Answer:
c. pi/2
Step-by-step explanation:
The answer is the option c. pi/2.
You must know that y = sin(x) is an odd function and also that y = cos(x) is an even function.
Also, you should know that sin(x + pi/2) = cos(x).
You can show it using the definition of the functions sine and cosine in the unit circle or using the formula of the sine of a sum: sin(A + B) = sin(A)*cos(B) + cos(A)*sin(B).
When you substitute B with pi/2 you get sin (A + pi/2) = sin(A)*0 + cos(A)*1 = cos(A).
Then, given that cos(A) is even sin(A+pi/2) is even.
Answer:
option b
Step-by-step explanation:
We are given that [tex]y=sin \frac{1}{2}(x-C)[/tex] be an even function
We have to find the value of C for which given function is even function
We know that sin x is odd function and cos is even function
Odd function : when f(x)[tex]\neqf(-x) [/tex] then the function is called an odd function.
Even function : When f(x)=f(-x) then the function is called an even function.
Sin(-x)=-Sin x
Cos (-x)= Cos x
When we take C=[tex]2\pi[/tex]
Then , y=Sin[tex]\frac{x}{2}-\frac{2\pi}{2}[/tex]
y=[tex]sin(\frac{x}{2}-\pi)[/tex]
[tex]y=-sin\frac{x}{2}[/tex] ( [tex]sin (x-\pi)=-sin x[/tex])
When x is replace by -x
Then, we get [tex]y=-sin(-\frac{x}{2})=sin\frac{x}{2}[/tex]
[tex]f(-x)\neq f( x)[/tex]
Hence, option a is false.
b.C=[tex]\pi[/tex]
[tex]y= sin (\frac{x}{2}-\frac{\pi}{2})[/tex]
[tex] y=-sin(\frac{\pi}{2}-\frac{x}{2})[/tex]
[tex]y=-cos \frac{x}{2}[/tex]
When x is replaced by -x then we get
[tex] y=-cos (-\frac{x}{2})=- cos \frac{x}{2}[/tex]
f(x)=f(-x) , Therefore, function is even,hence option b is true.
c.C=[tex]\frac{\pi}{2}[/tex]
[tex]y=sin (\frac{x}{2}-\frac{\pi}{4})[/tex]
[tex]Sin (A-B)=Sin A Cos B- Sin B Cos A[/tex]
[tex][y= sin \frac{x}{2} cos {\frac{\pi}{4}-cos\frac{x}{2} sin\frac{\pi}{4}[/tex]
[tex] sin\frac{\pi}{4}= cos \frac{\pi}{4}=\frac{1}{\sqrt2}[/tex]
[tex]y=\frac{1}{\sqrt2}(sin \frac{x}{2}- cos \frac{x}{2})[/tex]
When x is replaced by -x then we get
[tex]y=\frac{1}{\sqrt2}(-sin\frac{x}{2}-cos \frac{x}{2})[/tex]
[tex]f(x)\neq f(-x)[/tex]
Hence, function is odd .Therefore, option c is false.
Simplify. square root of (5/8)
To simplify the expression √(5/8), you can simplify the numerator and denominator separately. The square root of 8 can be simplified to 2√2. Rationalizing the denominator, the final simplified form is √10 / 4.
Explanation:To simplify the expression √(5/8), we can first simplify the numerator and denominator of the fraction separately. The square root of 5 is not a perfect square, so we cannot simplify it further. The square root of 8, however, can be simplified. We can write 8 as 4 * 2, and since 4 is a perfect square, we can take its square root. So, we have √(5/8) = √5 / √8.
Next, we can simplify the square root of 8. √8 can be written as √4 * √2, and since √4 is 2, we have √8 = 2√2. Substituting this back into our expression, we get √(5/8) = √5 / 2√2.
Finally, we can simplify the expression further by rationalizing the denominator. We can multiply the numerator and denominator by √2 to get rid of the radical in the denominator. This gives us the final simplified form: √(5/8) = (√5 * √2) / (2√2 * √2) = (√10) / (2 * 2) = √10 / 4.
At which values of x does the graph of the function F(x) have a vertical asymptote? Check all that apply. f(x)=x+4/x^2+5x-24
Answer:
x = -8 & at x = 3
Step-by-step explanation:
This is a rational function.
We can get the values of x at which vertical asymptotes occur by setting the denominator equal to 0 and solving for x.
Let's do this:
[tex]x^2+5x-24=0\\(x+8)(x-3)=0\\x=-8,3[/tex]
Hence, vertical asymptotes occur at x = -8 & at x = 3
The slope of a graphed line is 2/3 and the y-intercept is (0,4) what is the slope-intercept equation of the line?
Answer:
B. y = 2/3x + 4
Step-by-step explanation:
the equation is Y = mx + b
m = slope
b = y-intercept
your answer is B. y = 2/3x + 4
Answer:
Step-by-step explanation:
It's B
The general equation of a slope intercept line is
y = mx + b
m = the slope
m = 2/3
b = the y intercept
b = (0,4)
So the equation is
y = 2/3 x + 4
Julia went to the movies and spent $15 on her ticket and popcorn, if the popcorn cost $7 how much did her ticket cost ?
Final answer:
To find out how much Julia's movie ticket cost, we subtracted the cost of the popcorn ($7) from the total amount spent ($15) to get the movie ticket price of $8.
Explanation:
The student's question asks how much Julia's movie ticket cost if she spent a total of $15 on a movie ticket and popcorn combined, given that the popcorn cost $7. To solve this, we subtract the cost of the popcorn from the total amount spent.
Here's the calculation step by step:
Start with the total amount spent: $15.
Subtract the cost of the popcorn: $15 - $7.
The result gives us the cost of the movie ticket: $8.
Therefore, Julia's movie ticket cost $8.
A business owner pays $1,200 per month in rent and a total of $120 per hour in employee salary for each hour the store is open. On average, the store brings in $200 in net sales per hour.
Which equation can be solved to determine the break-even point if x represents the number of hours per month the store is open?
200x – 120x = 1,200
120x + 200x = 1,200
200x + 1,200 = 120x
120x – 1,200 = 200x
Answer: I'm pretty sure it's 200x - 120x = 1,200
Step-by-step explanation:
Answer:
200x - 120x = 1,200
Step-by-step explanation:
The break-even point is when the amount of money he spends equals the amount he earns.
Let's see how much he earns and how much he spends per month:
He earns $200 per hour. If x represents the number of hours per month, we can write the earns as 200x.
He spends $1,200 per month and $120 per hour. We can write it as 1,200 + 120x.
So, we need 200x = 1,200 + 120x
We don't have this exact equation in our options but if we subtract 120x from both sides, we have:
200x - 120x = 1,200 + 120x - 120x
200x - 120x = 1,200
The correct answer is the first equation.
digits to write the value of the 5 in this number.
587,096
Answer:
Step-by-step explanation:
hundred thousandths
In the number 587,096, the value of the digit 5 would be 500,000 because it is in the hundred thousands position. We can express this as 5*100,000.
Explanation:In the number 587,096, the digit 5 is in the hundred thousands place. This means that the value of the digit 5 is not simply 5, but rather 500,000. To express this, we can write the number as 5*100,000. We multiply the actual digit (5) by its place value (100,000).
Learn more about Place Value here:https://brainly.com/question/35447631
#SPJ2
What is the mean of this data set
12, 13, 15, 28, 28, 30, 42
Answer:
The mean of this data set is [tex]\mu = 24[/tex]
Step-by-step explanation:
By definition, the mean of a data set [tex]x_1, x_2, x_3, ..., x_n[/tex] is
[tex]\mu = \frac{\sum^n_i x_i}{n}[/tex]
Where n is the total number of data.
In this case we have 7 data
12, 13, 15, 28, 28, 30, 42
So the mean is:
[tex]\mu = \frac{12+ 13 +15 +28 +28 +30+ 42}{7}[/tex]
[tex]\mu = 24[/tex]
Solve for x. 4−2x · 4x = 64
[tex]4-2x \cdot 4x = 64\\-8x^2=60\\x^2=-\dfrac{15}{2}\\x\in\emptyset[/tex]
Type the correct answer in the box. Assume that I = 3.14, and round your answer to the nearest integer.
45 yards
35 yards
a= 2800
The figure shows an aerial view of a playground. If David runs around the field three times, he covers a distance of
yards.
