y^2 + y - 72 factorise
Answers
Answer:
y² + y - 72
= y² + 9y - 8y - 72
= y(y + 9) - 8(y + 9)
= (y - 8)(y + 9)
Step-by-step explanation:
Answer:
(y + 9) (y - 8)
Step-by-step explanation:
y² + y - 72
= y² + 9y - 8y - 72
= y (y + 9) - 8 (y + 9)
= (y + 9) (y - 8)
Hope it helps :)
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Related Questions
The sum of the interior angle measures of a convex polygon with n sides is given by the expression 180n–360 . Factor the expression.
Answers
Answer: 180(n-2)
You use the distribution rule to factor
The distribution rule is a(b+c) = a*b+a*c
These are 210 teacheas in a school of 3300 student find the ratio of teacher e to the number of the student
Answers
Answer:
7 : 210
Step-by-step explanation:
ratio of teachers : students
= 210 : 3300 ← divide both parts by 30
= 7 : 210
7 : 110
Step-by-step explanation:Known :There are 210 teachersThere are 3300 studentsAsked :The ratio of teacher to the studentSolution :Divide both sides by 30,
210 : 3300
= (210 / 30) : (3300 / 30)
= 7 : 110
Conclusion :The ratio of teacher to the student is 7 : 110
How can you write the value of 6 hundred thousandths?
Answers
We can write the value of 6 hundred thousandths by using multiplication and the required value is 6,00,000.
This problem can be done by using multiplication. Like 6 hundred can be multiplied with the thousand then the value gets. We can write the value of 6 hundred thousandths by using multiplication and the required value is 6lakhs.
In mathematics, the number has ones place, tens place and hundreds place, thousands place. So, by that we can conclude the required value.
The value can be get by multiplying the given terms
Given 600 and multiplied by thousandths
600 * 1000 = 6,00,000
So, the required value is 6 lakhs or 6,00,000.
Therefore, this problem can be done by using multiplication. Like 6 hundred can be multiplied with the thousand then the value gets. We can write the value of 6 hundred thousandths by using multiplication and the required value is 6lakhs.
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Assume the carrying capacity of the earth is 24 billion. Use the 1960 s peak annual growth rate of 2.1% and population of 3 billion to predict the base growth rate and current growth rate with a logistic model. Assume a current population of 6.8 billion. How does the predicted growth rate compare to the actual growth rate of about 1.2% per year? What is the base growth rate? \% (Round to four decimal places as needed.) What is the estimated current growth rate? \% (Round to two decimal places as needed.) How does the estimated growth rate compare to the actual current growth rate?
Answers
The base growth rate is approximately 2.0566% and the estimated current growth rate is approximately 1.12%. The estimated growth rate is lower than the actual current growth rate.
To find the base growth rate using a logistic model, we consider the peak annual growth rate of 2.1% in the 1960s when the population was 3 billion. Assuming a carrying capacity of 24 billion, we can estimate the base growth rate by dividing the peak growth rate by four times the difference between the current population (6.8 billion) and half the carrying capacity (12 billion).
Base growth rate = (2.1%)/(4 * (6.8 billion - 12 billion/2))
≈ 2.0566%
The estimated current growth rate is calculated by multiplying the base growth rate by the difference between the carrying capacity (24 billion) and the current population (6.8 billion), divided by the carrying capacity.
Estimated current growth rate = 2.0566% * (24 billion - 6.8 billion)/24 billion
≈ 1.12%
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For the question I just asked
Answers
Answer:
a = 36
Step-by-step explanation:
We use pythagoras theorem here.
h = 60
p = 48
b = a
h² = p² + b²
60² = 48² + b²
3600 = 2304 + b²
b² = 3600 - 2304
b² = 1296
b = 36
Answer:
A = 36
Step-by-step explanation:
A drawing of a basketball backboard was made using semicircle and rectangle
What is the area of the drawing of the backboard
A: 126 in
B: 253.17in
C:380.34in
D:122.5 in
Answers
100% sure
help please lol lol lol
Answers
Answer:
C
Step-by-step explanation:
Answer:
i think its C
Step-by-step explanation:
lol
A healthy human heart beats about 1,533,000 times in a year. A sparrow's heart beats about
241,776,000 times in a year.
About how many times faster does the sparrow's heart beat compared to the human heart?
Estimate using a single digit times a power of 10.
2x108
or about 100 times faster
2x10
=1 x 102
0 2x10°
2x106
= 1 x 103
or about 1,000 times faster
2x108
2x105
=1 103
or about 1,000 times faster
2x109
2x105
=1 104
or about 10,000 times faster
Answers
Answer:
About 100 times faster
=1 x 10²
Step-by-step explanation:
Estimate using a single digit times a power of 10.
We approximate to the nearest whole number
A healthy human heart beats about 1,533,000 times in a year.
= 1.533 × 10⁶
As a single digit = 2.0 × 10⁶
A sparrow's heart beats about
241,776,000 times in a year.
= 2.41776 × 10⁸
As a single digit = 2 × 10⁸
About how many times faster does the sparrow's heart beat compared to the human heart?
We find the difference in their powers of 10
= ( 10^8 - 6)
= 10²
This means the sparrows heart beats at about
1 × 10² or a 100 times faster
The expression 2x and x² have the same value for only two values of x. What are these values?
Answers
Answer:
0 and 2
Step-by-step explanation:
A boat is due South of a lighthouse and sails on a bearing of 292° for 51 km until it is due West of the lighthouse. How far away is it now from the lighthouse
Answers
The distance between the boat and the lighthouse is 47,29, 47,29, 47,29 kilometers.
What is an equation?An equation is a mathematical statement containing two algebraic expressions flanked by equal signs (=) on either side.
It shows that the relationship between the left and right printed expressions is equal.
All formulas hav LHS = RHS (left side = right side).
You can solve equations to determine the values of unknown variables that represent unknown quantities.
If a statement does not have an equals sign, it is not an equation. A mathematical statement called an equation contains the symbol "equal to" between two expressions of equal value.
According to our question-
tano = perpendicular/base
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PLEASE PLEASE HELP!! I NEED THE ANSWERS ASAP
Answers
Answer:
Pictures below showing the answer :)
Step-by-step explanation:
What percent is represented by the shaded area?
Answers
Answer: 52%
Step-by-step explanation:
There are 52 squares colored in. 52 divided by 100 equals 0.52. Then multiply the 100 back to 52 to get 52%.
Answer: 52%
Step-by-step explanation:
527.8317 Find the digits in the tens place, in the hundredths place, and in the thousandths place for the following number.
Answers
Earnings are expected to grow at 10 percent for the next year. Using the company's historical average pe as a benchmark, What is the target stock price in one year?
Answers
The target stock price in one year, based on the company's historical average PE as a benchmark and an expected earnings growth rate of 10%, is $825.
The target stock price in one year, based on the company's historical average PE as a benchmark and an expected earnings growth rate of 10%, is $825.
Based on the given information, to calculate the target stock price in one year, we need to consider the company's historical average PE ratio and the expected earnings growth rate.
1. Determine the historical average PE ratio of the company. Let's assume it is 15.
2. Calculate the expected earnings growth rate in decimal form by dividing it by 100. In this case, it is 10% or 0.10.
3. Multiply the historical average PE ratio by the expected earnings growth rate plus 1. For example, 15 * (1 + 0.10) = 16.5.
4. Multiply the result by the current stock price to find the target stock price in one year. Let's assume the current stock price is $50. Therefore, 16.5 * $50 = $825.
So, the target stock price in one year, based on the company's historical average PE as a benchmark and an expected earnings growth rate of 10%, is $825.
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express the number in trigonometric form. -2 + 2 √3 i
Answers
Given:
z = -2 + 2 √3 i
The objective is to write the number in trigonometric form.
The trigonometric form can be represented as,
\(z=r(\cos \theta+i\sin \theta)\)The general form of complex number is, z = x+iy.
