Answer:
a- p(x) = 2xy(2x -y)(2x + y)(4x² + y²) ⇒ 2nd answer
b- repeated differences of squares ⇒ 1st answer
Step-by-step explanation:
* Lets explain how to solve the problem
∵ p(x) = 32x^5y - 2xy^5
- The coefficients of the two terms are 32 and 2
∵ 2 is a common factor in 32 and 2
∵ 32 ÷ 2 = 16 and 2 ÷ 2 = 1
∴ p(x) = 2(16x^5y - xy^5)
* Now lets find the common factors of the variables x and y
∵ The common factor is x^5 and x is x
∵ The common factor in y and y^5 is y
∴ the common factors in 16x^5y - xy^5 are xy
∵ 16x^5y ÷ xy = 16x^4
∵ xy^5 ÷ xy = y^4
∴ p(x) = 2xy(16x^4 - y^4)
- Remember that a² - b² is called difference of two squares we
factorize it by distributed into two polynomials have same terms
with different middle sign (a + b)(a - b)
∵ 16x^4 - y^4 is a different of two squares because √(16x^4) = 4x²
and √9y^4) = y²
∴ The factorization of 16x^4 - y^4 is (4x² + y²)(4x² - y²)
∴ p(x) = 2xy[(4x² + y²)(4x² - y²)]
- The bracket 4x² - y² is also different of two squares because
√(4x²) = 2x and √(y²) = y
∴ The factorization of 4x² - y² is (2x - y)(2x + y)
∴ p(x) = 2xy(2x -y)(2x + y)(4x² + y²)
a- p(x) = 2xy(2x -y)(2x + y)(4x² + y²)
b- The methods used to factor p(x) are:
greatest common factor and repeated differences of squares
- But you ask to chose one answer of b so chose repeated
differences of squares
For O D, find mCBE.
A. 311.1°
B. 311.20
C.352 29
D. 332.19
Check the picture below.
Answer:
i think its d
Step-by-step explanation:
Can somebody help thanks if you do
Answer:
It is A i believe.
Step-by-step explanation:
Because, 15/100 = 0.15 and y is your regular price so;
y - 0.15
Sorry had to rewrite what i did, but i hope my answer has helped you.
What is the value of x?
2
3
6
7
Answer:
2
Step-by-step explanation:
So we are going to do
(sum of parts of the secant)(part on outside)=(sum of parts of the secant)(part on outside) .
This is what you get from doing that:
(1+x+4)(x+4)=(11+x+1)(x+1)
Simplifying:
(x+5)(x+4)=(x+12)(x+1)
We could see which value of x makes both side the same.
Choice 1: Plug in 2 for x:
(2+5)(2+4)=(2+12)(2+1)
(7 )(6 )=( 14 )(3)
42 = 42
This equation is true.
Choice 2: Plug in 3 for x:
(3+5)(3+4)=(3+12)(3+1)
( 8)( 7)=( 15)( 4)
56 = 60
This equation is not true.
Choice 3: Plug in 6 for x:
(6+5)(6+4)=(6+12)(6+1)
( 11 )( 10 )=( 18 )(7 )
110 = 126
This equation is not true.
Choice 4: Plug in 7 for x:
(7+5)(7+4)=(7+12)(7+1)
(12 )( 11 )=( 19 )(8)
132 =152
This equation is not true.
Answer:
The answer is A or "2"
Step-by-step explanation:
What is the solution to this equation?
x- 12 = 9
Answer:
x = 21
Step-by-step explanation:
x- 12 = 9
Add 12 to each side
x- 12+12 = 9+12
x = 21
Answer:
[tex]\huge \boxed{x=21}[/tex]
Step-by-step explanation:
[tex]\Huge\textnormal{Add 12 from both sides of the equation.}[/tex]
[tex]\displaystyle x-12+12=9+12[/tex]
[tex]\Huge \textnormal{Simplify and solve to find the answer.}[/tex]
[tex]\displaystyle 9+12=21[/tex]
[tex]\huge \boxed{x=21}[/tex], which is our answer.
