Answers
We have the given indefinite integral ;
[tex]{:\implies \quad \displaystyle \sf \int \dfrac{x+1}{x(xe^{x}+2)}dx}[/tex]
We will use substitution hence to solving this integral
Now , put ;
[tex]{:\implies \quad \sf e^{x}=u}[/tex]
So that :
[tex]{:\implies \quad \sf dx=\dfrac{du}{u}\quad and\quad log(u)=x}[/tex]
Now , putting the values in the integral , it can be written as ;
[tex]{:\implies \quad \displaystyle \sf \int \dfrac{log(u)+1}{log(u)\{ulog(u)+2\}}\times \dfrac{du}{u}}[/tex]
Now , we will again use substitution method for making the integral easy. So put ;
[tex]{:\implies \quad \displaystyle \sf ulog(u)+2=v}[/tex]
So that ;
[tex]{:\implies \quad \displaystyle \sf du=\dfrac{dv}{log(u)+1}\quad and\quad ulog(u)=v-2}[/tex]
Now , we have ;
[tex]{:\implies \quad \displaystyle \sf \int \dfrac{\cancel{\{log(u)+1\}}}{log(u)v}\times \dfrac{dv}{\cancel{\{log(u)+1\}}u}}[/tex]
[tex]{:\implies \quad \displaystyle \sf \int \dfrac{dv}{v\{ulog(u)\}}}[/tex]
Now , putting the value of ulog(u) = v - 2
[tex]{:\implies \quad \displaystyle \sf \int \dfrac{dv}{v(v-2)}}[/tex]
Now , using partial fraction decomposition , ths given integral can be further written as ;
[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{2}\int \left(\dfrac{1}{v-2}-\dfrac{1}{v}\right)dv}[/tex]
Now ,as integrals follow distributive property. So ;
[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{2}\left(\int \dfrac{1}{v-2}dv-\int \dfrac{1}{v}dv\right)}[/tex]
[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{2}(log|v-2|-log|v|)+C}[/tex]
[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{2}log\bigg|\dfrac{v-2}{v}\bigg| +C}[/tex]
Putting value of v ;
[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{2}log\bigg|\dfrac{ulog(u)+2-2}{ulog(u)+2}\bigg| +C}[/tex]
Now, putting value of u ;
[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{2}log\bigg|\dfrac{e^{x}log(e^{x})}{e^{x}log(e^{x})+2}\bigg| +C}[/tex]
[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{2}log\bigg|\dfrac{xe^{x}}{xe^{x}+2}\bigg| +C}[/tex]
[tex]{:\implies \quad \therefore \displaystyle \underline{\underline{\int \bf \dfrac{x+1}{x(xe^{x}+2)}dx=\dfrac{1}{2}log\bigg|\dfrac{xe^{x}}{xe^{x}+2}\bigg| +C}}}[/tex]
Used Concepts :- [tex]{\boxed{\displaystyle \bf \int \dfrac{1}{x}dx=log|x|+C}}[/tex][tex]{\boxed{\displaystyle \bf \dfrac{d}{dx}(u\cdot v)=v\dfrac{du}{dx}+u\dfrac{dv}{dx}}}[/tex][tex]{\boxed{\displaystyle \bf log(a)-log(b)=log\left(\dfrac{a}{b}\right)}}[/tex] [tex]{\boxed{\displaystyle \bf log(a^b)=blog(a)}}[/tex] [tex]{\boxed{\displaystyle \bf \dfrac{d}{dx}\{log(x)\}=\dfrac{1}{x}}}[/tex] [tex]{\boxed{\displaystyle \bf \dfrac{d}{dx}(e^x)=e^{x}}}[/tex]Related Questions
PLS HELP!! (40PTS.) (PRE-CALCULUS)
Answers
Step-by-step explanation:
All of these vectors are in DE Moviere Form, so let put them in Vector notation
To this this, multiply the modulus by the exact values of trig functions,
So using this, Vector u
[tex]u= 3j + 3 \sqrt{3} i[/tex]
Vector V
[tex]v = 2 \sqrt{2} j - 2 \sqrt{2} i[/tex]
Vector W
[tex]w = - 6 \sqrt{3}j + 6i[/tex]
So know we can compete the parts.
For Part A:
We first multiply the vector U by -7 then multiply that by v.
[tex] - 7u = - 21j - 21 \sqrt{3} j[/tex]
Know we do cross product
[tex] - 7u(v) = ( - 21j - 21 \sqrt{3} i)(2 \sqrt{2} j \: + 2 \sqrt{2} i[/tex]
First, multiply the j componets.
