The x-intercepts of an equation are simply the zeros of the equation
The equation [tex]\mathbf{y = bx(x - a)(x -a)(x + b)(x - b)}[/tex] has 4 distinct x-intercepts
The equation is given as:
[tex]\mathbf{y = bx(x - a)(x -a)(x + b)(x - b)}[/tex]
Set the equation to 0; i.e. calculate the zeros
[tex]\mathbf{bx(x - a)(x -a)(x + b)(x - b) = 0}[/tex]
Divide both sides by constant b
[tex]\mathbf{x(x - a)(x -a)(x + b)(x - b) = 0}[/tex]
Split the above equation, as follows
[tex]\mathbf{x= 0\ or\ x - a = 0\ or\ x -a = 0\ or\ x + b = 0\ or\ x - b = 0}[/tex]
Solve for x in each of the equation
[tex]\mathbf{x= 0\ or\ x = a\ or\ x = a\ or\ x= -b\ or\ x = b}[/tex]
Remove repeated solutions
[tex]\mathbf{x= 0\ or\ x = a\ or\ x= -b\ or\ x = b}[/tex]
The count of solutions above is 4
Hence, the equation has 4 distinct x-intercepts
Read more about x-intercepts at:
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A line extends from point T to point R. Point S is between points T and R. The space between T and S is labeled 3 x minus 4. The space between T and R is labeled 4 x + 1.
Which expression represents the measure of segment RS?
7x – 3
7x + 5
x + 5
x – 3
Answer:
x+5
Step-by-step explanation:
Answer:
which expression represents the measure of segment RS? x + 5
Step-by-step explanation:
on engenuity
Pam works on
commission from sellingE
stocks for a local bank.
She had a great month
and sold $2.5 million
dollars in investments
this month. She earns
4% commission on the
10% fee the bank
charges for sales over
$800,000. How much
did she earn?
Answer:
$10,000
Step by step:
Banks earnings(10%)=x
Pams earnings(4% of banks earnings)=y
10% of $2.5m= $250,000=x
4%(1/25) of $250,000=$10,000=y
Solve for Y
2x+ y/3 = 4
a. y = 6x + 12
b.y = -6x + 12
C. y = (x - 12
d. y = -6x - 12
Answer:
y=−6x+12
so A
Step-by-step explanation:
What is the slope of the line that passes |
through (-3, -1) and (-5, 4) ?
Plz I need help
Answer:
-2.5
basically use slope formula which is x2-x1/y2-y1
3 2/3 x 4 1/8 x 2 1/2
Answer:
=2/3^x62
Step-by-step explanation:
32/3^x41/8x21/2
Slope -2/3 , x-intercept at 3
Answer:
Y=(-3)x+6
Step-by-step explanation:
Which triangle correctly shows that the side opposite the larger angle is the larger side? A triangle has side lengths of 13, 5, 10 and angle measures of 30 degrees, 100 degrees, and 50 degrees. A triangle has side lengths of 5, 5, 5 and angle measures of 60 degrees, 60 degrees, 60 degrees. A triangle has side lengths 5, 13, 12 and angle measures of 90 degrees, 67 degrees, 23 degrees.
Answer:
C) is your choice
Step-by-step explanation:
So yeah can anyone help me out be a tone
Answer:
p = -4
Step-by-step explanation:
-3( 2+4p) + 7 = 49
Subtract 7 from each side
-3( 2+4p) + 7 -7= 49-7
-3( 2+4p) = 42
Divide by -3
-3( 2+4p) /-3 = 42/-3
( 2+4p) = -14
Subtract 2 from each side
2+4p-2 = -14-2
4p = -16
Divide by 4
4p/4 = -16/4
p = -4
PLEASE HELP PLEASe IT'S ONLY ONE QUESTION AND ITS SHORT
Answer:
Yes.
Step-by-step explanation:
It passes the line test.
