By the remainder theorem,
p(a) = 3a³ + a² + 5a = -7
so that
3a³ + a² + 5a + 7 = 0
Since you know a is an integer, you can try to factorize this, or use the rational root theorem to generate a list of potential rational roots, and from there you'd select the integer roots. The rational ones are of the form m/n, where m divides the constant term 7 and n divides the leading coefficient 3. They are
a = ± 1 or ± 1/3 or ± 7 or ±7/3
so there are 4 integer candidates,
a = -1 or 1 or -7 or 7
Check the value of f(a) = 3a³ + a² + 5a + 7 at each of these:
a = -1 → f(a) = 0
a = 1 → f(a) = 16
a = -7 → f(a) = -1008
a = 7 → f(a) = 1120
and only a = -1 is a root of 3a³ + a² + 5a + 7, so that's your answer. In fact,
3a³ + a² + 5a + 7 = (a + 1) (3a² - 2a + 7)
Plz answer this
(5x^2-3x+1)-(4x+2x^2-2)
For a field trip 5 students rode in
cars and the rest filled ten buses.
How many students were in each
bus if 215 students were on
the trip?
Answer:
21 students
Step-by-step explanation:
215-5=210
210/10 =21
help it’s also not D :)
Answer:
the answear is c
Step-by-step explanation:
i learnt in class that the number with the letter is used to divide what it equalls
Answer:
C
Step-by-step explanation:
Step 2 is correct, that is
8x = 10 ( divide both sides by 8 ), error made here by dividing by 10
x = [tex]\frac{10}{8}[/tex]
x = [tex]\frac{5}{4}[/tex]
The error was made at step 3
MATH! What is 2x5x7x8x7?
Answer:
3920
Step-by-step explanation:
Answer:
3920
Step-by-step explanation:
help immediately please
Answer:
1
Step-by-step explanation:
you just divide 6/4 and it will equal one
What is the mean of the measures of the three exterior angles of a triangle if two of the interior angles have measures of 63 and 78 degrees?
Answer:
Mean score=120Step-by-step explanation:
Areas of a triangle add upto 180degrees (63+78+x=180) 141+x= (x=180-141) x=39Areas on a straight line add upto 180degrees180-78=102
180-63=117
180-39=141
102+117+141=360Mean=360/3 =120A cup is in the shape of a cone. If the cup has a height of 6 inches and a diameter of 3 inches, which is closest to the amount of water the cup can hold? A 9.42 cubic inches B 14.13 cubic inches C 56.52 cubic inches D 113.04 cubic inches
Answer:
B.14.13in³
Step-by-step explanation:
Step one
The shape of the cup is that of a cone
The volume of a cone
V=1/3πr²h
Radius= d/2 = 1.5in
Height =6in
Substitute
V=1/3*3.142*1.5²*6
V=42.42/3
V=14.13in³
What is the slope of a line perpendicular to the given line plz
Answer:
it should be the negative repirocal of -2 so 1/2
Answer:
mPerpendicular= 1/2
Step-by-step explanation:
Betty is three times as old as her son now. In 12 years, Betty's age will be three years less than twice her son's age. How old is Betty's son now?
Answer:
Betty is 27. Her son is 9.
Step-by-step explanation:
We will use b to represent Betty's age. We will use s to represent her son's age.
This year:
b = 3s
In 12 years' time:
b + 12 = 2(s + 12) - 3
b + 12 = 2s + 24 - 3
b + 12 = 2s + 21
b = 2s + 9
We know that b = 3s, so we can substitute this value into our equation.
3s = 2s + 9
s = 9
b = 3 x 9
b = 27
one more ferda yk +100 cause i love you
i love you too thank u soo much ill do the same
pls helpppppppppppppp
Answer/Step-by-step explanation:
The following steps to solve equation given by join are shown below including the property of numbers applied for each reasons:
4(2a + 3) = -3(a - 1) + 31 - 11a ----› Given
Apply the distributive property to open the parentheses
4*2a + 4*3 = -3*a -3*-1 + 31 - 11a
8a + 12 = -3a + 3 + 31 - 11a ----› Distributive property
Combine like terms together
8a + 12 = 3 + 31 -3a - 11a
8a + 12 = 34 - 14a ---› Combining like terms
Add 14a to both sides
8a + 12 + 14a = 34 - 14a + 14a
22a + 12 = 34 ----› Addition property
Subtract 12 from both sides
22a + 12 - 12 = 34 - 12
22a = 22 ----› subtraction property of equality
Divide both sides by 22
22a/22 = 22/22
a = 1 ----› Division property of Equality
Holly begins with 1 penny in her piggy bank. She adds 2 pennies on day 1, 4 pennies on day 2, and 8 pennies on day 3. She continues this pattern for 30 days.
Which statement describes why this sequence is a function?
