[tex]\\ \sf\longmapsto 122^2[/tex]
[tex]\\ \sf\longmapsto (100+22)^2[/tex]
[tex]\\ \sf\longmapsto 100^2+2(100)(22)+22^2[/tex]
[tex]\\ \sf\longmapsto 10000+4400+484[/tex]
[tex]\\ \sf\longmapsto 14400+484[/tex]
[tex]\\ \sf\longmapsto 14884[/tex]
112²
Using Identity(a + b)² = (a² + 2ab + b²)
Solution⇛122²
⇛(100 + 22)²
⇛(100)² + 2 × 100 × 22 + (22)²
⇛10000 + 4400 + 484
⇛14400 + 484
⇛14884
Solve the following system of equations for x: y = 4 -x^2
X - y =
2
Answer:
B. x=2, x=-3
Step-by-step explanation:
Hello,
We are given this system of equations:
y=4-x²
x-y=2
And we want to solve it for x.
There are a couple ways to solve systems of equations, but let's use substitution in this problem, which we will set one variable equal to an expression containing the other variable, use that expression to solve for the variable the expression contains in the other equation, then use the value of the solved variable to find the value of the other variable.
But in this case, we just need to find x, which is just one of the variables, so there's no need to find the values of y.
In x-y=2, subtract x from both sides.
-y=-x+2
Multiply both sides by -1.
y=x-2
Substitute y as x-2 in y=4-x².
x-2=4-x²
Add x² to both sides.
x²+x-2=4
Subtract 4 from both sides.
x²+x-6=0
Now factor using FOIL.
1 (coefficient in front of x) is the sum of the numbers used in the binomials, while -6 is their product.
Two numbers that add up to 1 but multiply to get -6 are -2 and 3.
So now factor:
(x-2)(x+3)=0
Split and solve:
x-2=0
x=2
x+3=0
x=-3
The solutions for x are x=2 and x=-3, which means the answer is B.
Hope this helps!
Given the formula a=b+c, rewrite the formula to solve for c
9514 1404 393
Answer:
c = a - b
Step-by-step explanation:
Subtract b from both sides of the equation.
a = b + c
a - b = b + c - b . . . . . show the subtraction
a - b = c . . . . . . . . . . simplify
c = a - b . . . . . . write with c on the left
Angles 1 and 2 form a linear pair and the measure of angle two is 22 more than 4 times of the measure of angle 1. What degrees is angle 2
Answer:
m<2= 148.4
Step-by-step explanation:
A linear pair means that both angles add to 180.
m<2 = 4*m<1 +22
Together
m1 + m2 = 180
Put the value for m<2 into the above equation
m<1 + 4*m<1 + 22 = 180 Combine like terms\
5m<1 + 22 = 180 Subtract 22
5m<1 = 180 - 22
5m<1 = 158 Divide by 5
m<1 = 158/5
m<1 = 31.6
m<2 = 4*31.6 + 22
m<2 = 138.4
Charlie's flower bed has a length of 4 feet and a width of four sixths feet. Which of the following is true
1 The area of the flower bed is equal to 6 square feet.
2The area of the flower bed is larger to 6 square feet.
3 The area of the flower bed is equal to 4 square feet
4 The area of the flower bed is smaller than 4 square feet.
Answer:
Option 4) The area of the flower bed is smaller than 4 square feet.
Step-by-step explanation:
Let’s solve for the area of the flower bed.
Consider that the flower bed is a rectangle.
The area of a recrangle is given by the formula:
A = length x width
The area of the flower bed is:
4 ft x 4/6 ft = 2 2/3 ft^2
2 2/3 ft ^2 < 4 ft^2
Therefore option 4 is the correct answer.
If f(4x-15)=8x-27,find f(x)?
Answer:
If we put x=17/4
f(4×17/4-15)=8×17/4-27
f(2x=34-27
f(x)=7.
Hope i helped you.
A man starts repaying a loans with first insfallameny of rs.10 .If he increases the instalment by Rs 5 everything months, what amount will be paid by him in the 30the instalment.
