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3 years ago

PLease hurry! i need it! And the testing thing is happening, so before 6 pm?

Mathematics

1 answer:

ololo11 [35]3 years ago

8 0

$\begin{cases} -x+3y=9\\\\ y=\cfrac{2}{3}x \end{cases} \\\\[-0.35em] ~\dotfill\\\\ -x+3y=9\implies 3y=9+x\implies \underline{3y-9=x} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{substituting ont the 2nd equation}}{y=\cfrac{2}{3}(\underline{3y-9})\implies 3y=2(3y-9)}\implies 3y=6y-18\implies 18+3y=6y \\\\\\ 18=3y\implies \cfrac{18}{3}=y\implies \boxed{6=y}$

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Which function has a vertex on the y-axis? f(x) = (x – 2)2 f(x) = x(x + 2) f(x) = (x – 2)(x + 2) f(x) = (x + 1)(x – 2)

strojnjashka [21]

we know that

If the vertex is on the y-axis, then the x-coordinate of the vertex is equal to zero

we are going to verify the vertex of each one of the functions to determine the solution

Remember that

The equation in vertex form of a vertical parabola is equal to

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

where

(h,k) is the vertex

if $a>0$ -------> the parabola open upward (vertex is a minimum)

if $a$ -------> the parabola open downward (vertex is a maximun)

case A) $f(x)=(x-2)^{2}$

This is a vertical parabola open upward

the vertex is the point $(2,0)$

therefore

The function $f(x)=(x-2)^{2}$ does not have a vertex on the y-axis

case B) $f(x)=x(x+2)$

$f(x)=x(x+2)=x^{2}+2x$

convert to vertex form

Complete the square. Remember to balance the equation by adding the same constants to each side.

$f(x)+1=x^{2}+2x+1$

Rewrite as perfect squares

$f(x)+1=(x+1)^{2}$

$f(x)=(x+1)^{2}-1$

the vertex is the point $(-1,-1)$

therefore

The function $f(x)=x(x+2)$ does not have a vertex on the y-axis

case C) $f(x)=(x-2)(x+2)$

$f(x)=(x-2)(x+2)=x^{2}-2^{2}$

$f(x)=x^{2}-4$

the vertex is the point $(0,-4)$

The x-coordinate of the vertex is equal to zero

therefore

The function $f(x)=(x-2)(x+2)$ has a vertex on the y-axis

case D) $f(x)=(x+1)(x-2)$

$f(x)=(x+1)(x-2)\\ \\f(x)= x^{2}-2x+x-2 \\ \\f(x)= x^{2} -x-2$

convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)+2= x^{2} -x$

Complete the square. Remember to balance the equation by adding the same constants to each side.

$f(x)+2+0.25= x^{2} -x+0.25$

$f(x)+2.25= x^{2} -x+0.25$

Rewrite as perfect squares

$f(x)+2.25= (x-0.50)^{2}$

$f(x)=(x-0.50)^{2}-2.25$

the vertex is the point $(0.5,-2.25)$

therefore

The function $f(x)=(x+1)(x-2)$ does not have a vertex on the y-axis

the answer is

$f(x)=(x-2)(x+2)$

6 0

3 years ago

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Use prime factorization to find gcf of 57 and 27

Vadim26 [7]

Gcf (57,27) = 57×27/lcm(57,27)=1539/513 = 3

4 0

3 years ago

Find the slope of the line that passes through the pair points (4,5) (10,0)

barxatty [35]

Answer:

m= -5/6

Step-by-step explanation:

8 0

3 years ago

Hi can someone help me with these? 5 and 6 only though

cestrela7 [59]

Answer:

5) 2z - 15 = 9

2z.=9+15

2z =24

z =12

6) 4x-2 = 62°

4x=62°+2°

4x=64°

x=16

6 0

2 years ago

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A circle graph titled Bachelor's Degrees Earned in the United States from 2009 to 2010. 22 percent is business, 10 percent is so

Helga [31]

Answer:

a) 60 graduates

b) Business and social science.

Step-by-step explanation:

In United States, from 2009 to 2010 the Bachelor's Degrees graduates are made up of 22% for business, 10% for social science, 8% is health related, 6% is education and 54% is others. Given that a sample of 1000 college graduates where used,

a) Number of graduates with education degree is equal to 6% of the total college graduates. Therefore:

Number of graduates with education degree = 6% × 1000 = 0.06 × 1000 = 60 graduates

b) Number of graduates with business degree = 22% × 1000 = 0.22 × 1000 = 220 graduates

Number of graduates with social science degree = 10% × 1000 = 0.1 × 1000 = 100 graduates

Number of graduates with health related degree = 8% × 1000 = 0.08 × 1000 = 80 graduates

Number of graduates with other degree = 54% × 1000 = 0.54 × 1000 = 540 graduates

Since Many graduates earn degrees in fields that result in high-paying jobs, the two fields most likely pay more than the others are that of business and social science.

8 0

3 years ago

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