Which part of the triangle do you feel most confident of identifying and why and How might you use a perpendicular bisector or an angle bisector in the everyday life.
Answers
Hello there. To solve this question, we have to remember some properties about triangles.
Given a triangle ABC as follows:
We can show for each point what it is on this triangle.
1. Midsegment. This is the segment that is parallel to the base, in this case BC and has half its length. Another property: it divides the sides AB and AC into proportional parts. See the drawing.
2. Circumcenter. Take the triangle and inscribe it in a circumference (all its vertices are in the circumference. Now take the perpendicular bisector of each sides. The point in which at least two of them intersects is the circumcenter. See the drawing.
3. Incenter. Take the bisectors of the angles of ABC. The point in which they intersect is the incenter. Another property: It is the center of the inscribed circumference that is tangent to all sides of the triangle.
Related Questions
Exit Ticket Which method do you believe is the most efficient when solving for the following equations? n2 – 2n – 3=0 Factor/Zero Product Property Completing the Square Quadratic Formula
Answers
The factoYou ar/zero product property is the most efficient method for solving the equation
Explanation:The given quadratic equation can be factored as:
[tex]\begin{gathered} n^2-2n-3=0 \\ (n+1)(n-3)=0 \end{gathered}[/tex]The factor/zero product property is the most efficient method for solving the equation
Leila purchased 21.5 centimeters of wire for $17.20.Find the unit price in dollars per centimeter.If necessary, round your answer to the nearest cent.
Answers
Explanation
Given: Leila purchased 21,5cm of wire for $17.20.
Required: To determine the unit price in dollars per centimeter.
This is achieved thus:
To determine the unit price per centimeter, we divide the cost by the length of wire as follows:
[tex]\begin{gathered} 21.5cm=\text{ \$}17.20 \\ \therefore1cm=\frac{\text{ \$}17.20}{21.5}=\text{ \$}0.80 \end{gathered}[/tex]Hence, the answer is:
[tex]\text{ \$}0.80\text{ }per\text{ }centimeter[/tex]1) In 2014, the percentage of households that owned a 4K TV was found to be 18%. Using a sample of 300 households in which 60 of them owned a 4K TV, do we have sufficient evidence that the percentage of households with a 4K TV has increased? Use a level of significance of 0.10.
Answers
Hello there. To solve this question, we need to calculate the percentage of households that owns a 4K TV with the values given in the sample and compare with the other percentage to see if the value has increased.
Using that sample of 300 households, in which 60 of them owns a 4K TV, we get that the percentage will be calculated by the ratio:
60/300
Simplify the fraction by a factor of 60
1/5
Multiply it by 100%
20%, equal to 0.20
In 2014, we had that percentage being equal to 18%, which is equal to 0.18
So, we do have sufficient evidence that the percentage of households satifying this situation have increased with the time.
Translate the sentences into an algebraic inequality.A tour bus can seat 55 passengers. A minimum of 15 people must register for the tour to book the bus.
Answers
ANSWER
[tex]\text{15 }\leq\text{ x }\leq55[/tex]EXPLANATION
The tour bus can seat 55 passengers.
A minimum of 15 people must register for the tour to book the bus.
This means that the number of people that must register for the tour must be greater than or equal to 15 and less than or equal to 55.
Let the number of people that must register be x.
Then we have that the inequality that represents the situation is:
[tex]\begin{gathered} x\ge\text{ 15 and x }\leq\text{ 55} \\ \Rightarrow\text{ 15 }\leq\text{ x }\leq55 \end{gathered}[/tex]That is the inequality.
35 06286 rounded to the nearest ten thousandth is
Answers
35. 06 286 = 35.0629
2) y = -5 +4V7-2 A) Domain: { All real numbers. } Range: { All real numbers. } B) Domain: x 22 Range: y 2-5 + C) Domain: 'x z 2 Range: ys-5 D) Domain: x 2-2 Range: y z 5
Answers
Looking at the restrictions over the variable x, we know that the domain is:
[tex]x\ge2[/tex]To find the range, notice that:
[tex]\sqrt[]{x-2}\ge0[/tex]On the other hand, the function:
[tex]y=\sqrt[]{x-2}[/tex]is an increasing function (its value grows when x grows), and can get as large as we want provided a sufficiently large value for x. Then, the range of such a function would be:
[tex]y\ge0[/tex]Which does not get altered when we multiply the square root of (x-2) by 4.
