Answer:
[tex]y-\frac{3}{2}=\frac{-13}{3}(x-\frac{1}{2})[/tex] point-slope form
[tex]13x+3y=11[/tex] (standard form)
Let me know if you prefer another form.
Step-by-step explanation:
The slope of a line can be found using [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] provided you are given two points on the line.
We are.
Now you can use that formula. But I really love to just line up the points vertically then subtract them vertically then put 2nd difference over 1st difference.
(4/5 , 1/5)
-( 1/2 , 3/2)
-----------------
3/10 -13/10
2nd/1st = [tex]\frac{\frac{-13}{10}}{\frac{3}{10}}=\frac{-13}{3}[/tex] is our slope.
So the following is point-slope form for a linear equaiton:
[tex]y-y_1=m(x-x_1) \text{ where } m \text{ is slope and } (x_1,y_1) \text{ is a point on the line }[/tex]
Plug in a point [tex](x_1,y_1)=(\frac{1}{2},\frac{3}{2}) \text{ and } m=\frac{-13}{3}[/tex].
This gives:
[tex]y-\frac{3}{2}=\frac{-13}{3}(x-\frac{1}{2})[/tex]
I'm going to distribute:
[tex]y-\frac{3}{2}=\frac{-13}{3}x-\frac{-13}{6}[/tex]
Now I don't like these fractions so I'm going to multiply both sides by the least common multiply of 2,3, and 6 which is 6:
[tex]6y-9=-26x+13[/tex]
Add 26x on both sides:
[tex]26x+6y-9=13[/tex]
Add 9 on both sides:
[tex]26x+6y=22[/tex] This is actually standard form of a line.
It can be simplified though.
Divide both sides by 2:
[tex]13x+3y=11[/tex] (standard form)
Answer:
[tex]\large\boxed{y=-\dfrac{13}{3}x+\dfrac{11}{3}}-\bold{slope\ intercept\ form}\\\boxed{13x+3y=11}-\bold{standard\ form}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have two points
[tex]\left(\dfrac{4}{5},\ \dfrac{1}{5}\right),\ \left(\dfrac{1}{2},\ \dfrac{3}{2}\right)[/tex]
Convert fractions to the decimals
(divide the numerator by the denominator) :
[tex]\dfrac{4}{5}=0.8,\ \dfrac{1}{5}=0.2,\ \dfrac{1}{2}=0.5,\ \dfrac{3}{2}=1.5[/tex]
[tex]\left(\dfrac{4}{5},\ \dfrac{1}{5}\right)=(0.8,\ 0.2)\\\\\left(\dfrac{1}{2},\ \dfrac{3}{2}\right)=(0.5,\ 1.5)[/tex]
Calculate the slope:
[tex]m=\dfrac{1.5-0.2}{0.5-0.8}=\dfrac{1.3}{-0.3}=-\dfrac{13}{3}[/tex]
Put the value of slope and the coordinates of the first point to the equation of a line:
[tex]0.2=-\dfrac{13}{3}(0.8)+b[/tex] multiply both sides by 3
[tex]0.6=(-13)(0.8)+3b[/tex]
[tex]0.6=-10.4+3b[/tex] add 10.4 to both sides
[tex]11=3b[/tex] divide both sides by 3
[tex]\dfrac{11}{3}=b\to b=\dfrac{11}{3}[/tex]
Finally:
[tex]y=-\dfrac{13}{3}x+\dfrac{11}{3}[/tex] - slope-intercept form
Convert to the standard form (Ax + By = C):
[tex]y=-\dfrac{13}{3}x+\dfrac{11}{3}[/tex] multiply both sides by 3
[tex]3y=-13x+11[/tex] add 13x to both sides
[tex]13x+3y=11[/tex] - standard form
Describe an example of an augmented matrix.
Answer:
Step-by-step explanation:
When we join the columns of two or more matrices having the same number of rows it is known as augmented matrix.
