Answer:
2b³ +2a -2c . . . . degree 3 polynomial
Step-by-step explanation:
The monomials are ...
... 4a . . . . degree 1 in a
... -5b·b² = -5b³ . . . . degree 3 in b
... -3c . . . . degree 1 in c
... 7b³ . . . . degee 3 in b (like term with -5b³)
... +c . . . . degree 1 in c (like term with -3c)
... -2a . . . . degree 1 in a (like term with 4a)
So, we have 3 pairs of like terms. The like terms can be combined by summing their coefficients.
The degree of the polynomial is that of the highest-degree term. (Here, the b³ term makes it a polynomial of degree 3.)
... 4a -2a = (4-2)a = 2a . . . . combining the "a" terms
... -5b³ +7b³ = (-5+7)b³ = 2b³ . . . . combining the b³ terms
... -3c +c = (-3 +1)c = -2c . . . . combining the "c" terms
In standard form, we write the highest-degree term first. Follwing terms are in order by decreasing degree. It is convenient, but perhaps not required, to then write the terms of the same degree in alphabetical order.
... = 2b³ +2a -2c . . . . a 3rd degree polynomial
Which absolute value function, when graphed, represents the parent function, f(x) = |x|, reflected over the x-axis an Which absolute value function, when graphed, represents the parent function, f(x) = |x|, reflected over the x-axis and translated 1 unit to the right?d translated 1 unit to the right?
The absolute value function that represents the parent function f(x) = |x| reflected over the x-axis and translated 1 unit to the right is g(x) = -|x-1|.
The absolute value function that represents the parent function f(x) = |x|, reflected over the x-axis and translated 1 unit to the right is g(x) = -|x-1|.
Reflecting over the x-axis involves multiplying the function by -1 to get -|x|. Translating 1 unit to the right involves substituting (x-1) for x within the absolute value to get -|x-1|.
Therefore, the transformation involves two steps:
Reflection over the x-axis: Multiply the parent function f(x) by -1 to get -f(x).Translation to the right: Replace x with (x-1) to shift the graph 1 unit to the right.Evaluate 3x – 2 if x = 6.
16
20
18
6
Answer:
16
Step-by-step explanation:
We need to evaluate the expression 3x-2
Plugging in x=6, we get
3(6)-2
=18-2
=16
Answer:
16
Step-by-step explanation:
3x – 2 if x = 6
To solve this we substitute the x with 6.
3x – 2 = 3(6) - 2
= (3×6) - 2
= 18 - 2
= 16
i will give the brainlesit
Answer:
option 4
Step-by-step explanation:
tan30° = 17/x
=>1/√3 = 17/x
=>x = 17√3
for y,
sin30° = 17/y
=>1/2 = 17/y
=>y = 34
For this case we must find the value of y (Hypotenuse) and the value of x (leg adjacent to the 30 degree angle) of the triangle shown.
By definition:
[tex]Tangent (30) = \frac {17} {x}\\x = \frac {17} {Tangent (30)}\\x = \frac {17} {\frac {\sqrt {3}} {3}}\\x = \frac {17 * 3} {\sqrt {3}}\\x = \frac {51 \sqrt {3}} {3}\\x = 17 \sqrt {3}[/tex]
Now, we look for the value of y:
[tex]Sine (30) = \frac {17} {y}\\y = \frac {17} {sine (30)}\\y = \frac {17} {\frac {1} {2}}\\y = 34[/tex]
Answer:
[tex]x = 17 \sqrt {3}\\y = 34[/tex]
Option D
This is converting to polar form, I need help and the answer too.
Answer:
2 cis (7/6 pi)
Step-by-step explanation:
r = sqrt( a^2 + b^2)
r = sqrt (-sqrt(3) )^2 + (-1)^2)
= sqrt(3 +1)
= sqrt(4)
= 2
theta = arctan (b/a)
theta = arctan (-1/-sqrt(3))
theta = 30
but this is in the third quardrant -a and -b
so add 180
theta = 210 degrees
convert this to radians
210 * pi/180 = 210/180 * pi = 21/18 * pi = 7/6 * pi
r cis (theta)
2 cis (7/6 pi)
An art teacher has a total of 7/8 pound of clay. the teacher puts 1/16 pound of clay at each work station. The teacher sets up an equal number of work stations in each of 2 classrooms. How many work stations does the teacher set up in each of the classrooms?
