What is the factorization of the polynomial below?
x^3-4x^2+45x
Answers
x³-4x²+45x = x(x² - 4x + 45)
If you solve the quadratic equation inside the parenthesis using the quadratic formula, the roots are imaginary. Therefore, the quadratic equation is already a prime polynomial.
The final answer is x(x² - 4x + 45).
Related Questions
midpoint of 4 – 3i and –2 + 7i please help!!!!!
Answers
let : z = 4-3ii z' = -2+7i
the distance between the points 4-3i and -2+7i is : |z - z' |
|z - z' | = |4-3i+2-7i| = |6-10i | =√(6²+(-10)²) =√136
To the nearest degree what is the measure of each exterior angle of a regular hexagon ?
a.60°
b.45°
c.30°
d.51°
Answers
(n-2)*180
=(6-2)*180
=720
the size of each interior angle will be:
120°
N/B
the exterior and interior angles are supplementary to each other.
Therefore the size of the exterior angle will be:
180-120
=60°
the answer is A
Answer:
A
Step-by-step explanation:
The sum of measures of all the exterior angles of ANY POLYGON is 360°.
The measure of each exterior angle of ANY POLYGON is [tex]\frac{360}{n}[/tex]
where [tex]n[/tex] is the number of sides of the polygon
A hexagon has 6 sides, thus the measure of each exterior angle of a hexagon is:
[tex]\frac{360}{6}=60[/tex] degrees
Answer choice A is correct.
What is the next number in the sequence 5 10 3 15 20 13 25 30?
Answers
For 5 and 10, the difference is -5
For 10 and 3, the difference is 7
For 3 and 15, the difference is -12
For 15 and 20, the difference is -5
For 20 and 13, the difference is 7
For 13 and 25, the difference is -12
For 25 and 30, the difference is -5
Now, we can identify the next two numbers in the sequence since we already know that the format of the difference is -5, 7 and -12. So the next numbers are the following:
30 - 7 = 23
23- (-12) = 35
Therefore, the sequence is 5 10 3 15 20 13 25 30 23 35
How many cubic feet of space is there in a warehouse that is 610 feet wide by 140 feet deep and has an 18 foot ceiling?
Answers
Find the volume by multiplying the length, width, and height together.
(610)(140)(18)=1537200
Answer: 1,537,200 ft^3
Final answer:
The warehouse has a volume of 252,000 cubic feet, calculated using the corrected dimensions of 140 feet in length, 100 feet in width, and an 18-foot ceiling.
Explanation:
To calculate the volume of a warehouse, we use the formula for the volume of a rectangular prism, which is length × width × height. However, the question contains a typo about the width of the warehouse.
We are informed that the correct width is 100 feet, not 610 feet.
Given the corrected dimensions (140 feet by 100 feet with an 18 foot ceiling), we can now calculate the volume of the warehouse.
Volume = length × width × height
= 140 feet × 100 feet × 18 feet
= 252,000 cubic feet.
Therefore, the warehouse has a volume of 252,000 cubic feet of space.
Find the period of the function. y = 5 cos one divided by twox
Answers
[tex]\bf \bullet \textit{ stretches or shrinks}\\ \left. \qquad \right. \textit{horizontally by amplitude } |{{ A}}|\\\\ \bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\ [/tex]
[tex]\bf \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\ \bullet \textit{vertical shift by }{{ D}}\\[/tex]
[tex]\bf \left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\ \left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\ \bullet \textit{function period or frequency}\\ \left. \qquad \right. \frac{2\pi }{{{ B}}}\ for\ cos(\theta),\ sin(\theta),\ sec(\theta),\ csc(\theta)\\\\ \left. \qquad \right. \frac{\pi }{{{ B}}}\ for\ tan(\theta),\ cot(\theta)[/tex]
so.. with that template in mind, let's see
[tex]\bf \begin{array}{llll} y=5cos&\left(\frac{1}{2}x\right)\\ &\ \uparrow \\ &\ B \end{array}\qquad period\qquad \cfrac{2\pi }{B}\implies \cfrac{2\pi }{\frac{1}{2}}\implies \cfrac{2\pi }{1}\cdot \cfrac{2}{1}\implies 4\pi [/tex]
Please Help!! Find the measure of angle 2. Image Attached
Answers
opposite angles = 180 degrees
180-111 = 69
angle 2 = 69 degrees
In two or more complete sentences describe how to determine the appropriate model for the set of data, (0,2), (2,3), (5,4), (10,5).
Answers
Answer:
The closer this value is to 1 or -1, the better the fit. For linear, the correlation coefficient R2=.96. For quadratic, the R2=.99. For exponential, the R2=.91. This means quadratic is the best fit, very good actually since .99 is very close to 1.
Step-by-step explanation:
Foe the AP given by a1,a2,......,an,...with non zero common difference, the equation satisfied are
Answers
a₁, a₂, ..., [tex] a_{n} [/tex]
Because the given sequence is an arithmetic progression (AP), the equation satisfied is
[tex] a_{n}=a_{1}+(n-1)d [/tex]
where
d = the common difference.
The common difference may be determined as
d = a₂ - a₁
The common difference is the difference between successive terms, therefore
d = a₃ - a₂ = a₄ - a₃, and so on..
The sum of the first n terms is
[tex]S_{n}= \frac{n}{2} (a_{1}+a_{n})[/tex]
Example:
For the arithmetic sequence
1,3,5, ...,
the common difference is d= 3 - 1 = 2.
The n-th term is
[tex]a_{n}=1+2(n-1)[/tex]
For example, the 10-term is
a₁₀ = 1 + (10-1)*2 = 19
Th sum of th first 10 terms is
S₁₀ = (10/2)*(1 + 19) = 100
How many square meters are in 350 square centimeters?
Answers
~Ash
To convert 350 square centimeters to square meters, divide by the conversion factor that 1 square meter equals 10,000 square centimeters, resulting in 0.035 square meters.
Explanation:To convert 350 square centimeters to square meters, we should remember that 1 square meter is equal to 10,000 square centimeters because 1 meter is equal to 100 centimeters and for area, we need to square that conversion (100 cm × 100 cm).
We start with the given quantity of 350 square centimeters. Then, we use the conversion factor 1 square meter is 10,000 square centimeters to perform the calculation, which gives us:
350 cm² × (1 m² / 10,000 cm²) = 0.035 m².
Therefore, 350 square centimeters is equal to 0.035 square meters.
PLEASE HELP ^^^^^^^^^^^^
Answers
Step one:4(-2) = -8, right?
Step two: 3(-7) = -21, right?
Step 3: So, -8 + (21) = 13,right?
Your answer would be: 13 (option B.)
Express the number as a ratio of integers. 7.5336
Answers
division gives you 7.5336
Outside a home there is a keypad that will open the garage if the correct four digit code is entered.? How many codes are possible?
Answers
The number of ways to arrange 10 distinct digits is
10! = 10*9*8*7*6*5*4*3*2*1 = 3,628,800
Answer: 3,628,800
That is 3 million, 628 thousand, and 800.
There are 10,000 possible codes that can be entered into the keypad to open the garage.
Explanation:The number of possible codes is determined by the number of choices for each digit of the code. In this case, there are 10 possible choices for each digit (0-9). Since there are 4 digits in the code, we can multiply the number of choices for each digit together to find the total number of possible codes: 10 x 10 x 10 x 10 = 10,000. Therefore, there are 10,000 possible codes that can be entered into the keypad to open the garage.
Learn more about Possible codes for a keypad here:https://brainly.com/question/4443490
#SPJ11
In science class, Savannah measures the temperature of a liquid to be 50∘ Celsius. Her teacher wants her to convert the temperature to degrees Fahrenheit. What is the temperature of Savannah's liquid to the nearest degree Fahrenheit
Answers
Final answer:
To convert the temperature of Savannah's liquid from Celsius to Fahrenheit, use the equation °F = (°C × 9/5) + 32. Savannah's temperature in Celsius is 50°, so her temperature in Fahrenheit is 122°F.
Explanation:
To convert the temperature from Celsius to Fahrenheit, you can use the equation:
°F = (°C × 9/5) + 32.
In this case, Savannah's temperature in Celsius is 50°. Using the equation, we can calculate her temperature in Fahrenheit as:
°F = (50 × 9/5) + 32 = 122°F.
Therefore, the temperature of Savannah's liquid to the nearest degree Fahrenheit is 122°F.
Savannah's liquid, initially measured at 50°C, converts to 122°F using the formula F = C x (9/5) + 32.
Explanation:Converting Celsius to FahrenheitTo convert the temperature from degrees Celsius to degrees Fahrenheit, we use the conversion formula: F = \( C \times \frac{9}{5} + 32 \), where F is the temperature in degrees Fahrenheit and C is the temperature in degrees Celsius.
In Savannah's case, she measured the temperature as 50°C. Applying the conversion formula:
First, multiply the Celsius temperature by \( \frac{9}{5} \)50 \times \frac{9}{5} = 90Then, add 32 to this result to find the Fahrenheit temperature.90 + 32 = 122Therefore, the temperature of Savannah's liquid to the nearest degree Fahrenheit is 122°F.
What is the value of 10 C 2
Answers
n C r = (n!)/(r!*(n-r)!)
where the exclamation marks indicate factorial notation
Plug n = 10 and r = 2 into the formula
n C r = (n!)/(r!*(n-r)!)
10 C 2 = (10!)/(2!*(10-2)!)
10 C 2 = (10!)/(2!*8!)
10 C 2 = (10*9*8!)/(2!*8!)
10 C 2 = (10*9)/(2!)
10 C 2 = (10*9)/(2*1)
10 C 2 = 90/2
10 C 2 = 45
Answer: 45
Find 3 consecutive even intergers if the sum is 108
Answers
3x+6= 108
3x=102
x= 34
Final answer: 34, 36, 38
You are required to take five courses, one each in humanities, sociology, science, math, and music. you have a choice of 2 humanities courses, 2 sociology courses, 6 science courses, 6 math courses, and 8 music courses. how many different sets of five courses are possible?
Answers
By multiplying the course options together for Humanities, Sociology, Science, Math and Music (2*2*6*6*8), we found that there are a total of 576 different sets of five courses.
Explanation:To answer this question, we have to calculate the number of different sets of five courses. This can be done by multiplying the number of choices available for each requirement. So, if you have 2 humanities courses, 2 sociology courses, 6 science courses, 6 math courses, and 8 music courses to decide from, the calculation would be as follows:
We then multiply these options together (2*2*6*6*8) to get the total number of different sets of courses possible, which is 576.
Learn more about Course Combination here:
https://brainly.com/question/39300279
#SPJ12
To find the total number of different sets of five courses, multiply the number of choices for each course category: 2 (Humanities) × 2 (Sociology) × 6 (Science) × 6 (Math) × 8 (Music). This results in 1152 different sets of five courses.
To determine the number of different sets of five courses possible, we need to consider the choices available for each category:
- Humanities: 2 choices
- Sociology: 2 choices
- Science: 6 choices
- Math: 6 choices
- Music: 8 choices
The total number of different sets of five courses can be found by multiplying the number of choices in each category together. Here is the calculation:
2 × 2 × 6 × 6 × 8
Let's calculate this step-by-step:
1. 2 × 2 = 4
2. 4 × 6 = 24
3. 24 × 6 = 144
4. 144 × 8 = 1152
Therefore, the number of different sets of five courses possible is: 1152
Write the equation in exponential form.
Answers
What equation results from completing the square and then factoring? x2 + 6x = 13
Answers
x^2+6x−13=13−13x^2+6x−13=0
Step 2: Use quadratic formula with a=1, b=6, c=-13.
x=−b±√b2−4ac2ax=−(6)±√(6)2−4(1)(−13)2(1)
x=−6±√882
x=−3+√22 or x=−3−√22
Answer would be
x=−3+√22 or x=−3−√22
please help, show me the steps
Answers
what's three times "a"? well, 3*a or 3a.
ok... what's four more than that? well, 3a + 4
what's the square root of that? well, [tex]\bf \sqrt{3a+4}[/tex]
alrite, and we know that's equal to 7...so
[tex]\bf \sqrt{3a+4}=7\impliedby \textit{squaring both sides} \\\\\\ (\sqrt{3a+4})^2=7^2\implies 3a+4=49\implies 3a=45\implies a=\cfrac{45}{3} \\\\\\ \boxed{a=15}[/tex]
The rate of inflation is 3% . The cost of an item in future years can be found by iterating the function c(x) = 1.03x. Find the cost of a $1500 refrigerator in three years if the rate of inflation remains consistent .