Let A= [tex]\left[\begin{array}{ccc}1&6\\0&3\\\end{array}\right][/tex]
B= [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]
Then the augmented matrix is(A|B)
Note that a vertical line is used to separate te columns of A from the columns of B
(A|B) [tex]\left[\begin{array}{ccc}1&6\\0&3\\\end{array}\right | \left\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]
This is a simple example of augmented matrix....
Answer:
An augmented matrix refers to a matrix formed by appending the columns of two matrices.
The perfect example to show this is a linear systems of equations, because there we have a matrix formed by the coeffcients of the variables only, and we have a second matrix formed by the constant terms of the system.
If we have the system
[tex]2x+3y=5\\x-4y=9[/tex]
The two maxtrix involved here are
[tex]\left[\begin{array}{ccc}2&3\\1&-4\end{array}\right] \\\left[\begin{array}{ccc}5\\9\end{array}\right][/tex]
However, to solve the system using matrices, we have to formed an augmented matrix
[tex]\left[\begin{array}{ccc}2&3&5\\1&-4&9\end{array}\right][/tex]
So, as we defined it at the beginning, an augmented matrix is the appending of colums from two matrices to form one.
Use the tables to determine which function will eventually exceed the other, and provide your reasoning.
x f(x)
−1 −5
0 −6
1 −5
2 −2
x g(x)
−1 0.166
0 1
1 6
2 36
f(x) will eventually exceed g(x) because f(x) is an exponential function.
f(x) will eventually exceed g(x) because f(x) has a higher rate of change.
g(x) will eventually exceed f(x) because g(x) is an exponential function.
g(x) will eventually exceed f(x) because g(x) has a higher rate of change.
Answer:
g(x) will eventually exceed f(x) because g(x) is an exponential function.
Step-by-step explanation:
From the first table we can observe the following patterns:
[tex]f( - 1) = {( - 1)}^{2} - 6 = - 5[/tex]
[tex]f(0) = {( 0)}^{2} - 6 = - 6[/tex]
[tex]f( 1) = {( -1)}^{2} - 6 = - 5[/tex]
[tex]f(2) = {( 2)}^{2} - 6 = - 2[/tex]
In general,
[tex]f(x) = {x}^{2} - 6 [/tex]
From the second table we can observe the following pattern:
[tex]g( - 1) = {6}^{ - 1} = \frac{1}{6} [/tex]
[tex]g(0) = {6}^{ 0} = 1[/tex]
[tex]g(1) = {6}^{1} = 6[/tex]
[tex]g(2) = {6}^{2} = 36[/tex]
In general,
[tex]g( x) = {6}^{ x} [/tex]
Conclusion:
Since the f(x) represents a quadratic function and g(x) represents an exponential function, g(x) will eventually overtake f(x).
The correct answer is C.
Answer: C.
Step-by-step explanation:
Go it right on my test
PLEASE HELLPPPPPPPP
Answer:
6
Step-by-step explanation:
f(0) means let x=0
In the table when x=0 f(0) =6
You have$560 in an account which pays 4.8% compounded annually. If you invest your money for 8 years, then how many dollars of interest will you earn by the end of term
Answer:
$ 254.85
Step-by-step explanation:
Total amount invested = $ 560
Interest rate = r = 4.8% = 0.048
Time in years = t = 8 years
The formula for compound interest is:
[tex]A =P(1+\frac{r}{n})^{nt}[/tex]
Here,
A is the total amount accumulated after t years. P is the amount invested initially and n is the compounding periods per year. Since in this case compounding is done annually, n will be 1. Using the values in the above formula, we get:
[tex]A=560(1+\frac{0.048}{1})^{8} = \$ 814.85[/tex]
Thus, the total amount accumulated after 8 years will be $ 814.85
The amount of interest earned will be:
Interest = Amount Accumulated - Principal Amount
Interest = $ 814.85 - $ 560 = $ 254.85
By the end of 8 years, $ 254.85 would be earned in interest.
In triangle ABC, BG = 24 mm. What is the length of segment
GE?
12 mm
24 mm
36 mm
48 mm
Answer:
A. 12 mm
Step-by-step explanation:
May I have brainliest please? :)
Answer: A: 12 mm
Step-by-step explanation:
^^
one positive integer is 7 less than another. The product of two integers is 44. what are the integers?
