Answer:
The "possible" rational zeros are:
±
1
,
±
2
,
±
4
,
±
8
The actual zeros are:
−
1
,
4
,
±
√
2
Explanation:
f
(
x
)
=
x
4
−
3
x
3
−
6
x
2
+
6
x
+
8
By the rational root theorem, any rational zeros of
f
(
x
)
are expressible in the form
p
q
for integers
p
,
q
with
p
a divisor of the constant term
8
and
q
a divisor of the coefficient
1
of the leading term.
That means that the only possible rational zeros are:
±
1
,
±
2
,
±
4
,
±
8
We find:
f
(
−
1
)
=
1
+
3
−
6
−
6
+
8
=
0
So
x
=
−
1
is a zero and
(
x
+
1
)
a factor:
x
4
−
3
x
3
−
6
x
2
+
6
x
+
8
=
(
x
+
1
)
(
x
3
−
4
x
2
−
2
x
+
8
)
Notice that the ratio between the first and second terms of the remaining cubic is the same as that between the third and fourth terms. So this cubic will factor by grouping:
x
3
−
4
x
2
−
2
x
+
8
=
(
x
3
−
4
x
2
)
−
(
2
x
−
8
)
x
3
−
4
x
2
−
2
x
+
8
=
x
2
(
x
−
4
)
−
2
(
x
−
4
)
x
3
−
4
x
2
−
2
x
+
8
=
(
x
2
−
2
)
(
x
−
4
)
Finally we can factor the quadratic as a difference of squares:
x
2
−
2
=
x
2
−
(
√
2
)
2
=
(
x
−
√
2
)
(
x
+
√
2
)
So the zeros are:
−
1
,
4
,
±
√
2
what is the point in the middle of a circle called
Answer:
Step-by-step explanation:
Center: The center of a circle is defined as the point in the middle of the circle. The points that make up the curve that is the circle are all equidistant from the center point.
Answer:
Center of the circle.
Step-by-step explanation:
3/10y - 2/5 i need to find the coefficient and i dont know how
[tex] \frac{3}{10y} - \frac{2}{5} = \frac{3 - 4y}{10y} [/tex]
3x- 25 = 11x -5 + 2x
Please show working.
[tex]3x-25 =11x -5 +2x \\\\\implies 3x -25 = 13x-5\\\\\implies 13x -3x = 5-25\\\\\implies 10x = -20\\\\\implies x = -2[/tex]
How to multiply mixed fractions with same denominators.
Answer:
multiply the numerators; express that product over the product of the denominators
Step-by-step explanation:
Multiplication of fractions is done the same way regardless of whether the denominators are the same or different.
[tex]\dfrac{a}{b}\times\dfrac{c}{d}=\dfrac{ac}{bd}[/tex]
The numerator of the product is the product of the numerators.
The denominator of the product is the product of the denominators.
Find the equation of the line that passes through the given points, in Slope-Intercept Form. (-2, -7) and (3, 8)
Answer:
y=3x-1
Step-by-step explanation:
m=y2-y1/x2-x1
m=8-(-7)/3-(-2)
m=8+7/3+2
m=15/5
m=3
y-y1=m(x-x1)
y-(-7)=3(x-(-2)
y+7=3(x+2)
y+7=3x+6
y=3x+6-7
y=3x-1
- 2x + 4y = 17
3x - 10y = -3
Answer:
1.-2x+4y=17
if you want me to solve for x : x=-17/2 +2y
If you want me to solve for y: y=17/4+x/2
2. If you want me to solve for x: x=-1+10y/3
If you want me to solve for y: y=3/10+3x/10
3. If you want me to do it all together it would be:
x=-79/4, y=-45/8
Step-by-step explanation:
John always wears a shirt, pants, socks, and shoes. He owns 12 pairs of socks, 3 pairs of shoes, 5 pairs of pants, and 5 shirts. How many different outfits can John make?
Answer:
900
Step-by-step explanation:
12 * 3 * 5 * 5 = 900
900
What is the value of H in the diagram below?
Answer:
The answer is 6.5
Step-by-step explanation:
It was a long process, but overall if you look at how long the segment x looks, it has to be less than half of the segment that is 30 units long so the only one that makes sense is 6.5
5 sin^2 x = sin x
please help.
[tex]\\ \sf\longmapsto 5sin^2x=sinx[/tex]
Divide both sides by sin x[tex]\\ \sf\longmapsto \dfrac{5sin^2x}{sinx}=\dfrac{sinx}{sinx}[/tex]
[tex]\\ \sf\longmapsto 5sinx=1[/tex]
[tex]\\ \sf\longmapsto sinx=\dfrac{1}{5}[/tex]
[tex]\\ \sf\longmapsto sinx=0.2[/tex]
[tex]\\ \sf\longmapsto x=sin^{-1}(0.2)[/tex]
[tex]\\ \sf\longmapsto x=11.53[/tex]
what is 18,678,789 times 67,897,867
Which of the following lists of ordered pairs is a function?
A. (0,4),(1,2).(1,0). (2,3)
B. (1,7).(2,5),(3,6), (4,1)
C. (3,-2).(2-1).(3,4),(4,7)
D. (2,5), (3,8). (4, 11),(4,12)
Answer:
B
Step-by-step explanation:
When looking at cordinate points for functions, to be a function, the X-Values cannot come up more than once. B is the only one where there is no repeating X-value, so it is a function.
Hope this helps!!
1/9 × 3 9/10 = as a mixed number
Answer:
4 1/90
Step-by-step explanation:
I did It so yeah thats it
If Don drives 60 miles per hour, can he make it to the beach (200 miles away) in 3 1/2 hours?
Answer:
Yes
Step-by-step explanation:
If Don drives at 60 miles per hour and drives for 3.5 hours, then he can drive:
60 * 3.5 = 210 miles
Because 210 miles is more than 200 miles, the answer is yes, he can make it to the beach in that time.
how many kilograms of pure water is to be added to 100 kilograms of a 30% saline solution to make it a 10% saline solution
Answer:
200 kg
Step-by-step explanation:
If w is the amount of water added, then the concentration of the solution is ...
salt/solute = 100(0.30)/(100 +w) = 0.10
30 = 10 +0.10w . . . . . simplify
20 = 0.10w . . . . . . . . subtract 10
20/0.10 = w = 200 . . . . divide by 0.10
200 kg of water must be added to dilute the solution to 10%.
One yard of ribbon costs $0.49, and 3 yards of ribbon costs $1.49. Which is the better buy?
$0.49 ?
.........................................
Answer:
I think the better one is $1.49
Step-by-step explanation:
That's just my opinion
£160 in the ratio 3:5 how much does Oliver get compared to sue
Answer:
8x=160x=20first num=3×20=60sec num=5×20=100
Step-by-step explanation:
Can someone please help me?
75 POINTS
Answer:
1. 8
2. 4
3. 5
4. 8/125
5. 4/3
6. 6
7. 8
8. 2
Step-by-step explanation:
This is true believe me I checked each one :)
need help urgently vvvvvvv
Step-by-step explanation:
you understand coordinates and how to find them in the chart, yes ?
because I can't draw here, I can only give you the points through which the line has to go.
one point is, of course, (2, -3).
to find another good point we use the slope 3/4.
the slope is the ratio of y change/x change when going from one point to another.
so, we find another point with integer coordinates by e.g subtracting the slope units from the point (addition would also work) :
the other point on the line would be
(2 - 4, -3 - 3) = (-2, -6)
and then you draw a line that goes through both points.
The mean age of 5 people in a room is 39 years. A person enters the room. The mean age is now 36. What is the age of the person who entered the room?
Answer:
21
Step-by-step explanation:
Mean is the average of the objects
With five people, the mean is the average age of these people so what did you divide 5 into to get 39.
5 × 39 = 195
After a person enter the room, total 6 in the room with a mean of 36.
6 × 36 = 216
Now the age of the person who entered the room 216 - 195 = 21
the highest elevation in north america is denali,in alaska ,with an elevation of 20,320 feet above sealevel. the lowest elevation in california, with an elevation of 282 feet below sea level. what is the differce in the highest and lowest elevations in morth american?
