(0, 6), (0, -2)
I need help
Answer: The function that has these points is invalid because there can not be 2 different y-values in the same x-value.
A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola. What are the dimensions of such a rectangle with the greatest possible area?.
The dimensions of the rectangle such that the rectangle have the greatest area is length = 8 and width = 4 .
In the question ,
it is given that ,
a rectangle is inscribed with its base on the x axis , and its upper corner on the parabola y = 12 − x² ,
let the coordinate of the upper right corner be P(x,y) ,
and A be the area of the rectangle .
the point P lies on the parabola , given y = 12 − x² ,
So, P = P(x,12−x²)
Due to symmetry of the rectangle, the width of rectangle is half the distance between P and the y axis ,
that means width = 2x and length = y .
Area of the rectangle = width × Length
= 2x * y
= 2x (12 − x²)
= 24x - 2x³
To maximize the area we differentiate Area with respect to x ,
we get ,
dA/dx = 24 - 6x²
for critical point dA/dx = 0 ,
24 - 6x² = 0
6x² = 24
x² = 4
x = ±2 ,
since length cannot be negative ,
So , x = 2 .
to check for maximum and minimum ,we differentiate Area with respect to x,
we get
d²A/dx² = -12x
substituting , x = 2 ,
we get -12 < 0, So , the area is maximum .
hence the width = 2*2 = 4
and length = 12 - 4 = 8
and the maximum area is 32 .
Therefore , The dimensions of the rectangle such that the rectangle have the greatest area is length = 8 and width = 4 .
The given question is incomplete , the complete question is
A rectangle is inscribed with its base on the x axis and its upper corners on the parabola y = 12 − x² . What are the dimensions of such a rectangle with the greatest possible area ?
Learn more about Area here
https://brainly.com/question/12809115
#SPJ4
Need help please!
14. Write an equation of a line that is parallel to the line 2x – 3y = 6. Explain how you know that the graph of
your equation is parallel to 2x – 3y = 6.
15. A student drew the line y = 2x + 3
a. Write equations for two lines that are perpendicular to this line. Justify your answer.
b. What do you notice about the slopes of these two lines? What generalization can you make about two lines
that are both perpendicular to the same line?
Answer:
Step-by-step explanation:
14. y = -2/3x + 10. This is parallel to 2x -3y because they have the same slope.
15. y = -1/2x and y = -1/2x + 2. These are perpendicular because the slope is the opposite reciprocal to the slope of y = 2x + 3, which is 2.
The slopes of the lines of the 2 equations are the same. Because of that, we can state that 2 lines that are perpendicular to the same line are parallel. This can be further supported by the Perpendicular Transversal Theorem, which says the same thing.
Hope this helps!
There are
215 cars infront of the mall if each car has 4 wheels estimate the number of wheels infront of the mall round to nearest hundred
Answer:
It should be 860
Step-by-step explanation:
if there are 215 cars and each have 4 wheels, it should be 215 x 4 = 860
express the interval shown on the number line in inequality notation.
The given interval shown on the number line in inequality notation as (3, 6).
What are inequalities on a number line?
Inequalities on a number line allow us to visualise the values that are represented by an inequality.
To represent inequalities on a number line we show the range of numbers by drawing a straight line and indicating the end points with either an open circle or a closed circle.
An open circle shows it does not include the value.
A closed circle shows it does include the value.
The left endpoint is 3. The right endpoint is 6. Both endpoints are open holes, meaning we do not include them as part of the green shaded solution region. If x is a solution, then the solution can be described as
3 < X < 6 which converts to the interval notation (3, 6) . The curved parenthesis says "do not include the endpoint".
Note: this is not ordered pair notation (x,y).
The given interval shown on the number line in inequality notation as (3, 6).
To know more about inequality here.
https://brainly.com/question/13048073
#SPJ1
which of the following is not needed to determine the minimum sample size required to estimate a population proportion?
a. Standard Deviation
b. Margin of Error
c. α
d. z α/2
Answer:
Step-by-step explanation:
margin of error
a painter leans a ladder against a vertical wall. the top of the ladder is 15 meters above the ground. when the bottom of the ladder is moved 3 meters farther away from the wall, the top of the ladder is 11 meters above the ground. what is the length of the ladder? round to the nearest hundredth of a meter.
From the ground the length of the ladder is 15 feet.
