6. Find the distance from A to B for the hexagonal nut shown below: А 1.50 in BYo I've asked tutors and they have been unable to answer, after all it's only given one side and I need some help.
Answers
Let
x ------> the length side of the regular polygon
we have a regular hexagon
that means
the interior angle of this polygon is
180(6-2)/6=120 degrees
A regular hexagon can be divided into 6 congruent equilateral triangles
see the attached figure to better understand the problem
in the right triangle of the figure
we have that
sin(60)=0.75/x
solve for x
x=0.75/sin(60)
Remember that
[tex]\sin (60^o)=\frac{\sqrt[]{3}}{2}[/tex]substitute
[tex]\begin{gathered} x=0.75\colon\frac{\sqrt[]{3}}{2} \\ \\ x=\frac{1.50}{\sqrt[]{3}}\cdot\frac{\sqrt[]{3}}{\sqrt[]{3}}=\frac{1.50\sqrt[]{3}}{3}=\frac{\sqrt[]{3}}{2} \end{gathered}[/tex]Part 2
Find the distance AB
Applying the Pythagorean Theorem
AB^2=1.5^2+x^2
substitute the value of x
AB^2=2.25+(3/4)
AB^2=3
[tex]AB=\sqrt[]{3}\text{ in}[/tex]the distance AB is the square root of 3 inches
Related Questions
The speedometer on Leona's car shows the speed in both miles per hour and kilometers per hour. Using 1.6 km as the equivalent for 1 mi, find the mile per hour rate that is equivalent to 40 kilometers per hour.
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To find the mile per hour rate equivalent to 40 km per hour, let's convert 40km to miles using the given equivalence in the question.
[tex]\begin{gathered} 1.6\operatorname{km}=1mi \\ 40\operatorname{km}\times\frac{1mi}{1.6\operatorname{km}}=\frac{40\operatorname{km}mi}{1.6\operatorname{km}}=25mi \end{gathered}[/tex]Therefore, 40 km = 25 miles.
The mile per hour rate equivalent to 40km per hour is 25 miles per hour.
O is the center of the regular hexagon below. Find its perimeter. Round to the nearest tenth if necessary.
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To solve this problem, we have to find the side length and multiply it by the number of sides of the figure.
To find the length side we will use the following formula:
[tex]ap=\sqrt[]{I^2-(\frac{I^{}}{2})^2}\text{.}[/tex]Where ap is the length of the apothem, and I is the side length.
Substituting the given values, we get:
[tex]10=\sqrt[]{I^2-(\frac{I}{2})^2}.[/tex]Solving the equation for I, we get:
[tex]\begin{gathered} \\ I=\frac{2\times10}{\sqrt[]{3}}. \end{gathered}[/tex]Therefore, the perimeter of the hexagon is:
[tex]6I=6\times\frac{2\times10}{\sqrt[]{3}}\approx69.3\text{ units.}[/tex]Answer:
[tex]69.3\text{ units.}[/tex]Write 5.8% as a fraction in lowest terms.
Answers
Answer:
[tex]5.8\text{ \%}\rightarrow\frac{29}{500}[/tex]Explanation: We have to write 5.8% In fraction in lowest terms:
This percent number essentially is:
[tex]5.8\text{ \%=}\frac{5.8}{100}[/tex]Therefore we can write it as:
[tex]\frac{5.8}{100}=\frac{5.8\times10}{100\times10}=\frac{58}{1000}[/tex]In lowest terms, this would be:
[tex]\frac{58}{1000}=\frac{29}{500}[/tex]Which calculation and answer show how to convert 13 to a decimal?
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when evalueatong the expression 13/15,
13 serves as the dividend and
15 is the divisor
Divisor is always placed outside the division sign and the dividend inside.
According to the option, you can see that 15 which is the divisor is placed outside and 13 is placed inside.
check the diagram below:
Option A is the correct answer in this case
The figure below is a trapezoid:10011050mZ1 =m2 =mZ3=Blank 1:Blank 2:Blank 3:
Answers
STEP 1: Identify and Set Up
We have a trapezoid divided by a straight line that divides it assymetrically. We know from the all too famous geometric rule that adjacent angles in a trapezoid are supplementary. Mathematically, we can express thus:
[tex]100^o+<2+<3^{}=180^o=50^o+110^o+<1[/tex]Hence, from this relation, we can find our unknown angles.
STEP 2: Execute
For <1
[tex]\begin{gathered} 180^o=50^o+110^o+<1 \\ 180^o=160^o+<1 \\ \text{Subtracting 160}^o\text{ from both sides gives} \\ <1=180-120=60^o \end{gathered}[/tex]<1 = 60 degrees
For <2 & <3
We know from basic geometry that a transversal across two parallel lines gives a pair of alternate angles and as such, <1 = <3 = 60 degrees
We employ our first equation to solve for <2 as seen below:
[tex]\begin{gathered} 100^o+<2+<3^{}=180^o \\ 100^o+<2+60^o=180^o \\ 160^o+<2=180^o \\ \text{Subtracting 160}^{o\text{ }}\text{ from both sides gives:} \\ <2=180-160=20^o \end{gathered}[/tex]Therefore, <1 = <3 = 60 degrees and <2 = 20
can u find a b and c its parallelogramthank u
Answers
To answer this question, we need to remember two theorems of parallelograms:
1. If a quadrilateral is a parallelogram, the two sets of its opposite angles are congruent:
2. The consecutive angles of parallelograms are supplementary (they sum 180 degrees):
Then, with this information, we have that:
[tex]97\cong m\angle c\Rightarrow m\angle c=97[/tex]And also, we have that the diagonal forms two congruent triangles, and the sum of internal angles of a triangle is equal to 180, then, we have:
[tex]m\angle c+26+m\angle b=180\Rightarrow97+26+m\angle b=180\Rightarrow m\angle b=180-97-26[/tex]Then, we have:
[tex]m\angle b=180-123\Rightarrow m\angle b=57[/tex]Then, using that the consecutive angles of parallelograms are supplementary (they sum 180 degrees), we have:
[tex]97+m\angle a+m\angle b=180\Rightarrow97+m\angle a+57=180\Rightarrow m\angle a=180-97-57_{}[/tex]Thus, we have that the measure for angle a is:
[tex]m\angle a=180-154\Rightarrow m\angle a=26[/tex]In summary, we have that (all the measures in degrees):
m< a = 26
m< b = 57
m< c = 97
19. Write in algebraic terms: six times a number, minus five times the number, plus eight.
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Let the number be a
6a x 5a + 8
I haven’t got a clue about what it is or what to do
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EXPLANATION
Rotating the shape , give us the third shape form.
Over which interval(s) is the function decreasing?A) -4 < x < 3B) -0.5 < x < ∞C) -∞ < x < -0.5D) -∞ < x < -4
Answers
In the interval where the function is decreasingcreasing, the input or x values increase as the output or y values decrease. Looking at the graph, moving from the left to the right, the values of x are increasing whie the values of y are decreasing. This trend continued till we got to x = 0.5. Thus, in the interval from negative infinity to x = - 0.5, the function was decreasing.
The correct option is C
I need you to make a problem and solve it on the side and explain how explain it I’m making a practice test and I can show you examples of how I did the others This are the topics you can choose fromTopic 1: is the relation a function- domain and range Topic 2: zero is of a function
Answers
For topic (1), we have the following question:
Which of the following is a function: y=x² or x=y²?
Identify domain and range of each equation.
We can identify a given relation if it is a function or not by identifying the number of possible values of y.
The equations below are both relations.
[tex]y=x^2\text{ and }x=y^2[/tex]However, only one of them is a function.
For the first equation, note that for each value of x, there is only one value of y. Some of the points on the equation are as follows.
