Answers
Answer:
[tex]\frac{1}{3x+52}[/tex]
Step-by-step explanation:
Given
[tex]\frac{\frac{1}{x^2+51x+50} }{\frac{2}{x+50}+\frac{1}{x+1} }[/tex]
= [tex]\frac{\frac{1}{(x+50)(x+1)} }{\frac{2(x+1)+x+50}{(x+50)(x+1)} }[/tex]
= [tex]\frac{1}{(x+50)(x+1)}[/tex] × [tex]\frac{(x+50)(x+1)}{2x+2+x+50}[/tex] ← cancel (x + 50)(x + 1) on numerator/denominator
= [tex]\frac{1}{3x+52}[/tex]
Answer:
[tex]\Large\boxed{\sf \bf \ \ \dfrac{1}{3x+52} \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
We need to do something with that, right !?
[tex]\dfrac{\left(\dfrac{1}{x^2+51x+50\right)}}{\left(\dfrac{2}{x+50}+\dfrac{1}{x+1}\right)}[/tex]
What can we say from [tex]x^2+51x+50[/tex] ?
The sum of the zeroes is -51=(-1)+(-50) and the product is 50 = (-1) x (-50), so we can factorise. Let's do it !
[tex]x^2+51x+50=x^2+50x+x+50=x(x+1)+50(x+1)=(x+1)(x+50)[/tex]
That's a pretty cool first result !
Now, let's play with the denominator.
[tex]\dfrac{2}{x+50}+\dfrac{1}{x+1}\\\\\text{*** We put on the same denominator which is (x+1)(x+50) ***}\\\\=\dfrac{2(x+1)}{(x+50)(x+1)}+\dfrac{x+50}{(x+1)(x+50)}\\\\=\dfrac{2(x+1)+x+50}{(x+50)(x+1)}\\\\=\dfrac{2x+2+x+50}{(x+50)(x+1)}\\\\=\dfrac{3x+52}{(x+50)(x+1)}\\[/tex]
We are almost there.
Let's combine all these results together !
[tex]\dfrac{\left(\dfrac{1}{x^2+51x+50\right)}}{\left(\dfrac{2}{x+50}+\dfrac{1}{x+1}\right)}\\\\\\=\dfrac{\left(\dfrac{1}{(x+1)(x+50)\right)}}{\left(\dfrac{3x+52}{(x+50)(x+1)}\right)}}\\\\\\=\large\boxed{\dfrac{1}{3x+52}}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Related Questions
Driving on the highway, you can safely drive 60 miles per hour. "How far can you drive in ‘h' hours?" What is the range of the function which defines this situation? A. 60 B.The number of hours you drive C.The amount of gas you use D.The distance you drive
Answers
Answer:
D.The distance you drive
Step-by-step explanation:
If you describe this situation as function, then it will look as:
f(h)= 60hFor h=1 you have f(1)= 60 milesFor h=2 you have f(2)= 120 miles etc.The range of the function is the set of output values
In this case the range is the distance you drive
Correct option is D.
Answer:
The distance you drive
Step-by-step explanation:
i just took the test
I NEED HELP!! ASAP PLEASE!!!
Answers
Answer:
D
Step-by-step explanation:
a:angles given do not necessarily prove that ADP and BCP is 30 they can be different
c:angles given are not in triangles
b:with regards to the square I don't think you can really prove the statement
Find the area of the triangle. Round the answer to the nearest tenth. Triangle is SSA. a= 3.7 b= 3.7 β= 70° ----- A.4.4 square units B.5.2 square units C.6.8 square units D.8.8 square units
Answers
Answer:
A. 4.40 square units
Step-by-step explanation:
The triangle is isosceles with base angles of 70°. The a.pex angle will be ...
180° -2(70°) = 40°
The area of a triangle can be computed from two sides and the angle between them as ...
