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kykrilka [37]
3 years ago
13

Find the y and x-intercept for -x+3y+3

Mathematics
2 answers:
Darya [45]3 years ago
6 0
-x+3y+3=0 <-- This puts the expression into an equation to make it solvable.
3y+3=x  <-- Use Addition Property of Exponents to move the (x) to the right
3y=x-3 <-- Use Subtraction Property of Exponents to move the (3) to the right
y=\frac{1}{3}-1 <-- Use Division Property of Exponents to remove the 3 from y
y=\frac{1}{3}-1 < This is the equation for the y-intercept

-x+3y+3=0 <-- Same as above, makes it so the expression is an equation to solve
-x+3=-3y <-- Use Subtraction Property of Exponents to move the 3y to the right
-x=-3y-3 <-- Use Subtraction Property of Exponents to move the 3 to the right
x=3y+3 <--Use Divison Property of Exponents to remove the -1 from x
x=3y+3 <-- This is the equation for the x-intercept

Hope this helped!


11111nata11111 [884]3 years ago
5 0
Use y=mx+b
M=Slope
X= Point on x-axis
And y= point in y-axis
So ....... y is 3 x is -1
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why do we need imaginary numbers?explain how can we expand (a+ib)^5. finally provide the expanded solution of (a+ib)^5.(write a
zheka24 [161]

Answer:

a. We need imaginary numbers to be able to solve equations which have the square-root of a negative number as part of the solution.

b. (a + ib)⁵ = a⁵ + 5ia⁴b - 10a³b² - 10ia²b³ + 5ab⁴ + ib⁵

Step-by-step explanation:

a. Why do we need imaginary numbers?

We need imaginary numbers to be able to solve equations which have the square-root of a negative number as part of the solution. For example, the equation of the form x² + 2x + 1 = 0 has the solution (x - 1)(x + 1) = 0 , x = 1 twice. The equation x² + 1 = 0 has the solution x² = -1 ⇒ x = √-1. Since we cannot find the square-root of a negative number, the identity i = √-1 was developed to be the solution to the problem of solving quadratic equations which have the square-root of a negative number.

b. Expand (a + ib)⁵

(a + ib)⁵ =  (a + ib)(a + ib)⁴ = (a + ib)(a + ib)²(a + ib)²

(a + ib)² = (a + ib)(a + ib) = a² + 2iab + (ib)² = a² + 2iab - b²

(a + ib)²(a + ib)² = (a² + 2iab - b²)(a² + 2iab - b²)

= a⁴ + 2ia³b - a²b² + 2ia³b + (2iab)² - 2iab³ - a²b² - 2iab³ + b⁴

= a⁴ + 2ia³b - a²b² + 2ia³b - 4a²b² - 2iab³ - a²b² - 2iab³ + b⁴

collecting like terms, we have

= a⁴ + 2ia³b + 2ia³b - a²b² - 4a²b² - a²b² - 2iab³  - 2iab³ + b⁴

= a⁴ + 4ia³b - 6a²b² - 4iab³ + b⁴

(a + ib)(a + ib)⁴ = (a + ib)(a⁴ + 4ia³b - 6a²b² - 4iab³ + b⁴)

= a⁵ + 4ia⁴b - 6a³b² - 4ia²b³ + ab⁴ + ia⁴b + 4i²a³b² - 6ia²b³ - 4i²ab⁴ + ib⁵

= a⁵ + 4ia⁴b - 6a³b² - 4ia²b³ + ab⁴ + ia⁴b - 4a³b² - 6ia²b³ + 4ab⁴ + ib⁵

collecting like terms, we have

= a⁵ + 4ia⁴b + ia⁴b - 6a³b² - 4a³b² - 4ia²b³ - 6ia²b³ + ab⁴ + 4ab⁴ + ib⁵

= a⁵ + 5ia⁴b - 10a³b² - 10ia²b³ + 5ab⁴ + ib⁵

So, (a + ib)⁵ = a⁵ + 5ia⁴b - 10a³b² - 10ia²b³ + 5ab⁴ + ib⁵

5 0
3 years ago
Evaluate the following expression. [4 + (12 - 2) ÷ 5] ÷ 7
Anika [276]

Answer:

[4 + (12 - 2) ÷ 5] ÷ 7

[4 + 6 / 5] / 7

[10 / 5] / 7

2 / 7

= 2/7 or 0.28571428571

7 0
2 years ago
Read 2 more answers
EMERGENCY, EMERGENCY, I WILL GIVE BRAINLIEST
AlekseyPX
First you must distribute the 1/4 to get
: 1/2x^2-3=15
then you have to add three to both sides so it become
: 1/2x^2=18
then divide by 1/2 to get
:x^2 =36
then take the square root to get a final answer of
:x=6
8 0
2 years ago
William made 100 cupcakes this week. He baked 4 more than three times the total she made last week. Write an equation to find ou
evablogger [386]
I believe the answer is B.

It says that he made 100 cupcakes so we know that the total is 100. It says he baked 4 more than so that means that we are adding 4 to some value. It also says that he baked 3 times the total of cupcakes he made last week. Since the total for last week is unknown, we can express that as x.

So, your equation would be 3x+4=100.

Hope this helps!
5 0
2 years ago
The diagram below shows 5 identical bowls stacked one inside the other. The height of 1 bowl is 2 inches. The height of 5 bowls
padilas [110]

(Bowls, Height) (1, 2)  (5,5)

Slope is (5-2)/(5-1) = 3/4 inch
y = (3/4)x + b
(2) = (3/4)(1) + b
(2)-(3/4) = b

B=1.25.  Y= 0.75*x + 1.25. 

Part B
X is the number of bowls in the stack and Y is the corresponding height of the stack.

 

7 0
3 years ago
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