Represent geometrically the following numbers on the number line: √4.5 √8.3. (step by step explanation preferably done in notebook please) I’ll mark the best answer as brainliest
Answers
Answer:
To represent geometrically √x on a number line:
Draw a line segment AB with length x (where point A is -x and point B is zero on the number line).Extend AB by drawing a line segment BC of length 1 unit.Draw a line perpendicular to AC at point B.Let O be the midpoint of AC.Draw a semicircle with center O and radius OA.Let point D be where the semicircle intersects with the perpendicular line. BD = √xDraw an arc with center B and radius BD from point D to the number line.BE = √x ⇒ point E = √x on the number line.Attachment 1
To represent geometrically √4.5 on a number line:
Draw:
Point A = -4.5Point B = 0Point C = 1Draw a line perpendicular to AC at point B.
Let O be the midpoint of AC:
[tex]\implies \sf O=\dfrac{-4.5+1}{2}=-1.75[/tex]
Draw a semicircle with center O and radius OA
[tex]\implies \sf OA=\dfrac{AC}{2}=\dfrac{5.5}{2}=2.75[/tex]
Let point D be where the semicircle intersects with the perpendicular line
[tex]\implies \sf BD=\sqrt{AB}=\sqrt{4.5}[/tex]
Draw an arc with center B and radius BD from point D to the number line.
[tex]\implies \sf BE=\sqrt{4.5}[/tex]
⇒ Point E is [tex]\sf \sqrt{4.5}[/tex] on the number line.
Attachment 2To represent geometrically √8.3 on a number line:
Draw:
Point A = -8.3Point B = 0Point C = 1Draw a line perpendicular to AC at point B.
Let O be the midpoint of AC:
[tex]\implies \sf O=\dfrac{-8.3+1}{2}=-3.65[/tex]
Draw a semicircle with center O and radius OA
[tex]\implies \sf OA=\dfrac{AC}{2}=\dfrac{9.3}{2}=4.65[/tex]
Let point D be where the semicircle intersects with the perpendicular line
[tex]\implies \sf BD=\sqrt{AB}=\sqrt{8.3}[/tex]
Draw an arc with center B and radius BD from point D to the number line.
[tex]\implies \sf BE=\sqrt{8.3}[/tex]
⇒ Point E is [tex]\sf \sqrt{8.3}[/tex] on the number line.
Related Questions
ANOTHER BIG QUESTION, 100 POINTS
Write reciprocals, opposites, the same, or negative reciprocals in each blank.
The slopes of parallel lines are _.
The slopes of perpendicular lines are _.
Find the slopes of lines AB and CD. Show your work.
Line AB goes through points A(3, 4) and B(7, 7).
Line CD goes through points C(0, 0) and D(-6, 8).
Use Parts I and II to determine if AB and CD are parallel, perpendicular, or neither. Explain your answer.
Graph and on the grid to support your answer from Part III.
Answers
Answer:
The slopes of parallel lines are the same
The slopes of perpendicular lines are negative reciprocals
Line AB
[tex]\textsf{let}\:(x_1,y_1)=(3,4)[/tex]
[tex]\textsf{let}\:(x_2,y_2)=(7,7)[/tex]
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{7-4}{7-3}=\dfrac{3}{4}[/tex]
Line CD
[tex]\textsf{let}\:(x_1,y_1)=(0,0)[/tex]
[tex]\textsf{let}\:(x_2,y_2)=(-6,8)[/tex]
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{8-0}{-6-0}=-\dfrac{4}{3}[/tex]
As the slopes of AB and CD are negative reciprocals of each other, lines AB and CD are perpendicular.
The taylor series about x=5 for a certain function converges
Answers
The evaluation of the function [tex]f(x)=e^x[/tex] at a=0 and x=5 by the taylor series will have a value 65.37.
What is taylor's series?We know the fromula of taylor series is given as:
[tex]f(x)=f(a)+\dfrac{f'((a)}{1!}(x-a)+\dfrac{f''(a)}{2!}(x-a)^2+\dfrac{f'''(a)}{3!}(x-a)^3.................[/tex]
Now for the function [tex]f(x)=e^x[/tex] the taylor's series will become.
