Answer:
[tex]\frac{x^2}{16}-\frac{b^2}{4}=1[/tex]
Step-by-step explanation:
A hyperbola is the locus of a point such that its distance from a point to two points (known as foci) is a positive constant.
The standard equation of a hyperbola centered at the origin with transverse on the x axis is given as:
[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]
The coordinates of the foci is at (±c, 0), where c² = a² + b²
Given that a hyperbola centered at the origin with x-intercepts +/- 4 and foci of +/-2√5. Since the x intercept is ±4, this means that at y = 0, x = 4. Substituting in the standard equation:
[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\\\frac{4^2}{a^2}-\frac{0}{b^2} =1\\\frac{4^2}{a^2}=1\\ a^2=16\\a=\sqrt{16}=4\\ a=4[/tex]
The foci c is at +/-2√5, using c² = a² + b²:
[tex]c^2=a^2+b^2\\(2\sqrt{5} )^2=4^2+b^2\\20 = 16 + b^2\\b^2=20-16\\b^2=4\\b=\sqrt{4}=2\\ b=2[/tex]
Substituting the value of a and b to get the equation of the hyperbola:
[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\\\\\frac{x^2}{16}-\frac{b^2}{4}=1[/tex]
What are the coordinates of the vertex of the function f(x)=x2+ 10x-3?
O (-5. -28)
(-5, 28)
O (5,-28)
(5.28)
Answer:
(-5,-28)
Step-by-step explanation:
Use the vertex form y=a(x-h)^2
a=1
h=-5
k=-28
vertex=(h,k)
Answer: A. (-5, -28)
Step-by-step explanation:
f(x) = x² + 10x - 3
a=1 b=10
The axis of symmetry is the x-coordinate of the vertex:
[tex]AOS: x=\dfrac{-b}{2a}\quad =\dfrac{-(10)}{2(1)}=-5[/tex]
Input x = -5 into the original equation to find the y-coordinate of the vertex:
f(-5) = (-5)² + 10(-5) - 3
= 25 -50 -3
= -28
x, y coordinate of the vertex is: (-5, -28)
You are testing the claim that the mean GPA of night students is greater than the mean GPA of day students. You sample 30 night students, and the sample mean GPA is 2.36 with a standard deviation of 0.96 You sample 60 day students, and the sample mean GPA is 2.19 with a standard deviation of 0.66 Calculate the test statistic, rounded to 2 decimal places
Answer:
Z = 0.87
Explanation:
Given the following data;
Sample 1:
n1 = 30
Mean, X = 2.36
Standard deviation, Ox = 0.96
Sample 2:
n2 = 60
Mean, Y = 2.19
Standard deviation, Oy = 0.66
The formula for test statistics for two population is;
[tex]Z = \frac{X-Y}{\sqrt{(\frac{Ox^2} {n_1} } +\frac{Oy^2}{n_2} )}}[/tex]
Substituting the values, we have;
[tex]Z = \frac{2.36-2.19}{\sqrt{(\frac{0.96^2} {30} +\frac{0.66^2}{60} )}}[/tex]
[tex]Z = \frac{0.17}{\sqrt{(\frac{0.9216} {30} +\frac{0.4356}{60} )}}[/tex]
[tex]Z = \frac{0.17}{\sqrt{(0.03072 +0.00726)}}[/tex]
[tex]Z = \frac{0.17}{\sqrt{0.03798}}[/tex]
[tex]Z = \frac{0.17}{0.19488}[/tex]
Z = 0.8723
The test statistics to 2 d.p is 0.87
Therefore, Z = 0.87
please help!!!!! idk how to do this
Answer:
30 seconds.
Step-by-step explanation:
So, we have the equation:
[tex]h(t)=-16t^2+h[/tex]
Where t is the time in seconds and h is the initial height.
A barometer falls from a weather balloon at a height of 14,400 feet. In other words, the initial height is 14,400. Substitute for h:
[tex]h(t)=-16t^2+14400[/tex]
We need to find when the barometer hits the ground. Ground level is 0 feet. Therefore, we can substitute h(t) for 0 and solve for the equation (solve for t) in order to find how long (in seconds) it took for the barometer to fall:
[tex]0=-16t^2+14400\\-14400=-16t^2\\900=t^2\\t=\pm\sqrt{900} \\\text{Time cannot be negative.}\\t=\sqrt{900}\\ t=30 \text{ seconds}[/tex]
Therefore, it took 30 seconds for the barometer to hit the ground when it fell at a height of 14,400 feet.
