f(x)= 9x^3+ 2x^2 -5x+ 4
g(x)= 5x^3 -7x+ 4
f(x) - g(x)
= (9x^3+ 2x^2 -5x+ 4) - (5x^3 -7x+ 4)
= 9x^3+ 2x^2 -5x+ 4 -5x^3+ 7x -4
= (9x^3 -5x^3)+ 2x^2+ (7x -5x)+ (4-4) (combine like terms)
= 4x^3+ 2x^2+ 2x
= 2x* (2x^2+ x+ 1)
The final answer is 2x* (2x^2+ x+ 1).
The final answer in factored form is 2x(x² + x + 1).
f(x) = 9x³ + 2x² - 5x + 4
g(x) = 5x³ - 7x + 4
To find f(x) - g(x) ,, we subtract g(x) from f(x) term by term.
Subtract the like terms from f(x) and g(x):f(x) - g(x) = (9x³ + 2x² - 5x + 4) - (5x³ - 7x + 4) = 4x³ + 2x² + 2x
The final answer in factored form is 2x(x² + x + 1).
Been bought cell phone that came in a box shaped like a rectangular prism the box is 5 inches long by 3 inches wide by 2 inches high what is the surface area of the box
Answer: 62 in²
Step-by-step explanation:
You must apply the formula for calculate the surface area of a rectangular prims, which is shown below:
[tex]SA=2(wh+lw+lh)[/tex]
Where w is the width, l is the lenght and h is the height.
Based on the information given in the problem, you know that:
[tex]l=5in\\w=3in\\h=2in[/tex]
Therefore, when you substitute these values into the formula, you obtain that the surface area of the rectangular prism is:
[tex]SA=2[(3in*2in)+(5in*3in)+(5in*2in)]\\SA=62in^2[/tex]
What is 15.40 rounded off the nearest whole number
Answer:
15
Step-by-step explanation:
Please I need help ASAP
Answer:
B .22
Step-by-step explanation:
The number of people who are male and attended an action movie is 105
There were 479 people who attended
P(male and attended an action movie) = male and attended an action movie
---------------------------------------------------
attended
P(male and attended an action movie)=105/479
=.219206681
Rounded to two decimal places
=.22
Plz help!!!!!!!!!!!!!!
the answer is 12 place 2 , 4.5,12 In place of X and solve
Answer: x = 12
Step-by-step explanation:
[tex].\qquad \qquad \qquad \qquad \qquad \sqrt{2x+1}-4=1\\\\\text{Add 4 to both sides:}\quad \sqrt{2x+1}=5\\\\\text{Square both sides:}\quad \quad 2x+1=25\\\\\text{Subtract 1 from both sides:}\quad 2x=24\\\\\text{Divide both sides by 2:}\qquad \quad x = 12[/tex]
A Mathematical sentence that compares expressions that are not equal
Answer:
This would be an inequality. They use greater than (>) and less than (<) signs.
Step-by-step explanation:
A Mathematical sentence that compares expressions that are not equal is an inequality.
What is the inequality?An inequality is a mathematical sentence that compares the value of two expressions using a inequality symbol.
An inequality is a relationship between two different quantities or expressions.
An inequality may be expressed by a mathematical sentence that uses the following symbols:
< is less than
> is greater than
≤ is less than or equal to
≥ is greater than or equal to
≠ is not equal to
Hence, a mathematical sentence that compares expressions that are not equal is an inequality.
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a square tile is 20 cm wide. How many tiles are needed to cover 2 square metres
Answer:
50 tiles
Step-by-step explanation:
The area of a square is the square of the side. The area of each tile is
a = (20 cm)^2 = 20 cm * 20 cm = 400 cm^2
Now we convert 2 square meters into square centimeters.
2 m^2 * (100 cm)/m * (100 cm)/m = 20,000 cm^2
2 m^2 = 20,000 cm^2
Now we divide the total area by the area of one tile.
(20,000 cm^2)/(400 cm^2) = 50
Answer: 50 tiles
Round the number to the nearest thousand. 645,405
The answer is 645,000
Which is equivalent to 2 to the fourth power
Answer:
16
Step-by-step explanation:
2 times 2 is 4, 4 times 2 is 8, 8 times 2 is 16
An earthworm is crawling on top of the grass on a very sunny afternoon. It will immediately begin to dig back under the soil because of its sensitivity to light. What type of behavior is this?
Question 1 options:
inherited
learned
mimicked
imprinted
Answer: Your answer would be A. inherited
The behavior described in this scenario is most likely an inherited behavior.
What is Inherited behaviour?The innate behaviors that are passed to offspring from parents is called as Inherited behaviour
Earthworms are sensitive to light and often seek refuge in soil or other dark environments.
The response to light which is likely an innate behavior that has evolved over time in response to environmental pressures, such as predation risk from exposure to sunlight.
The earthworm's instinctive behavior to get shelter with response to light is likely a result of its genetic programming and not a learned, mimicked, or imprinted behavior.
Hence, the behavior described in this scenario is most likely an inherited behavior.
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The probability of rolling a 5 or 6 with a number cube is 1/3. What is the probability of not rolling a 5 or 6?
Answer:
Step-by-step explanation:
2/3
Answer:
2/3
Step-by-step explanation:
2/3 and add 1 to the numerator to get a whole number so 1 (whole number ) minus 2/3 is 1/3.
Hugo is buying DVDs that cost $15 each. He has a coupon for $5 off his total purchase. Write an equation to find the c the total amount he will spend on any number of DVDs d. Then use the equation to find the amount he will spend if he buys 6 DVDs.
Answer:
85
Step-by-step explanation:
15 times 6 is 90. This is how much money he spends on 6 DVDs if they're all $15. 90 subtracted by 5 (remember - he gets $5 off his entire purchase, not just each individual DVD) would be 85!
The product (x) of two numbers is 24 and their sum (+) is 10. What is the value of the largest of the two numbers?
To find the largest of two numbers when given their product and sum, we can use the quadratic formula. Let's denote the numbers as 'a' and 'b'. We know that 'a * b = 24' and 'a + b = 10'. We can rewrite the second equation as 'b = 10 - a' and substitute it into the first equation. Solving the quadratic equation, we find that the larger of the two numbers is 6.
Explanation:To find the largest of two numbers when given their product and sum, we can use the quadratic formula. Let's denote the numbers as 'a' and 'b'. We know that 'a * b = 24' and 'a + b = 10'. We can rewrite the second equation as 'b = 10 - a' and substitute it into the first equation.
Substituting 'b' into the equation 'a * b = 24', we get 'a * (10 - a) = 24'. Expanding and rearranging the equation, we have 'a^2 - 10a + 24 = 0'. Solving this quadratic equation, we find that the values of 'a' are 4 and 6. Therefore, the larger of the two numbers is 6.
What is the median of 5, 7, 2, 4, 3 (remember to place the numbers in order first.)
Answer:
4
Step-by-step explanation:
The numbers in order would be
2, 3, 4, 5, 7
The number in the middle is always the median
Therefore, 4 is the median
Final answer:
The median of the list 5, 7, 2, 4, 3 is 4, once the numbers are arranged in ascending order and we identify the middle value in the set.
Explanation:
To find the median of the list 5, 7, 2, 4, 3, we must first organize the numbers in either ascending or descending order. For this set, arranged in ascending order, we get 2, 3, 4, 5, 7. Since we have n = 5 numbers, the median will be the third value in the ordered set, which is the middle number. Therefore, the median of this data set is 4.
imagine you live only one mile from work and you decide to walk. if you walk four miles per hour, how long will it take you to walk one mile?
Answer:the distance to work is 1 mile and you can walk at 4 miles per hour, then you can walk 1 mile in ¼ hr = 15 minutes
Step-by-step explanation:
Dylan,
If the distance to work is 1 mile and you can walk at 4 miles per hour, then you can walk 1 mile in ¼ hr = 15 minutes.
To set up the "equation" think about it this way: (1 mile/ t) = (4 mile/ 1 hr)
so 1/t = 4/1 hr
now multiply both sides by t to get 1 = t·(4/1 hr), next divide both sides by (4/1 hr)
t = 1/(4/ 1 hr) = 1 hr/4 = ¼ hr = 15 min.
The answer is 15 minutes because if he can walk 4 miles for only an hour and we know that an hour is 60 minutes
4. 60m
1. 15m
So what I have done there is just divide it by 4 to get one mile and divide 60 by 4 to get the 15 minutes
Subtract [4 -4 -2] - [4 -3 5]
For matrix subtraction, you subtract the corresponding cell of the second matrix from the first. So, looking at the first spot, you have 4 (from the first matrix) - 4 (from the second matrix) = 0 (the first number in the output matrix). Continuing that for the next spot, -4 - -3 = -4 + 3 = -1. Finally, -2 - 5 = -7. This means your answer is [0 -1 -7].
Type the correct answer in the box. Rewrite the quadratic function in the form that best reveals the zeros of the function. 2(2x^2+4x)+3
Answer:
(2x + 3)(2x + 1)
Step-by-step explanation:
2(2x^2 + 4x) + 3
Distribute.
4x^2 + 8x + 3
Put this in factored form.
(2x + 3)(2x + 1)
Perform the indicated operation. 4/7x^2 - 3/2x^3
"The correct operation to perform is the subtraction of the two given polynomial terms:
[tex]\[ \frac{4}{7}x^2 - \frac{3}{2}x^3 \][/tex]
To subtract these terms, we simply combine them, keeping in mind that subtraction requires us to change the sign of the term being subtracted and then add the terms together. Since the terms are already in descending powers of \( x \), we do not need to rearrange them. The subtraction then yields:
[tex]\[ -\frac{3}{2}x^3 + \frac{4}{7}x^2 \][/tex]
This is the simplified expression after performing the indicated operation. There are no like terms to combine further, so this is the final answer.
The answer is: [tex]\[ -\frac{3}{2}x^3 + \frac{4}{7}x^2 \]"[/tex]
(PLEASE HELP) The histogram shows the number of hours that 25 college students spent studying for their final exams. Which statement is true about this histogram?
The statement on the bottom left is correct. (6 students studied for 20 to 24 hours)
Answer:
Bottom right corner.
Step-by-step explanation:
They spent between 20 to 24 hours in stead of studying for exactly one of them.
PLZ HELP (40 POINTS)
3 QUESTIONS
Answer:
first one is D
second is B
third is B
Step-by-step explanation:
Suppose we want to choose 2 objects, without replacement, from the 5 objects pencil, eraser, desk, chair, and lamp. (a)How many ways can this be done, if the order of the choices matters? (b)How many ways can this be done, if the order of the choices does not matter?
Answer:
a) 20 ways
b) 10 ways
Step-by-step explanation:
When the order of selection/choice matters, we use Permutations to find the number of ways and if the order of selection/choice does not matter, we use Combinations to find the number of ways.
Part a)
We have to chose 2 objects from a group of 5 objects and order of choice matters. This is a problem of permutations, so we have to find 5P2
General formula of permutations of n objects taken r at time is:
[tex]nPr=\frac{n!}{(n-r)!}[/tex]
Using the value of n=5 and r=2, we get:
[tex]5P2=\frac{5!}{(5-2)!} =20[/tex]
Therefore, we can choose 2 objects from a group of 5 given objects if the order of choice matters.
Part b)
Order of choice does not matter in this case, so we will use combinations to find the number of ways of choosing 2 objects from a group of 5 objects which is represented by 5C2.
The general formula of combinations of n objects taken r at a time is:
[tex]nCr=\frac{n!}{r!(n-r)!}[/tex]
Using the value of n=5 and r=2, we get:
[tex]5C2=\frac{5!}{2!(5-2)!} =10[/tex]
Therefore, we can choose 2 objects from a group of 5 given objects if the order of choice does not matters.
Answer:
20
10
Step-by-step explanation:
just took the test
A right triangle is drawn on a coordinate plane. Two vertices of the triangle are points D(6,−7) and F(−8,−5) . The third vertex of the triangle is point E, which lies in the fourth quadrant of the coordinate plane. What is the distance from point E to point F? Enter your answer in the box.
Answer:
7
Step-by-step explanation:
The answer is 7. Hope this helps
Answer:
14
Step-by-step explanation:
I am on k12 and that is what I got
I put in 7 and it was wrong
What is the quotient?
Answer:
(-7)³ or -7³
Step-by-step explanation:
Start with (-7)²
----------
(-7)^(-1)
Apply the rule that:
x^a
----------- = x^(a-b)
x^b
Then our:
(-7)²
----------- = (-7)^(2 - [-1] ) = (-7)^(2+1) = (-7)³
(-7)^(-1)
This answer could be left as is, or we could rewrite (-7)³ as
-7³, since (-1)³ = -1
Answer: FIRST OPTION
Step-by-step explanation:
According the quotient of powers property, when you have the division of two powers with the same base, then you must subtract the exponents.
Therefore, keeping the property above on mind, you have that the quotient is the shown below:
[tex]\frac{(-7)^2}{(-7)^{-1}}=(-7)^{(2-(-1))}=(-7)^{(2+1)}=(-7)^3=-343[/tex]
If the lengths of an object are measured in feet, then the area of the object will be measured in what measurement?
Answer:
Square feet.
Step-by-step explanation:
Feet are an example of what are called linear units. They're used to measure one dimensional things like length, width, or height. Area is two-dimensional, it takes up (flat) space, so we need to measure it in units that do the same thing. The simplest two-dimensional shapes to measure area with turn out to be squares (since the area of a square with side length s is just s²), so we usually measure area in square units. Since our linear units here are feet, the corresponding square units will be square feet.
Answer:
I think the answer is square feet.
I got it right on my test!
I hope this will help!
Given that (4,4) is on the graph of f(x), Find The Corresponding Point for the function f(x)+5
Answer:
(4,9)
Step-by-step explanation:
If f(x) is a function, the function f(x) + a is a function translated a units up vertically. Hence, all the y-coordinates of the coordinates of the points on the function will shift up by a.
For this problem, we need to find corresponding coordinate of (4,4) of f(x) + 5. This means that the y-coordinate of this coordinate will increase by 5 and x will stay the same.
Hence, corresponding point for f(x) + 5 for the point (4,4) would be (4,4+5) OR (4,9).
Consider the following equation.
5x^2 - 3x + 10 = (3x + 4)^2
If the above quadratic equation were used to solve for x, which of the following are the values for a,b, and c
A. a= 3,b = 12,c = 16
B. a=4,b =27,c = 6
C. a = 4,b =27,c = 26
D. a= 5,b = 3,c = 10
Answer:
B
Step-by-step explanation:
Expand the right side of the equation
5x² - 3x + 10 = 9x² + 24x + 16
Subtract 5x² - 3x + 10 from both sides
0 = 4x² + 27x + 6 ← in standard form
with a = 4, b = 27, c = 6
to fill out a sign chart, you will need to use test numbers before and after each of the function's zeros and ___
A. proportions
B. values
C. asymptotes
D. expressions
which fills the blank correctly
Answer:
C. asymptotes
Step-by-step explanation:
In the figure attached, a sign chart is shown. To fill it out you need to find the function's zeros and asymptotes. The zeros are those x values that makes the function equal to zero, in the example, those are the x values that make the denominator equal to zero (x = -1 and x = 5). In a rational function, the asymptotes are those x values that make the numerator equal to zero (x = -9 in the example)
Function in the example:
[tex]\frac{(-2x-2)(2x-10)}{-9x-81} [/tex]
Final answer:
To complete a sign chart accurately, one needs to use test numbers surrounding each of the function's zeros and asymptotes, determining the sign of the function in those intervals. This helps in understanding the behavior of the function and solving inequalities.
Explanation:
To fill out a sign chart, you will need to use test numbers before and after each of the function's zeros and C. asymptotes which fills the blank correctly. When you're dealing with functions, especially rational functions, the sign of the function can change around its zeros and asymptotes. Zeros are the points where the function crosses the x-axis, and the function's value is zero. Asymptotes, on the other hand, are lines that the function approaches but never touches; the function's value heads towards positive or negative infinity as it gets close to an asymptote.
When creating a sign chart, you select test numbers from intervals between these critical points -- zeros and asymptotes -- to determine if the function is positive or negative in those intervals. This process helps to understand the behavior of the function across its domain and is essential in solving inequalities.
Here's an example:
Identify the zeros and asymptotes of the function.
Place these values in increasing order on a number line to define test intervals.
Choose a test number from each interval and substitute it into the function to check the sign.
Fill in the sign chart with the corresponding signs for each interval.
amee buys 7 DVDs for $129.50. The total cost, c, is proportional to the number of DVDs purchased, d.
What equation represents the situation? What is the cost of 2 DVDs?
Answer:
get it down to a unit rate firstt by dividing the 129.5 by 7 dvds
$18.50
18.5x2=37
the 2 dvds were 37 dollars
Step-by-step explanation:
The basic operation that is used in finding the cost of n number of products is multiplication, if we know the cost of 1 article then we can find the cost of n numbers of articles by multiplying it with the cost of one article. Therefore, the cost price of 2 DVD's is $37.
Amee buys 7 DVDS for $129.50.
Thus,
The cost price of 7 DVDs is $129.50
We need to find the cost price of 2 DVDs.
First let us find the cost price of 1 DVD.
Therefore,
[tex]7 \;\rm{DVD's}= \$129.50\\1 \; \rm{DVD}=\frac{129.50}{7}\\1 \; \rm{DVD}=\$18.5[/tex]
Therefore, the cost price of 2 DVDs is $37.
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You invest $5,175.00 in a stock plan. It increases 9% the first year and then losses 5% of its value the second year. What is your gain compared to you original investment?
Answer: $183.71
Step-by-step explanation:
Original amount is $5,175.00
1st year: Increase of 9%
→ $5175(1 + 0.09)
= $5175(1.09)
= $5640.75
2nd year: Decrease of 5%
→ $5640.75(1 - 0.05)
= $5640.75(0.95)
= $5358.71
Gain: 2nd year - Original
→ $5358.71 - $5175.00
= $183.71
Answer:
$183.7
Step-by-step explanation:
We know that $5,175.00 was invested in a stock plan.
It increased by 9% in the first year:
[tex] 9% \times 5175.00 = 465.75 [/tex]
So value reached to (5175 + 465.75 = ) $5640.75
Then it second year, it lost 5% of its value:
[tex] 95% \times 5640.75 = $5358.7 [/tex]
Therefore, the gain compared to the initial original investment will be:
$5358.7 - $5175.0 = $183.7
I need help to solve this
Answer:
Step-by-step explanation:
The catch is to put this into the quadratic and solve for a b and c in three equations.
x = 1
a(1)^2 + b(1) + c= 0
a + b + c + 0 (1)
x = - 1
a(-1)^2 + b(-1) + c = 2
a - b + c = 2 (2)
x = 2
a(2)^2 + b(2) + c = 8
4a + 2b + c = 8 (3)
===================
Add 1 and 2 together
a + b + c = 0
a - b + c = 2
2a + 2c = 2 Divide by 2
a + c = 1 (4)
=====================
Multiply (2) by 2
2a - 2b + 2c = 4 (5)
======================
Add (5) + (3)
2a - 2b + 2c = 4
4a + 2b + c = 8
6a + 3c = 12 (6)
=====================
Multiply (4) by 3
3a + 3c = 3 (7)
===================
Subtract (7) from (6)
6a + 3c = 12
3a + 3c = 3
3a = 9 Divide by 3
3a/3 = 9/3
a = 3
=============
Use (4) to find c
a + c = 1
3 + c = 1 Subtract 3 from both sides
3-3 + c = 1-3
c = - 2
=================
Use 1 to find b
3 + b - 2 = 0 Combine 3 and -2
1 + b = 0 Subtract 1 from both sides
b = - 1
====================
Answers
a = 3
b = - 1
c = - 2
15 POINTS LMK ASAP..........
Answer:
The central angle ADC = 81°
Step-by-step explanation:
From the figure we can see a circle with circumference = 200 cm and arc ABC length = 45 cm
To find the central angle ADC
Circumference = 200 cm
Length of arc ABC = 45
we have
arc length = circumference * (central angle /360)
central angle = (arc length * 360)/circumference
= (45 * 360)/200
= 81 cm
Therefore the central angle ADC = 81°
Answer:
ADC=81
Step-by-step explanation: