If x = -4 is a root of f(x), then dividing f(x) by x + 4 leaves a remainder of 0.
Compute the quotient,
(x³ - kx + 12) / (x + 4)
x³ = x² • x, and
x² (x + 4) = x³ + 4x²
Subtract this from the dividend (f(x)) to get an initial remainder of
(x³ - kx + 12) - (x³ + 4x²) = -4x² - kx + 12
-4x² = -4x • x, and
-4x (x + 4) = -4x² - 16x
Subtract this from the previous remainder to get a new one of
(-4x² - kx + 12) - (-4x² - 16x) = (16 - k) x + 12
(16 - k) x = (16 - k) • x, and
(16 - k) (x + 4) = (16 - k) x + 64 - 4k
which gives the next remainder,
((16 - k) x + 12) - ((16 - k) x + 64 - 4k) = 4k - 52
4k - 52 does not divide x, so we're done and what we've shown is
f(x) / (x + 4) = x² - 4x + 16 - k + (4k - 52)/(x + 4)
(just gathering the bold terms above and the last remainder)
The remainder should be 0, so that
4k - 52 = 0
4k = 52
k = 13
I need help pls Simplify 6y+9+3y-7
Answer:
9y+2
Step-by-step explanation:
What is the BEST ANSWER for the slope of the line that passes through the points:
(12, 2) and (1, 23)
Answer: -2
Step-by-step explanation:
Find the ratio of 2p per gram to £2.12 per kilogram
Answer:
the answer is 1.06
Step-by-step explanation:
Jeremy is making a healthy ice cream using only ripe bananas and peanut butter, the recipe makes 4 servings and calls for a ratio of 5
bananas to 3 tablespoons of peanut butter if Jeremy has 30 bananas, how many tablespoons of peanut butter does he need
Tablespoons
Answer:
can u show me a pic of the question so it is easier
The healthy ice cream Jeremy is making has 30 bananas and requires 18 tablespoons of peanut butter.
What is a ratio?The ratio describes the amount of quantity in simplest form, a:b can be written as 'a/b' for convenience.
Given the healthy ice cream, Jeremy is making requires 5 bananas and 3 tablespoons of peanut butter.
From the given question itself, we can conclude that bananas and peanut butter are in direct proportion as the increase in one quantity will result in an increase of another quantity and we can write this in proportion and let the no. of tablespoons of peanut butter requires for 30 banans is x.
∴ 5 : 3 : : 30 : x.
Or
5/3 = 30/x.
5x = 90.
x = 18.
So, Jeremy needs 18 tablespoons of peanut butter for the 30 bananas he has.
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A chemist has 100 ml of 25% acid solution. how much of the solution does she need to drain and replace with 70% acid solution to obtain 100 ml of 60% acid solution?
Answer:
The proportion of acid at 70% that the chemist must use will be 77.8%, while the remaining 22.2% will be acid at 25%.
Step-by-step explanation:
Since the chemist has 100 ml of solution with 25% acid, and wants to obtain a solution of 60% acid by mixing the first with another 70% acid solution, to determine how much of each solution the chemical should use necessary to perform the following calculation:
70 x 1 + 25 x 0 = 70
70 x 0.9 + 25 x 0.1 = 65.5
70 x 0.8 + 25 x 0.2 = 61
70 x 0.7 + 25 x 0.3 = 56.5
Therefore, the proportion to be used is between 70% and 80% of acid at 70%, and 20% to 30% of acid at 25%.
70 x 0.75 + 25 x 0.25 = 58.75
70 x 0.76 + 25 x 0.24 = 59.2
70 x 0.77 + 25 x 0.23 = 59.65
70 x 0.78 + 25 x 0.22 = 60.1
Thus, the proportion should be between 77 and 78% of acid at 70% and 22 and 23% of acid at 25%.
70 x 0.778 + 25 x 0.222 = 60.01
Thus, finally, the proportion of acid at 70% that the chemist must use will be 77.8%, while the remaining 22.2% will be acid at 25%.
help asap plspls!! :)
Answer:
1/6
Step-by-step explanation:
1/3 ÷ 2 = 1/6
All you do is multiply the denominator by 2. This sounds incorrect, but my making the denominator lager it actually is shrinking the fraction and ultimately making it smaller than before.
Answer:
1/3÷2=1/6
Result in decimals: 0.16666666666667
Jeremy wants to give a 20% gratuity to his cab driver. His fare is $35.50. What is the total amount he will pay the driver?
Answer:
$42.60.
Step-by-step explanation:
You multiply 35.50 by .20 (that's decimal version of 20%) which equals 7.10. Then you add 35.50+7.10=42.60
the amount of sod needed to cover the circular green on a golf course?
Answer:
you would need just over 261 pounds of seed for 1 acre.
