Answer:
-20, -8, -3, 0, 16, 44
Step-by-step explanation:
A rectangular field is to be enclosed by a fence and divided
into two parts by another fence. Find the maximum area
that can be enclosed and separated in this way with 800 m
of fencing
Answer:
80000 square meters
Step-by-step explanation:
perimeter + dividing fence = 800
let a = length
let b = width
let c = length of dividing fence
perimeter = 2*a + 2*b
let's say...
c is the same as the length
2a + 2b + c = 800
2a + 2b + a = 800
3a + 2b = 800
area = length*width
area = a*b
area / b = a
3*(area/b) + 2b = 800
3*(area/b) = 800 - 2b
area/b = (800 - 2b)
area = (800 - 2b)*b
To make the area large, we make the right hand side large.
800b - 2b^2
If you put in terms of x, y it looks like a downward opening parabola, so the max area is at the vertex. Half way between the roots.
y = -2x^2 + 800x
y = -x^2 + 400x
0 = x*(-x + 400)
roots are x= 0 and x = 400
vertex is at x, aka b = 200
area at b=200 is (800 - 400)*200 = 80000
and a is area/b... 80000/400 = 200
What is the value of x?
Please help! what is an equation of a parabola with x-intercepts at (2,0) and (-7,0) and which passes through the point (1,32)?
Answer:
f(x) = - 4x² - 20x + 56Step-by-step explanation:
f(x) = a(x - x₁)(x - x₂) - factored form of the equation of the parabola with zeros x₁ and x₂
x-intercepts at (2,0) and (-7,0) means zeros: x₁=2 and x₂=-7
So:
f(x) = a(x - 2)(x + 7) - factored form of the equation of the parabola with x-intercepts at (2,0) and (-7,0)
The parabola passing through point (1, 32) means if x=1 then f(x)=32
Then:
32 = a(1 - 2)(1 + 7)
32 = a(-1)(8)
32 = - 8a
a = - 4
Therefore the equation of a parabola with x-intercepts at (2,0) and (-7,0) and which passes through the point (1,32):
f(x) = -4(x - 2)(x + 7)
Expanding to standard form:
f(x) = -4(x - 2)(x + 7)
f(x) = -4(x² + 7x - 2x - 14)
f(x) = -4x² - 20x + 56
The equation of the parabola with x-intercepts at (2,0) and (-7,0) and passes through the point (1,32) is
f(x) = -4 ( x - 2 ) ( x + 7 )
Its standard form is
f(x) = -4x² - 20x + 56.
What is a parabola?It is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line
We have,
To find the equation of a parabola we use the factored form of a quadratic equation.
f(x) = a ( x - m ) ( x - n)
Where a is the leading coefficient and m and n are the zeros of the quadratic.
The equation has x-intercepts at (2, 0) and (-7, 0) so we can say that,
m = 2
n = -7
Now the equation passes through (1, 32) = (1, 32) so we have,
32 = a ( 1 - 2 ) ( 1 - (-7) )
32 = a ( -1 ) ( 1 + 7 )
32 = a ( -1 )8
32 = -8a
a = -32 / 8
a = -4
We have,
m = 2
n = -7
a = -4
The equation of the parabola is:
f(x) = a ( x - m ) ( x - n)
f(x) = -4 ( x - 2 ) ( x + 7 )
We can expand to its standard form as:
f(x) = ( -4x + 8 ) ( x + 7 )
f(x) = -4x² - 28x + 8x + 56
f(x) = -4x² - 20x + 56
Thus the equation of the parabola with x-intercepts at (2,0) and (-7,0) and passes through the point (1,32) is f(x) = -4 ( x - 2 ) ( x + 7 ) and its standard form is f(x) = -4x² - 20x + 56.
Learn more about parabola here:
https://brainly.com/question/4074088
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Find the value of x. X=
Answer:
109°
Step-by-step explanation:
there are two ways to slove this kind of questions.
simply,x = 64 + 45
or x = 180-(180 - 64- 45)
Please help!!!!!! ASAP!!!!!!!!
Answer:
Step-by-step explanation:
Answer:
2. m∠4 + m∠5 = 210°
3. Alternate interior angles theorem.
4. 2 × m∠4 = 210°
5. 105°
Step-by-step explanation: i hope this helped youuuuuu have a wounderful thanksgiveing eat alot of food and you get to sleep in Imao!!!!
1 15/100 + 1/50 + 1.175
Answer:
Step-by-step explanation:
Change fractions to have the same denominator or change them all to a decimal. Then add.
Decimal method:
1 and 15/100 is equal to 1.15
1/50 is equal to 0.02
The final term is already a decimal
Add. 1.15 + 0.02 + 1.175 = 2.345
Write the equation of a line with the slope of -7 and passing through the point (2, 2).
Answer:
y=-7x+16
Step-by-step explanation:
y-y=m(x-x1)
y-2=-7(x-2)
y-2=-7x+14
+2 +2
y=-7x+16
5. A line has a slope of (-3/2) and a
y-intercept of (-4). Write the equation of
the line.
Explanation:
Answer:
y = - [tex]\frac{3}{2}[/tex] x - 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - [tex]\frac{3}{2}[/tex] and c = - 4 , thus
y = - [tex]\frac{3}{2}[/tex] x - 4 ← equation of line
6x + 3x - x + 9 = 33
Answer: x=3
Step-by-step explanation:
6x + 3x - x + 9 = 33
Combine like terms:
6x+3x-x=8x
The equation is now 8x+9=33
Subtract 9 on both sides:
8x+9-9=33-9
8x=24
Divide 8 on both sides:
8x/8=24/8
x=3
You notice a hot air balloon descending. The elevation h (in feet) of the balloon is modeled by the function h(x)=−11x+330, where x is the time (in seconds) since you first noticed the hot air balloon.
Graph the function and specify its domain and range. Then interpret the slope and intercepts of the graph.
Answer:
1) Please find attached, the graph of the function
The domain of the function is 0 ≤ x ≤ 30
The range of the function is 330 ≥ x ≥ 0
2) The slope of the given equation, shows that the elevation decreases, by (-)11 feet for each increase in time by one second
3) The y-intercept gives the initial elevation of the balloon at time t = 0 seconds
The x-intercept gives the final elevation of the balloon when it lands at time t = 30 seconds
Step-by-step explanation:
1) The function modelling the height of the balloon is h(x) = -11x + 330
Where;
x = The time of elevation of the balloon
The data for the graphing derived from Microsoft Excel are as follows
x [tex]{}[/tex] h(x)
0 [tex]{}[/tex] 330
5 [tex]{}[/tex] 275
10 [tex]{}[/tex] 220
15 [tex]{}[/tex] 165
20 [tex]{}[/tex] 110
25 [tex]{}[/tex] 55
30 [tex]{}[/tex] 0
Please find attached, the graph of the function
The domain of the function is 0 ≤ x ≤ 30
The range of the function is 330 ≥ x ≥ 0
Comparing the given function to the general equation of a straight line, y = m·x + c, we have that the slope, m = -11
2) The slope of a straight line graph gives the rate of change of the dependent variable, per unit change in the independent variable
Therefore, the slope of the given equation, -11 gives the rate of change of the function per unit increase in the independent variable x
Therefore, the elevation decreases, by (-)11 feet for each increase in time by one second
3) The y-intercept gives the initial elevation of the balloon at time t = 0 seconds
The x-intercept gives the final elevation of the balloon when it lands at time t = 30 seconds
Answer:
I had the same problem! Here is my work, pretty sure its the right answer!
Step-by-step explanation:
One wee, Ethan earned $391.00 at his job when he worked for 23 hours. If he is paid the same hourly wage, how many hours would he have to work the next week to earn $102.00
Answer:
6
Step-by-step explanation:
391/23=17 per hour
102/17=6 Hours
So he would have to work 6 hours to earn $102.00.
Solve the function below for y when x=12.
y=−3x+20
Answer:
y = -16
Step-by-step explanation:
y = -3(12) + 20
y = -36 + 20
y = -16
Hope this helps and pls do mark me brainliest if you can:)
find the value of 1/2×3/5 +1/2×2/5 by using suitable property.
please answer this friends
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Given
[tex]\frac{1}{2}[/tex] × [tex]\frac{3}{5}[/tex] + [tex]\frac{1}{2}[/tex] × [tex]\frac{2}{5}[/tex] ( perform multiplication before addition )
= [tex]\frac{3}{10}[/tex] + [tex]\frac{2}{10}[/tex]
= [tex]\frac{5}{10}[/tex] ( divide numerator/ denominator by 5 to simplify )
= [tex]\frac{1}{2}[/tex]
Answer:
0.5
Step-by-step explanation:
first put the given below:
1/2 × 3/5 + 1/2 × 2/5 = 0
second take the first and second for the first answer to make the whole answer:
((1/2 × 3)/5) = 0
( 1/2 ) × 3 = 1.5
1.5/5 = 0.3
FIRST SOLVATION ( ANSWER ): 0.3
third , after we take the first solvation the second is we need to compute the remaining given or number:
((1/2 × 2)/5) = 0
( 1/2 ) × 2 = 1
1/5 = 0.2
SECOND SOLVATION ( ANSWER ): 0.2
and the last but not the list , the last is add the first solvation and second solvation and you will see what is the answer:
0.3 + 0.2 = 0.5
FINAL ANSWER: 0.5
Two rectangles with the same side lengths are always congruent.
Answer:
true
Step-by-step explanation:
Two triangles are congruent if both of them have the same length of sides. Two rectangles are congruent if both of them have the opposite sides are equal. Two squares are congruent if both of them have the same edges.
What is the equation of the line that passes through the point (4,8) and has a slope of 0?
Answer:
The answer is
y = 8Step-by-step explanation:
To find an equation of a line when given the slope and a point we use the formula
[tex]y - y_1 = m(x - x_1)[/tex]
From the question we have
[tex]y - 8 = 0(x - 4) \\ y - 8 = 0 \\[/tex]
We have the final answer as
y = 8Hope this helps you
HELP! After finding area explain the reasoning you used to find the area and I’ll give brainliest!
Answer:
The answer is 180 yds squared.
Step-by-step explanation:
Segment the areas. One area has the measurements 5 and 6. Then the other one has measurements 15 and 10. This means you get 150 + 30. The answer is 180 yds squared.
A small kite starts 3.7meters off the ground and rises at 6.2 meters per second. A large kite starts at 20.65 meters off the ground and drops at a rate of 5.1 meters per second. After how many seconds are the kites at the same height? Write and solve an equation.
Answer: The kites are at the same height at 15.41s
Step-by-step explanation:
Step 1
Let t represent the time in seconds.
The equation that represents when both small and large kite are at the same height is given as
3.7 + 6.2t =20.65 +5.1t
Step 2----- Solving
3.7 + 6.2t =20.65 +5.1t
Taking like terms and subtracting
6.2t-5.1t = 20.65- 3.7
1.1t =16.95
t = 16.95/1.1
t=15.41s
The kites are at the same height at 15.41s
When two angles are supplementary their sum is equal to 180 degrees. Let x equal one of two supplementary angles. If the other angle is equal to 67 degrees, write
an equation in terms of x for the sum of the two angles.
since we know supplementary angles equal 180 degrees, we know that 67 plus x must equal 180 degrees, so the equation for this problem would be
67+x=180, and x is equal to 113
what’s is the slope?
Answer:
1/2
Step-by-step explanation:
(1,1) (2,3)
you have to do the difference of the x axis and y axis then divid them by each other
Solve for k
p(k + 12) = 8 – 4k
Solve for k:
k = 4 (2 − 3p)/p + 4
Answer:
k = 4(2 - 3p)/(p + 4).