A = (1/2)ab·sin(γ)
A = (1/2)(3.7)(3.7)sin(40°) ≈ 4.40 . . . square units
∫1/(1+sinx^2 +2cos^2x)
Answers
Answer:
Im not sure, is this correct?
18.2 divided by 18 what’s the answer??
Answers
Answer:1.0111111111
Step-by-step explanation:
18.2 - 18 = .2-18 =1.0111111
How to do this question plz plz plz plz plz plz plz plz
Answers
Answer:
6.4 cmStep-by-step explanation:
Volume of cartoon = 5 cm × 8 cm × 15 cm
= 600 cm³
Volume of milk = 5 cm × 8 cm × 12 cm
= 480 cm³
Space = 600 cm³ - 480 cm³ = 120 cm³
Let depth be ' h '
15 × 5 × h = 480
Multiply the numbers
75h = 480
Divide both sides of the equation by 75
75 h / 75 = 480 / 75
Calculate
h = 6.4 cm
therefore, The depth of the milk is 6.4 cm
Hope this helps...
Best regards!!
Answer options:
1) f(x)= -(x+5)^3 (x-2)^2
2) f(x)= (x-5) (x-510) (x+2)
3) f(x)= (x+5)^3 (x-2)^2
4) f(x)= (x-5)^2 (x+2)^3
Answers
Answer:
1) f(X) = ( X+5 )^3 ( x-2 )^2
3. Daniel is a very good television salesperson. His annual sales average at $187,400. His
commission on sales is 30% and his annual base salary is $40,000. On average what is his
annual gross income?
Answers
Answer:
$96,220
Step-by-step explanation:
Daniel is a very good sales person
His annual sales average is $187,400
His commission on sales is 30%
= 30/100
= 0.3
His annual base salary is $40,000
Therefore, Daniel's annual gross income can be calculated as follows
Annual gross income= Annual base salary + Commission on sales
= $40,000 + (30/100 × $187,400)
= $40,000 + 0.3×$187,400
= $40,000+$56,220
= $96,220
Hence Daniel's annual gross income is $96,220
need HELP ON THIS A S AP !!!!!
Answers
Answer:
803.84yd²
Step-by-step explanation:
Surface Area of A Sphere: [tex]A=4\pi r^2[/tex]
We are given the radius of 8 yards.
Using 3.14 for pi:
[tex]A=4*3.14*8^2\\\\A=4*3.14*64\\\\A=12.56*64\\\\\boxed{A=803.84}[/tex]
The correct answer should be 803.84yd².
Brainilest Appreciated.
Answer:
803.84 yd^2
Step-by-step explanation:
4*3.14*8^2
12.56*64
803.84
brainliest pls
hope i helped
-ZYLYNN
lf a bus travels 6 km in 10 minutes, what distance does it travel in 1second
Answers
Answer:
0.01 kmStep-by-step explanation:
[tex]6\: km\: in \:10\: minutes\\First\:lets\:convert\:10\:min\:to\:seconds\\\\1\:minute \:\:\:\:=60\:seconds\\\\10\:minutes = x \:seconds\\\\x = 60\times 10\\x = 600seconds\\\\6km\: = 600\:seconds\\x\:km = 1 \:second\\\\Cross\:Multiply\\600x =6\\\frac{600x}{600} =\frac{6}{600} \\\\x = 1/100\\\\ =0.01km[/tex]
What is the image of E for a 120° counterclockwise rotation about the center of the regular hexagon?
Answers
Answer:
N
Step-by-step explanation:
Since this hexagon has six sides, and to end up back at E again we’d need to rotate 360°, this means for every side we cross it’s a 60° turn.
Therefore, [tex]60 \cdot 2 = 120[/tex]° would be two sides.
Since we are moving counter-clockwise, the image for E would be to the left of it.
Two sides/points to the left of E is N, so the image of E for a 120° counterclockwise rotation around the center of this shape would be N.
