find the minimum or maximum value of this function by completing the square.
f(x) = x2 + 8x + 6
6. Which inequality is shown in the graph? Why? Show or explain.
A. Y S x + 2
B. ys x+1
C. y > 2x + 1
D. y < 2x + 1
What is the relation between direction cosines of a vector?
The direction cosines of a vector are the cosines of the angles between the vector and the three mutually perpendicular axes of a coordinate system.
The direction cosines of a vector [tex]$\mathbf{a}$[/tex] are denoted by l, m and n. Mathematically, the relation between these direction cosines is given by:
[tex]$$\mathbf{a}=l\mathbf{\hat{i}}+m\mathbf{\hat{j}}+n\mathbf{\hat{k}}$$[/tex]
where i,j and k are unit vectors along the three axes of the coordinate system.
To calculate the direction cosines of a given vector [tex]$\mathbf{a}$[/tex] with components [tex]$a_x$, $a_y$ and $a_z$[/tex], we can use the following formula:
[tex]$$l = \frac{a_x}{\sqrt{a_x^2+a_y^2+a_z^2}}$$[/tex]
[tex]$$m = \frac{a_y}{\sqrt{a_x^2+a_y^2+a_z^2}}$$ \\ $$n = \frac{a_z}{\sqrt{a_x^2+a_y^2+a_z^2}}$$[/tex]
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Angel missies 4% of the free throws he attempts in a season. How many total free throws did he attempt if he missed 55
Answer:
Step-by-step explanation:
55 times 25, making Angel attempt 1375 free throws
Answer:
Step-by-step explanation:
Its 700% because 7x3 = 11
Octagon ABCDEFGH with side lengthsABCDEFGII 10 and BC=DE FG = HA= 11 isformed by removing 6-8-10 triangles from the corners of a 23 x 27 rectanglewith side AH on a short side of the rectangle, as shown. Let J be the midpointof AH, and partition the octagon into 7 triangles by drawing segments JB,JC, JD, JE, JF, and JG. Find the area of the convex polygon whosevertices are the centroids of these 7 triangles.
Area of the convex polygon whose vertices are the centroids of these 7 triangles is 184.
What is a convex polygon?
A polygon that forms the edge of a convex set is said to be convex polygon. This indicates that the union of the interior and the boundary of the polygon has the line segment connecting two points of the polygon.
Given,
AB = CD = EF = GH = 10
BC = DE = FG = HA = 11
Triangles of side length 6,8,10 is cut from corners 23×27 rectangle.
Using the above information, we marked the position of A,B,C,D,E,F,G,H and J, taking the upper left corner of rectangle as origin.
The centroid of a triangle can be found using the formula,
Centroid = [tex](\frac{x_{1} + x_{2}+x_{3}}{3} , \frac{y_{1} +y_{2}+y_{3}}{3})[/tex]
For ΔJAB,
[tex]C_{1}[/tex] = (8/3 , -35/6)
For ΔJBC,
[tex]C_{2}[/tex] = ( 9 , -23/6)
For ΔJCD,
[tex]C_{3}[/tex] = ( 46/3, -35/6)
For ΔJDE,
[tex]C_{4}[/tex] = ( 18 , -23/2)
Area of convex polygon = [tex]\frac{1}{2} [x_{1} y_{2} + x_{2}y_{3}+.........+x_{n}y_{1}] - [y_{1}x_{2}+y_{2}x_{3}+......+y_{n}x_{1}][/tex]
From figure we find the area of C₁C₂C₃C₄C₈, where C₈ = (8/3 , -23/2)
Area =
[tex]\frac{1}{2} [8/3 (-23/6 )+ 9(-35/6)+46/3(-23/2)+18(-23/2)+8/3(-35/6)] - [(-35/9)9+(-23/6)46/3+(-35/6)18+(-23/2)8/3+(-23/2)8/3][/tex]
= 184 / 2
Therefore total area of convex polygon = 2 × 184/2 = 184 sq. units
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The cost of a class field trip is $15 per person, plus $50 for a bus ride. Which function can be used to find the total cost C(x) of a field trip for x students
The water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day. They would like the estimate to have a maximum error of 0.1 gallons. A previous study found that for an average family the variance is 5.76 gallons and the mean is 19.5 gallons per day. If they are using a 90% level of confidence, how large of a sample is required to estimate the mean usage of water? Round your answer up to the next integer.