Answer:
[tex]648\ yd[/tex]
Step-by-step explanation:
step 1
Find the circumference of the complete circle
The circumference is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=35\ yd[/tex]
substitute
[tex]C=2\pi(35)[/tex]
[tex]C=70\pi\ yd[/tex]
step 2
Find the measure of the arc length for a central angle of 280 degrees
Remember that the circumference subtends a central angle of 360 degrees
so by proportion
[tex]\frac{70\pi}{360}=\frac{x}{280}\\ \\x=280*(70\pi )/360\\ \\x=54.44\pi\ yd[/tex]
step 3
Find the perimeter of the playground
[tex]P=54.44\pi+45=54.44*3.14+45=215.96\ yd[/tex]
Multiply by 3
[tex]215.96*(3)=647.87\ yd[/tex]
Round to the nearest integer
[tex]647.87=648\ yd[/tex]
What is m2B?
Round the value to the nearest degree.
[1] •
29 cm
A
20 cm
B
Your question is so confused. Are you looking for the measure of angle B?
Below is my work on how to find the angle B.
Answer:
B = 46°
Step-by-step explanation:
Cos(B) = Adj./Hypo.
Cos(B) = AB/BC
Cos(B) = 20/29
Cos(B) = 0.6897
B = Cos^-1(0.6897)
B = 46°
For this case we have to define trigonometric relations of rectangular triangles that the cosine of an angle is given by the leg adjacent to the angle on the hypotenuse of the triangle. Then, according to the figure we have:
[tex]cos (B)= \frac {20} {29}\\cos (B)= 0.689655172414[/tex]
So:
[tex]B = arccos (0.689655172414)\\B = 46.39718103[/tex]
Rounding off we have that B is 46 degrees
Answer:
46 degrees
Olivia uses the work below to determine 55% of 720 which explains the error in Olivia’s solution
Answer:
Step 2: Olivia incorrectly determined 1/2 of 10% of 720
Step-by-step explanation:
1/2 of 720 = 360
10% of 720 = .10*720 = 72
1/2 of 72 = 36
This is not the same as 31
This is the incorrect step
Step 2
Answer:
Step 2: Olivia incorrectly determined One-half of 10% of 720.Step-by-step explanation:
What is the y-intercept of the line with a slope of − 1/4 that passes through the point (−2, −9/2 )?
[tex]\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{-\frac{9}{2}})~\hspace{10em} slope = m\implies -\cfrac{1}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\left( -\cfrac{9}{2} \right)=-\cfrac{1}{4}[x-(-2)] \\\\\\ y+\cfrac{9}{2}=-\cfrac{1}{4}(x+2)\implies y+\cfrac{9}{2}=-\cfrac{1}{4}x-\cfrac{1}{2}\implies y=-\cfrac{1}{4}x-\cfrac{1}{2}-\cfrac{9}{2}[/tex]
[tex]\bf y=-\cfrac{1}{4}x-\cfrac{10}{2}\implies y=-\cfrac{1}{4}x\stackrel{\stackrel{b}{\downarrow }}{\boxed{-5}}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
How do I Graph h(x)=8|x+1|-1
Answer:
Step-by-step explanation:
To graph the function h(x) = 8|x+1| - 1, plot key points at (-3, 15), (-1, -1), and (1, 15). The graph exhibits vertical stretching due to the coefficient 8 and symmetry around the line x = -1.
To graph the function (h(x) = 8|x+1| - 1), follow these steps:
1. Identify Key Points:
Determine critical points where the expression inside the absolute value becomes zero. Here, when (x = -1), (h(x) = -1). Additionally, consider points on either side of -1.
2. Plot Points:
Plot these points on the coordinate plane: (-3, 15), (-1, -1), and (1, 15).
3. Determine Behavior:
Understand that the absolute value function |x+1| ensures symmetry around the vertical line x = -1. The coefficient 8 stretches the graph vertically, and the constant -1 shifts it downward.
4. Connect Points:
Draw a smooth curve connecting the points, considering the shape of the absolute value function.
5. Label Axes:
Label the x-axis and y-axis appropriately.
The resulting graph represents the function [tex]\(h(x) = 8|x+1| - 1\)[/tex].
Here is the histogram of a data distribution. All class widths are 1.
4 5 6 7 8 9 10
Which of the following numbers is closest to the mean of this distribution?
From the given histogram, the mean of the distribution is 5. Therefore, option B is the correct answer.
What is mean?In statistics, the mean refers to the average of a set of values. The mean can be computed in a number of ways, including the simple arithmetic mean (add up the numbers and divide the total by the number of observations).
From the given histogram, the frequency distribution is
Number Frequency
1 1
2 2
3 3
4 1
5 1
6 2
7 3
8 1
9 1
Now, the mean is (1×1+2×2+3×3+4×1+5×1+6×2+7×3+8×1+9×1)/15
= (1+4+6+4+5+12+21+8+9)/15
= 70/15
= 4.67
≈ 5
Therefore, the mean is 5.