Answer:
30×5=150
so 150+10=160
thus his payment in the 30th installment is
rs.160
(2+1/2) (2^2-1+1/4) find the expression in the form of cubes and differences of two terms.
Answer:
Consider the following identity:
a³ - b³ = (a + b)(a² - ab + b²)Let a = 2, b = 1/2
(2 + 1/2)(2² - 2*1/2 + 1/2²) = 2³ - (1/2)³ =8 - 1/8Use the algebraic identity given below
[tex]\boxed{\sf a^3-b^3=(a+b)(a^2-ab+b^2)}[/tex]
[tex]\\ \sf\longmapsto (2+\dfrac{1}{2})(2^2-1+\dfrac{1}{4})[/tex]
[tex]\\ \sf\longmapsto (2+\dfrac{1}{2})(2^2-2\times \dfrac{1}{2}+\dfrac{1}{2}^2)[/tex]
Here a =2 and b=1/2[tex]\\ \sf\longmapsto 2^3-\dfrac{1}{2}^3[/tex]
[tex]\\ \sf\longmapsto 8-\dfrac{1}{8}[/tex]
Need Help
Please Show Work
Answer:
18 - 8 * n = -6 * n
The number is 9
Step-by-step explanation:
Let n equal the number
Look for key words such as is which means equals
minus is subtract
18 - 8 * n = -6 * n
18 -8n = -6n
Add 8n to each side
18-8n +8n = -6n+8n
18 =2n
Divide each side by 2
18/2 = 2n/2
9 =n
The number is 9
━━━━━━━☆☆━━━━━━━
▹ Answer
n = 9
▹ Step-by-Step Explanation
18 - 8 * n = -6 * n
Simple numerical terms are written last:
-8n + 18 = -6n
Group all variable terms on one side and all constant terms on the other side:
(-8n + 18) + 8n = -6n + 8n
n = 9
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Every high school senior takes the SAT at a school in St. Louis. The high school guidance director at this school collects data on each graduating senior’s GPA and their corresponding SAT test score. The guidance director is conducting a _________ in this experimental design.
A. sample survey
B. census
C. sample poll
D. random sample
The guidance director is conducting a sample poll in this experimental design.
What is sample?Sample is a part of population. It does not comprises whole population. It is representatitive of whole population.
How to fill blank?We are required to fill the blank with appropriate term among the options.
The correct option is sample poll because the guidance director collects data in his school only.
Census collects the whole population of the country.
Sample poll means collecting data from small population.
Random sample means collecting data from a part of popultion without identifying any variable.
Hence we found that he was doing sample poll.
Learn more about sample at https://brainly.com/question/24466382
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What is the value of this expression when x = -6 and y = — 1/2? 4(x^2+3) -2y A. -131 B. -35 C. 57 1/2 D. 157
Answer:
D
Step-by-step explanation:
[tex]4(x^2+3)-2y\\\\=4((-6)^2+3)-2(\frac{-1}{2} )\\\\=4(36+3)+1\\\\=4(39)+1\\\\=156+1\\\\=157[/tex]
The value of the expression 4(x² + 3) - 2y is 157, when x = -6 and y = -1/2.
What is an algebraic expression?An algebraic expression is consists of variables, numbers with various mathematical operations,
The given expression is,
4(x² + 3) - 2y
Substitute x = -6 and y = -1/2 to find the value of expression,
= 4 ((-6)² + 3) - 2(-1/2)
= 4 (36 + 3) + 1
= 4 x 39 + 1
= 156 + 1
= 157
The required value of the expression is 157.
To know more about Algebraic expression on:
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29. Identify the end behavior of the function f(x) = 3x^4 + x^3 − 7x^2 + 12.
options:
A. As x → –∞, y → +∞, and as x → +∞, y → –∞
B. As x → –∞, y → –∞, and as x → +∞, y → –∞
C. As x → –∞, y → +∞, and as x → +∞, y → +∞
D. As x → –∞, y → –∞, and as x → +∞, y → +∞
Answer:
C. As x → –∞, y → +∞, and as x → +∞, y → +∞
Step-by-step explanation:
The leading coefficient of this even-degree function is positive, so y goes to +∞ when the magnitude of x gets large.
