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3 years ago

Solve x2 – 8x + 15 < 0. Select the critical points for the inequality shown.

Mathematics

2 answers:

quester [9]3 years ago

4 0

Answer:

x=3,5

Explanation:

x2−8x+15=0

Try to express the terms of the equation in square form.

Adding 16 both sides of the equation,

(x2−2⋅x⋅4+42)+15=16

or,(x−4)2+15−16=0

or,(x−4)2−1=0

or,(x−4)2−12=0

This is the a2−b2=(a+b)(a−b)form.

(x−4+1)(x−4−1)=0

or,(x−3)(x−5)=0

Now, equate both the terms to zero since both of them when multiplied, give zero.

Either,

x−3=0

∴x=3

Or,

x−5=0

∴x=5

Ans:x=3,5 Hope this helpsXD...!!

olga_2 [115]3 years ago

3 0

Answer:

3<x<5

Step-by-step explanation:

an Univariate quadratic polynomial can be divided into the product of two first order equations

In this example, x2 - 8x + 15 = (x-3) * (x-5) <0

as a result. the answer is 3< x <5

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The circumference of a pizza is about 38 inches. What is the diameter of the pizza? Round to the nearest tenth if necessary

anygoal [31]

Answer:

The diameter of the pizza is 12 inches

Step-by-step explanation:

Given:

Circumference of a pizza = 38 inches

To Find:

The Diameter of the pizza =?

Solution:

Circumference:

The distance around the edge of a circle (or any curvy shape). It is a type of perimeter.

We know that the shape of the pizza is circle.

So the given circumference is circumference of a circle.

Now,

Circumference of the circle(pizza)= $2\pi r$

where r is the radius of the circle

circumference of the pizza =38

Thus

$2\pi r= 38$

$\pi r=\frac{38}{2}$

$\pi r=19$

$r=\frac{19}{3.14}$

r=6.050 inches

Now,

Diameter = $2\times r$

Diameter = $2\times 6.05$

Diameter=12.1 inches

Rounding to the nearest tenth

Diameter=12 inches

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The <em>expanded</em> expressions are shown below:

(x + 1)² = x² + 2 · x + 1
(x - 3)² = x² - 6 · x + 9
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<h3>How to expand perfect square trinomials</h3>

<em>Perfect square</em> trinomials are polynomials of grade 2 with the form (a + b)² = a² + 2 · a · b + b². In this case, we have to expand six perfect square trinomials:

a) (x + 1)² = x² + 2 · x + 1

b) (x - 3)² = x² - 6 · x + 9

c) (x + 4)² = x² + 8 · x + 16

d) (x - 1/2)² = x² - x + 1/4

e) 3 · (x - 5)² = 3 · (x² - 10 · x + 25) = 3 · x² - 30 · x + 75

f) (1/2) · (x - 2)² = (1/2) · (x² - 4 · x + 4) = (1/2) · x² - 2 · x + 2

To learn more on perfect square trinomials: brainly.com/question/385286

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3 years ago