Find the average rate of change of f(x) = 2x2 – 7x from x = 2 to x=6.
Simplify your answer as much as possible.
Answer:
-6Step-by-step explanation:
[tex]\text{The average rate of change of function}\ f(x)\\\text{over the interval}\ a\leq x\leq b\ \text{is given by this expression:}\\\dfrac{f(b)-f(a)}{b-a}\\\\f(x)=2x^2-7x\\\\\text{Put the values of x = 2 and x = 6 to the equation of the function:}\\\\f(2)=2(2^2)-7(2)=2(4)-14=8-14=-6\\f(6)=2(6^2)-7(6)=2(36)-42=72-42=-30\\\\\dfrac{f(6)-f(2)}{6-2}=\dfrac{-30-(-6)}{4}=\dfrac{-24}{4}=-6[/tex]
How does the graph of f(x) = 5
cos 1/2 X
Answer:
The graph of [tex]f(x)=5\cos(\frac{1}{2}x)[/tex] is a vertical stretch of 5 units and a horizontal stretch by 2 units of the parent graph
Step-by-step explanation:
We want to find out how the graph of [tex]f(x)=5\cos(\frac{1}{2}x)[/tex] compare with the graph of the parent function [tex]g(x)=\cos (x)[/tex].
We can observe that the transformation applied to the basic cosine function is of the form:
[tex]y=A \cos Bx[/tex]
The [tex]A=5[/tex] is a vertical stretch by a factor of 5 units.
[tex]B=\frac{1}{2}[/tex] is a horizontal stretch by a factor of 2 units.
Therefore the graph of [tex]f(x)=5\cos(\frac{1}{2}x)[/tex] will stretch vertically by a factor of 5 units and stretch horizontally by a factor of 2 units as compared to [tex]g(x)=\cos (x)[/tex].
See attachment
help pls ;-;
What is the perimeter of the figure?
a. 180 in.
b. 64 in.
c. 65 in.
d. 72 in.
Answer:
180 in
Step-by-step explanation:
The perimeter is just the sum of the lengths of the sides of the shape.
So all we need to do here is:
40+10+(40-18)+(50-10)+18+50.
I got (40-18) for the bottom of the top rectangle, the part that is poking out.
I got (50-10) for the right side of the rectangle that is poking out towards the bottom.
40+10+(40-18)+(50-10)+18+50
40+10+22 +40 +18+50
50 +62 +68
50+62+68
112+68
180
180 in
I'm going to post a drawing here to show the lengths I was talking about:
How old am I if 500 reduced by 3 times my age is 278?
Let your age = X
Now you have 500 - 3x = 278
Subtract 500 from each side:
-3x = -222
Divide both sides by -3:
x = -222 / -3
x = 74
You are 74 years old.
The age of an old man is 74 years old.
What is a word problem?A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
For the given situation,
Let the age of an old man be x.
500 reduced by 3 times my age is 278 can be expressed as
⇒ [tex]500-3x=278[/tex]
⇒ [tex]500-278=3x[/tex]
⇒ [tex]222=3x[/tex]
⇒ [tex]x=\frac{222}{3}[/tex]
⇒ [tex]x=74[/tex]
Hence we can conclude that the age of an old man is 74 years old.
