Answers
Answer:
y=5, y=[tex]\frac{38}{11}[/tex]
Step-by-step explanation:
Hi there!
We are given the equation
[tex]\frac{y+2}{y-3}[/tex]+[tex]\frac{y-1}{y-4}[/tex]=[tex]\frac{15}{2}[/tex] and we need to solve for y
first, we need to find the domain, which is which is the set of values that y CANNOT be, as the denominator of the fractions cannot be 0
which means that y-3≠0, or y≠3, and y-4≠0, or y≠4
[tex]\frac{y+2}{y-3}[/tex] and [tex]\frac{y-1}{y-4}[/tex] are algebraic fractions, meaning that they are fractions (notice the fraction bar), but BOTH the numerator and denominator have algebraic expressions
Nonetheless, they are still fractions, and we need to add them.
To add fractions, we need to find a common denominator
One of the easiest ways to find a common denominator is to multiply the denominators of the fractions together
Let's do that here;
on [tex]\frac{y+2}{y-3}[/tex], multiply the numerator and denominator by y-4
[tex]\frac{(y+2)(y-4)}{(y-3)(y-4)}[/tex]; simplify by multiplying the binomials together using FOIL to get:
[tex]\frac{y^{2}-2y-8}{y^{2}-7y+12}[/tex]
Now on [tex]\frac{y-1}{y-4}[/tex], multiply the numerator and denominator by y-3
[tex]\frac{(y-1)(y-3)}{(y-4)(y-3)}[/tex]; simplify by multiplying the binomials together using FOIL to get:
[tex]\frac{y^{2}-4y+3}{y^{2}-7y+12}[/tex]
now add [tex]\frac{y^{2}-2y-8}{y^{2}-7y+12}[/tex] and [tex]\frac{y^{2}-4y+3}{y^{2}-7y+12}[/tex] together
Remember: since they have the same denominator, we add the numerators together
[tex]\frac{y^{2}-2y-8+y^{2}-4y+3}{y^{2}-7y+12}[/tex]
simplify by combining like terms
the result is:
[tex]\frac{2y^{2}-6y-5}{y^{2}-7y+12}[/tex]
remember, that's set equal to [tex]\frac{15}{2}[/tex]
here is our equation now:
[tex]\frac{2y^{2}-6y-5}{y^{2}-7y+12}[/tex]=[tex]\frac{15}{2}[/tex]
it is a proportion, so you may cross multiply
2(2y²-6y-5)=15(y²-7y+12)
do the distributive property
4y²-12y-10=15y²-105y+180
subtract 4y² from both sides
-12y-10=11y²-105y+180
add 12 y to both sides
-10=11y²-93y+180
add 10 to both sides
11y²-93y+190=0
now we have a quadratic equation
Let's solve this using the quadratic formula
Recall that the quadratic formula is y=(-b±√(b²-4ac))/2a, where a, b, and c are the coefficients of the numbers in a quadratic equation
in this case,
a=11
b=-93
c=190
substitute into the formula
y=(93±√(8649-4(11*190))/2*11
simplify the part under the radical
y=(93±√289)/22
take the square root of 289
y=(93±17)/22
split into 2 separate equations:
y=[tex]\frac{93+17}{22}[/tex]
y=[tex]\frac{110}{22}[/tex]
y=5
and:
y=[tex]\frac{93-17}{22}[/tex]
y=[tex]\frac{76}{22}[/tex]
y=[tex]\frac{38}{11}[/tex]
Both numbers work in this case (remember: the domain is y≠3, y≠4)
So the answer is:
y=5, y=[tex]\frac{38}{11}[/tex]
Hope this helps! :)
Related Questions
Which similarity postulate or theorem can be used to verify that the two
triangles shown below are similar?
A. SAS theorem
B. SSS theorem
C. AA postulate
D. Similarity cannot be determined.
Answers
Answer:
C
Step-by-step explanation:
AA postulate because we are given 2 of the 3 angles of each triangle. They are both the same in each triangle. Also, we can find the 3rd angle in each triangle. Since both triangles have the exact same angles, they are similar.