There are 7 work stations.
This is because:
7/8 divided by 1/6 divided by 2 =
7/8 times 16/1 times 1/2 = 7
Hope this helps :)
Workstations the teacher set up in each of the classrooms is is mathematically given as,
⇒ x = 7
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 have to given that;
An art teacher has a total of 7/8 pound of clay.
And, The teacher puts 1/16 pound of clay at each workstation.
Since, The teacher sets up an equal number of workstations in each of 2 classrooms
Generally the equation for the workstations is mathematically given as,
1/16(x) = 7/8
x = 16 × 7/(8×2)
x = 7
Therefore, The workstations the teacher set up in each of the classrooms is, ⇒ x = 7
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PLEASE HELP NEED ASAP!!!
(a) To make use of the forms of the equation for a line this problem requires, we must first calculate the slope (m) of the line between the two given points. That is computed by ...
... m = (change in y)/(change in x)
... m = (8 -3)/(2 -0) = 5/2
The second given point tells us the y-intercept (b) is 3, so the equation for the line is ...
... y = mx + b
... y = 5/2x + 3
(b) As in part (a), we must calculate the slope of the line. That is ...
... m = (change in y)/(change in x)
... m = (4 -3)/(1 -3) = 1/(-2) = -1/2
Using the first point (h, k) in the point-slope form of the equation of a line, we have ...
... y -k = m(x -h)
... y -4 = -1/2(x -1) . . . . . point-slope equation
Simplifying this, we get
... y = -1/2x +1/2 +4
... y = -1/2x +9/2 . . . . . slope-intercept equation
(c) The slopes of the two equations are different, so they must intersect at exactly one point. The equations are consistent.
(d) We can substitute the "y" from one equation into the other to give ...
... 5/2x +3 = -1/2x +9/2
... 3x = 3/2 . . . . . . . add 1/2x -6/2
... x = 1/2 . . . . . . . . divide by 3
Using the first equation to find y:
... y = (5/2)·(1/2) +3 = 5/4 +12/4
... y = 17/4
The point of intersection is (x, y) = (1/2, 17/4).
Question is in the picture, I dont get it.
Answer:
a = 0, b = 1/2
Step-by-step explanation:
Multiplication and division of complex numbers in polar form is pretty simple.
... a·Cis(α) × b·Cis(β) = ab·Cis(α+β) . . . . . multiply magnitudes; add angles
... a·Cis(α) / (b·Cis(β)) = (a/b)·Cis(α-β) . . . divide magnitudes, subtract angles
In your case, you have ...
... 2·Cis(120°) / (4·Cis(30°)) = (2/4)·Cis(120° -30°) = (1/2)·Cis(90°)
Of course, Cis(90°) = cos(90°) +i·sin(90°) = 0 +i.
... (1/2)·Cis(90°) = 1/2·(0 +i) = 0 + 0.5i
_____
Comment on the use of a calculator
It helps to be aware of how your calculator handles complex numbers. This one can express complex numbers in exponential format, equivalent to a polar form, but requiring specific notation. In this case, the variable D has been assigned the value π/180 so multiplying by it converts degrees to radians. The result of the division is (1/2)i, not 1/(2i).
A cylindrical coffee can has a height of 14 centimeters. The radius of the base is 5 centimeters. What is the area of its label?
The area of the label for a cylindrical coffee can with a height of 14 cm and a radius of 5 cm is approximately 440 square centimeters.
Explanation:The subject in this case is Mathematics, and the question pertains to the use of geometry to determine the area of a label on a cylindrical coffee can. Specifically, the question asks to calculate the area of the cylindrical surface (lateral surface), which will be used as the label area. To calculate this, one needs to use the formula for the lateral surface area of a cylinder, which is 2πrh, where r is the radius and h is the height of the cylinder.
