A librarian sorts 450 books at a constant rate. After 4 days, the librarian still has 150 books to sort. How much time does it take to sort the books from start to finish?

Answer:

Part 1) [tex]f(x)=-5(x-10)(x+2)[/tex]

Part 2) After 10 seconds.

Step-by-step explanation:

We have the function:

[tex]f(x)=-5x^2+40x+100[/tex]

Where f(x) represents the height x seconds after it is released into the air.

Part 1)

First, let's distribute a -5 out of the function:

[tex]f(x)=-5(x^2-8x-20)[/tex]

Now, let's factor. We want to pick two number that multiplies to -20 and adds to -8.

We can use -10 and 2. So:

[tex]f(x)=-5(x^2+2x-10x-20)[/tex]

Factor:

[tex]\begin{aligned}f(x)&=-5(x^2+2x-10x-20) \\ f(x)&=-5(x(x+2)-10(x+2)) \\ f(x)&=-5(x-10)(x+2) \end{aligned}[/tex]

Hence, our factored form is:

[tex]f(x)=-5(x-10)(x+2)[/tex]

Part 2)

We want to find after how many seconds does it take for the projectile to reach the ground.

If it reaches the ground, the height above the ground, f(x), will be 0.

So, we can set f(x) equal to 0 and solve for x. Instead of using the original equation, we can use the factored form. So:

[tex]0=-5(x-10)(x+2)[/tex]

Zero Product Property:

[tex]x-10=0\text{ or } x+2=0[/tex]

Solve for x:

[tex]x=10 \text{ or } x=-2[/tex]

Since x measures time, -2 does not make sense in this context.

Therefore, our solution is x=10.

So, after 10 seconds, the projectile will hit the ground.

Answer: 4

Step-by-step explanation:

Alice ride her bicycle in 1 day for a distance of 4 miles.

Division is one of the operation in mathematics where number is divided  into equal parts as that of a definite number.

Given that,

Alice rode her bicycle the same number of miles every day for 17 days.

Let x be the number of miles that Alice rode for 1 day.

She rode x miles for 17 days.

Total number of miles that she rode in 17 days = 68 miles

So, we have,

17x = 68

Dividing both sides by 17,

x = 4

Hence the number of miles Alice rode in 1 day is 4 miles.

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Discount on shirt, [tex]D_s = 19.95\times 0.25=\$4.9875[/tex] .

So, Price payed for shirt is :

[tex]P=P_s-D_s\\\\P=19.95 - 4.9875\\\\P=\$14.9625[/tex]

Discount on shorts, [tex]D_{sh}=35.95\times 0.30=\$10.785[/tex]

Discounted price :

[tex]P=P_{sh}-D_{sh}\\\\P=35.95-10.785\\\\P=\$25.165[/tex]

Therefore, discounted price of shirt and shorts are $14.9625 and $25.165.

Hence, this is the required solution.

Step-by-step explanation:

the third sequence(0,2,4,6) is not a geometrical sequence

this may help you(:

Answer:

0, 2, 4, 6, …  because the following sequence is arithmetic not geometric

Answer:

(3,-4)

Step-by-step explanation:

because the two lines meet at that point.

Answer:

112 ounces

Step-by-step explanation:

Malia bought 14 cans of cat food

Each of the can weighs 8 ounces

Therefore the total ounces of cat food bought can be calculated as follows

= 14×8

= 112 ounces

Answer:

1: [tex]3[/tex]×[tex]2[/tex]

2: [tex]y^6[/tex]

Step-by-step explanation:

1:

Multiply the numbers: [tex]y(^3^*^2)[/tex]

[tex]3*2 = 6[/tex]

Write it without exponents:

[tex]y * y * y * y *y *y[/tex] so [tex]6y[/tex].

2:

[tex](y^3)^2[/tex]

Apply exponent rule : [tex](a^b)^c=a^b^c,[/tex] assuming [tex]a\geq 0[/tex]

[tex](y^3)^2=y^3^*^2[/tex]

[tex]=y^3^*^2[/tex]

Multiply the numbers: [tex]3 * 2 = 6[/tex]

[tex]= y^6[/tex]

Hope I helped! If so, may I get Brainliest and a Thanks?

Thank you, have a good one! =)

Answer:

ask your mom for the answer

Step-by-step explanation:

thank me later

Answer: y= -1x+ 5

Step-by-step explanation:

Y = slope x + y- intercept

Answer:

12 times

Step-by-step explanation:

Given that :

Amount of potting soil in bag = 9 cups

Size of scooping cup = 3/4 cup

The number of times scooping will be done to use entire bag of potting soil will be ;

(Amount of potting soil in bag ÷ size of scooping cup)

(9 ÷ 3/4)

9/ 1 * 4/3

= 36/3

= 12 times

Hence, scooping will have to be done 12 times in other to use entire bag if potting soil.

Answer:

B

Step-by-step explanation:

Equation of A is

y = 0.0105x

Equation of B is

y = 0.01

B is smaller than A

Answer:

The answer would be B=-8>80

Step-by-step explanation:

Answer:

Number 2, or {(0,1),(1,-3),(2,-5),(3,-7)(4,-9)}

Explanation:

Every x-value matches to exactly one y-value, which is the definition of a function.

Answer: hahshejehdbddndb

Step-by-step explanation:

Answer:

you chose poison thanks for the points payback

Step-by-step explanation:

don't do this to people

its rude and people actualy need help not free points

Answer:x = 0.028571 cm3

Step-by-step explanation:

I the density is constant and a mass of 3.5 g takes up 1 cubic centimeter, how much volume will a mass of 0.20 g take (in cubit centimeters)?

