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3 years ago

What is the equation of the line? Write in standard form. (4,5).

Mathematics

1 answer:

dezoksy [38]3 years ago

4 0

Answer:

$\large\boxed{5x+4y=20}$

Step-by-step explanation:

The equation of a line in slope-intercept form:

$y=mx+b$

m - slope

b - y-intercept → (0, b)

We have the x-intercept = 4 → (4, 0), and y-intercept = 5 → b = 5.

Therefore we have the equation:

$y=mx+5$

Put the coordinates of x-intercept to the equation:

$0=4m+5$ subtract 4m from both sides

$-4m=5$ divide both sides by (-4)

$m=-\dfrac{5}{4}$

Finally we have the equation of a line if slope-intercept form:

$y=-\dfrac{5}{4}x+5$

The standard form:

$Ax+By=C$

Convert:

$y=-\dfrac{5}{4}x+5$ multiply both sides by 4

$4y=-5x+20$ add 5x to both sides

$5x+4y=20$

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Answer:

$16 per hour

Step-by-step explanation:

He earns $16 per hour as shown in the figure

7 0

3 years ago

(x+3)^2+4=46 what is the solution of this equation

I am Lyosha [343]

Answer:

x = -3 + √42

Step-by-step explanation:

1) Expand the square

2) Distribute
3) Distribute

4) Distribute

5) Combine like terms

6) Add the numbers

7) Move terms to the left side

8) Subtract the numbers

9) Use the quadratic formula

10) Simplify

11) Separate the equations

12) Solve

Therefore, the solution of this equation is x = -3 + √42

4 0

2 years ago

Read 2 more answers

Show your solution follow the steps need an answer, please need an answer, please.

STatiana [176]

Answer:

Step-by-step explanation:

27 ) 2x² - x - 1 = 0

2x² - 2x + x - 1 = 0

2x ( x - 1) + (x - 1) = 0

(x - 1)(2x + 1) = 0

x - 1 = 0 ; 2x + 1 = 0

x = 1 ; 2x = -1

x = -1/2

x = 1 ; -1/2

Option b

28) Area of a rectangle = 24 cm²

length * width = 24

(3x +2 )(2x -1) = 24

3x(2x -1) + 2(2x - 1) = 24

3x *2x - 3x *1 + 2*2x - 2*1 = 24

6x² -3x + 4x - 2= 24

6x² + x - 2 -24 = 0

6x² + x - 26 = 0

6x² -12x + 13x - 26 = 0

6x(x - 2) + 13(x - 2) = 0

(x -2)(6x +13) = 0

x = 2 {Ignore 6x + 13 as it gives negative value}

length = 3x + 2 = 3*2 + 2 = 6 + 2 = 8 cm

Width = 2x - 1 = 2*2 - 1 = 4 - 1 = 3 cm

29) Area of square = 900 cm²

Side² = 900

(5x)² = 900

25x² = 900

x² = 900/25

x² = 36

x = √36 = √6*6

x = 6 cm

30) base = b cm

height = b + 2

Area of triangle = 24 cm²

$\dfrac{1}{2}base*height = 24\\\\\dfrac{1}{2}*b*(b+2) = 24\\$

b(b + 2) = 24*2

b² + 2b = 48

b² + 2b - 48 = 0

b² - 6b + 8b - 48 = 0

b(b - 6) + 8(b - 6) = 0

(b - 6) (b + 8) = 0

b - 6 = 0 {Ignore b +8 = 0 as it gives negative value}

b = 6 cm

height = 6+ 2 = 8 cm

5 0

3 years ago

If f(x)=5x+1 and g(x)=2f(x)+5 then g(-1)=

ollegr [7]

We know f(x)=5x+1. Plug in f(x) in the g(x) function.
We get $g(x)=2(5x+1)+5$ Distribute the 2 to 5x and 1.
$g(x)=10x+2+5$
Simplify to get $g(x)=10x+7$
Now, we plug in -1 for x.
$g(-1)=10(-1)+7$
$g(-1)=-10+7$
$g(-1)=-3$

4 0

3 years ago

2x^3-3x^2-11x+6 divide by x-3

Alexxx [7]

Answer: $2x^2+3x-2$

Step-by-step explanation:

You can do long division, which is very very hard to show with typing on a keyboard. You essentially want to divide the leading coefficient for each term. Ill try my best to explain it.

Do $\frac{2x^3}{x}=2x^2$ . Write 2x^2 down. Now multiply (x - 3) by it. Then subtract it from the trinomial.