Given a cylinder with a height of 14 centimeters and a radius of 5 centimeters, the area of the label can be calculated as follows:
Area = 2π(5 cm)(14 cm) = 2π×5 cm×14 cm = 2×3.1416×5 cm×14 cm ≈ 440 cm².
15. convert the following values into scientific notation, a) 42,670,000 B) 0.0000008
Answer:
8x10^-7
Step-by-step explanation:
First one you have correct however the second one you were close lets figure it out:
0.0000008
In order to move the decimal in front of the eight we have to "jump" 7 times to the right. Furthermore since we have to move the decimal to the right our exponent will be negative. That means that we have:
[tex]0.0000008=8 \times 10^{-7}[/tex]
~~~Brainliest Appreciated~~~
To express in scientific notation, move the decimal so it is after the first non-zero digit, and count the number of steps as the power of 10. 42,670,000 becomes 4.267 * 10^7 and 0.0000008 becomes 8 * 10^-7.
Explanation:To convert a value to scientific notation, you need to express it as a product of a number between 1 and 10 and a power of 10.
For the value 42,670,000 we rewrite it as 4.267 * 10^7 which means first you move the decimal to the left until it is after the first digit and then count how many places you moved it to determine the power of 10. For the value 0.0000008, it's a similar process, but slightly different because it is less than one. We get 8 * 10^-7, the power of 10 is negative to reflect that we moved the decimal to the right.Learn more about Scientific Notation here:
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Standard FIF.2 DOK: 18. An outfielder throws a ball vertically upward with a velocity of 30 meters per second. Its distance from the ground after t seconds is approximately equal to 30t -5t2 meters. How many seconds will it take the ball to reach its maximum distance from the ground?
Answer:
t = 3
Step-by-step explanation:
y = - 5t^2 + 30t Take out - 5 as a common factory = -5(t^2 - 6t) Complete the squarey = -5(t^2 - 6t + (6/2)^2) Add (6/2)^2 outside the brackets. Why add?y = -5(t^2 - 6t + 9) + 9 Express the bracketed part as a perfect squarey = -5(t - 3)^2 + 9 The highest point reached will be nineThat occurs when -5(t -3)^2 = 0That happens when t = 3The ball thrown vertically upward reaches its maximum height after 3 seconds, as calculated by setting the derivative of the position function, which represents the velocity, to zero.
The question is about determining how many seconds it will take for a ball thrown vertically upward to reach its maximum height. The ball's position as a function of time is given by 30t - 5t2 meters. To find when the ball reaches its maximum height, we need to find the time at which the velocity is zero. The velocity function is the derivative of the position function, which is 30 - 10t. Setting the velocity equal to zero gives us the time when the ball reaches its maximum height:
0 = 30 - 10t
t = 3 seconds
The ball will reach its maximum distance from the ground after 3 seconds.
Jana paid a $75 initial fee to join a sports club and a monthly fee of $14 per month. Write an expression that shows how much Jana spends after x months of membership at the sports club.
Answer:
y=14x+75 where y is equal to 14x+75. Hope this helps.
Step-by-step explanation:
Answer:
y=14x+75
Step-by-step explanation:
y=mx+b is the slope intercept form which you will use for equations like these.
the M represents what it recurring, and in this case it is 14 dollars per month
The b represents your initial value and in this case it is 75 dollars
The 14x represents that it is 14 per, and the 75 represents the initial cost.
Which statement is true about the product square root of 2 (5 + square root of 8 )?
It is rational and equal to 7.
It is rational and equal to 9.
It is irrational and equal to 4 + square root of 10.
It is irrational and equal to 4 + 5 square root of 2.
Answer:
It is irrational and equal to 4 + 5 square root of 2.
Step-by-step explanation:
[tex]\sqrt{2}(5+\sqrt{8})=5\sqrt{2}+\sqrt{2\cdot 8}=5\sqrt{2}+\sqrt{16}\\\\=4+5\sqrt{2}[/tex]
The square root of 2 in the result makes the result irrational.
Answer:
It is irrational since the square root sign in the answer is present.