_____
When the function is even degree, its value for large magnitude x heads toward the infinity with the same sign as the leading coefficient.
When the function is odd degree, its value for large magnitude x will head toward the infinity with the sign that matches the product of the sign of x and the sign of the leading coefficient.
What is the length of AD
A.17
B.15
C.7
D.1
Answer:
15 units
Step-by-step explanation:
Point D is at 8
Point A is at -7
D - A
8 - -7
8+7
15 units
Answer:
the answer is 15
you can just count the number of steps going forward from -7 to 8.
Integers that are not whole numbers
Answer:
a negative integer
Step-by-step explanation:
n a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of inches and a standard deviation of inches. A study participant is randomly selected. Complete parts (a) through (d) below. (a) Find the probability that a study participant has a height that is less than inches. The probability that the study participant selected at random is less than inches tall is nothing. (Round to four decimal places as needed.) (b) Find the probability that a study participant has a height that is between and inches. The probability that the study participant selected at random is between and inches tall is nothing. (Round to four decimal places as needed.) (c) Find the probability that a study participant has a height that is more than inches. The probability that the study participant selected at random is more than inches tall is nothing. (Round to four decimal places as needed.) (d) Identify any unusual events. Explain your reasoning. Choose the correct answer below.
Answer:
(a) The probability that a study participant has a height that is less than 67 inches is 0.4013.
(b) The probability that a study participant has a height that is between 67 and 71 inches is 0.5586.
(c) The probability that a study participant has a height that is more than 71 inches is 0.0401.
(d) The event in part (c) is an unusual event.
Step-by-step explanation:
The complete question is: In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 67.5 inches and a standard deviation of 2.0 inches. A study participant is randomly selected. Complete parts (a) through (d) below. (a) Find the probability that a study participant has a height that is less than 67 inches. The probability that the study participant selected at random is less than inches tall is nothing. (Round to four decimal places as needed.) (b) Find the probability that a study participant has a height that is between 67 and 71 inches. The probability that the study participant selected at random is between and inches tall is nothing. (Round to four decimal places as needed.) (c) Find the probability that a study participant has a height that is more than 71 inches. The probability that the study participant selected at random is more than inches tall is nothing. (Round to four decimal places as needed.) (d) Identify any unusual events. Explain your reasoning. Choose the correct answer below.
We are given that the heights in the 20-29 age group were normally distributed, with a mean of 67.5 inches and a standard deviation of 2.0 inches.
Let X = the heights of men in the 20-29 age group
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean height = 67.5 inches
[tex]\sigma[/tex] = standard deviation = 2 inches
So, X ~ Normal([tex]\mu=67.5, \sigma^{2}=2^{2}[/tex])
(a) The probability that a study participant has a height that is less than 67 inches is given by = P(X < 67 inches)
P(X < 67 inches) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{67-67.5}{2}[/tex] ) = P(Z < -0.25) = 1 - P(Z [tex]\leq[/tex] 0.25)
= 1 - 0.5987 = 0.4013
The above probability is calculated by looking at the value of x = 0.25 in the z table which has an area of 0.5987.
(b) The probability that a study participant has a height that is between 67 and 71 inches is given by = P(67 inches < X < 71 inches)
P(67 inches < X < 71 inches) = P(X < 71 inches) - P(X [tex]\leq[/tex] 67 inches)
P(X < 71 inches) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{71-67.5}{2}[/tex] ) = P(Z < 1.75) = 0.9599
P(X [tex]\leq[/tex] 67 inches) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{67-67.5}{2}[/tex] ) = P(Z [tex]\leq[/tex] -0.25) = 1 - P(Z < 0.25)
= 1 - 0.5987 = 0.4013
The above probability is calculated by looking at the value of x = 1.75 and x = 0.25 in the z table which has an area of 0.9599 and 0.5987 respectively.
Therefore, P(67 inches < X < 71 inches) = 0.9599 - 0.4013 = 0.5586.
(c) The probability that a study participant has a height that is more than 71 inches is given by = P(X > 71 inches)
P(X > 71 inches) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{71-67.5}{2}[/tex] ) = P(Z > 1.75) = 1 - P(Z [tex]\leq[/tex] 1.75)
= 1 - 0.9599 = 0.0401
The above probability is calculated by looking at the value of x = 1.75 in the z table which has an area of 0.9599.