Step-by-step explanation: For example, if the recommended seeding rate for a specific blend of grasses is 6 pounds per 1,000 square feet, multiply 6 by 43.56 to get 261.36. Thus you would need just over 261 pounds of seed for 1 acre.
how many minutes is 40% of 120 minutes?
Answer:
48 mins
Step-by-step explanation:
40 x 120 /100
= 48
Melissa’s family is driving out of state to her grandmother’s house. They know that it takes 20 gallons of gas to get there, and the cost of three gallons of gasoline is $10.50. How much should the family budget to make the one-way trip?
Answer: 20/3 * $10.50 = &73.5
.
HOPE THIS HELPS TOUCH THANKS PLEASEStep-by-step explanation:
Answer:
73.5$
Step-by-step explanation:
21/7=3 so 10.50*7 will give the budget
At the beginning of the semester, a professor tells students that if they study for the tests, then there is a 55% chance they will get a B or higher on the tests. If they do not study, there is a 20% chance that they will get a B or higher on the tests. The professor knows from prior surveys that 60% of students study for the tests. What is the probability that a randomly selected student studies for a test and gets a B or higher?
0.08
0.11
0.33
0.55
Answer:
.33
Step-by-step explanation:
solve the equation 4p + 2 =22,using a double number line
Answer:
the answer is 5
Step-by-step explanation:
please help solve this.
Find the greatest common factor of the terms in the following expression 18x+12xy
=============================================
Explanation:
Ignoring the variables for now, the GCF of 18 and 12 is 6. This is the largest factor found in both values
18 = 6*312 = 6*2Now let's consider the variables. Both terms have an 'x' in them, but not a y. This means x will be tacked on the 6 we found earlier to get the overall GCF to be 6x.
Note how
18x + 12xy = 6x*3+6x*2y = 6x(3+2y)
Showing we can factor out the GCF using the distributive property.
Match each equation to the situation it represents
1st one says Leilah
2nd one says Stetson
Answer:
leiah has not yet studied...... = 2400 - 40x = 600
stetson rests studios spaces...... = 40x - 600 = 2400
a kit contains.... =. (600 + 40) x = 2400
Step-by-step explanation:
that might make it a bit easier
Find the angle of rotation about the center of the square that maps A to C.
The angle of rotation to map A into C is 180°.
How to find the angle of rotation?The rotation is around the center of the square. Let's assume that the center coincides with the origin of a coordinate axis.
Then we would have A on the second quadrant and C on the fourth quadrant.
Then we need to apply a rotation of two quadrants, remember that each quadrant has an angle of 90°, then a rotation of two quadrants has an angle of 2*90° = 180°.
The correct option is 180°.
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Please help!! I just need help with question 40!!
Answer:
a. 70%
b. 6 more times
c. subtract from 100% with percentages, subtract from 1 with decimals.
Step-by-step explanation:
a. To find the percentage of red and yellow, skip back the decimal point two times: 0.26 > 26% 0.04 > 4%
Add all of the percentages together to get 70%
b. To find how many times more students said red than yellow, divide yellow from red. It shows you how many times yellow can go into red, giving you the correct answer.
0.26 ÷ 0.04
26 ÷ 4
6
c. 14% + 26% + 40% + 4% = 84%
100% - 84%
16%
(do the same thing with decimals and pick your favorite method)
:)
The sum of the tens digit and the hundreds digit of a number is three times the units digit. 1/5 of the sum of all three digits is 1 less than the units digit. Find all three-digit numbers that satisfy these conditions.
Answer: The numbers are:
965
875
785
695
Step-by-step explanation:
We have a 3 digit number that can be written as:
a*100 + b*10 + c
Where a, b, and c are single-digit numbers.
a is the hundreds
b is the tens
c is the unit.
We know that:
"The sum of the tens digit and the hundreds digit of a number is three times the units digit."
a + b = 3*c
" 1/5 of the sum of all three digits is 1 less than the units digit."
(a + b + c)/5 = c - 1
Then we have the two conditions:
a + b = 3*c
(a + b + c)/5 = c - 1
From the first one, we can write:
(a + b)/3 = c
Replacing that in the other equation we get:
(a + b + a/3 + b/3)/5 = a/3 + b/3 - 1
(4/3)*(a + b)/5 = (a/3 + b/3) - 1
(4/15)*(a + b) = (a + b)/3 - 1
(4/15)*(a + b) - (a + b)/3 = - 1
-(1/15)*(a + b) = -1
a = 15 - b
Then we can give different values for b, and find the values of a and c, where a and c must be positive.
b = 9
a = 15 - 9 = 6
Then:
c = (9 + 6)/3 = 5
(notice that a + b = 15, then c will be always equal to 5, reggardless of the values of b and a).
This number will be:
695.
if b = 8, then:
a = 15 - 8 = 7
and c = 5, same as before.
the number is 785.
If b = 7, then:
a = 15 - 7 = 8
The number is 875
if b = 6, then:
a = 15 - 6 = 9
The number is:
965
i need help idk how to solve this plz help. y - 2= 7/3 (x-(-2))
Im sure it's -3 Because well thats what i got
at a pet store at the mall there are 21 dogs, 13 cats, 12 rabbits, 5 hamsters, and 3 ferrets. What percent of the animals mare rabbits
Answer:
28.57%
Step-by-step explanation
I added all the animals together and got the precentage of rabbits
Hopefully its right :)
A bakery is making apple pies and carrot cakes. Each
apple pie nets $5 profit. For each carrot cake, they
make $10 profit. Each pie take 4 hours to prepare and
1.5 hours to bake. The carrot cakes take 0.5 hours to
prepare and 0.5 hours to bake. The maximum
preparation time is 20 hours. The maximum baking
time is 10 hours. How many pies and cakes should be
made to maximize profits?
Answer:
8 thats how many pies and cakes you can do
Step-by-step explanation:
you have 20 minutes and 10 and the most cakes you can get with left over is 8
The pies and cakes should be made to maximize profits is 8 pies.
What is profit?Profit is defined as the sum of revenue and income after all costs have been deducted by a business. A function with a business-oriented focus is called a profit function. The main goal of a business is to generate income through the sale of goods and services, minus the costs associated with producing those goods and services, in order to turn a profit.
Revenue minus costs equals profit.
Costs comprise both variable costs and fixed costs, whereas revenue is the total amount of positive cash flow that a business generates.
The maximum number of cakes you can get with leftovers in 20 minutes and 10 is 8.
Thus, the pies and cakes should be made to maximize profits is 8 pies.
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Please help me out quickly
Answer:
I dont see the stuff I think my internet is slow but I will help you when its up again im using hotspot just remind me
Step-by-step explanation:
Someone help plzzzzz
Answer:
for the first box the answer is 4x but I dont know the y intercept
Step-by-step explanation:
get 2 points the do y2-y1/x2-x1 then you get your x
PLEASE HELP! IMAGE ATTACHED
PLEASE I WILL GIVE YOU POINTS!
Answer:
None
Step-by-step explanation:
y=(2x)^(1/3)-7 wrong
y= -2(3x)^(1/6) wrong
y=-x^(1/2)+5 wrong
y=(x+2)^(1/4) wrong
Solve the inequality
Answer:
x<2
Step-by-step explanation:
5x+10>14x-8
18>9x
2>x
Does anyone know the answer to this question
Geometry homework. Please help.
Answer: Sure
Step-by-step explanation:
Step-by-step explanation:
✬ Radius = 2.5 cm ✬
Step-by-step explanation:
Given:
Radius of spherical ball is 3 cm.
Radii of new spherical balls are 1.5 cm and 2 cm.
To Find:
Radius of third spherical ball ?
Solution : Let the radius of third spherical ball be x cm.
If something is melted and recasted into another thing then their volumes will be equal. In short
Volume of 1st thing = Volume of second one.
➯ Let's see here
Volume of big spherical ball will be equal to the sum of volumes of that three small spherical balls.
As we know that
★ Volume of Sphere = 4/3πr³ ★
[ Taking big spherical ball ]
Radius = 3 cm
⟹ Volume = 4/3 × π × (3)³
⟹ 4π/3 × 27
Volume we got = 4π/3 × 27 cm³
[ Taking 3 small spherical balls ]
Radius of first ball (r¹) = 1.5 cm
For second (R) = 2 cm
For third (x) = x cm
Volume = 4/3 × π( sum cubes of radii)
⟹ Volume = 4/3 × π(1.5³ + 2³ + r³)
⟹ 4π/3 (3.375 + 8 + x³)
⟹ 4π/3 ( 11.375 + x³)
Volume we got = 4π/3 (11.375 + x³) cm³
A/q
First volume = Second volume
➮ 4π/3 × 27 = 4π/3 (11.375 + x³)
➮ 27 = 11.375 + x³
➮ 27 – 11.375 = x³
➮ 15.625 = x³
➮ 15625/1000 = x³
➮ 3125/200 = 625/40 = 125/8 = x³
➮ ³√125/8 = x³
➮ 5/2 = x²
➮ 2.5 cm = x
Hence, the measure of radius of third spherical ball is 2.5 cm.
Which expression has a value different from the others?
A. -108 + 105
B. 9.9 + (12.9)
C. -7 2/9 - ( -4 2/9)
D. 637 - 641
Answer:
I think B
Step-by-step explanation:
A. -108+105
-3
B. 9.9+(12.9)
22.8
C. -7 2/9 -(-4 2/9)
-3
D. 637 - 641
-4
Is the last one written wrong because if that one is 637-640 or 638-641 than it would equal -3. Then the answer would be B.
write a polynomial equation for each set of roots 5 and 7
Answer:
x²-2x-35
Step-by-step explanation:
(x-7)(x+5)
x²+5x-7x-35
x²-2x-35