Step-by-step explanation:
From the Pythagorean Theorem, the situation described can be expressed mathematically as:
x² +9² = (x+3)²
or,
x² + 81 = x² + 6x + 9
Now, cancelling equal terms on either side of the equation and reducing gives:
x = 12
Since the ladder is defined to be 3 feet longer than the distance of its foot to the wall the ladder’s length must be:
12 feet + 3 feet
=15 feet
Learn more about Pythagorean Theorem:
https://brainly.com/question/14930619
#SPJ4
Factor each of the following.
x^3−8=0
Answer:
(x - 2)(x² + 2x + 4) = 0
Step-by-step explanation:
x³ - 8 ← is a difference of cubes and factors in general as
a³ - b³ = (a - b)(a² + ab + b²) , then
x³ - 8
= x³ - 2³
= (x - 2)(x² + 2x + 2²) = (x - 2)(x² + 2x + 4)
A rental company charge $65a day and 20 cent a mile for renting a truck. Michael rented a truck for 3 day, and hi bill came to $275. How many mile did he drive?
A rental company charge $65 a day and 20 cent a mile for renting a truck. Michael rented a truck for 3 day, and he bill came to $275. He drive 400 mile.
In the given question we have to find how many mile did he drive.
From the given question, a rental company charge $65 a day and 20 cent a mile for renting a truck.
Michael rented a truck for 3 day, and he bill came to $275.
The rental company charges for three days renting
$(65×3)=$195
Also there is a expense of a mile for renting the truck is
20 cents =$0.20
Let Michel drove x miles in 3 days.
Therefore total bill in 3 days is $(0.20x+195).
According to the question,
0.20x+195 = 275
Subtract 195 on both side we get
0.20x = 80
Divide by 0.20 on both side we get
x = 400
Hence, he drive 400 mile.
To learn more about distance link is here
brainly.com/question/28288931
#SPJ4
Tori and her two best friends are all dressing up as superheroes for Halloween
this year. Their costumes are almost ready, but each person still needs to
make a cape. If each cape uses 4 feet of cloth, how many yards of cloth will
they use for the 3 capes?
Answer:
4×3=12
Step-by-step explanation:
that is the answer
the graph of a linear function is shown . which word describes the slope of the line
The slope of the line is 1/5 which is positive.
From the graph:
slope:
Slope is the steepness of a line as it moves from LEFT to RIGHT. Slope is the ratio of the rise, the vertical change, to the run, the horizontal change of a line. The slope of a line is always constant (it never changes) no matter what 2 points on the line you choose.
Take any points:
(0,0) and (5,1)
slope m = y2 - y1 / x2 -x1
= 1 - 0 / 5 - 0
= 1/5
Therefore the slope of the line is 1/5 which is positive.
Learn more about the slope here:
https://brainly.com/question/3605446
#SPJ1
in the moring the temputure starts out around 50 F As the day gose on the temperature rises first slowly then more quickly it stays constant for an hour before droping slowly select the graph that best represents this description
Ivy's Lawn Care Service
# of
minutes
15
20
40
55
Cost
$37.50
$40.00
$50.00
$57.50
Slope:
Check
X
Y-intercept:
Check
Continue that pattern backwards to find the Y-
INTERCEPT (where x=0).
X
Hints:
Just pick any two of the points to find a pattern between
to solve for SLOPE (it doesn't matter which two)
Suggestion? Use the 20 and 40 points...cuz then you
can just count by 20's backwards to find the y-intercept.
A 132
40
1:15 PM
11/10/2022
A linear equation in two variable can be written in general form as y = mx + c. The slope and y-intercept are 1 / 2 and 30 respectively.
What is a Linear equation ?A linear equation is an equation having only one variable.
Its degree is one and it can be used to find the value of only one unknown quantity.
Suppose, the cost be y and the number of minutes be x.
Then, the slope from the given table can be found by by taking the ratio of the difference of cost and minutes from any two rows of the table as given below,
Slope = (50-40)/(40-20)
=> slope = 1/2
Now, the equation for the line representing the given table can be given as,
(y-40)/(x-20) = 1 / 2
=> y - 40 = 1 / 2 (x - 20)
=> y = x / 2 - 10 + 40
=> y = x / 2 + 30
The y-intercept is given at x = 0.
therefore y-intercept is given as,
y = 0 / 2 + 30
y = 30.
Hence, the slope is given as 1 / 2 and the y-intercept is 30.
To know more about linear equation click on,
https://brainly.com/question/13738061
#SPJ1
What combination of transformations is shown below?
reflection, then rotation
reflection, then translation
translation, then rotation
translation, then reflection
Answer:
translation, then rotation
Step-by-step explanation:
HELLLLPPP WILL GIVE BRAINLIST HELP PLEASE DUE SOON
pluto is the furthest planet in our solar system and moves in an orbit at an average of 5900 million km from the sun. find this distance in standard form.