Since the function:
[tex]y=-5+4\sqrt[]{x-2}[/tex]is a 5-units shift downwards, then the variable y can take any value from -5 onwards.
Then, the range of the function is:
[tex]y\ge-5[/tex]Another way to find the range is to isolate x from the equation:
[tex]\begin{gathered} y=-5+4\sqrt[]{x-2} \\ \Rightarrow y+5=4\sqrt[]{x-2} \\ \Rightarrow\frac{y+5}{4}=\sqrt[]{x-2} \\ \Rightarrow(\frac{y+5}{4})^2=x-2 \\ \Rightarrow x-2=(\frac{y+5}{4})^2 \\ \Rightarrow x=(\frac{y+5}{4})^2+2 \end{gathered}[/tex]Since we already know that x must be greater than 2, then:
[tex]\begin{gathered} 2\le x \\ \Rightarrow2\le(\frac{y+5}{4})^2+2 \\ \Rightarrow0\le(\frac{y+5}{4})^2 \\ \Rightarrow0\le|\frac{y+5}{4}| \\ \Rightarrow0\le|y+5| \end{gathered}[/tex]From here, there are two options:
[tex]\begin{gathered} 0\le y+5 \\ \Rightarrow-5\le y \\ \text{ Or} \\ 0\le-y-5 \\ \Rightarrow y\le-5 \end{gathered}[/tex]Since we know an equation for y, then:
[tex]\begin{gathered} -5\le-5+4\sqrt[]{x-2} \\ \Rightarrow0\le4\sqrt[]{x-2} \end{gathered}[/tex]Or:
[tex]\begin{gathered} -5+4\sqrt[]{x-2}\le-5 \\ \Rightarrow4\sqrt[]{x-2}\le0 \end{gathered}[/tex]The second case is not true for every x.
Therefore:
[tex]-5\le y[/tex]Therefore:
[tex]\begin{gathered} \text{Domain: }x\ge2 \\ \text{Range: }y\ge-5 \end{gathered}[/tex]Question 12 of 19 What is the solution to the system of equations graphed below? -5 y= x + 2 N 5 5 y = -2x - 4 -5 y = -2x - 4 y = x+2
Answers
For finding the solutions, you need to match the equations
[tex]\begin{gathered} x+2=-2x-4 \\ x+2x=-4-2 \\ 3x=-6 \\ x=-2 \end{gathered}[/tex]For the next step, you should replace the value for x in any of the equations given
y=x+2
y=-2+2
y=0
(-2,0) Letter a
what is the polar form of -3+sqrt3i
Answers
Solution
For this case we have the following number given:
[tex]-3+\sqrt[]{3}i[/tex]We can see that x = -3 and y = - sqrt(3)
The angle is given by:
[tex]\arctan (\frac{-\sqrt[]{3}}{3})=-30=-\frac{\pi}{6}[/tex]The radius would be:
[tex]r=\sqrt[]{(3)^2+(-\sqrt[]{3})^2}=\sqrt[]{12}[/tex]And the polar form would be given by:
[tex]z=\sqrt[]{12}(\cos (-\frac{\pi}{6})+i\sin (-\frac{\pi}{6}))\text{ }[/tex]Answer:
The answer is D!!
Step-by-step explanation:
Right on edg 2022
Solve the equation3x + 15 = 3(x + 5)
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Given the following equation:
[tex]3x+15=3\mleft(x+5\mright)[/tex]You must solve for "x" as following:
1. Apply the Distributive property:
[tex]\begin{gathered} 3x+15=(3)(x)+(3)(5) \\ 3x+15=3x+15 \end{gathered}[/tex]2. Observe the equation. You can notice that left side is equal to right side. If you try to solve for "x", you get:
[tex]\begin{gathered} 3x-3x=15-15 \\ 0=0 \end{gathered}[/tex]A mechanic has a length of hose 3 ft long. What is the length after 9in is cut off?The length is _ ft _ in?
