Answer:
85/12 fewer bushels per acre
Step-by-step explanation:
Hi, to answer this question we have to write an expression with the information given and solve it:
We simply have to divide the total loss (21 1/4) by the number of acres (3):
Mathematically speaking:
21 1/4 ÷3 = (21(4) +1)/4 ÷3 = 85/4 ÷ 3= 85/12 fewer bushels per acre
Feel free to ask for more if needed or if you did not understand something
Find the missing y-coordinate that makes the two triangles congruent. Triangle ABC: A(8,4), B(2,6), C(5, 0) Triangle MNO: M(7,4), N(1,2), O(4, y)
Answer:
y = 8
Step-by-step explanation:
Two triangles are said to be congruent if all the three sides and three angles of both triangles are equal.
The distance between two points on the coordinate plane is given as:
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\[/tex]
In triangle ABC:
[tex]|AB|=\sqrt{(2-8)^2+(6-4^2)}=\sqrt{40} =2\sqrt{10}\\\\|AC|=\sqrt{(5-8)^2+(0-4)^2}=5\\\\|BC|=\sqrt{(5-2)^2+(0-6)^2 }=\sqrt{45}[/tex]
In triangle MNO:
[tex]|MN|=\sqrt{(1-7)^2+(2-4^2)}=\sqrt{40} =2\sqrt{10}\\\\|MO|=\sqrt{(4-7)^2+(y-4)^2}\\\\|NO|=\sqrt{(4-1)^2+(y-2)^2 }[/tex]
Since triangle ABC and triangle MNO are congruent, hence:
|AB| = |MN| = 2√10, |AC| = |MO| = 5, |BC| = |NO| = √45
[tex]|AC|=|MO|=5\\\\\sqrt{(4-7)^2+(y-4)^2}=5\\\\(4-7)^2+(y-4)^2=25\\\\9 +(y-4)^2=25\\\\(y-4)^2=16\\\\square\ root\ of\ both\ sides:\\\\y-4=4\\\\y=4+4\\\\y=8[/tex]
Hence O = (4, 8)
Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = y i + (z − y) j + x k S is the surface of the tetrahedron with vertices (0, 0, 0), (8, 0, 0), (0, 8, 0), and (0, 0, 8)
Answer:
[tex]\dfrac{-8^3}{6}[/tex]
Step-by-step explanation:
According to the divergence theorem;
The flux through the surface S is given by the formula:
[tex]\iint _S F.dS = \iiint_E \ div (F) \ dV[/tex]
where the vector field is:
F = [tex]\langle y,z-y,x \rangle[/tex]
Then the divergence of the vector field is:
[tex]div (F) = \bigtriangledown.F = \Bigg [ \dfrac{\partial (y)}{\partial x} + \dfrac{\partial (z-y)}{\partial (y)}+ \dfrac{\partial (x)}{\partial (z)} \Bigg ][/tex]
= 0 - 1 + 0
= -1
Thus, the flux through the surface of the tetrahedron is:
[tex]\iint_S . FdS = \iiint _E(-1) \ dV \\ \\ = - \iiint_E \ dV[/tex]
To determine the volume of the tetrahedron with vertices O(0,0,0), A(8,0,0), B (0,8,0) & C(0,0,6)
The equation of the plane P moving through the vertices A, B and C is:
[tex]P = \dfrac{x}{8}+ \dfrac{y}{8}+ \dfrac{z}{8} = 1[/tex]
x + y + z = 8
Range:
For z: 0 ≤ z ≤ 8 - x - y
For y: 0 ≤ y ≤ 8 - x
For x; 0 ≤ x ≤ 8
Thus;
[tex]\iiint_E \ dV = \int ^8_0 \int ^{8-x}_{0} \int ^{8-x-y}_{0}[/tex]
[tex]\int ^8_0 \int ^{8-x}_{0} [z] ^{8-x-y}_{0} \ dydx = \int ^8_0 \int ^{8-x}_{0} \ (8 -x-y) \ dy dx[/tex]
[tex]\int ^8_0 [ (8-x)^2 - \dfrac{(8-x)^2}{2} ] dx = \dfrac{1}{2} \int ^8_0 (8-x)^2 \ dx[/tex]
i.e.
[tex]= \dfrac{1}{2} [ \dfrac{(8-x)^3}{(-1)^3}]^8_0[/tex]
[tex]= \dfrac{-1}{6}[(8-8)^3-(0-8)^3][/tex]
[tex]= \dfrac{-8^3}{6}[/tex]
This question is based on the Gauss Divergence theorem. Therefore, the surface integral [tex]\int\limits {F.dS}[/tex] is -85.33.
Given:
F(x, y, z) = y i + (z − y) j + x k S in outward orientation.