Hope this helped!
adi used algebra tiles to represent the product (-2x-2)(2x-1) which is true regarding axis use of algebra tiles
Answers
Answer:
She did not represent the two original factors correctly on the headers.
Step-by-step explanation:
Adi Algebra titles method is based on the field of values. In the given question the representation of of the product is not correct. The two negative titles must be in the top header so the correct sign in incorporated with the variables.
Answer:
A. She used the algebra tiles correctly.
Step-by-step explanation:
She represents each step of the equation with algebra tiles correctly, even if it could be simplified more.
Factor 1
Which expression is the factored form of
x2 - 7x + 10?
+x
-X
42
-
+
0 (x+3)(x + 4)
o (x - 3)(x - 4)
(x-2)(x - 5)
(x + 2)(x + 5)
ON
-
+
+
-X
Factor
+
+
-
+
+
LY
+
+
-
+
+
Reset
Intro
ODNO
Answers
Answer:
(x - 2)(x - 5)Step-by-step explanation:
[tex]x^2 - 7x + 10=\\\\=x^2 - 5x -2x + 10=\\\\=x(x-5)-2(x-5)=\\\\=(x-5)(x-2)[/tex]
Answer:
[tex]\boxed{(x-2)(x-5)}[/tex]
Step-by-step explanation:
=> [tex]x^2-7x+10[/tex]
Using mid-term break formula
=> [tex]x^2-5x-2x+10[/tex]
=> x(x-5)-2(x-5)
Taking (x-5) as common
=> (x-2)(x-5)
Can anyone help me with this question? Which reason justifies the conclusion that ∆PST ≅ ∆RST?
Answers
Answer:
A) SAS postulate
Step-by-step explanation:
Answer:
SAS
Step-by-step explanation:
you know that ST is equal and you also know two equal angles and one other equal side
Complete the proof of the Law of Sines/Cosines.
Given triangle ABC with altitude segment AD labeled x. Angles ADB and CDB are _____1._____ by the definition of altitudes, making triangle ABD and triangle BCD right triangles. Using the trigonometric ratios sine of B equals x over c and sine of C equals x over b. Multiplying to isolate x in both equations gives x = _____2._____ and x = b ⋅ sinC. We also know that x = x by the reflexive property. By the substitution property, _____3._____. Dividing each side of the equation by bc gives: sine of B over b equals sine of C over c.
Answer choices:
1. altitudes
2. b ⋅ sinB
3. b ⋅ sinB = c ⋅ sinC
1. right angles
2. b ⋅ sinB
3. b ⋅ sinB =c ⋅ sinB
1. altitudes
2. c ⋅ sinB
3. c ⋅ sinB = b ⋅ sinC
1. right angles
2. c ⋅ sinB
3. c ⋅ sinB = b ⋅ sinC
Answers
Corrected Question:
Complete the proof of the Law of Sines/Cosines.
Given triangle ABC with altitude segment AD labeled x. Angles ADB and CDA are _____1._____ by the definition of altitudes, making triangle ABD and triangle ACD right triangles. Using the trigonometric ratios sine of B equals x over c and sine of C equals x over b. Multiplying to isolate x in both equations gives x = _____2._____ and x = b ⋅ sinC. We also know that x = x by the reflexive property. By the substitution property, _____3._____. Dividing each side of the equation by bc gives: sine of B over b equals sine of C over c.
Answer:
(1) right angles
(2) c sin B
(3) c sin B = b sin C
Step-by-step explanation:
As shown in the diagram attached to this response,
(i) the given triangle is ABC with altitude segment AD labeled as x,
(ii) side AB is labeled as c, side AC is labeled as b, and
(iii) angles ADB and CDA are right angles by definition of altitudes.
(iv) Therefore, triangle ABD and CDA are right-angled triangles.