By comparing with the given equation.
x = -2
y = 2 √3
The value of r can be calculated as,
\(\begin{gathered} r=\sqrt[]{x^2+y^2} \\ r=\sqrt[]{(-2)^2+(2\sqrt[]{3})^2} \\ r=\sqrt[]{4+4\cdot3} \\ r=\sqrt[]{4+12} \\ r=\sqrt[]{16} \\ r=4 \end{gathered}\)The value of theta can be calculated as,
\(\begin{gathered} \theta=\tan ^{-1}(\frac{y}{x}) \\ \theta=\tan ^{-1}(\frac{2\sqrt[]{3}}{-2}) \\ \theta=\tan ^{-1}(-\sqrt[]{3}) \\ \theta=-^{}60^0 \\ \theta=-\frac{\pi}{3} \end{gathered}\)Now, substitute the obtained values of r and theta in the general equation of trigonometric form.
\(z=4\lbrack\cos (-\frac{\pi}{3})+i\sin (-\frac{\pi}{3})\rbrack\)Since,
\(\begin{gathered} \cos (-\theta)=\cos \theta \\ \sin (-\theta)=-\sin \theta \end{gathered}\)Then,
\(z=4\lbrack\cos \frac{\pi}{3}-i\sin \frac{\pi}{3}\rbrack\)Hence, the required trigonometric form is obtained.
The curve y tan x crosses the line y = 7x at a non-zero x-value between x = 0 and X Ξ . Use Newton's method to find where the curves intersect. The curve y = tan x crosses the line y = 7x at x = (Type an integer or decimal rounded to seven decimal places as needed.) Enter your answer in the answer box. 8:04 PM O Type here to search
Previous question
Next
Answers
To find the intersection point between the curve y = tan(x) and the line y = 7x, we can use Newton's method. Newton's method is an iterative numerical method used to approximate the root of a function.
We need to find the x-value where the curves intersect, so we can set up the equation tan(x) - 7x = 0. We want to find a solution between x = 0 and some unknown value denoted as X.
Using Newton's method, we start with an initial guess x_0 for the solution and iterate using the formula:
x_(n+1) = x_n - f(x_n) / f'(x_n),
where f(x) = tan(x) - 7x and f'(x) is the derivative of f(x).
We continue this iteration until we reach a desired level of accuracy or convergence. The resulting value of x will be the approximate intersection point between the two curves.
Please note that without specific values or range for X or an initial guess x_0, it is not possible to provide a specific numerical answer. However, you can apply Newton's method using an initial guess and the given function to find the approximate intersection point.
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there are two boxes one box contains 6 red and 3 yellow balls. the other box contains 2 blue, and 3 green marbles. if one ball from each box is randomly drawn, what is the probability that a red and blue ball will be drawn?
Answers
Answer:
\(\frac{2}{15}\)
Step-by-step explanation:
1. There are 9 balls in total in the first box, and 6 red balls in there so we would represent this as \(\frac{6}{9}\) and that can be simplified to \(\frac{1}{3}\) .
2. There are 5 balls in total in the second box, and 2 blue balls in there, so we would represent this as \(\frac{2}{5}\) . This can't be simplified, so we leave it like that.
3. Because it's a consecutive event we multiply the probabilities, which gives us \(\frac{2}{15}\) . This can't be simplified, and that gives us our answer.
Use each method to solve system of linear equation. Show your solution.
-3x + y = 7
5x + 2y = 3
Substitution B. Elimination
Answers
Answer:
x=-1 y =-1
Step-by-step explanation:
multiply equation 1 with (-2)
+6x-2y=-14
5x+2y=3
now add equation 1 to equation 2
11x=-11
x=-1
now substitute x=1 in 1 or 2
5(1)+2y=3 5+2y=3 2y=3-5 2y= -2 y= -1
At the fabric store, you spent $51.30 for 15 yards of fabric. How much did each yard cost
Answers
suppose z=x2siny, x=1s2 3t2, y=6st. a. use the chain rule to find ∂z∂s and ∂z∂t as functions of x, y, s and t
Answers
The required partial derivatives ∂z/∂s and ∂z/∂t are 18t³ sin(6st) + 27/2 t⁵ cos(6st) and 9t⁴ sin(6st) + 27/2 t⁴ cos(6st), respectively, as functions of x, y, s, and t.