Then, do the I componets and then add the product together.
[tex] - 42 \sqrt{2} j - 42 \sqrt{6} i[/tex]
So the answer to part A is the vector above.
Part B:
Let first find the dot product of u and w.
First, the cross product of u and w is
[tex] - 18 \sqrt{3} j + 18\sqrt{3} i[/tex]
The magnitudes of each respective vector is
6 and -12. So if we use dot product formula
[tex] \cos( \alpha ) = \frac{xy}{ |x| |y| } [/tex]
So we get
[tex] \cos( \alpha ) = \frac{ - 18 \sqrt{3} + 18 \sqrt{3} }{ - 72} [/tex]
[tex] \cos(a) = \frac{0}{ - 12} [/tex]
[tex] \cos(a) = 0[/tex]
[tex]a = \frac{\pi}{2} [/tex]
Since the angle is pi/2, the vectors are orthogonal.
Answer:
correct
Step-by-step explanation:
Find the missing value.
Hint: Use the number line to find the missing value.
-3=7-?
Answers
Answer:
X = 10
Step-by-step explanation:
-3=7-x
-7 -7
-10=-x
10=x
A pair of jeans cost £40 there is a discount of 15% on everything In the shop how much do the jeans cost after the discount
Answers
Answer:
34 Euros
Step-by-step explanation:
15% of 40 is 6.
40 minus 6 = 34
[tex][Hello,BrainlyUser][/tex]
Answer:
£34
Step-by-step explanation:
Given:
A pair of jeans cost £40
Discount of 15%
Question:
How much do the jeans cost after the discount
Solve:
£40 x 15% =6
£40 - 6 = 34
Hence, Jeans cost £34 after the discount
[CloudBreeze]
Please help
Use the distributive property to fill in the blanks below. 9x(7-2)=(_x7)-(_x2)
Answers
Answer:
9x(7-2)=(9x7)-(9x2)
Step-by-step explanation:
You're just multiplying 9 by the numbers inside the parenthesis... I hope this helps you :)
Evaluate the integral. (Use C for the constant of integration.)
2x^2+ 5x + 2/(x² + 1)2 dx
Answers
Answer:
[tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = 2 \arctan x - \frac{5}{2(x^2 + 1)} + C[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Derivative Rule [Basic Power Rule]:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Integration
IntegralsIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Integration Method: U-Substitution
Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx[/tex]
Step 2: Integrate Pt. 1
[Integrand] Rewrite [Factor]: [tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = \int {\frac{2(x^2 + 1) + 5x}{(x^2 + 1)^2}} \, dx[/tex]Rewrite [Integration Property - Addition/Subtraction]: [tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = \int {\frac{2(x^2 + 1)}{(x^2 + 1)^2}} \, dx + \int {\frac{5x}{(x^2 + 1)^2}} \, dx[/tex][Left Integral] Simplify: [tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = \int {\frac{2}{x^2 + 1}} \, dx + \int {\frac{5x}{(x^2 + 1)^2}} \, dx[/tex][Integrals] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = 2 \int {\frac{1}{x^2 + 1}} \, dx + 5 \int {\frac{x}{(x^2 + 1)^2}} \, dx[/tex][Left Integral] Trigonometric Integration: [tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = 2 \arctan x + 5 \int {\frac{x}{(x^2 + 1)^2}} \, dx[/tex]Step 3: Integrate Pt. 2
Identify variables for u-substitution for the remaining integral.
Set u: [tex]\displaystyle u = x^2 + 1[/tex][u] Differentiate [Derivative Properties and Rules]: [tex]\displaystyle du = 2x \ dx[/tex]Step 4: Integrate Pt. 3
[Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = 2 \arctan x + \frac{5}{2} \int {\frac{2x}{(x^2 + 1)^2}} \, dx[/tex][Integral] U-Substitution: [tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = 2 \arctan x + \frac{5}{2} \int {\frac{1}{u^2}} \, du[/tex]Apply Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = 2 \arctan x + \frac{5}{2} \bigg( \frac{-1}{u} \bigg) + C[/tex][u] Back-substitute: [tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = 2 \arctan x + \frac{5}{2} \bigg( \frac{-1}{x^2 + 1} \bigg) + C[/tex]Simplify: [tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx = 2 \arctan x - \frac{5}{2(x^2 + 1)} + C[/tex]∴ the integration of the given integral [tex]\displaystyle \int {\frac{2x^2 + 5x + 2}{(x^2 + 1)^2}} \, dx[/tex] is equal to [tex]\displaystyle \bold{2 \arctan x - \frac{5}{2(x^2 + 1)} + C}[/tex].
