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bearhunter [10]
1 year ago
5

Write the equation of the line that passes through the points (-6,-1) and (-4,2). Put your answer in fully simplified point-slop

e form, unless it is a vertical or horizontal line.
Mathematics
1 answer:
Archy [21]1 year ago
4 0

(\stackrel{x_1}{-6}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{-4}-\underset{x_1}{(-6)}}} \implies \cfrac{2 +1}{-4 +6} \implies \cfrac{ 3 }{ 2 }

\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{\cfrac{3}{2}}(x-\stackrel{x_1}{(-6)}) \implies {\large \begin{array}{llll} y +1= \cfrac{3}{2} (x +6) \end{array}}

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The height of a rectangular prism is 3 feet. The length and width can be expressed as x-1 and x+4. If the volume of the prism is
SashulF [63]

Answer:

Step-by-step explanation:

Volume  = 198 ft

length * width * height = 198

(x - 1) * (x + 4) * 3 = 198

(x - 1) * (x + 4)  = 198/3

(x - 1) * (x + 4) = 66

x*x + x*4 -1*x - 1*4 = 66   {Use FOIL method to multiply}

x² + 4x - x - 4 = 66

x² + 3x - 4 =66

x² + 3x - 4 - 66 = 0

x² + 3x - 70 = 0

Now factorize.

x² + 10x - 7x - 7*10 = 0

x(x +10) - 7(x + 10 ) = 0

(x + 10)(x - 7) = 0

x - 7 = 0 {x + 10 is ignored because measurement cannot be in negative}

x = 7

length = x - 1 = 7 - 1 = 6ft

Width = x + 4 = 7 + 4 = 11 ft

4 0
3 years ago
The figure below shows a shaded rectangular region inside a large rectangle: (pic)
mariarad [96]

Answer:

D


Step-by-step explanation:

Probability of falling NOT in the shaded region is "area of white region" <em>divided by</em> "area of whole rectangle (big one)".


<u>Area of whole rectangle:</u>

Area of rectangle = length * width = 10 * 5 = 50


<u>Area of White Region:</u>

First, area of shaded region = length * width = 4 * 2 = 8

Now,

Area of white region = area of whole rectangle - area of shaded rectangle

Area of white region = 50 - 8 = 42


Hence, probability is \frac{42}{50}=0.84

0.84 = 84%

Answer choice D is right.





8 0
3 years ago
What is the area of the sector with a central angle of 97 degrees and a diameter of 10cm
vampirchik [111]

Answer:

21. 162 (rounded to nearest thousandth)

Step-by-step explanation:

Area of a sector: (degree/360) (pi*radius^2)

degree given= 97

radius= diameter/2 = 5

(97/360) (pi*5^2)

(97/360) (pi*25) = 21.16211718

4 0
2 years ago
Solve for y 3x+11y=-5
mars1129 [50]
\displaystyle 3x+11y=-5\quad\Big| -3x\\\\11y=-5-3x\quad\Big|:11\\\\y= -\frac{5+3x}{11}
6 0
3 years ago
Anna is in a cave 30 feet below the cave entrance. She descends 17 feet, then ascends 22 feet. Find her new position relative to
stiv31 [10]

Answer:35

Step-by-step explanation:

We add or subtract from left to right to find the value of the expression:

3

Because the result is negative, she is below the cave entrance (by 35 feet).

6 0
2 years ago
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