If the length of a rectangle in terms of x is 9x² + 5x + 2 and its width is 6x + 1, what is the perimeter of the rectangle?
Answer:
18x^2 + 22x + 4 -----i dont know for sure if this is correct but i tried my best so dont complain pls if its not correct
Step-by-step explanation:
____________________
I I ----srry this helps me
I I
I I 9x^2 + 5x + 2
I I
_____________________
6x + 1
So you times both by 2 by doing first:
2(6x+1) = 12x + 2
and
2(9x^2 + 5x + 2) = 18x^2 + 10x + 2
Then you need to find the like terms. To find the like terms you need to find two similar terms and add or minus. For example:
2x + 4 - 3x + 2
The two similar terms are: [2x] + 4 [-3x] + 2
so minus them 2x - 3x = -1x and then
4 + 2 = 6 so the final equation is -
6 - 1x . you cant find the like terms of that because they arent the same terms. The same can be said with 2x and 2x^2. Theyre not the same terms.
So continuing with the initial question,
find the like terms of:
18x^2 [+ 10x] (+ 2) [+ 12x] (+ 2) ----- the brackets are just so you know which are like terms.
so the final equation is:
18x^2 + 22x + 4.
Please help!
i do not understand my homework!
Answer:
I believe the answer is A.
Answer:
the answer is D I believe
Select the correct expanded form for (Two-thirds) Superscript 4.
Two-thirds times two-thirds times two-thirds times two-thirds
Two-thirds times two-thirds times two-thirds
Two-thirds + two-thirds + two-thirds + two-thirds
Two-thirds times 4
The correct expanded form using Laws of exponents is:
Two-thirds times two-thirds times two-thirds times two-thirds
How to use laws of exponents?Some of the laws of exponents are:
1) When multiplying like bases, keep the base the same and add the exponents.
2) When raising a base with a power to another power, keep the base the same and multiply the exponents.
3) When dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent.
Now, we want to solve the expression given as: (²/₃)⁴
When we expend this, we arrive at:
²/₃ × ²/₃ × ²/₃ × ²/₃
This among the options is Option A which is:
Two-thirds times two-thirds times two-thirds times two-thirds
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3/8=4/7x what is x please help me omg
The value of the variable x = 21/32
What are algebraic expressions?Algebraic expressions are simply described as expressions that are composed of variables, coefficients, terms, constants and factors.
These expressions are also made up of certain arithmetic or mathematical operations.
These operations includes;
SubtractionDivisionAdditionMultiplicationBracketParenthesesFrom the information given, we have that;
3/8=4/7x
cross multiply the values, we have;
7x(3) = 8(4)
multiply the values and expand the brackets, we get the values;
21x = 32
Divide both sides by the coefficient of the variable x, we get;
x = 32/21
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Simplify:
x² + 3x + 2 /x² - 4x - 5
x² + 7x + 12 / x²-3x - 28
\(\\ \rm\Rrightarrow \dfrac{x^2+3x+2}{x^2-4x-5}\)
\(\\ \rm\Rrightarrow \dfrac{x^2+2x+x+2}{x^2-5x+x-5}\)
\(\\ \rm\Rrightarrow {(x+2)(x+1)}{(x-5)(x+1)}\)
\(\\ \rm\Rrightarrow \dfrac{x+2}{x-5}\)
And
\(\\ \rm\Rrightarrow \dfrac{x^2+7x+12}{x^2-3x-28}\)
\(\\ \rm\Rrightarrow \dfrac{x^2+4x+3x+12}{x^2-7x+4x-28}\)
\(\\ \rm\Rrightarrow \dfrac{(x+4)(x+3)}{(x-7)(x+4)}\)
\(\\ \rm\Rrightarrow \dfrac{x+3}{x-7}\)
i need to solve this question, please!!
The table should be completed as follows;
Year Starting Balance Interest Ending Balance
1 $8500 $510 $9010
2 $9010 $510 $9520
3 $9520 $510 $10030
4 $10030 $510 $10540
5 $10540 $510 $11050
How to calculate the simple interest and future value?In Mathematics, simple interest can be calculated by using this formula:
S.I = PRT or S.I = A - P
Where:
S.I represents the simple interest.P is the principal or starting balance.R is the interest rate.A is the future value or ending balance.T represents the time measured in years.By substituting the given parameters into the simple interest formula, we have;
S.I = 8500 × 6/100 × 1
S.I = 8500 × 0.06 × 1
S.I = $510.
Note: The simple interest rate of $510 would be constant.
After 1 year, we have:
Ending balance, A = S.I + P
Ending balance, A = $510 + $8500
Ending balance, A = $9010.
After 2 years, we have:
Ending balance, A = $510 + $9010
Ending balance, A = $9520.
After 3 years, we have:
Ending balance, A = $510 + $9520
Ending balance, A = $10030.
After 4 years, we have:
Ending balance, A = $510 + $10030
Ending balance, A = $10540.
Next, we would calculate the ending balance after 5 years as follows;
Ending balance, A = $510 + $10540
Ending balance, A = $11050.
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This is a rhombus. Solve for x, Then label each angle with its correct measures:
Answer:
Step-by-step explanation:
In the given rhombus, the value of x is 18.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We know that;
Diagonal bisect the angles of a rhombus.
Hence, We can formulate;
⇒ (2x + 16)° = (3x - 2)°
Solve for x as;
⇒ 2x + 16 = 3x - 2
Subtract 2x both side,
⇒ 2x + 16 - 2x = 3x - 2 - 2x
⇒ 16 = x - 2
Add 2 both side,
⇒ 16 + 2 = x - 2 + 2
⇒ 18 = x
⇒ x = 18
Thus, The value of x in rhombus = 18
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Problem’s in the image
The growth rate function indicates that the number of years The Iron Man's net worth will reach the net worth of T'Challa is about 87 years
What is a growth rate?The growth rate is the rate of growth of a function with regards to the input variable.
T'Challa's net worth in the Marvel comics = 80 trillion (8 × 10¹³) Dollars
The Iron Man's net worth = 20 billion (2 × 10¹⁰) Dollars
The growth rate per annum of The Iron Man's net worth = 10% per annum
The number of years it will take to reach T'Challa can therefore, be found as follows;;
(2 × 10¹⁰) × (1 + 0.1)ˣ = (8 × 10¹³)
(1 + 0.1)ˣ = (8 × 10¹³)/(2 × 10¹⁰)
x·ln(1 + 0.1) = ln((8 × 10¹³)/(2 × 10¹⁰))
x = (ln((8 × 10¹³)/(2 × 10¹⁰)))/(ln(1 + 0.1)) ≈ 87 years
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PLSSS HELP!! Ty whoever helped me! :) Question: Select the statement that is true about the two-dimensional figure.
A quadrilateral with the vertices labeled L, M, N and O. Angles M L O and L M N are greater than 90 degrees, and angles L O N and M N O are less than 90 degrees.
∠LMN is an acute angle.
∠LMN is an obtuse angle.
∠MNO is an obtuse angle.
∠MNO is a right angle.
∠LMN is an obtuse angle.
==========================================
Explanation
Let's go through the answer choices to see which are true, and which are false.
A. This is false. It is stated that "LMN is greater than 90 degrees", so this angle is obtuse. Acute angles are less than 90 degrees.B. This is true. See choice A above.C. This is false. We're told that "angle MNO is less than 90 degrees". That makes the angle acute. D. This is false. See choice C above. Right angles are 90 degrees exactly. Often a small square marker is used to denote a 90 degree angle.What is the slope of the line that passes through the points (-6, -6) and (-9,-5)? Write your answer in simplest form. What is the slope of the line that passes through the points ( -6 , -6 ) and ( -9 , -5)?
Answer:
\(y=-\frac{1}{3}x -8\)
Step-by-step explanation:
1) Write down the standard form of an equation of a line and the formula to find m.
\(y=mx+b\)
\(m=\frac{y_{2} - y_{1} }{x_{2} - x_{1} }\)
2) Find m using the formula then substitute it into \(y=mx+b\).
\(m=\frac{-5 - (-6) }{-9 - (-6)}\\m=\frac{-5 +6 }{-9 +6}\\m=\frac{1}{-3} \\m=-\frac{1}{3}\)
So, \(y=-\frac{1}{3}x +b\).
3) Find b by substituting a pair of coordinates the line goes through.
\(-6=-\frac{1}{3}(-6) +b\\-6=2+b\\-6 - 2=b\\-8=b\)
4) Substitute b into \(y=-\frac{1}{3}x +b\) to get your final answer.
\(y=-\frac{1}{3}x -8\)
Evaluate the expression 4w² + w-6, when w = -4
a.) 54
b.) 22
c.) -54
d.) 74
\( \huge \pink{ \underline \mathfrak{ \green{Answer}}} \: \\ \\ \: \: \rightarrow \fbox{ a). \blue{ \: 54 \: }}\)
Step-by-step explanation:
\( \bf{Given} \: \colon 4w² + w-6, when \: \: w = -4 \\ \\ \tt \underline \red{Solution} \colon \\ \\ \rightarrow \: 4w {}^{2} + w \: - 6 \\ \\ \: put \: \: value \: \: of \: \: w \: \: in \: \: given \: \: equation \\ \\ \rightarrow \: 4( - 4) {}^{2} + \: (- 4 )\: - 6 \\ \\ \rightarrow \: 4(16) \: - 4 \: - 6 \\ \\ \rightarrow \: 64 \: - 10 \\ \\ \bf \rightarrow54\)
h= -16t^2+16t+192 When will the ball hit the ground?
Answer:
t = 4 s
Step-by-step explanation
We can infer the origin from the t⁰ term of the quadratic as being 192 feet above the ground. Initial velocity is 16 ft/s from the t¹ term, gravity is -32 ft/s² from the t² term
0 = -16t² + 16t + 192
0 = -t² + t + 12
0 = t² - t - 12
0 = (t - 4)(t + 3)
so either
t - 4 = 0
t = 4 s
or
t + 3 = 0
t = -3 s which we ignore as it occurs before the ball is released.
PLEASE PLEASE Help
Answer:
1 number of lunches a day and cost is varibley different
Terri buys five and seven-eighths ounces of chocolate chips. She uses four and four-sixths ounces in a recipe. How many ounces of chocolate chips does she have left?
Answer:
1 5/24 ounces--------------------------
Find the difference of the initial and used amounts:
5 7/8 - 4 4/6 = 5 - 4 + 7/8 - 4/6 = Combine whole and fraction parts1 + 7/8 - 2/3 = Simplify1 + 21/24 - 16/24 = Common denominator is 241 + 5/24 = Convert to mixed fraction1 5/24Here help my sis needs help
Let's complete
(2,8)(3,12)(4,16)Rule following=4n
(5,20)(6,24)#2
The rule is 4n
#3
Let's see
4n=48n=12ydIn a class of students, the following data
table summarizes how many students have a
cat or a dog. What is the probability that a
student chosen randomly from the class has
a cat?
Has a dog
Does not have a
dog
Has a cat
2
3
Does not have a
cat
12
10
The table can be summarized as follows:
| | Has a dog | Does not have a dog |
|----------|-----------|---------------------|
| Has a cat | 2 | 3 |
| Does not have a cat | 12 | 10 |
To find the probability that a student chosen randomly from the class has a cat, we need to find the total number of students who have a cat (regardless of whether or not they have a dog), and divide it by the total number of students in the class.
The number of students who have a cat is 2 (those who have a dog and a cat) + 3 (those who have a cat but do not have a dog) = 5.
The total number of students in the class is the sum of all four categories: 2 (has a cat and a dog) + 3 (has a cat, does not have a dog) + 12 (does not have a cat, has a dog) + 10 (does not have a cat, does not have a dog) = 27.
So, the probability that a student chosen randomly from the class has a cat is 5/27.
Find the greatest common factor of 6m² and 7m².
Answer:
your answer is 4 my friend
Step-by-step explanation:
A puppy weighs534pounds.
How many ounces does the puppy weigh?
Answer:
I believe that the question is "A puppy weighs 5 3/4 pounds. How many ounces does the puppy weigh."
Step-by-step explanation:
The answer is 23 ounces.
A population of values has a normal distribution with μ= 180.1
and σ=100. You intend to draw a random sample of size n=94
What is the mean of the distribution of sample means?
What is the standard deviation of the distribution of sample means?
(Report answer accurate to 2 decimal places.)
A sample of size n taken from a normally distributed population with mean µ and standard deviation σ has a sample mean of µ and standard deviation of σ/√n.
So the sample mean would still be 180.1, while the sample standard deviation would be 100/√94 ≈ 10.31.
Solve the following quadratic inequality x^2+x-6>0
Answer:
x < -3 or x > 2
Step-by-step explanation:
x² + x - 6 > 0
Convert the inequality to an equation.
x² + x - 6 = 0
Factor using the AC method and get:
(x - 2) (x + 3) = 0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
x - 2 = 0
x = 2
x + 3 = 0
x = -3
So, the solution is x < -3 or x > 2
what's 2/5 + 2 1/6 divided by 5/6?