Tetrahedron with vertices (0, 0, 0), (8, 0, 0), (0, 8, 0), and (0, 0, 8).
We have to evaluate the surface integral [tex]\int\limits {F.dS}[/tex] .
According to the Gauss divergence theorem ,
The flux through the surface S is given by the formula:
[tex]\int\int _s F.dS = \int \int \int_e div (F)\; dV[/tex]
Where the vector field is:
F = ( y, z-y, x )
Therefore, the divergence of the vector field is:
[tex]div(F) = \bigtriangledown .F = ( \dfrac{\partial( y)}{\partial (x)} + \dfrac{\partial(z-y)}{\partial(y)} + \dfrac{\partial(x)}{\partial(z)} )\\\\div(F) = \bigtriangledown .F = 0-1+0=-1[/tex]
Thus, the flux through the surface of the tetrahedron is:
[tex]\int\int _s F.dS = \int \int \int_e (-1)\; dV = -\int \int \int_e \; dV[/tex]
Now, determine the volume of the tetrahedron with vertices O(0,0,0), A(8,0,0), B (0,8,0) & C(0,0,6).
The equation of the plane P moving through the vertices A, B and C is:
[tex]P = \dfrac{x}{8} +\dfrac{y}{8} +\dfrac{z}{8} = 1[/tex]
x + y + z = 8
Range:
For z: 0 ≤ z ≤ 8 - x - y
For y: 0 ≤ y ≤ 8 - x
For x; 0 ≤ x ≤ 8
Thus,
[tex]\int\int\int_e dV = \int\limits^8_0\int\limits^{8-x} _ 0 \int\limits^{8-x-y}_0 \; dzdxdy\\= \int\limits^8_0\int\limits^{8-x} _ 0 [z]\limits^{8-x-y}_0 dx \\= \int\limits^8_0\int\limits^{8-x} _ 0 (8-x-y) dy dx\\= \int\limits^8_0 [ 8y-xy-\dfrac{y^{2} }{2} ]\limits^{8-x}_ 0 dx\\= \int\limits^8_0 ([ 8-x]^{2} - \dfrac{ [ 8-x]^{2}}{2} ) dx\\= \dfrac{1}{2} [\dfrac{(8-x)^{3} }{(-1)^{3} } ] \limits^8_0\\=\dfrac{-8^{3} }{6} \\\\= -85.33[/tex]
Therefore, the surface integral [tex]\int\limits {F.dS}[/tex] is -85.33.
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******time limit******
Answer:
1 hour 12minutes
Step-by-step explanation:
What is 4/5 as a decimal representation and as a percent representation
Answer:
decimal=0.8
percentage=80%
Find the inverse:
-3x+7y=14
9514 1404 393
Answer:
-3y +7x = 14
Step-by-step explanation:
The inverse relation is found by swapping the x- and y-variables. The relation that is the inverse of ...
-3x +7y = 14 . . . . given relation
is
-3y +7x = 14 . . . . inverse relation
2. What is an example of personification? *
Answer:
D. a pencil can not have thoughts like a person, so it is personification.
Answer:
The answer is D.
Help
Please help find b
Answer:
70°
Step-by-step explanation:
1. the rule is: m(∠1)+m(∠2)+m(∠3)=180°.
2. the substitution according to the rule above:
b+2b-90+b-10=180;
4b=280;
b=70°
1. A truck is carrying passion fruit juice, grapefruit juice, and grape juice bottles in a ratio of 1 : 4 : 2. If there are 12 passion fruit juice bottles, then how many grapefruit juice bottles are there
12 : 48 : 24
thats the answer
12 passion fruit
48 grapefruit
24 grape juice
31 days x 160 residents=
Answer:
4960?
Step-by-step explanation:
31 times 160 = 4960
7. What is most likely the slope of the line graphed?
A.-2
B. 0
C. 2
D. Undefined
Answer:
Undefined
Step-by-step explanation:
If the slope was a horizontal line, then we could say y=2, however, it is only going through the x-axis so it would be x=2, but in terms of y it is undefined.
An employee is asked to calculate the chi-square value, for company data set for which observed frequency is 9.5 and expected frequency is 19. What will be the Chi-Square value
Answer:
X² =4.75
Step-by-step explanation:
The formula for calculating the chi square value is expressed as
X² = [ (O - E)²/ E ].
O is the observed frequency
E is the expected frequency
Given
O = 9.5
E = 19
Substitute into the formula:
X² = (9.5-19)²/19
X² = 9.5²/19
X² = 90.25/19
X² = 4.75
Hence the chi square value will be 4.75
what is the
lmc of 12 and 15
Answer:
the lowest common multiple is 60
Step-by-step explanation:
The multiples of 12 are : 12, 24, 36, 48, 60, 72, 84,
The multiples of 15 are : 15, 30, 45, 60, 75, 90, ....
60 is a common multiple (a multiple of both 12 and 15), and there are no lower common multiples.
Therefore, the lowest common multiple of 12 and 15 is 60.
Answer:
[tex]60[/tex]
Step-by-step explanation:
Least Common Multiplier (LCM)
The LCM of [tex]a,b[/tex] is the smallest positive number that is divisible by both [tex]a[/tex] and [tex]b[/tex]
Prime factorization of [tex]12[/tex]
[tex]12[/tex]
[tex]12[/tex] divides by [tex]2[/tex] [tex]12=6*2[/tex]
[tex]=2*6[/tex]
[tex]6[/tex] divides by [tex]2[/tex] [tex]6=3*2[/tex]
[tex]2,3[/tex] are both prime numbers, therefore no further factorization is possible
[tex]=2*2*3[/tex]
Prime factorization of [tex]15[/tex]
[tex]15[/tex]
[tex]15[/tex] divides by [tex]3[/tex] [tex]15=5*3[/tex]
[tex]3,5[/tex] are both prime numbers, therefore no further factorization is possible
Multiply each factor the greatest number of times it occurred in either [tex]12[/tex] or [tex]15[/tex]
[tex]=2*2*3*5[/tex]
Multiply the numbers: [tex]2*2*3*5=60[/tex]
[tex]=60[/tex]
Please help!!!! 8th grade math
Answer: (4,12) or (1/3) simplified
Answer:
2/6
Step-by-step explanation:
so do rise of run but you would move down on the rising. So you go down 2 and run 6
Completely factor this quadratic expression: 4x2 + 12x − 72.
Answer:
4(x-3)(x+6)
Step-by-step explanation:
Answer:
Have a great rest of your day :)
Step-by-step explanation:
X=number of hours
Y=number of tents made
X=0,1,2,3,4,5,6,7,8
Y=6,7,8,9,10,11,12,13,14
If the slope is 1, What does it represent?
Which expression best represents "7 fewer than 4 times a number x"?
Answer:
4x - 7
Step-by-step explanation:
What equation is the rule for the function illustrated by the table of values?
Answer:
The equation which determined the rule for the function is:
y = 3x+2Thus, option B is true.
Step-by-step explanation:
We know the slope-intercept form of line function is
y = mx+b
where m is the slope and b is the y-intercept
Given the table
x -2 -1 0 1 2
y -4 -1 2 5 8
Finding the slope between the points (-2, -4) and (-1, -1)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-2,\:-4\right),\:\left(x_2,\:y_2\right)=\left(-1,\:-1\right)[/tex]
[tex]m=\frac{-1-\left(-4\right)}{-1-\left(-2\right)}[/tex]
[tex]m=3[/tex]
Thus, the slope of the function = m = 3
We know that the y-intercept can be determined by setting x = 0 and determining the corresponding y-value.
It is clear,
at x=0, y = 2
Thus, the y-intercept 'b' = 2
now substituting m = 3 and b =2 in the slope-intercept form
y = mx+b
y = 3x + 2
Therefore, the equation which determined the rule for the function is:
y = 3x+2Thus, option B is true.
factorise x^2-3xy-18y^2
plzzzzz it's urgent
Step-by-step explanation:
here,
x^2 -3xy-18xy^2
=x^2-(6-3)xy-18xy^2
=x^2-6xy+3xy-18y^2
=x(x-6y)+3y(x-6y)
=(x-6y)(x-3y)
What is √80k3 expressed in simplest radical form?
Answer:
The answer is A.
Step-by-step explanation:
Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
√[tex]80k^3[/tex] expressed in simplest radical form is 4√[tex](5k^2)[/tex].
To simplify the expression √[tex]80k^3[/tex] (square root of [tex]80k^3[/tex]) in its simplest radical form, you can break down [tex]80k^3[/tex] into its prime factors:
[tex]80k^3 = 2^4 * 5 * k^3[/tex]
Now, take the square root of each factor:
√[tex]80k^3[/tex] = √[tex](2^4 * 5 * k^3)[/tex]
Since square roots of perfect squares simplify to whole numbers, and the square root of [tex]k^3[/tex] is [tex]k^{3/2}[/tex], the simplified radical form is:
√[tex]80k^3[/tex] = [tex]2^2[/tex] * √[tex](5k^2)[/tex] = 4√[tex](5k^2)[/tex]
Therefore, √[tex]80k^3[/tex] expressed in its simplest radical form is 4√[tex](5k^2)[/tex].
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Which of the following is a negative integer?
-1/7
-7
.07
7
3/8-1/3
I rly need help and FAST
Answer:
Step-by-step explanation:
1/24
Mark can make 42birthday cakes in 7 days.
How many birthday cakes can Mark make in 5 days?
Answer:
30 birthday cakes
Step-by-step explanation:
42÷7=6
6×5=30
PLS HELP ! 100 POINTS!!!!! Select the correct answer. This graph represents a quadratic function. What is the value of a in the function’s equation?
Answer:
a = 3
Step-by-step explanation:
The vertex form of a quadratic is
y = a(x-h) ^2 +k where ( h,k) is the vertex
the vertex is (-2,2)
y = a(x- -2) ^2 +2
y = a(x+2) ^2 +2
Pick another point on the graph to determine a
(-1,5) and substitute into the equation
5 = a( -1+2) ^2 +2
5 = a(1)^2 +2
5 = a(1) +2
Subtract 2 from each side
5-2 = a+2-2
3 = a
Answer:
A=3
Step-by-step explanation:
I got it right on the test
PLZ PLZ PLZ ANSWER!! I WILL GIVE YOU BRAINLIEST!!!
Which answer choice shows the numbers in order from least to greatest?
• -2/3, -1/2, 7/12, 0.82
• -1/2 , -2/3, 7/12, -0.45, 0.82
• -0.45, -1/2, -2/3, 7/12, 0.82
• -0.45, -1/2, 7/12, -2/3, 0.82
Answer:
option 1 is correct
Step-by-step explanation:
yes makes me brain list
93 + 12m = 3(4m – 1) + 96
Answer:
m=0
Step-by-step explanation:
We simplify the equation to the form, which is simple to understand
93+12m=3(4m-1)+96
Reorder the terms in parentheses
93+12m=+(+12m-3)+96
Remove unnecessary parentheses
+93+12m=+12m-3+96
We move all terms containing m to the left and all other terms to the right.
+12m-12m=-3+96-93
We simplify left and right side of the equation.
m=0
Hope this helps!
Brain-List?
Answer:
infinite solutions
Step-by-step explanation:
First, you do the property of distribution
93+12m=3(4m-1) +96
93+12m=12m-3+96
then you combine like terms
93+12m=12m+93
0=0 is the answer if you were to continue.
HELP I CAN GIVE BRAINLIEST
Answer:
[tex]m=\frac{2}{3}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Find points from graph.
Point (40, 10)
Point (70, 30)
Step 2: Find slope m
Substitute [Slope Formula]: [tex]m=\frac{30-10}{70-40}[/tex]Subtract: [tex]m=\frac{20}{30}[/tex]Simplify: [tex]m=\frac{2}{3}[/tex]f(x)=-x^2-10x find f(-7)
=Answer:
Step-by-step explanation:
f(-7) = -(-7)^2 - 10(-7) = -49 +70 = 21
If a square has the sides of 6 cm then how far will it be from one corner of the square to the opposite corner?
Answer:
8.5 cm
Step-by-step explanation:
We know that the square has side lengths of 6cm. To calculate the distance from one corner of the square to the opposite corner, we are calculating the diagonal of the square.
Along the diagonal is where the square gets split in half into two right triangles. The Pythagorean theorem states that [tex]a^2+b^2=c^2[/tex] where c is the longest side of a right triangle and a and b are the other two sides.
To find the length of the square's diagonal, we essentially need to calculate c, the longest side of the triangles. We can do this by plugging 6 into the equation as a and b.
[tex]a^2+b^2=c^2\\6^2+6^2=c^2\\36+36=c^2\\72=c^2\\\sqrt{72} =c[/tex]
[tex]8.5[/tex] ≈ [tex]c[/tex]
Therefore, it will be approximately 8.5cm from one corner of the square to the opposite corner.
I hope this helps!
The pitcher from the home team had 12 strikeouts for 32 batters, While the pitchers for the visiting team had 15 strikeouts for 35 battters. which pitching team had a greater fraction of strikeouts?
really think about this one to help me!
Answer:
The visiting team had a greater fraction of strikeouts
Step-by-step explanation:
Ratios
The ratios are useful to compare rates of change or average values. In our case, we need to compare the average of strikeouts from two teams.
The home team had 12 strikeouts for 32 batters. This gives an average of:
[tex]\frac{12}{32}=0.38[/tex]
The visiting team had 15 strikeouts for 35 batters for an average of:
[tex]\frac{15}{35}=0.43[/tex]
The visiting team had a greater fraction of strikeouts
Solve for x using the
distributive property.
3(-3 - 3x) = 27
Answer:
-9-9x=27+9
-9x=36÷(-9)
x=-4
Step-by-step explanation:
prove me wrong