Step-by-step explanation:
We are given with two factors: square root of 2 and 5 + square root of 8. We use a scientific calculator that displays irrational answers. The product of the two factors is 4 + 5 square root of 2. The answer is irrational since the square root sign in the answer is present.
Which graph can be used to find the solution for the equation 4x + 2 = x + 3?
Answer:
option C
Step-by-step explanation:
to find the solution for the equation 4x + 2 = x + 3, graph the equations
y= 4x+2 and y=x+3
Lets make a table for each equation
x y= 4x+2
-1 4(-1) + 2= -4+2 = -2
0 4(0) + 2= 2
1 4(1) + 2= 6
plot all the points on graph
Lets make table for second equation
x y= x+3
-1 -1+3 = 2
0 0+3 = 3
1 1+3 = 4
Plot the point on the graph and make a line
option C is correct
Answer:
The required graph of the equation is shown below:
Step-by-step explanation:
Consider the provided equation.
[tex]4x + 2 = x + 3[/tex]
Solve the equation for x.
[tex]4x-x=3-2[/tex]
[tex]3x=1[/tex]
[tex]x=\frac{1}{3}[/tex]
Now substitute x=1/3 in [tex]y=4x + 2[/tex]
[tex]y=\frac{4}{3} + 2=\frac{10}{3}[/tex]
So, the graph will be the lines which intersect at (1/3,10/3)
The correct graph is 3rd one.
Alternate method:
The equation [tex]4x + 2 = x + 3[/tex] can be written as:
[tex]y= 4x + 2 \\y= x + 3[/tex]
Draw the graph for both equation.
For [tex]y= 4x + 2[/tex]
Substitute x=0 in above equation,
[tex]y= 4(0) + 2[/tex]
[tex]y=2[/tex]
Substitute y=0 in above equation,
[tex]0= 4x + 2[/tex]
[tex]-2=4x[/tex]
[tex]x=\frac{-1}{2}[/tex]
Now use the coordinate (0,2) and (-1/2,0) to draw the graph of straight line.
For [tex]y=x + 3[/tex]
Substitute x=0 in above equation,
[tex]y=3[/tex]
Substitute y=0 in above equation,
[tex]0=x + 3[/tex]
[tex]x=-3[/tex]
Now use the coordinate (0,3) and (-3,0) to draw the graph of straight line.
Hence, the required graph of the equation is shown below:
find the mean of the following numbers.
-2, 9, -10, 3, 5, 1
A. -6
B. -1
C. 1
D. 6
Answer:
C - 1
Step-by-step explanation:
The mean is the sum total of all the given value within the data set divided by the number of values in the data set. By counting, you can find that we have 6 values in our data set.
First thing you need to do is add all the numbers given together in order to get the sum of the values in the given data set. Follow these steps presented below:
-2 + 9 - 10 + 3 + 5 + 1
7 - 10 + 3 + 5 + 1
- 3 + 3 + 5 + 1
0 + 5 + 1
5 + 1
6
Now, in order to find the mean, take the sum (6) and divide by the amount of numbers there are; 6.
6/6 = 1
Therefore, the mean is 1.
Hope this helps!
What is m<PTX
someone please help me
Answer:
60°
Step-by-step explanation:
The triangle PTX is equilateral, so all of its angles are 60°.
___
Adding up the lengths that make PX, you find they're the same as the lengths that make PT. The sides of ΔPQU are all the same length, so all the triangles are similar and equilateral.
rusty burns 6 calories per minute swimming and 10 calories per minute jogging. In the morning Rusty burns 175 calories walking and swims for x minutes. In the afternoon Rusty will jog for x minutes. How many minutes must he jog to burn at least as many calories y in the afternoon as he did in the morning
Answer:
at least 43 1/4 minutes (or 44 rounded)
Step-by-step explanation:
I set up an equation:
175+6x=10x
Isolate x:
175=4x
x=43.25
is this a college question? (just curious)
What is the exact value of x?
5*21^5x = 16
[tex]\bf \textit{Logarithm of exponentials} \\\\ log_a\left( x^b \right)\implies b\cdot log_a(x) \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf 5\cdot 21^{5x}=16\implies 21^{5x}=\cfrac{16}{5}\implies \stackrel{\textit{taking \underline{log } to both sides}}{\log\left( 21^{5x} \right)=\log\left( \cfrac{16}{5} \right)} \\\\\\ 5x\log(21)=\log\left( \cfrac{16}{5} \right)\implies 5x=\cfrac{~~\log\left( \frac{16}{5}\right)~~}{\log(21)}\implies x=\cfrac{~~\log\left( \frac{16}{5}\right)~~}{5\log(21)} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill x\approx 0.0764094095937~\hfill[/tex]
Answer:
X=log 3.2/5 log 21
Step-by-step explanation:
X=0.0764094
Solve the equation. PPLLLLLLLLZZZZZZZZ HELP!!!!!!!!!!!!!!!!!!!!!
-7/3n = - 42
A. n = 92
B. n = 294
C. n = -21 4/7
D. n = 18
Answer:
The correct answer is 1 / 18.
Step-by-step explanation:
We are given the following equation for which we need to solve for the variable n:
[tex]-\frac{7}{3n} =-42[/tex]
So for solving this, we will rearrange the equation in a manner that isolates the variable n, making it the subject of the equation.
[tex]-\frac{7}{3n} =-42[/tex]
[tex]-\frac{7}{42} =3n[/tex]
[tex]\frac{1}{6} =3n[/tex]
[tex]n=\frac{1}{6*3} \\\\n=\frac{1}{18}[/tex]
Therefore, the value of n is equal to 1 / 18.
Receive 99 points if answered correctly with steps!
Point E is the midpoint of side BC of parallelogram ABCD (labeled counterclockwise) and AE ∩ BD =F. Find the area of ABCD if the area of △BEF is 3 cm2.
Answer:
36 cm²
Step-by-step explanation:
1. ΔBEF & ΔADF are similar; 2. the height of ΔABE is 3height of ΔBEF; 3. area of ΔABE is 3 area of ΔBEF; 4. area of ΔABE= area of ΔACE; 5. area of ΔABC = 2 area of ΔACE; 6. Area of ABCD = 2 area of ΔABC = 12 area of BEF.
36 cm²
Step-by-step explanation:
1. ΔBEF & ΔADF are similar; 2. the height of ΔABE is 3height of ΔBEF; 3. area of ΔABE is 3 area of ΔBEF; 4. area of ΔABE= area of ΔACE; 5. area of ΔABC = 2 area of ΔACE; 6. Area of ABCD = 2 area of ΔABC = 12 area of BEF.
NEED HELP PLEASE!
Consider the function represented by the equation 16b = 4r - 12. write the equation in function notation, where b is the independent variable. Must show work for full credit
Answer:
r(b) = 4b +3
Step-by-step explanation:
There are only two variables and the one that is not b is r. So, this amounts to solving for r. Divide the given equation by the coefficient of r:
... 4b = r -3
Add the constant:
... 4b +3 = r
Express in function notation.
... r(b) = 4b +3
A square is cut in half on the diagonal creating two equal triangles each triangle has an area of 0.72 square units what is the side length in units of the original square?
The side length of the original square is calculated by associating the area of the triangle with the square's side length. It is determined to be 1.2 units.
Explanation:To find the side length of the original square, we need to first understand how the area of a triangle is related to the square. When a square is cut on the diagonal, it forms two triangles. The area of a triangle is given by the formula 1/2 * base * height. In the case of these triangles, the base and height are the same, and equal to the side length of the square, which we'll call 'a'.
The area of one triangle is given as 0.72 square units. So, 0.72 = 1/2 * a * a. Simplifying this, we get a² = 2*0.72 = 1.44. Taking the square root of both sides, we find that a = √1.44 or a = 1.2 units.
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Determine if each function is linear or nonlinear.
Answer:
To see if a table of values represents a linear function, check to see if there's a constant rate of change. If there is, you're looking at a linear function!
Step-by-step explanation:
Answer:
linear: y = x+5; 5x +5y = 25nonlinear: everything elseStep-by-step explanation:
If it has an exponent, it's non-linear. (There are other ways it can be non-linear, too, but this is the one applicable here.)
During a one-month sales contest, Joaquin sold 56 cars and Annette sold 49 cars. Which ratio is equivalent to the ratio of the number of cars Annette sold to the number of cars Joaquin sold? A. 56:49 B. 3:4 C. 8:7 D. 98:112
Answer:
D. 98:112
Step-by-step explanation:
We want to find Annette:Joaquin
49:56
Both of these numbers are divisible by 7. so we need to divide both of them by 7.
7: 8
Now multiply by each side by 14
7*14 : 8*14
98: 112
The glee club has $90 to spend on pens and pencils. Each pen costs $0.75 and each pencil costs $0.15. Let x represent the number of pens, and let y represent the number of pencils.
Part A
Select the equation that describes the number of club pens and pencils that the glee club can buy.
A. 0.15x + 0.75y = 90
B. 0.75x + 0.15y = 90
C. 0.90(x + y) = 90
Part B
What is the greatest number of each type of writing tool that the club can buy?
greatest number of pens = ?
greatest number of pencils = ?
Answer:
Step-by-step explanation:
Given that total amount available is 90$
x represent the number of pens, and y represent the number of pencils.
cost of each pen is 0.75 and cost of each pencil is 0.15
Then we have total cost = cost of pens + cost of pencils
= [tex]0.75x+0.15y[/tex]=90
Hence option B is right
For finding out the greatest number of each type of writing tool, we can make the other 0 and find out
Hence maximum x = [tex]\frac{90}{0.75} =120[/tex]
maximum y =[tex]\frac{90}{0.15} \\=600[/tex]
Part A
The equation that describes the number of club pens and pencils that the glee club can buy is 0.75x + 0.15y = 90
Part B
Greatest number of pens that the club can buy = 120
Greatest number of pencils that the club can buy = 600
Cost of each pen = $0.75
Number of pens = x
Cost of each pencil = $0.15
Number of pencils = y
Total cost on pens and pencils = $90
(Cost of each pen) x (Number of pens) + (Cost of each pencil)x(Number of pencils) = Total cost
The equation that describes the number of club pens and pencils is:
0.75x + 0.15y = 90
The club buys the greatest number of pens when:
0.75x = 90
x = 90/0.75
x = 120
Greatest number of pens that the club can buy = 120
The club buys the greatest number of pens when:
0.15x = 90
x = 90/0.15
x = 600
Greatest number of pencils that the club can buy = 600
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Joshua read 1/6 of his book in 1/3 hour. At this rate, how much of his book will he read in an entire hour?
Answer:
1/2 of his book
Step-by-step explanation:
1/3 of an hour = 1/6 of the book
3/3 of an hour = 3/6 or 1/2 of the book read
A.) A diver descends 12 feet below sea level. She then ascends 4 feet. State the depth of the diver in terms of sea level. Explain how the depth was determined. B.) Suppose the diver now descends an additional 12 feet. State the new depth of the diver in terms of sea level. Explain how this depth was determined. C. ) Explain how the diver will reach sea level from the position found in part B.
22
-22
8
-8
-20
20
-4
4
Swim up 4 feet
Swim up 20 feet
Swim up 8 feet
Swim up 20 feet
Answer for part A:
Answer for part B:
Answer to part C:
Answer:
1: The diver is 8 feet below sea level.
2: -20
3: -20 + 20 = 0
Step-by-step explanation:
1: This is determined by adding 4 to negative 12. -12 +4 = -8
2: You get this by subtracting 12 from negative 8. -8 - 12 = -20
3: This is done by adding 20 to negative 20. -20 + 20 = 0
The diver's depth in relation to sea level is determined by subtracting the ascent from the initial descent and subsequent descents are added or subtracted accordingly. To reach sea level from a negative depth, the diver needs to ascend by swimming.
Explanation:Answer for part A:The depth of the diver in terms of sea level is -8 feet. This was determined by subtracting the ascent of 4 feet from the initial descent of 12 feet below sea level, resulting in -8 feet.
Answer for part B:The new depth of the diver in terms of sea level is -20 feet. This was determined by adding the additional descent of 12 feet to the previous depth of -8 feet below sea level, resulting in -20 feet.