Answer:
4 and 11
Step-by-step explanation:
Lets call the smallest n
And the other one n+7
Then,
n.(n+7)=44
n²+7n=44
Subtract 44 from both sides.
n²+7n-44=44-44
n²+7n-44=0
Factorize the equation.
n²+11n-4n-44=0
n(n+11)-4(n+11)=0
(n+11)(n-4)=0
n+11=0 , n-4=0
n=-11 , n=4
n=4 is the only positive solution, so the numbers are:
4 and 11....
Answer:
The two integers are: 4 and 11.
Step-by-step explanation:
We are given that one positive integer is 7 less than another. Given that the product of two integers is 44, we are to find the integers.
Assuming [tex]x[/tex] to be one positive integer and [tex]y[/tex] to be the other, we can write it as:
[tex]x=y-7[/tex] --- (1)
[tex]x.y=44[/tex] --- (2)
Substituting x from (1) in (2):
[tex](y-7).y=44[/tex]
[tex]y^2-7y-44=0\\\\y^2-11y+4y-44=0\\\\y(y-11)+4(y-11)[/tex]
y = 11
Substituting y = 11 in (1) to find x:
[tex]x=11-7[/tex]
x = 4
Answer these questions please: You don't need to plot the point just answer B & C. Also every single coordinate plane is like a normal coordinate plane except there are only 5 and 10 labeled.
1) Use the coordinate plane below to answer the questions.
a. Plot a point at the origin. Label the point O.
b. Plot another point that is three units to the right and four units down from the
origin.
c. What are the coordinates of this point?
2)Use the coordinate plane below to answer the questions.
a. Plot a point at (5, 2). Label the point P.
b. Plot another point that is four units to the left and two units down from point P.
c. What are the coordinates of this point?
3)Use the coordinate plane below to answer the questions.
a. Plot a point at (-6, -1). Label the point Q.
b. Plot another point that is eight units to the right and five units up from point Q.
c. What are the coordinates of this point?
4)Use the coordinate plane below to answer the questions.
a. Plot a point in Quadrant II. Label the point R. What are the coordinates of point
R?
b. Plot another point that is two units to the right and six units down from point R.
c. What are the coordinates of this point?
5)Use the coordinate plane below to answer the questions.
a. Plot a point in the Quadrant IV. Label the point S. What are the coordinates of
point S?
b. Plot another point that is seven units to the left and four units up from point S.
c. What are the coordinates of this point?
Step-by-step explanation:
When moving left, subtract from the x-coordinate and when moving right, add in the x-coordinate. When moving down, subtract from the y-coordinate and when moving up, add in the y-coordinate.
1) Given point = (0, 0). 3 units right and 4 units down means (0+3, 0-4) = (3, -4).
2) Given point = (5, 2). 4 units left and 2 units down means (5-4, 2-2) = (1, 0).
3) Given point = (-6, -1). 8 units right and 5 units up means (-6+8, -1+5) = (2, 4).
4) In Quadrant II, the x-coordinate is negative and the y-coordinate is positive. So taking R = (-6,6). 2 units right and 6 units down means (-6+2, 6-6) = (-4, 0).
5) In Quadrant IV, the x-coordinate is positive and the y-coordinate is negative. So taking R = (6,-6). 7 units left and 4 units up means (6-7, -6+4) = (-1, -2).
Is the following number rational or irrational? -3+π
Choose 1 answer:
A)Rational
B)Irrational
Answer:
B, irrational
Step-by-step explanation:
We know that π is irrational, since it can not be written as a division between natural numbers (a sub class of Real numbers called N), it's value is 3,1415(a whole bunch of decimals after this)
If you remove the decimal part of π by subtracting the integer part of it, that is the number 3. the result will still being and irrational number
Since π= 3(the rational part) +0,1415... (the irrational part)
The resut of π-=3= 0,1415...
Answer:
B). Irrational
If you are doing this on khan academy this should work
Step-by-step explanation:
Patrick David's charge account statement shows an unpaid balance of $110. The monthly finance charge is
2% of the unpaid balance. What is the new account balance?
Answer:
Step-by-step explanation:
You take the upaid balance of $110 and multiply it by 2%
which will give you $2.20. Then you add the two together and you get your answer of $112.20.
$110.00 x 2% = $2.20
$110.00
+2.20
$112.20
The new balance on the charge account after applying a 2% finance charge to the unpaid balance of $110 is $112.20.
Explanation:The student is asking about calculating the new balance on a charge account after a monthly finance charge is applied. To find this, we use the original balance and calculate the finance charge based on the given percentage. Since the unpaid balance is $110 and the monthly finance charge is 2%, we compute the finance charge as $110 × 0.02 = $2.20. Adding this to the unpaid balance gives us the new balance: $110 + $2.20 = $112.20.
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The graph shows the solution to a system of inequalities:
Which of the following inequalities is modeled by the graph?
A.
[tex]4x + 3y \leqslant 12;x \geqslant 0[/tex]
B.
[tex]4x + 3y \geqslant 12;x \geqslant 0[/tex]
C.
[tex]4x - 3y \leqslant 12;x \geqslant 0[/tex]
D.
[tex] - 4x - 3y \leqslant 12;x \geqslant 0[/tex]
Answer:
Option A. [tex]4x+3y\leq 12[/tex] and [tex]x\geq 0[/tex]
Step-by-step explanation:
we know that
The solution of the first inequality is the shaded area below the solid line [tex]4x+3y=12[/tex]
The solid line passes through the points (0,4) and (3,0) (the y and x intercepts)
therefore
The first inequality is
[tex]4x+3y\leq 12[/tex]
The solution of the second inequality is the shaded area to the right of the solid line x=0
therefore
The second inequality is
[tex]x\geq 0[/tex]
Instructions:Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). The native bird population in a city is decreasing at a rate of 10% per year due to industrialization of the area by humans. The population of native birds was 14,000 before the decrease began. Complete the recursively-defined function to describe this situation. f(1) = f(n) = f(n - 1) · , for n ≥ 2 After 3 years, birds will remain.
Answer:
The recursive function is;
f(n)=f(n-1)×0.9 for n≥2
After 3 years, 11340 birds will remain.
Step-by-step explanation:
First the native population was 14,000 before decreasing started, hence this is your f(1)
f(1)=14000
⇒A decrease of 10% is similar to multiplying the native value of birds with 90%
New number of birds = native value × 90% ⇒f(1)×0.9
For second year , you multiply the value you get after the first decrease by 0.9 to get the new number of birds;
f(2)=f(1)×0.9= 0.9f(1)=0.9×14000=12600
For the 3rd year, the value of the second year,f(2) is then reduced by 10%. This is similar to multiplying value of f(1) by 90%
f(3)=f(2)×0.9=12600×0.9=11340
Apply the same for the 4th year and above, hence for nth year;
f(n)=f(n-1)×0.9 for n≥2
4. A student is chosen at random from the student body at a given high school. The probability that the
student selects Math as the favorite subject is 1/4. The probability that the student chosen is a junior is
116/459. If the probability that the student selected is a junior or that the student chooses Math as the
favorite subject is 47/108, what is the exact probability that the student selected is a junior whose
favorite subject is Math?
Answer:
The exact probability that the student selected is a junior whose favorite subject is Math is [tex]\frac{124}{459}[/tex].
Step-by-step explanation:
Let the following events represents by the alphabets A and B.
A: Student selects Math as the favorite subject
B: Student chosen is a junior
The probability that the student selects Math as the favorite subject is 1/4.
[tex]P(A)=\frac{1}{4}[/tex]
The probability that the student chosen is a junior is
[tex]P(B)=\frac{116}{459}[/tex]
The probability that the student selected is a junior or that the student chooses Math as the favorite subject is 47/108.
[tex]P(A\cup B)=\frac{47}{108}[/tex]
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]
[tex]\frac{47}{108}=\frac{1}{4}+\frac{116}{459}-P(A\cap B)[/tex]
[tex]P(A\cap B)=\frac{1}{4}+\frac{116}{459}-\frac{47}{108}=\frac{31}{459}[/tex]
The exact probability that the student selected is a junior whose favorite subject is Math is
[tex]P(\frac{B}{A})=\frac{P(A\cap B)}{P(A)}[/tex]
[tex]P(\frac{B}{A})=\frac{\frac{31}{459}}{\frac{1}{4}}=\frac{124}{459}[/tex]
Therefore the exact probability that the student selected is a junior whose favorite subject is Math is [tex]\frac{124}{459}[/tex].
The exact probability that the student selected is a junior whose favourite subject is maths is 124/459
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
The probability that the student selects Maths the favourite subject:
P(A) = 1/4
The probability that the student chosen is a junior:
P(B) = 116/459
The probability that the student selected is a junior or that the student chooses maths the favourite subject:
P(A∪B) = 47/108
We know:
P(A∩B) = P(A) + P(B) _P(A∪B)
P(A∩B) = 1/4 + 116/459 - 47/108
P(A∩B) = 31/459
The exact probability that the student selected is a junior whose favourite subject is maths:
P(B|A) = P(A∩B) /P(A)
= (31/459)/(1/4)
= 124/459
Thus, the exact probability that the student selected is a junior whose favourite subject is maths is 124/459
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The celsius and Fahrenheit scales are related by the equation C=5/9(f-32). What temperature fahrenheit would give a temperature of 5C?
Answer:
41F
Step-by-step explanation:
41-32=9
9*5/9=5
Answer:
41 degrees F.
Step-by-step explanation:
C = 5/9(f - 32)
5 = 5/9 (f - 32) Multiply both sides by 9/5:
5 * 9/5 = f - 32
9 = f - 32
f = 9 + 32
= 41.
P is a prime number and q is a positive integers such that p + q = 1696 IF P and Q are co primes and their Lcm is 21879 Then find p and q
Answer:
P = 1 3
Q = 1 6 8 3
Step-by-step explanation:
through factorization of 21879
The perimeter of a rectangle can be found using the equation P = 2L + 2W, where P is the perimeter, L is the length, and W is the width of the rectangle. Can the perimeter of the rectangle be 60 units when its width is 12 units and its length is 18 units?
A)No. If the rectangle has L = 18 and W = 12, P would not equal 60.
B) No. The rectangle cannot have P = 60 and L = 18 because L + W is less than 24.
C) Yes. The rectangle can have P = 60 and L = 18 because 60 = 24 + 18.
D)Yes. The rectangle can have P = 60 and L = 18 because P = 2(18) + 2(12) would equal 60.
Answer:
D)Yes. The rectangle can have P = 60 and L = 18 because P = 2(18) + 2(12) would equal 60
Step-by-step explanation:
The formula for the perimeter of a rectangle is [tex]P=2L+2W[/tex].
If the width is [tex]W=12\:units[/tex] and the length is [tex]L=18\:units[/tex], then the perimeter becomes:
[tex]P=2\times 12+2\times 18[/tex].
[tex]\implies P=24+36[/tex].
[tex]\implies P=60[/tex].
Therefore the answer is
D)Yes. The rectangle can have P = 60 and L = 18 because P = 2(18) + 2(12) would equal 60
Answer:
D)Yes. The rectangle can have P = 60 and L = 18 because P = 2(18) + 2(12) would equal 60
Step-by-step explanation:
The formula for the perimeter of a rectangle is .
If the width is and the length is , then the perimeter becomes:
.
.
.
Therefore the answer is
D)Yes. The rectangle can have P = 60 and L = 18 because P = 2(18) + 2(12) would equal 60
The constraints of a problem are graphed below. What are
vertices of the feasible region?
Answer:
(0,0),(0,15),(20,25),(40,0)
Step-by-step explanation:
we know that
The feasible region is a quadrilateral
Let
A,B,C and D the vertices of the feasible region
see the attached figure
Observing the graph we have that
The coordinates of point A are (0,0)
The coordinates of point B are (0,15)
The coordinates of point C are (20,25)
The coordinates of point D are (40,0)
therefore
The answer is
(0,0),(0,15),(20,25),(40,0)
Answer:
A
Step-by-step explanation:
(0,0),(0,15),(20,25),(40,0)
four less than the quotient of a number cubed and seven, increased by three
Answer:
(a^3/7) - 4 + 3
Step-by-step explanation:
We need to translate the words into equations:
The quotient of a number cubed and seven: (a^3/7)
four less than the quotient of a number cubed and seven: (a^3/7) - 4
four less than the quotient of a number cubed and seven, increased by three:
(a^3/7) - 4 + 3
in triange ABC, AB=5 and AC=14. Find The measure of angle c to the nearest degree
Answer:
The answer is ∠C= 20 degree
Step-by-step explanation:
The answer is ∠C= 20 degree
We have given:
AB= 5
AC = 14
and we have to find ∠c to the nearest degree.
So,
We know that:
tan(C)= AB/AC
tan(C)= 5/14
tan(C)= 0.3571
C=20 degree
Thus the answer is ∠C = 20 degree ....
If the Zeros of a quadratic equation are seven and -4 what would be the x intercepts
Answer:
7, -4
Step-by-step explanation:
The zeros are just another name for the x intercepts
7, -4
Help me with this please
Answer:
see explanation
Step-by-step explanation:
Given
4(px + 1) = 64 ( divide both sides by 4 )
px + 1 = 16 ( subtract 1 from both sides )
px = 15 ( divide both sides by p )
x = [tex]\frac{15}{p}[/tex]
When p = - 5, then
x = [tex]\frac{15}{-5}[/tex] = - 3
If a = m 2 + 2, what is the value of a when m = -3? -7 -4 8 11
Given
a = m(2) + 2value of a when m = -3Substitute m with -3
a = -3*2 + 2
a = -6 + 2
a = -4
Answer
The value of a when m = -3 is -4
Answer:
=11
Step-by-step explanation:
The equation given is a=m²+2
To find a when m= -3 , we substitute for m in the equation.
a=(-3)²+2
=9+2
=11
Therefore a=11 when m is -3
Solve equation -4a/5-8=2
Answer:
a = 3/2
Step-by-step explanation:
Multiply both sides by -3
Simplify
Divide both sides by -4
Take a look at the photo:
Jake has just become the senior marketing rep for a new chain of upscale hotels. His first responsibility is to develop a
plan, commonly referred to as the
Answer:
placement plan
Step-by-step explanation:
<3
As the senior marketing rep, Jake needs to develop a marketing plan. This plan would outline the business's advertising and marketing efforts for the year, including goals, strategies, tactics, a market analysis, and a budget.
Explanation:Jake, as the senior marketing rep for a new chain of upscale hotels, is tasked with creating a marketing plan. A marketing plan is a comprehensive document or blueprint that outlines a company's advertising and marketing efforts for the coming year.
It would detail the business's marketing goals, the strategies and tactics to achieve those goals, an analysis of the current market situation, and a budget for the marketing activities. For an upscale hotel chain, it might include strategies such as premium pricing, high-quality service, and targeted advertising.
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when numbers are divided, you (add / subtract) exponents and (multiply / divide) the bases.
(Scientific Notation)
Answer:
you subtract the exponents and divide the bases
Wuts the slope formula
Answer:
The Slope Formula ( x1, y1 ) And ( x2, y2 )
Consider the polynomial p(x)=x^3-9x^2+18x-25, which can be rewritten as p(x)=(x-7)(x^2-2x+4)+3 . The number _[blank 1]_ is the remainder whenp(x) is divided by x-7, and so _[blank 2]_ a factor of p(x)
What is blank 1 and 2?
options:
a)7
b)is
c)is not
d)0
e)3
Answer:
Blank 1: 3 is the remainder
Blank 2: not a factor
Step-by-step explanation:
If p(x)=(x-7)(x^2-2x+4)+3, then dividing both sides by (x-7) gives:
[tex]\frac{p(x)}{x-7}=(x^2-2x+4)+\frac{3}{x-7}[/tex].
The quotient is [tex](x^2-2x+4)[/tex].
The remainder is [tex]3[/tex].
The divisor is [tex](x-7)[/tex].
The dividend is [tex]p(x)=x^3-9x^2+18x-25[/tex].
It is just like with regular numbers.
[tex]\frac{11}{3}[/tex] as a whole number is [tex]3\frac{2}{3}[/tex].
[tex]3\frac{2}{3}=3+\frac{2}{3}[/tex] where 3 is the quotient and 2 is the remainder when 11 is divided by 3.
Here is the division just for reminding purposes:
3 <--quotient
----
divisor-> 3 | 11 <--dividend
-9
---
2 <---remainder
Anyways just for fun, I would like to verify the given equation of
p(x)=(x-7)(x^2-2x+4)+3.
I would like to do by dividing myself.
I could use long division, but I have a choice to use synthetic division since we are dividing by a linear factor.
Since we are dividing by x-7, 7 goes on the outside:
x^3-9x^2+18x -25
7 | 1 -9 18 -25
| 7 -14 28
-------------------------------
1 -2 4 3
We have confirmed what they wrote is totally correct.
The quotient is [tex]x^2-2x+4[/tex] while the remainder is 3.
If p/(x-7) gave a remainder of 0 then we would have said (x-7) was a factor of p.
It didn't so it isn't.
Just like with regular numbers. Is 3 a factor of 6? Yes, because the remainder of dividing 6 by 3 is 0.
Use the elimination method to solve the system of equations. Choose the
correct ordered pair,
2y = x + 2
x - 3y = -5
Answer:
x = 4, y = 3 → (4, 3)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}2y=x+2&\text{subtract x from both sides}\\x-3y=-5\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-x+2y=2\\x-3y=-5\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-y=-3\qquad\text{change the signs}\\.\qquad\boxed{y=3}\\\\\text{put the value of y to the second equation:}\\\\x-3(3)=-5\\x-9=-5\qquad\text{add 9 to both sides}\\\boxed{x=4}[/tex]
Find the tenth term of the
geometric sequence, given the
first term and common ratio.
a =4 and r=1/2
Answer:
[tex]\frac{1}{128}[/tex]
Step-by-step explanation:
The n th term of a geometric sequence is
[tex]a_{n}[/tex] = a [tex](r)^{n-1}[/tex]
where a is the first term and r the common ratio, hence
[tex]a_{10}[/tex] = 4 × [tex](\frac{1}{2}) ^{9}[/tex] = 4 × [tex]\frac{1}{512}[/tex] = [tex]\frac{1}{128}[/tex]
Final answer:
The tenth term of the geometric sequence with the first term 4 and the common ratio of 1/2 is calculated using the formula for the nth term. Substituting the given values into the formula and simplifying yields the tenth term as 1/128.
Explanation:
To find the tenth term of a geometric sequence, we use the formula for the nth term in a geometric sequence which is an = a1 x r(n-1), where a1 is the first term, r is the common ratio, and n is the term number.
In this case, the first term a1 is given as 4 and the common ratio r is 1/2. To find the tenth term, we substitute n with 10 in the formula:
a10 = 4 x (1/2)(10-1)
This simplifies to:
a10 = 4 x (1/2)9 = 4 x 1/512 = 4/512 = 1/128
Therefore, the tenth term of the geometric sequence is 1/128.
Find the distance between the points (-3, 2) and (4, -5)
Answer:
[tex]\large\boxed{7\sqrt2}[/tex]
Step-by-step explanation:
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have the points (-3, 2) and (4, -5). Substitute:
[tex]d=\sqrt{(4-(-3))^2+(-5-2)^2}=\sqrt{7^2+(-7)^2}=\sqrt{49+49}=\sqrt{(49)(2)}\\\\\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt{49}\cdot\sqrt2=7\sqrt2[/tex]
What is the 20th digit after the decimal point of the sum of the decimal equivalents for the fractions 1/7 and 1/3?