[tex]f(x)=e^a+e^ax+\dfrac{e^ax^2}{2!}+\dfrac{e^ax^3}{3!}+\dfrac{e^ax^4}{4!}[/tex]
[tex]f(x)=1+x+\dfrac{x^2}{2!}+\dfrac{x^3}{3!}+\dfrac{x^4}{4!}[/tex]
So at x=5 the values will become
[tex]f(x)=1+5+12.5+20.83+26.04=65.37[/tex]
hence the evaluation of the function [tex]f(x)=e^x[/tex] at a=0 and x=5 by the taylor series will have a value 65.37.
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Find the value of p .
A. 15
B. 3
C. 30
D. 28
Answers
Answer:
7p+7=37-3p
10p=30
p=3
answer : p=3 because ke=be
simplify 5^-4/5^4 help me please
Answers
Answer:
[tex]5^{-8}[/tex]
Step-by-step explanation:
Exponent law:[tex]\sf \boxed{\dfrac{a^{m}}{a^n}=a^{m-n}}[/tex]
[tex]\sf \dfrac{5^{-4}}{5^{4}}=5^{-4-4}[/tex]
[tex]= 5^{-8}[/tex]
She is serving hot coffee and cold coffee in two rectangular-shaped tanks, each with dimensions width 8.75 inches, length 8.75 inches, height 23 inches.
The hot coffee has a density of 5.8 oz/in3 and the cold coffee has a density of 3.5 oz/ in3
(A) What is the volume of the coffee in each tank?
Show all math work needed to complete this problem.
(B) What is the mass of the coffee in each the tank?
Show all math work needed to complete this problem.
(C) How many tanks can be placed on a table which can support a maximum weight of 800 lb?
Explain why or why not.
Show all math work needed to complete this problem.
Answers
The volume of the coffee in each tank will be 1760. in³. The mass of cold coffee and hot coffee will be 6163.29 oz and 10213.45 oz. Then the number of the tank placed on a table is one only.
How to find the density and volume?She is serving hot coffee and cold coffee in two rectangular-shaped tanks, each with dimensions width of 8.75 inches, a length of 8.75 inches, and a height of 23 inches.
The hot coffee has a density of 5.8 oz/in³ and the cold coffee has a density of 3.5 oz/ in³.
Then the volume of the coffee in each tank will be
We know that the dimension of both tanks is equal. Then the volume will remains equal.
Volume = L × B × H
Volume = 8.75 × 8.75 × 23
Volume = 1760.9375 ≅ 1760.94 in³
Then the mass of the coffee in each the tank will be
The mass of hot coffee will be
Mass = Density × Volume
Mass = 5.8 × 1760.94
Mass = 10213.45 oz
The mass of cold coffee will be
Mass = Density × Volume
Mass = 3.5 × 1760.94
Mass = 6163.29 oz
Then the number of the tank placed on a table is one only.
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Which set of order pairs does not represent a function?
A. {(−2,−6),(0,−4),(1,9),(3,−4)}
B. {(4,3),(−4,−8),(5,3),(−5,4)}
C. {(−6,−2),(6,2),(−7,−4),(−7,−3)}
D. {(0,−4),(−6,9),(7,5),(2,5)}
Answers
If f(x) = x2 is compared to g(x) = 2x2, how would the graphs be different?
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g(x) = 2x^2
Substituting x^2 with f(x)
g(x) = 2f(x)
Therefore, the values of g(x) are 2 times that of f(x)
For the same values of x, g(x) is 2 times greater than f(x)
39 and 25 same setup as the problem to the left. Fill in the blanks
Answers
The rangers at two park stations spot a signal flare at the same time. Based on the measurements shown in the diagram, what is the distance between park station 1 and the point where the flare was set off? Round to the nearest tenth.
Answers
The distance between park station 1 and the point where the flare was set off is 73.9 km.
What is distance?Distance is the length between two points expressed in meters or kilometers.
To calculate the distance between park station 1 and the point where the flare was set off can be calculated using Sine Rule
Formula:
a/sinA = b/sinB....................... Equation 1Where:
a = Distance between park station 1 and the point where the flare was set off.Make a the subject of the equation
a = bsinA/sinB............ Equation 2From the diagram,
Given:
A = 59°B = (180-59-75) = 46°b = 6.2 kmSubstitute these values into equation 2
a = 6.2(sin59°)/(sin46°)a = 73.9 kmHence, the distance between park station 1 and the point where the flare was set off is 73.9 km.
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PLS HELP!!! BRAINLY UP FOR GRABS!!! what are triangles with same angles but varying side lengths called??
Answers
Answer:
Congruent triangles
Or
Similar triangles
4n^2-15n-25 factor trinomials pls help me on this i would love if you would put the steps too thank you
Answers
---Multiply a x c
Quadratic Form: ax^2 + bx + c
4 x -25 = -100
---Find a factor pair of -100 that adds up to -15
-20 x 5 = - 100
-20 + 5 = -15
---Separate the b term into your two factors
4n^2 + 5n - 20n - 25
This can take some trial and error (though there are only two options) because when you factor, you want the inside of the parentheses to be the same. If you look at the next step, (4n + 5) appears twice.
---Factor each binomial
n(4n + 5) - 5 (4n + 5)
---Rewrite
(n - 5)(4n + 5)
What you're really doing here is factoring out the (4n + 5), which leaves you with the terms that you factored out in the previous step. You then combine these terms into one set of parenthesis.
Answer: (n - 5)(4n + 5)
Hope this helps!
Please help!!!
Give clear explanation for questions
Answers
Answer:
See below ~
Step-by-step explanation:
Finding the distance of each side length :
AB = √(3 - 0)² + (0 - 4)² = √9 + 16 = √25 = 5BC = √(7 - 3)² + (3 - 0)² = √16 + 9 = 5CD = √(4 - 7)² + (7 - 3)² = √9 + 16 = 5DA = √(4 - 0)² + (7 - 4)² = √16 + 9 = 5All sides are equalHence, it is a squarePerimeter :
4 x side length4 x 520 unitsArea :
(side length)²(5)²25 square unitsAnswer:
Step-by-step explanation:
Hunh put 4000 in a savings account that earns 7% simple inerest annually after 5 years, how much money will hunh have ?
Answers
Answer:
5,400.00
Step-by-step explanation:
hope this helps
The lines shown below are perpendicular. If the green line has a slope of 2/5, what is the slope of the red line?
A. - 2/5
B. - 5/2
C. 5/2
D. 2/5
Answers
an apartment company has 2 buildings. each building has 3 floors. each floor has 16 windows how many windows are there in total
Answers
In total there are 96 window
Explanation:
I’ve attached my work
(Don’t mind my terrible drawing :o )
the area of the triangle below is 29.25 square centimeters the height is 6.5. what is the length of the base?
Answers
Answer: 9
Step-by-step explanation:
½bh = 29.25
½ × 6.5 × b = 29.25
B= 29.25/ 3.25
The length of the base of the triangle is 9 centimeters.
What is the base length of the triangle?The area of a triangle is simply expressed as half base multiplied by height.
Area A = 1/2 × base length × height
Given the dimensions of the triangle:
Area A = 29.25 square centimeters
Height = 6.5 centimeters
Base length =?
To find the height of the triangle, plug the given values into the above formula and solve for h:
Area A = 1/2 × base length × height
29.25 = 1/2 × base length × 6.5
29.25 = base length × 3.25
Base length = 29.25 / 3.25
Base length = 9 cm.
Therefore, the base length measures 9 centimeters.
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Solve for k
18 = -k + 3
Answers
[tex] \Large{\boxed{\sf k = -15}} [/tex]
[tex] \\ [/tex]
Explanation :Given equation:
[tex] \sf 18 = -k + 3 [/tex]
[tex] \\ [/tex]
Subtract 3 from both sides:
[tex] \sf 18 - 3 = -k + 3 - 3 \\ \\ \sf 15 = -k [/tex]
[tex] \\ [/tex]
Divide each side by -1:
[tex] \sf \dfrac{15}{-1} = \dfrac{-k}{-1} \\ \\ \\ \boxed{\boxed{\sf k = -15}} [/tex]
[tex] \\ \\ [/tex]
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Two bags of grass seed cover 1,500 square feet of
ground. If Mitch's front yard is 1,850 square feet and his
back yard is 5,635 square feet, how many bags of
grass seed would he need to buy to completely cover
his front and back yard?
Answers
Answer:
10 bags
Step-by-step explanation:
help due today this might be confusing but try to answer
Answers
Answer:
56
Step-by-step explanation:
25 times 4 = 100
14 times 4 = 56
A triangle has a base that is 19 inches long, and a height of 12 inches. What is the area of the triangle?
Answers
Answer:
[tex]144[/tex] [tex]inches^2[/tex]
Step-by-step explanation:
Hey there!
In order to find the area of a triangle, you need to:
Multplipy the base by the height
Then you take that product and multiply it by 1/2 (basically divide it by 2)
Then you get your area!
Base: 19
Height: 12
19 x 12
228
228 x 1/2
228/2
114
So the area of this triangle is [tex]144[/tex] [tex]inches^2[/tex]
Keshawn is taking a multiple choice test with a total of 40 points available. Each question is worth exactly 2 points. What would be Keshawn's test score (out of 40) if he got 6 questions wrong? What would be his score if he got xx questions wrong?
Answers
Answer:
28
Step-by-step explanation:
each question is worth 2 points and he missed 6,6 times 2 is 12.therefore you subtract 40 by 12 and get 28 :)
Can someone please help me with this?
During elementary school, Malik received a weekly allowance of $16 for completing all of his chores. These days he receives 25% more. What is Malik's weekly allowance now?
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the perimeter of an equilateral triangle is 6cm find its area
Answers
Answer:
√3 cm
or
1.73 cm to the nearest hundredth.
Step-by-step explanation:
Each side must be 2 cm long
Using Heron's formula
Area = √(s(s-a)(s-b)(s-c) where s = semi-perimeter, a , b and c are the 3 side lengths.
So here s = 6/2 = 3 and all the sides = 2 so
Area = √(3(3-2)^3
= √3 cm.
create an expression equivalent to 4 (2x-3) -3x
Answers
You would multiply 4 by 2x and then -3.
You would end up with 8x-12-3x
Once combined, you would end up with 5x-12
Which figure repeats in the tessellation shown below?
A
B
C
D
A. Figure A
B. Figure C
C. Figure B
D. Figure D
Answers
Answer:
D. Figure
Step-by-step explanation:
Because it go's black cream black cream and D is the only one that shows that
Hope This Helped
The correct figure for repeats in the tessellation shown is shown in
''Option D''.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
The tessellation shown in image.
Now, By figure of the tessellation shown we get;
Figure shown in option D is figure for repeats in the tessellation
Thus, The correct figure for repeats in the tessellation shown is shown in
''Option D''.
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helpppppp adappppppppppp
Answers
Answer:
MEAN = 14 (AS PER ESTIMATION)
MEDIAN = 17
Step-by-step explanation:
Mean=Sum of terms/No.of terms
Then,
→13+16+14+17+17+8+16/ = 101/7 = 14.428571....…
Given, there is a chance to estimate,Thus, The mean is 14 as per estimation.And.....Median = The middle number
= 17
ThankYouYou flip a coin and use a random numer generator to generate a number 1 to 8. What is the probability that the coin shows tails and is the number 2
Answers
probability of getting a tail , PA = 1/2
probability of gettin a number 2 , PB = 1/8
now ,
the probability to get tail and 2 = PA x PB = 1/2 x 1/8 = 1/16.
hence it's the answer.
By : Modern Einstein
A box contains a total of 30 paper clips with colors in the ratio red:white:blue = 2:5:3. Suppose that one paper clip of each color is removed from the box and not replaced. What is the probability that the next paper clip chosen will be blue?
A: 5/27
B: 2/7
C: 8/27
D: 3/10
Answers
Answer:
C.8/27
Step-by-step explanation:
URGENT: (TIMED) Determine the equation of the circle graphed below.
Answers
Answer:
[tex](x-3)^2 + (y-2)^2 = 16[/tex]
Step-by-step explanation:
This is because the centre is at (3,2) and the radius of the circle is 4 and you square all the terms to find the equation of the circle.
When an integer m is divided by 5, the remainder is 3. When m is divided by 7, the remainder is 1. If m is greater than 40 but less than 80, what is one possible value of m.
Answers
Answer:
Possible value of m is 14
Step-by-step explanation:
