Answer: Mika can eat 21 hot dogs in 6 minutes. She wants to know how many minutes it would take her to eat
35 hot dogs if she can keep up the same pace.
Step-by-step explanation: Hope I am right.
a farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. no fencing is needed along the barn, and the fencing along the west side of the plot is shared with a neighbor who will split the cost of that portion of the fence. if the fencing costs per linear foot to install and the farmer is not willing to spend more than , find the dimensions for the plot that would enclose the most area.
The constraint for the maximum enclosed area is the amount the farmer is
willing to spend on fencing.
The width of the plot that will give the most area, y = 83.[tex]\underline{\overline 3}[/tex] feet
The length of the plot that will give the most area, y = 125 feet
Reasons:
The given parameters are;
The cost of fencing per foot = $20
The maximum amount the farmer is willing to spend = $5000
Number of sides of fencing = 3 sides
Cost of the west side of the = Split with neighbor
Solution:
Let, y, represent the length of the fence, and let x represent the width of
the fence, we have;
Length of fence required = y + 2·x
Cost of the fence = 20·y + 20·x + (20÷2)·x = 20·y + 30·x
Therefore;
Maximum amount to be spent on the fence, 5000 = 20·y + 30·x
[tex]\therefore y = \dfrac{5000 - 30 \cdot x}{20} = 250 - \dfrac{3}{2} \cdot x[/tex]
[tex]y = \mathbf{250 - \dfrac{3}{2} \cdot x}[/tex]
Area of a rectangle = Length × Width
The enclosed rectangular area of the fencing, A = y × x
[tex]\therefore A = \left(250 - \dfrac{3}{2} \cdot x\right) \cdot x = 250 \cdot x - \dfrac{3}{2} \cdot x^2[/tex]
[tex]\therefore A = -\mathbf{ \dfrac{3}{2} \cdot x^2 + 250 \cdot x}[/tex]
The leading coefficient of the quadratic function of the area is negative,
therefore, the function only has a maximum point.
At the point of the most area, the slope, [tex]\dfrac{dA}{dx} = 0[/tex]
Finding the value of x at the maximum point, we get;
[tex]\dfrac{dA}{dx} = \mathbf{ \dfrac{d}{dx} \left( 250 \cdot x - \dfrac{3}{2} \cdot x^2\right)} = 250- 3 \cdot x = 0[/tex]
Therefore;
[tex]\mathrm{ The \ width \ of \ the \ plot \ that \ will \ enclose \ the \ area}, \ x = \dfrac{250}{3} \ feet = \underline{83.\overline 3 \ feet}[/tex]
[tex]\mathrm{ The \ length \ of \ the \ plot \ that \ will \ enclose \ the \ area}, \ y = 250 - \dfrac{3}{2} \times \dfrac{250}{3} = 125[/tex]
The length of the plot that will give the most area, y = 125 feet
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which ordered pair is a solution to the equation?
Classify the sample space as finite or infinite. If it is finite, write the sample space. If it is infinite, classify whether it is discrete or continuous.
A letter is randomly chosen from the alphabet.
Answer 1:
A. Infinite
B. Finite
Answer 2:
A. Discrete
B. Continuous
Answer:
Answer 1
Because the alphabet can end,it is not unlimited
Factor completely by finding the greatest common factor:
12xy^4 − 21x^2y^5z + 36xy^3
Answer:
the coomon factor is 3xy³
by factoring we get
3xy³(4y-7xy²z+12)
Which of the following are cube numbers. select all that apply
8/9
27
30
8/27
1/27
27/64
64
1/9
Answer:
Step-by-step explanation:
8/9 8 is a cube but 9 is not. 8/9 is not a cube
27 27 = 3^3, a perfect cube
30 Not a cube
8/27 Both 8 and 27 are perfect cubes, and so 8/27 is one also.
1/27 This is equivalent to 1^3 / 3^3 and is a perfect cube.
27/64 Both 27 and 64 are perfect cubes, so 27/64 is one also
64 64 = 4^3, a perfect cube
1/9 9 is not a cube, so 1/9 is not one either.
Juan alquiló un auto por un día. La tarifa mínima es $490.00, con un cargo adicional de $9.70 por cada kilómetro que maneje. Juan pagó $2847.10 cuando entregó el auto. ¿Qué cantidad de kilómetros manejó? kilómetros Х $ ?
Answer:
243 km
precio de los kilómetros: $2357.10
Step-by-step explanation:
precio total = tarifa mínima + precio de los kilómetros
Para x kilómetros,
P = 490 + 9.7x
P = 2847.1
490 + 9.7x = 2847.1
9.7x = 2357.1
x = 243
precio de los kilómetros: 243 × $9.70/km = $2357.10
Respuesta: 243 km
precio de los kilómetros: $2357.10
Eric bought a few marbles and divided equally among four of his friends and his brother, Imer. Eric lost 2 marbles and has only 7 marbles left. How many marbles did Eric buy in all.