Answer for part C:The diver will reach sea level from the position found in part B by swimming up 20 feet. This will bring the depth of the diver to 0 feet below sea level, which is equivalent to sea level.
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Choose the equation below that represents the line passing through the point (2, -4) with a slope of one half.
y = one halfx + 5
y = one halfx − 3
y = one halfx − 5
y = one halfx + 3
y = (1/2)x - 5
Step-by-step explanation:Try the answers:
... -4 ≠ (1/2)·2 + 5
... -4 ≠ (1/2)·2 - 3
... -4 = (1/2)·2 - 5 . . . . . the third choice works
... -4 ≠ (1/2)·2 + 3
___
You can write the point-slope form equation and simplify.
... y -k = m(x -h) . . . . . . equation for line of slope m through point (h, k)
... y -(-4) = (1/2)(x -2) . . . filled in with your values, m=1/2, (h, k) = (2, -4)
... y = (1/2)x -1 -4 . . . . subtract 4, eliminate parentheses
... y = (1/2)x - 5 . . . . . simplified. (Matches the 3rd selection.)
Answer: y = one half x − 5
Step-by-step explanation:
We know that , the equation of line that passes through point (a,b) and has slope m is given by :-
[tex](y-b)=m(x-a)[/tex]
Given : Point = (a,b)=(2, -4)
Slope = [tex]\dfrac{1}{2}[/tex]
Then, the equation of the line will be (substitute all the values in the above formula) :-
[tex](y-(-4))=\dfrac{1}{2}(x-2)[/tex]
[tex]\Rightarrow\ y+4=\dfrac{1}{2}(x-2)[/tex]
[tex]\Rightarrow\ y+4=\dfrac{1}{2}x-1[/tex]
Subtract 4 from both sides , we get
[tex]y=\dfrac{1}{2}x-1-4[/tex]
[tex]y=\dfrac{1}{2}x-5[/tex]
Hence, the correct answer is y = one half x − 5
What is the quotient (6x4 − 15x3 − 2x2 − 10x − 4) ÷ (3x2 + 2)? (6 points)
2x^2 -5x -2
Step-by-step explanation:See the attached for the polynomial long division.
Which is the graph of the equation y−2=0.5(x+3)?
Answer:
Step-by-step explanation:
First put the point slope form equation into slope intercept form.
y−2=0.5(x+3)
y - 2 = .5x + 1.5
y - 2 + 2 = .5x + 1.5 + 2
y = .5x + 3.5
With it in the slope intercept form we can see that the y intercept is at (0,3.5)
Find a graph that has this as the y intercept. Next we can graph it like the picture I have attached. You graph the equation by inserting numbers for x.
Answer:
Step-by-step explanation:
The given equation is y - 2 = 0.5(x + 3)
Since the equation is of a straight line so we further rewrite the equation in the form of intercept form.
y - 2 = 0.5x + 1.5
y = 0.5x + 1.5 + 2
y = 0.5x + 3.5
Now plot the graph for the points suitable for the equation
x 0 2 -2 4 -4
y 3.5 4.5 2.5 5.5 1.5
Now the graph which matches the graph plotted will be the graph of the equation.
HELP!!
Monette began heating a liquid with a starting temperature of 62.5°F. The temperature increased by 5° per minute.
What is the recursive rule that represents this situation?\
an=
a1=
Answer:
an = 65 + 5[tex]_{n - 1}[/tex]
a1 = 65
Step-by-step explanation:
If the begining value is 65, then a1 has to be itL
a1 = 65
Then, if this amount increased every minute then 5 has to be added to this value each time:
an = 65 + 5
But this means that 5 is added to 65 every time with no increase, so the five must me multiplied by the n value:
an = 65 + 5[tex]_{n}[/tex]
a2 = 65 + 10 = 75
But this value should be 70 because it is the first point after 65 so it should be +5 not +10
To do this we can simply subtract one from the n value that is being multiplied by 5:
an = 65 + 5[tex]_{n - 1}[/tex]
Which is the recursive rule!