Answer:
The right solution is "1559".
Step-by-step explanation:
The given values are:
Variance,
[tex]\sigma=\sqrt{5.76}[/tex]
[tex]=2.40[/tex]
Maximum error,
[tex]M.E=0.1[/tex]
At 90% confidence level,
[tex]\alpha=0.1[/tex]
According to the z-table, the critical value will be:
[tex]Zc=1.645[/tex]
Now,
The sample size will be:
⇒ [tex]n=(Zc\times \frac{\sigma}{E} )^2[/tex]
On substituting the values, we get
⇒ [tex]=(1.645\times \frac{2.4}{0.1} )^2[/tex]
⇒ [tex]=(1.645\times 24)^2[/tex]
⇒ [tex]=(39.48)^2[/tex]
⇒ [tex]=1558.67[/tex]
or,
⇒ [tex]=1559[/tex]
Please answer these questions with steps explaining how to solve them. Also please go step by step explaining what you did.
x/3 - 3 = x/9 + 3
Answer:
what does x mean, like what number does it represent in this situation
Answer:
x = 27
Step-by-step explanation:
I made '3' into 9/3
x/3 - 9/3 = x/9 + 9/3
convert terms to fractions with a denominator of 9
x/3 = 3x/9
9/3 = 27/9
3x/9 - 27/9 = x/9 + 27/9
(3x-27)/9 = (x+27)/9
since each denominator equals 9 we can set the numerators equal to each other:
3x - 27 = x + 27
3x = x + 54
2x = 54
x = 27
In a triple batch of spice mix, there are 6 teaspoons of garlic powder and 15 teaspoons of salt. Answer the following questions about the mix. If you get stuck, create a double number line.
In a double number line diagram, equal ratios are represented by two parallel number lines. On both number lines, the tick marks are in the same places. Though the other numbers are frequently varied, the tick marks labeled with 0 always line up.
How to create a double number line?According to question:-
How much more garlic powder than salt is in the triple batch?
Answer: 6 teaspoons of garlic powder - 15 teaspoons of salt = -9 teaspoons. So there is 9 teaspoons less garlic powder than salt in the triple batch.
How much spice mix is in the triple batch?
Answer: 6 teaspoons of garlic powder + 15 teaspoons of salt = 21 teaspoons of spice mix.
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A. X=9
B. X=14
C. X=16
D. X=12
E. X=10
Answer:
Angle K is 1/2 the measure of arc JL, so JL = 228. Add arc KL to arc JL to get 268 and subtract from 360. 360 - 268 = 92. 8x - 36 = 92. X = 16.
Step-by-step explanation:
The table shows the shoe sizes of women of different ages. A 2-column table with 4 rows. The first column is labeled age with entries 18, 30, 52, 64. The second column is labeled shoe size with entries 7, 10, 6, 9. Which best describes the strength of the model? a weak positive correlation a strong positive correlation a weak negative correlation a strong negative correlation
Answer:
A.) weak positive correlation
The person above just wanted to steal points.
Step-by-step explanation:
Answer:
The correct answer is a weak positive correlation
or
A
Step-by-step explanation:
What is the nature of the roots of the quadratic equation 5x^2 4x 1?
The nature of roots of quadratic equation 5x² = 4x - 1 is imaginary roots.
The standard form of a quadratic equation is:
ax² + bx + c = 0
The discriminant is defined as:
D = b² - 4ac
Using the value of discriminant, we can determine the nature of roots of a quadratic equation.
If:
D > 0, the quadratic equation has two distinct real roots or the roots are real and distinct.
D = 0, the quadratic equation has 1 real equal roots or the roots are unique
D < 0, the quadratic equation has complex conjugate roots or the roots are imaginary.
In this case, the quadratic equation is:
5x² = 4x - 1
transform it into the standard form:
5x² - 4x + 1 = 0
Calculate the discriminant:
D = (-4)² - 4 (5)(1)
= 16 - 20 = -4
Since D < 0, the roots are imaginary.
Your question is incomplete, but most probably your question was:
What is the nature of roots of quadratic equation 5x² = 4x - 1?
