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vfiekz [6]
3 years ago
12

The solution set for 6a^2-a-5=0

Mathematics
1 answer:
Alex_Xolod [135]3 years ago
4 0

Answer:

a=1 or a=5/6

Step-by-step explanation:

I'm going to attempt to factor 6a^2-a-5

a=6

b=-1

c=-5

Find two numbers that multiply to be a*c and add to be b.

a*c=-30                                   =-6(5)

b=-1                                          =-6+5

So replace -a with -6a+5a in the expression we started with

6a^2-6a+5a-5

now we factor by grouping

6a(a-1)+5(a-1)

(a-1)(6a-5)

Now let's solve the equation:

(a-1)(6a-5)=0

So a=1 or a=5/6

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6 0
3 years ago
Find the area of triangle DEF with vertices D(-1,2), E(3,-2) and F(-2,-2).*
Veronika [31]

Answer:

<em>The area of the triangle DEF is 10.</em>

Step-by-step explanation:

<u>Area of a Triangle:</u>

A triangle of base B and height H (both must be perpendicular) has an area of:

\displaystyle A=\frac{BH}{2}

The image below shows the triangle formed by the points DEF. It's important to notice the points E and F lie on the same horizontal line because they both have the same y-coordinate.

This fact simplifies the calculations since we can easily compute the length the of base as the difference of their x-coordinates:

B=3-(-2)=3+2=5

Being the base of a horizontal line, the height of the triangle can be calculated as the difference of y-coordinates of D and the height of that line.

H=2-(-2)=4

With these two values, we calculate the area:

\displaystyle A=\frac{5*4}{2}=10

The area of the triangle DEF is 10.

4 0
3 years ago
If the ratio of the length of a rectangle to its width is 9/4 and its length is 18 cm, what is the width of the rectangle?
Kruka [31]

Answer:

The width is 8

Step-by-step explanation:

if the ratio of length to width is 9 to 4. and we know the length is 18, 18 is 2 times as much as 9, so 4*2=8.                   9*2=18,4*2=8

6 0
3 years ago
Read 2 more answers
Find the equation of this line. y= [?]x+[?]
DochEvi [55]

Answer:

y=3x-4

Step-by-step explanation:

Hi there!

Slope-intercept form: y=mx+b where <em>m</em> is the slope and <em>b</em> is the y-intercept (the value of y when x=0)

<u>1) Determine the slope (</u><u><em>m</em></u><u>)</u>

m=\displaystyle\frac{y_2-y_1}{x_2-x_1} where two points that fall on the line are (x_1,y_1) and (x_2,y_2)

On the graph, two points are highlighted for us: (0,-4) and (2,2). Plug these into the formula:

m=\displaystyle\frac{2-(-4)}{2-0}\\\\m=\displaystyle\frac{2+4}{2}\\\\m=\displaystyle\frac{6}{2}\\\\m=3

Therefore, the slope of the line is 3. Plug this into y=mx+b:

y=3x+b

<u>2) Determine the y-intercept (</u><u><em>b</em></u><u>)</u>

y=3x+b

Recall that the y-intercept occurs when x=0. Given the point (0,-4), the y-intercept is therefore -4. Plug this into y=3x+b:

y=3x+(-4)\\y=3x-4

I hope this helps!

5 0
2 years ago
The given line passes through the points (−4, −3) and (4, 1).
dimulka [17.4K]
1+3/4+4
4/8
1/2
y-3=-2(x+4)
y - 3 = -2(x + 4)
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3 years ago
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