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Learn more about integration: https://brainly.com/question/21023287
Learn more about calculus: https://brainly.com/question/23558817
---
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
The radius of the wheel is 11 inches. What is the diameter of the wheel?
Answers
Answer:
22 inches
Step-by-step explanation:
Diameter = 2*radius = 2(11) = 22 inches
copy machine makes 253 copies in 5 minutrs 45 seconds . How many per minute?
Answers
Answer:
46 copies I guess
Step-by-step explanation:
253÷5.45 =46
Correct me if i wrong
Answer:
46.422
Step-by-step explanation:
The answer is 46.422 because it's asking for how many copies per minute. And since we know there are 253 copies, we will divide 253 by 5.45. When you divide those you get 46.422
Consider the work sample and statements below. Select ALL that apply.
Answers
Answer:
A, B, D, F
Step-by-step explanation:
The work of solving the standard-form equation that is the difference of squares is properly shown except for Line 4. Statement [F] correctly describes the proper solution, which results in the solution set shown in Statement [B].
The first step was necessary to put the equation into standard form (Statement [D]). That form is the difference of squares (Statement [A]).
The statements that correctly describe the work are A, B, D, F.
what is 5a + 2/3= -1/6 with two step equations fractions
Answers
Answer:
-1/6
Step-by-step explanation:
5a+2/3=-1/6
5a=-1/6-2/3
5a=-1/6-4/6
5a=-5/6
a=(-5/6)/5
a=(-5/6)(1/5)
a=-5/30
simplify
a=-1/6
Glen needs at least $225 for a new audio system. She he already saved $90. He earns $15 per hour at his part-time job. Write and solve an inequality to find how many hours he will need to work to buy the system.
Answers
Answer:
90+15x=225
Step-by-step explanation:
90 already saved plus 15 an hour equals 225
Find the 40th term 360,353,346,...
Answers
Answer:
87
Step-by-step explanation:
First method:
- Open Excel and enter 360, 353 and 346 in column A (below each other)
- Select all 3 cells and drag the bottom-right square down to row 40.
Second method:
- Use the equation t(n) = 360-7(n-1)
- Solve for n=40
- t(40) = 360 - 7*39 = 87
Find the equation of the line having a slope of 4 and a y-intercept on (0,3)
Answers
[tex]\mathbb{FINAL\:ANSWER:}[/tex]
[tex]\huge\boxed{\sf{y=4x+3}}[/tex]
[tex]\mathbb{SOLUTION\:WITH\:STEPS:}[/tex]
Hi! Hope you are having a nice day!
We are given the slope of the line and its y-intercept.
So, let's find the equation.
The y-intercept is written in the form (0, b).
No worries! b is the y-intercept.
Thus, the y-intercept equals 3.
Now, let's find the equation of the line with a slope of 4 and a y-intercept of 3.
We can write the equation in Slope-intercept form:
y=mx+b, where m stands for the slope and b stands for the y-intercept.
Since we have both m and b, we can just plug the given values:
y=4x+3 ✓
Hope you could understand everything.
#CarryOnLearning
Find the average rate of change of the function between the given values of x.
y = -5x - x^2 between x = -5 and x = 7
Answers
Answer:
Use integrals to find the area between the curves.
32
3
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Point Form:
(
0
,
0
)
,
(
4
,
4
)
Equation Form:
x
=
0
,
y
=
0
x
=
4
,
y
=
4
To find the volume of the solid, first define the area of each slice then integrate across the range. The area of each slice is the area of a circle with radius
f
(
x
)
and
A
=
π
r
2
.
V
=
π
∫
4
0
(
f
(
x
)
)
2
−
(
g
(
x
)
)
2
d
x
where
f
(
x
)
=
−
x
2
+
5
x
and
g
(
x
)
=
x
Simplify the integrand.
Tap for more steps...
V
=
x
4
−
10
x
3
+
24
x
2
Split the single integral into multiple integrals.
V
=
π
(
∫
4
0
x
4
d
x
+
∫
4
0
−
10
x
3
d
x
+
∫
4
0
24
x
2
d
x
)
By the Power Rule, the integral of
x
4
with respect to
x
is
1
5
x
5
.
V
=
π
(
1
5
x
5
]
4
0
+
∫
4
0
−
10
x
3
d
x
+
∫
4
0
24
x
2
d
x
)
Combine
1
5
and
x
5
.
V
=
π
(
x
5
5
]
4
0
+
∫
4
0
−
10
x
3
d
x
+
∫
4
0
24
x
2
d
x
)
Since
−
10
is constant with respect to
x
, move
−
10
out of the integral.
V
=
π
(
x
5
5
]
4
0
−
10
∫
4
0
x
3
d
x
+
∫
4
0
24
x
2
d
x
)
By the Power Rule, the integral of
x
3
with respect to
x
is
1
4
x
4
.
V
=
π
(
x
5
5
]
4
0
−
10
(
1
4
x
4
]
4
0
)
+
∫
4
0
24
x
2
d
x
)
Combine
1
4
and
x
4
.
V
=
π
(
x
5
5
]
4
0
−
10
(
x
4
4
]
4
0
)
+
∫
4
0
24
x
2
d
x
)
Since
24
is constant with respect to
x
, move
24
out of the integral.
V
=
π
(
x
5
5
]
4
0
−
10
(
x
4
4
]
4
0
)
+
24
∫
4
0
x
2
d
x
)
By the Power Rule, the integral of
x
2
with respect to
x
is
1
3
x
3
.
V
=
π
(
x
5
5
]
4
0
−
10
(
x
4
4
]
4
0
)
+
24
(
1
3
x
3
]
4
0
)
)
Simplify the answer.
Tap for more steps...
V
=
384
π
5
The result can be shown in multiple forms.
Exact Form:
V
=
384
π
5
Decimal Form:
V
=
241.27431579
…
image of graph
To find the volume of the solid, first define the area of each slice then integrate across the range. The area of each slice is the area of a circle with radius
f
(
x
)
and
A
=
π
r
2
.
V
=
π
∫
4
0
(
f
(
x
)
)
2
−
(
g
(
x
)
)
2
d
x
where
f
(
x
)
=
−
x
2
+
5
x
and
g
(
x
)
=
x
Simplify the integrand.
Tap for more steps...
V
=
x
4
−
10
x
3
+
24
x
2
Split the single integral into multiple integrals.
V
=
π
(
∫
4
0
x
4
d
x
+
∫
4
0
−
10
x
3
d
x
+
∫
4
0
24
x
2
d
x
)
By the Power Rule, the integral of
x
4
with respect to
x
is
1
5
x
5
.
V
=
π
(
1
5
x
5
]
4
0
+
∫
4
0
−
10
x
3
d
x
+
∫
4
0
24
x
2
d
x
)
Combine
1
5
and
x
5
.
V
=
π
(
x
5
5
]
4
0
+
∫
4
0
−
10
x
3
d
x
+
∫
4
0
24
x
2
d
x
)
Since
−
10
is constant with respect to
x
, move
−
10
out of the integral.
V
=
π
(
x
5
5
]
4
0
−
10
∫
4
0
x
3
d
x
+
∫
4
0
24
x
2
d
x
)
By the Power Rule, the integral of
x
3
with respect to
x
is
1
4
x
4
.
V
=
π
(
x
5
5
]
4
0
−
10
(
1
4
x
4
]
4
0
)
+
∫
4
0
24
x
2
d
x
)
Combine
1
4
and
x
4
.
V
=
π
(
x
5
5
]
4
0
−
10
(
x
4
4
]
4
0
)
+
∫
4
0
24
x
2
d
x
)
Since
24
is constant with respect to
x
, move
24
out of the integral.
V
=
π
(
x
5
5
]
4
0
−
10
(
x
4
4
]
4
0
)
+
24
∫
4
0
x
2
d
x
)
By the Power Rule, the integral of
x
2
with respect to
x
is
1
3
x
3
.
V
=
π
(
x
5
5
]
4
0
−
10
(
x
4
4
]
4
0
)
+
24
(
1
3
x
3
]
4
0
)
)
Simplify the answer.
Tap for more steps...
V
=
384
π
5
The result can be shown in multiple forms.
Exact Form:
V
=
384
π
5
Decimal Form:
V
=
241.27431579
…
y
=
3
x
+
4
,
[
2
,
3
]
y
=
3
x
−
2
,
(
0
,
4
)
y
=
√
x
,
[
1
,
4
]
Step-by-step explanation:
How can 10% of 45 be used to determine 30% of 45?