[tex]\begin{gathered} x=-2 \\ y=x^2^{} \\ y=(-2)^2=4 \\ \\ x=0 \\ y=x^2 \\ y=0^2=0 \\ \\ x=2 \\ y=x^2 \\ y=2^2 \\ y=4 \end{gathered}[/tex]Thus, the equation passes through the following points.
[tex](-2,4),(0,0),(2,4)[/tex]Notice that no value of x is repeated. Therefore, the given relation is a function.
We can also determine it using graphs. The image below is the graph of the first equation.
If we test it using the vertical line test, no vertical line can pass through the graph twice. Therefore, it shows that the equation is a function.
On the otherhand, the other equation is not a function. This is because when we substitute -2 and 2 to the value of y, we will have the same value of x, which is equal to 4.
[tex]\begin{gathered} y=-2^{} \\ x=y^2 \\ x=(-2)^2=4 \\ \\ y=2 \\ x=y^2^{} \\ x=2^2=4 \end{gathered}[/tex]Since there are two values of y for only one value of x, the equation must not be a function.
To illustrate this using its graph, we can notice that the vertical line below passes through two points on the graph when x=4.
Therefore, the second equation is not a function.
As for the domain and range, we can obtain it from both graphs.
The domain the set of all possible values of x. Thus, for the first equation, since it extends indefinitely to the left and right, the domain must be from negative infinity to positive infinity.
[tex]D_1\colon(-\infty,\infty)[/tex]On the otherhand, since the second equation extends indefinitely to the right from 0, the domain must be from 0 to positive infinity, inclusive.
[tex]D_2\colon\lbrack0,\infty)[/tex]As for the range, it is the set of all possible values of y.
Thus, for the first equation, since the graph extends indefinitely upwards from 0, the range must be from 0 to positive infinity, inclusive.
[tex]R_1\colon\lbrack0,\infty)[/tex]On the otherhand, the graph of the second equation extends indefinitely upwards and downwards. Thus, its range must be from negative infinity to positive infinity.
[tex]R_2\colon(-\infty,\infty)[/tex]To summarize, here are the questions and the answers for each question.
Which of the following is a function: y=x² or x=y²?
Answer: y=x²
Identify domain and range of each equation.
Answer:
For y=x²:
[tex]\begin{gathered} D\colon\text{ (-}\infty,\infty\text{)} \\ R\colon\lbrack0,\infty) \end{gathered}[/tex]For x=y²:
[tex]\begin{gathered} D\colon\lbrack0,\infty) \\ R\colon(-\infty,\infty) \end{gathered}[/tex]The table below shows the probability distribution of students in a highschool with 1500 students. What is the expected value for the ageof arandomly chosen student?Age131415161718Probability.0.010.250.300.280.150.01A. 15.28B. 15.64C. 15.34D. 15.36
Answers
Solution
We are required to determine the expected value of the given distribution
The formula for expected value is shown below
Thus,
[tex]\begin{gathered} Expected\text{ value =13\lparen0.01\rparen+14\lparen0.25\rparen+15\lparen0.30\rparen+16\lparen0.28\rparen+17\lparen0.15\rparen+18\lparen0.01\rparen} \\ = \end{gathered}[/tex][tex]=0.13+3.5+4.5+4.48+2.55+0.18[/tex][tex]=15.34[/tex]The correct option is C
Question 3 of 14What are the factors of the product represented below?TILESX2 X2 X2 X2X X X XA. (2x + 1)(4x + 3)B. (4x + 2)(3x + 1)C. (8x + 1)(x+2)D. (4x + 1)(2x + 3)
Answers
Hi!
To solve this exercise, we can analyze the sides of this rectangle, which indicate the size of each side.
Let's do it:
On the superior side, we have: x+x+x+x+1, which means 4x+1, right?
