Solve algebraically the simultaneous equations
x^2– y^2 = 24
x= 3 + 2y
Write your two pairs of answers in this form:
when x =... y =...
When x=... y=...
Answers
Answer:
(5, 1) and (-5, -7)
Step-by-step explanation:
Given the simultaneous equations
x^2– y^2 = 24 .... 1
x= 3 + 2y .... 2
Substitute 2 into 1
(3-2y)^2-y^2 = 24
Expand
9 - 12y + 4y^2 - y^2 = 24
9 - 12y + 3y^2 = 24
3y^2 - 12y + 9-24 = 0
3y^2 -12y -15 = 0
y^2-4y-5 = 0
y^2+5y - y - 5 = 0
y(y+5) - 1 (y+5) = 0
y-1 = 0 and y+5 = 0
y = 1 and -5
Substitute the values of y into 2
Recall that x = 3+3y
when y = 1
x = 3 + 2(1)
x = 5
when x = -5
x = 3 + 2(-5)
x = 3 - 10
x = -7
Hence the solutions are (5, 1) and (-5, -7)
Related Questions
a=960 rounded to the nearest 10
b=89.0 rounded to 1 DP
Find the minimum (to 2 DP) of a÷b
Answers
Step-by-step explanation:
a÷b=960÷89=10.78651685=10.79 or 17.8
1. x+1 when x=10
2. 5y-8 when y=6
3. 6t-9m when t=5 and m=3
4. 62/2 when x=10
5. 5h3-3j2+20 when h=4 and j=5
Answers
Answer:
1
X is equal to 10
10 plus 1 equals 11
2
y is equal to 6
30 minus 8
is equal to 22
3
m equals 3 and t equals 5
30 minus 27
is equal to 3
4 not written properly
5 not written properly
A train travels 20 miles in 15 minutes. how far will it travel in an hour and a half
Answers
Answer:
120
Step-by-step explanation:
One hour is 90 minutes 90/15=6 then you take 20X6=120miles
Answer:
It will travel 120 miles
Step-by-step explanation:
First, convert the hour and half to minutes: 90 minutes.
Then divide 90 with 15: 6
Then since there are 6 sections of 15 minutes, you would multiply 20 times 6 which is 120.
what is the exact value of cos5pie/12
Answers
Answer:
Exact Form: −e12
Decimal Form: −0.22652348…
Step-by-step explanation:
Plz, answer this question plz!
Answers
Answer:
the second option im pretty sure
Answer:
4/48. I don't know for sure, but I think B is the correct answer
What is the slope for (-2,1) and (7,1)
Answers
Answer:
m=0
Step-by-step explanation:
the slope (m) can be calculated from two points with the formula (y2-y1)/(x2-x1)
we are given the points (-2,1) and (7,1)
label the points:
x1=-2
y1=1
x2=7
y2=1
now substitute into the equation
m=(1-1)/(7--2)
m=0/9
m=0
the slope of the line is 0
Hope this helps!
Find the slope of the line that passes through (4, 1) and (9, 8).
Answers
the slope is 7/5
a baby weights 7 pounds at birth. the table shows the birth weight after each month of life, up to six months
Answers
Answer:
they are adding by 7 because 6 +7=13
x+1/3=5
help plzzzzzzz
Answers
Answer:
x = 4 2/3
Step-by-step explanation:
x = 5 - 1/3
x = 4 2/3
Answer:
x = [tex]\frac{14}{3}[/tex]
Step-by-step explanation:
Subtract [tex]\frac{1}{3}[/tex] from both sides
x + [tex]\frac{1}{3}[/tex] - [tex]\frac{1}{3}[/tex] = 5 - [tex]\frac{1}{3}[/tex]
x = [tex]\frac{14}{3}[/tex] or 4 [tex]\frac{2}{3}[/tex]
HELP PLEASE!! need this asap.
y = 4x + 3
y = -x - 2
Answers
Answer:pls check out the image. The answer is in the image ans hope this helps and can u give me brainliest
Step-by-step explanation:
John runs 6.5 miles in 30 minutes. If he continues at this rate for 1 hours, determine his rate of change .