Answer:
54 marbles
Step-by-step explanation:
7+2=9(amount Eric had in all)
9×6=54
so in all, he bought 54 marbles which he shared among his friends and brother.
ANS:54 marbles
Select all that are solutions to the inequality below:
3x - 15 > 3
Answer:
solutions are all values greater than 6
Step-by-step explanation:
add 15 to each side to get:
3x > 18
divide each side by 3 to get:
x > 6
solutions are all values greater than 6
A rectangular field is four times as long as it is wide. If the perimeter of the field is 410 yards, what are the field's dimensions?
The length of the rectangular field is 164 yards and the width is 41 yards
From the question,
We are to determine the fields dimensions
From the given information
A rectangular field is four times as long as it is wide
That is
l = 4w -------- (1)
The perimeter of a rectangle is given by
P = 2(l + w)
Where
P is the perimeter
l is the length
and w is the width
From the given information
The perimeter of the field is 410 yards
∴ 2(l + w) = 410 ------ (2)
Substitute equation (1) into equation (2)
2(4w + w) = 410
2(5w) = 410
10w = 410
∴ w = 410 ÷ 10
w = 41 yards
Substitute the value of w into equation (1)
l = 4(41)
l = 164 yards
Hence, the length of the rectangular field is 164 yards and the width is 41 yards.
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$6.00 for 3 chocolate bars how many did he pay per bar
Answer:
$2.00
Step-by-step explanation
To solve this problem, divide $6 by 3 bars which is $2 a bar
Answer:
One bar= $2
Step-by-step explanation:
6 is the amount paid, 3 is the amount of bars he got. so to find the amount for one bar you divide, 6÷3= 2
please help me 8x-3+4x+3
Answer:
12xStep-by-step explanation:
please help me 8x-3+4x+3
8x - 3 + 4x + 3 =
8x + 4x - 3 + 3 =
12x
Answer:
12x
Step-by-step explanation:
1. To simplify this expression, we must group like terms.
[tex](8x + 4x) + (-3 + 3)[/tex] [tex]12x + (-3+3)[/tex] [tex]12x[/tex]Therefore, the answer is 12x.
write down, all the multiples of 8 less than 80
Answer:
The multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, and 72.
Answer:
8, 16, 24, 32, 40, 48, 56, 64, 72
Step-by-step explanation:
8, 16, 24, 32, 40, 48, 56, 64, 72
question below on photo pls quick
I hope youre asking for the y=mx+b kind of equation… if so its y=2x-1
Answer this and explain please
Answer:
x = 3
Step-by-step explanation:
The sum of two interior angles in a triangle is equal to an exterior angle that's supplementary to the third interior angle:
15x + 5 + 22x + 4 = 120 add like terms
37x + 9 = 120 subtract 9 from both sides
37x = 111 divide both side by 37
x = 3 and to find the angles replace x with 3 in given expressions
Rose spent 124 on 10 cars & 4 cats what is the cost for 1 car & 1 cat.
Answer:
$6 per cat, $10 per car
Step-by-step explanation:
I guess and checked my work.
If triangle he an area of 36 and a height of 12 calculate the length of the base.
Answer:
Below.
Step-by-step explanation:
A = 1/2bh for a triangle.
36 = 1/2b(12)
36 = 6b
---- ----
6 6
b = 6
Find the equation of this line.
(0,1)
(-3,0)|
y =
x+
Answer:
y = 1/3x +1
Step-by-step explanation:
y intercept is 1 and the rise is one with a run of 3
What is the value of x?
Answer:
AC is straight line.
72°+3x=180°[linear pair]
3x=180°-72°
3x=108°
x=108°/3
x=36°
option c.
a number y divided by 4 is greater than 22
Answer:
y ÷ 4 ≥ 22
Step-by-step explanation:
I can't find the greater than symbol, but just write the "≥" without the line underneath
Answer:
44
Step-by-step explanation:
Let the number be X
B/P,
X/4=22 Or, X=22*4
X=88
X/2=88/2=44
So the quotient of the number when divided by 2 is 44.
Hope it help and if it its correct please give brainliest
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Thank You
Mallika and Kishore have the same numbser o marbles. To have 100 marbles they must pool their marbles together and then gset 30 more. " which equation represents the above relationship?
Number of marbles with Mallika = x
Number of marbles with Kishore = x (same number of marbles)
To get 100 marbles = x + x + 30
=》x + x + 30 = 100
2x + 30 = 100
2x = 100 - 30
2x = 70
x = 70/2
x = 35
■ Final answer =》Mallika & Kishore both have 35 marbles each.
■ Equation =》2x + 30 = 100
■ Equation type =》Linear equation in 1 variable
______
Hope it helps ⚜
The equation for the given situation will be;
⇒ 2x + 30 = 100
Where, 'x' is represent the number of marbles.
