The graph of y = x2 + 4x + 3 is shown.
a) What are the coordinates of the turning point?
b) What are the coordinates of the roots of the equation x + 4x + 3 = 0 ?

Answer:

b

Step-by-step explanation:

Since it intercepts y at 4, and x at 2, we use y=ax+b and rearrange to get the equation from y=2x+4 to 2x-y=-4

Answer:

b) 2x - y = -4

Step-by-step explanation:

The y-intercept is the y-coordinate of the point (0, b) where the graph crosses the y-axis. It is also the value of y when x = 0.

The crosses the y-axis at point (0, 4). Therefore, the y-intercept, b = 4.

Next, we need to determine which of the given options matches the graph.  It helps to transform each of them into their slope-intercept form, y = mx +b:

2x - 2x + y = - 2x + 4

y = -2x + 4  (This is not the correct answer because the slope, m = -2. The given graph has a positive slope).

2x - 2x - y = - 2x - 4

-y = -2x - 4

Divide both sides by -1:

[tex]\frac{-y}{-1} = \frac{-2x - 4}{-1}[/tex]

y = 2x + 4 This is the correct answer because it matches the y-intercept (0, 4), and has a positive slope of 2.

We could easily disregard the last two options because both of their y-intercept is 0.

Therefore, the correct answer is Option b) 2x - y = - 4

Answer:

A. THE RULE WHICH ASSIGNS EACH PERSON USERNAME

Step-by-step explanation:

MARK PLS

Answer:

punta ka sa settings bi tapos I change ng Pilipinas yong server mo baka may makasagot ng tanong mo

Answer:

y = 2x+1

Step-by-step explanation:

Given, the slope of a line is 2 and y-intercept is 5.

Here, m=2 and c=1.

The equation of the line in slope-intercept form is given by

              y=mx+c

∴             y=2x+1 is a required equation.

Not sure if it correct or not.

Answer:

√10−√14+√15−√21

Step-by-step explanation:

Answer:

√10−√14+√15−√21

Step-by-step explanation:

Correct on Edge 2022

Answer:

Step-by-step explanation: -3(m-2)=-9

                                           -3m + 6 = -9

                                           -3m = -15

                                                 m=5

Answer:

[tex]m=5[/tex]

Step-by-step explanation:

[tex]-3(m-2)=-9~(Given)\\\\-3m+6=-9~(Distributive~Property)\\\\-3m+6-6=-9-6~(Addition~Property~of~Equality)\\\\-3m=-15~(Simplify)\\\\\frac{-3m}{-3}=\frac{-15}{-3}~(Division~Property~of~Equality)\\\\m=5~(Simplify)[/tex]

$224

...................

Answer:

34

Step-by-step explanation:

115.6/340 = 0.34 x 100 = 34 percent

Answer:

Find the LCM of 3 and 4

Divide 12 by 4 and multiply with 3 which is 9

Divide 12 by 3 and multiply with 1 which is 4

9 plus 4 is 13

so the answer is 13/14

Answer:

24

Step-by-step explanation:

Answer:

n=1/24

Step-by-step explanation:

8/n=1/3

n=1/3÷8

=1/3×1/8

=1/24

Step-by-step explanation:

20-17+3=6

18+1-5=14

7-8+6=5

20-18+7=9

17+1-8=10

3-5+6=4

Answer:

X=-2.4

Step-by-step explanation:

3x+4=8x+16

-5x+4=16

-5x=12

x=-2.4

Problem 1

I'm assuming your teacher means "list all the possible rational roots".

If so, then we use the rational root theorem. This is the idea where we'll divide the factors of the last term over the factors of the first coefficient.

If we divide said factors in the order mentioned, then we get this list of possible positive rational roots:

1/1, 1/3, 5/1, 5/3

That list simplifies to

1, 1/3, 5, 5/3

That takes care of the positive possible rational roots. We double the list to incorporate the negative possible rational roots as well

-1, -1/3, -5, -5/3

Note: We can rewrite that list in bold into [tex]\pm 1, \pm\frac{1}{3}, \pm 5, \pm \frac{5}{3}[/tex] to shorten it.

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

Problem 2

We'll follow the same idea as the previous problem

Factors of 36:  1, 2, 3, 4, 6, 9, 12, 18, 36

Factors of 4:  1, 2, 4

To keep track of everything, I made a spreadsheet table. Refer to the diagram below. The factors of 36 are laid across the top while the factors of 4 are along the left side. Each inner cell represents dividing the headers.

For example, 36/4 = 9 is in the bottom right corner. The first table is before the fractions are reduced, and the second table after the fractions are reduced.

As the second table shows, we have a few repeats. The unique items here are:

1,2,3,4,6,9,12,18,36,1/2,3/2,9/2,1/4,3/4,9/4

We'll then mirror this set to include negative values as well to write the full list of all possible rational roots.

