A school bus can hold a maximum of 45 students. The correct inequality for this word problem is b ≤ 45. Why did I use ≤ not < in this problem?

9514 1404 393

Answer:

  a.  f(x) = (4x +5)(x -3)

  b.  x-intercepts: {-1.25, +3}

  c.  f(x) goes to +infinity as x goes to ±infinity

  d. plot the x-intercepts, the vertex, and a few other points; draw a smooth curve through them

Step-by-step explanation:

a. Here, you're looking for factors of (4)(-15) = -60 that have a sum of -7. Those factors will be -12 and +5, so we can factor the function as ...

  f(x) = (4x -12)(4x +5)/4

  f(x) = (x -3)(4x +5)

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b. The x-intercepts are the values of x that make the factors zero:

  x -3 = 0   ⇒   x = 3 . . . . (add 3)

  4x +5 = 0   ⇒   x = -5/4 . . . . (add -5, divide by 4)

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c. As with all even-degree polynomials with positive leading coefficients, the end behavior of f(x) matches that of |x|:

  as x → ∞, f(x) → ∞

  as x → -∞, f(x) → ∞

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d. The vertex of the function will be located halfway between the x-intercepts, at x = (3-5/4)/2 = (7/4)/2 = 7/8. The value of f(x) there is ...

  f(7/8) = (4(7/8) +5)(7/8 -3) = -289/16 = -18.0625

Since the leading coefficient is 4, the normal x^2 function behavior is stretched vertically by a factor of 4. So, additional points would be

  x = 7/8 ±1, f(x) = -18.0625 +4·1 = -14.0625

  x = 7/8 ±2, f(x) = -18.0625 +4·2^2 = -2.0625

The answers of part B locate two points on the graph, and help find the vertex. The answer of part C confirms the graph as opening upward.

__

Additional comment

I find a graphing calculator to be very helpful finding the roots and making the graph.

Answer:

540 jumps in 9 minutes.

Step-by-step explanation:

60 jumps a minute. Chen is fast, but we need to find how many jumps in 9 minutes.

Let's say one minute is m

m = 60

9m = 60x9

We do x9 because from m to 9m you need to multiply by 9, so lets do that on both sides.

9m = 540

9 minutes = 540 jumps

Hope this helps!

--Applepi101

Answer:

56.25°

Step-by-step explanation:

cos x° = b/h = 15/27 = 5/9

x° = cos^(-1) (5/9) = 56.25°

Answer:

1695.6 cubic feet

Step-by-step explanation:

Given that,

The corn fills 25% of the height of the silo.

The diameter of silo, d = 12 feet

Radius, r = 6 feet

Height, h = 60 feet

The volume of the part of the silo that is filled with corn is given by :

[tex]V=25\%\ of\ \pi r^2 h\\\\=\dfrac{25}{100}\times 3.14\times 6^2\times 60\\\\V= $$1695.6\ feet^3[/tex]

So, the required volume is equal to 1695.6 cubic feet.

Answer:

4x + 5y = 20

Step-by-step explanation:

4x + 5y = 20

5y = -4x + 20      (Subtract 4x to isolate 5y. Put the 4x in front of the 20)

y = [tex]-\frac{4}{5}x[/tex] + 4         (Divide all by 5 to isolate y)

And then it's done and in slope-intercept form

[tex]-1< -\frac{4}{5} < 0[/tex]        or [tex]-\frac{4}{5}[/tex] is greater than -1 but less than 0

I hope this helped :)

Answer:

i didnt get it

Step-by-step explanation:

can you explain

Answer:

1) 13 Students were surveyed

2) 3 students

3) 7 Students

4) 10 Books

Pls mark brainliest

Answer:

13 students were surveyed

3 students read 5 fiction books

7 students read more than 5 fiction books

The maximum number was 10

Step-by-step explanation:

Hope this helps

-Unbrand-

Sadly even though I answered first I didn't get any credit. Quite sickening.