The given triangles ΔABC and ΔLMN are similar by AA postulate.
What is a triangle?A triangle is a three sided polygon that consist of three edges and three vertices .
Here two given triangles are ΔABC and ΔLMN. In these two triangles ∠A=∠L=53° and ∠B=∠M= 72°.
Therefore, the two corresponding angles of triangles ΔABC and ΔLMN are equal . So the third angle of ΔABC is also equal to the corresponding angle of ΔLMN.
Hence two triangles are similar by AA postulate.
Thus two triangles are similar by AA postulate. So option (C) is correct.
To learn more about triagles click here:
https://brainly.com/question/24147586
#SPJ7
Given f(x) and g(x) = k-f(x), use the graph to determine the value of k.
f(x)
g(x)
A. -5
B. -1/5
C. 1/5
D. 5
Answers
===========================================================
Explanation:
The point (-2,2) is on the red f(x) line. This point is marked in black.
It corresponds to the point (-2,-10) on the g(x) blue line.
The point (-2,2) moves to (-2,-10). The x coordinate stays at x = -2. The y coordinate has gone from y = 2 to y = -10. This is a jump of "times negative 5".
-5*2 = -10
So we see that k = -5
Saying g(x) = k*f(x) is the same as g(x) = -5*f(x)
Recall that y = f(x), so saying -5*f(x) is really saying "whatever the y coordinate is on f(x), multiply it by -5 to get the corresponding y coordinate on g(x)".
Answer:
-5
y = -x + 4 (red)
y=5x -20 (blue)
-5*(-x+4) = 5x-20
Step-by-step explanation:
A 3 by 3cm grid shows nine 1 by 1 cm squares and uses 24cm of wire.
What length would the wire be for a similar 20 by 20cm sqaure
Answers
Answer:
840 cm
Step-by-step explanation:
Given that in the question we have, : 9, 1 cm × 1 cm squares setting a 3 × 3 grid.
Therefore wire required in 3 x 3 grid is
3(3+1) + 3(3+1)
= 3 × 4 + 3 × 4
= 24 I'm
Similarly, the length of the wire required in 20 by 20 grid will be
=> 20(20+1) + 20(20+1)
=> 20 × 21 + 20 × 21
=> 420 + 420
= 840cm
9. Simplify by rationalising the denominator: 2+√3 2−√3 + 2−√3 2+√3 .
Answers
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { 14 }}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex] \frac{2 + \sqrt{3} }{2 - \sqrt{3} } + \frac{2 - \sqrt{3} }{2 + \sqrt{3} } [/tex]
[tex] \\= \frac{2 + \sqrt{3} }{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } + \frac{2 - \sqrt{3} }{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } [/tex]
[tex] \\= \frac{2 \: (2 + \sqrt{3} )+ \sqrt{3} \: (2 + \sqrt{3} )}{ ({2})^{2} - ({ \sqrt{3} })^{2} } + \frac{2 \: (2 - \sqrt{3} ) - \sqrt{3} \: (2 - \sqrt{3} ) }{ ({2})^{2} - ( { \sqrt{3} })^{2} } [/tex]
[tex]\\ = \frac{4 + 2 \sqrt{3} + 2 \sqrt{3} + 3 }{4 - 3} + \frac{4 - 2 \sqrt{3} - 2 \sqrt{3} + 3}{4 - 3} [/tex]
[tex]\\ = \frac{7 + 4 \sqrt{3} }{1} + \frac{7 - 4 \sqrt{3} }{1} [/tex]
[tex] \\= 7 + 4 \sqrt{3} + (7 - 4 \sqrt{3} )[/tex]
[tex] \\= 7 + 4 \sqrt{3} + 7 -4 \sqrt{3} [/tex]
[tex] \\= 14[/tex]
Note:[tex] (a + b)(a - b) = {a}^{2} - {b}^{2} [/tex]
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♨}}}}}[/tex]
The volume of a cylinder, V, in terms of radius, r,
and height, h, is given by V = πr 2
h. If a cylinder has
a height of 6 meters, express the radius as a function
of V and find the radius of a cylinder with volume of
300 cubic meters.
