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3 years ago

Georgia buys 4 books online. Each book is the same price. She has a discount code

Mathematics

1 answer:

dybincka [34]3 years ago

7 0

Without the discount each book is 16.25 with the discount theyre 15 each

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A ladder 25 feet long is placed so that it’s top reaches 24 feet up the side of the house. How far from the house is the bottom

marishachu [46]

Use Pythagoras theorem

25^2 = 24^2 + x^2

x^2 = 25^2 - 24^2

x^2 = 49
x = 7 feet Answer

8 0

3 years ago

At noon, ship A is 150 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 30 km/h. How fast is

Marrrta [24]

Answer:

150 km/h

Step-by-step explanation:

because it's then 2 together

4 0

3 years ago

20 POINTS!!!!

Nata [24]

Answer:

0.5+3.7 =4.2

You meant translate into numbers, correct?

5 0

3 years ago

The equation a<img src="https://tex.z-dn.net/?f=x%5E%7B2%7D" id="TexFormula1" title="x^{2}" alt="x^{2}" align="absmiddle" class=

andrezito [222]

Answer:

$\displaystyle \left(\alpha+1\right)\left(\beta + 1\right) = \frac{a+c-b}{a}\:\: \left(\text{ or } 1+\frac{c-b}{a}\right)$

Step-by-step explanation:

We are given the equation:

$ax^2+bx+c=0$

Which has roots α and β.

And we want to express (α + 1)(β + 1) in terms of a, b, and c.

From the quadratic formula, we know that the two solutions to our equation are:

$\displaystyle x_1 = \frac{-b+\sqrt{b^2-4ac}}{2a}\text{ and } x_2=\frac{-b-\sqrt{b^2-4ac}}{2a}$

Let x₁ = α and x₂ = β. Substitute:

$\displaystyle \left(\frac{-b+\sqrt{b^2-4ac}}{2a} + 1\right) \left(\frac{-b-\sqrt{b^2-4ac}}{2a}+1\right)$

Combine fractions:

$\displaystyle =\left(\frac{-b+2a+\sqrt{b^2-4ac}}{2a} \right) \left(\frac{-b+2a-\sqrt{b^2-4ac}}{2a}\right)$

Rewrite:

$\displaystyle = \frac{\left(-b+2a+\sqrt{b^2-4ac}\right)\left(-b+2a-\sqrt{b^2-4ac}\right)}{(2a)(2a)}$

Multiply and group:

$\displaystyle = \frac{((-b+2a)+\sqrt{b^2-4ac})((-b+2a)-\sqrt{b^2-4ac})}{4a^2}$

Difference of two squares:

$\displaystyle = \frac{\overbrace{(-b+2a)^2 - (\sqrt{b^2-4ac})^2}^{(x+y)(x-y)=x^2-y^2}}{4a^2}$

Expand and simplify:

$\displaystyle = \frac{(b^2-4ab+4a^2)-(b^2-4ac)}{4a^2}$

Distribute:

$\displaystyle = \frac{(b^2-4ab+4a^2)+(-b^2+4ac)}{4a^2}$

Cancel like terms:

$\displaystyle = \frac{4a^2+4ac-4ab}{4a^2}$

Factor:

$\displaystyle =\frac{4a(a+c-b)}{4a(a)}$

Cancel. Hence:

$\displaystyle = \frac{a+c-b}{a}\:\: \left(\text{ or } 1+\frac{c-b}{a}\right)$

Therefore:

$\displaystyle \left(\alpha+1\right)\left(\beta + 1\right) = \frac{a+c-b}{a}$

4 0

3 years ago

What is the y intercept of this line y+4=-4(x-2)

Alex_Xolod [135]

Y + 4 = -4 (x - 2)

Y - INTERCEPT:
y + 4 = -4 ((0) - 2)
y + 4 = -4 (-2)
y + 4 = 8
y = 4
(0, 4)

STANDARD FORM:
Ax + By = C
y + 4 = -4x + 8
4x + y + 4 = 8
4x + y = 4

X INTERCEPT:
(0) + 4 = -4 (x - 2)
4 = -4 (x - 2)
4 = -4x +8
-4 = -4x
x = 1
(1, 0)

PERPINDICULAR LINE:
y + (1) = (1/4) (x - (5))
y + 1 = 1/4x - 5/4
-1/4x + y + 1 = -5/4
-1/4x + y = -9/4
x - 4y = 9

X INTERCEPT OF PERPINDICULAR LINE:
x - 4(0) = 9
x - 0 = 9
x = 9
(9, 0)

PARALLEL LINE:
y + (-2) = -4 (x - (0))
y - 2 = -4x + 0
4x + y - 2 = 0
4x + y = 2

ORDERED PAIR FOR PARALLEL LINE:
4(-2) + y = 2
-8 + y = 2
y = 10
(-2, 10)

4 0

3 years ago