********PLEASE HELP********
Answers
cost after 1 year:
c(1)=1.03*1500
=1545
cost after 2 years
c(2)=1.03*1545
=1591.35
the cost after 3 years will be:
c(3)=1.03*1591.35
=$1,639.09
WILL GIVE BRAINLIEST PLEASE HELP!!
What is the fifth term of the recursive formula an=2an-1 with the first term of 3?
A.
7
B.
17
C.
33
D.
65
Answers
Your answer is going to be
C.) 33
Hope this helps! :)
An electronic device that previously sold for $21 has been reduced to 17.43. the price reduction, rounded to the nearest whole percent is
Answers
= (21 - 17.43) / 21....* 100
= 3.57 / 21....* 100
= 0.17 * 100
= 17%.....the price reduction was 17%
The price reduction, rounded to the nearest whole percent is [tex]17[/tex]%.
What is whole number?
The whole numbers are the part of the number system which includes all the positive integers from 0 to infinity. These numbers exist in the number line.
What is Percentage?
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
According to question, an electronic device that previously sold for $[tex]21[/tex] has been reduced to [tex]17.43[/tex]
We have to find the price reduction, rounded to the nearest whole percent .
So percentage reduction
[tex]=\frac{21-17.43}{21}[/tex]×[tex]100[/tex]%
[tex]=0.17[/tex]×[tex]100[/tex]%
[tex]=17[/tex]%
Hence, price reduction, rounded to the nearest whole percent is [tex]17[/tex]%.
Learn more about Percentage here:
https://brainly.com/question/92258?referrer=searchResults
#SPJ2
andy states, " if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram."
A.True
B.False
Answers
The statement "If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram." is True .
What is parallelogram?"It is a quadrilateral whose opposite sides are parallel and equal in length."
What is diagonal?"It is a straight line that connects the opposite corners of a polygon through its vertices."
According to the question
The statement states that
"if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram."
Now ,
As per properties of parallelogram
In any quadrilateral the two diagonals bisect each other is a parallelogram .
Hence, The statement is True .
To know more about parallelogram here:
https://brainly.com/question/1563728
#SPJ3
the ratio of the corresponding side of two regular polygons is 3:4 the area of the larger polygon is 320 m squared what is the area of the smaller polygon?
Answers
The area of the smaller polygon with a side ratio of 3:4 is 180 m2 for the smaller polygon.
When dealing with the areas of similar polygons, if the ratio of corresponding sides is given, such as 3:4 in this case, the ratio of their areas is the square of the ratio of their sides. This is because the area is a two-dimensional measure, so each dimension is scaled by the ratio.
Given that the area of the larger polygon is 320 , we establish that the scale factor is 3 for the smaller polygon and 4 for the larger one.
To find the area of the smaller polygon, we use the fact that the ratio of the areas is (3/4)2 = 9/16.
This means that the area of the smaller polygon is 9/16 times the area of the larger polygon. Therefore, focusing on the comparison of areas, we calculate:
Area of smaller polygon = (9/16) x Area of larger polygon
= (9/16) x 320
Area of smaller polygon = 180
geometry. helppp!!! please explain this
Answers
----------------------------------------------
Explanation:
Segment TU must be congruent (equal in length) to segment UV in order for the angle TSV to be bisected by segment SU
Bisected = cut in half
So because TU = UV, we can say,
TU = UV
3x+18 = 4x+8
3x+18-3x = 4x+8-3x
18 = x+8
18-8 = x+8-8
x = 10
linear function graph express in slope intercept form
Answers
PLEASE HELP 50 POINTS
A sports club rewards teams based on overall points earned in a season. The data for points are shown in the table, where Low represents the fewest points scored and High represents the highest points scored by a single team member.
