simplify 15r+7r+9r-7s
Selecting a red pen and then a blue pen, when selecting 2 pens from a bag of 10 red pens
In the expansion of (3a + 4b)8, which of the following are possible variable terms? Explain your reasoning. a2b3; a5b3; ab8; b8; a4b4; a8; ab7; a6b
The [tex]a^5b^3[/tex], [tex]ab^8[/tex], [tex]b^8[/tex], [tex]a^4b^4[/tex], [tex]a^8[/tex], and [tex]ab^7[/tex] are the possible variable terms and this can be determined by using the arithmetic operations.
Given :
Expression --- [tex]\rm (3a + 4b)^8[/tex]
The following calculation can be used in order to determine the possible variables from the given expression.
The given expression can be written as:
[tex]\rm (3a + 4b)^8=(3a+4b)^2(3a+4b)^2(3a+4b)^2(3a+4b)^2[/tex]
[tex]\rm (3a + 4b)^8=(9a^2+16b^2+12ab)(9a^2+16b^2+12ab)(9a^2+16b^2+12ab)(9a^2+16b^2+12ab)[/tex]
Now, further simplify the above expression.
[tex]\rm (3a + 4b)^8=(81a^4+144a^2b^2+108a^3b+144a^2b^2+256b^4+192a^3b+108a^3b+192ab^3+144a^2b^2)(81a^4+144a^2b^2+108a^3b+144a^2b^2+256b^4+192a^3b+108a^3b+192ab^3+144a^2b^2)[/tex]
So, from the above calculation, it can be concluded that [tex]a^5b^3[/tex], [tex]ab^8[/tex], [tex]b^8[/tex], [tex]a^4b^4[/tex], [tex]a^8[/tex], and [tex]ab^7[/tex] are the possible variable terms.
For more information, refer to the link given below:
https://brainly.com/question/13101306
A city has a population of 260,000 people. Suppose that each year the population grows by 6.75% . What will the population be after 7 years? Use the calculator provided and round your answer to the nearest whole number.
The population of the city after 7 years will be approximately 393,574.
Explanation:To find the population after 7 years, we'll use the formula for exponential growth:
P = P0(1 + r)t
Where P is the future population, P0 is the initial population, r is the growth rate as a decimal, and t is the number of years.
In this case, P0 = 260,000, r = 6.75% = 0.0675 (decimal form), and t = 7.
Plugging in these values, we have:
P = 260,000(1 + 0.0675)7
Using a calculator, the population after 7 years is approximately 393,574.
Learn more about Exponential growth here:https://brainly.com/question/12490064
#SPJ11
Jacob drove from town a to town b at an average rate of x miles per hour, then returned along the same route at y miles per hour. if he then drove back to town b at z miles per hour along the same route, what was jacob's average rate of speed for the entire trip, in miles per hour?
Frazier has $1,200 in savings. He works because he is saving money for college, and he earns $9 an hour. If Frazier saves 25 percent of his net pay, after 20 percent is taken out for tax, identify the expression which represents Frazier's savings.
A) 1.8x + 1,200
B) 3.6x + 1,200
C) 7.2x + 1,200
D) 9x + 1,200
the correct answer is A..!! I think...:(
Answer: The correct option is (A) [tex]1.8x+1200.[/tex]
Step-by-step explanation: Given that Frazier is saving money for college and has $1200 in savings. He earns $9 per hour. He saves 25% of his net pay after 20% taken out for tax.
We are to identify the expression that represents Frazier's savings.
Let, x represents the number of hours for which Frazier works.
So, the net pay of Frazier = $ 9x.
Since 20% of the net pay is taken out for tax, so total pay of Frazier after taking out tax is given by
[tex]I_t=9x-20\%\times 9x=9x-\dfrac{20}{100}\times 9x=9x-\dfrac{9x}{5}=\dfrac{36x}{5}.[/tex]
Now, Frazier's savings from his net pay is given by
[tex]I_s=25\%\times \dfrac{36x}{5}=\dfrac{25}{100}\times \dfrac{36x}{5}=\dfrac{9x}{5}=1.8x.[/tex]
Since Frazier has $1200 already in savings, so the equation representing Frazier's savings will be
[tex]1.8x+1200.[/tex]
Thus, the required equation is [tex]1.8x+1200.[/tex]
Option (A) is CORRECT.
Complete the equation of the line through (-6,5) and (-3,-3) Use exact numbers. y=
The equation of the line passing through the points (-6,5) and (-3,-3) will be y = -(8/3)x - 11.
What is the equation of a line passing through two points?Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).
Then the equation of the line is given as,
[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]
The points are given below.
(-6,5) and (-3,-3)
Then the equation of the line passing through the points (-6,5) and (-3,-3) will be
[tex]\rm (y + 3) = \left (\dfrac{-3-5}{-3+6} \right ) (x + 3)[/tex]
Simplify the equation, then the equation of the line will be
y + 3 = -(8/3)(x + 3)
y = -(8/3)x - 8 - 3
y = -(8/3)x - 11
Then the equation of the line passing through the points (-6,5) and (-3,-3) will be y = -(8/3)x - 11.
More about the line passing through two points link is given below.
https://brainly.com/question/12740817
#SPJ2
BRAINLIESTTT ASAP!
please help
A bag contains 6 red, 7 blue, and 5 green coins. If 3 coins are randomly selected in succession, what is the probability of selecting a red coin, then a blue coin, and then a green coin, if replacement occurs each time?
How to find two numbers that sum equal 15 and product are maximized?
Use the x-intercept method to find all real solutions of the equation. x^3-9x^2+20x-12=0
Answer:
D= 1,2,or 6
Step-by-step explanation:
A number cube numbered from 1 to 6 is rolled. what is the probability of the number cube showing a 5 or an even number?
A normal distribution has a mean of 0.40 and standard deviation of 0.028. What percentage of observations will lie between 0.372 and 0.428?
To find the percentage of observations between two values in a normal distribution, we can convert the values to z-scores and use a z-table to find the corresponding areas. In this case, the percentage of observations between 0.372 and 0.428 is 68.26%.
Explanation:To find the percentage of observations that will lie between 0.372 and 0.428 in a normal distribution with a mean of 0.40 and standard deviation of 0.028, we need to find the area under the curve between these two values.
Using a standard normal distribution table or z-table, we can convert the values to z-scores by subtracting the mean and dividing by the standard deviation. The z-score for 0.372 is (0.372 - 0.40) / 0.028 = -1, and the z-score for 0.428 is (0.428 - 0.40) / 0.028 = 1.
By looking up the corresponding area for these z-scores in the z-table, we find that the area to the left of -1 is 0.1587 and the area to the left of 1 is 0.8413. To find the percentage between -1 and 1, we subtract the smaller area from the larger area: 0.8413 - 0.1587 = 0.6826 or 68.26%.
Learn more about Normal distribution here:https://brainly.com/question/34741155
#SPJ11
How do you simplify # (x+3)/(x^2+7x+12)#?
If you answer 110 questions and get a 94% how many did you get wrong
WILL MAKE BRAINLIEST!!!!!!!The arc length of a sector is equal to twice the radius. Express the arc length s as a function of the area a of the sector.
s=
The arc length as a function of the area of the sector is l=2√A.
What is the area of a sector?Area of a sector = 1/2 * arc length(l) * radius(r)
[tex]A=[/tex] [tex]\frac{1}{2} l*r[/tex]......(1)
It is given that the arc length of a sector is equal to twice the radius.
This means [tex]l=2r\\[/tex]
So, [tex]r=\frac{l}{2}[/tex]
Putting the value of r in (1)
[tex]A = \frac{l^{2} }{4}[/tex]
[tex]l^{2} =4A[/tex]
[tex]l=2\sqrt{A} \\[/tex]
So, the required function is l=2√A
Hence, the arc length as a function of the area of the sector is l=2√A.
To get more about arc length visit:
https://brainly.com/question/2005046
Simplify 72x6 y7 z .
Anyone know this? Will give brainiest
Please help asap, 70 points, THREE questions (:
Answer:
the answer for number 1 is 1.82
Step-by-step explanation:
Please Help!!!
Let x2−12x=61 . What values make an equivalent number sentence after completing the square?
The given equation is [tex] x^2-12x=61 [/tex]. Add 36 to both the sides of the equation, then
[tex] x^2-12x+36=61+36 [/tex].
The equation becomes,
[tex] x^2-12x+6^2=97\\
(x-6)^2=97 [/tex]
if it takes 18 gallons of gas to go 400 miles how many gallons would it take to go 300 miles
A. 5.5 gallons
B. 13.5 gallons
C. 16.6 gallons
D. 22.2 gallons
E. 24 gallons
We will use the ratio and proportion method ( an equation formed with two ratios that are equal) to solve the question “if it takes 18 gallons of gas to go 400 miles, how many gallons would it take to go 300 miles?”
Let x= the number of gallons for the gas to go 300 miles
18:400=X:300
400x=300*18
400x=5400
X=5400/400
X=13.5 so the answer is B.
Answer:
B
Step-by-step explanation:
its 13.5 gallons
Find the equation of a line perpendicular to y - 12 = 2x – 8 that passes through the point (2, 3). (answer in slope-intercept form)
The equation of the line perpendicular to y - 12 = 2x – 8 that passes through the point (2, 3) is y = (-1/2)x + 4.
What is the general equation of straight line? What is a mathematical function, equation and expression?straight line : The general equation of a straight line is -[y] = mx + c
function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is to find the equation of a line perpendicular to y - 12 = 2x – 8 that passes through the point (2, 3).
The given equation is -
y - 12 = 2x - 8
y = 2x - 8 + 12
y = 2x + 4
Assume the equation of the line to be -
y = mx + c
Now -
m = -1/2 {m (1) x m (2) = - 1 → for perpendicular lines}
So, the equation can be written as -
3 = - 1/2 x 2 + c
c = 3 + 1
c = 4
Therefore, the equation of the line perpendicular to y - 12 = 2x – 8 that passes through the point (2, 3) is y = (-1/2)x + 4.
To solve more questions on functions, expressions and polynomials, visit the link below -
brainly.com/question/17421223
#SPJ3
can someone please explan how I got this wrong?
Solve for x in the triangle
using laws of cosine
EASY 14 POINTS, PLEASE HELP ASAP.
Go into a dark room with a flashlight and face the beam toward a wall. Change the flashlight's distance from the wall as well as the way you hold the flashlight. Which conic sections can you form? Explain.
Describe how you formed different conic sections with your flashlight. Take and upload digital pictures as needed. Look at other students' descriptions and pictures and tell whether you agree with them.
What other simple tasks can you do in your home to form any of the conic sections? Again, describe these and/or take pictures to share with other students.
Well really it would have to depend on the flashlight. Is it an led bulb or a regular bulb?
Let 40 x 55 = n. Which of the choices shown is also equal to n?
A) (550 x 40)
B) (4 x 50) + (40 x 5)
C) (50 x 40) + (50 x 40)
D) (10 x 55) + (10 x 55) + (10 x 55) + (10 x 55)
Anyone know this geometry question? 10 min left! Will give brainiest
Consider the function f(x)=(x-9)/(x^3-81x)
Find the vertical asymptote(s) of f(x)
Answer:
Its A
x=0, -9
Step-by-step explanation:
just got it correct
The function f(x)=(x-9)/(x^3-81x) has three vertical asymptotes at x = 0, x = 9, and x = -9.
Explanation:To find the vertical asymptote(s) of the function f(x) = (x-9)/(x^3-81x), we need to determine the values of x for which the denominator equals zero. Setting the denominator equal to zero and solving for x, we get:
x^3 - 81x = 0x(x^2 - 81) = 0x(x - 9)(x + 9) = 0Therefore, the function has three vertical asymptotes at x = 0, x = 9, and x = -9.
Learn more about vertical asymptotes here:https://brainly.com/question/4084552
#SPJ3
Fifty-eight boys were asked if they play football and/or baseball. Thirty-one of them said they do not play baseball. Sixteen of them said they play football. Twenty of them said they do not play baseball or football.
Enter your answers in the boxes to complete the two-way table based on the given data.
You choose a marble at random from a bag containing 8 brown marbles 6 yellow marbles and one purple marble. You replace the marble and then choose again.find p (both yellow)
The path of a rocket ship is given by the parametric equations x(t)=3t and y(t)=4t^2+1, where t is the time in seconds after launch. Where is the ship after 10 seconds?
A.) (3,4)
B.) (3,5)
C.) (30,401)
D.) (30,501)