(d) The event in part (c) is an unusual event because the probability that a study participant has a height that is more than 71 inches is less than 0.05.
consider the functions f(x)=-2x+4 and g(x)=8x-2 calculate the coordinates of the x and y interceptes of f(x)
Answer:
It more complex .Try to take help toggely
In the nation of Gondor, the EPA requires that half the new cars sold will meet a certain particulate emission standard a year later. A sample of 64 one-year-old cars revealed that only 24 met the particulate emission standard. The test statistic to see whether the proportion is below the requirement is
Complete Question
In the nation of Gondor, the EPA requires that half the new cars sold will meet a certain particulate emission standard a year later. A sample of 64 one-year-old cars revealed that only 24 met the particulate emission standard. The test statistic to see whether the proportion is below the requirement is:
A -1.645
B -2.066
C -2.000
D-1.960
Answer:
The correct option is C
Step-by-step explanation:
From the question we are told that
The population mean is [tex]p = 0.50[/tex]
The sample size is [tex]n = 64[/tex]
The number that met the standard is [tex]k = 24[/tex]
Generally the sample proportion is mathematically evaluated as
[tex]\r p = \frac{24}{64}[/tex]
[tex]\r p =0.375[/tex]
Generally the standard error is mathematically evaluated as
[tex]SE = \sqrt{ \frac{p(1- p )}{n} }[/tex]
=> [tex]SE = \sqrt{ \frac{0.5 (1- 0.5 )}{64} }[/tex]
=> [tex]SE = 0.06525[/tex]
The test statistics is evaluated as
[tex]t = \frac{ \r p - p }{SE}[/tex]
[tex]t = \frac{ 0.375 - 0.5 }{0.0625}[/tex]
[tex]t = -2[/tex]
Nine students took the SAT. Their scores are listed below. Later on, they read a book on test preparation and retook the SAT. Their new scores are listed below. Test the claim that the book had no effect on their scores.Use α=0.05. Assume that the distribution is normally distributed. Student 1 2 3 4 5 6 7 8 9 Scores before reading book 72 0 86 0 850 88 0 86 0 710 85 0 1200 95 0 Scores after reading book 74 0 86 0 840 92 0 89 0 720 84 0 1240 97 0 Nine students took the SAT. Their scores are listed below. Later on, they read a book on test preparation and retook the SAT. Their new scores are listed below. Test the claim that the book had no effect on their scores. Use α = 0.05. Assume that the distribution is normally distributed. Student 1 2 3 4 5 6 7 8 9 Scores before reading book 72 0 86 0 850 88 0 86 0 710 85 0 1200 95 0 Scores after reading book 74 0 86 0 840 92 0 89 0 720 84 0 1240 97 0
Answer:
t= 0.4933
t ≥ t ( 0.025 ,8 ) = 2.306
Since the calculated value of t= 0.4933 is less than t ( 0.025 ,8 ) = 2.306 therefore we accept the null hypothesis at 5 % significance level . On the basis of this we conclude that the book had no effect on their scores.
Step-by-step explanation:
We state our null and alternative hypotheses as
H0: ud= 0 Ha: ud≠0
The significance level is set at ∝= 0.05
The test statistic under H0 is
t= d`/ sd/√n
which has t distribution with n-1 degrees of freedom
The critical region is t ≥ t ( 0.025 ,8 ) = 2.306
Computations
Student Scores before Scores after Difference d²
reading book ( after minus before)
1 720 740 20 400
2 860 860 0 0
3 850 840 -10 100
4 880 920 40 1600
5 860 890 30 900
6 710 720 10 100
7 850 840 -10 100
8 1200 1240 40 1600
9 950 970 20 40
∑ 6930 8020 140 4840
d`= ∑d/n= 140/9= 15.566
sd²= 1/8( 4840- 140²/9) = 1/8 (4840 - 2177.778) = 2662.22/8= 332.775
sd= 18.2422
t= 3/ 18.2422/ √9
t= 0.4933
Since the calculated value of t= 0.4933 is less than t ( 0.025 ,8 ) = 2.306 therefore we accept the null hypothesis at 5 % significance level . On the basis of this we conclude that the book had no effect on their scores.
The height of a triangle is 5 yards greater than the base. The area of the triangle is 273 square yards. Find the length of the base and the height of the triangle.
Answer:
Base = 21 while Height = 16
(Algebra) PLZ HELP ASAP!
Answer: Its everthing except irrational
Step-by-step explanation:
find the length of the arc. round your answer to nearest tenth
41.9 mi
Step-by-step explanation:
First, we convert the angle from degree measure to radian measure:
[tex]\theta = 240°×\left(\dfrac{\pi}{180°}\right)= \dfrac{4\pi}{3}\:\text{rad}[/tex]
Using the definition of an arc length [tex]s[/tex]
[tex]s = r\theta[/tex]
[tex]\:\:\:\:=(10\:\text{mi})\left(\dfrac{4\pi}{3}\:\text{rad}\right)[/tex]
[tex]\:\:\:\:= 41.9\:\text{mi}[/tex]
The difference of two numbers is 9. The sum of the two numbers is 15. What are the two numbers?
Let numbers be a and b
a+b=15--(1)a-b=9---(2)Adding both
[tex]\\ \qquad\quad\sf\longmapsto 2a=24[/tex]
[tex]\\ \qquad\quad\sf\longmapsto a=\dfrac{24}{2}[/tex]
[tex]\\ \qquad\quad\sf\longmapsto a=12[/tex]
Put value in eq(2)[tex]\\ \qquad\quad\sf\longmapsto 12-b=9[/tex]
[tex]\\ \qquad\quad\sf\longmapsto b=12-9[/tex]
[tex]\\ \qquad\quad\sf\longmapsto b=3[/tex]
Which expression simplifies to 7W+5?
. – 2w + 3 + 5W – 2
C. -3w + 5(2W + 1)
Cual es la respuesta
Answer:
[tex]\large \boxed{\mathrm{-3w + 5(2w + 1)}}[/tex]
Step-by-step explanation:
-2w + 3 + 5w - 2
Combine like terms.
3w + 1
-3w + 5(2w + 1)
Expand brackets.
-3w + 10w + 5
Combine like terms.
7w + 5
Answer:
The answer is C.
-3w +5(2w +1)
Step-by-step explanation:
Find the Correlation of the following two variables X: 2, 3, 5, 6 Y: 1, 2, 4, 5
Answer:
The correlation of X and Y is 1.006
Step-by-step explanation:
Given
X: 2, 3, 5, 6
Y: 1, 2, 4, 5
n = 4
Required
Determine the correlation of x and y
Start by calculating the mean of x and y
For x
[tex]M_x = \frac{\sum x}{n}[/tex]
[tex]M_x = \frac{2 + 3+5+6}{4}[/tex]
[tex]M_x = \frac{16}{4}[/tex]
[tex]M_x = 4[/tex]
For y
[tex]M_y = \frac{\sum y}{n}[/tex]
[tex]M_y = \frac{1+2+4+5}{4}[/tex]
[tex]M_y = \frac{12}{4}[/tex]
[tex]M_y = 3[/tex]
Next, we determine the standard deviation of both
[tex]S = \sqrt{\frac{\sum (x - Mean)^2}{n - 1}}[/tex]
For x
[tex]S_x = \sqrt{\frac{\sum (x_i - Mx)^2}{n -1}}[/tex]
[tex]S_x = \sqrt{\frac{(2-4)^2 + (3-4)^2 + (5-4)^2 + (6-4)^2}{4 - 1}}[/tex]
[tex]S_x = \sqrt{\frac{-2^2 + (-1^2) + 1^2 + 2^2}{3}}[/tex]
[tex]S_x = \sqrt{\frac{4 + 1 + 1 + 4}{3}}[/tex]
[tex]S_x = \sqrt{\frac{10}{3}}[/tex]
[tex]S_x = \sqrt{3.33}[/tex]
[tex]S_x = 1.82[/tex]
For y
[tex]S_y = \sqrt{\frac{\sum (y_i - My)^2}{n - 1}}[/tex]
[tex]S_y = \sqrt{\frac{(1-3)^2 + (2-3)^2 + (4-3)^2 + (5-3)^2}{4 - 1}}[/tex]
[tex]S_y = \sqrt{\frac{-2^2 + (-1^2) + 1^2 + 2^2}{3}}[/tex]
[tex]S_y = \sqrt{\frac{4 + 1 + 1 + 4}{3}}[/tex]
[tex]S_y = \sqrt{\frac{10}{3}}[/tex]
