Noah bought x apples, and Elena bought 1/4 more
apples. Write an expression for the number of apples
Elena bought.

hi

You are making  f ° h  

f(x) = 9x-5

h(x) = 2x²  

You must first calculate   h(-5)   :     so remplace  x  by -5 in h :

h(-5) = 2 (-5)² =  2* 25 = 50

then apply  f(x) to result  :   f(50) = 9 *50 -5 = 450 -5 = 445  

Answer:First suppose that the roots of the equation

x2−bx+c=0(1)

are real and positive. From the quadratic formula, we see that the roots of (1) are of the form

b±b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√2.

For the root or roots to be real, we require that b2−4c≥0, that is, b2≥4c. In order for them to be positive, we require that

b−b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√>0.

This immediately tells us that b>0, but we can go further. We can rearrange this to get

b>b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√,

which (assuming that b>0) is true if and only if

b2>b2−4c,

since both sides of the inequality are positive so we may square. But then

4c>0.

That is, if the roots are real and positive then b>0 and b2≥4c>0.

Now suppose that b>0 and b2≥4c>0.

Then the roots of (1) are real since b2−4c≥0, and b>0 guarantees that the root b+b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√ is positive.

So it remains to show that b−b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√>0. We have that

4c>0,

so that

b2>b2−4c,

then square rooting shows that

b>b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√,

so the roots of (1) are real and positive, as required.

Approach 2

the curve y equals x squared minus b x plus c showing two positive roots for y equals zero

This is intended to be a proof without words! We have from the diagram that:

If c, b and b2−4c are all positive, there are two real positive roots for x2−bx+c=0 (if b2=4c, we have two real positive equal roots).

If there are two real positive roots for x2−bx+c=0, then c and b are positive and b2−4c is non-negative.

(Why is the distance between the roots b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√?)

Approach 3

When solving problems about the roots of polynomials, it is often useful to find expressions those roots must satisfy and see if this tells us anything new. If α and β denote the roots of the equation, then

x2−bx+c=(x−α)(x−β)=x2−(α+β)x+αβ

and so α+β=b and αβ=c.

We also know that the roots of a quadratic equation are real if and only if the discriminant is non-negative, that is, if and only if b2−4c≥0.

Using these facts, if α and β are both real and positive, then b=α+β>0, c=αβ>0 and b2≥4c, as above.

Conversely, if b>0 and b2≥4c>0, then we know the discriminant is positive and hence both roots are real. We also have that

αβ>0(2)

and

α+β>0.(3)

As α and β are both real, by (2), we know that α and β are either both positive or both negative. However, if α and β were both negative, then (3) could not possibly hold. Hence α and β are both positive, as required.

We now sketch on a graph the region where b>0, c>0 and b2≥4c:

The curve b squared = 4 c as a quadratic with the c-axis vertical and the b-axis horizontal. The region below it is shaded.

The region of the b-c plane for which b>0, c>0 and b2≥4c

Sketch the region of the b-c plane in which the roots of the equation are real and less than 1 in magnitude.

We know that in order for the roots to be real we need b2≥4c as in the first part. We now need to find the region where

−1<b±b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√2<1.(4)

We have b−b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√2≤b+b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√2 so we only need to consider the values for which both

−1<b−b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√2andb+b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√2<1.

Firstly, we will consider the values for which

b+b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√<2.

Rearranging gives

b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√<2−b.

So b<2, as the square root is non-negative, and we can square both sides to get

b2−4c<4−4b+b2,

which we may rearrange to find c>b−1.

We will now consider the values for which

−2<b−b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√.

Similarly, we can rearrange to get

b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√<b+2.

So b>−2, and we can, as before, square to get

b2−4c<b2+4b+4,

and hence c>−b−1.

To sketch the graph, we start by considering the boundary curves b2=4c, c=b−1 and c=−b−1, and the points at which they intersect. We can see that the two lines only intersect when b=0 and c=−1, and the lines intersect the curve when

b2=4b−4andb2=−4b−4

which rearrange to

(b−2)2=0and(b+2)2=0.

This tells us that each line intersects with the curve in only one place and so these lines must be tangent.

Is there a way we could have deduced this directly from (4)?

What do the lines being tangent signify in terms of our equation x2−bx+c=0?

Is this a representation of a well-known property of these equations?

Sketching the graph then yields the following picture:

The graph with the previous curve and the lines 4 c = 4 b minus 4 and 4 c = minus 4 b - 4. Each line touches the curve once and the two lines intersect at (0, minus 1). The region between the three lines/curves is shaded.

The shaded region is where b2≥4c, c>b−1, c>−b−1 and −2<b<2

We might notice that when we derived the inequalities c>b−1 and c>−b−1, a lot of the work we did was very similar.

We might also notice that the graph above is symmetric about the c axis. Why is this?

Does the graph give us any ideas about how we might deduce one inequality from the other?

Step-by-step explanation:

Answer:

8+11

Step-by-step explanation:

Answer:

3(2x + 1) +2(x + 4)

6x + 3 + 2x + 8

8x + 11

Step-by-step explanation:

Answer:

54

Step-by-step explanation:

hi

Answer:

Step-by-step explanation:

p =  b + c/5                     Subtract b from both sides

p - b = c/5                       Put brackets around the left side

(p - b) = c/5                     Multiply by 5

5(p - b) = c

B.) The horizontal asymptote y = 11.95 represents that the cost per person approaches $11.95 as the number of people increases.

Good luck with the test! :)

The horizontal asymptote y = 0 represents that the cost per person approaches $0 as the number of people increases.

"An asymptote is a straight line that constantly approaches a given curve but does not meet at any infinite distance. In other words, Asymptote is a line that a curve approaches as it moves towards infinity."

"The curves visit these asymptotes but never overtake them. The method opted to find the horizontal asymptote changes involves comparing the degrees of the polynomials in the numerator and denominator of the function. If both the polynomials have the same degree, divide the coefficients of the largest degree terms."

From the equation, y = 11.95x + 25

And from the given graph it is clear that the horizontal asymptote y = 0 represents that the cost per person approaches $0 as the number of people increases.

Hence, A is the correct option.

To know more about asymptotes here

https://brainly.com/question/17767511

#SPJ2

Answer:

the answer is 90° because you need to figure out the degree.

Step-by-step explanation:

2 and 3 equals to 6 .

That's how you got that.

Answer:

204 R45

Step-by-step explanation:

Answer: The answer will be 205 R2

Step-by-step explanation:

I know this because the steps to dividing are:

D - Divide

M - Multiply

S - Subtract

B - base(total)

If you do all of those steps then you'll get 205 R2

R = remainder(left overs)

So, the answer will be 205 R2

Answer:

Step-by-step explanation:

[tex]a_1=-8\\a_2=-2\\a_3=4\\\\d=a_2-a_1=a_3-a_2=...=a_n-a_{n-1}\qquad\qquad \{n\ge2\}\\\\\left{\big{a_2-a_1=-2-(-8)=-2+8=6}\atop\big{a_3-a_2=4-(-2)=4+2=6\quad\ \,}\right\}\implies\ \ d=6[/tex]

Answer:

[tex]a = p*q\\b = (p*s)+(q*r)\\c = r*s[/tex]

Step-by-step explanation:

The standard form of trinomial is given as:

[tex]ax^2+bx+c[/tex]

And the factored form is:

[tex](px+r)(qx+s)[/tex]

In order to find the values of a,b and c in terms of p,q,r and s we will take the factored form, multiply it and then compare it with the standard form.

