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3 years ago

The axis of symmetry for the graph of the function is f(x) = 1/4x^2 + bx + 10 is x = 6. What is the value of b?

1 answer:

7 0

X-coordinate of vertex (or axis of symmetry) of a quadratic function f(x)=ax2+bx+c is given as:
x=−b2a=−b12=−2b-2b = 6 --> b=6−2=−3
b = -3

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Plz help don’t understand

saul85 [17]

Answer:

Step-by-step explanation:

every time x goes up 1, y goes up 4

x = 3 minus x = 2 is a delta (a change of 1)

x = 4 minus x = 3 is a delta (a change of 1)

x = 5 minus x = 4 is a delta (a change of 1)

the delta x is ALWAYS 1 for this table you can always substract x's to find the delta delta is symbolized by Δ Δx for the delta x

y = 7 minus y = 3 is a delta (a change of 4)

y = 11 minus y = 7 is a delta (a change of 4)

y = 15 minus y = 11 is a delta (a change of 4)

the delta y is ALWAYS 4 for this table you can always substract y's to find the delta delta is symbolized by Δ Δy for the delta y

the slope m = Δy / Δx m = 4 / 1 m = 4

y = mx + b when x = 0 then y = b (called the y intercept)

so how do we find the y intercept?

look at the pattern in the TABLE Δx and Δy

when x = 1 y = (3 - 4) = -1

x = 0 y =( -1 - 4) = -5

so y = 4x - 5 is a line equation for the data in this table

I believe there are other forms for linear equations

I chose the y-intercept form

use the point slope equation

(y - y1) = m(x - x1) where (x1, y1) are the coordinates of a point on

the line

when you know the slope of the line and a point on the line

as before

m = (y2 - y1) / (x2 - x1) from the table

= (7 - 3) / (3 - 2) still equals

= 4/1 = 4

pick a point on the line say x= 4 and y = 11 (4, 11)

(y - y1) = m(x - x1)

y - 11 = 4(x - 4) point slope form

solving point slope form for y

y - 11 = 4x - 16 add 11 to both sides

y = 4x - 5 back to the y-intercept form

7 0

3 years ago

Which point could be removed in order to make the relation a function? (–9, –8), (–{(8, 4), (0, –2), (4, 8), (0, 8), (1, 2)}

stepan [7]

We are given order pairs (–9, –8), (–{(8, 4), (0, –2), (4, 8), (0, 8), (1, 2)}.

We need to remove in order to make the relation a function.

Note: A relation is a function only if there is no any duplicate value of x coordinate for different values of y's of the given relation.

In the given order pairs, we can see that (0, –2) and (0, 8) order pairs has same x-coordinate 0.

<h3>So, we need to remove any one (0, –2) or (0, 8) to make the relation a function.</h3>

7 0

3 years ago

Read 2 more answers

-(7p+6)-2(-1-2p) what is that simplified?

charle [14.2K]

Answer:

-3p-40

Step-by-step explanation:

-(7p+6)-2(-1-2p)

-7p-42+2+4p

-3p-40

4 0

3 years ago

The perimeter of a rectangular field is 320320 yd. the length is 2020 yd longer than the width. find the dimensions.

hichkok12 [17]

The sum of length and width is half the perimeter, 160 yd. The length is the average of the sum and difference of dimensions:
.. (160 +20)/2 = 90
Then the width is 160 -90 = 70

The rectangular field is 70 yd by 90 yd.

6 0

3 years ago

At a 20th high school reunion, all the classmates were asked the number of children they had. The probability of having a partic

finlep [7]

Answer:

a) We need to check two conditions:

1) $\sum_{i=1}^n P_i = 1$

$0.05+0.14+0.34+0.24+0.11+0.07+0.02+0.02+0.01= 1$

2) $P_i \geq 0 , \forall i=1,2,...,n$

So we satisfy the two conditions so then we have a probability distribution

b) $P(C \geq 1)$

And we can use the complement rule and we got:

$P(C \geq 1)= 1-P(C$

c) $P(C=0) = 0.05$

d) For this case we see that the result from part b use the probability calculated from part c using the complement rule.

Step-by-step explanation:

For this case we have the following probability distribution given:

C 0 1 2 3 4 5 6 7 8

P 0.05 0.14 0.34 0.24 0.11 0.07 0.02 0.02 0.01

And we assume the following questions:

a) Verify that this is a probability distribution

We need to check two conditions:

1) $\sum_{i=1}^n P_i = 1$

$0.05+0.14+0.34+0.24+0.11+0.07+0.02+0.02+0.01= 1$

2) $P_i \geq 0 , \forall i=1,2,...,n$

So we satisfy the two conditions so then we have a probability distribution

b) What is the probability one randonmly chosen classmate has at least one child

For this case we want this probability:

$P(C \geq 1)$

And we can use the complement rule and we got:

$P(C \geq 1)= 1-P(C$

c) What is the probability one randonmly chosen classmate has no children

For this case we want this probability:

$P(C=0) = 0.05$

d) Look at the answers for parts b and c and explain their relationship

For this case we see that the result from part b use the probability calculated from part c using the complement rule.

5 0

3 years ago