Enter your answers in the boxes to correctly complete the sta
10% of 45 is
so 30% of 45 is
Answers
Answer: 10% of 45 is 4.5
So 30% of 45 is 13.5
Step-by-step explanation:
I dont understand this question, i did the factor of 36x^2 - 49 but I dont understand the second part
Answers
Answer:
a = 6
b = 7
Step-by-step explanation:
Since both 36 and 49 are perfect squares, you can find their square roots which are 6 and 7.
To check to see if it is correct, replace the a with 6 and replace the b with 7, then evaluate the exponents.
Need help with Geometry math
problem #9
Answers
Answer:
Let ABC be a triangle such that CA is produced to meet at E.
We know, an exterior angle of a Triangle is equal to non- adjacent interior angle, so
8x - 10 = x + 15 + 2x + 20
or, 8x - 3x = 35 + 10
or, 5x = 45
or, x = 9
3. Explain why (x – 4)2 = -9 has no real solutions.
Answers
Answer:
an equation is said to have no real solutions when value of x < 0
Step-by-step explanation:
here,
(x-4) 2= -9
2x - 8 = -9
2x = -1
x = -1/2
which is less than 0
The equation (x – 4)² = -9 has no real roots.
What is the solution of a quadratic equation?The solution of a quadratic equation is the value of the variable for which the expression becomes true.
Given,
(x – 4)² = -9
The LHS of the equation is either positive or zero.
But, the RHS of the equation is a negative value.
Therefore, RHS and LHS can never be equal.
Hence, the equation (x – 4)² = -9 has no real roots.
To learn more about quadratic equations visit:
https://brainly.com/question/17177510
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AB of the right triangle ABC is twice the length of the leg BC. Find the number of degrees in angle ABC
Answers
Answer:
It is 45 degree angle
Step-by-step explanation:
AB is the tilted angle of the triangle
BC is the height and the vertical part of the triangle
If AB is 10 then BC is 5 and AC is possibly about 6-8
If that is so then 2 right triangles is a square
A square has 90 degree angles on any angle
Divide 90 by 2 which is 45 because a right triangle is half of a square
Therefore angle ABC is 45 degrees
two friends share 1/2 of a pizza equally. What fraction of the pizza does each friend get?
Answers
Answer:
1/4
Step-by-step explanation:
In this equation, from the beginning we know two things, that there are two people, and that the whole is 1/2
So we just have to divide! Use this equation whenever dealing with word problems like these and you’re stuck.
Amount of object (Pizza Size) divided by Number of Groups (People) = Amount of object in group
So our equation is 1/2 divided by 2
Calculate this and we will get our final answer of
1/4!
Hope this helped and please award brainliest!
Hello po ^^
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Complete answer = Brainliest
Perfect answer = Brainliest
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Nonsense answer = Report
Wrong answer = Report
Incomplete answer = Report
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Thank you!!
Answers
The order goes alphabetical by every second letter
J, (k) l, (m) n, so on
2.
The order goes backwards alphabetically
Instead of
q, r, s
It goes
s, r, q,
3.
The arrows move clockwise by 90 degrees
So first down then left then up then right and repeat
4.
up in number and up in letters alphabetical
so from 4 to 5 and a to b
4a, 5b so on
5.
Goes up by number of x’S
First 1x which is just x
Then 2x
Then 3x
And so on
You are buying carpet to cover a room that measures 42 ft by 42 ft. The carpet cost $ 25 per square yard. How much will the carpet cost?
Answers
Ok so, 42 ft. by 42 ft.
$25 per square yard
1 square yard = 9 square feet
The total square footage is 1,764 ft.
Total square yards is 196.
The total cost would be $4,900.
How to do this question
Answers
Answer:
b = 5
Step-by-step explanation:
Area of the triangle = b * 12/2 = 6b
Area of the rectangle = 9 * 12 = 108
Total area = 6b + 108 = 138
6b = 138 - 108 = 30
so b = 30/6 = 5
Which of the following choices are equivalent to the expression below? Check
all that apply.
318
A. (40)
B. x
c C. ()"
D. x
E. (88)
OF. (10)
Answers
Answer:
A
Step-by-step explanation:
because A is a Equivalent when you times it by 4
Please help its due on friday
Answers
Answer:
28 cups
Step-by-step explanation:
If 7 cups will only fill 1/4 of her pot, multiply 4 by 7 to get 28.