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2. Given the objective function C=3x−2y and constraints x≥0, y≥0, 2x+y≤10, 3x+2y≤18, find the maximum value of C. (2.0 Points)
Answer:
The maximum value of C is 15
Step-by-step explanation:
we have
[tex]x\geq 0[/tex] -----> constraint A
[tex]y\geq 0[/tex] -----> constraint B
[tex]2x+y\leq 10[/tex] -----> constraint C
[tex]3x+2y\leq 18[/tex] -----> constraint D
using a graphing tool
The solution area of the constraints in the attached figure
we have the vertices
(0,0),(0,9),(2,6),(5,0)
Substitute the value of x and the value of y in the objective function
(0,0) -----> [tex]C=3(0)-2(0)=0[/tex]
(0,9) -----> [tex]C=3(0)-2(9)=-18[/tex]
(2,6) -----> [tex]C=3(2)-2(6)=-6[/tex]
(5,0) -----> [tex]C=3(5)-2(0)=15[/tex]
therefore
The maximum value of C is 15
To find the maximum value of the objective function $C = 3x - 2y$ subject to the given constraints, we can use the method of linear programming. We have the given constraints:
1. $x \geq 0$ (x is non-negative)
2. $y \geq 0$ (y is non-negative)
3. $2x + y \leq 10$
4. $3x + 2y \leq 18$
The first two constraints define that our solution must lie in the first quadrant of the Cartesian plane, as both x and y must be non-negative.
The third and fourth constraints define linear inequalities which we will represent graphically to find the feasible solution region.
Let's start by finding the intercepts of the lines represented by constraints 3 and 4:
For the third constraint, $2x + y = 10$:
- If $x = 0$, then $y = 10$.
- If $y = 0$, then $x = 5$.
For the fourth constraint, $3x + 2y = 18$:
- If $x = 0$, then $y = 9$.
- If $y = 0$, then $x = 6$.
Plotting these lines on a graph will give us two lines which intersect with the axes to form their intercepts and bound a certain area on the first quadrant.
The feasible region is the area that satisfies all the inequalities simultaneously, including the non-negativity constraints of x and y.
Next, we find the vertices of the feasible region. The vertices occur where the lines of the constraints intersect each other as well as with the axes. From the graph, we could find that the feasible region is a polygon formed by intersecting the lines corresponding to the constraints. The vertices are:
1. Where $2x + y = 10$ and $3x + 2y = 18$ intersect.
2. Where $2x + y = 10$ and the y-axis intersect.
3. Where $3x + 2y = 18$ and the x-axis intersect.
We solve for each vertex by solving the system of equations corresponding to the constraints that intersect:
For vertex 1, solving $2x + y = 10$ and $3x + 2y = 18$ simultaneously, we could do this by multiplying the first equation by 2 to eliminate y, and then subtract it from the second equation:
$4x + 2y = 20$
$3x + 2y = 18$
Subtracting the second equation from the first gives
$x = 2$
Plug this value of x into one of the original equations:
$2(2) + y = 10$
$4 + y = 10$
$y = 6$
So, vertex 1 is at (2, 6).
Vertex 2 is at the y-intercept of $2x + y = 10$ which is (0, 10).
Vertex 3 is at the x-intercept of $3x + 2y = 18$ which is (6, 0).
Now, we calculate the value of the objective function at each vertex:
For (2, 6):
$C = 3(2) - 2(6) = 6 - 12 = -6$
For (0, 10):
$C = 3(0) - 2(10) = 0 - 20 = -20$
For (6, 0):
$C = 3(6) - 2(0) = 18 - 0 = 18$
The maximum value of C within the feasible region is found at the intersection points of the constraints. Among the calculated values for the objective function $C$ at the vertices, the maximum value is $18$ at the point $(6, 0)$.
Therefore, the maximum value of the objective function $C = 3x - 2y$ given the constraints is 18.
Step 1: -10 + 8x < 6x-4
Step 2: -10 <-2x - 4
Step 3: -6 <-2x
Step 4:
What is the final step in solving the inequality --215-4x)
6x - 4?
O x<-3
O x>-3
O x<3
O x>3
Help!!
Answer:
The final step in solving inequality is x>3.
Step-by-step explanation:
To solve this problem, first thing to do is switch sides of -2x>-6, and divde -2 from both sides.
-2x>-6
-2x/-2>-6/-2
Divide numbers from left to right.
