For each function below, choose the correct description of its graph.

Answers

Answer 1

Answer:

The nature of graph of each function is given below.

What is the general equation of a Parabola? What is the general equation of a straight line?

A parabola is a curve which forms by joining all the points which are at an equal distance from a fixed point (the focus) and a fixed straight line (the directrix). The general equation of a parabola is -

y = ax² + bx + c

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

Given is a table with some functions.

[A] -

g(x) = - 4x - 5

m = - 4

Line with a negative slope.

[B] -

k(x) = 5

y = 5

A horizontal line parallel to [x] - axis

[C] -

f(x) = - 4x² + 2x + 3

A parabola opening down.

Therefore, the nature of graph of each function is given above.

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Answer 2

Answer:

Answer:

1. line with a positive slope

2. Vertical line

3. Porabola opening down

Step-by-step explanation:

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Find the value 1/2+1/3+1/4=
plz answer step by step
i will give you 5 star

Answers

Answer:

$(13)/(12)$

Step-by-step explanation:

Find the LCM of 2, 3, 4: 12
Alter the numerators to fit the denominators (steps not shown): $(6)/(12) + (4)/(12) + (3)/(12)$
$(6)/(12) + (4)/(12) + (3)/(12) = (13)/(12)$

I hope this helps!

find the first,fourth,and tenth terms of the arithmetic sequence described by the given rule. A(n)=5+(n-1)(1/6)

Answers

Answer:

First term is 5

Fourth term is 5.5

Tenth term is 6.5

Step-by-step explanation:

Given :The rule as $A(n)=5+(n-1)((1)/(6))$

We have to find find the first,fourth,and tenth terms of the arithmetic sequence.

Consider the given rule ,

$A(n)=5+(n-1)((1)/(6))$

For first term , put n = 1

$A(1)=5+(1-1)((1)/(6))$

Simplify , we have,

$A(1)=5$

For fourth term, Put n = 4

we have,

$A(4)=5+(4-1)((1)/(6))$

Simplify, we have,

$A(4)=5+(3)((1)/(6))$

$A(4)=5+(1)/(2)=5.5$

For tenth term, put n = 10 ,

We have,

$A(10)=5+(10-1)((1)/(6))$

$A(10)=5+(9)((1)/(6))$

$A(4)=5+(3)/(2)=6.5$

Thus, First term is 5

Fourth term is 5.5

Tenth term is 6.5

a₁ = 5 an = a₁ + ( n-1) * r
wyliczymy jednak - so we enumerate
a₁ = 5 + (1-1) * (1/6) = 5 + 0* 1/6 = 5 + 0 = 5
a₄ = 5 + (4 - 1) * (1/6) = 5 + 3 * (1/6) = 5 + 3/6 =5 1/2 = 5,5
a₁₀ = 5 + (10 - 1) * (1/6) = 5 + 9 * (1/6) = 5 + (9/6) = 5 + 3/2 = 6 1/2 = 6,5

The area of a square is found by squaring one of its sides, (A = s2). A certain square has an area of z2 + 18z + 81. Factor the trinomial to find a side of the square.a. side = z + 27
b. side = z + 18
c. side = z + 9

Answers

A = s²
A = z² + 18 z + 81
z² + 18 z + 81 = z² + 9 z + 9 z + 81 = z ( z + 9 ) + 9 ( z + 9 ) =
= ( z + 9 ) ( z + 9 ) = ( z + 9 )²
Answer:
C ) side = z + 9

Answer:

option c is correct.

side = z+9

Step-by-step explanation:

Area of a square(A) is given by:

$A = s^2$

where,

s is the side of the square.

As per the statement:

A certain square has an area of $z^2 + 18z + 81.$

⇒ $A = z^2 + 18z + 81$

Substitute in [1] we have;

$z^2 + 18z + 81 = s^2$

Taking square root both sides we have;

$√(z^2 + 18z + 81) =s$

Using identity rule:

$(a+b)^2 =a^2+2ab+b^2$

then;

$√(z^2 + 2(1)(9)z + 9^2) =s$

⇒ $√((z+9)^2) =s$

Simplify:

$z+9 = s$

s = z+9

Therefore, a side of the square. is, z+9

Unknown g (x) = ax + b and g (g (x)) = 16x - 15. Calculate the value of a and b.

Answers

g(g(x))=16x-15
means that when you subsituted g(x) for x in g(x), you got 16x-15

a(ax+b)+b=16x-15
distribute
xa^2+ab+b=16x-15d
we look at the x terms
therefor
xa^2=16x
a^2=16
a=-4 or 4
we will find out

look a constant terms
ab+b=-15
undistribute b
b(a+1)=-15

if a is -4 then
b(-4+1)=-15
b(-3)=-15
b=5

if a=4 then
b(4+1)=-15
b(5)=-15
b=-3

so
g(x)=-4x+5 or
g(x)=4x-3

if a=-4, b=5
if a=4, b=-3

Evaluate 10 + 8 ÷ 2 − 4.

10
5
6
14

Answers

the rank of ( divide and multiply) is higher than ( summation and subtraction ) so we divide 8/2 first
10+(8/2)-4
10+4-4= 10

Hi Brainiac

10+8 ÷ 2-4

10+4-4

= 14-4

= 10

I hope that's help:)

What is the range of possible sizes for side x? it is a triangle with one side having 4.0, and the other having 5.6. picture attached below, thanks in advance :)

Answers

Given:

Given that the two sides of the triangle are x, 4.0 and 5.6

We need to determine the range of possible sizes for the side x.

Range of x:

The range of x can be determined using the triangle inequality theorem.

The triangle inequality theorem states that, "if any side of a triangle must be shorter than the other two sides added together".

Thus, applying the theorem, we have;

$x=4.0+5.6$

$x=9.6$

Also, the the triangle inequality theorem states that, "the third side must be also larger than the difference between the other two sides".

Thus, we have;

$x=5.6-4.0$

$x=1.6$

Thus, the range of possible values for x are $1.6<x<9.6$

Final answer:

In accordance with the triangle inequality theorem, the range for the length of the third side (x) in a triangle with sides of 4.0 and 5.6 is greater than 1.6 but less than 9.6.

Explanation:

In the field of Mathematics, specifically geometry, to find the range of possible lengths of a side of a triangle, you need to understand the triangle inequality theorem. The triangle inequality theorem states that the length of a side of a triangle must be less than the sum of the lengths of the other two sides, but more than the absolute difference.

Given you have two sides, 4.0 and 5.6, the possible length for side x should be less than (4.0 + 5.6 = 9.6) and greater than the absolute difference (5.6 - 4.0 = 1.6). So, the range for side x should be 1.6 < x < 9.6.

Learn more about Triangle Inequality Theorem

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