Answers
Answer: 13 miles
Step-by-step explanation:
30 min plue 30 min is 1 hour
if he runs 6.5 in 30 you just have to add 6.5 and 6.5 which equals 13
Arcola bought 8 virtual reality headsets for $400 each and 8 laptops for
$500 each. How much total money did Arcola spend?
Answers
Answer:
arcola spent 916 dollars
Answer:
the answer is 916
Step-by-step explanation:
What is the area of the triangle
Answers
5 in x 1 ft = 5 ft in
divide by 2 is 2.5 ft in
Answer:
30 inches squared
Step-by-step explanation:
The formula for a RIGHT triangle is:
[tex]A= \frac{ab}{2}[/tex]
We are given..
a = 5 inchesb = 1 foot = 12 inchesTherefore...
[tex]A = \frac{5(12)}{2}[/tex]
[tex]A=\frac{60}{2}[/tex]
[tex]A = 30[/tex]
Find the excluding values for the equations a^3+3a^2-10a/5a^3-20a
Answers
Answer:
a+5/5(a+2)
Step-by-step explanation:
sorry it took so long
Help, I wanna pass this iready lesson or im going to get yelled at.
Answers
Answer:
1/10 is the correct answer
Step-by-step explanation:
3/5=6/10
7/10-6/10=1/10
Answer:
1/10 hour
Step-by-step explanation:
7/10
convert 3/5 to 6/10 for same denominator
7/10 - 6/10 = 1/10
pls help! ill give brainless to the best answer !!
what is 25% of 75? show your work.
Answers
Answer:
18.75
Step-by-step explanation:
25% of 75 =
0.25 x 75 =
18.75
Hope that helps!
Answer:
18.75
Step-by-step explanation: I don't really know what work to show it was all mental
El costo de un teléfono celular con un descuento del 30% sobre el precio de lista, está dado por p(x)= x-0.30x. El impuesto a pagar por un artículo que cuesta x pesos está dado por i(x)= 0.15x.
a) Hallar e interpretar i(p(x))
b) ¿cuánto pagarás por un teléfono cuyo precio de lista es de $1,200?
Answers
slope of 1/2 and y-intercept is -5.
Answers
Answer:
Y= 1/2x-5
Step-by-step explanation:
give the center and the radius of the circle of x^2+y^2+6x-8y=0
Answers
(x+a)² + (y+b)² = R²
C (a,b)
R = 5 C( 3 , -4 )
Given the equation of the line -6x + 2y = 10
Answers
Answer:
x= 1 /3 y+ −5 /3
y=3x+5
Step-by-step explanation:
brainliest?
Answer:
Give my man brainliest
Step-by-step explanation:
Don't report this
I need the answer for real fast. Question below
A square has a perimeter of 12x + 52 units. Which expression represents the side length of the square in units?
x + 4
x + 40
3x + 13
3x + 43
Who started the whole link thing anyways?
Answers
Answer:
It's x + 4
Step-by-step explanation:
And I don't know who started this link thing
Hope this helps and have a great day *(:^w^:)
Answer:
It's 3x + 13
Step-by-step explanation:
brainlyest ^（｀ω´ ）^ψ
i need to talk with you
52/4=13
12x/4=3x
3x+13
Convert the equation into standard form.
25x2 – 9y2 + 200x + 18y + 166 = 0
StartFraction (x minus 8) squared Over 9 EndFraction minus StartFraction (y + 2) squared Over 25 EndFraction = 1
It's D on edge
Answers
Answer:
d
Step-by-step explanation:
it says it in the question lol
Answer:
The answe is D on edge
Step-by-step explanation:
The students of a high school are 51% males. Of the students at this high school 45% of males and 40% of females said they regularly attend concerts.
Answers
Answer:
(b) Probability that a student is male and attends concert = 22.95%
(c) Probability that a student is female and does not attend concert = 29.4%
(d) Probability that a student attends concerts = 42.55%
Step-by-step explanation:
P.S - The exact question is -
Given - The population of a high school is 51% male. 45% of the males and 40% of the females attend concerts.
To find - (a) Make a tree diagram based on the information above.