On the left side, we have: x+x+1+1+1, or 2x+3
So, we can say that the factors of this rectangle are (4x+1)*(2x+3), last alternative.
drag the location of each ordered pair after a reflection over the x axis stated. then, drag the correct algebraic representation of the reflection to the white box. answer choices: (y, x), (-2,-6),(x,-y),(-3,-2),(5,8),(-5,-8),(-x, y),(-6,-6),(-6,-1),(2,-6),(6,-1),(3,2),(-x, -y),(-7,-2),(6,-6),(7,2)
Answers
Reflection over the x-axis transform the point (x, y) into (x, -y)
Applying this rule to the vertex of the triangle ABC, we get:
A(-6, 6) → A'(-6, -6)
B(-2, 6) → B'(-2, -6)
C(-6, 1) → C'(-6, -1)
Algebraic representation: (x, -y)
A line passes through the point (-6,1) and has a slope of -5/2
Write an equation in slope - intercept form for this line .
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Answer: [tex]y=-\frac{5}{2}x+16[/tex]
Step-by-step explanation:
The equation in point-slope form is [tex]y-1=-\frac{5}{2}(x+6)[/tex]. To find the equation in slope-intercept form, isolate [tex]y[/tex].
[tex]y-1=-\frac{5}{2}(x-6)\\\\y-1=-\frac{5}{2}x+15\\\\y=-\frac{5}{2}x+16[/tex]
If the trend shown in the graph above continued into the next year, approximately how many sport utility vehicles were sold in 1999?
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ANSWER :
EXPLANATION :
a. Rotate the letter W 180° around the origin. Then translate the image up 4 units. Draw the final image. What new letter did you form? b. Is the new letter congruent to the original letter? Explain.
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ANSWER and EXPLANATION
We have letter W on the graph.
The cordinates of its vertices are:
(0, 4), (1, 0), (2, 2), (3, 0), (4, 4)
Now, on a cartesian plane, (x - y plane), we have 4 quadrants. The letter is on the first quadrant.
Because it rotates 180 degrees around the origin, it means that it mmoves by 2 quadrants:
So, it moves from quadrant 1 to quadrant 4.
The new cordinates become:
(0, -4), (-1, 0), (-2, -2), (-3, 0), (-4, -4)
Then it is translated 4 units up, so we add 4 units to each of the y values (Remember that cordinates are written as (x, y)):
(0, 0), (-1, 4), (-2, 2), (-3, 4), (-4, 0)
Now, plot those:
a) It forms the letter M.
b) For one shape to be congruent to another, it means that they have the same size. So, yes, the M is congruent to the W.
During a Super Bowl day, 19 out of 50 students wear blue-colored jersey upon entering the campus. If there are 900 students present on campus that day, how many students could be expected to be wearing a blue-colored jersey? T T
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Be sure to include the correct unit in your answer
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The fence required is:
[tex]388.3125ft^2[/tex]Explanation:For the farmer to build an accurate fence, he needs to know the area of the rose garden. The area is the sum of the area of the rectangle and the area of the semicircle.