Given, z = x²sin(y),
Where x = 1/2 3t² and y = 6st.
We are required to find ∂z/∂s and ∂z/∂t using the chain rule of differentiation.
Using the Chain Rule, we have:
\(\frac{dz}{ds} = \frac{\partial z}{\partial x} \frac{dx}{ds} + \frac{\partial z}{\partial y} \frac{dy}{ds}\)
\(\frac{dz}{dt} = \frac{\partial z}{\partial x} \frac{dx}{dt} + \frac{\partial z}{\partial y} \frac{dy}{dt}\)
Let's find out the required partial derivatives separately:
Given, x = 1/2 3t²
\(\frac{dx}{dt} = 3t\)
Given, \(y = 6st\frac\\\)
\({dy}/{ds}= 6t\)
\(\frac{dy}{dt} = 6s\)
\(\frac{\partial z}{\partial x} = 2x sin(y)\)
\(\frac{\partial z}{\partial y}= x² cos(y)\)
Now, substituting the values of x, y, s, and t, we get:
\(\frac{\partial z}{\partial x} = 2(1/2 3t²) sin(6st)\)
= \(3t² sin(6st)\)
\(\frac{\partial z}{\partial y}\) = (1/2 3t²)² cos(6st)
= \(9/4 t⁴ cos(6st)\)
Substituting these values in the chain rule formula:
\(\frac{dz}{ds}\)= 3t² sin(6st) (6t) + 9/4 t⁴ cos(6st) (6t)
= 18t³ s in (6st) + 27/2 t⁵ cos(6st)
Therefore, ∂z/∂s as a function of x, y, s, and t is:
\(\frac{\partial z}{\partial s} = 18t³ sin(6st) + 27/2 t⁵ cos(6st)\)
Substituting the values of x, y, s, and t in the formula:
\(\frac{dz}{dt} = 3t² sin(6st) (3t²) + 9/4 t⁴ cos(6st) (6s)\)
= \(9t⁴ s in (6st) + 27/2 t⁴ cos(6st)\)
Therefore, ∂z/∂t as a function of x, y, s and t is:
\(\frac{\partial z}{\partial t} = 9t⁴ sin(6st) + 27/2 t⁴ cos(6st)\)
Hence, the required partial derivatives ∂z/∂s and ∂z/∂t are 18t³ sin(6st) + 27/2 t⁵ cos(6st) and 9t⁴ sin(6st) + 27/2 t⁴ cos(6st), respectively, as functions of x, y, s, and t.
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Mr. Garvey is almost finished working on his rectangular patio. He has ordered enough patio stones to cover an area of 600ft2. He knows that his yard is 30ft wide. He also remembers that there is an equation for areas of a rectangle: FASTTTTT
Answers
Answer:
20 ft
Step-by-step explanation:
Area of a rectangle = length x width
600 ft^2 = 30 ft x length
length = 600 / 30
= 20 ft
Find the mean absolute deviation of the set: 10,5,7,14,19,32,25
Answers
Answer: I believe it would be 8.
Step-by-step explanation:
Whats the answer y’all
Answers
The expressions that will give you a difference of 5 are: -3 - (-8) and 1 - (-4).
What is the Difference of Two Expressions?The difference of two expressions is determined by subtracting one from the other.
Find the difference of each of the expressions given to determine which will give us 5.
-3 - (-8)
= -3 + 8
= 5
-2 - 3 = -5 [this is not the same as 5]
1 - (-4)
= 1 + 4
= 5
7 - (-2)
= 7 + 2
= 9
-3 - (-8) and 1 - (-4) will give us a difference of 5.
