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3 years ago

The function f(x) = x2 + 10x – 3 written in vertex form is f(x) = (x + 5)2 – 28. What are the coordinates of the vertex?

2 answers:

5 0

The vertex of the quadratic equation is (-5, - 28). In vertex form, y = a(x - h)2<span> + </span><span>k, (h, k) is the vertex of the equation.</span>

dalvyx [7]3 years ago

5 0

Answer:

The coordinates of the vertex are $(-5,-28)$

Step-by-step explanation:

we know that

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

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

where

(h,k) is the vertex of the parabola

In this problem we have

$f(x)=(x+5)^{2}-28$

$a=1. h=-5,k=-28$

therefore

Is a vertical parabola open upward

The vertex is a minimum

The vertex is the point $(-5,-28)$

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Is 12/30 and 18/45 proportional, or not proportional?

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Answer:

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Step-by-step explanation:

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Explain the meaning of (0,0) on a coordinate plane

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3 years ago

At Information and Communications University: 31 female seniors were on the dean’s list 62 women were on the dean’s list who wer

inessss [21]

Step-by-step explanation:

There's a lot of information here, so first things first, let's get organized.

Let's start by assigning variable names to each group. We want the variables to be short but easy to understand.

For example, let's say the number of female seniors on the dean's list is FSD (F for female, S for senior, and D for dean's list).

FSD = 31

Sticking to this naming scheme:

FD = 62

MSD = 45

FS = 87

MS = 96

F = 275

MD = 88

M = 227

Now we can begin.

a) We want to know how many seniors there are. So all we have to do is add up all the variables with an S in them.

FSD + MSD + FS + MS

31 + 45 + 87 + 96

259

b) We want to know how many women there are. So add up all the variables with an F in them.

FSD + FD + FS + F

31 + 62 + 87 + 275

455

c) We want to know how many are on the dean's list. So add up all the variables with a D in them.

FSD + FD + MSD + MD

31 + 62 + 45 + 88

226

d) Now we want to know how many are seniors AND on the dean's list. So add up all the variables that have both an S and a D.

FSD + MSD

31 + 45

e) We want to know how many female seniors there are, so add up all the variables with both an F and an S.

FSD + FS

31 + 87

118

f) We want to know how many women were on the dean's list, so add up all the variables with both an F and a D.

FSD + FD

31 + 62

g) Finally, we want to know how many students there are total. So add up all the variables.

FSD + FD + MSD + FS + MS + F + MD + M

62 + 45 + 87 + 96 + 275 + 88 + 227

880

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3 years ago

ASAP HELP FOR NUMBER 6!! ANSWER CORRECTLY FOR 6a and B!!

Gelneren [198K]

See the attached image to see how all of the answers fill out.

=========================================
Problem 6a

The slope of line A is -1/1 or just -1
The reason why is because we start at (0,3) and move down 1 and over to the right 1 to get to the next point (1,2). Alternatively you can use the slope formula m = (y2-y1)/(x2-x1) to get the same result.

Since the slope of line A is -1, this means that we'll write "-1" in the first row of the "constant rate of change" column.

-----------------------------------------
The two points (0,2) and (1,3) are on the line B

Use the slope formula to get

m = (y2-y1)/(x2-x1)
m = (3-2)/(1-0)
m = 1/1
m = 1

The slope of line B is 1. Write "1" in the second row of the "constant rate of change" column.
-----------------------------------------
The points (0,-4) and (1,-2) are on line C

Slope:
m = (y2-y1)/(x2-x1)
m = (-2-(-4))/(1-0)
m = (-2+4)/(1-0)
m = 2/1
m = 2

The slope of line C is 2, which is written in the last row of the "constant rate of change" column.
-----------------------------------------
Now onto the y intercept column.

Line A crosses the y intercept at the point (0,3) or simply 3 on the y axis. So we'll have 3 in the first row.

Write 2 in the next row under the "3" to indicate that the y intercept of line B is 2. The black line B crosses the y axis at 2 on the vertical number line.

Similarly, the y intercept for line C is -4. This red line crosses the vertical y axis at -4

-----------------------------------------

Now onto the x intercept

The x intercept of line A is 3. This is where the blue line crosses the horizontal x axis.

The x intercept of line B is -2. This is where the black line crosses the horizontal x axis.

The x intercept of line C is 2. This is where the red line crosses the horizontal x axis.
=========================================
Problem 6b

Equation D: y = 2+x
is the same as
y = x+2

The slope here is 1 (since y = x+2 is the same as y = 1x+2) and the y intercept is 2.

The fact that
Slope = 1
and
y intercept = 2
means we have a match with line B

-----------------------------------------

The equation y = -4+2x is the same as y = 2x-4

Slope = 2
y intercept = -4
this matches with line C

-----------------------------------------

y = 3-x is the same as y = -x+3
which can be written as y = -1x+3

Slope = -1
y intercept = 3
This matches with line A

=========================================

See the attached image to see how all of the answers fill out.

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3 years ago