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

Problem 3

Divide the factors of 15 over the factors of 5 to get

1/1, 1/5, 3/1, 3/5, 5/1, 5/5, 15/1, 15/5

That list reduces to

1, 1/5, 3, 3/5, 5, 1, 15, 3

we can then toss out the duplicates to get

1, 3, 5, 15, 1/5, 3/5

Don't forget to include the negative values as well

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Problem 4

The steps will be effectively the same as before. You can write out the factors like done in problem 3, or make a table like done in problem 2. I'll skip the steps shown here unless you need me to go over them.

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

Problem 5

There's not really much new here, except for the fact that the first term has coefficient of 1. This is a special case where all we have to do is list the factors of the last term -40 to generate all the roots we need. This is because each time we're dividing over +1 or -1 which doesn't really change the overall result (except for the sign part).

Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40

Don't forget the negative values as well

Answer:

15*4=60;60*3.5=210

Step-by-step explanation:

60 is the number of baskets Lucy makes in an hour,210 is her 3.5 hours of baskets

Answer:

answer is 1/4 × 3 1/2 =

3 1/8

Answer:

y= -2x+1

Step-by-step explanation:

y=mx+b

y= -2x +b

3= -2(1) +b

3= -2 +b

b=1

y= -2x+1

Answer:

12 * 1.07 = 12.84

Step-by-step explanation:

You an can pick any number to express another number in this example we find  0.84 = 7% and 12 = 1 as 12 represents 1 whole.

Answer:

f(x)=-6*(x+1)^2+-7

Step-by-step explanation:

This is because the vertex is at (-1|-7)

f(x)=-6*x^2+-12*x+-13

f(x)=-6*(x^2+2*x+13/6) ( Factor out )

f(x)=-6*(x^2+2*x+(1)^2+-1*(1)^2+13/6) ( Complete the square )

f(x)=-6*((x+1)^2+-1*(1)^2+13/6) ( Use the binomial formula )

f(x)=-6*((x+1)^2+1*7/6) ( simplify )

f(x)=-6*(x+1)^2+-7 ( expand )

Hope this Helps

Answer:

1)

Step-by-step explanation:

The opposite angles formed by two intersecting lines are of equal measures.

They are called vertically opposite angles.

Answer:

527 is your answer

Step-by-step explanation:

Answer:

The third one

Step-by-step explanation:

y=>x+1

y=<x-1

removing y

x-1 => x+1

removing x

we have no solution

Answer:

About 1205.12352941 people per square mile in 2010

About 1329.36306853 people per square mile in 2015

Explanation:

take population and divide by land area

for 2015 pop do total pop divided by 9.7 plus total pop

is not a function.

The relation is not a function.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The lowest common denominator of 10 and 6 is 30.

9/10 = 3*9/10*9 = 27/30

1/6 = 5/1/(6 * 5) = 5/30

6 27/30 - 5/30 = 6 22/30 = 6 11/15

Answer 6 11/15

Answer:

59049

Step-by-step explanation:

nine times negative 3 8 times

Answer:

a₉ = 59049

Step-by-step explanation:

The nth term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

Here a₁ = 9 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-27}{9}[/tex] = - 3 , then

a₉ = 9 × [tex](-3)^{8}[/tex] = 9 × 6561 = 59049

13. M=4/3

14. m=-6

Step-by-step explanation:

Answer:

845

Step-by-step explanation:

I think that's what it's asking??

Answer:

845

Step-by-step explanation:

We are looking for a new number which is 120 less than 965.

We will get the new number by subtracting 120 from 965.

We write it down as:

965-120=845

And finally the solution for: What number is 120 less than 965?

is 845

Have a good day :)

Please check this out #TeamSeas

Answer:

EF ║ CD and AB ║ CD are the parallel segments.

Step-by-step explanation:

The given question is incomplete without picture; here is the picture attached with the answer.

Since m∠A = m∠D = 42°

Therefore, AB ║ CD and segment AD is the transverse.

Now ∠AEF + ∠IEF = 180° [Supplementary angles]

138° + ∠IEF = 180°

∠IEF = 180 - 138

       = 42°

∠IHG + ∠DHG = 180° [ Supplementary angles ]

∠IHG + 122 = 180

∠IHG = 180 - 122

∠IHG = 58°

But ∠IEF ≠ ∠IHG

Therefore, EF and GH are not parallel.

If the segments AB and GH are parallel then ∠IHG = ∠IAB (By the property of alternate angles)

But ∠IHG ≠ ∠IAB

Therefore, AB and GH are not parallel.

Now ∠IEF ≅ ∠IDC ≅ 42° [alternate angles]

which reveals that EF ║ CD

Therefore, EF ║ CD and AB ║ CD

Answer:

Michael's daily income is $96

Step-by-step explanation:

Given

john's income=$120

by question

John's income is 20%more than Micheal's

so,. Micheal's income= John's income - 20%of John's income

=$120 - 20%of $120

=$120 -20/100*$120

=$120 - $24

=$96

Answer:

100

Step-by-step explanation:

[tex]x + \frac{20x}{100} = 120 \\ x + \frac{x}{5} = 120 \\ 5x + x = 600 \\ 6x = 600 \\ x = 100[/tex]