[tex]S_y = \sqrt{3.33}[/tex]
[tex]S_y = 1.82[/tex]
Find the N pairs as [tex](x-M_x)*(y-M_y)[/tex]
[tex](2 - 4)(1 - 3) = (-2)(-2) = 4[/tex]
[tex](3 - 4)(2 - 3) = (-1)(-1) = 1[/tex]
[tex](5 - 4)(4 - 3) = (1)(1) = 1[/tex]
[tex](6-4)(5-3) = (2)(2) = 4[/tex]
Add up these results;
[tex]N = 4 + 1 + 1 + 4[/tex]
[tex]N = 10[/tex]
Next; Evaluate the following
[tex]\frac{N}{S_x * S_y} * \frac{1}{n-1}[/tex]
[tex]\frac{10}{1.82* 1.82} * \frac{1}{4-1}[/tex]
[tex]\frac{10}{3.3124} * \frac{1}{3}[/tex]
[tex]\frac{10}{9.9372}[/tex]
[tex]1.006[/tex]
Hence, The correlation of X and Y is 1.006
A normal population has a mean of 65 and a standard deviation of 13. You select a random sample of 25. Compute the probability that the sample mean is: (Round your z values to 2 decimal places and final answers to 4 decimal places): Greater than 69.
Answer:
0.0618
Step-by-step explanation:
z = (x - μ)/σ, where
x is the raw score = 69
μ is the sample mean = population mean = 65
σ is the sample standard deviation
This is calculated as:
= Population standard deviation/√n
Where n = number of samples = 25
σ = 13/√25
σ = 13/5 = 2.6
Sample standard deviation = 2.6
z = (69 - 65) / 2.6
z = 4/2.6
z = 1.53846
Approximately to 2 decimal places = 1.54
Using the z score table to determine the probability,
P(x = 69) = P(z = 1.54)
= 0.93822.
The probability that the sample mean is greater than 69 is
P(x>Z) = 1 - 0.93822
P(x>Z) = 0.06178
Approximately to 4 decimal places = 0.0618
Evaluate S_5 for 600 + 300 + 150 + … and select the correct answer below. A. 1,162.5 B. 581.25 C. 37.5 D. 18,600
Answer:
A. 1,162.5
Step-by-step explanation:
Write the next two terms and add them up:
S5 = 600 +300 +150 +75 +37.5 = 1162.5 . . . . matches choice A
================================================
Explanation:
{600, 300, 150, ...} is a geometric sequence starting at a = 600 and has common ratio r = 1/2 = 0.5, this means we cut each term in half to get the next term. We could do this to generate five terms and then add them up. Or we could use the formula below with n = 5
Sn = a*(1-r^n)/(1-r)
S5 = 600*(1-0.5^5)/(1-0.5)
S5 = 1,162.5
-----------
Check:
first five terms = {600, 300, 150, 75, 37.5}
S5 = sum of the first five terms
S5 = 600+300+150+75+37.5
S5 = 1,162.5
Because n = 5 is relatively small, we can quickly confirm the answer. With larger values of n, a spreadsheet is the better option.
La'Vonn rolled a die 100 times. His results are below. What is the relative frequency for La'Vonn rolling a 3?
Answer:
.15
Step-by-step explanation:
find the greatest common factor of 108d^2 and 216d
Answer:
Below
Step-by-step explanation:
If d is a positive number then the greatest common factor is 108d.
To get it isolate d and d^2 from the numbers.
108 divides 216. (216 = 2×108)
Then the greatest common factor of 216 and 108 is 108.
