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The Greeks limited themselves to using only compass and ruler in their formal geometric constructions.
Answer: Options B and D.
Related Questions
Find the lenghts of the sides of the rectangle ABCD shown on the coordinate plane. Suppose you double the length of each side. What would be the new coordinates of point C if the coordinate of point A stay the same
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Looking at the diagram,
each small box represents one unit
The number of units from A to B is 4 units
The number of units from B to C is 3 units
Thus, the length of rectangle ABCD is 4 units and its width is 3 units.
The original coordinates are
A(0, 0)
B(0, 4)
C(3, 4)
D(3, 0)
If
I need to use substitution to solve each system of equations then use ordered pairs
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From the given question
There are given that the equation
[tex]\begin{gathered} 2x+5y=38\ldots(1) \\ x-3y=-3\ldots(2) \end{gathered}[/tex]Now,
From the equation (1)
[tex]\begin{gathered} 2x+5y=38 \\ 2x=38-5y \\ x=\frac{38}{2}-\frac{5}{2}y \\ x=19-\frac{5}{2}y\ldots(3) \end{gathered}[/tex]Then,
Put the equation (3) into the equation (2)
So,
[tex]\begin{gathered} x-3y=-3 \\ 19-\frac{5}{2}y-3y=-3 \\ 38-5y-6y=-6 \\ 38-11y=-6 \\ -11y=-6-38 \\ -11y=-44 \\ y=4 \end{gathered}[/tex]Then,
Put the value of y into the equation (3)
So,
[tex]\begin{gathered} x=19-\frac{5}{2}y \\ x=19-\frac{5}{2}(4) \\ x=19-\frac{20}{2} \\ x=19-10 \\ x=9 \end{gathered}[/tex]Hence, the value of x is 9 and y is 4.
how do I use a right triangle to write the following expression as an algebraic expression?
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So, we want to express the following:
[tex]\sec (\sin ^{-1}(\frac{x}{\sqrt[]{x^2+81}}))[/tex]As an algebraic expression.
If:
[tex]\begin{gathered} \sin ^{-1}(\frac{x}{\sqrt[]{x^2+81}})=\theta \\ \text{Then,} \\ \sin (\theta)=\frac{x}{\sqrt[]{x^2+81}} \end{gathered}[/tex]We could draw the following triangle:
Remember that the secant function relations the hypotenuse of the triangle and the adjacent side of the triangle. So first, we should find the adjacent side using the pythagorean theorem:
[tex]\begin{gathered} a^2=(\sqrt[]{x^2+81})^2-x^2 \\ a^2=x^2+81-x^2 \\ a^2=81\to a=9 \end{gathered}[/tex]Therefore, the adjacent side is 81. And, the value of:
[tex]\sec (\sin ^{-1}(\frac{x}{\sqrt[]{x^2+81}}))[/tex]Is:
[tex]\sec (\sin ^{-1}(\frac{x}{\sqrt[]{x^2+81}}))=\frac{\sqrt[]{x^2+81}}{9}[/tex]please help figure out this problem i’m trying to determine if the lines that appear to be tangent are tangent
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Suppose that the two lines that form the missing angle are tangents to the circle. Then, the measure of the missing angle can be found using the following equation:
[tex]\measuredangle ABC=\frac{arc\text{ AEC - arc AGC}}{2}[/tex]Notice that we can complete the information about the arcs of the circle with the central angle:
then, we can find the angle x with the following expression:
[tex]\begin{gathered} \measuredangle x=\frac{243-117}{2}=\frac{126}{2}=63 \\ \Rightarrow\measuredangle x=63\degree \end{gathered}[/tex]therefore, the measure of the missing angle is 63 degrees.
what is 234,181 rounded to the nearest thousand
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The figure 234,181 has the digit 4 in the thousands place.
Rounding to the nearest thouand would therefore be
234,000
This is because, the digit 1 that follows is not up to 5 and therefore is insignificant. So the digit 1 and the others after it are all rounded up to zeros.
find the value of n in each equation the name the property that is used
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14.
n=11+0
Add numbers ( 11+ 0 = 11)
n=11
Addition property
A manufacturer knows that their items have a normally distributed length, with a mean of 8.4 inches, and standard deviation of 1.4 inches.If one item is chosen at random, what is the probability that it is less than 11.8 inches long?
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We will make use of the z-score to calculate the probability. The z-score is calculated using the formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where x is the score, μ is the mean, and σ is the standard deviation.