Answer:
Step-by-step explanation:
The highest point in North America, Mount McKinley, in the Alaska Range, is 20,320 feet above sea level. The lowest point m North America is 282 feet below sea level and is in Death Valley in California. Which student correctly calculated the difference in elevations? Explain the error.
\begin{matrix} \text{Student A} & \text{Student B}\\ \text{20,320 - 282} & \text{20,320 - ( -282)}\\ \text{20,320 + (-282)} & \text{20,320 + ( + 282)}\\ \text{20,038 feet} & \text{20,602 feet}\\ \end{matrix}
Student A
20,320 - 282
20,320 + (-282)
20,038 feet
Student B
20,320 - ( -282)
20,320 + ( + 282)
20,602 feet
Write the steps you follow when you want to graph an equation y=2x +3.
Step 1;......
Step 2:.....
Step 3:.....
Answer:
1.Pick the point x= 0, y=3 as your starting point.
2. write the slope as a fraction, in this case 2/1. Move up as many times the numerator says (2), and forward as many times the denominator says (1). If either is negative, you move the opposite direction.
3. You got a second point. Put a ruler between them - or any straight edge - and draw the line.
[tex](x+7)(x-2)[/tex]
Answer:
x^2+5x-14
Step-by-step explanation:
Using FOIL method, we get (x^2)+(-2x)+(7x)+(-14), which is just x^2+5x-14
FOIL = First, Outer, Inner, Last
If Maria designs a function to predict the amount of revenue, r, generated as a function of the number of people, n, who attend a fundraiser, explain why 13.5 would not be a member of this function's domain?
Answer:
Only whole numbers of people, n, are assumed in the calculation.
Step-by-step explanation:
The function relating the number of people, n, to the revenue, r, implicity assumes that only whole people will purchase tickets. 13.5 would mean that 13 normal people and 1/2 of a person bought tickets. This can't be in the domain, since the ticket saleperson would run away if 1/2 of a person showed up: thus no ticket sale.
Actually, it may depend on how one defines a person. Is it 1/2 physically, or 1/2 mentally? I've personally seen the latter show up at some fundraisers.
Sixteen Students Have Registered For A Summer Sports Camp. They Are To Be Divided Into Either A Swimming Or A Tennis activity, with no more than 10 students IN EITHER GROUP. in how many ways could the group in the tennis activity be chosen?
There are 5 ways you could choose the group in tennis.
What is division?It is the basic arithmetic operation, in which you are separating the number into some parts.
Given:
The total no of students is 16,
As there can be only a maximum of 10 students in a group,
If the student in Swimming is 10 then in Tennis it will be 6,
If the student in Swimming is 9 then in Tennis it will be 7,
If the student in Swimming is 8 then in Tennis it will be 8,
If the student in Swimming is 7 then in Tennis it will be 9,
If the student in Swimming is 6 then in Tennis it will be 10,
Therefore, there are 5 ways you could choose the group in tennis.
To know more about division:
https://brainly.com/question/27566440
#SPJ3
please help asap…………
Answer:
not linear
Step-by-step explanation:
a linear function contains x and y only with the exponent 1.
this allows the function to be a line (hence the term "linear"), a constant ratio of y changes to x changes for any values of x which defines linear relation between x and y.
but this equation contains a term with x², which changes the size of change of y for every value of x.
e.g. when x changes by 1 from 1 to 2, y changes by 3 from 1² to 2² (1 to 4). but if x changes again by 1 from 2 to 3, y changes by 5 from 2² to 3² (4 to 9).
this is clearly not constant.
help for brainliest plz help i am stuck at thing
Answer:
= cot²A
Step-by-step explanation:
ito na po step by step explanation
[tex](1-sin^{2}A)(1+cot^{2}A) = cos^{2}A .\frac{1}{sin^{2}A } = \frac{cos^{2}A }{sin^{2}A } = (\frac{cosA}{sinA} )^{2} =cot^{2}A[/tex]
ok done. Thank to me :>
how do I find a slope that does not have zero as a point of origin
Answer:
See answer below.
Step-by-step explanation:
Pick any two ordered pairs that is on the given graph line.
The Slope = (the change in the y-values)/(the change in the x-values) or
what is the answer to this question
6(3/4 + 2/3) - 4(1/6 + 1/2)
Answer:
5.83333333333
Step-by-step explanation: there you go
what is the x intercept
Answer:
The answer is B
Find the perimeter. Simplify your answer.
Please help me!