To learn more about an arithmetic mean visit:
https://brainly.com/question/15196910.
#SPJ7
The mean of the data distribution is 6.3.
The mean of a data distribution can be calculated by summing all the values and dividing by the total number of values. Considering the data set 4, 5, 6, 6, 6, 7, 7, 7, 7, 8, the mean is:
(4 + 5 + 6 + 6 + 6 + 7 + 7 + 7 + 7 + 8) / 10 = 63 / 10 = 6.3
Write the equation in general quadratic form: plz help!!!
Answer:
7x² - 40x - 12 = 0
Step-by-step explanation:
Solve the rational equation by combining expressions and isolating the variable. After doing that, then apply the Quadratic Formula to the listed answer choices to see if they give you the exact same x-intercepts, EXCEPT for this one, where you can easily factor this one. It is "process of elimination". Sometimes you have to try it.
if g(x)*x+1/x-2 abd h(x)=4-x, what is the value of (g*h) (-3)
Answer:
The value of (g*h) (-3) is [tex]=-\frac{112}{3}[/tex]
Step-by-step explanation:
If [tex]g(x) = x+\frac{1}{x}-2[/tex] and [tex]h(x)=4-x[/tex]
We have to find (g*h) (-3)
First multiply g(x) with f(x)
[tex] (x+\frac{1}{x}-2)\times (4-x)[/tex]
[tex]Distribute\:parentheses[/tex]
[tex]=x\cdot \:4+x\left(-x\right)+\frac{1}{x}\cdot \:4+\frac{1}{x}\left(-x\right)+\left(-2\right)\cdot \:4+\left(-2\right)\left(-x\right)[/tex]
[tex]\mathrm{Apply\:minus-plus\:rules}[/tex]
[tex]+\left(-a\right)=-a,\:\:\left(-a\right)\left(-b\right)=ab[/tex]
[tex]=4x-xx+4\cdot \frac{1}{x}-\frac{1}{x}x-2\cdot \:4+2x[/tex]
simplify
[tex]=-x^2+6x+\frac{4}{x}-9[/tex]
Now, put x= -3 in above expression
[tex]=-(-3)^2+6(-3)+\frac{4}{-3}-9[/tex]
[tex]=\left(-\frac{1}{3}-3-2\right)\left(4+3\right)[/tex]
[tex]=\left(-\frac{16}{3}\right)\left(4+3\right)[/tex]
[tex]=7\left(-\frac{16}{3}\right)[/tex]
[tex]=-\frac{16}{3}\cdot \:7[/tex]
[tex]=-\frac{112}{3}[/tex]
Therefore, the value of (g*h) (-3) is [tex]-\frac{112}{3}[/tex]
Based on the graph how many real number solutions to the equation X^3+6x^2+12x+8=0have
ANSWER
One real root.
EXPLANATION
The graph of the function
[tex]f(x) = {x}^{3} + 6{x}^{2} + 12x + 8[/tex]
is shown in the attachment.
According to the Fundamental Theorem of Algebra, this function must have 3 roots including real and complex roots.
The x-intercepts gives the number of real roots.
Observe that the graph has only one intercept.
This implies that, the equation:
[tex]{x}^{3} + 6{x}^{2} + 12x + 8 = 0[/tex]
has only one real solution.
What is the value of Y in the question 5x+2y=20 when x=0.3
Answer:
y = 9.25Step-by-step explanation:
Put the value of x = 0.3 to the equation 5x + 2y = 20, and solve it for y:
5(0.3) + 2y = 20
1.5 + 2y = 20 subtract 1.5 from both sides
2y = 18.5 divide both sides by 2
y = 9.25
Spencer surveyed five of his friends to find out how many pets they have. His results are shown in the table below. What is the mean number of pets? Lara has 4, Cody has 2, Sam has 5, Ella has 1, Maria has 3
Answer:
3
Step-by-step explanation:
You add the total number of pets, and get 15. Then divide it by the number of people and get 3.
Answer: The mean is 3
Step-by-step explanation: In order to find the mean, you must add all the numbers (4+2+5+1+3) and then in this problem, you have to divide it by five since Spencer surveyed only five of his friends.