(v) Now, using trigonometric ratios, sine of B equals x over c. i.e
sin B = [tex]\frac{x}{c}[/tex] --------(i)
(vi) Also, sine of C equals x over b. i.e
sin C = [tex]\frac{x}{b}[/tex] ------------(ii)
(vii) Multiplying to isolate x in both equations gives;
x = c sin B [from equation (i)] ------------(iii)
x = b sin C [from equation (ii)] -----------(iv)
(viii) We know that x = x by the reflective property. i.e x in equation (iii) is equal to x in equation (iv). By substitution property, this becomes,
c sin B = b sin C -----------------(v)
(ix) Dividing each side of the equation in equation (v) by bc gives: sine of B over b equals sine of C over c i.e
[tex]\frac{csinB}{bc} = \frac{bsinC}{bc}[/tex]
[tex]\frac{sinB}{b} = \frac{sinC}{c}[/tex] [This is the sine rule]
i will give you 45 for this what is 12*12/12-3/4
Answers
Answer:
11.25
Step-by-step explanation:
12*12/12-3/4
PEMDAS says multiply and divide first
from left to right
144/12 - 3/4
12 -3/4
12 - .75
Then add and subtract
11.25
Answer:
[tex]\frac{45}{4}[/tex]
Step-by-step explanation:
Apply PEDMAS
P - parenthesis
E - exponents
D - division
M - multiplication
A - addition and S - subtraction
Division is first.
12 × [tex]\frac{12}{12}[/tex] - [tex]\frac{3}{4}[/tex]
12 × 1 - [tex]\frac{3}{4}[/tex]
Followed by multiplication.
12 - [tex]\frac{3}{4}[/tex]
Subtract the numbers next.
[tex]\frac{12}{1} -\frac{3}{4}[/tex]
Make the denominators same by LCM.
[tex]\frac{48}{4} -\frac{3}{4}[/tex]
[tex]\frac{45}{4}[/tex]
A certain circle can be represented by the following equation x^2+y^2+18x+14y+105=0 What is the center and radius of the circle?
Answers
Answer:
Center of the circle is (-9, -7)
Radius of the circle = 5 units
Step-by-step explanation:
Given question is incomplete: here is the complete question.
Certain circle can be represented by the following equation. x^2+y^2+18x+14y+105=0.
What is the center of this circle ?
What is the radius of this circle ?
Since equation of the circle has been given by the equation,
x² + y² + 18x + 14y + 105 = 0
Now we will convert this equation to the standard form of the circle.
x² + 18x + y² + 14y = -105
[x² + 2(9)x] + [y² + 2(7)x] = -105
[x² + 2(9)x + 9²] + [y² + 2(7)y + 7²] = 9² + 7² - 105
(x + 9)² + (y + 7)² = 81 + 49 - 105
(x + 9)² + (y + 7)² = 25
(x + 9)² + (y + 7)² = 5²
By comparing this equation with the standard equation of the circle → (x - h)² + (y - k)² = r²
1 less than a doubled number is equivalent to 5 more than 3 lots of the number
Answers
Answer:
the number is -6 (assuming "3 lots of" means 3 times)
Step-by-step explanation:
Let the number be x
1 less than a doubled number
2x-1
5 more than 3 lots of (times???) the number
3x+5
Solve for x
2x-1 = 3x + 5
-x = 5+1
x = -6
The main triangular sail on a sailboat is 25 feet tall and 10 feet wide at the bottom. If the sides of another sail are proportional to the main sail, and the bottom of this sail is 8 feet wide, how tall is it?
Answers
Answer:
20 feetStep-by-step explanation:
Here,,
Sides of two sail are proportional.
Let the height be 'x'
Now,
[tex] \frac{a1}{b1} = \frac{a2}{b2} [/tex]
plug the values
[tex] \frac{25}{10} = \frac{x}{8} [/tex]
Apply cross product property
[tex]10x = 25 \times 8[/tex]
Multiply the numbers
[tex]10x = 200[/tex]
Divide both sides of the equation by 10
[tex] \frac{10x}{10} = \frac{200}{10} [/tex]
Calculate
[tex]x = 20 \: ft[/tex]
Hope this helps...