Answer: 5.9 × 10 to the power of 9
Given that y varies directly as x, write an equation
for the relationship if y=-4 when x=10.
A) y=-4x+10
B) y=-0.4x
C) y=0.4x
D) y=-2.5x
X^2 - x - 6 simplified
Yo! Please quickly help me solve this! Select the equivalent expression (2^5/x^2)^4
( Would give more points if I had more, but THANK YOU!! )
Answer:
(2⁵/x²)⁴
(32/X²)
32⁴+x⁶
1,048,576 + X⁶
Step-by-step explanation:
i don't know if this is right. this is all I know
Mrs. Jones put this extra credit problem on the board and asked to determine the missing
length of the side of this parallelogram. What answer should the students come to?
2x+10
5x- 20
4x-1
The length of the missing side is 39 units
What is parallelogram:The parallelogram is a simple 2D-shaped quadrilateral with two pairs of parallel sides. In a parallelogram, the opposite sides and opposite angles are equal.
Here we have,
The length of the sides of a parallelogram is 2x+10, 5x- 20 and 4x-1
As we know parallel lines of a Parallelogram are equal
Take any two sides as equal and find the missing side
Let the sides with lengths be equal 2x+10, 5x- 20
=> 2x+10 = 5x- 20
=> 5x - 2x = 20+ 10
=> 3x = 30
=> x = 10
Therefore, the lengths of the 3 sides are
2x+10 = 2(10) + 10 = 30
5x- 20 = 5(10) - 20 = 30
4x-1 = 4(10) - 1 = 40 - 1 = 39
The length of the missing side is 39 units
Learn more about Parallelogram at
https://brainly.com/question/12917185
#SPJ1
PLAY
Emma and Evie are saving for a new car. Emma has $2000 and she plans to save an additional $50 per month. Evie has $1600 and she plans to save an additional $100 per month. In how many months will Emma
and Evie have the same amount of money saved?
After 12 months for Emma and 10 months for Evie they will have the same amount of money that is $ 2,600
Given:
Case 1 : Amount of money Emma already has = $ 2000
Amount she plans to save per month = $ 50
Thus according to the above data after 12 months Emma would have
12 × 50 = 600 + 2000
this is equal to $ 2600
Case 2 : Amount of money Evie has = $ 1,600
Amount of money she plans to save every month = $ 100
Thus after 10 months she will have 10 multiplied by 100 which is $ 1000
Thus the total amount she will have = 1000 + 1600
which is equal to $ 2,600
Thus after 12 months for Emma and 10 months for Evie they will have the same amount of money that is $ 2,600
To know more about savings and expenditure you may visit the link below:
https://brainly.com/question/13511360
#SPJ1
(02.04 MC)
(Multiple Choice Worth 2 points)
For the function f(x) = -(x + 1)² + 4, identify the vertex, domain, and range.
O The vertex is (-1, 4), the domain is all real numbers, and the range is y ≥ 4.
O The vertex is (-1, 4), the domain is all real numbers, and the range is y ≤ 4.
O The vertex is (1, 4), the domain is all real numbers, and the range is y ≥ 4.
O The vertex is (1, 4), the domain is all real numbers, and the range is y ≤ 4.
The vertex is (-1, 4), the domain is all real numbers, and the range is y ≤ 4.
What are the domain and range of a function?
The range of values that we are permitted to enter into our function is known as the domain of a function. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.
if you use the foil method it will come out to -(x^2+2x+1)+4. then distribute the negative and simplify the equation (add the four) the equation comes out to be -x^2-2x+3.
The vertex is at -b/(2A).
The vertex is at x=2/(2*-1), which is -1. plug -1 into the original equation to find y, (y=-(-1)^2-2*(-1)+3) which is y=4. so the vertex is at (-1,4).
since the parabola opens down (negative a value) and has a maximum at 4, y is always less than or equal to 4. x is all real numbers as it goes on forever. so b is your answer.
To learn more about the domain and range from the given link
https://brainly.com/question/28801359
#SPJ1
Consider the equation and its solution.
Negative 15 (x minus box) = 25. Negative 15 x + 30 = 25. Negative 15 x = negative 5. x = one-third.
What number should be in the empty box?
