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Delvig [45]
4 years ago
6

7r-r=54 what is r? HELP!

Mathematics
1 answer:
Natasha2012 [34]4 years ago
4 0

Answer:

r =9

Step-by-step explanation:

7r-r=54

Combine like terms

6r = 54

6r/6 = 54/6

r =9

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Consider the polynomials p(x) = 3x + 27x^2 and q(x)= 2 . Find the x -coordinate(s) of the point(s) of intersection of these two
Tom [10]

Answer:

The x -coordinate(s) of the point(s) of intersection of these two polynomials are x=\frac{2}{9}\approx0.2222,\:x=-\frac{1}{3}\approx-0.3333

The sum of these x -coordinates is \frac{2}{9}+\left(-\frac{1}{3}\right)=-\frac{1}{9}

Step-by-step explanation:

The intersections of the two polynomials, p(x) and q(x), are the roots of the equation p(x) = q(x).

Thus, 3x + 27x^2=2 and we solve for x

3x+27x^2-2=2-2\\27x^2+3x-2=0\\\left(27x^2-6x\right)+\left(9x-2\right)\\3x\left(9x-2\right)+\left(9x-2\right)\\\left(9x-2\right)\left(3x+1\right)=0

Using Zero Factor Theorem: = 0 if and only if = 0 or = 0

9x-2=0\\9x=2\\x=\frac{2}{9}

3x+1=0\\3x=-1\\x=-\frac{1}{3}

The solutions are:

x=\frac{2}{9}\approx0.2222,\:x=-\frac{1}{3}\approx-0.3333

The sum of these x -coordinates is

\frac{2}{9}+\left(-\frac{1}{3}\right)=-\frac{1}{9}

We can check our work with the graph of the two polynomials.

4 0
4 years ago
Patty is 50 mi. due north of Todd. Emma is due east of Todd. The angle between the direction of the shortest distance from Emma
hammer [34]
For this it would be helpful if you draw a diagram of the situation. You will see that a right triangle can be formed from the problem. We use trigonometric functions to solve. We do as follows:

sin 40 = 50/y
tan 40 = 50/x


Solving we obtain,
x = 60 mi
y = 78 mi

Hope this answers the question. Have a nice day.
4 0
3 years ago
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Neporo4naja [7]

Answer:

assume 13 = z \\ 8 =x  \\ bc = y

by phytagorean theorem

{y}^{2}  +  {x}^{2}  = z^{2}

so

bc = y =  \sqrt{ {z}^{2}  -  {x}^{2} } =  \sqrt{169 - 64}   =  \sqrt{105}

3 0
2 years ago
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A ball is projected upward at time t = 0.0 s from a point on a roof 90 m above the ground. The ball rises, then falls and strike
kykrilka [37]
UPWARD JOURNEY
(g is -ive)
u= 80.5m/s
Height reached= u^2/2g= 324m

Height of the ball at topmost point of journey= 414m

DOWNWARD JOURNEY
(g is +ive)
u=0
We need to find the velocity at 89m from ground, which is equivalent to finding velocity at 325 m from the topmost point in downward direction.

v= √2gh= √2*10*325= 80.6= 81 m/sec(Answer)
5 0
3 years ago
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Points equal to y = - 1/2x + 5
Ulleksa [173]

Answer:

x= (-10,0)

y= (0,5)

Step-by-step explanation:

Find the x-intercepts.

Tap for more steps...

x-intercept(s):

(-10,0)

y-intercept(s):

(0,5)

7 0
3 years ago
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