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3 years ago

Solve by graphing y= -4x+5 y=3x-2

1 answer:

4 0

Y = -4x + 5
y = 3x - 2

-4x + 5 = 3x - 2
+ 4x    + 4x
   5 = 7x - 2
      + 2 + 2
   7 = 7x
   7    7
   1 = x
   y = -4x + 5
   y = -4(1) + 5
   y = -4 + 5
   y = 1
   (x, y) = (1, 1)

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Half a number increased by 15 is equal to the sum of 5 and the product of 3 and the number.

son4ous [18]

Answer:

(x/2) + 15 = 5 + 3x

Step-by-step explanation:

Follow the steps in the equation. X is your number. First you halve it, then you add 15. Next, set it equal to the other side. The second side is 5 + (because it is the sum) and 3x (the product of 3 and x means multiply them)

3 0

3 years ago

Polynomial equation when zeros are -4, -2, 1, 4

jek_recluse [69]

<h2>The required poynomial equation is $x^{4}+x^{3}-18x^{2}-16x+32$ .</h2>

Step-by-step explanation:

Given,

The zeros of the polynomial are - 4, - 2, 1 and 4

To find, the polynomial equation = ?

We know that,

The polynomial equation = (x - A)(x - B)(x - C)(x - D)

= (x + 4)(x + 2)(x - 1)(x - 4)

= [(x + 4)(x - 4)] [(x + 2)(x - 1)]

= ( $x^{2}-16$ )( $x^2-x+2x-2$ )

= ( $x^{2}-16$ )( $x^2+x-2$ )

= $x^{4}+x^{3}-2x^{2}-16x^{2}-16x+32$

= $x^{4}+x^{3}-18x^{2}-16x+32$

Thus, the required poynomial equation is $x^{4}+x^{3}-18x^{2}-16x+32$ .

4 0

3 years ago

Given a triangle MTN, prove that

cupoosta [38]

Answer:

$\angle m + \angle t + \angle n = 180$

Step-by-step explanation:

Required

Show that:

$\angle m + \angle t + \angle n = 180^o$

To make the proof easier, I've added a screenshot of the triangle.

We make use of alternate angles to complete the proof.

In the attached triangle, the two angles beside $\angle m$ are alternate to $\angle t$ and $\angle n$

i.e.

$\angle 1 = \angle t$

$\angle 2 = \angle n$

Using angle on a straight line theorem, we have:

$\angle 1 + \angle m + \angle 2 = 180$

Substitute values for (1) and (2)

$\angle t + \angle m + \angle n = 180$

Rewrite as:

$\angle m + \angle t + \angle n = 180$ -- proved

5 0

3 years ago

6^7/6^5 in index form help me

brilliants [131]

Answer:

12^12

Step-by-step explanation:

can u please help me

7 0

3 years ago

Solve the following quadratics. State the FACTORS AND SOLUTIONS. 1. 2x^2 - 7x + 3 2. 3x^2 + 7x +2

tekilochka [14]

Answer:

1. x = 3, 1/2 (solutions); (x - 3)(2x - 1) (factors)

2. x = -1/3, -2 (solutions); (3x + 1)(x + 2) (factors)

Step-by-step explanation:

1. 2x^2 - 7x + 3

To solve problem 1, you will need to identify your a, b, and c values in this quadratic function.

Since this problem is in standard form, it will be easy to identify these values. The standard form of a quadratic function is ax^2 + bx + c.

The a value is 2, the b value is -7, and the c value is 3 if we use our standard form and see which numbers are plugged into it.

Since we know that

a = 2
b = -7
c = 3

we can use the quadratic formula: $x = \frac{-b~\pm~\sqrt{b^2~-~4ac} }{2a}$

Substitute the a, b, and c values into the quadratic formula: $x=\frac{-(-7)\pm\sqrt{(-7)^2-4(2)(3)} }{2(2)}$

Now simplify using the laws of pemdas: $x=\frac{7\pm\sqrt{(49)-(24)} }{4}$

Simplify even further: $x=\frac{7\pm\sqrt{(25)} }{4} \rightarrow x=\frac{7\pm (5) }{4}$

Now split this equation into two equations to solve for x: $x=\frac{12 }{4} ~~and~~ x=\frac{2 }{4}$

12/4 can be simplified to 3, and 2/4 can be simplified to 1/2.

This means your solutions to problem 1 is 3, 1/2.

$\boxed {x=3,\frac{1}{2} }$

There is also another way to solve for the quadratic functions, and this was by factoring.

If you factor 2x^2 - 7x + 3 using the bottoms-up method, you will get (x - 3)(2x - 1).

After factoring, solving for the solutions is simple because all you have to do is set each factor to 0.

x - 3 = 0
2x - 1 = 0

After solving for x by adding 3 to both sides, or by adding 1 to both sides then dividing by 2, you will end up with the same solutions: x = 3 and x = 1/2.

2. 3x^2 + 7x + 2

To save time I'll be using the bottoms-up factoring method, but remember to refer back to problem 1 (quadratic formula) if you prefer that method.

Factor this quadratic function using the bottoms-up method. After factoring you will have (3x + 1)(x + 2). These are your factors.

Now to solve for x and find the solutions of the quadratic function, you will set both factors equal to 0.

3x + 1 = 0
x + 2 = 0

Solve.

First factor: 3x + 1 = 0

Subtract 1 from both sides.

3x = -1

Divide both sides by 3.

x = -1/3

Second factor: x + 2 = 0

Subtract 2 from both sides.

x = -2

Your solutions are x = -1/3 and x = -2.

$\boxed {x = -\frac{1}{3} , -2}$

7 0

3 years ago