The angle o represents the phase shift, determined by the initial conditions of the experiment or the position of the weight at t = 0. If the weight is at its maximum positive position (weight is above equilibrium) at t = 0, then o = 0. If the weight is at its maximum negative position (spring is stretched and weight is below equilibrium) at t = 0, then o = pi. If the weight is traveling in the negative direction and passing through equilibrium at t = 0, then o = pi/2. In the response box, describe the initial condition of our experiment; specifically, describe the position of the weight and the direction in which it was traveling.
Answer
initially t=0 => c2sin(0)+c1cos(0) => y=0+c1 => y=0+5 => y=5
The weight was approaching the equilibrium position from the positive direction. The weight was on its way down, with the spring stretching
Step-by-step explanation:
c1=5
If 6 candy bars cost a total of $12, then $2 is the ___________ of the candy bars. *
Pls help me ASAP!!!!!
Answer:
2 4/5
Step-by-step explanation:
You first see how many times the bottom number can fit in the top number. The number 5 can go in 14 two times. It can't go in three because then it would be over 14. So you take that "2" and that is your hole number and you are left with 4/5. so 2 4/5
Answer:
It is c, 2 4/5
Step-by-step explanation:
5 goes into 14 2 times with 4/5 left over
Pam rented a bike from Jim's bike shop. Jim charges a rental fee of $6 and then $3 per hour
to rent the bike. If Pam paid $27, for how many hours did she rent the bike?
Answer:
7 hours
Step by step instructions:
$3 x 7 hours = $21
$21 + $6 = $27
Who can help we with this ?, if you can please show the work
piece #1 is x
the answer is c
2. Liz claimed that the polynomial 4x -12 + 2x is a trinomial because it has three
terms.
Is Liz correct? Explain your reasoning in complete sentences. Be specific!
Answer:
see below
Step-by-step explanation:
The first step is to combine like terms
4x -12 + 2x
6x -12
Then determine the number of terms
2 terms so it is a binomial
Answer:
Im not sure if I’m correct but I think she is correct because a trino Mila doesn’t always have to have a exponent but three terms
Step-by-step explanation:
not positive
Use the distributive property to write an equivalent expression.
4(p - 7q+3)
Answer:
4p - 28q + 12
PLEASE ANSWER REALLY EASY
Answer:
I will answer here because I am glitching.
Step-by-step explanation:
1. 1.36 < [tex]\sqrt{2}[/tex] < 2.45
2. 1.65 < [tex]\sqrt{3}[/tex] < 2.34
3. 1.65 < [tex]\sqrt{4}[/tex] < 2.34
4. 2.14 < [tex]\sqrt{5}[/tex] < 3.56
5. 2.41 < [tex]\sqrt{6}[/tex] < 3.56
I believe this is correct but check if I am wrong.
Given three collinear points A, B and C. How many line segments do
they determine? Name them.
Answer:
Three segments: AB, BC, AC
Step-by-step explanation:
Remember to put the line on top since they’re segments.
Hope this helps!
Mercurys average distance fron the sun is 35,000,000 miles. It takes 3 minutes for light to travel from the sun to Mercury. Neptune with an average of 2.8 x 10 to the power or 9 miles from the sun. How many times farther from the sun is Neptune than Mercury? How ling does it take light to reach Neptune?
Answer:
Neptune is 80 times farther from the Sun than Mercury.
It takes 4 hours to reach the light from the Sun to Neptune.
Step-by-step explanation:
Given that the average distance between the Sun and Mercury,
[tex]d_1=35,000,000[/tex] miles [tex]=3.5\times 10^7[/tex] miles.
The time to reach the light from the sun to Mercury, [tex]t_1 = 3[/tex] minutes
Let v m/s be the speed of light.
So, [tex]v=\frac{d_1}{t_1}\cdots(i)[/tex] [as speed = distance/time]
Now, the average distance between the Sun and Neptune,
[tex]d_2=2.8\times 10^9[/tex] miles.
The ration of the average distance of Neptune and Mercury from Sun,
[tex]\frac{d_2}{d_1}=\frac{2.8\times 10^9}{3.5\times 10^7}[/tex]
[tex]\frac{d_2}{d_1}=80\cdots(ii)[/tex]
So, Neptune is 80 times farther from the Sun than Mercury.
The time to reach the light from the sun to Neptune,
[tex]=\frac{d_2}{v}[/tex] [as time=distance/speed]
[tex]=\frac{d_2}{d_1/t_1}[/tex] [using equation(i)]
[tex]=\frac {d_2}{d_1}\times t_1[/tex]
[tex]=80\times 3[/tex] [using equation(ii)]
=240 minutes
=4 hours [as 1 hour =60 minutes]
Hence, it takes 4 hours to reach the light from the Sun to Neptune.
Using the speed - distance relationship, we can deduce that Neptune is 80 times farther from the sun than Mercury and it will take 240 minutes for light from the sun to reach Neptune.
Given the Parameters :
Mercury's average distance from sun = 35000000 miles Time taken for light to travel to mercury = 3 minutes Neptune's average distance from sun = [tex] 2.8 \times 10^{9} [/tex]Number of times Neptune is father from the sun than Mercury :
(Neptune's distance) ÷ Mercury's distance [tex] \frac{2.8 \times 10^{9}}{35000000}= 80 [/tex]Hence, Neptune is 80 times farther from the sun than Mercury.
Time taken for light to reach Neptune :
Time taken to each mercury × 803 minutes × 80 = 240 Minutes
60 minutes = 1 hour
240 minutes = (240 ÷ 60) = 4 hours
Therefore, it would take 4 hours for light to reach Neptune.
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Help! look at the image of the table of values below. Over which interval of x is the average rate of change the largest?
Answer:
A
Step-by-step explanation:
There is no way to tell a pattern.
(Help me ASAP please) Which table contains only corresponding X-values in a Y-values where the value of Y is 3 more than the quotient of X and 2?
Answer:
Step-by-step explanation:
first ,you put it in a equation :y=x/2 +3 and you get an ordered pair from the graph like 7 is x and 6.5 is y ,answer =7/2 =3.5 +3=6.5 and the y is also 6.5 so that is your answer.
Lerna's Hydra is a mythological character that appears in some stories such as the 12 Tasks of Hercules. The Hydra was a one-headed monster but when it is cut off, 2 more heads grow in its place. If a hero tried to conquer it by cutting off all of its heads every day, how many heads would the Hydra have on the third day? And at the end of 10 days of trying to kill it? *
Answer:
Step-by-step explanation:
Initially the monster is one-headed, when it is cut off, 2 more heads grow in its place, when the two heads are cut off, 4 will grow in its place. This will go on an on and the amount of heads that grows each day will form a geometric sequance as shown;
1, 2, 4...
The nth term of an arithmetic sequence is expresses as;
[tex]T_n = ar^{n-1}[/tex] where;
a is the first term
r is the common ratio
n is the number of terms
To get the number of heads that the Hydra have on the third day, we will have to find the fourth term of the sequence since the first cutting was done the next day (second day).
from the sequence above;
a = 1
r = 2/1 = 4/2 = 2
T4 = 1(2)^{4-1}
T4 = 2^3
T4 = 8
Hence the hydra will have 8 heads on the third day.
To know the number of heads at the end of 10 days, we will find the 11th term of the progression
T11 = 1(2)^{11-1}
T4 = 2^10
T4 = 1024
He will have 1024 heads after 10 days of trying to kill the monster.
The number of heads that would the Hydra have on the third day is 8
And, at the end of 10 days of trying to kill it is 1024.
The calculation is as follows:a = 1
r = 2 by 1 = 2
T4
= 8
So the hydra will have 8 heads on the third day.
Now
To know the number of heads at the end of 10 days, we will determine the 11th term of the progression
= 1024
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Solve for x:
3x-3=x-19
Answer: x = -8
Step-by-step explanation: 2x=-16, x=-8
Answer:
-8
Step-by-step explanation:
3x - 3 =x - 19
3x - x =-19 +3
2x =-16
x=-16 :2
x=-8
1/2*x=3/4(x-2) what is the answer?