The answer would be 3
Answer:
77/25
Step-by-step explanation:
First, 2/5 + 2 1/6 is 77/30, and then you divide the answer by 5/6.
The answer your get is 77/25.
Given the points P (3, 5) and Q (-5, 7) on the cartesian plane such that R (x, y) is
the midpoint of PQ, find the equation of the line that passes through R and
perpendicular
to PQ.
Answer:
-22=22
Step-by-step explanation:
3,5-5,7=
-22/22
The equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.
To find the equation of the line passing through the midpoint R and the points P and Q, we first need to find the coordinates of the midpoint R. The midpoint coordinates can be found by taking the average of the x-coordinates and the average of the y-coordinates of P and Q.
The x-coordinate of the midpoint R is (3 + (-5)) / 2 = -1/2.
The y-coordinate of the midpoint R is (5 + 7) / 2 = 6.
So, the coordinates of the midpoint R are (-1/2, 6).
Next, we can use the two-point form of the equation of a line, which states that the equation of the line passing through points (x₁, y₁) and (x₂, y₂) is given by:
(y - y₁) = (y₂ - y₁) / (x₂ - x₁) \(\times\) (x - x₁)
Substituting the coordinates of R (-1/2, 6) and P (3, 5) into the equation, we have:
(y - 6) = (7 - 5) / (-5 - 3) \(\times\)(x - (-1/2))
Simplifying the equation:
(y - 6) = (2 / -8) \(\times\)(x + 1/2)
(y - 6) = -1/4 \(\times\)(x + 1/2)
4(y - 6) = -x - 1/2
Therefore, the equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.
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Postcards cost $2.50 for six.
What's the price for 1 postcard?
Answer:
about 41 cents
Step-by-step explanation:
4. You have been offered $3,000 in 4 years for providing $2,000 today into a business venture with a friend. If interest rates are 10%, is this a good investment for you?
Step-by-step explanation:
To determine if this is a good investment, we can use present value calculations to see what the $3,000 payment in 4 years is worth today:
Present value of $3,000 in 4 years at 10% interest rate = $3,000 / (1 + 0.10)^4 = $2,102.50.
If we invest $2,000 today and get a payment of $2,102.50 in 4 years, our net gain would be:
Net gain = $2,102.50 - $2,000 = $102.50
Therefore, investing $2,000 today with an interest rate of 10% and receiving $3,000 in 4 years would yield a net gain of $102.50.
While any gain is better than no gain, a return of $102.50 on an investment of $2,000 over a period of 4 years may not be considered a great investment. It's up to the individual to decide whether they feel that the potential gain is worth the initial investment and risk involved.
Please help me out with this
Answer:
I would say D
Step-by-step explanation:
since it already tells you what y equals it makes it easier to substitute the others take more work so the best first step is substituting for y
Answer:
Option D) Substitute for y in the first equation
Step-by-step explanation:
When solving for a system of equation, we always need 1 equation to have x or y already isolated by itself. This makes it easy to substitute that variable into the other equation, solve, then substitute the other variable into another equation.
This will give us an ordered pair, known as the solution.
In this system, we have 2 equations. In the first one, we have no variables isolated. In the second one, we have y isolated on the left side of the equal sign. This means we can take what y equals (3x+2) and substitute that in for y in the first equation.
Hope this helps! :)
what would be your first step in completely factoring 6a^2-15a+6
The completely factoring form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).
To completely factor the expression 6a^2 - 15a + 6, the first step is to check if there is a common factor among the coefficients (6, -15, and 6) and the terms (a^2, a, and 1).
In this case, we can see that the common factor among the coefficients is 3, so we can factor out 3:
3(2a^2 - 5a + 2)
Now we need to factor the quadratic expression inside the parentheses further. We are looking for two binomials that, when multiplied, give us 2a^2 - 5a + 2. The factors of 2a^2 are 2a and a, and the factors of 2 are 2 and 1. We need to find two numbers that multiply to give 2 and add up to -5.
The numbers -2 and -1 fit this criteria, so we can rewrite the expression as:
3(2a - 1)(a - 2)
Therefore, the completely factored form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).