PLEASE MARK ME AS BRAINLIEST I REALLY WANT TO LEVEL UP
Lesson 4.10 - Analytic Geometry
1) Prove that the following is a square. You must show all of your
work and give a written explanation of why the figure is a square. (First picture)
2) Prove that the following is a right - isosceles triangle. You must
show all of your work and give a written explanation of why the
figure is a right-isosceles triangle.
(Isosceles Triangles are triangles with 2 equal sides.) second picture
Answers
Geometric shapes are mathematical shapes that include squares and triangles
How to prove the shape is a squareThe side lengths of a square are congruent, and the adjacent sides are perpendicular.
So, we start by calculating the side lengths using the following distance formula
[tex]d = \sqrt{(x_1 -x_2)^2 + (y_1 -y_2)^2}[/tex]
Using the above formula, we have:
[tex]AB = \sqrt{(3-2)^2 + (4+2)^2} = \sqrt{37[/tex]
[tex]BC = \sqrt{(2+4)^2 + (-2+1)^2} = \sqrt{37[/tex]
[tex]CD = \sqrt{(-4+3)^2 + (-1-5)^2} = \sqrt{37}[/tex]
[tex]DA = \sqrt{(-3-3)^2 + (5-4)^2} = \sqrt{37}[/tex]
The above shows that the side lengths of the square are congruent.
Next, calculate the slope of the sides using:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m_{AB} = \frac{4 +2}{3 -2} = 6[/tex]
[tex]m_{BC} = \frac{-2 + 1}{2+4} = -\frac 16[/tex]
[tex]m_{CD} = \frac{-1 -5}{-4+3} = 6[/tex]
[tex]m_{DA} = \frac{5 -4}{-3-3} = -\frac 16[/tex]
Notice that the opposite slopes are congruent, and the adjacent slopes are opposite reciprocal.
The above highlight, and the equal side lengths show that the figure (1) is a square
How to prove the shape is a right isosceles triangleThe legs of a right isosceles triangle are congruent, and the legs are perpendicular.
So, we start by calculating the lengths of the legs using the following distance formula
[tex]d = \sqrt{(x_1 -x_2)^2 + (y_1 -y_2)^2}[/tex]
Using the above formula, we have:
[tex]XY = \sqrt{(5-4)^2 + (-1-4)^2} = \sqrt{26[/tex]
[tex]XZ = \sqrt{(5-0)^2 + (-1+2)^2} = \sqrt{26[/tex]
The above shows that the legs of the right isosceles triangle are congruent.
Next, calculate the slope of the legs using:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m_{XY} = \frac{5-4}{-1 -4} = -\frac{1}{5}[/tex]
[tex]m_{XZ} = \frac{5-0}{-1+2} = 5[/tex]
Notice that the slopes are opposite reciprocal.
The above highlight, and the equal legs show that the figure (2) is a right isosceles triangle
Read more about geometric shapes at:
https://brainly.com/question/14285697
The following three shapes are based only on squares, semicircles, and quarter circles. Find the perimeter and the area of each shaded part. Give your answer as a completely simplified exact value in terms of π (no approximations).
Answers
57cm
because you get to subtract
6. A person mailing postcards earns a fixed amount for each postcard he mails,
and yesterday his average hourly wage was $14.00 an hour. If he worked 5 hours
yesterday and mailed 300 postcards, how much does he earn for each postcard
mailed?
Answers
Answer:
If he worked 5 hours and his rate is $14/hr, then he earned a total of $70.He mailed 300 postcard, so each postcard mailed is $0.2333
Step-by-step explanation:
mark me brainliest!!
Fresh Fruits sells 10 lemons for $2.50. What is the price for 1 lemon
Answers
Answer:
25 cents per lemon
Step-by-step explanation:
Simply divide
Answer:
See below
Step-by-step explanation:
When solving real world problems relating to unit price, divide the cost by the amount.
2.5/10
The unit price is 0.25.
-hope it helps
so basically i just need help on calculating a percentage of a number, for example 30% of 40 and stuff like that. please help asap :')
Answers
Answer:
Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. The formula used to calculate percentage is: (value/total value)×100%.
Step-by-step explanation:
Quadrilaterals LMNO and STUV are similar. What is the value of x in inches?
A. 27.1
B. 9.2
C. 22.9
D. 6.6
Answers
Answer:
D
Step-by-step explanation:
2.2 : x = 4.1 : 12.3
2.2/x = 4.1/12.3 = 1/3
so x = 2.2 * 3 = 6.6
D