Edit: Spelling.
Lupe va al mercado y compra abarrotes con los 2/5 de su dinero ; luego va a la seccion de carnes y compra con los 3/3 de lo que le queda ; si gasta 3 soles en pasaje de ida y vuelta ; ¿con cuanto dinero salio de su casa si llega de regreso a su casa con 48 soles?
Answer:
Cantidad que Lupe dejó en casa con inicialmente = 127.5 soles.
Amount that Lupe left home with initially = 127.5 soles.
Step-by-step explanation:
Pregunta correcta
Lupe va al mercado y compra abarrotes con los 2/5 de su dinero ; luego va a la seccion de carnes y compra con los 1/3 de lo que le queda ; si gasta 3 soles en pasaje de ida y vuelta ; ¿con cuanto dinero salio de su casa si llega de regreso a su casa con 48 soles?
Solución
Deje que la cantidad de dinero que Lupe dejó en casa sea x soles.
Lupe compra comestibles con 2/5 de su dinero. Es decir, Lupe gasta (2/5) × x = (2x/5)
En este punto, Lupe se queda con
x - (2x/5) = (3x/5) soles.
Lupe luego gasta 1/3 de lo que queda en la carne
(1/3) de lo que queda = (1/3) × (3x/5) = (x/5)
Lo que significa que Lupe gasta (x/5) soles en la sección de carne.
Cantidad restante después de la sección de carne = (3x/5) - (x/5) = (2x/5)
Lupe gasta 3 soles en el viaje de ida y vuelta al mercado y se queda con 47 soles después de todo.
(2x/5) - 3 = 48
(2x/5) = 48 + 3 = 51
2x = 5 × 51 = 255
2x = 255
x = (255/2) = 127.5 soles
¡¡¡Espero que esto ayude!!!
English Translation
Lupe goes to the market and buys groceries with 2/5 of her money; then he goes to the meat section and buys with 1/3 of what he has left; if you spend 3 soles on a round trip ticket; How much money did you leave your home with if you arrive home with 48 soles?
Solution
Let the amount of money Lupe left home with be x soles.
Lupe buys groceries with 2/5 of her money
That is, Lupe spends (2/5) × x = (2x/5)
At this point, Lupe is left with
x - (2x/5) = (3x/5) soles.
Lupe then spends 1/3 of what is left on meat
(1/3) of what is left = (1/3) × (3x/5) = (x/5)
Meaning that Lupe spends (x/5) soles at the meat section.
Amount left after the meat section = (3x/5) - (x/5) = (2x/5)
Lupe spends 3 soles on round ticket trip to market and is left with 47 soles after everything.
(2x/5) - 3 = 48
(2x/5) = 48 + 3 = 51
2x = 5 × 51 = 255
2x = 255
x = (255/2) = 127.5 soles
Hope this Helps!!!
HELPPPP The equation 2x = 3y – 5 when written in slope-intercept form is: y = 2x – 5. y = -2x + 5. y = 2x + 5. None of these choices are correct.
Answer:
Y= 2/3x +(5/3)
Step-by-step explanation:
First, have to get Y alone on one side 3y=2x+5
Second, have to get read of the 3 with the Y so divide each side by three.
Which table represents a direct variation function? A table with 6 columns and 2 rows. The first row, x, has the entries, negative 3, negative 1, 2, 5, 10. The second row, y, has the entries, negative 4.5, negative 3.0, negative 1.5, 0.0, 1.5. A table with 6 columns and 2 rows. The first row, x, has the entries, negative 5.5, negative 4.5, negative 3.5, negative 2.5, negative 1.5. The second row, y, has the entries, 10, 8, 6, 4, 2. A table with 6 columns and 2 rows. The first row, x, has the entries, negative 5.5, negative 5.5, negative 5.5, negative 5.5, negative 5.5. The second row, y, has the entries, negative 3, negative 1, 2, 5, 10. A table with 6 columns and 2 rows. The first row, x, has the entries, negative 3, negative 1, 2, 5, 10. The second row, y, has the entries, negative 7.5, negative 2.5, 5.0, 12.5, 25.0.
Answer:
The correct option is;
A table with 6 columns and 2 rows. The first row, x, has entries, negative 3, negative 1, 2, 5, 10. The second row, y, has entries, negative 7.5, negative 2.5, 5.0, 12.5, 25
Please find attached the graphs of the table data
Step-by-step explanation:
Each of the given table data of in the tables are analysed to find direct variation;
Table 1
x, -3, -1, 2, 5, 10
y, -4.5, -3.0, -1.5, 0.0, 1.5
-4.5/-3 = 1.5 ≠ -3.0/-1 = 3
No direct variation
Table 2
x, -5.5, -4.5, -3.5, -2.5, -1.5
y, 10, 8, 6, 4, 2
10/(-5.5) = -20/11 ≠ 8/(-4.5) = -16/9
However, 10/(-5.5 + 0.5) = -2 = 8/(-4.5 + 0.5) = -2
Adjusted direct variation
Table 3
x, -5.5, -5.5, -5.5, -5.5, -5.5
y, -3, -1, 2, 5 , 10
-3/(-5.5) ≠ -1/-5.5
No direct variation
Table 4
x, -3, -1, 2, 5, 10
y, -7.5, -2.5, 5.0 , 12.5, 25
-7.5/-3 = 2.5 = -2.5/(-1) = 5.0/2 = 12.5/5 =25/10
Direct variation exists
Answer:
so D
Step-by-step explanation:
Suppose your car has hhh liters of engine oil in the morning. During the day, some oil may have leaked, you may have added more oil, or both. The oil level in the evening is ggg liters.
Answer:
g = (h+a) - l
None of them
Step-by-step explanation:
Suppose your car has h liters of engine oil in the morning. During the day, some oil may have leaked, you may have added more oil, or both. The oil level in the evening is g liters. Which of the following expressions always represents how far away the new oil level is from the previous oil level? H+G lGl none of them
Let
h = liters of oil in the morning
l= liters that has leaked
a= liters that were added during the day
g= amount of liters at the end of the evening
Total liters of oil in the evening= (litres of oil in the morning + litres of oil added during the day) - litres of oil that leaked
Substituting each variable into the formula, we have
g = (h+a) - l
The slope of the line below is -3 which is the following is the point - slope from the line ?
Answer:
D. y + 6 = -3(x - 2)
Step-by-step explanation:
To find the equation in point-slope form, you need to use the slope and a point from that line. The slope is -3 and the point given is (2, -6).
Point-slope form is y - y₁ = m(x - x₁). Plug in the slope and point.
y - (-6) = -3(x - 2)
y + 6 = -3(x - 2)
Answer:
D. [tex]y - 2 = -3(x+6 )[/tex]
Step-by-step explanation:
Well point slope form is,
[tex]y - y_{1} = m(x-x_{1} )[/tex]
So we already have slope meaning we can plug that in for m.
[tex]y - y_{1} = -3(x-x_{1} )[/tex]
And with the given point (2,-6),
we can create point slope form.
[tex]y - 2 = -3(x+6 )[/tex]
Therefore,
the answer is d. [tex]y - 2 = -3(x+6 )[/tex].
Hope this helps :)
10 pts
A 25-foot ladder is placed against a building and the top of the ladder makes a 32° angle with the
building. How many feet away from the building is the base of the ladder? Write only the number
rounded to the nearest tenth of a foot.
Answer:
13.2 ft
Step-by-step explanation:
We are given a ladder, a building, and an angle. Let's construct a right triangle (see attachment).
In this right triangle, we know that the hypotenuse (the ladder) is 25 feet, while the angle made between the top of the ladder and the building is 32°. Since we want to find the number of feet between the building and the base of the ladder, we will use the trigonometric function sine, which is opposite divided by hypotenuse.
Here, the opposite side is the value we want to find, while the hypotenuse is the length of the ladder.
We have:
sin(32°) = opposite / hypotenuse = x / 25
x = 25 * sin(32°) ≈ 13.2 ft
The answer is thus 13.2 ft.
~ an aesthetics lover
URGENT!!!!!!
Identify the sequence graphed below and the average rate of change from n = 0 to n = 3 . (2, 10) (3, 5) (4, 2.5) (5, 1.25)
A) a_n=8(1/2)^(n-2); average rate of change is -3
B) a_n=10(1/2)^(n-2); average rate of change is -(35/3)
C) a_n=8(1/2); average rate of change is 3
D) a_n=10(1/2)^(n-2); average rate of change is 35/3
Answer: Choice B
a_n = 10(1/2)^(n-2) is the nth term
average rate of change = -35/3
=======================================================
Explanation:
Each time x increases by 1, y is cut in half. For instance, going from (2,10) to (3,5) shows this.
If we want to go in reverse, decreasing x by 1 will double the y value. So (1,20) is another point and (0,40) is another. We'll be using (0,40) and (3,5) because we want the average rate of change from x = 0 to x = 3. I'm using x in place of n here.
Use the slope formula to find the slope of the line through (0,40) and (3,5)
m = (y2-y1)/(x2-x1)
m = (5-40)/(3-0)
m = -35/3
The negative slope means the line goes downhill as you read it from left to right. The average rate of change from n = 0 to n = 3 is -35/3
The nth term of this geometric sequence is 20(1/2)^(n-1) since 20 is the first term (corresponds to n = 1) and 1/2 is the common ratio. Your teacher has done a bit of algebraic manipulation to change the n-1 into n-2. This means the 20 has to change to 10 to counterbalance.
In other words, 20(1/2)^(n-1) is equivalent to 10(1/2)^(n-2) when n starts at n = 1.
Which of the following is a factor of x3+ 6x2 + 5x – 12?
A.X + 1
B. x - 3
C. x + 2
D. x + 4
1,3,4 that is the answer
Answer:
The answer is option D.Step-by-step explanation:
x³ + 6x² + 5x - 12
A factor of the polynomial is the value of x when substituted into the expression will make it zero
Choosing x + 4
x = - 4
We have
(- 4)³ + 6(- 4)² + 5(- 4) - 12
-64 + 96 - 20 - 12 = 0
Since the result is zero
x + 4 is a factor of the polynomial
Hope this helps you
what is the value of the exponent expression below?
Answer:
6Option C is the correct option.
Step-by-step explanation:
[tex] {36}^{ \frac{1}{2} } [/tex]
Write the number in exponential form with a base of 6
[tex] =( {6}^{2}) \: ^{ \frac{1}{2} } [/tex]
Simplify the expression by multiplying the exponents
[tex] = 6[/tex]
Hope this helps..
Best regards!!
Find the value of x.
Answer:
x = 84°Step-by-step explanation:
A radius to the tangent point always forms a right angle with the tangent.
m∠OAB = m∠OCB = 90°
[tex]m\angle AOC=\stackrel{\big{\frown}}{ADC}=96^o[/tex]
The sum of the angles in the quadrilateral is 360°, so:
x = 360° - 2•90° - 96° = 84°
if m∠2= 137 and m∠P= 22, what is m∠O? answers are 43,21,65,115
Answer:
21
Step-by-step explanation:
since it is a triangle subtract 180 by 137 and 22
180-(137+22) or 180-132-22
hope this helps
Answer:
21
Step-by-step explanation:
We khow that the sum of a triangle's angles sizes is 180°
137+22 = 159°substract the sum of the two khown angles from 180°
180°-159° = 21 °so m<0 = 21°
It takes 4 people 2 days to paint a wall. How long would it take if we got 8 people to do it?
Answer:
if it takes 4 people for 2 days
4+4= 8
so it would only take 8 people for 1 day
Answer:
1 day
Step-by-step explanation:
4 people = 2 days
→ Work out how long 1 person takes
4 people = 2 days
( ÷ 4 ) ( × 4 )
1 person = 8 days
→ Work out how long 8 people can do it
1 person = 8 days
( × 8 ) ( ÷ 8 )
8 people = 1 day
Find the value of this expression if x=3 x^2 + 3/x-1
Answer: 9
Step-by-step explanation:
[tex]3^2 + \frac{3}{3}-1\\\\=9+1-1\\\\=9[/tex]
If a circle is dilated by a scale factor of
what will be the lenth of the new radius?
18m
12 m
9 m
36 m
27 m
Answer/Step-by-step explanation:
The scale factor is missing in the question. However, here's how to find the length of the new radius if given a known scale factor.