From the question, we have the following parameters:
[tex]\begin{gathered} x=11.8 \\ \mu=8.4 \\ \sigma=1.4 \end{gathered}[/tex]Therefore, we have the z-score to be:
[tex]\begin{gathered} z=\frac{11.8-8.4}{1.4} \\ z=2.43 \end{gathered}[/tex]Using a calculator, we can get the probability value to be:
[tex]P=0.9925[/tex]The probability is 0.9925 or 99.25%.
the radius of the circle is 5 inches. what is the area?give the exact answer in simplest form.
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The area is 25π square inches
Explanation:Given a radius, r = 5 in.
The area of a circle is given by the formula:
[tex]A=\pi r^2[/tex]Substituting the value of r, we have:
[tex]A=\pi(5^2)=25\pi[/tex]The area is 25π square inches
Need answer for 3a please. This is for homework :)
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Given the supplementary angle below for 3a,
Supplementary angles is 180°,
To find x,
[tex]\begin{gathered} 132^0+2x^0+3=180 \\ 2x^0+135^0=180^0 \\ 2x^0=180^0-135^0 \\ 2x^0=45^0 \\ x=\frac{45^0}{2}=22.5^0 \\ x=22.5^0 \end{gathered}[/tex]Hence, x = 22.5°
Louis and Jenny each wrote an equation to represent the graphed linear function. Louis’s answer is y=2x. Jenny’s answer is y=x+2. Which student is correct?
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Concept
First, find the slope of the line, and secondly use a slope-intercept form of the equation to find the equation of the line.
Step 1: find the slope
From the graph, choose two coordinates at the intercept
( 0, 2 ) and ( -2, 0 )
x1 = 0
y1 = 2
x2 = -2
y2 = 0
Substitute the values in slope equation
[tex]\begin{gathered} \text{Slope m = }\frac{rise}{\text{run}}\text{ }=\text{ }\frac{y_2-y_1}{x_2-x_1} \\ \\ \text{Slope = }\frac{0-2}{-2-\text{ 0}} \\ \text{m = 1} \end{gathered}[/tex]Step 2: Find the intercept c
The intercept on the y-axis is c = 2
Step 3: Write the equation of a line in slope-intercept form
y = mx + c
Step 4: substitute the values of m and c to find the equation
y = 1(x) + 2
y = x + 2
Final answer
y = x + 2 Jenny's is correct
the lettuce i have is 25 calories per serving. serving size is 85 grams. i had 27 grams . how many calories would this be? if you don’t know , don’t respond
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There would be 91.8 calories in 27 grams.
Define unitary method.The unitary approach involves determining the value of a single unit, from which we can calculate the values of the necessary number of units. We must first determine the number of objects at the unit level in order to answer questions based on the unitary technique, after which we must determine it for higher values. For instance, if the price of 5 chocolates is $10, it is preferable to first determine the price of 1 chocolate in order to get the price of 6 chocolates. Once we get the price for 6 chocolates, we multiply it by 6.
Given,
Calories per serving = 25
Serving size = 85 grams
Calories per serving using unitary method:
Dividing,
[tex]\frac{85}{25}[/tex]
3.4
Calories per serving using unitary method is 3.4 calories.
Now, we have 27 grams,
Multiplying:
27 (3.4)
91.8
There would be 91.8 calories in 27 grams.
To learn more about unitary method, visit:
https://brainly.com/question/22056199
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What is the solution to the equation below?A.x = -1B.x = 0C.x = -5D.x = 3
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We must solve the following equation for x:
[tex]x+3=\sqrt{3-x}[/tex]We can square both sides of the equation so we can get rid of the radical:
[tex]\begin{gathered} (x+3)^2=(\sqrt{3-x})^2 \\ (x+3)^2=3-x \end{gathered}[/tex]We expand the squared binomial on the left:
[tex]\begin{gathered} (x+3)^2=x^2+6x+9=3-x \\ x^2+6x+9=3-x \end{gathered}[/tex]Then we substract (3-x) from both sides:
[tex]\begin{gathered} x^2+6x+9-(3-x)=x-3-(3-x) \\ x^2+6x+9+x-3=0 \\ x^2+7x+6=0 \end{gathered}[/tex]Then we have to find the solutions to this last equation. Remember that the solutions to an equation of the form ax²+bx+c have the form:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]In our case a=1, b=7 and c=6 so we get:
[tex]\begin{gathered} x=\frac{-7\pm\sqrt{7^2-4\cdot1\cdot6}}{2\cdot1}=\frac{-7\pm\sqrt{49-24}}{2}=\frac{-7\pm\sqrt{25}}{2}=\frac{-7\pm5}{2} \\ x=\frac{-7+5}{2}=-1\text{ and }x=\frac{-7-5}{2}=-6 \end{gathered}[/tex]So we have two potential solutions x=-1 and x=-6. However we should note something important, in the original equation we have the term:
[tex]\sqrt{3-x}[/tex]Remember that the result of the square root is always positive. Then the term in the left of the expression has to be positive or 0. Then we impose a restriction in the value of x:
[tex]x+3\ge0\rightarrow x\ge-3[/tex]From the two possible solutions only x=-1 is greater than or equal to -3 so this is the correct one.
AnswerThen the answer is option A.
Write the expression as a product of two factors. 12s + 10 + 6y
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to write the expression as a product between two factors you must identify the common factor between all the terms in tis case the common factow will be 2
[tex]12s+10+6y=2\cdot(6s+5+3y)[/tex]Factor 6z^2 + 31z + 18
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May I please get help with this. I have tried multiple times but still could not get the correct or at least accurate answers
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step 1
Find out the value of y
we have that
y+75=180 degrees ------> by same side ineterior angle
Comment on the similarities and differences for the graph of every polynomial function.
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There are different graphs of polynomial functions. In terms of shape, it can go from a straight line, slanting line, parabola, to curvy graphs especially when we are graphing polynomial functions with degrees 3 or higher.
See examples below:
However, what is similar to these graphs is that each graph is continuous or has no breaks and the domain of every polynomial function is the set of all real numbers.
Find the solution(s) to the system of equations represented in the graph.0, −2) and (2, 0) (0, −2) and (−2, 0) (0, 2) and (2, 0) (0, 2) and (−2, 0)
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Solution
The solution is the point of intersection.
Therefore, the answer is
[tex](0,2)\text{ and }(-2,0)[/tex]I need help with question 4-8, can you please help me?Use f(X) as g(X) for question 5 and 6
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Question 4
The x values for which g(x) = 3
From the graph, we have this value to be:
[tex]0\text{ }\leq\text{ x }\leq\text{ 2}[/tex]Question 5
f(x) = 6, What is x?
From the graph, we can determine the value of x corresponding to f(x)= 6:
[tex]x\text{ = }4[/tex]Question 6:
f(x)= 0, What is x?
From the graph, we can determine the value of x corresponding to f(x) = 0
[tex]x\text{ = 7}[/tex]Question 7
The domain of the function:
The domain is the set of allowable inputs.
[tex]\lbrack0,\text{ 12\rbrack}[/tex]Question 8
The range is the set outputs
[tex]\lbrack0,\text{ 6\rbrack}[/tex]Solve for w.4w²-24w=0If there is more than one solution, separate them with commas.If there is no solution, click on "No solution".W =0U08Nosolution
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ANSWER
[tex]\begin{equation*} w=0,\text{ }w=6 \end{equation*}[/tex]EXPLANATION
We want to solve the given equation for w:
[tex]4w^2-24w=0[/tex]To do this, we have to factorize the equation and simplify it.
Let us do that now:
[tex]\begin{gathered} (4w*w)-(4w*6)=0 \\ \\ 4w(w-6)=0 \\ \\ \Rightarrow4w=0\text{ and }w-6=0 \\ \\ \Rightarrow w=0,\text{ }w=6 \end{gathered}[/tex]That is the answer.
The displacement (in meters) of a particle moving in a straight line is given by s = t^2 - 9t + 15,where t is measured in seconds.(A)(i) Find the average velocity over the time interval [3,4].Average Velocity = ___ meters per second(ii) Find the average velocity over the time interval [3.5,4].Average Velocity=____meters per second(iii) Find the average velocity over the time interval [4,5].Average Velocity= ____meters per second(iv) Find the average velocity over the time interval (4,4.5] Average Velocity = ____meters per.(B) Find the instantaneous velocity when t=4.Instantaneous velocity= ____ meters per second.
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Given
The displacement (in meters) of a particle moving in a straight line is given by s = t^2 - 9t + 15,
giving that -3+20=5x-4 write 3 more equations that you know are true
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Answer:
Step-by-step explanation:
ft7654
Which of the following shapes is the cross-section for a cylinder?A. SquareB. TriangleC. CircleD. Pentagon
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Solution:
Concept:
The vertical cross-section of a cylinder is a rectangle, and the horizontal cross-section is a circle.
From the explanation above,
The final answer is CIRCLE
OPTION C is the right answer
if f(x)=-2x-3, find f(-1)
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Solve;
[tex]\begin{gathered} f(x)=-2x-3 \\ f(-1)=-2(-1)-3 \\ f(-1)=2-3 \\ f(-1)=-1 \end{gathered}[/tex]The answer is -1
That is f(-1) = -1
How many different lineups can Coach Lay create using 10 girls to fill 5 spots on the basketball court. Positions do not matter.
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This is the formula for combinations
In this case, n = 10 and k = 5
C = 10!/(10-5)!(5)! = 3628800/(120)(120) = 3628800/14400 = 252
Answer:
252 different line u
Lisa's rectangular living room is 15 feet wide. If the length is 7 feet less than twice the width, what is the area of her living room?
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345ft²
1) Since we have the following data then we can write it down:
width: 15 ft
length: 2w-7
2) And we can write out the following equation regarding that the area of a rectangle is given by:
[tex]S=l\cdot w[/tex]We can plug into that the given data:
[tex]\begin{gathered} S=15(2(15)-7)) \\ S=15(30-7) \\ S=15\cdot23 \\ S=345 \end{gathered}[/tex]Notice we have used the FOIL acronym. And the PEMDAS order of operations prioritizing the inner parentheses.
3) So we can state that the area of her living room is 345ft²
check the image I got y=-xsqrt3/3 but I want to double check
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Answer:
To convert the polar equation to a rectangular equation .
Given polar equation is,
[tex]\theta=\frac{11\pi}{6}[/tex]we know the convertion of polar coordinates (r,theta) to rectangular equation as,
[tex]\begin{gathered} x=r\cos \theta \\ y=r\sin \theta \end{gathered}[/tex]we get,
[tex]\theta=\frac{11\pi}{6}=(2\pi-\frac{\pi}{6})[/tex]Substitute this in the above equation we get,
[tex]\begin{gathered} x=r\cos (2\pi-\frac{\pi}{6}) \\ \\ y=r\sin (2\pi-\frac{\pi}{6}) \end{gathered}[/tex]Solving we get,
[tex]\begin{gathered} x=r\cos (\frac{\pi}{6}) \\ \\ y=-r\sin (\frac{\pi}{6}) \end{gathered}[/tex]we get,
[tex]x=r(\frac{\sqrt[]{3}}{2})[/tex][tex]y=-r(\frac{1}{2})[/tex]Substitute r=-2y in x we get,
[tex]x=-2y(\frac{\sqrt[]{3}}{2})[/tex][tex]y=-\frac{x}{\sqrt[]{3}}[/tex][tex]y=-\frac{\sqrt[]{3}x}{3}[/tex]The required rectangular form of the given plar equation is,
[tex]y=-\frac{\sqrt[]{3}x}{3}[/tex]g(x)= x^2 + 2hx) = 3x - 2Find (g+ h)(-3)
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Given the following functions;
f(x) = x^2 + 2
g(x) = 3x - 2
(g+h)(x) = g(x)+h(x)
(g+h) = x^2 + 2 + 3x - 2
(g+h) = x^2+3x + 2-2
(g+h) = x^2 + 3x
To get (g+h) (-3), we will subtitute x = -3 into the resulting function as shown;
(g+h) (-3) = (-3)^2+3(-3)
(g+h) (-3) = 9 - 9
(g+h) (-3) = 0
Hence the value of the expression (g+h) (-3) is 0
Find the circumference of each circle .(use 22/7 as an approximation for PI
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Let us find the circumference of each circle.
The circumference of a circle is given by
[tex]C=2\pi r\: \: or\: \: C=\pi D[/tex]Where r is the radius and D is the diameter of the circle.
Circle 1:
Here we are given the diameter of the circle
D = 21 cm
[tex]C=\pi D=\frac{22}{7}\cdot21=22\cdot3=66\operatorname{cm}[/tex]So, the circumference of the circle is 66 cm.
Circle 2:
Here we are given the diameter of the circle
D = 91 ft
[tex]C=\pi D=\frac{22}{7}\cdot91=286\: ft[/tex]So, the circumference of the circle is 286 ft.
Circle 3:
Adding mixed fractions (A)1 1/14 + 3 1/14 =
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Explanation:
To add mixed fractions we have to follow these steps:
[tex]1\frac{1}{14}+3\frac{1}{14}=[/tex]1. Add the whole numbers together
[tex]1+3=4[/tex]2. Add the fractions
[tex]\frac{1}{14}+\frac{1}{14}=\frac{2}{14}=\frac{1}{7}[/tex]3. If the sum of the fractions is an improper fraction then we change it to a mixed number and add the whole part to the whole number we got in step 1.
In this case the sum of the fractions results in a proper fraction, so we can skip this step.
Answer:
The result is:
[tex]4\frac{1}{7}[/tex]
Does the least-squares fit line always go through at least one point in the plot?
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Not necessarily. The least-squares line is the best fit for all the points in the scatterplot. if it so happens that in order to get close to some point on the plot the line has to go a little further away from some other point, the line will be adjusted to accommodate that.
Hence, the least square line does not always pass through at least one point on the line.