(b) Find the probability that a student is male and attends
concerts.
(c) Find the probability that a student is female and does not
attend concerts.
(d) Find the probability that a student attends concerts.
Proof -
Let the total population of the high school = 100 x
Given that,
The students of a high school are 51% males
⇒Total males in the high school = 51% × 100 x
= [tex]\frac{51}{100}[/tex] × 100 x = 51 x
⇒Total males in the high school = 51 x
⇒Total females in the high school = 100 x - 51 x = 49 x
Now,
Given that,
Of the students at this high school 45% of males and 40% of females said they regularly attend concerts.
⇒Total number of males that attend the concert = 45% × 51 x
= [tex]\frac{45}{100}[/tex] × 51 x = 22.95 x
⇒Total number of males that attend the concert = 22.95 x
And
Total number of males that do not attend the concert = 51 x - 22.95 x
= 28.05 x
⇒Total number of males that do not attend the concert = 28.05 x
Also,
Total number of females that attend the concert = 40% × 49 x
= [tex]\frac{40}{100}[/tex] × 49 x = 19.6 x
⇒Total number of females that attend the concert = 19.6 x
And
Total number of females that do not attend the concert = 49 x - 19.6 x
= 29.4 x
⇒Total number of females that do not attend the concert = 29.4 x
(a)
The tree diagram is as follows :
(b)
Probability that a student is male and attends concert = [tex]\frac{22.95 x}{100 x}[/tex] × 100 %
= 22.95%
⇒Probability that a student is male and attends concert = 22.95%
(c)
Probability that a student is female and does not attend concert = [tex]\frac{29.4x}{100x}[/tex] × 100%
= 29.4%
⇒Probability that a student is female and does not attend concert = 29.4%
(d)
Probability that a student attends concerts = [tex]\frac{22.95x + 19.6x}{100x}[/tex] ×100%
= [tex]\frac{42.55}{100}[/tex] ×100%
= 42.55%
⇒Probability that a student attends concerts = 42.55%
A organização de um novo campeonato de futebol recebereu inscrição de 14 equipes.Se cada equipe tinha 12 jogadores,quantos atletas se inscreveram?
Answers
Answer:
168 jugadores.
Step-by-step explanation:
De la pregunta anterior:
Tenemos 14 equipos
1 equipo = 12 jugadores
14 equipos = x jugadores
Multiplicar cruzada
1 equipo × x jugadores = 14 equipos × 12 jugadores
x jugadores = 14 equipos × 12 jugadores / 1 equipo
x jugadores = 168 jugadores
Por tanto, se unirán 168 jugadores.
Question 16
What is the slope of a line passing through (2, 2) and (3,5)?
Answers
5 because of slope equation
A castle has to be guarded 24 hours a day. Five knights are ordered to split each day's guard duty equally. How long will each knight spend on guard duty in one day? Record your answer in hours as a decimal.
Answers
Answer: 4.8 hours
Step-by-step explanation:
Given
The castle must be guarded 24 hr by 5 knights
If duty is split equally among them
No of hours spent by each knight on duty
[tex]\Rightarrow n=\dfrac{24}{5}=4.8\ \text{hours}[/tex]
Therefore, each guard must serve a duty of 4.8 hours
Triangle JKL is shown below.
K
24
L
28
Which equation should be used to find the
length of JK?
Answers
write an equation of the line that passes through the given points (3,1) (0,10)
Answers
Answer:
y = -3x + 10
Step-by-step explanation:
10-1/0-3 = -3
y = -3x + b
1 = -3(3) + b
1 = -9 + b
10 = b
check your answer:
10 = -3(0) + 10
10 = 10
b should be 10
A square pyramid is shown. 4 m 6 m 6 m What is the surface area of the pyramid?
Answers
A painter can paint 120 square feet with 4 gallons of paint. Which statement about the unit rate is true?
Answers
Answer:
30 (ft^2/gal)
Step-by-step explanation:
The "unit rate" in this problem is (number of square feet covered) / (1 gallon paint).
Here we have the unit rate
120 ft^2
---------------- = (30 ft^2)/gal or 30 (ft^2/gal)
4 gallons