Answers
Answer:
See explanation
Step-by-step explanation:
Volume of a cylinder = πr²h
Solve for r
V = π * r² * h
r² = V/πh
Find the square root of both sides
r = √V/πh
If height = 6 meters and volume = 300 cubic meters. Find r
r = √V/πh
= √(300/3.14*6)
= √(300/18.84)
= √15.923566878980
r = 3.9904344223381
Approximately,
r = 4 meters
PLEASE HELP
what is the amount of an investment $10,000 compounded quarterly for 3 years at a rate of 4 percent?
Answers
Answer:
10000 times 3 times 0.04 = 1200
Answer:
11268.25
Step-by-step explanation:
[tex]P(1+\frac{i}{n})^{n*t}=10000(1+\frac{.04}{4})^{4*3}=11268.2503[/tex]
Solve 4(x - 3) - 2x - 1) > 0
Answers
Answer:
x > 5.5
Step-by-step explanation:
4(x - 3) - (2x - 1) > 0
4x - 12 - 2x + 1 > 0
4x - 2x - 11 > 0
2x - 11 > 0
2x - 11 + 11 > 0 + 11
2x > 11
2x ÷ 2 > 11 ÷ 2
x > 5.5
Answer:
x>13/2
Step-by-step explanation:
4x-12-2x-1>0
2x-13>0
2x>13
X>13/2
Fill in the blank with <,> or = . 11.01-----11.001
Answers
Answer: Greater than sign
In other words, 11.01 > 11.001
========================================================
Explanation:
For each given number, move the decimal point 3 spots to the right.
The value 11.01 becomes 11010
The value 11.001 becomes 11001
Since 11010 > 11001, this means 11.01 > 11.001
---------------
As an alternative method, you can subtract the values to see which is larger
The rule or idea is that
(large) - (small) = positive(small) - (large) = negativeFor example, 5-2 = 3 showing that 5 is larger than 2. As another example, 7-9 = -2 meaning 7 is smaller than 9. The order of subtraction matters.
In this case, 11.01 - 11.001 = 0.009 showing that 11.01 is larger than 11.001
Dominic is deciding if he should become a member of his local ice rink. The $144 annual membership fee at the ice rink includes admission and parking, members pay $4.00 per visit to rent ice skates. Non-members pay $11 admissions, $5.00 for parking and they also pay $4.00 per visit to rent ice skates. 1. When is it better to be a member? After 4 visits how much would each pay? Member: $_________ Non-Member: $__________ After 6 visits how much would each pay? Member: $_________ Non-Member: $__________
Answers
Answer:
1. members = $ 160 , non members = $ 80
2. members = $ 168 , non members = $ 120
Step-by-step explanation:
For members
Annual membership = $ 144
rent per visit charges = $ 4
For Non members
parking charges = $ 5
admission charges = $ 11
rent per visit = $ 4
(1) for 4 visits
Members pay = $ 144 + 4 x $ 4 = $ 160
Non members pay = 4 x $ 11 + 4 x $ 5 + 4 x $ 4 = $ 80
So, non member ship is better.
(2) for 6 visits
Members pay = $ 144 + 6 x $ 4 = $ 168
Non members pay = 6 x $ 11 + 6 x $ 5 + 6 x $ 4 = $ 120
So, non member ship is better.
Help please guys! Thank youuu
Answers
Answer:
Step-by-step explanation:
12b + 1 5c = 420
b ---> number of hour baby sitting
c-----> number of hours cleaning
c = 32 hours
Plugin c = 32 in the equation,
12b + 15*32 = 420
12b + 480 = 420
Subtract 480 from both sides
12 b = 420 - 480
12b = -60
So, This is not a reasonable value.
2) b = 10 hours
Plugin b = 10 hours
12*10 + 15c = 420
120 + 15c = 420
15c = 420 - 120
15c = 300
Divide both sides by 15
c = 300/15
c = 20 hours
He has to do cleaning for 20 hours
Yes, It is reasonable value
pls tell me the correct option
Answers
Answer: I would go with C I hope i am right!!
Step-by-step explanation:
Answer:
b. [tex] \frac{1}{16} [/tex]
Step-by-step explanation:
A = {2, 3}
B = {4, 6}
C = set of all possible fractions where, the numerators are in set A and the denominators are found in Set B
The 4 possible fractions we can get for set C are as follows:
Set C: { [tex] \frac{2}{4} [/tex] , [tex] \frac{2}{6} [/tex] , [tex] \frac{3}{4} [/tex] , [tex] \frac{3}{6} [/tex] }
Multiply all to get the product of all elements in Set C:
[tex] \frac{2}{4}*\frac{2}{6}*\frac{3}{4}*\frac{3}{6} [/tex]
Simplify where necessary
[tex] \frac{1}{2}*\frac{1}{3}*\frac{3}{4}*\frac{1}{2} [/tex]
[tex] \frac{1*1*3*1}{2*3*4*2} [/tex]
[tex] \frac{3}{48} [/tex]
Simply further
[tex] \frac{1}{16} [/tex]
Use the number line to find the measure of SV
Answers
Answer:
8
Step-by-step explanation:
S = -7 to V= 1 you count from -7 to 1
Podemos ver una muestra de laboratorio que contiene 32 bacterias inicialmente, y que luego de aplicar una vacuna, se autodestruyen a la mitad cada una hora. ¿Al cabo de cuántas horas no quedará ninguna bacteria?. Resuelve utilizando potencias y sus propiedades.
Answers
Answer:
10 horas.
Step-by-step explanation:
Dado que una muestra de laboratorio contiene 32 bacterias inicialmente, y luego de aplicar una vacuna, se autodestruyen a la mitad cada una hora, para determinar al cabo de cuántas horas no quedará ninguna bacteria se debe realizar el siguiente cálculo:
32 / 2 = 16
16 / 2 = 8
8 / 2 = 4
4 / 2 = 2
2 / 2 = 1
1 / 2 = 0.5
0.5 / 2 = 0.25
0.25 / 2 = 0.125
0.125 / 2 = 0.0625
0.0625 / 2 = 0.03125
Por lo tanto, al cabo de 10 horas no quedará ninguna bacteria.
find the value of 525²-475² using suitable identity
Answers
Answer to this question:
I think the answer is 3
What is the inverse of the function f(x) = x +3?
Answers
Answer:
The inverse is x-3
Step-by-step explanation:
y = x+3
To find the inverse, exchange x and y
x = y+3
Solve for y
x-3 = y+3-3
x-3 =y
The inverse is x-3
Answer:
x - 3
Step-by-step explanation:
f(x) = x + 3
y = x + 3
x = y - 3
Inverse is h(x) = x - 3
Determine the intercepts of the line.
y
=
11
x
+
6
Answers
Answer:
intercepts are (-6/11 , 0) and ( 6,0 )
Does the set of numbers form a Pythagorean triple? Explain.
Answers
Explanation:
Pythagorean Triples are sets of whole numbers for which the Pythagorean Theorem holds true. The most well-known triple is 3, 4, 5. This means that 3 and 4 are the lengths of the legs and 5 is the hypotenuse.
Can someone help me with this. Will mark brainliest. Thank you.
Answers
Answer:
∠SVU = 49°
Step-by-step explanation:
∠SVU is an inscribed angle and arc SU is the arc it intercepts
If you didn't know an inscribed angle is equal to half the measure of its intercepted arc.
Hence ∠SVU = arc SU / 2
if arc SU = 98
Then ∠SVU = 98/2 = 49
pls help I'll mark brainliest
Answers
Answer:
305°
Step-by-step explanation:
The angle between the north line at L and the line connecting PL is
125° (75° + 50° ) ← alternate angle between parallel lines
Then
bearing of P from L is 180° + 125° = 305°
!$P¡D£R €ŁÆŃ!!$P¡D£R €ŁÆŃ!
Answers
Answer:
A is correct because there are only 2 sides to flip to, giving it a probability of 0.50, or 1/2 that they will lands heads up.
Answer:
I would go with D
Step-by-step explanation:
Because there are 4 possibilities.
1) they both land heads up
2) they both land tails up
3) one lands heads up and the other tails up
4) one lands tails up and the other heads up
Hope this helps!
Find the measure of angle "b"
Answers
Answer:
43°
Step-by-step explanation:
Angle B is congruent to the opposite angle.
The cost of one scooter is Rs.52,136. What is the cost of 34 scooters?
----------------------------------------------------------------------------------------------------------------------------
Rs.17,72,624
Rs.1,77,26,204
Rs.1,24,56,658
Answers
Answer:
Rs.1772624
Step-by-step explanation:
Multiply 52,236 by 34
Dan, Harry and Regan sell cars.
Dan sells x cars.
Harry sells 5 more cars than Dan.
Regan sells twice as many cars as Dan.
Write an expression, in terms of x, for the mean number of cars Dan, Harry and Regan sell.
Answers
Explanation:
D = x
H = x + 5
R = 2x
Mean = (D + H + R)/3
= (x + x + 5 + 2x)/3
= (4x + 5)/2
if I have a 94% in art class and I don’t do one of my assignments and get a 68 what will my grade drop down to?
Answers
Answer:
81
Step-by-step explanation:
It depends on how many different grades you have and the values of each one of them.
I don't have those things, so Ill just use average.
You'll have an 81
change from improper fraction to mix number 51/7
Answers
Answer:
7 3/7
Step-by-step explanation:
Can somebody help I’ll give brainless plss
Answers
Answer:
$93.22
Step-by-step explanation:
bill = $79
tip = 18%
tip amount = tip % of bill
=18/100 * $79
=$1422/100
=$14.22
total cost = $79 + $14.22
=$93.22
Answer:
93.22
Step-by-step explanation:
Find the amount of the tip
79*18%
79 * .18
14.22
Add this to the amount of the bill
79+14.22
93.22
Indicate the method you would use to prove the two A's =. If no method applies, enter "none".
O SSS
O SAS
O ASA
O AAS
ONone
Answers
Explanation: The two equal eachother, that would mean that the corresponding angles equal eachother as well as the other side length. Let me know if otherwise.
Given 3x+y=1
Write the equation in general form Ax+By+C =0
3* -y+=0
-3x +y-1=0
3x-y=-1
Answers
QUESTION:- Given 3x+y=1
Write the equation in general form Ax+By+C =0
3x-y+1=0
-3x +y-1=0
3x-y=-1
[tex]3x + y - 1 = 0 \: \: ✔[/tex]
ANSWER:-
Equation-->[tex]3x + y = 1 [/tex]
Form of the given equation->
[tex]Ax + By = C[/tex]
so we need to change the side of the C !
while changing side of C we need to change the sign of C !
[tex] \bold{ \red{SO :- }}[/tex]
[tex]3 x + y = 1 \\ 3x + y - 1 = 0[/tex]
FORM OF THE RESULTED EQUATION:-
[tex]Ax + By + C = 0 \\
A = 3 \\ B = 1 \\ C = - 1[/tex]
Tiana has 8 purple daisies. In all, she counts 128 petals on all her flowers. If each flower has the same number of petals, how many petals are on one flower?
Answers
Answer:
the answer is 16 dividing 128 by 8 to get the petals in each flower.
Answer:
There are 16 petals per flower
Step-by-step explanation:
Take the number of petals and divide by the number of flowers
128/8
16
There are 16 petals per flower
what is the measure of each exterior angle of a regular dodecagon?
Answers
Answer:
30°
Hope this answer is right!
Step-by-step explanation:
to go around the shape, you make a complete circle: 360°. So, divide 360° by the dodecagon's twelve exterior angles. Each exterior angle is 30°.