Answer:
Step-by-step explanation:15(x+2) =25
15x+30=25
15x=5
3x=1
x=1/3
Select all the equations equivalent to
6x9=12
a )2x + 3 = 4
B)0x + 9 = 6
C)6x + 12 = 9
D) 3= 2x + 4
E)3x + 9 = 6
F)6x=3
Equation which is equivalent to the given equation 6x + 9 = 12 is given by 2x + 3 = 4.
As given in the question,
Given equation is equal to :
6x + 9 = 12
Simplify by writing each number into prime factors of the given equation 6x + 9 =12 to get the equivalent equation,
( 2 × 3 )x + ( 3 × 3 ) = ( 2 × 2 × 3 )
3 is the common factor in all we get,
3 ( 2x + 3) = 3(4)
Divide by 3 both the side of the equation we get,
2x + 3 = 4
Therefore, equation which is equivalent to the given equation 6x + 9 = 12 is given by 2x + 3 = 4.
The complete question is:
Which equation is equivalent to the equation 6x + 9 = 12?
A. x +9=6
B. 2x + 3 = 4
C. 3x + 9 = 6
D. 6x + 12 = 9
E. 6x = 3
F. 3 = 2x + 4
Learn more about equivalent here
brainly.com/question/14672772
#SPJ1
Miss Jackson asked the 32 students in her tutor group which language they study.
Each student studies one language only.Half of the students in the tutor group study Spanish. Six more students study German than French. Find the values of French and German.
Answer:
French = 5 ; German = 11
Step-by-step explanation:
G + F = 16
G = 6 + F
6 + F + F = 16
6 + 2F = 16
2F = 16 - 6
2F = 10
2/2 F = 10/2
F = 5
G = 5 + 6 = 11
The perimeter of a rectangle is 30 cm. Its width is 3 cm. Which equation can represent the perimeter of the rectangle if L= length? (please explain how you got the answer)
A.) 3 + L = 30
B.) 3L = 30
C.) 6 + 2L = 30
D.) 6L = 30
The equation that can represent the perimeter of the given rectangle is
6 + 2L = 30, option c is correct.
Given,
width of rectangle = 3 cm
length of rectangle = L
perimeter of rectangle = 30 cm
equation of perimeter of rectangle = 2 × (L + W)
By substituting the values of width and perimeter we can get the equation,
perimeter = 2 × (L + W)
=> 30 = 2 × (L + 3)
=> 30 = 2L + 6
=> 6 + 2L = 30
Therefore, the equation of the perimeter of a rectangle is 6 + 2L = 30.
of the grid is blank?
bers, insert a less-than symbol (<), a greater-than symbol
pol (=) between the numbers to make a true statement.
b. 0.123 2 0.1002
0.123 < 2 > 0.1002, is the true statement after inserting symbols.
What is greater than symbol refer?
In mathematics, the larger than sign is used between two numbers to indicate that the first number is greater than the second. For instance, 10 > 5. 10 is more than 5 in this case.The greater than symbol, which consists of two strokes of equal length joined at an acute angle at the right, is always pointed toward the greater value in inequality. ( >).What is lesser than symbol refer?
In a situation when one number is less than another, a less than symbol is positioned between the two numbersWhen referring to an inequality, the less than symbol () represents the smaller value where two strokes of equal length meet at a sharp angle on the left.The reader may easily understand the message thanks to the larger than less than sign, which also decreases the time complexity.What is equal to symbol refer?
The "equal to" symbol is used to indicate that two numbers or values are equal. The greater than and less than signs are in conflict with this one. We employ the equal to symbol even while writing equations. '=' is used to indicate it.Hence, 0.123 < 2 > 0.1002, is the true statement after inserting symbols.
To know more about symbols check the below link:
https://brainly.com/question/14062194
#SPJ9
One hundred people came to the company's Thanksgiving dinner. There were fifty-two more vegetarians at the dinner than non-vegetarians. How many vegetarians were at the dinner?
Answer:
76
Step-by-step explanation:
Let the number of vegetarians be x. Then, the number of non-vegetarians is x-52.
[tex]x+x-52=100 \\ \\ 2x=152 \\ \\ x=76[/tex]
Please help! I don’t understand what I need to do!
Answer:
Step-by-step explanation:
What is the first time after 1 PM at which the inute hand and hour hand of a clock point in exactly opposite directions?
Answer:
9 : 30
Step-by-step explanation:
1 PM - 1 hour = 12 PM
12 PM - 2 hours = 10 PM
10 PM - 20 minutes = 9 : 40
9 : 40 PM - 10 minutes = 9 : 30 PM
So, it is 9 : 30 PM