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Choose the correct description of how the graph of f(x)=x2 changes due to the transformation. Graph the function using your graphing calculator to check your answer. g(x)=−5x2
The answers are:
B. The graph of f(x) is shifted up 50 units
E. The graph of f(x) is shifted right 10 units
F. The graph of f(x) is reflected over the x-axis
How to calculate transformation?The given function is f(x) = x²
This is an upward-facing vertical parabola.
The vertex is the smallest.
The vertex's origin is at (0, 0).
g(x) = –5x² + 100x – 450
This is an open downhill vertical parabola.
The vertex is the greatest
The first thing to notice is that fx) opens up whereas g(x) opens down, indicating that a reflection across the x-axis was used.
Find the g(x) vertex.
change the form to vertex
g(x) = –5x² + 100x – 450
Complete the square
g(x) = -5(x² - 20x) - 450
g(x) = -5(x² - 20x + 100) - 450 + 500
g(x) = -5(x² - 20x + 100) + 50
g(x) = -5( x - 10)² + 50
The vertex is located at (10, 50).
To the vertex from (0,0) to (10,50)
The translational principle is
(x,y) ------> (x+10,y+50)
This implies ----> The translation is 50 units up and 10 units to the right.
The adjustments are
The f(x) graph is moved forward by 50 units.
The f(x) graph is 10 units to the right.
Over the x-axis is a reflection of the f(x) graph.
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The complete question is,
Which transformations have been applied to the graph of f(x) = x² to produce the graph of g(x) = –5x² + 100x – 450? Check all that apply.
A.The graph of f(x) = x² is shifted up 25 units.
B.The graph of f(x) = x² is shifted up 50 units.
C.The graph of f(x) = x² is shifted down 950 units.
D.The graph of f(x) = x² is shifted left 10 units.
E.The graph of f(x) = x² is shifted right 10 units.
F.The graph of f(x) = x² is reflected over the x-axis.
The images below show a picture of ricoffy tin container with no dimensions indicated.the container is 2,5 times smaller than what it is in reality. Measure the diameter of the tin in mm and write down the real diameter in mm
The diameter of the tin in the picture is \(3d/5\) where 'd' is the diameter of the tin in reality.
What is the measurement of the diameter?Determining the diameter of tin:
Since there is no indication of dimensions, represent the diameter with a variable 'd' and find the diameter of the tin according to the given condition in the problem.
Here we have assumed that the diameter of the tin is 'd' in reality and the diameter of the tin picture can be calculated as given below.
Here we have
A ricoffy tin container with no dimensions indicated
Let d and h be the diameter and height of the tin
Given that the container is 2/5 times smaller than d
then the diameter of the tin in the picture \(= d - 2/5(d)\)
\(= [5d - 2d]/5 = 3d/5\)
Therefore, The diameter of the tin in the picture is \(3d/5\) where 'd' is the diameter of the tin in reality.
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Does it matter which coordinate is (x1,y1) and (x2,y2) or can I just choose which coordinate I want it to be?
Answer:
Technically not on a graph but on a table yes it matter but here if I were you I would do (2,2) and (-1,-4)
Step-by-step explanation: y=mx+b
(2,2) and (-1,-4) 2=2(2)+b Answer is: y=2x+(-2)
x1 y1 x2 y2 2=4+b
-4-2=-6 -2=b
-1-2=-3 y-intercept
m=2
slope
Answer:
No, it doesn't matter which coordinate you assign \((x_1,y_1)\) and \((x_2,y_2)\)
Step-by-step explanation:
Proof
\(\textsf{let}\:(x_1,y_1)=(-1,-4)\)
\(\textsf{let}\:(x_2,y_2)=(2,2)\)
\(\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{2-(-4)}{2-(-1)}=2\)
\(\begin{aligned}y-y_1&=m(x-x_1)\\\implies y-(-4) &=2(x-(-1)\\y&=2x-2\end{aligned}\)
\(\textsf{let}\:(x_1,y_1)=(2,2)\)
\(\textsf{let}\:(x_2,y_2)=(-1,-4)\)
\(\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-4-2}{-1-2}=2\)
\(\begin{aligned}y-y_1&=m(x-x_1)\\\implies y-2 &=2(x-2)\\y&=2x-2\end{aligned}\)
For which inequality is x = 5 a solution
Answer:
4<x<6
Step-by-step explanation:
4 is smaller than x
and x is samller than 6
so its 5