Using polynomial division, it is found that the expression that represents the amount of candy sold each year per type at Cassandra's Candy Corner is:
[tex]2x^2 - 5x + 52[/tex]
The amount of candy sold per type is given by the following division:
[tex]\frac{C(x)}{T(x)} = \frac{4x^3 + 10x^2 + 54x + 520}{2x + 10}[/tex]
The denominator can be written as:
[tex]2x + 10 = 2(x + 5)[/tex]
At the numerator, to see if we can simplify, we verify if x = -5 is a factor:
[tex]C(-5) = 4(-5)^3 + 10(-5)^2 + 54(-5) + 520 = 0[/tex]
Since C(-5) = 0, it is a factor of the numerator, and thus, since the numerator is of the 3rd degree, it can be written as a 3 - 1 = 2nd degree polynomial multiplying x + 5:
[tex](ax^2 + bx + c)(x + 5) = 4x^3 + 10x^2 + 54x + 520[/tex]
[tex]ax^3 + (5a + b)x^2 + (5b + c)x + 5c = 4x^3 + 10x^2 + 54x + 520[/tex]
Equaling both sides:
[tex]a = 4[/tex]
[tex]b = 10 - 5a = -10[/tex]
[tex]5c = 520 \rightarrow c = 104[/tex]
Thus:
[tex]C(x) = (4x^2 - 10x + 104)(x + 5)[/tex]
And:
[tex]\frac{C(x)}{T(x)} = \frac{(4x^2 - 10x + 104)(x + 5)}{2(x + 5)} = 2x^2 - 5x + 52[/tex]
Thus, the expression is:
[tex]2x^2 - 5x + 52[/tex]
A similar problem is given at https://brainly.com/question/13586325
(5x+30 what is the value of x
Plzzzz help
ANSWER: 5 (× + 6)
Step-by-step explanation:
Hope this helpಠ◡ಠ
have a good day!❤️
Which is more, 9 pints or 16 cups?
Answer:
9 pints
Step-by-step explanation:
there are two cups in a pint, so we need to divide 16 by 2 to convert the cups to pints.
16 ÷ 2 = 8
9 is greater than 8, so 9 pints.
Identify the terms and coefficients of −4 √ x + y − 5x
Answer:
The coefficient of -4√x is -4; that of y is 1; and that of -5x is -5.
Step-by-step explanation:
The terms include -4√x, y, -5x.
The coefficient of -4√x is -4; that of y is 1; and that of -5x is -5.
Help me on 1. Please
nnnnnnnnnnnnjnjnnnnnnnjjjnjnjhj
Answer:
Thank you for the points and you sertanly right
Step-by-step explanation:
Answer:
7:3 35:65 56/104 14/26
Step-by-step explanation:
You can pick three!
6/7 + 1/3 in simplest forms plz
Answer: 1 4/21
Step-by-step explanation:
6/7+1/3= 25/21= 1 4/21
Step-by-step explanation:
[tex]\frac{6}{7}[/tex] + [tex]\frac{1}{3}[/tex] = [tex]\frac{25}{21}[/tex]
Simplify
[tex]\frac{25}{21}[/tex] = 1 [tex]\frac{4}{21}[/tex]
25 ÷ 21 = 1 remainder 4
Hope it helps. =D
Mass refers to the amount of matter that an object contains.
Question 1 options:
True
False
Answer:
true
Step-by-step explanation:
true the definition is right
Over a 5-hour period, the
temperature dropped a total of
12. If the temperature is now
72", what was the temperature at
the beginning of the 5-hour
period?
Answer:
12°F
Step-by-step explanation:
Temperature dropped
2°F
every
1
hour
After
6
hours
6
hours
×
2°F drop
1
hour
=
12°F drop
There is a drop in
12°F
help me with this sum I will mark you as brainiest
Answer:
1.21
2.42
3.249.67
4.155.25
5.63.25
6.86
7.80.83
8.47.125
9.153
10.438
Step-by-step explanation:
hope helful pls follow and give brainliest tq
Answer:
21
42
249 2/3
77 5/8
63 1/2
86
80 5/6
47 1/8
153
43 8/9
Step-by-step explanation:
those are quotients not sums
Aloha!
Looking for some help with an Algebra 1 equation please. See photo below.
Answer:
3, 0
Step-by-step explanation:
So, if we rewrite our given equation to have its 0x its easier to picture factorising it.
Factorise into (x+3)(x-3)
Make this equation equal to zero
Solve for your two pairs, -3, 0 (which was given in the question- I wrote this in green)
and 3, 0 (I wrote this in blue)
9514 1404 393
Answer:
(-3, 0) (given) and (3, 0)
Step-by-step explanation:
Apparently, the "solution" you're looking for is the solution to f(x) = 0.
To find the solutions, look for table values where y = 0. The solutions are the corresponding x-values. The (x, y) pairs that are solutions can be read from the table:
(-3, 0) and (3, 0)
(2)/(7):0.6x=(4)/(21):0.25
Answer:
= 1.6
Unless you meant to clarify what in the equation you needed, but that is the answer to it.
Whoever answers i’ll mark brainliest
Draw out a two column proof
which table represents a function? will give brainliest and maybe money
Answer:
3)
Step-by-step explanation:
The x side of the table can't have the same numbers, while the f(x) side can.
:)
also f(x) is the same as y on a table therefore has the same rule.
Round 45.395 to the nearest hundredth
8. Use mental math to multiply. a) 235 times 0.1, b) 235 times 0.01, c) 876 times 0.01, d) 876 times 0.001,
Step-by-step explanation:
235•0.1=23.5
235•0.01=2.35
876•0.01=87.6
876•0.001=8.76
Answer:
23.5, 2.35
8.76, 0.876
Step-by-step explanation:
What is greater 0.5 or 2/4 plz help
Step-by-step explanation:
Both are equal
0.5 and 2/4 = ½ = 0.5
Answer:
they are both the same
.5
and 2/4 as a decimal is .5
Step-by-step explanation:
14. As x increases in the equation 3x – 2y = 6, the value of y
a. increases
b. decreases
c. does not change
d. cannot be determined
Answer or you will get 0 doritos
Answer:
answer is b
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
When you are subtracting a negative, it is the same as just adding a positive.
[tex]-9\frac{2}{7} + 10\frac{3}{7}[/tex]
We can rearrange the problem to read:
[tex]10\frac{3}{7} -9\frac{2}{7}[/tex]
Now, we can subtract the numbers and fractions separately.
[tex]10+\frac{3}{7} -(9+\frac{2}{7})[/tex]
[tex](10-9)+(\frac{3}{7}-\frac{2}{7} )=1+\frac{1}{7}=1\frac{1}{7}[/tex]
This is B
5. Kathy plans to purchase a car that
depreciates (loses value) at a rate of 14% per
year. The initial cost of the car is $21,000.
How much will the car be worth
in 6 years?
Answer:
At the end of the 1st year you have 21,000-0.14(21000)
= (1-0.14)21000 = 0.86(21,000)
So after three years you have 21000(0.86)(0.86)(0.86)
= 21000(0.86)^3
Answer:
3360
Step-by-step explanation:
Find 14% of 21,000 then multiply by six which gives you 17,640. Then you subtract 21,000-17640. that is your answer.
A theater has 576 seats arranged in 64 rows. If there is the same number of seats in each row, how many seats are in one row?
Answer:
9 seats in each row
Step-by-step explanation:
576/64
Answer: in each row there are 9 seats
Step-by-step explanation:
Louise got scores 88 and 78 on her first two tests. What score must she
make on her third test to keep an average of 80 or greater?
Answer:
You want the average of three scores to be at least 80:
(88 + 78 + x)/3 ≥ 80
88 + 78 + x ≥ 80(3)
166 + x ≥ 240
x ≥ 74
You must make at least 74 on the 3rd test to maintain an average of at least 80%
Step-by-step explanation:
f(x) -2x-6 and g(x)=3x+9 find (f-g)(x)
9514 1404 393
Answer:
(f -g)(x) = -5x -15
Step-by-step explanation:
(f -g)(x) = f(x) -g(x) = (-2x -6) -(3x +9) = -2x -6 -3x -9
(f -g)(x) = -5x -15
The scale of a map says that 4 cm represents 5 km. a. what distance on the map (in centimetres) represents an actual distance of 4 kilometres? b. What is the actual number of kilometres that is represented by 5 centimetres on the map?
Answer:
a. 3 cm
b. 6 km
Step-by-step explanation:
to be completely honest, I just shoot my answer based on the pattern.
if you notice that when the scale is 4 cm, the actual distance is 5 km. When the distance is 4 km, the scale should probably be 3 cm. It's the same with the 5 cm scale, then the distance should be 6 km
Step-by-step explanation:
Use ratios to solve it
a)
4 cm → 5 kmx cm → 4 kmx = 4*4/5 = 3.2 cm
b)
4 cm → 5 km5 cm → x kmx = 5*5/4 = 6.25 km
REALLY URGENT!!!
Question: Find the equation of the line specified.
Perpendicular to 3x + y = -7 and passing through (1,8)
(i really need an explanation on how to do this)
Answer:
[tex]y=\frac{1}{3}x+7.6666[/tex]
Step-by-step explanation:
First we must convert [tex]3x+y=-7[/tex] into slope-intercept form!
To do this we simply just need to subtract -3x from the 3x on the left and move it to the right side. This would result in: [tex]y = -3x-7[/tex]
Now that we have our slope-intercept form for the equation remember that to find the equation that is perpendicular to the given equation, you need to use the opposite reciprocal of the slope. This would be [tex]\frac{1}{3}[/tex] as that is the reciprocal and opposite of [tex]-\frac{3}{1}[/tex]
Now in order to find the "b" variable of the equation that goes through the ordered pair (1, 8) we need to plug it in to the given equation!
That equation would be: [tex]y=\frac{1}{3}x-7[/tex]
Given that x = 1 and y = 8 we can plug those in like so:
[tex]8=\frac{1}{3}(1)+b[/tex]
(make sure to set the -7 to b as that's what we're solving for)
1 / 3 is 0.3333 (infinitely repeating)
Next we need to subtract 0.3333 from 8, which would be 7.6666 (infinitely repeating) Remember that the variable needs to be "alone"!
Now we have our "b" for the equation! Hence the equation would be:
[tex]y=\frac{1}{3}x+7.6666[/tex]
(you can also use [tex]\frac{23}{3}[/tex] for the b as that is the "exact form" of 1 / 3 but they both work)
Hope this helps! Feel free to ask questions!
Help to find the correct answer please
Answer:
The slope is -3/2
The y intercept is (0, -5) :)
Step-by-step explanation:
the slope is whatever is times by x
the y intercept is what’s being subtracted by it
The values of m and b from the equation of the given line are;
m = -3/2 and b = -5
Slope intercept formWe are given the equation;. y = -(3/2)x - 5
Now, the general form of an equation of a line in slope intercept form is;
y = mx + b
Where;
m is slope
b is y-intercept
Thus, comparing the general form to our given equation, we can see that;
m = -3/2 and b = -5
Read more about slope intercept form at; https://brainly.com/question/1884491
Oliver drove the first 90 miles of his journey in 1.5 hours and the remaining 120 miles in 3 hours. What was the total average speed?
Answer:
46.6666667
Step-by-step explanation:
we need to know the TOTAL average speed. To do that, we need to know how to get the speed, which is distance/time. Now we have to substitute. The equation we get is: s= (90+120)/(1.5+3). After solving, you should get s= (210miles)/(4.5hrs). Now all we have to do is divide, which equals 46.6666667.
Hope this helps! (:
The required average speed of Oliver is 46.67 miles per hour.
Given that,
Oliver drove the first 90 miles of his journey in 1.5 hours and the remaining 120 miles in 3 hours, what was the total average speed is to be determined.
Speed is defined as when an object is subjected to move, the distance covered by the object in a certain time interval is the speed of that object.
What is average?The average of the values is the ratio of the total sum of values to the number of values.
Here,
Total distance traveled = 90 + 120 = 210 miles
Total time taken = 1.5 + 3 = 4.5 hours
Average speed = distance / time
= 210 / 4.5
= 46.67 miles per hour
Thus, the required average speed of Oliver is 46.67 miles per hour.
Learn more about averages here:
brainly.com/question/24057012
#SPJ2
Find the value of x
Answer:
2
Step-by-step explanation:
please mark brainiest hope it works out for you
If a pair of alternate exterior angles are supplementary, what is the measure of each angle?
solve pls brainliest
Answer:
j*14 + 8
Step-by-step explanation:
Solve equation for 5(x - 3) + 2 = 5(2x - 8) - 3
Answer:
Easy pie
Step-by-step explanation:
5(x - 3) + 2 = 5(2x - 8) - 3
5x - 15 + 2 = 10x - 40 - 3
5x - 10x = 15 - 2 - 40 - 3
-5x = -30
5x = 30
x = 6