Step-by-step explanation:
p(k + 12) = 8 – 4k
pk + 12p = 8 - 4k
pk + 4k = 8 - 12p
k(p + 4) = 8 - 12p
k = (8 - 12p)/(p + 4)
k = 4(2 - 3p)/(p + 4).
Which inequality is true?
A. I +9< 12
B. 57 > 15
C.
6
27
:> 1
D. 41 - 2 < 10
i need help please
Answer:
B
Step-by-step explanation:
Answer:
thx for 5 points
Step-by-step explanation:
someone sole this please?!
Answer:
[tex] \frac{3x}{5} - \frac{1}{10} = \frac{x + 2}{10} - 2 \\ \frac{6x - 1 = x + 2 - 20}{10} \\ 6x - x = - 18 + 1 \\ 5x = - 17 \\ x = - \frac{17}{5} [/tex]
Answer:
x= -17/5 or x=-3.4
Step-by-step explanation:
1. multiply both sides of equation by 10 (6x-1 = x+2-20)
2, calculate the difference (6x -1=x-18)
3. move the terms ( 6x-x-1=-18)
4. collect like terms ( 5x=-18+1)
5. divide both sides (x=-17/5)
The marked price of an article is Rs.100. If its sold at Rs.80 , find the discount rate.
Please answer quick.
Answer:
20%
Step-by-step explanation:
Given parameters:
Marked price = Rs. 100
Selling price = Rs. 80
Unknown:
Discount rate = ?
Solution:
The price on the label of an article is the marked price;
Discount amount = Marked price - selling price
= Rs. 100 - Rs. 80
= Rs. 20
Discount rate = [tex]\frac{Discount }{Marked price } x 100[/tex]
Discount rate = [tex]\frac{20}{100}[/tex] x 100 = 20%
help pleaseeeeeeeeee
Answer:
C.
Step-by-step explanation:
Write an expression equivalent 6x+3y-4x+2
Abdul's average speed is 30 mph in heavy traffic, and his average speed is 50 mph in light traffic. If he was in heavy traffic for 1 hour and light traffic for 2 hours, how far did Abdul travel?
Answer: Abdul traveled 130 miles
Step-by-step explanation:
Step 1
Using the formula to calculate how far Abdul traveled
Distance = speed x time.
Step 2---- Solving
In heavy traffic
Distance covered = speed x time = 30miles /hour x 1 hour = 30 miles
In light traffic
Distance covered = speed x time = 50miles/ hour x 2 hour = 100 miles
Total distance covered = Distance covered in heavy traffic + distance covered in light traffic = 100+ 30 = 130miles
I need an answer as soon as possible
Answer:
The answer x = 75
Step-by-step explanation:
A triangle's angles must add up to 180 degrees.
We already have 47 and 58 which is 105. 180 - 105 = 75.
if f(x)=10x+3 whar is the value when f(x)=19
Answer:
x = 1.6
Step-by-step explanation:
Given f(x) = 10x + 3 and f(x) = 19, then equate right sides, that is
10x + 3 = 19 ( subtract 3 from both sides )
10x = 16 ( divide both sides by 10 )
x = 1.6
Answer:
x = 1.6Step-by-step explanation:
Given
f(x)=10x+3and
f(x) = 19 ⇒ x = ?Solution
10x + 3 = 1910x = 16x = 16/10x = 1.6BRAINLIEST! Please help me with the following riddle (its part of an assignment):
If an electric train is traveling south, which way is the smoke going?
Answer:
The electric train produces no smoke.
Step-by-step explanation:
Hope this helped! :>
Answer:
There is no smoke. This is because the train is electric so it does not even matter the direction.
At the first track meet, Bobby threw the shot put feet. At the second track meet he threw the shot put feet.
Which of the following expressions could be used to find the distance he improved his throw from the first track meet to the second track meet?
A. 423/4 + 44 1/2
B. 42 3/4 - ( -44 1/2 )
C. 44 1/2 - ( 42 3/4 )
D. 42 3/4 - 44 1/2
Answer: it has to be D
Answer:
The Answer is D) Just did the test!!
Step-by-step explanation: