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2 years ago

Find the equation of a line that passes through the points (1,2) and (5,6). Leave your answer in the form y=mx+c

Mathematics

1 answer:

Ainat [17]2 years ago

5 0

Answer:

y=x+1

Step-by-step explanation:

first find the slope using the two coordinates:

use the slope formula- m=y^2-y^1/x^2-x^1

6-2/5-1

=4/4

y=mx+b

now plug in one of the coordinates, and the slope we just found into the slope intercept formula

2=1(1)+b

2=1+b

subtract 1 from both sides

1=b

1=b; m=1,

y=x+1

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X+y+z=1 2x+4y+6z=2 -x+3y-5z=11

sleet_krkn [62]

x = 0 y = -x/2+2 z = -x-y+1
hope this helps fam :)

4 0

2 years ago

Find the area of the shaded polygon.

Inessa [10]

Answer:

8 square units

Step-by-step explanation:

Split the polygon into 3 triangles as pictured below

They have base and height:

4 and 3, 1 and 1, 3 and 1

Find the area of 3 triangles and add up:

A = 1/2bh

A = 1/2*4*3 + 1/2*1*1 + 1/2*1*3 = 6 + 1/2 + 3/2 = 8 square units

6 0

3 years ago

Read 2 more answers

Five widgets and three gadgets cost $109. 90.

erma4kov [3.2K]

Answer:

one gadget costs $15.80

Step-by-step explanation:

Let w = cost of one widget

Let g = cost of one gadget

Given:

Five widgets and three gadgets cost $109. 90

⇒ 5w + 3g = 109.9

Given:

One widget and four gadgets cost $75. 70

⇒ w + 4g = 75.7

Rewrite w + 4g = 75.7 to make w the subject:

⇒ w = 75.7 - 4g

Substitute into 5w + 3g = 109.9 and solve for g:

⇒ 5(75.7 - 4g) + 3g = 109.9

⇒ 378.5 - 20g + 3g = 109.9

⇒ 378.5 - 109.9 = 20g - 3g

⇒ 268.6 = 17g

⇒ g = 15.8

Therefore, one gadget costs $15.80

To find the cost of one widget, substitute the found value for g into
w = 75.7 - 4g and solve for w:

⇒ w = 75.7 - 4(15.8)

⇒ w = 75.7 - 63.2

⇒ w = 12.5

Therefore, one widget costs $12.50

5 0

2 years ago

Find the next four terms in the arithmetic sequence. a - 6, a - 2, a + 2, ...

labwork [276]

The next four terms in the sequence are a + 6, a + 10, a + 14, a + 18. This is because you are adding 4 to what is being done to “a” each time. If you look at the pattern, you’ll see that 4 is being added and the “a” stays the same.

5 0

2 years ago

An expression is shown below: 2x3y + 18xy − 10x2y − 90y Part A: Rewrite the expression by factoring out the greatest common fact

SCORPION-xisa [38]

Answer:

Part A : 2y( x³ + 9x - 5x² - 45 ), Part B : 2y( x - 5 )( x² + 9 )

Step-by-step explanation:

Part A : Let's break every term down here to their " prime factors ", and see what is common among them,

2x³y + 18xy − 10x²y − 90y -

2x³y = 2 $*$ x³ $*$ y,

18xy = 2 $*$ 3 $*$ 3 $*$ x $*$ y,

− 10x²y = 2 $*$ - 5 $*$ x² $*$ y, - so as you can see for this example I purposely broke down - 10 into 2 and - 5. I could have placed the negative on the 2, but as that value was must likely common among all the terms, I decided to place it on the 5. The same goes for " − 90y. " I placed the negative there on the 5 once more.

− 90y = 2 $*$ - 5 $*$ 3 $*$ 3 $*$ y

The terms common among each term are 2 and y. Therefore, the GCF ( greatest common factor ) is 2x. Let's now factor the expression using this value.

2y( x³ + 9x - 5x² - 45 )

Part B : Let's simply factor this entire expression. Of course starting with the " factored " expression : 2y( x³ + 9x - 5x² - 45 ),

$2y\left(x^3+9x-5x^2-45\right)$ - Factor out " $(x^3+9x-5x^2-45\right))$ " by grouping,

$\left(x^3-5x^2\right)+\left(9x-45\right)$ - Factor 9 from 9x - 45 and x² from x³ - 5x²,

$9\left(x-5\right)+x^2\left(x-5\right)$ - Factor out common term x - 5,

$\left(x-5\right)\left(x^2+9\right)$ - And our solution is thus 2y( x - 5 )( x² + 9 )

3 0

3 years ago