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Find the slope between these two points: (2,-1) and (10,-13)
Answers
Answer:
-3/2
Step-by-step explanation:
Answer:
-3/2
Step-by-step explanation:
(y2-y1) / (x2-x1)
(-13-(-1)) / (10-2)
=-12/8
simplify
= -3/2
the
net migration is confusing me. i thought of using the formula:
[ (births + immigration) - (deaths + emmigration)] / total
population • 100 but im not sure how to do it with net migration?
do i p
Answers
The value of the rate of growth in Japan is - 0.55.
From the question above, :Birth rate = 7.7 per thousand
Death rate = 9.8 per thousand
Net migration = 0.55 per thousand
The rate of growth can be calculated using the following formula:
r = (birth rate - death rate) + net migration
Where,r = rate of growth
birth rate = number of live births per thousand in a population in a given year
death rate = number of deaths per thousand in a population in a given year
net migration = the difference between the number of people moving into a country (immigrants) and the number of people leaving a country (emigrants) per thousand in a given year
Putting the values in the formula we get,r = (7.7 - 9.8) + 0.55r = - 1.1 + 0.55r = - 0.55.
Therefore, the rate of growth in Japan is - 0.55.
Your question is incomplete but most probably your full question was:
thenet migration is confusing me. i thought of using the formula:[ (births + immigration) - (deaths + emmigration)] / total
population • 100 but im not sure how to do it with net migration.
Japan's birth rate is 7.7 per thousand and its death rate is 9.8 per thousand with a net migration of 0.55 ner thousand. Calculate r for Japan
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a rectangle has a perimeter of 116 units if the length is 2 less than 5 times the width what’s the width
Answers
The width of rectangle is 10 units.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Perimeter of rectangle = 116 units
let the width be x.
then the length is 5x - 2.
so, Perimeter of rectangle = 116 units
2 (5x -2 + x)= 116
2(6x - 2) = 116
6x - 2 = 58
6x = 60
x= 10
So, the width is 10 units and length is 5(10)-2 = 48 units
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the ratio of peter's age to richard's age is $5:8.$ the ratio of john's age to peter's age is $7:12.$ none of the three are over $100$ years old. what is the sum of their ages?
Answers
The sum of Peter, Richard, and John's ages is 191.
We know that the ratio of Peter's age to Richard's age is = 5/8 --(i)
The ratio of John's age to Peter's age is = 7/12 --(ii)
Similarly, the ratio of John's age to Richard's age is = (5*7)/(8*12)= 35/96 -(iii)
Using the value of (i),(ii),(iii), we get -
Age of Peter = (5*12)/(8*12) = 60/96
= 60 years of age
Age of John = (7*5)/(12*5) = 35/60
=35 years of age
From the value of (iii), since no one is over 100 years of age, the age of Richard= 96 years of age
Hence the sum of their ages is = 96+35+60
= 191
Therefore, we know that the sum of their ages is 191.
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what’s the answer i need help? Find slope using triangles and rise over run
Answers
Answer:
slope is 1/3
Step-by-step explanation:
notice the points on the line, from the first point go one square up and three to the right, thats how i got 1/3
How do you solve this?
(3^{x-1}*27^x*9^2)/(3^{2x-4)*81^x}
Answers
Answer: The expression can be simplified as follows:
(3^{x-1} * 27^x * 9^2) = 3^{x-1 + 2} * 27^x
(3^{2x-4) * 81^x} = 3^{2x-4 + 2x} * 3^{-2x}
Replace in the expression: (3^{x-1 + 2} * 27^x) / (3^{2x-4 + 2x} * 3^{-2x}) = 3^{x-1 + 2 - 2x + 4} * 27^x / 3^4 = 3^3 * 27^x / 81
So the simplified expression is 3^3 * 27^x / 81.
Step-by-step explanation:
Mia rode 3 miles in a taxi. What was the total cost ,in dollars,of her ride the ride costs 2.50 a mile
Answers
Answer:
Total cost = $7.5
Step-by-step explanation:
Given the following data;
Total distance = 3 miles
Cost per distance = $2.50
To find the total cost ofof ride, we would use the following mathematical expression;
Total cost = total distance * cost per distance
Total cost = 3 * 2.5
Total cost = $7.5
Therefore, the total cost, in dollars, of Mia's ride is 7.5.