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2 years ago

13

Drag a statement or reason to each box to complete this proof. If 3x−4=14, then x=6.

1 answer:

Sergeu [11.5K]2 years ago

4 0

Answer:

Step-by-step explanation:

3x-4=14 x=6

3x=18

x=18

x=6

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Consider the quadratic equation x2 − 6x = 16.

e-lub [12.9K]

Answer:

C) (x − 3)2 = 25
C) Factor out 4 from 4x2 + 40x.

Step-by-step explanation:

1. Adding the square of half the x-coefficient to both sides of the equation will "complete the square." That square is 9, so the result on the right is 16+9 = 25. Only selection C matches.

___

2. To complete the square, you want to be able to put the quadratic into the form a(x -h)^2 = -k. For the purpose, it is most convenient to first factor "a" from the given quadratic. Then you can determine "-h" to be half the x-coefficient inside the parentheses.

Here, that looks like ...

4(x² +10x) = 80 . . . . . . . . . . step 1: factor out 4

4(x² +10x +25) = 180 . . . . . add 25 inside parentheses and the same number (4·25) on the right side of the equation

4(x +5)² = 180 . . . . . . . . . . . written as a square

8 0

2 years ago

Prove algebraically that r = 10/2+2sinTheta is a parabola

Xelga [282]

Answer:

$y = - \frac{ 1 }{10} {x}^{2} + \frac{5}{2}$

Step-by-step explanation:

We want to prove algebraically that:

$r = \frac{10}{2 + 2 \sin \theta}$

is a parabola.

We use the relations

${r}^{2} = {x}^{2} + {y}^{2}$

and

$y = r \sin \theta$

Before we substitute, let us rewrite the equation to get:

$r(2 + 2 \sin \theta) = 10$

Or

$r(1+ \sin \theta) = 5$

Expand :

$r+ r\sin \theta= 5$

We now substitute to get:

$\sqrt{ {x}^{2} + {y}^{2} } + y = 5$

This means that:

$\sqrt{ {x}^{2} + {y}^{2} }=5 - y$

Square:

${x}^{2} + {y}^{2} =(5 - y)^{2}$

Expand:

${x}^{2} + {y}^{2} =25 - 10y + {y}^{2}$

${x}^{2} =25 - 10y$

${x}^{2} - 25 = - 10y$

$y = - \frac{ {x}^{2} }{10} + \frac{5}{2}$

This is a parabola (0,2.5) and turns upside down.

4 0

2 years ago

19. Using clay, a student made a right circular cone of height 48cm and base

aev [14]

Answer:

fhgiignngmtotmtjfntktngigmtkgitmrjrnrkr28395027

Step-by-step explanation:

jejf ygm no fmfijfpnfimf

3 0

2 years ago

When you multiply a function by -1 what is the effect on its graph?

vlada-n [284]

Answer:

Step-by-step explanation:

Depends on what you mean by multiplying by - 1. I assume you are not going to multiply the y or f(x) term by - 1.

If that is so, take an example. Suppose you have a graph that is y=x^2

That's a parabola that opens upwards and it has a line going through its focus which is a point on the +y axis.

When you multiply the right hand side by - 1, the graph you get will be y = - x^2.

That opens downward and the focus is on the - y axis.

That means that the effect of the graph is that it flips over the x axis, which I think is the third answer.

5 0

2 years ago

What is the solution of the inequality: -6x - 17 2 8x + 25? *

nata0808 [166]

Answer:

its option 4

Step-by-step explanation:

8 0

2 years ago