The area of the rectangle is:
[tex]\begin{gathered} A=wl \\ =15ft\times20ft \\ =300ft^2 \end{gathered}[/tex]The area of the semicircle is:
[tex]\begin{gathered} A=\frac{\pi}{2}r^2 \\ \\ \text{Where r is the radius }=\frac{15}{2}=7.5ft,\pi=3.14 \\ \\ A=\frac{3.14}{2}(7.5)^2=88.3125ft^2 \end{gathered}[/tex]The area of the rose garden is:
[tex]300ft^2+88.3125ft^2=388.3125ft^2[/tex]what is a youth group that
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(3+ 1i) (2 - 2i)
open the parenthesis
3(2 - 2i) + 1i(2 - 2i) (note: i² = -1)
6 - 6i + 2i + 2
Rearrange
6 + 2 - 6i + 2i
8 - 4i
comparing with a + bi
The real number a equals 8
The real number b equals -4
I’m not sure how to graph the equation and not sure what it means by “interpret”
Answers
(a) Graphing the equation
(i) let x = 0 ; then
y = -0.05 (0) +16
∴ y = 16
Point 1 = ( 0;16 )
(ii) let y = 0 , then
0 = -0.05x +16
0.05x = 16
x = 16 /0.05
∴ x = (320 )
point 2 = ( 320; 0 )
The graph of the line ( y = -0.05x+16) will then be as follows :
(b) Interpret the x and y intercept :{To interpret means to explain in details or translate in writing the meaning of the values of x and y . }
• x represents the number of miles travelled
,• y represents gasoline used i gallons
Interpretation:
• when ,x is 0 miles, , the ,gasoline ,is sitting at, 16 gallons.,( this might be the initial stage of travelling)
,• however, when the, person has travelled 320 miles,, all gasoline is ,completly used up and sits at 0 gallons, .( this might be the end stage of travelling)
The employees in a firm earn $8.50 an
hour for the first 40 hours per week, and
1.5 times the hourly rate for any hours
worked over 40. How much does an
employee who works 52 hours in one
week eam?
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Using mathematical operations, we know that the salary of a person working for 52 hours a week will be $493.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands. The rules that specify the order in which we should solve an expression involving multiple operations are known as the order of operations. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, and Addition Subtraction (from left to right).So, the amount earned by a person who works 52 hours a week:
Salary if a person works for 40 hours: $8.50 per hourSalary if a person works for more than 40 hours: 1.5 times $8.50 per hour that is, 8.50 × 1.5 = $12.75 per hour.So, if a worker works for 52 hours, his salary will be:
52 - 40 = 12 Hours40 × 8.50 = $34012 × 12.75 = $153Sum: $493Therefore, using mathematical operations, we know that the salary of a person working for 52 hours a week will be $493.
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Look at triangles A through F shown in the rectangles below.Which triangles are acute triangles?
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The acute triangles are those whose all 3 angles have a measure less than 90 degrees.
We need to follow the next image:
Let us check each triangle.
Triangle A:
It has a right angle, hence, it can not be an acute triangle.
Triangle B:
All three sides are less than 90 degrees. Hence, it is an acute triangle
Triangle C:
It has an angle with a measure of more than 90 degrees. Hence, it can not be an acute triangle.
Triangle D
All three sides are less than 90 degrees. Hence, it is an acute triangle.
Triangle E
It has a side with a measure of more than 90 degrees. Hence, it can not be an acute triangle.
Triangle F
It has a right angle, hence, it can not be an acute triangle.
Hence, the correct answer is H. B and D
3. In one linear function, when you subtracteach y-coordinate from the x-coordinate,the difference is 3. If the x-coordinate isnot greater than 10 and the y-coordinateis a positive whole number, how manyordered pairs are there?
Answers
Problem
3. In one linear function, when you subtract each y-coordinate from the x-coordinate, the difference is 3. If the x-coordinate is not greater than 10 and the y-coordinate is a positive whole number, how many ordered pairs are there?
Solution
Here are the conditions
x- y= 3
x <10
y >0
And then we have these as possible answers:
4-1 =3
5-2= 3
6-3=3
7-4=3
8-5=3
9-6=3
Then the total possible pairs are: 6
Which sample size will produce the widest 95% confidence interval, given asample proportion of 0.5?A. 40B. 70C. 60D. 50
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The confidence interval depends on the margin of error. When finding the margin of error, the z score corresponding to the 95% confidence level would be multiplied by the square root of the product of the estimated proportion of success and failure divided by the sample size. The greater the sample size, the smaller thie value that would be gotten from this operation. The smaller the sample size, the greater the value that would be gotten from this operation. A greater value would give a bigger margin of error. Thus, the confidence interval would be wider. Hence, the correct option for the sampe size is
A. 40
Look at the graphs and their equations below. Then fill in the information about the coefficients A, B, C, and D.
Answers
Given:
Aim:
We need to find the coordinates and The sign of the equation.
Explanation:
[tex]We\text{ know that y=a\mid x\mid is upside and y}\ge\text{0 when a >0 and downside and y}\leq\text{owhen a<0}[/tex]The coefficient of the given functions are
[tex]y=A|x|\text{ is positive}[/tex][tex]y=B|x|\text{ is positive}[/tex][tex]y=C|x|\text{ is negative}[/tex][tex]y=D|x|\text{ is negative}[/tex]The coefficient is closest to zero.
Comparing the graph of y=A|x| and y=B|x|, we get y=A|x| is wider than y=B|x|.
[tex]A
Comparing the graph of y=C|x| and y=D|x|, we get y=D|x| is wider than y=C|x|.
[tex]CComparing the graph of y=A|x| and y=C|x|, we get y=C|x| is wider than y=A|x|.
[tex]C The coefficient is closest to zero y=C|x|.The coefficient with the greatest value.
Comparing the graph of y=B|x| and y=D|x|, we get y=D|x| is wider than y=B|x|.
[tex]D The coefficient with the greatest value is y=B|x|. .Which equation represents the values in the table? x–1012y–13711A.y = 4x + 3B.y = −x − 1C.y = 3x − 1D.y = 1/4x − 3/4
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We know it's a linear function, which is like
[tex]f(x)=mx+b[/tex]We can find the slope "m" of the linear function doing
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]There the points x₂, x₁, y₂ and y₁ we can take what's more convenient for us, just be careful, if you do x₁ = 0, you must take the correspondent y₁, the value of y on the same column, therefore y₁ = 3, for example.
I'll do x₁ = 0 which implies y₁ = 3 and x₂ = 1 which implies y₂ = 7. Therefore
[tex]\begin{gathered} m=\frac{7_{}-3}{1_{}-0_{}} \\ \\ m=\frac{7_{}-3}{1_{}}=4 \end{gathered}[/tex]Therefore the slope is m = 4, then
[tex]y=4x+b[/tex]To find out the "b" value we can use the fact that when x = 0 we have y = 3, therefore
[tex]\begin{gathered} y=4x+b \\ \\ 3=4\cdot0+b \\ \\ 3=b \\ \end{gathered}[/tex]Then b = 3, our equation is
[tex]y=4x+3[/tex]The correct equation is the letter A.
5) Find the volume of the cylinder whose radius is 10in and height is 20in.V-π r 2 h
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During a food drive, a local middle school collected 3,195…
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Answer:
100 cans
Explanation:
• The total number of canned food items collected = 3,195
,• The number of classrooms that participated = 28
To estimate the number of items each classroom donated, divide 3195 by 28.
[tex]\frac{3195}{28}\approx\frac{3000}{30}=100[/tex]Note: Round to a whole number since the number of cans cannot be a decimal.
Each class donated about 100 cans.
Si A = 5x 2 + 4 x 2 - 2 (3x2), halla su valor numérico para x= 2.
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Based on the calculations, the numerical value of A is equal to 12.
How to determine the numerical value of A?In this exercise, you're required to determine the numerical value of A when the value of x is equal to 2. Therefore, we would evaluate the given equation based on its exponent as follows:
Numerical value of A = 5x² + 4x² - 2(3x²)
Numerical value of A = 5(2)² + 4(2)² - 2(3 × (2)²)
Numerical value of A = 5(4) + 4(4) - 2(3 × 4)
Numerical value of A = 20 + 16 - 24
Numerical value of A = 36 - 24
Numerical value of A = 12
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Complete Question:
If A = 5x² + 4x² - 2(3x²), find its numerical value for x = 2.
What is the answer to this equation?
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Answer:
D 7.5
Step-by-step explanation:
n + n-3 + 2n-4 = perimeter ≥ 37
4n-7≥37
4n≥30
n≥7.5