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.
Given that;
Mallika and Kishore have the same number of marbles.
And, To have 100 marbles they must pool their marbles together and then get 30 more.
Now,
Since, Mallika and Kishore have the same number of marbles.
Hence, Let the number of marbles = x
So, We can formulate;
⇒ x + x + 30 = 100
⇒ 2x + 30 = 100
⇒ 2x = 100 - 30
⇒ 2x = 70
⇒ x = 35
Thus, Number of marbles each have = 35
And, The equation for the given situation will be;
⇒ 2x + 30 = 100
Where, 'x' is represent the number of marbles.
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Make x the subject of the equation x2+3=h
Answer:
x2\2+3\2=h/2 therefore x= -3\2+h\2
ANSWER FAST PLEASE !!
Use synthetic division and the remainder theorem to find P(a).
P(x) = x^3 + 5x^2 - 6x +6; a = 4
P(a) =
Simplify your answer
Answer:
[tex]1 + 2 = [/tex]
answer
Which expression is equivalent to this expression?
34(4h – 6)
A. 3h – 92
B. 4h + 92
C. 3h – 6
D. 4h + 6
Answer:
the answer is d
Step-by-step explanation:
Write an equation in point-slope form of the line that passes through (-3, 2) and (6, - 1)
Answer:
y - 2 = -1/3 (x + 3)
Step-by-step explanation
Sorry!
Point-slope form )
Slope = (-1 -2)/(6 - (-3)
Slope = -3/9
Slope = -1/3
Using the point-slope formula and point (-3, 2)
y - 2 = -1/3(x - (-3)
y - 2 = -1/3 (x + 3) This is = to y = -1/3(x + 3) +2
Dan is buying turkey cutlets for $2.69 per pound. The package weighs 4 pounds, 8 ounces.
How much will the cutlets cost?
if I did it right then it's $32.38.
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the systems of equations to their solutions.
2x + y = 12
x = 9 - 2y
x + 2y = 9
2x + 4y = 20
x + 3y = 16
2x - y = 11
y = 11 - 2x
4x - 3y = -13
y = 10 + x
-3x + 3y = 30
2x + y = 11
x - 2y = -7
x = 2, y = 7
x = 5, y= 2
x= 3, y=5
x = 7, y=3
Answer:
the answer is 87 keep trying also the answer 45 aha tricked you
Step-by-step explanation:
um not sure of the answer but loo-kit u p on o just keep trying quay
Answer:
Hey I got you!
Step-by-step explanation:
These are the correct answers I use another easier platform you could say
h=19+3.5w. What could the number 3.5 represent in the equation?
Answer:
the slope of the equation
Step-by-step explanation:
Help me pls
Find angle fgh
Answer:
116
Step-by-step explanation:
Fast and loose: The two triangles are congruent by SSS (they are both right triangles, the hypotenuse is in common, one of the sides is congruent as a given, the second has to be because of pythagorean theorem). The two angles are thus congruent, and their measure is the same:
[tex]2x+20 = 5x-37 \rightarrow 3x=57 \rightarrow x=19[/tex]
Found x, we can find the measure of the larger angle which is [tex](2\times 19 + 20 )\times 2 = 58 \times 2 = 116[/tex]
Answer:
Angle fgh=116
Step-by-step explanation:
Since segments FI and HI are congruent and angles H and F are congruent we can safely assume that angles FGI and HGI are congruent too. Since they are congruent we're going to set up our equation like so:
(2x+20)=(5x-37)
Now we set the equations equal to each other to solve for x
-3x=-57
Divide the -3 by both sides
x=19
Now we have to plug the x into the equations
2(19)+20 and 5(19)-37
Our answer is 58 for both equations
Now we have to add 58+58 because we're solving for FGH not just FGI or HGI.
SO our final answer is 116
(Hope this helps! If I did this wrong someone please correct me and respond to this answer so that I can delete it. Have a great day!)
A jar contains 450 beans. Of all beans, 1/5 are mung beans and the rest are pinto beans. What is the ratio of mung beans to pinto beans?
PLEASE HELP ME!
=======================================================
Explanation:
1/5 of the beans are mung, so 4/5 of the beans are pinto. The two fractions add to 5/5 = 1.
Ignore the denominators and focus on the numerators for each fraction. We have 1 mung and 4 pinto. The values are read in this order to form the ratio 1:4 which is our answer. We cannot reduce this ratio any further.
The order is important because saying 4:1 would mean that we have 4 mung beans and 1 pinto, when it's the other way around.
Side note: The value 450 isn't needed. We could easily change it to any other multiple of 5 and get the same exact answer.
auestion is in the picture, 10 points!
Answer:
y = K/(16z)
Step-by-step explanation:
[tex]K=16yz\qquad\text{given}\\\\\boxed{y=\dfrac{K}{16z}}\qquad\text{divide by the coefficient of y}[/tex]