So,

[tex](px+r)(qx+s)\\=px(qx+s)+r(qx+s)\\= pqx^2+psx+qrx+rs\\= pqx^2+(ps+qr)x+rs[/tex]

Now comparing it with the standard form of trinomial

We will compare the co-efficients of x^2, x and the constant

By comparing, we get

[tex]a = pq = p*q\\b = ps+qr = (p*s)+(q*r)\\c = rs = r*s[/tex]

Hence,

[tex]a = p*q\\b = (p*s)+(q*r)\\c = r*s[/tex]

a=associates / p=partners

1a= $800 / 1p= $1500

(6)a + (2)p = 800 x 6 + 1500 + 2 = $7800

(x)a + (y)p = $z

hope this helps :)

Answer:

look it up

Step-by-step explanation:

Try and find a way to look it up.

Answer:

Im gussing you are talking about this website/app you dont have to answer all the questios you ca skip them if you dont know them and find another one to answer

Step-by-step explanation:

Answer:

umm

Step-by-step explanation:

what? XD wdym

confusion...

Answer:

use the linear equation of a line

equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept.

now u do the rest

45- 3, 5, 9

369- 3, 9

7870- 2, 5, 10

1976- 2, 4,

6003- 3, 9

136- 2, 3, 4

1674- 2, 3, 6, 9

35496- 2, 3, 4, 6, 9

Answer:

-30

Step-by-step explanation:

7x-4=-28-6=-34+4=-30

Pls mark as brainliest!!!!!

Answer:

The answer for this is -30.

Step-by-step explanation:

Basically, you start out with solving the equation from left to right (as always). First, you multiply 7* -4, and you get -28. Then you have -28 - |-6| + |4|. Now, |-6| is equal to 6, since it's the absolute value of -6. |4| is equal to 4 for the same reason as well. That leaves you with -28 - 6 + 4. Now you just solve left to right. -28 - 6 is -34, so then you have -34 + 4, which is equal to -30.

Hope that helped!

Answer:

uh is  it 2 and o.6 i think

Step-by-step explanation:

Answer:

11 months

26+33(11)=389

59+30(11)=389

The 11 is in going for x and represents the months.

Answer:

25 + 0.55x ≤ 212

Step-by-step explanation:

Bart can only spend 212, hence the less than or equal to symbol. The cost of using the car must be at most 212, so 25 and 0.55x are on the same side. 0.55x represents the cost of driving an unknown amount of miles.

Answer:

A. They have the same domain and range.

Step-by-step explanation:

Edge 2021

Answer:

$125,263.10

Step-by-step explanation:

In order to calculate the total amount that each one of the children will receive we simply need to divide Mr. Jordan's total savings by the total amount of children that he has. This will evenly divide his savings to the children so that each one has the exact same amount.

501,052.40 / 4 = 125,263.10

Therefore, each of the four children will receive a grand total of $125,263.10

Step-by-step explanation:

H hvuvuvuvuvuv9yvig kg

Answer:

Step-by-step explanation:

So basically what you want to do is set up an inequality to where 30 is on one side and the variable and the payment is on the other side. The payment is taking away from the profit, so you subtract it. It should look something like this:

30≥7t-5

Now we shall solve for t. Get all like terms to one side:

35≥7t

And divide

5≥t

At least 5 hours to make 30 dollars

Answer:

y = 2x -2

Step-by-step explanation:

When you shift down or up, you move down or up the y-axis. Here, the 6 was the y-intercept, so you subtract 8 from 6.

Answer:

w=1.5 or w=13.5

Step-by-step explanation:

this is one answer:

multiply w on both sides to leave u with

4.5=3w

divide both sides by 3

[tex]\frac{4.5}{3}=\frac{3w}{3}[/tex]

1.5=w

_____________________

this is the second one if the first one is wrong:

multiply 4.5 on both sides so that the 4.5/w would leave u with just only w alone.

then 3*4.5=13.5

w=13.5

hope dis helps if not then im not dat smart enough ;?

Answer:

Step-by-step explanation:

3.8-2.923

Change to 3.800 to match the number of digits in the second number. Work from right to left. 3 minus 0 is 7. work our way over until the end. You should get 0.877 for an answer.