4+2+5+1+3=15
15 divided by 5 equals 3
As shown in the accompanying diagram, a dog is tied to a 16-foot leash,
which is attached to a corner where the house and fence meet. At this
corner, the angle between the house and the fence is 130°. When the dog
pulls the leash tight and walks from the house to the fence, what is the
distance that the dog walks, to the nearest tenth of a foot?
Backyard
Fence
(1) 11.6 feet
(2) 18.2 feet
(3) 32.0 feet
(4) 36.3 feet
House
(Not drawn to scale)
Find the circumference of the full circle:
Circumference = 2 x PI x radius.
The radius is given as the length of chain 16 feet.
Circumference = 2 x 3.14 x 16 = 100.48 feet.
The dog can walk 130 degrees.
Multiply the circumference by the fraction of a complete circle ( 360 degrees)
Distance = 100.48 x (130/360) = 36.28 feet
Round to 36.3 feet.
The answer is (4) 36.3 feet.
One x-intercept for a parabola is at the point
(-5,0). Use the factor method to find the other
X-intercept for the parabola defined by this
equation:
y=x2 + 3x - 10
Separate the values with a comma.
Answer:
(2, 0)
Step-by-step explanation:
Given
y = x² + 3x - 10
To find the x- intercepts let y = 0, that is
x² + 3x - 10 = 0 ← in standard form
Consider the factors of the constant term (- 10) which sum to give the coefficient of the x- term (+ 3)
The factors are + 5 and - 2, since
5 × - 2 = - 10 and 5 - 2 = + 3, hence
(x + 5)(x - 2) = 0
Equate each factor to zero and solve for x
x + 5 = 0 ⇒ x = - 5
x - 2 = 0 ⇒ x = 2
x- intercepts are (- 5, 0) and (2, 0)
−3z−(−z−2)
simplified exspression pls
-2z +2
-3z+z+2 distribute the - to make them positive
-3z+z equals -2z
What is the solution to this equation? x + 8 = –2 A. x = –10 B. x = 10 C. x = 6 D. x = –6
Answer:a -10
Step-by-step explanation:
-10 +8 = 2
ANSWER
[tex]x = - 10[/tex]
EXPLANATION
The given equation
[tex]x + 8 = - 2[/tex]
This is a linear equation in x.
To solve this equation, we add the additive inverse of 8 to both sides to get;
[tex]x + 8 + - 8 = - 2 + - 8[/tex]
We simplify to get:
[tex]x + 0 = - 10[/tex]
This implies that,
[tex]x = - 10[/tex]
The correct answer is A.
The side lengths of a triangle are given by the expressions 5x + 3, 5x + 5, and 3x – 2. Write and simplify a linear expression for the perimeter of the triangle.
Answer:
13 x + 6
Step-by-step explanation:
Perimeter of triangle = All the sides added together
( 5 x + 3 ) + ( 5 x + 5 ) + ( 3 x - 2 ) = 13 x + 6
Final answer:
The perimeter of the triangle, given its side lengths as linear expressions 5x + 3, 5x + 5, and 3x – 2, is found to be 13x + 6 after combining like terms.
Explanation:
To calculate the perimeter of the triangle, we simply need to add together the lengths of its three sides. The expressions for the side lengths are given as 5x + 3, 5x + 5, and 3x – 2.
The perimeter (P) can be written as a linear expression by summing these expressions:
P = (5x + 3) + (5x + 5) + (3x – 2)
Now, let's combine like terms:
P = 5x + 5x + 3x + 3 + 5 – 2
P = 13x + 6
Hence, the linear expression for the perimeter of the triangle is 13x + 6, which is the simplified form.
A playground is in the shape of a square with each side equal to 109 yards. It has skating rinks in the shape of the quadrants of a circle at each corner. If the area of the remaining field is 9055, find the radius of each skating rink. Also, find the cost of cementing the skating rinks at $2.50 per square yards. Use
Answer:
radius = 30 yd , cost of cement = $7065
Step-by-step explanation:
First we will find the area of the circular sectors. From that we can find the cost of cement and their radius.
The area of the playground is ...
playground area = (109 yd)^2 = 11,881 yd^2
Then the area of the skating rinks is:
rink area = playground area - remaining field
rink area = 11,881 yd^2 - 9,055 yd^2 = 2,826 yd^2
Then the cost of cement for the rink area is ...
(2826 yd^2)($2.50 yd^2) = $7065
The four quarter-circle skating rinks add to a total area of a full circle. That area is given by ...
A = πr^2
Put the values in the formula:
2826 = 3.14r^2
Divide both sides by 3.14
900 = r^2
By taking square root at both sides we get,
30 = r
The radius of each quadrant is 30 yards....
Solve for (x, y, z), if there is a solution to the given system of linear equations:
x - 3y - 2z = -3
3x + 2y - z = 12
-x - y + 4z = 3
(- 4, 1, 0)
No solution
( 4, 1, 2)
(3, - 4, 2)
Answer:
(4, 1, 2)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}x-3y-2z=-3&(1)\\3x+2y-z=12&(2)\\-x-y+4z=3&(3)\end{array}\right\\\\\text{add both sides of the equations (1) and (3):}\\\\\underline{+\left\{\begin{array}{ccc}x-3y-2z=-3\\-x-y+4z=3\end{array}\right}\\.\qquad-4y+2z=0\qquad\text{add 4y to both sides}\\.\qquad2z=4y\qquad\text{divide both sides by 2}\\.\qquad\boxed{z=2y}\\\\\text{Put it to (2)}:\\\\3x+2y-2y=12\\3x=12\qquad\text{divide both sides by 3}\\\boxed{x=4}\\\\\text{Put the value of x to (1) and (3):}[/tex]
[tex]\left\{\begin{array}{ccc}4-3y-2z=-3&\text{subtract 4 from both sides}\\-4-y+4z=3&\text{add 4 to both sides}\end{array}\right\\\left\{\begin{array}{ccc}-3y-2z=-7&\text{multiply both sides by 2}\\-y+4z=7\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-6y-4z=-14\\-y+4z=7\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-7y=-7\qquad\text{divide both sides by (-7)}\\.\qquad\boxed{y=1}\\\\\text{Put the value of y to the second equation:}[/tex]
[tex]-1+4z=7\qquad\text{add 1 to both sides}\\4z=8\qquad\text{divide both sides by 4}\\\boxed{z=2}[/tex]
Howard flips a coin 335 times. What is the probability (p) of having ALL tails?
Step-by-step explanation:
The probability of getting tails is 0.5. The probability of getting tails 335 times is:
P = (0.5)^335
P = 1.43×10^-101
P ≈ 0
Rewrite the polynomial -9x5 + 36x4 + 189x3 in factored form.
Answer:
-9x^3(x - 7)(x + 3)
Step-by-step explanation:
Let f(x)=−12(x+2)2+5 . What is the average rate of change for the quadratic function from x=−3 to x = 1?
Answer:
Average rate of change = -6
Step-by-step explanation:
The average rate of change over the interval (a,b) is given by;
[ f(b) - f(a)] / (b-a)........................where interval is (a,b)
(a,b) interval =(-3,1)
Where;
f(x)= -12 (x+2)² +5
[tex]f(a)=f(-3)=-12(-3+2)^2+5\\f(a)=f(-3)=-12(-1)^2+5\\f(a)=f(-3)=-12(1)+5\\=-12+5=-7\\\\\\f(b)=f(1)=-12(1+2)+5\\f(b)=f(1)=-12(3)+5\\=-36+5=-31\\\\f(b)-f(a)=-31--7=-24\\\\b-a=1--3=4\\\\f(b)-f(a)/b-a=\frac{-24}{4} =-6[/tex]
Given y inversely proportional to x and x = 3 for y = 6, what is x if y = 9?
Answer: [tex]x=2[/tex]
Step-by-step explanation:
Inverse proportion equation has this form:
[tex]y=\frac{k}{x}[/tex]
Where "k" is the constant of variation.
We know that "y" is inversely proportional to "x" and when [tex]x=3[/tex], [tex]y=6[/tex]
Then, we can substittute these values into the equation and solve for "k" to find its value:
[tex]6=\frac{k}{3}\\\\6*3=k\\\\k=18[/tex]
Finally, we need to substitute "k" and [tex]y=9[/tex] into the equation and solve for "x":
[tex]9=\frac{18}{x}\\\\x=\frac{18}{9}\\\\x=2[/tex]
Answer:
x=2
Step-by-step explanation:
y is inversely proportional to x is written as:
x ∝ 1/y
When the proportion is removed, a constant is introduced. We have to find the constant first to find the value of x in y = 9
So,
Removing the proportionality symbol will give us:
x=k/y
As we know that x=3 for y=6 so
3 = k/6
3*6=k
So,
k=8
Hence the value of proportionality constant is 8.
Now putting the value of y which is 9
x=k/y
=>x=18/9
=>x=2