What is the x-intercept of the line with the equation 4x 2y = 12?

Answers

Answer 1

Answer: x-int:let y=0
4x+2(0)=12
4x=12
divide both side by 4
threfore x=3 from what I found

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Find the length of side a. Round to the nearest tenth.A) 12

B) 378.4

C) 18.3

D) 19.5

Answers

Answer:

D) 19.5

Step-by-step explanation:

The law of cosines gives you the relation ...

a² = b² + c² - 2bc·cos(A)

Substituting the given values, you have ...

a² = 13² + 11² - 2·13·11·cos(108°) ≈ 378.379

a ≈ √378.379 ≈ 19.452 . . . . take the square root

a ≈ 19.5

The function f(x) = −x^2 + 48x − 432 models the profit, in dollars, a game developer makes for selling a new game, where x is the number of games sold and f(x) is the amount of profit.Part A: Determine the vertex. What does this calculation mean in the context of the problem? (5 points)

Part B: Determine the x-intercepts. What do these values mean in the context of the problem?

Answers

f(x) = −x^2 + 48x − 432

Part A

Find the zeros:

−x^2 + 48x − 432 = 0

x^2 - 48x + 432 = 0

Factor

(x - 36 ) (x - 12 )=0

Two solutions: x = 36 and x = 12

The vertex is in x = (36 +12 )/ 2 = 24

f(24) = -(24)^2 + 48(24) − 432 = 144

The vertex is (24, 144).

Given that the coefficient of x^2 is negative, the parabole opens downward, that mean that the vertex is a maximum value.

In the context of the problem that means that the maximum profit is 144 and is obtainded when the number of games sold is 24.

Part B.

The x-intercepts are the values of x when y=0. Which we calculated above.

They are x = 24 and x = 36.

Those values are the number of games for which the profit is zero.

Write an algebraic expression for two fifths the cube of a number

Answers

n - the number

$(2)/(5)n^3$

In two or more complete sentences, explain the theorem used in solving for the range of possible lengths of the third side, AB of triangle ABC

Answers

Answer:

Step-by-step explanation:

In triangle if two sides are known and included angle is known we can use cosine formula as follows:

Say in a triangle, sides a,b are known and also included angle C

Then the third side

$c^(2) =a^(2)+b^(2) -2abCos C$

Since all values on right side are known, we can find the third side c easily.

Case II:

If alternately two sides and one angle not included is known. i.e we know a,b and either angle A or B.

then to find third side we use sine formula.

$(a)/(sinA)=(b)/(sinB) =(c)/(sinC)$

Using the above we can find the unknonwn side c easily.

You can use the Pythagorean Theorem to find the length of the third side AB (Identified as "x" in the figure attached in the problem), which says that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the legs:
a² = b²+c²
As we can see the figure, the triangle does not have an angle of 90°, but it can be divided into two equal parts, leaving two triangles with a right angle. We already have the values of the hypotenuse and a leg in triangle "A" , so we can find the value of the other leg:
b = √(a²-c²) b = √(10²-4²) b = 9.16
With these values, we can find the hypotenuse in the triangle "B": x = √b²+c² x = √(9.16)²+(4)² x = 10

The following graph shows a proportionality between y and x in the graph ?

Answers

Answer:

3/1 is the ans

Step-by-step explanation:

here y is in 3

and x is in 1

so proportonality will be 3/1

Which correctly describes how the graph of the inequality 5x + 2y ≥ 13 is shaded? (1 point) Above the solid line Below the solid line Above the dashed line Below the dashed line

Answers

Answer:

The graph of inequality $5x+2y\geq 13$ is above the solid line.

Step-by-step explanation:

Step-by-step explanation:

An inequality on a coordinate plane consist of a boundary line and an area in which each point is a possible solution.

* If the inequality has a sign or , then the line will be a solid line and its point are included in the solution.

* If the inequality has a sign '>' or '<' , then the line will be a dotted line and its point are not included in the solution.

Given: The linear inequality: $5x+2y\geq 13$

Then, the equation of the boundary line is; 5x+2y =13 ......[1]

we can write this as;

$2y = -5x+13$

Divide by 2 we get;

$y = -(5)/(2) x + (13)/(2)$ ......[2]

Compare this boundary line equation with the general point slope intercept line i.e, y = mx+b where m is the slope and b is the y-intercept.

Therefore, the slope of the this line is, m = $-(5)/(2)$

and a y-intercept (b) = $(13)/(2)$ = 6.5

To find x -intercept:

Substitute y =0 in to solve for x;

$5x+0 =13$

Simplify:

$x =(13)/(5) = 2.6$

Therefore, the x-intercept is 2.6

Now,

Plot $y = -(5)/(2) x + (13)/(2)$ ( as a solid line because $y\geq$ included equal to)

and shade the area above as $5x+2y\geq 13$ as shown below in the graph

The answer is above the solid line.
Tip: On problems like these, go to the website, desmos.com, press the big red button that says "Start Graphing", and you can graph any equation by typing it in on the side and it show you the graph to get the answer!

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