Length of new radius = length of the radius of the dilated circle × scale factor of dilation
Length of the radius of the dilated circle is given as 18m
Therefore,
Length of new radius = 18m × scale factor.
If the scale factor is a fraction, it means the new length would be smaller than 18m. But if the scale factor is a whole number, the new length of the radius would be greater than 18m.
Let's assume any of the following scale factors was what was given in the question:
*If scale factor given is ½, new radius length = 18m × ½ = 9m
*If scale factor given is 2, new radius length = 18m × 2 = 36m
A regular polygon has 10 sides. What is the measure of each interior angle of the polygon? 36° 1440° 144° 72°
Answer:
144°
Step-by-step explanation:
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
Here n = 10, thus
sum = 180° × 8 = 1440°
Each interior angle = 1440° ÷ 10 = 144°
Answer:
144 deg
Step-by-step explanation:
Sum of the measures of the angles of a polygon with n sides:
(n -2)180
For a 10-sided polygon, n = 10.
The sum of the measures is
(10 - 2)180 = (8)180 = 1440
Since the polygon is regular, all angles have the same measure, so the measure of 1 angle is
1440/10 = 144
Answer: 144 deg
The functions f(x) and g(x) are shown on the graph.
f(x) = x2
What is g(x)?
A. g(x) = -x2 + 2
B. g(x) = -X2 - 2
C. g(x) = (-x)2 - 2
D. g(x) = (-x)2 + 2
B. [tex]-x^2-2[/tex].
Hope this helps.
Answer:
i think its g(x)=-x^2-2
Step-by-step explanation:
Simplify. Your answer should contain only positive exponents.
9) 3^-1 • 3^0
Answer:
1 / 3^1
Step-by-step explanation:
3^-1 • 3^0
When multiplying exponents with the same base, we add the exponents
3^ (-1+0)
3 ^-1
We know that a^ - b = 1/a^b
3 ^ -1 = 1/3^1
One angle of an isosceles triangle is 80º. What are the other two angles?
Answer:
80 and 20
Step-by-step explanation:
80+80+20=180
A box contains 6 red, 3 white, 2 green, and 1 black (total 12) identical balls. What is the least number of balls necessary to take out randomly (without looking) to be sure of getting: at least three the same color?
Answer:
We shall need to pick at least 4 balls to be sure that we are getting balls with the same color
Step-by-step explanation:
Here, we want to know the least number of balls to be taken out of the box to be sure that we have all the three colors represented.
We know there are 12 identical balls, with the least numbers of balls being 1 and 2. Hence, to be able to know we have all the colors of balls represented, we will need to have taken all the less represented ones i.e the 1 and 2 , and this means that the next number of ball which would be taken will confidently confirm that we have taken all the colors since we would have exhausted picking other balls at this point.
So we shall be needing at least 4 balls picked to ensure that we have all the colors represented
can someone answer the underlined question? (number 9)
Answer:
Slope = -6/7
Step-by-step explanation:
You need to use the formula m = y2 - y1 ÷ x2 - x1
The formula means: slope = the y coordinate of point 2 subtract the y coordinate of point 1, divided by the x coordinate of point 2 subtract the x coordinate of point 1
So,
m = 2 - 5 ÷ 3/2 - (-2)
m = -3 ÷ 7/2
m = -6/7
Hope this helps :)
There are 5 orange bumper cars and 3 green bumper cars that are being tested
for safety for a ride at an amusement park. Two bumper cars are tested at
random, one at a time, without retesting the same car.
Find the probability that both cars are orange.
Enter the correct answer in the box.
Answer:
5/14
Step-by-step explanation:
I assume after testing the 1st car, it is not placed back into the pool.
So, 1st test orange is 5/8
2nd test orange is 4/7.
Both had to be true, so 5/8 x 4/7 = 5/14
Antonio's toy boat is bobbing in the water next to a dock. Antonio starts his stopwatch, and measures the vertical distance from the dock to the height of the boat's mast, which varies in a periodic way that can be modeled approximately by a trigonometric function. The vertical distance from the dock to the boat's mast reaches its highest value of -27 \text{ cm}−27 cmminus, 27, space, c, m every 333 seconds. The first time it reaches its highest point is after 1.31.31, point, 3 seconds. Its lowest value is -44\text{ cm}−44 cmminus, 44, space, c, m. Find the formula of the trigonometric function that models the vertical height HHH between the dock and the boat's mast ttt seconds after Antonio starts his stopwatch. Define the function using radians.
