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Agata [3.3K]
3 years ago
9

Factor the following Polynomial both 13 and 14

Mathematics
1 answer:
Maksim231197 [3]3 years ago
8 0
A•B=C
A•B=-21
Find factors of 21 ( it doesn't matter that it's negative ) that at up to be 4
It's 7and 3
Then put x^2+7x+3x-21 and then factor by grouping
Do the same steps for #2
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(x^(2)-11x+30)/(x^(2)-25)*(x^(2)+6x+5)/(x-5x-6) simplify the rational expression
DanielleElmas [232]
Simplify the following:
((x^2 - 11 x + 30) (x^2 + 6 x + 5))/((x^2 - 25) (x - 5 x - 6))

The factors of 5 that sum to 6 are 5 and 1. So, x^2 + 6 x + 5 = (x + 5) (x + 1):
((x + 5) (x + 1) (x^2 - 11 x + 30))/((x^2 - 25) (x - 5 x - 6))

The factors of 30 that sum to -11 are -5 and -6. So, x^2 - 11 x + 30 = (x - 5) (x - 6):
((x - 5) (x - 6) (x + 5) (x + 1))/((x^2 - 25) (x - 5 x - 6))

x - 5 x = -4 x:
((x - 5) (x - 6) (x + 5) (x + 1))/((x^2 - 25) (-4 x - 6))

Factor -2 out of -4 x - 6:
((x - 5) (x - 6) (x + 5) (x + 1))/(-2 (2 x + 3) (x^2 - 25))

x^2 - 25 = x^2 - 5^2:
((x - 5) (x - 6) (x + 5) (x + 1))/(-2 (x^2 - 5^2) (2 x + 3))

Factor the difference of two squares. x^2 - 5^2 = (x - 5) (x + 5):
((x - 5) (x - 6) (x + 5) (x + 1))/(-2(x - 5) (x + 5) (2 x + 3))

((x - 5) (x - 6) (x + 5) (x + 1))/((x - 5) (x + 5) (-2) (2 x + 3)) = ((x - 5) (x + 5))/((x - 5) (x + 5))×((x - 6) (x + 1))/(-2 (2 x + 3)) = ((x - 6) (x + 1))/(-2 (2 x + 3)):
((x - 6) (x + 1))/(-2 (2 x + 3))

Multiply numerator and denominator of ((x - 6) (x + 1))/(-2 (2 x + 3)) by -1:

Answer: (-(x - 6) (x + 1))/(2 (2 x + 3))
4 0
3 years ago
Three people pull simultaneously on a stubborn donkey. Jack pulls directly ahead of the donkey with a force of 90.5 N , Jill pul
Radda [10]

Answer:

Fn= 174.9 N : Magnitude of the net force the people exert on the donkey.

Step-by-step explanation:

We find the components of the forces in x-y-z

Force of  Jack in z   =F₁z=90.5 N in direction (+z)

Force of  Jill  in x     = F₂x= -82.3*cos45°= - 58.19 N (-x)

Force of  Jill  in y     =F₂y=-82.3*sin45°=   + 58.19 N (+y)

Force of  Jane  in x  =F₃x=125*cos45°=   + 88.4 N (+x)

Force of  Jane  in y   =F₃y=125*sin45°=   + 88.4  N (+y)

Calculating of the components of the net force the people exert on the donkey.

Fnx= F₂x+F₃x=( - 58.19+ 88.4 )N=30.2N (+x)

Fny= F₂y+F₃y=( 58.19+88.4 ) = 146.59 N (+y)

Fnz =F₁z=90.5 N  (+z)

Calculating of the magnitude of the net force the people exert on the donkey.

F_{n} =\sqrt{(F_{nx})^{2}+(F_{ny}) ^{2} +(F_{nz}) ^{2}   }

F_{n} =\sqrt{(30.2)^{2}+( 146.59) ^{2} +(90.5) ^{2}   }

F_{n} = 174.9 N

7 0
3 years ago
Multiply. Write the answer in lowest terms. <br> 5/7 x 11/7 x 5/6
marusya05 [52]
Hi

5/7 × 11/7 × 5/6 = 55/49 × 5/6 = 275/294

5/7 × 11/7 = (5×11)/(7×7) = 55/49
55/49 × 5/6 = (55×5)/(49×6) = 275/294 (irreducible)

Answer: 275/294
6 0
3 years ago
Read 2 more answers
What is the equation of the following graph?
dangina [55]

There are a couple of different ways you could do this, but I'll show the simpler way. We will use the formula

y=a(x-h)^2+k

along with the fact that the vertex has h and k coordinates of 1 and 4 respectively, and that a point on the graph is (3, 5). We could have used any point on the graph where there is a definite integer coordinate pair. We will fill in accordingly and solve for a.

5=a(3-1)^2+4 and

5 = 4a + 4. If we subtract 4 from both sides we get that a=\frac{1}{4}. Now we will fill in the formula and expand as needed:

y=\frac{1}{4}(x-1)^2+4 and

y=\frac{1}{4}(x^2-2x+1)+4. If we distribute the 1/4 in and then add the constants the final equation for that graph will be

y=\frac{1}{4}x^2-\frac{1}{2}x+\frac{17}{4}

7 0
3 years ago
Which ordered pair is a solution of the equation?
uysha [10]
Only b

apply -1 to x and it will give you y=-5


5 0
3 years ago
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