Answer:

don't

Step-by-step explanation:

i don't know

Answer:

Option C

Step-by-step explanation:

same logic as in 2D problems. if C wasn't true, then the two planes couldn't be parallel

Answer:

x = 5.1

Step-by-step explanation.

Our first step is to find all the angles. If b = 91 degree and c is 38, a. has to be 51 because all triangles add up to 180 degree. Because we have both B and b, we can use sine law.

a/A     13/sin91      c/38

we can use b in this situation.

The legnth  of a is 10.1.

So,  x-5 would be 5.1

Answer:

22is the answer cuz it is

Answer:

Step-by-step explanation:

using pythagoras theorem

a^2 + b^2 = c^2

here 4 and 9 are the legs of the right angled triangle so let them be a and b respectively . third side is the hypotenuse because it is opposite to 90 degree so let it be c.

4^2 + 9^2 = c^2

16 + 81 = c^2

97 = c^2

[tex]\sqrt{97} = c[/tex]

Answer:4

Step-by-step explanation:

The Mean Absolute Deviation is 4 from the data given

Answer:

The solution to the inequality would be n < -3 or n > -2 . Isolate the variable be diving each side by the factors that don’t contain the variable.

Step-by-step explanation:

Answer:

About 1 1/2 :)

Step-by-step explanation:

The answer is 1.46 which is close to 1.5

Answer:

4b+8 is 12b I'm pre sure

dont know about the rest sorry

Answer:

1/2

Step-by-step explanation:

y2 - y1 / x2 - x1

-3 - 3 / -6 - 6

-6 / -12

= 1/2

We want to find the slope of a line given that we know that the line passes through the points (6, 3) and (-6, -3).

We will find that the slope is: 1/2

A general line can be written as:

[tex]y = a\cdot x + b[/tex]

Where a is the slope and b is the y-intercept.

If the line passes through the points (x₁, y₁) and (x₂, y₂) then we can write the slope as:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

We know that our line passes through (6, 3) and (-6, -3), then the slope of our line will be:

[tex]a = \frac{-3 - 3}{-6 - 6} = \frac{-6}{-12}[/tex]

Now to simplify this, we know that:

-12 = 2×(-6)

Replacing that in the above equation we get:

[tex]a = \frac{-3 - 3}{-6 - 6} = \frac{-6}{-12} = \frac{-6}{2\cdot -6} = \frac{1}{2}[/tex]

Then the slope written as a simplified fraction is:

a = 1/2

If you want to learn more, you can read:

https://brainly.com/question/3605446

Answer:just hart me n I will help

Step-by-step explanation:

Answer:

Step-by-step explanation:

(x - 2)(x + 4)

=x(x + 4) -2(x + 4)

=x^2 + 4x - 2x - 8

=x^2 + 2x - 8

(x + 1)(x + 6)

=x(x + 6) +1(x + 6)

=x^2 + 6x + x + 6

=x^2 + 7x + 6

(x - 4)(x + 2)

=x(x + 2) -4(x + 2)

=x^2 + 2x - 4x - 8

=x^2 - 2x - 8

(x + 5)(x - 3)

=x(x - 3) +5(x - 3)

=x^2 - 3x + 5x - 15

=x^2 + 2x - 15

(x - 6)(x - 2)

=x(x - 2) -6(x - 2)

=x^2 - 2x - 6x + 12

=x^2 - 8x + 12

Answer:

×=50,×+09+673-23

×=(33)+(2×)

3.10

Step-by-step explanation:

If you round 3.14 to the nearest tenth 4 is nearer to 10 than 20. Therefore, the answer is 3.10

Answer:

52b

Step-by-step explanation:

She has 52 cards per deck, and b decks.

This means she has 52b cards.

How this works:

For 1 deck, she has 52 cards, or 52×1 cards.

For 2 decks, she has 104 cards, or 52×1 cards.

For 5 decks, she has 260 cards, or 52×5 cards.

For 10 decks, she has 520 cards, or 52×10 cards.

Therefore, for b decks, she has 52×b, or 52b cards.

**This content involves writing algebraic expressions, which you may wish to revise. I'm always happy to help!

Answer:

x = 23

Step-by-step explanation:

Sum of 25 and x = 48

25 + x = 48

Subtract 25 from both sides

25 - 25 cancels out

48 - 25 = 23

We would be left with x = 23

Answer:

[tex]x =23[/tex]

Step-by-step explanation:

Sum of 25 and x

[tex]25 + x[/tex]

Sum of 25 and x is 48

[tex]25 + x = 48[/tex]

Now lets simply Solve the equation

[tex]25 + x = 48 \\ x = 48 - 25 \\ x =23[/tex]

Hope this helps you.

Have a nice day!

Ansfdfgh gggghjtyuhjrswzargfyf

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

The worst scenario is that of a slight possibility, the first 5 balls you took are completely different color. The chance of this happening is tiny, but if you want to be sure, then you should consider about it.

But, after taking out the sixth ball, you can be sure that the ball, now right on your hand, must share a same color with at least one of the balls you took out, since there are only five colors.

The phrases best describes the line that passes through the points (5, -7) and (a, -4) is rise from left to right.

Coordinates are two numbers (Cartesian coordinates), or sometimes a letter and a number, that locate a specific point on a grid, known as a coordinate plane. A coordinate plane has four quadrants and two axes: the x axis (horizontal) and y axis

As, we locate this coordinate in graph we can see the line will either rise from left to right or falls from right to left.

Hence, line that passes through the points (5, -7) and (a, -4) will rise from left to right.

Learn more about coordinates here:

https://brainly.com/question/12149933

#SPJ2

Answer:

-0.4

fraction form: -4/10 or -2/5

Answer:

f(x)= x2 -4

Step-by-step explanation:

it is because it has no complex roots

Answer:

d(x)  =  - 2666.67*a  +  42000

Step-by-step explanation:

Vamos a llamar a d(x) la ecuación de la demanda de CD, entonces como la relación entre las dos variables es lineal la ecuación de la demanda es del tipo:

d(x) = a*x  + b        (1)

en esa relación a es la pendiente de la recta y b es el intercepto con el eje y que en este cas es el eje de valores de d(x).

Tenemos dos condiciones que cumplir y dos incógnitas que determinar ( a y b).

Cuando el precio ( x = 18 $ ) el monto de d(x)  es de 10000 entonces por sustitución en la ecuación general (1)

10000 = 18*a  +  b   (2)

Y cuando   (  x  =  12  $) d(x) =  26000

26000 = 12*a  +b    (3)

Resolviendo para a y b el sistema de dos ecuacions con dos incógnitas tenemos:

restando  ec 3  -  ec 2

16000 =  - 6*a

de donde   a = - 16000/6

a =  - 2666.67

Llevando ese valor a ec 2

10000  =  12 *(- 2666.67) + b

10000 + 32000 = b

b  = 42000

Finalmente la ecuación buscada es:

d(x)  =  - 2666.67*a  +  42000

Como la pendiente es negativa significa que d(x) va decreciendo cuando x va en aumento

Answer:

the anwser is d

Step-by-step explanation:

Here we are given that C is between A and B.

So using the midpoint rule, sum of whole length AB will be addition of lengths AC and BC

Hope that helps

Answer:

AC Or CA

Step-by-step explanation:

So, this is what a b and c would look like on a number line:

A----C----B

However, we dont know exactly what these variables are. THey could be somerthing like this:

A------------------C-B

But this doesnt matter.

If we look at the first numberline, A and C make up the first half of the numberline.

C to B make up the later half.

AB is the total numberline.

SO tecnically, A to C+ C to B = AB

Or:

AC + CB = AB

This can also be seen in the second numberline.

A to C make up almost all of the numberline.

C to B make up a smll amount.

But in the end, AC + CB will still make AB.

Hope this helps you! :D