Answers
ANSWER
[tex]2ft\text{ 3 in}[/tex]EXPLANATION
We want to find the length of the hose after 9 inches have been cut off.
First, convert the original length of the hose from feet to inches by multiplying by 12:
[tex]\begin{gathered} 1ft=12in \\ \Rightarrow3ft=3\cdot12in=36in \end{gathered}[/tex]Next, subtract 9 inches from that value:
[tex]\begin{gathered} 36-9 \\ \Rightarrow27in \end{gathered}[/tex]Finally, convert the length to feet by dividing by 12:
[tex]\begin{gathered} \frac{27}{12}ft \\ \Rightarrow2\frac{3}{12}ft \\ \Rightarrow2ft3in \end{gathered}[/tex]That is the answer.
In simplified radical form, the person can see how many miles?
Answers
We are given the equation:
[tex]d(x)=\sqrt{\frac{3x}{2}}[/tex]Where x is the height over the sea level, where d is in miles, and x in feet. We want to know the value of the function at x = 18 feet. Thus:
[tex]d(18)=\sqrt{\frac{3\cdot18}{2}}[/tex]We can now simplify by dividing 18 by 2:
[tex]d(18)=\sqrt{3\cdot9}[/tex]Now, using properties of radicals:
[tex]d(18)=\sqrt{3}\cdot\sqrt{9}=3\sqrt{3}[/tex]The answer in simplified radical form is:
[tex]d(18)=3\sqrt{3}\text{ }miles[/tex]Using the calculator, we can find the answer to the nearest tenth of a mile d(18)= 5.2 miles
Tavon and Raven are feeling backpacks for Arlington woods elementary Schoolthey have 24 boxes of markers 56 coloring books and 72 packages of modeling claywhich of the following are possible answers for the greatest number of backpacks they can fill if the markers books and clay are equally distributed
Answers
we have that
they have 24 boxes of markers 56 coloring books and 72 packages of modeling clay
so
24=(2^3)(3)
56=(2^3)(7)
72=(2^3)(3^2)
24/8=3
56/8=7
72/8=9
the number of backpacks is 8
therefore
teh answer is option B
There is a rectangular garden with an area of 24 square leel. The garden is 2 feet longer than it is wide. Create an equation that can be used to determine the length and wath of the garden
Answers
The equation that can be used to determine the length and width of the garden is x² + 2x - 24 =0, the length is 6 feet and the width is 4 feet.
There is a rectangular garden with an area of 24 square feet
The garden is 2 feet longer than it is wide
Let the width of the garden be x
Then, the length of the garden is x + 2
The area of a rectangular garden = length of the garden x width of the garden
24 = x (x + 2)
x² + 2x - 24 =0
x² + 6x - 4x - 24 = 0
x(x + 6) -4(x + 6) = 0
(x - 4)(x + 6) = 0
x - 4 = 0
x = 4
Width of the rectangular garden is 4 feet
Length of the rectangular garden is (4 + 2) feet = 6feet
Therefore, the equation that can be used to determine the length and width of the garden is x² + 2x - 24 =0, the length is 6 feet and the width is 4 feet.
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I don't understand how to do this problem. Could you explain to me how to do this problem? The formula for the perimeter of a rectangle is P=2l + 2w, where l is the length and w is the width. A rectangle has a perimeter of 24 inches. Find it's dimensions if it's length is 3 inches greater than it's width.
Answers
Given:
• Perimeter of the rectangle = 24 inches
,• The length is 3 inches greater than it's width.
Let's find the dimensions of the rectangle.
To find the dimensions, apply the formula for perimeter of a rectangle:
P = 2l + 2w
Where l is the length and w is the width.
Given that the length is 3 inches greater than the width, the length can be expressed as:
l = (w + 3) inches
Substitute 24 for P and (w + 3) for l in the formula:
P = 2l + 2w
24 = 2(w + 3) + 2w
Let's solve the equation for w:
24 = 2(w + 3) + 2w
APply distributive property:
24 = 2(w) + 2(3) + 2w
24 = 2w + 6 + 2w
Combine like terms:
24 = 2w + 2w + 6
24 = 4w + 6
Subtract 6 from both sides:
24 -6 = 4w + 6 - 6
18 = 4w
Divide both sides by 4:
[tex]\begin{gathered} \frac{18}{4}=\frac{4w}{4} \\ \\ 4.5=w \\ \\ w=4.5\text{ } \end{gathered}[/tex]The width of the rectangle is 4.5 inches.
Since the lengh is 3 inches greater than the width, add 3 to 4.5 inches to get the length of the rectangle.
l = w + 3
l = 4.5 + 3
l = 7.5
The length of the rectangle is 7.5 inches.
Therefore, the dimensions of the rectangle are:
Length = 7.5 inches
Width = 4.5 inches
ANSWER:
Length = 7.5 inches
Width = 4.5 inches
Find intervals of concavity and points of inflection of function y = x^4 - 6x + 2
Answers
SOLUTION:
Step 1:
In the question, we are given the following:
Find intervals of concavity and points of inflection of function
[tex]y\text{ = x }^4\text{ - 6 x + 2}[/tex]Step 2:
The details of the solution are as follows:
PART A:
Find intervals of concavity of function:
[tex]y\text{ = x}^4\text{ - 6 x + 2}[/tex]PART B:
Find the points of inflection of the function:
[tex]y\text{ = x}^4\text{ - 6 x + 2}[/tex]
3x +5= 2x +7How will the equation look if you subtract 2xfrom both sides?Click on the correct answer.5x +5= 7x+5=73x +5=7
Answers
If you subtract 2x from both sides of the equation you have:
[tex]\begin{gathered} 3x+5=2x+7 \\ 3x+5-2x=2x+7-2x \\ \text{ Operate similar terms} \\ x+5=7 \end{gathered}[/tex]Therefore, if you subtract 2x both sides, the equation will look like
[tex]x+5=7[/tex]Which of the terms cannot be combined with the others?ОЗху2x-5xОх
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0x cannot be combined with other terms
Because when it is combined it always results in 0.
PLEASE HELPFind the value of x.B68ХDx = [?]
Answers
Since the triangles are similar, that means the the prop
9. the product of c and 10
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SOLUTION
9. We want to find the product of c and 10.
Product means multiplication. So the product of c and 10 means
[tex]c\times10[/tex]So we bring 10 and c together, to get 10c.
Hence the answer is 10c
Find the area:*1 point8 in- .Your answerI
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Evaluate the function for the given value of x.p(x) = x2-9x, q(X) = VX-6,(p. q)(x) = ?
Answers
The functions are:
[tex]\begin{gathered} p(x)=x^2-9x \\ q(x)=\sqrt[]{x-6} \end{gathered}[/tex]So the product (p*q) is
[tex](p\cdot q)(x)=(x^2-9x)(\sqrt[]{x-6})[/tex]So the solution is is B)
ASAP Please help and ThankyouThis graph shows how the total distance jack has walked depends on the number of trips he has made to school. What is the rate of change?
Answers
we will take two points on the line,
first is (0,2) and other is (1, 4)
the rate of change will be the slope of the line,
[tex]\begin{gathered} m=\frac{4-2}{1-0} \\ m=\frac{2}{1}=2 \end{gathered}[/tex]so the rate of the change is 2 km per trip
so the answer is 2
Please Help. I will mark you BRAINLIST
Answers
Answer:
(D). f(x) = [tex]-\frac{3}{2}[/tex] x² + [tex]\frac{17}{2}[/tex] x - 7
Step-by-step explanation:
( x , y )
ax² + bx + c = y ............ ( 1 )
~~~~~~~~~~~~~~
( 2 , 4 ) --------> ( 1 )
a(2)² + b(2) + c = 4
4a + 2b + c = 4 .............. (2)
( 3 , 5 ) ---------> ( 1 )
a(3)² + b(3) + c = 5
9a + 3b + c = 5 ............... (3)
( 4 , 3 ) ----------> ( 1 )
a(4)² + b(4) + c = 3
16a + 4b + c = 3 .............. (4)
[tex]delta[/tex] = Δ = [tex]\left[\begin{array}{ccc}4&2&1\\9&3&1\\16&4&1\end{array}\right][/tex] = - 2
[tex]delta_{a}[/tex] = [tex]\left[\begin{array}{ccc}4&2&1\\5&3&1\\3&4&1\end{array}\right][/tex] = 3
[tex]delta_{b}[/tex] = [tex]\left[\begin{array}{ccc}4&4&1\\9&5&1\\16&3&1\end{array}\right][/tex] = - 17
[tex]delta_{c}[/tex] = [tex]\left[\begin{array}{ccc}4&2&4\\9&3&5\\16&4&3\end{array}\right][/tex] = 14
a = [tex]delta_{a}[/tex] / [tex]delta[/tex] = [tex]-\frac{3}{2}[/tex]
b = [tex]delta_{b}[/tex] / [tex]delta[/tex] = [tex]\frac{-17}{-2}[/tex] = [tex]\frac{17}{2}[/tex]
c = [tex]delta_{c}[/tex] / [tex]delta[/tex] = [tex]\frac{14}{-2}[/tex] = - 7
f(x) = [tex]-\frac{3}{2}[/tex] x² + [tex]\frac{17}{2}[/tex] x - 7 (D)
54. Foucault Pendulum
Foucault used a pendulum to demonstrate the Earth’s rotation. There are now over 30 Foucault pendulum displays in the United States. The Foucault pendulum at the Smithsonian Institution in Washington, DC, consists of a large brass ball suspended by a thin 52-ft cable. If the ball swings through an angle of 1°, how far does it travel?
Answers
The distance travelled by the ball is 0.9076 feet.
Foucault used a pendulum to demonstrate the earth’s rotation. There are now over 30 Foucault pendulum displays in the United States. The Foucault pendulum at the Smithsonian Institution in Washington, DC, consists of a large brass ball suspended by a thin 52-foot cable. The ball swings at an angle of 1°. We have to find the distance travelled by the ball.
The ball travels in a circular motion. The radius of the circle is equal to the length of the cable. The distance travelled by the ball is equal to the arc length traversed in circular motion. Let the radius, angle, and distance be denoted by the variables "r", "θ", and "d", respectively.
r = 52 feet
We need to convert the angle from degrees into radians.
θ = 1°
θ = 1°*(π/180°)
θ = π/180
The formula for arc length is used below to calculate the distance.
d = r*θ
d = 52*(π/180)
d = 0.9076
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1) Two integers have a sum of 47 and a difference of 23. Find the product of the numbers.
Answers
Given:
Two intergers have a sum of 47 and a difference of 23.
Let's find the product of the two numbers.
Let x and y represent the numbers.
We have:
Two integers have a sum of 47: x + y = 47
Two integers have a difference of 23: x - y = 23
We gave the system of equations:
x + y = 47.......................equation 1
x - y = 23.......................equation 2
Let's solve the system simultaneously using substitution method.
Rewrite equation 1 for x:
x = 47 - y
Substitute (47 - y) for x in equation 2:
(47 - y) - y = 23
47 - y - y = 23
47 - 2y = 23
Subtract 47 from both sides:
47 - 47 - 2y = 23 - 47
-2y = -24
Divide both sides of the equation by -2:
[tex]\begin{gathered} \frac{-2y}{-2}=\frac{-24}{-2} \\ \\ y=12 \end{gathered}[/tex]Now, substitute 12 for y in either of the equations.
Let's take equation 1.
x + y = 47
x + 12 = 47
Subtract 12 from both sides:
x + 12 - 12 = 47 - 12
x = 35
Therefore, we have:
x = 35, y = 12
The numbers are 35 and 12.
To find the product of the numbers, let's multiply the numbers:
35 x 12 = 420
Therefore, the product of the numbers is 420.
ANSWER:
420
5(y + 1) = 10 Submit Answer
Answers
5(y + 1) = 10 → 5y + 5 = 10
Now to subtract 5 on both sides:
5y + 5 = 10 → 5y = 5
Finally, we can divide by the coefficient:
5y = 5 → y = 1
Therefore, y = 1.
hi how are you I need help with this question.
Answers
Hello
Question one requires us to find the value of the angle
Using trigonometric ratios
SOHCAHTOA
[tex]\begin{gathered} \tan \theta=\frac{\text{opposite}}{\text{adjacent}} \\ \text{opposite}=8 \\ \text{adjacent}=10 \\ \tan \theta=\frac{8}{10} \\ \tan \theta=0.8 \\ \theta=\tan ^{-1}0.8 \\ \theta=38.66\approx38.7^0 \end{gathered}[/tex]For question b, we can use trigonometric ratio to find the value of the missing side or use pythagoran's theorem
I would use pythagoran's theorem here because we would arriave at our answer faster
[tex]\begin{gathered} x^2=y^2+z^2 \\ x^2=8^2+10^2 \\ x^2=64+100 \\ x^2=164 \\ \text{take the square root of both sides} \\ x=\sqrt[]{164} \\ x=12.81\approx12.8 \end{gathered}[/tex]From the calculations above, the value of the angle is 38.7 degree and the missing side is 12.8 units
Please help with this
Answers
Answer:
[tex]y = 100 - \frac{17}{3} x[/tex]
Here you go the visual explanation should be there for you, if your still confused i suggest asking your teacher for help on how to find the slope.
3. Given the picture below, find the value of x:
Answers
The value of x for the given triangle is 65°.
According to the question,
We have the following information:
A figure of triangle is given where two of its angles are 68° and 47°.
We know that the sum of all three angles of a triangle is 180°.
(More to know: all angles in an equilateral triangle are equal and in an isosceles triangle two angles are equal however the sum of three angles is 180°.)
So, we have the following expression:
x+68+47 = 180
x+115 = 180
x = 180-115
x = 65°
Hence, the value of x for the given triangle is 65°.
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Which relations are functions?Select Function or Not a function for each graph. FunctionNot a functionGraph of a line on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A line passes through the origin and the points begin ordered pair negative 2 comma negative 4 end ordered pair and begin ordered pair 2 comma 4 end ordered pair.Function –Not a function –The graph of a parabola on a coordinate plane. The x axis ranges from negative 5 to 5 in increments of 1. The y axis ranges from negative 5 to 5 in increments of 1. The vertex is located at begin ordered pair 1 comma 0 end ordered pair. The parabola opens upward. It passes through the vertical axis at begin ordered pair 0 comma 1 end ordered pair. It passes through begin ordered pair 2 comma 1 end ordered pair.Function –Not a function –An absolute value function graphed on a coordinate plane. The x axis ranges from negative 5 to 5 in increments of 1. The y axis ranges from negative 5 to 5 in increments of 1. The vertex is at the origin. The V-shaped graph passes through the points begin ordered pair 1 comma 1 end ordered pair and begin ordered pair 1 comma negative 1 end ordered pair.Function –Not a function –A circle on a coordinate plane centered at the origin, begin ordered pair 0 comma 0 end ordered pair. The circle passes through points begin ordered pair negative 2 comma 0 end ordered pair, begin ordered pair 0 comma negative 2 end ordered pair, begin ordered pair 2 comma 0 end ordered pair, and begin ordered pair 0 comma 2 end ordered pair.Function –Not a function –
Answers
SOLUTION
To identify or determine which relation in the graph is a function, we use the vertical line test.
The vertical line test explains that If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because that x-value has more than one output. A function has only one output value for each input value.
Hence, from the explanation above, we cam see that
Graph 1 is a Function
Graph 2 is a Function
Using similar approach
Graph 3 is not a function
Graph 4 is not a function