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Which graph represents the following system of inequalities? y>(1)/(2)x-1 y<=-x+1 y>-2x-1
Answer:
? We don't see any graphs to choose from
Step-by-step explanation:
[tex]y>\frac{1}{2}x-1[/tex] Graph a dotted line (to show it's not included) with y-intercept 1 and slope 1/2. Test the origin (0, 0) in the inequality:
[tex]0 > \frac{1}{2}0 - 1 = -1[/tex] This is true, so shade the side of the line that the origin is on (above the line).
Next inequality...
[tex]y \le x+1[/tex] Graph a solid line with y=intercept 1 and slope 1. Test the origin.
[tex]0 \le 0+1=1[/tex] True! Shade the side of the line the origin is on (below the line). See image2, attached.
[tex]y>-2x-1[/tex] Graph a dotted line with y-intercept -1 and slope -2. Test the origin (0, 0).
[tex]0>-2(0)-1=-1[/tex] True, so shade the side the origin is on (above the line).
The solutions are located where all the shadings intersect. See image3. The solutions are above the red line, above the green line and below the blue line.
Select the theorem that can be used to prove that RST = VUT
I need help on this question: Triangle ABC is similar to triangle XYZ. What is the length of AC in inches?
Answer: 3√13
Step-by-step explanation:
To find the length of AC we need to use the Pythagorean theorem.
Which is AC^2 = BC^2 + AB^2
AC^2 = 6^2 + 9^2
AC^2 = 36 + 81
AC^2 = 117
AC = √117
You accumulated a balance of $2,300 on your credit card that carries an interest rate of 17%. You can't afford to pay the $2,300 all at once, but you can pay the minimum payment, which is 2% per month or $25, whichever is greater. What is the balance on your card after 5 years?
Answer:
$1,591.67
Step-by-step explanation:
The computation of the balance after 5 years is shown below:
Given that
Accumulated Balance on Credit Card = P = $2,300
r = Monthly interest amount = 17% ÷ 12 = 1.41666667%
M = Minimum payment = 2%
Now
Balance on Credit Card after t year = P × (1+r) ×(1-M)
= $2,300 × (1+1.41666667%)^t × (1 - 2%)^t
= $2,300 × (0.993883337)^t
SO,
Balance on Credit Card after 5 years is
= $2,300 × (0.993883337)^60
= $2,300 × 0.692029437
= $1,591.66771
= $1,591.67
HELP ASAP
A snail is moving away from a rock.
The equation d=3t represents the relationship between the distance, d , in inches that the snail is from the rock and time, t, in minutes. What does the number 3 represent in this equation?
Distance and time here is directly proportional to each other and the term '3' shows that the distance is increasing, is 3 times of the time, increased.
Given,
A snail is moving away from a rock.
The equation d=3t represents the relationship between the distance, d , in inches that the snail is from the rock and time, t, in minutes.
The number '3' is constant term, which basically represents the the distance covered by the snail, in terms of time or, the rate of increment of distance is terms of time.
Distance and time here is directly proportional to each other and the term '3' shows that the distance is increasing, is 1/3 of the time, increased.
For example if the snail is moving for 1 unit time, the t will be considered as 1. so, the d will be 3*1 = 3, i.e. 3 unit distance will be covered by the snail in 1 unit time.
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Mr. Mutler posts his students' artwork on a bulletin board.
The width and length of the bulletin board are whole
numbers. What could be the dimensions of the bulletin board
Mr. Butler uses?
Area - 15 square feet
The dimensions of the bulletin board could be as follows:
length = 5 ft.
width = 3 ft.
What is the are of rectangle?[tex]A = l\times w[/tex]
where, 'l' represents the length of the rectangle
and 'w' represents the width of the rectangle
What are factors?"If multiplying two whole numbers gives us a number, then the numbers we are multiplying are the factors of the product number."
For given example,
An area of the rectangular bulletin board is 15 sq. ft.
⇒ A = 15 sq. ft.
⇒ l × w = 15
Given that, the width and length of the bulletin board are whole
numbers.
Factors of 15 are,
15 = 5 × 3
15 = 15 × 1
From given figure we can say that he could use the dimension 5 ft. × 3 ft. for the bulletin board.
This means, the length of the bulletin board could be 5 ft. and the width could be 3 ft.
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Gianna has $760 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $356.46.
She buys 2 bicycle reflectors for $10.01 each and a pair of bike gloves for $20.72.
She plans to spend some or all of the money she has left to buy new biking outfits for $45.35 each.
Write and solve an inequality which can be used to determine
o
o, the number of outfits Gianna can purchase while staying within her budget.
Answer:
Gianna has $760 to spend and she has already spent $356.46 on a new bicycle, $10.01 on 2 bicycle reflectors, and $20.72 on a pair of bike gloves.
The total amount spent on these items is $356.46 + $10.01 + $20.72 = $387.19.
Gianna has $760 - $387.19 = $<<760-387.19=372.81>>372.81 left to spend on biking outfits.
She wants to buy biking outfits that cost $45.35 each.
We can write an inequality to represent the number of outfits Gianna can purchase while staying within her budget as follows:
45.35o <= 372.81
This inequality can be solved by dividing both sides by 45.35:
o <= 8.24
Therefore, Gianna can purchase 8 biking outfits while staying within her budget.
Step-by-step explanation:
Find the perimeter of the parallelogram using the Pythagorean Theorem
Answer:
The perimeter of the paralellogram is [tex]24 + 2\sqrt{34}[/tex] units.
Step-by-step explanation:
We shall use the Pythagorean Theorem to determine the length of the two oblique line of the figure. From Geometry, we know that the perimeter of the parallelogram is the sum of the lengths of the four sides of the parallelogram.
First, we calculate the length of the oblique line, that is:
[tex]l_{O} = \sqrt{5^{2} + 3^{2}}[/tex]
[tex]l_{O} = \sqrt{34}[/tex]
Second, we determine the length of the vertical line by direct observation, that is:
[tex]l_{V} = 12[/tex]
Lastly, the perimeter is determined by the following formula:
[tex]p = 2\cdot (l_{O}+l_{V})[/tex]
[tex]p = 24+2\sqrt{34}[/tex]
The perimeter of the paralellogram is [tex]24 + 2\sqrt{34}[/tex] units.
Answer: 35.7
(This is the answer squared by the way)
Step-by-step explanation:
what can 7 and 5 both be divided by
A small business makes bottles of
temonade. Today, they have 528 ounces
of lemonade to bottle. Each bottle holds
24 ounces of lemonade. They sell each
bottle for $2.
Write two equations with variables that
can be used to find how many dollars
the business will receive by selling all of
the bottles.
The amount of money that the business will receipt is $44.
given:
Small business makes bottles of lemonade today they have 528 oz of lemonade to the bottle each bottle holds 24 oz of lemonade they sell each bottle for $2 how much money will the business receipt
From the above question:
24oz of Lemonade = 1 bottle
528 oz of Lemonade = x
Cross Multiply
24 × x = 528
x = 528/24
x = 22 bottles
We are told that: they sell each bottle for $2
Hence:
1 bottle = $2
22 bottles = y
Cross Multiply
y = 22 × $2
y = $44
Therefore, the amount of money that the business will receipt = $44
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please help me with these 4 questions will mark branliest whoever gets all of it right
Answer:
1. The answer is 40 degrees
2. Adjacent angles are sometimes congruent.
3. UPR is vertical to TPQ
4. The answer is 132 Degrees
a number is 6.14 what way represent the value of the 4 in 6.14
Answer:
Step-by-step explanation:
the value of the 4 in 6.14 is 0.04.
this is because the 4, or in this case 0.04
is in the hundredths place. So it is
suppose to have 0, where the 6 goes (also
the ones or units) The decimal point, another 0
where the 1 goes, ( the tenths) and finally back
to the 4. (Like I said, it’s the hundredths place)
so there you have it. Your answer will be 0.04
Write and solve an inequality to find the values of x for which the perimeter of the rectangle is less than 112.
x+4
The inequality to discover the values of x for which the rectangle's perimeter is under 112 is x< 26.
what is inequality ?An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal symbol (). Different inequalities are used to contrast values, no matter how small or large. Many simple inequalities can be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.
given
perimeter of a rectangle = length + length + width + width
length + length + width + width = perimeter of a rectangle
(x +4) + (x+4) + x + x < 112
x + 4 + x + 4 + x + x < 112
4x + 8 < 112
4x < 104
x < 26
So ,The inequality to discover the values of x for which the rectangle's perimeter is under 112 is x< 26.
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