Best regards!!
Answer:
20
Step-by-step explanation:
On each of three pieces of paper a three digit number is written two of the digits are covered . The sum is 826. What is the sum of two covered digits?
Answers
Answer:
9
Step-by-step explanation:
The diagram showing the three pieces of paper of three digit in which two of the letters were covered can be seen below.
From the diagram; we have;
243 , 1_7 , _26
Assuming the covered digits are _
The sum is 826.
i.e
243 + 1_7 + _26 = 826
The objective is to determine the sum of the two unknown digits
So; we need to think about what number can we add put in 1_7 to determine the covered digit in _26
From ; 1_7 , we have the choice to pick from 0 - 9
Assuming the covered digit is 0; let's check if we are right
So; 243 + 107 + _26 = 826
350 + _26 = 826
_26 = 826 - 350
_26 = 476
So; the covered digit is in the position of 4 , but it doesn't tally together
i.e 426 is not the same as 476, which makes our assumption to be wrong.
Let consider the covered digit to be 5 for example.
So; 243 + 157 + _26 = 826
400 + _26 = 826
_26 = 826 - 400
_26 = 426
The covered digit is in the position of 4
SO;
426 = 426
Here , our assumption is right.
As such , the covered digits are 5 and 4
The sum of the two covered digits are = 5 + 4 = 9
How many sides does a convex polygon have with the given sum for its interior angles. If not possible, answer with the
number zero in the box.
2205°
Answers
0
Explanation
Formula for sum of interior angles:
(n - 2) • 180 = sum = 2205 °
Where n = number of sides
2205/180 = n - 2
12.25 = n - 2
14.25 = n
Answer is 0 as you can’t have a quarter of a side
Please Help! Which description best describes the solution to the following system of equations? y = −x + 4 y = 3x + 3 Line y = −x + 4 intersects the line y = 3x + 3. Lines y = −x + 4 and y = 3x + 3 intersect the x-axis. Lines y = −x + 4 and y = 3x + 3 intersect the y-axis. Line y = −x + 4 intersects the origin.
Answers
Answer:
Line y = −x + 4 intersects the line y = 3x + 3.
Step-by-step explanation:
Please Help! Which description best describes the solution to the following system of equations?
y = −x + 4
y = 3x + 3
Line y = −x + 4 intersects the line y = 3x + 3.
This is the response because the solution to a system of two equations is represented by the intersection of the equations of the two lines/curves.
Lines y = −x + 4 and y = 3x + 3 intersect the x-axis.
Lines y = −x + 4 and y = 3x + 3 intersect the y-axis.
Line y = −x + 4 intersects the origin.
PLEASE HELP A store is having a sale on chocolate chips and walnuts. For 5 pounds of chocolate chips and 3 pounds of walnuts, the total cost is $21. For 2 pounds of
chocolate chips and 6 pounds of walnuts, the total cost is $24. Find the cost for each pound of chocolate chips and each pound of walnuts.
Answers
Answer:
Chocolate Chips cost $2.25 and Walnuts cost $3.25 per pound each
Step-by-step explanatChocion:
Let x = cost of pounds of chocolate chip cookies and y = cost of pounds of walnuts.
From the question, we get 5x+3y = 21 and 2x+6y = 24. To solve the equation, we use substitution. From the first equation, we get y = (21-5x)/3. We substitute the y into the second equation to get 2x + 6(21-5x)/3 = 24. This turns out to be 2x+(42-10x) = 24. Adding like terms you should get 42-8x = 24. Solving for x, x = $2.25 per pound. Plugging this into the first equation, we get 5(2.25)+3y = 21. Solving for y, we get $3.25 per pound of walnuts. If we plug in the numbers into the 2 equations, we will get the right total.
