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3 years ago

How many solutions does this linear system have?

Mathematics

1 answer:

gayaneshka [121]3 years ago

4 0

Answer:

One solution: (2.5,0)

Step-by-step explanation:

We can use substitution for the solution. Substitute y=2x-5 to -8x-4y=-20 so that you end up with -8x-8x+20=-20. Next you want to add like terms which will be -16x+20=-20, next you want isolate x by subtracting 20 from both sides and leaves you with -16x=-40. Divide -16 on both sides to fully isolate x and will leave you with x=2.5. Now substiture in 2.5 for x in y=2x-5 to get y=2(2.5)-5 which will then lead to y=0.

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given that a1=5 and a2=15 are the first two terms of a geometric sequence, determine the values of a3 and a10. Show the calculat

Alekssandra [29.7K]

a_3 is 45 and a_10 is 98415

Step-by-step explanation:

Given

a_1 = 5

a_2 = 15

First of all we have to calculate the common ratio of the sequence. The common ratio is the ratio between two consecutive terms of a geometric sequence.

So,

$r=\frac{a_2}{a_1} = \frac{15}{5} = 3$

The explicit formula for geometric sequence is:

$a_n = a_1.r^{n-1}$

Putting the value of r and a_1

$a_n = 5.(3)^{n-1}$

Putting n=3 in the explicit formula

$a_3 =5.3^{3-1}\\= 5 * 3^2\\=5 * 9\\= 45$

Putting n=10 for tenth term

$a_{10} =5.3^{10-1}\\=5*3^9\\=5 * 19683\\=98415$

Hence,

a_3 is 45 and a_10 is 98415

Keywords: Geometric sequence, Explicit formula

Learn more about geometric sequence at:

#LearnwithBrainly

7 0

3 years ago

How do you simplify 10+6x

Ivenika [448]

Answer:

6x + 10, all ready simplified

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Help me find surface area of this shape

lozanna [386]

The triangle <span>pyramid</span> is made up of 4 triangles.

------------------------------------
Formula:
------------------------------------
Area of triangle = 1/2 x base x height

------------------------------------
Area of the bottom triangle:
------------------------------------
Area = 1/2 x 9 x 7.8
Area = 35.1 yd²

------------------------------------
Area of the 3 side triangles:
------------------------------------
Area = 3 [ 1/2 x 9 x 10 ]
Area = 135 yd²

------------------------------------
Total Area:
------------------------------------
Total Area = 135 + 35.1
Total Area = 170.1 yd²

------------------------------------------------------------------------
Answer: Surface Area = 170.1 yd².
------------------------------------------------------------------------

4 0

3 years ago

What is the slope-intercept equation of this line?

levacccp [35]

Answer:

y=-2x+8

Step-by-step explanation:

Slope=-2

Y intercept= 8

4 0

3 years ago

a line passes through (9, –9) and (10, –5).write an equation for the line in point-slope form. rewrite the equation in standard

Cerrena [4.2K]

The equation of the line in point-slope form is given by:
$y-yo = m (x-xo)
$
Where,
(xo, yo): point that belongs to the line
m: slope of the line
The slope is given by:
$m = \frac{y2-y1}{x2-x1}$
Substituting values:
$m = \frac{-5-(-9)}{10-9}$
Rewriting:
$m = \frac{-5+9}{10-9}$
$m = \frac{4}{1}$
$m=4$
Now we choose an ordered pair:
$(xo, yo) = (10, -5)
$
Substituting values we have:
$y-(-5)=4(x-10)$
$y+5=4(x-10)$
We now rewrite the equation in its standard form:
$y = mx + b
$
Where,
b: cut with the y axis.
We have then:
$y = 4x - 40 - 5

y = 4x - 45$
Answer:
point-slope form:
$y+5=4(x-10)$
or
$y+9=4(x-9)$
standard form
$y = 4x- 45$

3 0

3 years ago