Team Low High Range Mean Median IQR σ
Team A 22 58 36 42.1 44 18.25 10.35
Team B 38 49 11 43.9 44.5 3.5 2.97
Team C 27 36 9 31.8 32 3.75 2.55
Part A: If the club wants to award the team that has the most consistent scoring among its team members, which team should it choose and why? Justify your answer mathematically. (5 points)
Part B: If the club wants to award the team with the highest average score, which team should it choose and why? Justify your answer mathematically. (5 points)
Answers
Part B: Team B should be chosen if the club wants to award the team w/ the highest average score
hope this helps:)
please mark thanks and brainliest:)
Part B: Team A, because they have the highest median.
Your welcome:)
if it was wrong I am sorry:(
If f(x)=x-7 and g(x)=x^3, what is G(f(x))?
A. x^3+x-7
B. x^3(x-7)
C. X^3-7
D. (x-7)^3
Answers
g(f(x)) = (x-7)^3
Its D
Answer:
D. [tex](x-7)^3[/tex]
Step-by-step explanation:
Given functions are,
[tex]f(x) = x-7-----(1)[/tex]
[tex]g(x)=x^3-----(2)[/tex]
Now,
[tex]g(f(x))=g(x-7)[/tex] ( From equation (1) ),
[tex]=(x-7)^3[/tex] ( From equation (2) ),
[tex]\implies g(f(x)) = (x-7)^3[/tex]
Hence, Option D is correct.
A sample of size 40 is taken from an infinite population whose mean and standard deviation are 68 and 12 respectively. the probability that the sample mean is larger than 70 equals:
Answers
To solve this problem, we can use the z statistic to find for the probability. The formula for z score is:
z = (x – u) / s
Where,
u = the sample mean = 68
s = standard deviation of the samples = 12
x = sample value = 70
In this case, what is asked is the probability that the sample mean is larger than 70, therefore this corresponds to the right of z on the graph of normal distribution.
z = (70 – 68) / 12
z = 2 / 12
z = 0.17
Therefore finding for P at z ≥ 0.17 using the standard distribution tables:
P (z = 0.17) = 0.5675
But this is not the answer yet since this is the P to the left of z. Therefore the correct one is:
P (z ≥ 0.17) = 1 - 0.5675
P (z ≥ 0.17) = 0.4325 = 43.25%
The probability that the sample mean is larger than 70 is 43.25%
The probability that the sample mean is larger than 70 for a sample size of 40 from a population with a mean of 68 and standard deviation of 12 is approximately 14.69%.
To determine this probability, we can use the Central Limit Theorem (CLT), which states that the distribution of sample means will be approximately normal if the sample size is large enough (n ≥ 30 is a common benchmark).
The standard error of the mean is calculated using the formula:
SE = σ / √n
Where σ is the population standard deviation and n is the sample size.
In this case:
σ = 12
n = 40
Therefore,
SE = 12 / √40 ≈ 1.8974
The z-score is calculated using the formula:
z = (M - μ) / SE
Where M is the sample mean,
μ is the population mean,
SE is the standard error.
Given,
μ = 68
M = 70
Therefore,
z = (70 - 68) / 1.8974 ≈ 1.054
Using the z-table, we find the probability that a z-score is less than 1.054 is approximately 0.8531.
However, we need the probability that the sample mean is greater than 70, so we subtract this from 1,
1 - 0.8531 ≈ 0.1469
Thus, the probability that the sample mean is larger than 70 is approximately 0.1469, or 14.69%.
Find the volume of a sphere that has a surface area of 16 sq. in.
A. (32/3) cubic inches
B.8 cubic inches
C.(4/3) cubic inches
Answers
S.A=4πr^2
hence the radius can be calculated as follows;
16=4πr^2
4=πr^2
r=(4/π)^(1/2)
volume of a sphere is given by:
V=4/3πr^3
=4/3*π*(4/π)^(1/2))^3
=32/3 cubic inches
Answer:
A is the answer