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damaskus [11]
2 years ago
8

What is the slope of the line that passes through the points (-4, -9) and (5, 3)

Mathematics
1 answer:
egoroff_w [7]2 years ago
5 0

Answer:

4/3

Step-by-step explanation:

Moving from (-4, -9) to (5, 3), x (the 'run') increases by 9 from -4 to 5, and y (the 'rise') increases by 12 from -9 to +3.  Thus, the slope of the line connecting the two points is

m = rise / run = 12/9 = 4/3

It may help to think of the change in x (9) as the horizontal leg of a right triangle and the change in y (12) as the vertical leg.  Then  

m = (vertical leg length) / (horizontal leg length) = 12/9 = 4/3

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What is the y-value of the vertex of the function f(x)=−(x−3)(x+11)? −8 −4 33 49
alisha [4.7K]

Answer:

y - value of the vertex is 49.

Step-by-step explanation:

Given function is f(x) = -(x - 3)(x + 11)

f(x) = -(x² - 3x + 11x - 33)

     = -(x² + 8x - 33)

     = -(x² + 8x + 16 - 49)

     = -[(x + 4)² - 49]

     = -(x + 4)² + 49

Comparing this equation with the vertex form of a quadratic function,

f(x) = -(x - h)² + k

Where (h, k) is the vertex of the function.

Vertex of the parabola is (-4, 49)

Therefore, y-value of the vertex is 49.

4 0
2 years ago
Read 2 more answers
What is 5 to the power of 5 - 9 (200 divided by 4) - (10x90) divided by 5 - (4 to the power of 4) x 5 + 156 - 256
yanalaym [24]

5^5-9(200/4)-(10*90)/5-4^4(5)+156-256

= 3125-9( 200/4)-(10*90)/5-(4^4)(5)+156-256

= 3125-(9)(50)- (10*90)/5-(4^4)(5)+156-256

= 3125-450- (10*90)/5-(4^4)(5)+156-256

= 2675-(10*90)/5-(4^4)(5)+156-256

= 2675 - 900/5 - (4^4)(5)+156-256

= 2675 - 180 - (4^4)(5)+156-256

= 2495 - (4^4)(5)+156-256

= 2495 - 1280 + 156 -256

= 1215 + 156 - 256

= 1371 - 256

= 1115


I hope that's help , please if you have question(s) just let me know !


6 0
2 years ago
Find the distance between the two points. Round your solution to 2 decimal points.
VashaNatasha [74]
Notice the grid, the points are (-5, -2) and (4, -1), thus

\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\ \quad \\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
%  (a,b)
&&(~{{ 4}} &,&{{ -1}}~) 
%  (c,d)
&&(~{{ -5}} &,&{{ -2}}~)
\end{array}~~
%  distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
d=\sqrt{[-5-4]^2+[-2-(-1)]^2}\implies d=\sqrt{(-5-4)^2+(-2+1)^2}
\\\\\\
d=\sqrt{(-9)^2+(-1)^2}\implies d=\sqrt{81+1}\implies d=\sqrt{82}
6 0
3 years ago
?÷(−7)=(−4) what is the missing number
Hunter-Best [27]

Answer:

The answer is 28.

Step-by-step explanation:

To find the solution, you must multiply the other two numbers together to find the original number that is divided.

-7 * -4 = 28 Answer

28/-7 = -4

Hope this helps!

3 0
3 years ago
Read 2 more answers
A vertical cylinder is leaking water at a rate of 4m3/sec. If the cylinder has a height of 10m and a radius of 2m, at what rate
Lyrx [107]

Answer:

Therefore the rate change of height is  \frac{1}{\pi} m/s.

Step-by-step explanation:

Given that a vertical cylinder is leaking water at rate of 4 m³/s.

It means the rate change of volume is 4 m³/s.

\frac{dV}{dt}=4 \ m^3/s

The radius of the cylinder remains constant with respect to time, but the height of the water label changes with respect to time.

The height of the cylinder be h(say).

The volume of a cylinder is V=\pi r^2 h

                                                 =( \pi \times 2^2\times h)\ m^3

\therefore V= 4\pi h

Differentiating with respect to t.

\frac{dV}{dt}=4\pi \frac{dh}{dt}

Putting the value \frac{dV}{dt}

\Rightarrow 4\pi \frac{dh}{dt}=4

\Rightarrow \frac{dh}{dt}=\frac{4}{4\pi}

\Rightarrow \frac{dh}{dt}=\frac{1}{\pi}

The rate change of height does not depend on the height.

Therefore the rate change of height is  \frac{1}{\pi} m/s.

3 0
2 years ago
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