So, let x be the volume in cubit centimeters.

   the mass is to the volume is as the mass is to the volume

        3.5g /(1 cm3)  =  0,1g / (x cm3)

Cross-multiply to get:

       3.5x = 0.1

         x = 0.1 / 3.5                (divide both sides by 3.5)

         x = 0.028571 cm3      (you probably should round this, but diamonds are expensive !)

Answer:

112 degrees

Step-by-step explanation:

In this case, the two angles are considered alternating exterior angles, which signifies that they are equal

Answer:

lines 1 and 4

Step-by-step explanation:

they are both horizontal lines because when solved equal a number without an x so they is no slope so they are horizontal and have the same slope which means they are parallel to each other

Answer:

y=1/3x+2

Step-by-step explanation:

Assuming that all of the '13' 's are suppost to be 1/3, it is y=1/3x+2

The equation of the line in slope intercept form is

[tex]y= \frac{1}{3} x+2[/tex]

Given :

A line passes through (0, 2) and has a slope of 1/3

The equation of a line in slope intercept form is y=mx+b

where m is the slope and b is the y intercept

From the given information , we know that slope [tex]m=\frac{1}{3}[/tex]

The line passes through (0,2) that is our y intercept b

b= 2

Replace slope [tex]m= \frac{1}{3}[/tex] and b=2 in slope intercept form y=mx+b

[tex]y= \frac{1}{3} x+2[/tex]

The equation of the line in slope intercept form is

[tex]y= \frac{1}{3} x+2[/tex]

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Answer:

x = 0

Step-by-step explanation:

4x = 7(3x)

4x = 21x

-4x   -4x

17x = 0

Answer:

25x

Step-by-step explanation:

Answer:

x/2-4

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

this question is not very detailed but I think ik what u mean. take a number, 8 for example. halve it, (divide by 2) and then subtract 4 & u are left with 0

Answer: D. 5 > x > 1

1 < 3x -2 < 13

<=> 3 < 3x < 15

<=> 1< x < 5

Step-by-step explanation:

x>1 and x<5 and 1<x<5 are  the solution of the inequality 1 < 3x-2 < 13.

a relationship between two expressions or values that are not equal to each other is called 'inequality.

The given inequality is 1 < 3x-2 < 13

One less than three times of x minus two less than thirteen.

We need to find the solution of the inequality.

Let us divide the given inequality into two parts

3x-2>1 and 3x-2<13

For first inequality

3x-2>1

3x>3

x>1

and the second inequality  3x-2<13

3x<15

x<5

Hence, x>1 and x<5 and 1<x<5 are  the solution of the inequality 1 < 3x-2 < 13.

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Answer:

just look that up and walla insta answer

a,d,e

Step-by-step explanation:

I took the question

Answer:

A D E

Step-by-step explanation:

Answer:

$8

Step-by-step explanation:

25% is .25, also known as 1/4. So if you think of it that way, $2 is 1/4 of the entire payment that was added to it. 2*4 is 8, so the price of the tacos was $8 before any tip was added. Andrea paid $10 in total if you include the tip.

Answer:

a) 30 parcelas

b) Para árboles de cedro: 5 por parcela

Para árboles de Guayacán: 7 por parcela

Step-by-step explanation:

a) ¿Cuál es el mayor número de parcelas?

De la pregunta tenemos:

150 árboles de cedro y 210 árboles de guayacán

Para encontrar la mayor cantidad de parcelas, resolvemos usando los métodos del mayor factor común.

Encontramos los factores de 150 y 210

Los factores de 150 son: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150

Los factores de 210 son: 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210

Entonces el máximo común divisor es 30.

Por lo tanto, la mayor cantidad de parcelas que podemos tener es de 30 parcelas.

b) ¿Cuántos árboles de cedro y de guayacán plantar en cada parcela?

Para cedros

Tenemos 150 árboles de cedro

Por lo tanto, la cantidad de árboles de cedro por parcela = 150 ÷ ​​30 = 5 árboles de cedro por lote

Para los árboles de Guayacán

Tenemos 210 árboles de Guayacán

Por lo tanto, el número de árboles de Guayacán por parcela = 210 ÷ 30 = 7 árboles de Guayacán por lote

Step-by-step explanation:

The question is not well written. Let us say the function given as expressed as;

f(x) = -1/x + 3/x⁴

f'(x) means we are to differentiate the function with respect to x;

Given f(x) = axⁿ

f'(x) = naxⁿ⁻¹

f(x) = -x⁻¹ + 3x⁻⁴

Applying the differentiation formula we will have;

f'(x) = -1(-x⁻²)+(-4)3x⁻⁴⁻¹

f'(x) = x⁻²-12x⁻⁵

Express as a fraction

f'(x) = 1/x²-12/x⁵

To get f'(4), we will have to substitute x = 4 into the resulting expression

f'(4) = 1/4²-12/4(5)

f'(4) = 1/16-12/20

f'(4) = 1/16-3/5

Find the LCM

f'(4) = (5-48)/80

f'(4) = -43/80

Note that the function used was assumed but the same method can be employed to any other functions.

Answer:

B

Step-by-step explanation:

Start with the slope formula.

m = y₂ - y₁ / x₂ - x₁

m = -6 - 3 / 5 - -2

m = -9 / 7

So the slope is -9/7.