-6/-2=3
The final step in solving the inequality is x>3, which is our answer.
I hope this helps!
Thank you! for submitting question on Brainly.
If s(x) = x-7 and f(x) = 4x? – X+3, which expression is equivalent to (tos)(x)?
04(x-7)2 – X-7 + 3
0 4(x-7)2 – (x-7) + 3
(4x2 - x + 3)-7
0 (4x2 – x+3)(x-7)
Answer:
4(x-7)^2-(x-7)+3 (Assuming t is f)
Step-by-step explanation:
Let s(x)=x-7 and t(x)=4x^2-x+3 .
(t o s)(x)=t(s(x))=t(x-7)
Before I continue this means replace the orginal x in t with x-7.
This will then give you
4(x-7)^2-(x-7)+3
in a gymnastics competition an athletes final score is calculated by taking 75% of the average technical score and adding 25% of the artistic score all scores are out of 10 and one gymnast has a 7.6 average technical score what artistic score does the gymnast need to have a final score of at least 8.0
Answer:
x ≥ 9.2
Step-by-step explanation:
If in a gymnastics competition an athletes final score is calculated by taking 75% of the average technical score and adding 25% of the artistic score all scores are out of 10 and one gymnast has a 7.6 average technical score, the gymnast needs x ≥ 9.2 to have a final score of at least 8.0.
7.6 x 75 / 100 = 5.7
Final answer:
The gymnast requires an artistic score of at least 9.2 to achieve a final score of at least 8.0, calculated by taking 75% of their average technical score and adding 25% of their artistic score.
Explanation:
To find out what artistic score the gymnast needs to achieve a final score of at least 8.0, we use the given information that the final score is composed of 75% of the average technical score plus 25% of the artistic score. Let's represent the artistic score as A.
First, calculate 75% of the average technical score:
0.75 × 7.6 = 5.7
Now, set up the equation using the required final score (8.0) and the known technical score (5.7):
5.7 + 0.25A ≥ 8.0
To find the minimum artistic score (A), we subtract 5.7 from both sides of the equation:
0.25A ≥ 8.0 - 5.7
0.25A ≥ 2.3
Finally, divide by 0.25 to solve for A:
A ≥ ÷ 0.25
A ≥ 9.2
So, the gymnast would need an artistic score of at least 9.2 to achieve a final score of at least 8.0.
I dentify the domain and range and sketch the graph
[tex] y = sqrt { - x - 3 - 3} [/tex]
Answer:
Step-by-step explanation:
y=√(-x-3) - 3
y exisit : - x -3 ≥ 0
- x ≥ 3
x ≤ - 3 the domain is : D=] -∞,-3 ]
y=√(-x-3) - 3
y + 3 = √(-x-3)
x exisit : y + 3 ≥ 0 ; y ≥ -3
the range is : w = [- 3,+ ∞ [
look the graph
The temperature is 50°F The temperature will decrease by 4°F each hour. Let
h be the number of hours,
When will the temperature be below 32°F?
Write an inequality for this problem,
A. 50 - 4h: 32
B. 50 - 4h32
c. 50 + 4h3 32
D. 50 + 4h+ 32
Answer:
50-4h<32
Step-by-step explanation:
If the temperature starts at 50 and the temperature is decreased by 4 per each hour, then:
1) after the first hour, the temperature is 50-4 or 46
1) after the second hour, the temperature is 46-4 or (50-4)-4 or 50-4(2).
So what I'm trying to show you that if I continue this pattern our equation for what happens h hours later is: 50-4h.
We want to know when is the temperature below 32 so less than 32.
Temperature<32
Put in our variable expression for temperature.
50-4h<32
The question is about using algebra to solve a real-life problem of temperature decrease. The correct inequality for the given problem is '50 - 4h < 32', which shows the number of hours it takes for the temperature (50 and decreasing 4 every hour) to be less than 32 degrees.
Explanation:The subject matter of this question is mathematics, specifically algebra and inequalities. The question provides that the temperature in degrees Fahrenheit is reducing by 4 each hour from a starting point of 50°F and seeks to find the number of hours (h) it takes for the temperature to decrease below 32°F.
We can represent this situation as an inequality: 50 - 4h < 32. In English, this states that the temperature (50, decreasing by 4 each hour) should be less than 32 degrees. So, to answer your question, option B with '50 - 4h < 32' is the correct inequality for this problem.
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(4.0 •10^6) divided by (5.0•10^9) in scientific notation
Answer: [tex]8.0*10^{-4}[/tex]
Step-by-step explanation:
You need to remember the Quotient of powers property:
[tex]\frac{a^m}{a^n}=a^{(m-n)}[/tex]
Then, given the expression:
[tex]\frac{(4.0*10^6)}{(5.0*10^9)}[/tex]
You must divide the coefficients and subtract the exponents. Then:
[tex]=0.8*10^{-3}[/tex]
In order to write this result in Scientific notation form, you need to move the decimal point one place to the right. Therefore, you get:
[tex]=8.0*10^{-4}[/tex]
rectangle ABCD is shown on the coordinate grid below. which of the following graphs represent the translation of rectangle ABCD over the following: (x, y) —> (x + 1, y-2)?
Answer:
the answer is c glad i could help
There are 12 girls and 10 boys in the student council. What is the ratio of the number of girls to the total number of members? F. 6:5. G. 5 to 6. H. 6 to 11. I. 1 to 2.
Answer:
i think the answer is choice H
Step-by-step explanation:
the number of girls to total number of members is 12:22, if you simplify this it's 6:11
Answer:
6:11
Step-by-step explanation:
There are 12 girls.
There are 12+10 member in all.
That means there are 22 members in all.
So the ratio of girls to total members is 12 to 22 or 12:22. To reduce this, look for a common factor. 12 and 22 both share 2 as a common factor so divide both by 2 gives you 6:11.
14 points!!
Is this shape a polygon?
Answer:
TRUEStep-by-step explanation:
A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain or polygonal circuit.
What is the following product? square root 10× square root 10
[tex]\huge{\boxed{10}}[/tex]
We can rewrite this using an exponent. [tex]\sqrt{10}^2[/tex]
When you square a square root, you basically just cancel out the square root, leaving whatever was inside the square root symbol. In this case, you end up with a final answer of [tex]\boxed{10}[/tex].
Step-by-step explanation:
First, you must find the square root of 10, which is 3.16.
Now, multiply 3.16x3.16, or find 3.16 squared.
This is 9.98
If 0 is in quadrant 3 and sin0= -3/5 then cos0=
If angle θ is in quadrant 3 and the value of sin θ = -3/5, then we can say that; cos θ = -4/5
How to work with Trigonometric Ratios?
We are told that the angle θ is in quadrant 3.
Now, we are told that; sin θ = -3/5
In the third quadrant, only tan θ is positive.
Thus, cos θ will be negative.
Thus;
cos θ = -4/5
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Answer:
If angle θ is in 3rd quadrant and the value of [tex]sin\theta =\frac{-3}{5}[/tex], then [tex]cos\theta =\frac{-4}{5}[/tex]
Step-by-step explanation:
Given that , angle θ is in 3rd quadrant and the value of [tex]sin\theta =\frac{-3}{5}[/tex]
We know that ,
[tex]sin^2\theta + cos^2\theta =1[/tex]
[tex]cos^2\theta =1 - sin^2\theta[/tex]
By replacing the value of [tex]sin\theta =\frac{-3}{5}[/tex] we get,
[tex]cos^2\theta =1 - (\frac{-3}{5})^2[/tex]
[tex]cos^2\theta =1 - \frac{9}{25} = \frac{16}{25}[/tex]
Taking roots at the end of both sides we get,
[tex]cos\theta = \frac{4}{5}[/tex] or [tex]cos\theta = \frac{-4}{5}[/tex]
We know that , In third quadrant, only tan θ and cot θ are positive.
