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This is easy if you use coordinates.

The closing speed between Mark and Trisha  is   16-12 = 4 m/hr      It will take Mark:  8 miles / 4 mi/hr = 2 hrs to catch up.

x * .40 =360      solve for 'x'

x = total fans

(x - .65x - .25x ) * .4 = 640           solve for 'x'

thank youuuu

The graph of y = f(x) is a parabola whose vertex is at (1,-2). The graph of y = f(x + 4) - 3 is also a parabola. Where is the vertex of the graph of y = f(x + 4) - 3?

Hello Guest!

The graph of  \(y=f(x)=( x-1)^2-2\) is a parabola whose vertex is at (1,-2).

The graph of y = f(x + 4) - 3 or  \(y=f(x)=(x-1{\color{blue}+4})^2-2-\color{blue}3=(x+3)^2-5\)  is also a parabola.

whose vertex  is at (-3,-5).

  !

Smaller circle center => Q

∠LOQ = ∠MOQ = 1/2(arc 78º)

∠LQO = ∠MQO = 180 - 2(39) = 102

Arc LOM = 2 * 102 = 204 degrees

Ok I explained a bit more.

Next time please comment on the original.  Answerers do not like to be ignored.

You can still put a new post to say that you have done so.

You want more hints ... ok

\(\frac{x - 7}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}\\ \frac{x - 7}{x^2 - x - 2} = \frac{A(x+1)}{(x - 2)(x+1)} + \frac{B(x-2)}{(x + 1)(x-2)} \)

I answered this qeustion a short time ago.

anyway...

Add the fractions on the right side (get a common denominator first). Then equate coefficients.

let

\(x=Z+\delta\qquad \text{where Z is an integer and }0\le\delta<1\)

\(\lceil x \rceil+\lfloor x \rfloor + x = Z+1+Z+Z+\delta\\ 3Z+\delta+1=4.8\)

and you can finish it.   Remember that Z is an integer and delta is between 0 and 1

answered

The largest possible value of b is 8.

triangle can ONLY be 1. (since 2 + 2 + 2 + 2 + 2 > 9)

so that rhombus = 5

so square  = 2

As shown in the figure, two bisectors of ABC, BE and CF, intersect at P. If EPF = 111 °, what is \(\angle A \) in degrees?

Hello Guest!

\(\dfrac{180°-\alpha }{2}+\dfrac{180°-111°}{2}\color{BrickRed}=90°\ |\ mistake!\\ 180°-\alpha +180°-111°=2\cdot 90°\\ \alpha=180° +180°-111°-2\cdot 90° \)

\(\alpha \neq69°\)

\(\frac{\angle B}{2}+\frac{\angle C}{2}+111°=180°\)

\(\frac{\angle B}{2}+\frac{\angle C}{2}=180°-111°\\ (\angle B+\angle C)=2\cdot (180°-111°)\\ (\angle B+\angle C)+\angle A=180°\\ \angle A=180°-(\angle B+\angle C)\\ \angle A=180°-2\cdot (180°-111°)\)

\(\angle A=42° \)

  !

*** EDIT ****

SInce you probably do not want leading zeroes in your 3 digit number

x 21     and   x 12   would not be on the list

48 -2 = 46 numbers    as Guest below computed

how the c**p did you get 150. the angles not even 75

102  120  123  124  125  126  127  128  129  132  142  152  162  172  182  192  201  210  213  214  215  216  217  218  219  231  241  251  261  271  281  291  312  321  412  421  512  521  612  621  712  721  812  821  912  921  >>Total permutations = 46 such numbers.

I've already tried it, but it's incorrect.