A Little League baseball coach wants to know if his team is representative of other teams in scoring runs. Nationally, the average number of runs scored by a Little League team in a game is 5.7. He chooses five games at random in which his team scored 5 , 9, 4, 11, and 8 runs. Is it likely that his team's scores is different from the national distribution
Answers
Answer:
Yes, it is likely due to the significant difference in their average scores.Step-by-step explanation:
The average number of runs scored by a Little League team in a game is 5.7. If he chooses five games at random in which his team scored 5 , 9, 4, 11, and 8 runs, their average score of the five games is expressed as shown;
Average score of 5 games = (5+9+4+11+8)/5
Average score of 5 games = 37/5
Average score of 5 games = 7.4
Comparing the average score in 5 games to the the average number of runs scored nationally, it can be seen that their difference is 7.4 - 5.7 which is 1.7. Since the difference is quite significant, then it is most likely that his team's scores is different from the national distribution.
A piece of land ABCD is in the shape of a trapezium
as shown in the diagram. AB = 40 m, BC = 39 m,
AD = 30 m, and <ABC = <BAD = 90°. Find
(a) the length of the side CD,
(b) angle BCD,
(c) the area of the land.
Answers
Answer:
a) CD = 41 m
b) 77.32°
c) 1380 square metres
Step-by-step explanation:
We can divide the trapezium as shown in the diagram below.
a) To find CD, we use Pythagoras Rule:
[tex]CD^2 = 9^2 + 40^2[/tex]
[tex]CD^2 = 81 + 1600\\\\CD^2 = 1681\\\\=> CD = 41 m[/tex]
b) To find <BCD, we use trigonometric function SOHCAHTOA:
sin(BCD) = opp / hyp
sin(BCD) = 40 / 41
sin(BCD) = 0.9756
=> <BCD = 77.32°
c) The area of a trapezium is given as:
A = 1/2 (a + b) * h
where h = height = 40 m
a = top length = 30 m
b = bottom length = 39 m
A = 1/2 * (30 + 39) * 40
A = 1/2 * 69 * 40
A = 1380 square metres
(x+1)(x-2)=0
Solve the quadratic equation using factoring
Answers
Answer:
x= -1 or x= 2
Step-by-step explanation:
(x+1)(x-2) = 0x+1 = 0 or x-2=0 x = -1 or x = 2i will mark brainlist
Answers
Answer:
[tex]\boxed{x = 30}[/tex]
Step-by-step explanation:
x + 2x + 3x = 180 (Interior angles of a triangle add up to 180 degrees)
=> 6x = 180
Dividing both sides by 6
=> x = 180 / 6
=> x = 30
Answer:
x= 30
Step-by-step explanation:
3x + 2x + x = 180
6x= 180
x = 180/6
:• x = 30
Which is the best estimate for the percent equivalent of 7 Over 15
Answers
Approximate what the value of [tex]7/15[/tex] is by using calculator.
[tex]7/15\approx0.47[/tex].
And now just multiply by 100 to get percentage.
[tex]100\cdot0.47=\boxed{47\%}[/tex].
Hope this helps.
Answer:
24%
Step-by-step explanation:
7\15 x 100
simplify and get=140\3
dived140\3=48\2
simplify 48\2=24%
50 Pts!!! Answer ASAP.
Answers
Answer:
0.8
Step-by-step explanation:
because the template should be axr^n-1
where r is the common ratio
r=0.8
Answer:
0.8
Step-by-step explanation:
To mix mortar to lay bricks,you need 2.5Kg of cement,4kg of sand and 3 liters of water.Sand is sold in 10kg bags.How much cement and water will I need to add to make mortar?
Answers
Answer:
6.25 kg cement, 7.5 L water
Step-by-step explanation:
2.5 kg cement / 4 kg sand = x kg cement / 10 kg sand
x = 6.25
3 L water / 4 kg sand = y L water / 10 kg sand
y = 7.5