Select EACH correct answer.
a Each amount of pennies corresponds to a unique day in this sequence.
b The graph of this sequence would pass the horizontal line test.
c Each day corresponds to a unique amount of pennies in this sequence.
d The graph of this sequence would pass the vertical line test.
Answer:
The answer is c and b
Step-by-step explanation:
I took the test
Options B, C and D are correct.
The Graph of this sequence would pass the horizontal line test.Each day corresponds to a unique amount of pennies in this sequence.The Graph of this sequence would pass the vertical line test.We have Holly and her penny collection.
We have to select the correct alternatives from the given.
Starting from 1 marble if you add 'x' marble every day for n days, then you have a total of 40 marbles. Find n.1 + nx = 40
nx = 39
n = 39/x
According to the question-
Initial Amount in piggy bank = 1 penny.
Now -
She adds -
2 Pennies on Day 1.
4 Pennies on Day 2.
8 Pennies on Day 3.
Therefore, the following sequence represents her collection -
1, 2, 4, 8 .....
It can be seen that each day corresponds to a unique amount of pennies in this sequence.
Now -
Vertical line test → to satisfy this test the graph should not have two or more points going through a vertical line.
Horizontal Line test → to clear this test the graph should not have two or more points going through a Horizontal line.
If we plot the graph of this function - Refer to image attached. It can be seen that the graph of this sequence passes horizontal line and vertical line test.
Hence, Options B, C and D are correct.
To solve more questions on Coulomb's law, visit the link below-
brainly.com/question/10933224
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Problem 1: Bob’s Citrus and Nursery sells cartons of citrus fruits. There are 24 oranges in each carton. They have 5,643 oranges to pack into cartons. How many cartons can they fill?
Problem 2: This year, 4,338 grapefruits have been harvested so far. Bob’s has 18 storage bins for grapefruits. If the grapefruits are distributed evenly among 18 bins, how many grapefruits are in each bin?
248 per bin.
The number of cartons that the oranges would fill in Bob’s Citrus and Nursery would be 235 cartons.
The number of grapefruits in each bin would be 241 grapefruits per bin.
How to find the number of cartons ?To find the number of cartons of oranges that would be filled, use the number of oranges that go into carton in Bob’s Citrus and Nursery and the number of oranges they have to pack. The formula would be:
= Number of oranges / Number of oranges per carton
= 5, 643 / 24
= 235 cartons
How to fin the number of grapefruits per bin ?The same logic is applied to find the number of grapefruits that would be in each bin. If each bin would have an equal number of grapefruits, the number of grapefruits per bin would be:
= Number of grapefruits / Number of bins
= 4, 338 / 18
= 241 grapefruits per bin
Find out more on grapefruits at https://brainly.com/question/7943300
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Find the equation of the straight line which is perpendicular to the straight line 3x+4y=12 such that perpendicular distance from the origin is equal to the perpendicular distance from (3,2) on the given line
Answer:
3y-4x = -6Step-by-step explanation:
First get the slope of the given line;
Given the equation of the line 3x+4y=12
Rewrite in standard form y = mx+c where m is the slope;
3x+4y=12
4y = -3x + 12
y = -3x/4 + 12/4
y = -3x/4 + 3
Hence the slope of the given line is -3/4
Since the required line is perpendicular to this line, the slope of the required line will be M = -1/(-3/4) = 4/3
Get the equation:
Substitute M = 4/3 and the point (3,2) into the point slope equation of a line as shown;
y-y0 = m(x-x0)
y - 2 = 4/3(x-3)
Cross multiply
3(y-2) = 4(x-3)
3y - 6 = 4x - 12
3y - 4x = -12 + 6
3y-4x = -6
Hence the required equation of the line is 3y-4x = -6
Morgan took out a $500 cash advance on her credit card. If the interest rate is 9%, and it takes her 1 year to pay back the loan, what is the total amount of money Morgan will have to pay back to her credit card?
Answer: $777.60
Step-by-step explanation:
8/100 = 0.08
0.08 * 720 = 57.6
57.6 + 720 = 777.6
Answer:
545
Step-by-step explanation:
9/100=0.09
0.09*500=45
45+500=545
Real answer: 545 Hope this helped C:
If r is the radius of a circle and d is its diameter, which of the following is an
equivalent formula for the circumference C = 2 pie r?
A. C= pie d
B. C= 2 pie d
C. C=2 pie d^2
D. C = 2 pie rd
Answer:
A
Step-by-step explanation:
because r is 1/2 of d so you would have 1 d instead of 2 r
A clearance rack is marked as 60% off the regular price to be taken at the register. If a jacket on the clearance rack is marked $239.99, what will it ring up for at the register
Answer:
$399.98
Step-by-step explanation:
Given
Mark down percent = 60%
Mark down price = $239.99
Required
Original price of the rack
Let x be the original price of the product. The equation to get x is as expressed below;
60% of x = 239.99
0.6x = 239.99
x = 239.99/0.6
x = 399.98
Hence the rack will ring up for $399.98 at the register
WILL GIVE 100 POINTS AND BRAINLIEST TO FIRST TO ANSWER CORRECT
RQ = TQ
1 2
RS _____ ST
Choose the relationship symbol to make a true statement.
Answer:
>
Step-by-step explanation:
In the lesson, we learned that the side opposite the larger angle was larger. In this case; angle 1 is larger than angle 2. This makes line segment RS > ST. Hope this helps!
Also I did this question myself and this was correct. :D.
Fractions please help ?
Answer:
D) 12 1/14
Step-by-step explanation:
6 2/7+5 11/14
1)
6+5=11
2)
2/7+11/14=
2/7 x 2/2=4/14
3)
4/14+11/14=15/14
4)
15/14= 1 1/14
5)
11+ 1 1/14= 12 1/14
Answer:
The answer to the question is D
Step-by-step explanation:
Salim walked113miles to school and then212miles to work after school. How far did he walk in all?
ok so tomorrow i have exams omg haha im so scareddd!!!!!
Answer:
Best of luck! I hope your exam goes well!!!
7. You are ordering sweaters from American Eagle. Each sweater costs $25. They also charge a shipping fee of $7. You spent. $132 How many sweaters?
Answer:
Step-by-step explanation:
Alright, after reading this problem, let’s highlight some key points. Each sweater costs $25, we can write that down as 25x because will represent the amount of sweaters we buy. But we have a shipping fee of $7, so we will +7 to our highlights. And the total money spent was $132.
So far, we have: 25x + 7 = 132
Let’s subtract the 7 from the 132. Now we have: 25x = 125
Then we can divide by 25 on each side, and get x by itself.
X = 5 sweaters.
BONUS: Let’s replace 5 for our x to prove our answer
25(5) + 7 = 132 >>> 125 + 7 = 132 >>> 132 = 132 :D
There you go!! We buy 5 sweaters from American Eagle..!
HELP!! EASY ANSWER
The radii of a circumcircle are segments that are equidistant from the ____________________ to the _______________(#8) of a triangle.
Answer:
Step-by-step explanation:
Same I need this to help plz hurry
y - (-9) = –16
linear equations
Answer: y=-25
Step-by-step explanation:
step 1: simplify both sides of the equation
y+9=−16
step 2: subract 9 from both sides
y+9−9=−16−9
y=−25
A series is defined by 5+9+13+17+.......+805 a. Find the number of terms of the series. b. Find the sum of the first 20 terms.
Answer: the number of terms of the series is 201 numbers
the sum of the first 20 terms is 890
the number of terms of the series is [tex]\frac{805-5}{4}+1=201[/tex]
the series have:
u1 = 5
d = 4
=> u(n) = 5 + 4.(n - 1)
=> u(20) = 5 + 19.4 = 81
so the sum of the first 20 terms is (81 + 5).20/2 = 890
( u1 is the first number of the series, d is the distance between front and rear numbers, u(n) is the overall term of the sequence, u(20) is the 20th of the series)
Step-by-step explanation:
i need an opinion, my other note is in anouther question. what do y'all think.
Dear Chelsea
I'm tierd of you scraching me
I mean I love you can't you see
You may not see it but your rude to Sue
you tell me a secret like the one about you know who
Do you like to hurt Sue and me
Dose it make very you happy
I'm done with all the disrespect
I always helped you last I checked
I'm always there for you
I have fun doing all the things we do
I love you like my own child
Evan though you're a little wild
Your pretty and strong
Your hair is not so long
But what do I care
I mean it's your hair
I geuss what I'm trying to say
Is that no matter what you do ill still love you anyway
You are my little cousin more like a sister
And I hope to be there when you get your mister
I may not always be there
But I want you to know I still care
So as I look up at the sky
I write this not to say goodbye
Answer:
good job its very good
Step-by-step explanation:
A purse containing at most 3.15 in quarters and dimes has, in all 20 coins. Find the maximum number of quarters in the purse.
Answer:
4
Step-by-step explanation:
Can you help me with this question please
tje volume of a rectangle box with l=3x,b=5y,h=4z
Answer:
60xyz
Step-by-step explanation:
Have a nice Day , Hope this helped you I would appreciate it if you could mark my answer brainliest
Consider a large population with a mean of 100 and a standard deviation of 21. A random sample of size 36 is taken from this population. The standard error of the sampling distribution of sample mean.
Answer:
3.5
Step-by-step explanation:
Given that:
Population mean (m) = 100
Standard deviation (σ) = 21
Sample size (n) = 36
The standard error of the sampling distribution of sample mean :
Standard Error is given by:
Standard deviation / sqrt(n)
Thus,
Standard Error = 21 / sqrt(36)
Standard Error = 21 / 6
Standard Error = 3.5