Answer:
Step-by-step explanation:
Since we're given a time at which the height is maximum, we can use a cosine function for the model.
The amplitude is half the difference between the maximum and minimum: (-27 -(-44))/2 = 8.5 cm.
The mean value of the height is the average of the maximum and minimum: (-27 -44)/2 = -35.5 cm.
The period is given as 3 seconds, and the right shift is given as 1.31 seconds.
This gives us enough information to write the function as ...
H(t) = (amplitude)×cos(2π(t -right shift)/period) + (mean height)
H(t) = 8.5cos(2π(t -1.31)/3) -35.5 . . . . cm
In the figure, OM is perpendicular to AB. Prove that M is the the midpoint of AB.
we know by looking at the picture that m is the midpoint of AB since O to M doted lines had half into two equal parts.so M is in the midpoints of AB.
Step-by-step explanation:
to prove: M is the midpoint of AB
given: OM is perpendicular to AB
construction: joint AO and BO
proof: in the given fig,
OA and OB are joined
In Δ AOM and ΔBOM
AO = BO ( two sides of Δ AOB )
OM = OM ( common )
∴ Δ AOM ≅ Δ BOM ( by SAS rule )
∴ AM = BM ( by CPCT ) -------- 1
∴ M is the midpoint of AB ( from 1 )
⇒hence proved
HOPE THIS HELPED and PLEASE MAKE ME AS THE BRAINLIEST
A track star runs twice a day. In the morning, he runs on a track that is 2 1/2 miles per lap and he runs 3 1/2 laps. In the afternoon he runs on a track that is 1 3/10 miles per lap and he runs 3 laps. How
many total miles does he run in a day?
Answer:
12.65 miles
Step-by-step explanation:
he runs on a track that is 2 1/2 miles per lap and he runs 3 1/2 laps:
2 1/2 *3 1/2= 5/2 * 7/2=35/4=8.75 miles
afternoon he runs on a track that is 1 3/10 miles per lap and he runs 3 laps
1 3/10 *3=13/10*3=39/10= 3.9
total miles he runs in a day: 8.75+3.9= 12.65 miles
Can someone help me with this problem?
━━━━━━━☆☆━━━━━━━
▹ Answer
Slope = 1
▹ Step-by-Step Explanation
y = mx + b
'm' represents the slope. since there is no number before the x, the coefficient will always be 1. therefore, the slope is 1.
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Cheryl is planning to go to a four-year college in two years. She develops a monthly savings plan using the estimates shown. What should her monthly savings be? (rounded to the nearest cent)
Answer:
$541.67 per month
Step-by-step explanation:
Tuition and other expenses = $8,250 per semester.
There are two semesters in a year
She has 4 years to spend
Total semester=4years*2semesters
=8 semesters
4 years in college which is a total of 8 semesters.
Total Tuition and other expenses = $8,250 * 8
= $66,000
She needs a total of $66,00 to complete her college
Assistance from parents=$15,000
Financial aid(per semester)=$4750
Total financial aid=$38,000
Total assistance=
Assistance from parents+ financial aid
=$15000+$38,000
=$53,000
Total savings=Total amount needed - Total assistance
=$66,000 - $53,000
=$13,000
She needs to save $13,000 in two years
There are 12 months in one year
2 years=2*12=24 months
Monthly savings=Total savings/24 months
=$13,000/24
=$541.666666
To the nearest cent
=$541.67
Answer: $541.67
Step-by-step explanation: Got it right on TTM.
pls help !!!! i do not know or understand this at all
Answer:
(3, -3)
Step-by-step explanation:
Given functions:
f(x)= x² - 5x + 3and
f(x)= -3Solution is the Intersect which is found by equalizing the two functions:
x² - 5x + 3= -3Solving for x:
x² - 5x + 6=0x² - 2x -(3x -6) =0x(x-2) - 3(x-2)=0(x-2)(x-3)= 0x= 2 and x= 3As both values of x for the first function reveal f(x) = -3, the pairs are:
(2, -3) and (3, -3)