Thus, cos θ will be negative.
So [tex]cos\theta = \frac{-4}{5}[/tex]
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Someone please help me with this question. I would greatly appreciate it. Please and thank you.
[tex]\dfrac{15(15-1)}{2}=\dfrac{15\cdot14}{2}=15\cdot7=105[/tex]
A group of students is arranging squares into layers to create a project. The first layer has 5 squares. The second layer has 10 squares. Which formula represents an arithmetic explicit formula to determine the number of squares in each layer?
Answer:
[tex]a_n=5n[/tex]
Step-by-step explanation:
They gave us the first two terms in the sequence which is 5,10.
They then tell us the sequence is arithmetic which means all you need to do to get the next term is add/subtract.
To get from 5 to 10, you would need to add 5.
So that is what we are doing every time here.
5,10,15,20,25,... so on...
Now we want to make an equation for this.
When you see arithmetic sequence, you should think linear equations.
x | y
-----------
1 5
2 10
3 15
4 20
Can you see the relationship between y and x?
Slope is 5 because that is what the sequence is going up by.
y=5x+b
Maybe you can already see b is 0. If not, you can use a point on the line to find b.
Let's use (1,5).
5=5(1)+b
5=5+b
0=b
So b=0.
The equation is y=5x.
Our since we are talking about sequences maybe you prefer to say [tex]a_n=5n[/tex]
Multiply
6.421. 10 =
0.6421
• 64.21
64210
6,421
Gujb
Answer:
64.21
Step-by-step explanation:
Here we are given with the a number in decimals and need to find its product with 10.
please note the rule of multiplication in decimals . When we multiply any decimal with 10, 100, 1000 , 10000 and so on.. the position of decimal in the number given to us shifts to its right by the number of places as we have the number of 0 in the multiplier
6.421 X 10
here we have only one 0 in the multiplier , hence the position of decimal in 6.421 will be shifted to one place towards right
6.421 x 10 = 64.21
Answer:
64.21
Step-by-step explanation:
Whatis the domain and range of f(x)=2[x-4]
Answer:
Domain: All Real Numbers
Range: All real numbers
Step-by-step explanation:
The given function is:
[tex]f(x) = 2(x-4)[/tex]
Domain:
The given function will not be undefined on any value of x as there is no denominator involved in the function.
So, the domain of the function is all real numbers
Range:
Similarly the range of the function is also all real numbers.
What is the range of f(x) = 3x + 9?
{y | y < 9}
{y | y > 9}
{y | y > 3}
{y | y < 3}
Answer:
All real numbers
Step-by-step explanation:
we have
f(x) = 3x +9
The linear function has a range of all real numbers -------> (-∞, ∞)
f(x) can take any real value.
Please see attached image below, for more information
Answer:
I think its B because K is = to Y
So if K is 9 then the asymptote would be 9
Limiting the Y to the to be only greater than 9
Step-by-step explanation:
In the diagram below, what is the length of ST?
Check the picture below.
If sides SX=5,SY=10,XU=4,YT=x then the length of ST=18.
What is triangle?A triangle is a two dimensional figure having three sides, three angles, three vertex. Th sum of all the angles is equal to 180°.
How to find length?We have been given SX=5, XU=4,SY=10 and we are required to find the length of ST. We can write the sides as under:
SX/SU=SY/T
SX=5,SU=5+4=9,SY=10,ST=10+x
5/9=10/(10+x)
Solving this for the value of x.
5(10+x)=10*9
50+5x=90
5x=90-50
x=40/5
x=8
We know that ST=10+x.
We have to put the value of x in ST.
ST=10+8
=18
Hence if sides are SX=5,SY=10,XU=4,YT=x then the length of ST=18.
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Type the expression as radicals.
Y3/5
Answer:
[tex]\sqrt[5]{y^{3} }[/tex]
Step-by-step explanation:
[tex]y^{\frac{3}{5} } = y^{\frac{1}{5} * 3}[/tex] = [tex]\sqrt[5]{y^{3} }[/tex]
This is true because of the fractional exponent rule.
Answer:
Step-by-step explanation:If
n
is a positive integer that is greater than
x
and
a
is a real number or a factor, then
a
x
n
=
n
√
a
x
.
a
x
n
=
n
√
a
x
Use the rule to convert
y
3
5
to a radical, where
a
=
,
x
=
, and
n
=
.
5
√
y
3
I need help with this problem please ! Evaluate 3/7r + 5/8s when r=14 and s=8.
Answer:
11
Step-by-step explanation:
It is given that:
r = 14 & s = 8
Plug in the corresponding numbers to the corresponding variables:
(3/7)(14) + (5/8)(8)
Solve. Remember to simplify. Do multiplication & division first, then add:
(3/7)(14) + (5/8)(8)
(3 * 14)/7 + (5 * 8)/8
(3 * 2) + 5
(6) + 5
11
11 is your answer.
~
Because of a problem in the program, the timer in a video player did not begin counting until the video had been playing for several seconds. The player began counting at 0 seconds, even though the video had already played 190 frames. The video plays 25 frames per second. How many frames had the video already played when the time was equal to -3 2/5 seconds?
Answer:
105 frames
Step-by-step explanation:
Given that 25 frames are played per second
25 frames= 1 sec
The video already played 3 and 2/5 seconds before the player started to count 0
Write 3 and 2/5 seconds as an improper fraction
=(5*3)+2 / 5 = 17/5 seconds
Multiply by 25 frames
17/5 *25 =85 frames
So according to the video counter,after 17/5 seconds,it should count 85 frames.However,at 0 seconds,it indicated a count of 190 frames.Thus,to get the number of frames that were already in count you subtract 85 frames from the 190 frames.
190-85=105 frames.
The video had played 275 frames when the timer showed [tex]-3\frac{2}{5}[/tex] seconds.
To determine how many frames had been played when the timer showed [tex]-3\frac{2}{5}[/tex] seconds, we first need to convert [tex]-3\frac{2}{5}[/tex] seconds to an improper fraction or decimal. We have [tex]-3\frac{2}{5}[/tex] = [tex]-\frac{17}{5}[/tex] seconds.
Since the video plays at a rate of 25 frames per second, we can calculate the number of frames played during [tex]-\frac{17}{5}[/tex] seconds as follows:
Total frames = 25 frames/second × [tex]-\frac{17}{5}[/tex] seconds = -85 frames.
This means that 85 frames had been played before the timer started counting (since negative time indicates frames played before the recorded start time).
Since at 0 seconds, the video had already played 190 frames, we add the frames played during the negative time interval:
Total frames = 190 frames (initial) + 85 frames = 275 frames.
Find the standard equation and graph of a parabola that matches the given set of characteristics. vertex (0, 0) focus (-2, 0)
The standard equation of a parabola with vertex (0, 0) and focus (-2, 0) is y^2 = -8x. It opens to the left with the directrix x = 2.
To find the standard equation of a parabola with vertex (0, 0) and focus (-2, 0), we can use the definition of a parabola as the set of all points equidistant from a point (the focus) and a line (the directrix).
Since the focus is at (-2, 0), the directrix is a vertical line equidistant from the vertex on the opposite side of the focus, which is x = 2. The distance between the vertex and the focus (or the vertex and the directrix) is 2 units, so q = 2. This means that the parabola opens to the left.
The standard equation for a parabola that opens horizontally is of the form (y - k)^2 = 4p(x - h), where (h, k) is the vertex and p is the distance from the vertex to the focus. Here, p = -2 because the parabola opens to the left.
Therefore, the standard equation for the given parabola is y^2 = -4(2)x or y^2 = -8x.