Tell whether f(x)=—5x^2+10x+7 has a minimum or a maximum value, find the value

The sum of two integers is -1. the product of the integers is -72 find the integers.

Elis [28]

$\left\{\begin{array}{ccc}x+y=-1\\x\ \times\ y=-72\end{array}\right\\\left\{\begin{array}{ccc}x=-y-1\\x\ \times\ y=-72\end{array}\right\\\\sunbstitute:\\\\(-y-1)y=-72\\-y^3-y+72=0\\\\a=-1;\ b=-1;\ c=72\\\Delta=b^2-4ac\to\Delta=(-1)^2-4\cdot(-1)\cdot72=1+288=289\\\\y_1=\frac{-b-\sqrt\Delta}{2a}\to y_1=\frac{1-\sqrt{289}}{2\cdot(-1)}=\frac{1-17}{-2}=\frac{-16}{-2}=8\\\\y_2=\frac{-b+\sqrt\Delta}{2a}\to y_2=\frac{1+\sqrt{289}}{2\cdot(-1)}=\frac{1+17}{-2}=\frac{18}{-2}=-9$

$
if\ y=8\ then\ x=-8-1=-9\\\\if\ y=-9\ then\ x=-(-9)-1=9-1=8\\\\Answer:8\ and\ -9.$

8 0

4 years ago

Read 2 more answers

Solvex2<br> - 4x=21 <br> using the zero product property.

Ierofanga [76]

Answer:

The answer is (x + 3) (x - 7) = 0

Step-by-step explanation:

x² - 4x = 21

x² - 4x - 21 = 0

x² - 7x + 3x - 21 = 0

x(x - 7) + 3(x - 7) = 0

(x + 3) (x - 7) = 0

Thus, The answer is (x + 3) (x - 7) = 0

<em><u>-TheUnknownScientist</u></em>

5 0

3 years ago

What substitution should be used to rewrite 6(x 5)2 5(x 5) – 4 = 0 as a quadratic equation? u = (x 5) u = (x – 5) u = (x 5)2 u =

Korolek [52]

The substitution that should be used to rewrite 6(x+5)^2 + 5(x+5) - 4 = 0 is u = x + 5

<h3>Quadratic equations</h3>

These are equations that has a leading degree of 2. Given the expression

6(x+5)^2 + 5(x+5) - 4 = 0

In order to simplify this equation, we will replace the reoccuring term by a variable.

From the equation we can see that (x+5) is occuring the most. Let u = x + 5 so that:

6u^2 - 5u - 4 = 0

Hence the substitution that should be used to rewrite 6(x+5)^2 + 5(x+5) - 4 = 0 is u = x + 5

Learn more on quadratic equation here: brainly.com/question/1214333

#SPJ4

4 0

2 years ago

The points A BC :(2, 2,1), :(1,1,3), :(2,0,5) − are the vertices of a right triangle. The radius of the sphere with center at th

ElenaW [278]

Answer:

r=1

Step-by-step explanation:

First we need to know the length of each side of the triangle, so we use the formula of the vector modulus:

$|AB|= \sqrt{(b_{1}-a_{1})^{2}+(b_{2}-a_{2})^{2}+(b_{3}-a_{3})^{2}$

By doing so, we find:

$|AB|=\sqrt {6}\\|BC|=\sqrt {6}\\|AC|=2\sqrt {5}$

With this we know that the triangle is not right, but, we assume the longest side as the hypotenuse of the problem.

As we have two equal sides, we know that the line between point |AB| and the center of the hypotenuse is perpendicular, therefore, we can calculate it using Pythagoras theorem:

$|BC|^{2}=r^{2}+(\frac{|AC|}{2})^{2}\\\\r^{2}=|BC|^{2}-(\frac{|AC|}{2})^{2}\\\\r^{2}=(\sqrt{6})^{2}- (\frac{2\sqrt{5}}{2})^{2}\\\\r^{2}=6-5=1\\r=1$

4 0

3 years ago

Help plzzzzzzzzzzzzzzzz

Alik [6]

Answer:

I think the awnser is for AOC is 120 I think

6 0

3 years ago