MATHEMATICS MIDDLE SCHOOL

I need help with 6-8

Answers

Answer 1

Answer:

Answer:

6. y² = 169x

7. y² = 12x

8. $y^(2) = (1)/(2)x$

Step-by-step explanation:

The equation of a quadratic function in vertex form is given by

(y - α)² = 4a(x - β)

Where, (α,β) is the vertex of the function and a is the distance from vertex to its focus.

6. Here, (α,β) ≡ (0,0) and a point on the equation is (1,13)

So, the equation will be y² = 4ax

⇒ 13² = 4a(1)

⇒ 4a = 169

Therefore, the original equation will be y² = 169x (Answer)

7. Here also the vertex is (0,0) and a point on the equation is (3,-6),

So, (-6)² = 4a(3)

⇒ 4a = 12

So, the equation is y² = 12x (Answer)

8. Here also the vertex is (0,0) and a point on the equation is ( $(1)/(2),(1)/(2)$ ),

So, $((1)/(2))^(2) = 4a((1)/(2))$

⇒ $4a = (1)/(2)$

So, the equation is $y^(2) = (1)/(2)x$ (Answer)

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Which pair of numbers is relatively prime? A.
12 and 25
B.
24 and 45
C.
9 and 24
D.
18 and 39

Answers

a. 3*4=12 & 5*5=25. nope
b. 12*2=24& 9*5=45. not at one
c. 3*3=9 & 12*2=24. nope
d. 9*2=18 & 3*13=39. Nada

non of them are prime numbers

2b−15>21? How do I do this and what is the answer???

Answers

2b - 15 > 21

add 15 to both sides:

2b-15+15 > 21 + 15

2b > 36

Divide both sides by 2 :

2b/2 > 36/2

2b = 36

b = 36 / 2

b > 18

hope this helps!

2b - 15 > 21

2b > 21 + 15

2b > 36

b > 18

The current temperature in Smallville is 20 degrees. This is 6 degrees less than twice the temperature that it was six hours ago. What was the temperature six hours ago?

Answers

ANSWER:

The temperature in Small ville, six hours ago was 13 degrees.

SOLUTION:

Given, current temperature in Smallville is 20 degrees.

And this is 6 degrees less than twice the temperature that it was six hours ago.

We need to find what was the temperature six hours ago.

Let the temperature six hours ago be x.

Then, 2x - 6 = 20 [ according to the given information

2x = 20 + 6

2x = 26

x = $(26)/(2)$

x = 13 degrees.

Temperature six hours ago was 13 degrees

Hence, the temperature in smallville , six hours ago was 13 degrees.

X-8=-2 what is X I think its 6 but plz tell me if I am right or wrong

Answers

add 8 to both sides x = 6

Hints: Please allow a bit more room when you write out X-8=-2:

x - 8 = -2 is easier to read.

Add 8 to both sides, obtaining x = 6. This is the answer. You are right. Next time, please share your work.

According to the Fundamental Theorem of Algebra, the graph of f(x) = x2 - 4x + 3, has roots. From the graph we can see that it has zeros.

Answers

Answer:

The graph $f(x)=x^2-4x+3$ has two zeros namely 3 and 1.

Step-by-step explanation:

Consider the given equation of graph $f(x)=x^2-4x+3$

According to the Fundamental Theorem of Algebra

For a given polynomial of degree n can have a maximum of n roots.

Thus, for the given equation $f(x)=x^2-4x+3$ the degree of polynomial is 2 , thus the function can have maximum of 2 roots.

We know at roots the value of function is 0 that is f(x) = 0,

Substitute f(x) = 0 , we get, $f(x)=x^2-4x+3=0$

This is a quadratic equation, $x^2-4x+3=0$

We first solve it manually and then check by plotting graph.

Quadratic equation can be solved using middle term splitting method,

here, -4x can be written as -x-3x,

$x^2-4x+3=0 \Rightarrow x^2-x-3x+3=0$

$\Rightarrow x(x-1)-3(x-1)=0$

$\Rightarrow (x-3)(x-1)=0$

Using zero product property, $a\cdot b=0 \Rightarrow a=0\ or \ b=0$

$\Rightarrow (x-3)=0$ or $\Rightarrow (x-1)=0$

$\Rightarrow x=3$ or $\Rightarrow x=1$

Thus, the two zero of f(x) are 3 and 1.

We can also see on graph attached below that the graph $f(x)=x^2-4x+3$ has two zeros namely 3 and 1.

Answer:

2 roots

2 zeros

Step-by-step explanation:

Number 1 I need help with confused

Answers

So these are set up into groups. you have 4 groups. you want to find 1/4 of the group and that would be 3 squares because 4 times 3 = 12

It would be 3\4 because 1/4 x 12 (or12/1)=3/4.

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