suppose a parabola has an axis of symmetry at x=-2 a minimum height at -6 and passes through the point (0,10)

Let A = { x ∈ R : x 2 − 5 x + 4 ≤ 0 } , B = (3 , 5), and C = (3 , 4]. Show that A ∩ B = C . (Recall, you must show two separate

kolbaska11 [484]

Answer:

You can proceed as follows:

Step-by-step explanation:

First solve the quadratic inequality $x^{2}-5x+4\leq 0$ . To do that, factorize, then we have that $(x-4)(x-1)\leq 0$ . This implies that

$x-1\leq 0\, \text{and}\, x-4\geq 0$

or

$x-1 \geq 0\, \text{and}\, x-4\leq 0$

In the first case the solution is the empty set $\emptyset$ . In the second case the solution is the interval $1\leq x \leq 4$ . Now we have that

$A=[1,4]$

$B=(3,5)$

$C=(3,4]$ .

To show that $A\cap B\subseteq C$ consider $x\in A\cap B$ . Then $1\leq x \leq 4\, \text{and}\, 1$ , this implies that $3$ , then $x\in C$ . Now, to show that $C\subseteq A\cap B$ consider $x\in C$ , then $3$ , then $1\leq x \leq 4\, \text{and}\, 3$ , then $x\in [1,4] \, \text{and}\, x\in (3,5)$ , this implies that $x\in A\cap B$ .

Observe the image below.

7 0

3 years ago

How do u slove this and whats the answer. 2b + 9x + (2 + 5)

e-lub [12.9K]

2b + 9x +(2 + 5).

2b + 9x + 7=2b + 9x + 7

4 0

3 years ago

Determine the coordinates of the point p on the line y=-x+6 such that p is equidistant from the points a(10,-10) and o(0,0) (tha

Katena32 [7]

Solution,

Let P = ( x, -x + 6) = (x, 6 - x)

We want to solve this

( Distance from P to (0,0) )^2 = (Distance from P to (10, -10) )^2

x^2 + (6 - x)^2 = [ ( x - 10)^2 + ( 6 - x + 10)^2

x^2 + x^2 - 12x + 36 = x^2 - 20x + 100 + x^2 - 32x + 256 simplify

-12x + 36 = -52x + 356

40x = 320

x = 8

And y = -(8) + 6 = -2

So...P = ( 8, -2)

In mathematics, an equation is an equation that expresses two equations by joining them with an equal sign =. Equations in other languages and the word their relatives can have slightly different meanings; for example, in French, an equation is defined as containing one or more variables, but in English, it is an equal sign.

A well-formed expression consisting of two combined equations is an equation, and a variable makes the equation true. The variable for which the equation must be solved is also called the unknown, and the value of the unknown that satisfies the equation is called the solution of the equation. There are two types of equations: identities and constraint equations. The ID applies to all values of the variable. Constraint equations apply only to specific values of variables

Learn more about Equations here: brainly.com/question/2972832

#SPJ4

6 0

1 year ago

ANSWER BOTH OR REPORT

jeka57 [31]

437 and 250 and 422 there you goooooo

6 0

2 years ago

Help find area of this

hram777 [196]

Answer:

120 sq feet

Step-by-step explanation:

1. 8 x 10 = 80

2. 8 x 5 = 40

3. 80 + 40 = 120 ft2 (sq feet)

8 0

2 years ago