For d^2 and d we will follow the same strategy
d divides d^2 (d^2 = d*d)
Then the greatest common factor of them is d.
So the greatest common factor will be 108d if and only if d is positive. If not then 108 is the answer
Answer:
[tex]\boxed{108d}[/tex]
Step-by-step explanation:
Part 1: Find GCF of variables
The equation gives d ² and d as variables. The GCF rules for variables are:
The variables must have the same base.If one variable is raised to a power and the other is not, the GCF is the variable that does not have a power.If one variable is raised to a power and the other is raised to a power of lesser value, the GCF is the variable with the lesser value power.The GCF for the variables is d.
Part 2: Find GCF of bases (Method #1)
The equation gives 108 and 216 as coefficients. To check for a GCF, use prime factorization trees to find common factors in between the values.
Key: If a number is in bold, it is marked this way because it cannot be divided further AND is a prime number!
Prime Factorization of 108
108 ⇒ 54 & 2
54 ⇒ 27 & 2
27 ⇒ 9 & 3
9 ⇒ 3 & 3
Therefore, the prime factorization of 108 is 2 * 2 * 3 * 3 * 3, or simplified as 2² * 3³.
Prime Factorization of 216
216 ⇒ 108 & 2
108 ⇒ 54 & 2
54 ⇒ 27 & 2
27 ⇒ 9 & 3
9 ⇒ 3 & 3
Therefore, the prime factorization of 216 is 2 * 2 * 2 * 3 * 3 * 3, or simplified as 2³ * 3³.
After completing the prime factorization trees, check for the common factors in between the two values.
The prime factorization of 216 is 2³ * 3³ and the prime factorization of 108 is 2² * 3³. Follow the same rules for GCFs of variables listed above and declare that the common factor is the factor of 108.
Therefore, the greatest common factor (combining both the coefficient and the variable) is [tex]\boxed{108d}[/tex].
Part 3: Find GCF of bases (Method #2)
This is the quicker method of the two. Simply divide the two coefficients and see if the result is 2. If so, the lesser number is immediately the coefficient.
[tex]\frac{216}{108}=2[/tex]
Therefore, the coefficient of the GCF will be 108.
Then, follow the process described for variables to determine that the GCF of the variables is d.
Therefore, the GCF is [tex]\boxed{108d}[/tex].
The equation of a circle centered at the origin with a radius of unit length is x2 + y2 = 1. This equation changes if the center of the circle is not located at the origin or the radius is not of unit length.
Answer:
The equation for a unit radius circle, centered at the origin is:
x^2 + y^2 = 1
Now, if we want to move it horizontally, you can recall to the horizontal translations:
f(x) -----> f(x - a)
Moves the graph to the right by "a" units.
A vertical translation is similar.
Then, if we want a circle centered in the point (a, b) we have:
(x - a)^2 + (y - b)^2 = 1.
Now, if you want to change the radius, we can actually write the unit circle as:
x^2 + y^2 = 1^2
Where if we set x = 0, 1 = y, this is our radius
So if we have:
x^2 + y^2 = R^2
And we set the value of x = 0, then R = y.
So our radius is R.
Then:
"A circle of radius R, centered in the point (a, b) is written as:
(x - a)^2 + (y - b)^2 = R^2
Solve 45 - [4 - 2y - 4(y + 7)] = -4(1 + 3y) - [4 - 3(y + 2) - 2(2y -5)] (make sure to type the number only - rounded to the tenth)
Answer:
Rounded: -5.5
Step-by-step explanation:
Work above :)
Find the equation of a parabola that has a vertex (3,5) and passes through the point (1,13).
Oy= -27 - 3)' +5
Oy=2(x + 3) - 5
Oy=2(0 - 3)' + 5
Oy= -3(2 – 3) + 5
PLEASE HELP ME!!
Answer:
y = 2(x - 3)² + 5
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (3, 5), thus
y = a(x - 3)² + 5
To find a substitute (1, 13) into the equation
13 = a(1 - 3)² + 5 ( subtract 5 from both sides )
8 = 4a ( divide both sides by 4 )
a = 2, then
y = 2(x - 3)² + 5 ← equation of parabola in vertex form