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3 years ago

12

Solve n for the following preportion :

7D%7Bn%7D%20" id="TexFormula1" title=" \frac{3}{5} = \frac{12}{n} " alt=" \frac{3}{5} = \frac{12}{n} " align="absmiddle" class="latex-formula">

1 answer:

Gemiola [76]3 years ago

5 0

N=20

3 times 4 is 12. Anything u multiple the top u multiple the bottom. So 5 times 4 is 2

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Which of the following equations have complex roots?

mestny [16]

Answer:

A

Step-by-step explanation:

Complex roots of quadratic functions occur when the <u>discriminant is negative</u>.

<u>Discriminant</u>

$b^2-4ac\quad\textsf{when}\:\:ax^2+bx+c=0$

Evaluate the discriminant of each of the given equations.

$\textsf{A.} \quad 3x^2+2=0$

$\implies a=3, \quad b=0, \quad c=2$

$\implies b^2-4ac=0^2-4(3)(2)=-24$

As -24 < 0 the equation will have complex roots.

$\textsf{B.} \quad 2x^2+1=7x$

$\implies 2x^2-7x+1=0$

$\implies a=2, \quad b=-7, \quad c=1$

$\implies b^2-4ac= (-7)^2-4(2)(1)=41$

As 41 > 0 the equation does not have complex roots.

$\textsf{C.} \quad 3x^2-1=6x$

$\implies 3x^2-6x-1=0$

$\implies a=3, \quad b=-6, \quad c=-1$

$\implies b^2-4ac=(-6)^2-4(3)(-1)=48$

As 48 > 0 the equation does not have complex roots.

$\textsf{D.} \quad 2x^2-1=5x$

$\implies 2x^2-5x-1=0$

$\implies a=2, \quad b=-5, \quad c=-1$

$\implies b^2-4ac=(-5)^2-4(2)(-1)=33$

As 33 > 0 the equation does not have complex roots.

Learn more about discriminants here:

brainly.com/question/27444516

brainly.com/question/27869538

Learn more about complex roots here:

brainly.com/question/26344541

6 0

2 years ago

The axis of symmetry for the function f(x) = –2x2 + 4x + 1 is the line x = 1. Where is the vertex of the function located?

egoroff_w [7]

Answer:

(1, 3)

Step-by-step explanation:

You are given the h coordinate of the vertex as 1, but in order to find the k coordinate, you have to complete the square on the parabola. The first few steps are as follows. Set the parabola equal to 0 so you can solve for the vertex. Separate the x terms from the constant by moving the constant to the other side of the equals sign. The coefficient HAS to be a +1 (ours is a -2 so we have to factor it out). Let's start there. The first 2 steps result in this polynomial:

$-2x^2+4x=-1$ . Now we factor out the -2:

$-2(x^2-2x)=-1$ . Now we complete the square. This process is to take half the linear term, square it, and add it to both sides. Our linear term is 2x. Half of 2 is 1, and 1 squared is 1. We add 1 into the set of parenthesis. But we actually added into the parenthesis is +1(-2). The -2 out front is a multiplier and we cannot ignore it. Adding in to both sides looks like this:

$-2(x^2-2x+1)=-1-2$ . Simplifying gives us this:

$-2(x^2-2x+1)=-3$

On the left we have created a perfect square binomial which reflects the h coordinate of the vertex. Stating this binomial and moving the -3 over by addition and setting the polynomial equal to y:

$-2(x-1)^2+3=y$

From this form,

$y=-a(x-h)^2+k$

you can determine the coordinates of the vertex to be (1, 3)

5 0

3 years ago

Read 2 more answers

The table below lists the masses and volumes of several pieces of the same type of metal. There is a proportional relationship b

galben [10]

In effect, there is a proportional relationship between the mass and the volume of the pieces of metal. The equation of the line that adapts to the given data is given by: y = 0.1174x. Therefore the proportionality constant is 0.1174

8 0

3 years ago

Over the last three evenings, Diane received a total of 105 phone calls at the call center. The third evening, she received 4 ti

sergij07 [2.7K]

Answer:

Make an eqaution from here.
Let’s make evening 2 “x”

So the first evening has 9 less then the secon evening so…
x-9
Of course theres the second evening (x).

X-9+x
Then the third evening has 4 times as much as the second meeting so…
x-9+x+4x

And when solved, it has to equal 105.

So solve from here.
Combine like terms.

6x-9=105
Isolate

6x=114
x= 19

First evening is 9 less then 19, so 10.

The second evening was 19 calls.
The third evening was 4 times the second evening so, 19*4= 76

1st night = 10

2nd night= 19 calls
Thrid night= 76 calls

8 0

2 years ago

If y varies directly with x and y = 2 when x = 10, then what is the value of y when x = 40? A. 8 B. 45 C. 200 D. 320

Leto [7]

Answer:

A

Step-by-step explanation:

given that y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

to find k use the given condition y = 2 when x = 10

k = $\frac{y}{x}$ = $\frac{2}{10}$ = $\frac{1}{5}$

y = $\frac{1}{5}$ x ← equation of variation

when x = 40, then

y = $\frac{1}{5}$ × 40 = 8 → A

3 0

3 years ago

Read 2 more answers