Answer:
3
Step-by-step explanation:
because it tje best answer on there ferl me
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)
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!
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.
For further details, prefer this link:
https://brainly.com/question/3283106
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:
helpppppppppppppppppp
Answer:
0
Step-by-step explanation:
(2m)/(2m+3)-(2m)/(2m-3)=1
Simplifying the left hand first
(2m)/(2m+3)-(2m)/(2m-3) = {2m(2m-3) - 2m(2m+3)}/(4m²-9)
(4m²-6m-4m²-6m)/(4m²-9) = (-12m) / (4m²-9)
Now this equates to 1
(-12m) / (4m²-9) = 1
-12m = 4m²-9
4m²+ 12m -9 =0 ⇒⇒⇒ This is a quadratic equation that has 2 real solutions.
4m²+ 12m -9 =0
m² + 3m + (3/2)²= 9/4 + 9/4
(m + 3/2)² = 18/4
m = √18/2 - 3/2 or m = -√18/2 - 3/ = 0.621 = -3.621
So we can say that the equation has NO extraneous solutions.
Answer = 0
(I'm pretty sure it's correct)
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
The width of a rectangular room is 3 feet shorter than it is long. If the perimeter of the room is 42 feet, what is the width of the room? Show work
Answer:
Should be 9 feet.
Step-by-step explanation:
Well I just set up the equation 2x + 2(x-3) = 42 Then solved x and subtracted x by 9.
Answer:
9 feetStep-by-step explanation:
Let width be w and length be l
Then we have equations below:
w = l - 32(w + l) = 42Substitute l = w + 3 in the second equation and solve for w:
w + l = 21w + w + 3 = 212w = 21 - 32w = 18w = 18/2w = 9 feetRotate 90 clockwise wxyz
Answer:
Rotate 90 clockwise wxyz
Step-by-step explanation:
Which of the following is a negative integer?
-1/7
-7
.07
7
f(x)=-x^2-10x find f(-7)
=Answer:
Step-by-step explanation:
f(-7) = -(-7)^2 - 10(-7) = -49 +70 = 21
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?
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°
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.
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.
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
translate the sentence into an equation
Eight times the sum of a number and 6 is 9.
use the variable w for the unknown number
Answer:
8(w+6)=9
You must add parentheses to show the order in which you will complete the problem. Because it says “eight times the sum of a number and 6” you have to find the sum first, then multiply 8.
⚠️PLEASE HELP!!⚠️
find the measures of the angles labeled in the figure below.
measure angle EFD
measure angle EHF
measure angle HFG
measure angle G
Answer:
Angle EFG= 90
Angle EHF= 130
Angle HFG=56
Angle G =74
Answer:
angle EFD = 90
angle HFG=56
angle EHF= 29
angle G=73
Step-by-step explanation:
angle EHF=180-51=29
In triangle FGH :
angle FHG = 51 (given)
angle HFG= 90-34= 56( angle EFG given 90)
angle HGF= 180-(51+56) (anglesome prop)
angle G=180-107=73
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
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
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
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]
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].
To know more about Probability, refer here:
https://brainly.com/question/27784798
#SPJ2
Solve and check: x + 10 + 4x + 90 = 180
Answer:
40
Step-by-step explanation:
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)
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
Which value from the set (5,7,9,11,13) make inequality w-4<8 true?
Answer:
5,7,9,11
Step-by-step explanation:
Which expression best represents "7 fewer than 4 times a number x"?
Answer:
4x - 7
Step-by-step explanation:
3/8-1/3
I rly need help and FAST
Answer:
Step-by-step explanation:
1/24
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.
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