Hmm...I plugged it into google translate, as I am not fluent in Vietnamese, but this is what it replied:
"base 90 times 6 times 4"
So...should it be in a different base? Base 90 seems insane, as not many people use it...
This is just algebra in disguise. Since the 4th angle is equal to 3x + 7 degrees, and the 5th angle is equal to 9x-43 degrees, we can form a linear equation and solve.
3x + 7 + 9x - 43 = 180 <------- 180 degrees on a line
12x + 7 - 43 = 180
12x - 36 = 180
12x = 216
x = 18
To solve for UPS, we plug 18 into the 4th angle.
3(18) + 7 = 61
But, we also need to add 90 degrees:
61 + 90 = 151 degrees
Maybe you actually will see this answer. Maybe not, as you are a guest, and you can't save topics.
:)
If m angle ABD=79 degrees , what are m angle ABC and m angle DBC
Since together they equal 79o just add them together, solve for x, and then plug it back in.
ABC + DBC = ABD
(8x – 3) + (5x + 4) = 79
add like terms 13x + 1 = 79
13x = 78
x = 6
Plug 6 back in to ABC (8 • 6) – 3 = 45 so angle ABC = 45o
Plug 6 back in to DBC (5 • 6) + 4 = 34 so angle DBC = 34o
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the measure of one angle of a triangle is three times the measure of a second angle. the measure of the third angle is 12 less than the sum of the other two. what are the measures of the 3 angles?
Let the angles be A, B and C
We have three equations connecting them:
A+B+C = 180
A = 3B
C = A+B-12
(I'm assuming the 12 is degrees not radians).
Can you take it from here?
Write the equation of the line perpendicular to 2x-3y=12 that passes through the point (16,-7)
Rewrite the equation as y = (2/3)x - 4 This has slope 2/3
A perpendicular line will have slope -3/2 so the equation of a perpendicuar line is y = -(3/2)x + c where c is a constant found from the fact that the line must go through point (16, -7).
-7 = -(3/2).16 + c
c = 24 - 7
c = 17
Hence perpendicular line has equation y = -(3/2)x + 17
Because triangle ABC is isosceles, angle ABC = angle ACB = (180 - 30)/2 = 75°
Angles on a straight line must sum to 180°, so 4x + 2x + 75 = 180 giving x = 17.5°, which makes angle ABE = 35°. This doesn't match any of your options!
\(90 \times 6 \times 4 = 540 \times 4 = \boxed{2160}\)
Let z = (sqrt(6) - sqrt(2)) + (sqrt(6) + sqrt(2))*i. Compute z^(24).
Convert to polar notation
z = r.exp(i.θ) where r = √(√6 - √2)2 + (√6 + √2)2 ) = 4 and θ = tan-1( (√6 + √2)/ (√6 - √2) ) = 75°
z24 = r24.exp(i.24.θ) = 424.exp(1800°) = 424.(cos(1800°) + i.sin(1800°)) = 424.(cos(0°) + i.sin(0°)) = 424
Good work Juriemagic,
It is good to see you here again too
Hi dp,
Why haven't you posted your LaTex properly?
x/25 = 63/35
x =63/35*25
x = 45
Angle ABE = 80 degrees.
The line is y = 3/2*x - 1.
(r,theta) = (4,2*pi/3).
The distance is 25 cm.
|v + w| = 2, |w + z| = 2*sqrt(3), |v + z| = 1.
System of equations, seriously, it helps.
Let the 3 numbers be x, y, and z. We know:
x + y + z = 52
2z = x
x - 8 = y
What do we see? Well, we can rewrite everything in terms of x:
x = x (obviously)
z = x/2
y = x - 8
x + x - 8 + x/2 = 52
2x - 8 + x/2 = 52
5x - 16 = 104
5x = 120
x = 24
Knowing that x = 24, we see:
z = 12
y = 32
a=1;p=0; b=1;c=1;n= (a+2*b+3*c)%7;m=(2*a+3*b+c)%7;k=(3*a+b+2*c)%7;if(n==0 and m==4 and k==4, goto loop, goto next);loop:p=p+1;printp," =",a,b,c;next:a++;if(a<15, goto4,0);a=1;b++;if(b<15, goto4, 0);a=1;b=1;c++;if(c<15, goto4,0)
a=1, b=2, c=3, and abc mod 7 =(1*2*3) mod 7 =6
Since are looking for a cubic polynomial, let it be ax^3 + bx^2 + cx + d = 0. So
\(a(\sqrt[3]{2} + \sqrt[3]{4})^3 + b(\sqrt[3]{2} + \sqrt[3]{4})^2 + c(\sqrt[3]{2} + \sqrt[3]{4}) + d = 0\)
This expands to
\( a (2 + 3 \sqrt[3]{2^2} \sqrt[3]{4} + 3 \sqrt[3]{2} \sqrt[3]{4^2} + 4) + b(\sqrt[3]{2^2} + 2 \sqrt[3]{2} \sqrt[3]{4} + \sqrt[3]{4^2}) + c(\sqrt[3]{2} + \sqrt[3]{4}) + d = 0\)
Expanding everything out, and comparing the coefficients, we get
a + 3b + 3c + d = 16, -6b + 3c + 3d = -24, c - 3d = 22, d = -6.
The solution to this system is a = 1, b = 3, c = 4, d = -6, so the cubic is x^3 + 3x^2 + 4x - 6.
Acute scalene triangle.
Sides: XZ = 4 XY =2sqrt(6) = 4.899 YZ = 5.464
Area: T = 9.464 Perimeter: p = 14.363 Semiperimeter: s = 7.182
Angle ∠ Y = 45° = 0.785 rad Angle ∠ Z = 60° = 1.047 rad Angle ∠ X = 75° = 1.309 rad
These are the products of the 10 numbers chosen:
(-8, -6, -4, -4, -3, -2, -2, -1, 1, 2, 2, 3, 3, 4, 4, 4, 6, 6, 8, 8, 9, 12, 12, 16) Total =>> 24
If you count the positive products, you get 16
So, the probability is: 16 / 24 = 2 / 3
Let the width of the rectangle = W The length of the rectangle = 2W + 2
2W + 2[2W + 2] = 28 2W + 4W + 4 = 28 6W = 28 - 4 =24
W = 24 / 6 = 4 m - width of the rectangle 4 x 2 + 2 = 10 m - length of the rectangle.
Let the price of an adult's ticket = A
Let the price of a child's ticket = C
11C + 3A = 122.......................(1)
6C + 4A =102........................(2)
Now, you have 2 simultaneous equations. Can you solve them?
Using the Binomial Theorem, expand (-2t + 7)^3.
-8 t^3 + 84 t^2 - 294 t + 343