Answer:
x=6
Step-by-step explanation:
1/2x=3/4(x-2)
1/2x=3/4x-1.5 (distribute)
+1.5 +1.5
1/2x+1.5=3/4x
-1/2x -1/2x
1.5=1/4x
6=x
hope this helps
brainliest?
In ΔVWX, w = 520 cm, ∠W=93° and ∠X=68°. Find the length of x, to the nearest centimeter.
Answer:
482.7972612 cm. Just round from here.
Step-by-step explanation:
Ah, the sine law questions. Ok so you know [tex]\frac{sin(A)}{a} = \frac{sin(B)}{b} = \frac{sin(C)}{c}[/tex]. If you don't, voila. Obviously, the variables are different but we can use the same formula. So, we have
[tex]\frac{sin(X)}{x} = \frac{sin(W)}{w}[/tex]
Plug in:
[tex]\frac{sin(68)}{x} = \frac{sin(93)}{520}[/tex]
The answer when solving for x is the above
Answer:
483
Step-by-step explanation:
delta math
Help Me need help please it is due today please help ASAP
Answer:
87
Step-by-step explanation:
you subtract 3:32-2:45
Mr. Heath owns a game store.
He offers workshops where students learn about different kinds of games and how to design their own games.
Sia designs a board game in which a card is drawn on each turn.
• A blue card means move forward 4 squares.
• A red card means move back 6 squares.
Sia begins at 0. She draws a blue card on each of her first three turns.
Then Sia draws only red cards and ends up back at 0. How many red cards did Sia draw?
he drew 2 cards
Step-by-step explanation:
because 4x3 is 12 and to get back to zero u would have to draw 2 red cards which are 6 each. so 4x3=12 and then 6x2=12 12-12=0
The balance y (in dollars) of your savings account after t years is represented by y=300(1.05)'. The beginning balance of your friend's account is $340, and the balance increases by $10 each year. a. Compare the account balances by calculating and interpreting the average rates of change from t=2 to t=6.
Answer:
My balance grows faster than my friends balance.
Step-by-step explanation:
My balance
[tex]y=300(1.05)^t[/tex]
where
t = Time
Average rate from t=2 to t=6 is given by
[tex]\dfrac{t(6)-t(2)}{6-2}\\ =\dfrac{300(1.05)^6-300(1.05)^2}{4}\\ =\mathbf{17.82}[/tex]
My friend's balance is given by
[tex]y=340+10t[/tex]
Average rate is given by
[tex]\dfrac{t(6)-t(2)}{6-2}\\ =\dfrac{(340+10\times 6)-(340+10\times 2)}{4}\\ =\mathbf{10}[/tex]
My balance grows faster than my friends balance.
helpgchjsghjcvbxnvbsvjdgasghgbhdvbahgvgbd
Answer:
yeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeet
Step-by-step explanation:
The vertices of triangle FGH are F(4, 1), G(0, 3), and H(2, -1). After a translation of 6 units left and 2 units down, triangle FGH becomes triangle F'G'H'. After a translation of 1 unit right and 5 units up, triangle F'G'H' becomes triangle F"G"H". What translation would move triangle FGH to triangle F"G"H" directly? a. 6 units left and 2 units down c. 5 units left and 3 units up b. 1 unit left and 5 units up d. 2 units right and 6 units down Please select the best answer from the choices provided A B C D
Answer:
c. 5 units left and 3 units up
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation is translation, rotation, reflection and rotation.
If a point A(x, y) is translated a units right and b units up, the new location is at A'(x+a, y+b), while if a point A(x, y) is translated a units left and b units down, the new location is at A'(x-a, y-b)
The vertices of triangle FGH are F(4, 1), G(0, 3), and H(2, -1). A translation of 6 units left and 2 units down, triangle FGH becomes triangle F'(-2, -1) G'(-6, 1) H'(-4, -3). A translation of 1 unit right and 5 units up, triangle F'G'H' becomes triangle F"(-1, 4) G"(-5, 6) H"(-3, 2)
The translation of FGH to F"G"H" is a translation of (x -5, y + 3), that is 5 units left and 3 units up