Joseph is playing with blocks to create a design. With each step he continues to add
blocks. How many blocks will be required in the 5th and 6th step? Explain how you
know.

Solving a cubic equation, it is found that the dimensions of the container are of 1 inch, 9 inches and 5 inches.

The volume of the cubic container is given by the following equation:

[tex]V(h) = 2h^3 - 9h^2 + 4h[/tex]

Since it holds 45 cubic inches of merchandise, we have that [tex]V(h) = 45[/tex], then:

[tex]V(h) = 2h^3 - 9h^2 + 4h[/tex]

[tex]45 = 2h^3 - 9h^2 + 4h[/tex]

[tex]2h^3 - 9h^2 + 4h - 45 = 0[/tex]

Using a cubic equation calculator, the real solution is [tex]h = 5[/tex], thus, the dimensions are:

[tex]h = 5[/tex]

[tex]h - 4 = 5 - 4 = 1[/tex]

[tex]2h - 1 = 2(5) - 1 = 10 - 1 = 9[/tex]

The dimensions of the container are of 1 inch, 9 inches and 5 inches.

A similar problem is given at https://brainly.com/question/16606259

Answer:

cyclist will travel 64 kilometres in 4 hours

Step-by-step explanation:

speed of cyclist = 10 miles per hour

given 1 mile is equal to 1.6 kilometres.

1*10 miles will be equal to 1.6*10 kilometres

thus , 10 mile is equal to 16 kilometres

using 16 km in place of 10 miles in 10 miles per hour

we have

speed of cyclist = 16 kilometres per hour

we know that distance = speed * time

speed is 16 kilometres per hour

time 4 hours

thus , distance = 16*4 kilometres= 64 kilometres.

cyclist will travel 64 kilometres in 4 hours.

(Hope this helps can I pls have brainlist (crown)☺️)

Given :-

To find :-

Solution :-

According to Question,

So that ,

Step-by-step explanation:

=3/0.05

=60ans.

mark me as a brainlist plz.

the answer is 60

You can solve it in calculator

Answer:

Your answer is -5

Step-by-step explanation:

On paper;

The height of the triangle if the base is 8 is 3.96 units

Given the following parameters

Base of a triangle = 8 units

Let the hypotenuse be "c"

Let the height be "h"

If the length of the hypotenuse of a right triangle is one unit more than twice the height, then;

c = 2h + 1

According to the Pythagoras theorem:

c² = b² + h²

(2h + 1)² = 8² + h²

Expand

4h²+4h+1 = 64 + h²

4h²-h² + 4h + 1 - 64 = 0

3h² + 4h - 63 = 0

Factorize the result

On factorizing, the value of the height is 2

h = [tex]\frac{-2}{3}+\frac{\sqrt{193} }3\\[/tex]

h = 11.89/3

h = 3.96 units

Hence the height of the triangle if the base is 8 is 3.96 units

Learn more here: https://brainly.com/question/20545047

Answer: y = -1/2x + 8

Step-by-step explanation:

Answer: Y=-1/2x+8

Step-by-step explanation:

You have to divide

Answer:

C

Step-by-step explanation:

There are two negative numbers must be before zero and one positive number must be after zero

A = 2 1/2 = 2.5 between 2 and 3

B = -2.75 between -2.5 and -3

C = -0.25 between 0 and -0.5

Answer:

It should 120 students

Step-by-step explanation:

Answer:

120 students

Step-by-step explanation:

4/7×210=120

Answer:

-2csc^2(x)cot(x)

Step-by-step explanation:

by derivative sin^-2(x)

Answer:

two triangles, the top of one figure with the bottom of the other figure, 8 and 4

Step-by-step explanation:

I am not sure if it's right but I hope it is!

Answer:

Step-by-step explanation:

Uhm the third one number 3

Answer: 0.556

Step-by-step explanation:

Answer:

5/9 as a decimal is .5 repeating. I hope this helps.

Answer:

Hey mate.....

Step-by-step explanation:

This is ur answer....

Hope it helps!

Brainliest pls!

Follow me! ♧

Answer:

a

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex] {4x}^{2} - 16x + 12 = 0 \\ {4x}^{2} - 4x - 12x + 12 = 0 \\ 4x(x - 1) - 12(x - 1) = 0 \\ (4x - 12)(x - 1) = 0 \\ [/tex]

(4x - 12) = 0 or (x - 1) = 0

[tex](4x - 12) = 0 \\ 4x - 12 = 0 \\ 4x = 0 + 12 \\ 4x = 12 \\x = \frac{12}{4} \\ x = 3 \\ [/tex]

[tex](x - 1) = 0 \\ x - 1 = 0 \\ x = 0 + 1 \\ x = 1[/tex]

x = 3 or x = 1 should be.

hello again!

you can calculate the distance between A and B by subtracting

distance = B-A=0.5m-(-1.5)m=2m

Answer:15

Step-by-step explanation:

9514 1404 393

Answer:

  25°, 65°

Step-by-step explanation:

Essentially, you want two angles that have a sum of 90 degrees and a difference of 40 degrees.

The smaller is half the sum less half the difference: 90/2 -40/2 = 45 -20 = 25.

The larger is half the sum plus half the difference: 90/2 +40/2 = 45 +20 = 65.

Of course, once you know either value, you can add or subtract the difference (as needed) to find the other value.

The two angles are 25° and 65°.

_____

Additional comment

There are many ways you can arrive at this conclusion. Algebraically,  we can write ...

  a+b = sum

  a-b = difference

Adding these two equations gives ...

  2a = sum +difference

Multiplying by 1/2, we get ...

  a = 1/2sum +1/2difference . . . . . . as described above

Subtracting the difference gives ...

  b = a -difference = 1/2sum -1/2difference

Answer:

x≤-3 or 2≤x∠7

Step-by-step explanation:

It would be the first answer on the paper

Answer:

A

Step-by-step explanation:

[tex]\frac{x^2+x-6}{x-7} \leq 0\\[/tex]

hence numerator and denominator are of opposite sign.

case1 .

let x²+x-6≥ 0

and x-7<0

x²+x≥6

x²+x+1/4≥6+1/4

(x+1/2)²≥25/4

(x+1/2)²≥(5/2)²

|x+1/2|≥5/2

x+1/2≥5/2

x≥5/2-1/2

x≥2

or

x+1/2≤-5/2

x≤-5/2-1/2

x≤-3

also x-7<0

x<7

combining

x≤-3 or 2≤x<7

case 2.

x²+x-6<0

and x-7≥0

x²+x<6

x²+x+1/4<6+1/4

(x+1/2)²<25/4

|x+1/2|<5/2

so -5/2 <x+1/2<5/2

-5/2-1/2<x<5/2-1/2

-3<x<2

also x-7≥0

so x≥7

combining

we get no vlaue satisfying both the values.

Hence rejected.

The answer is:

11

Hopefully this is right

Answer:

11

Step-by-step explanation:

[tex]4^{2}[/tex]-3*4+7 = 16 -12+7 = 4+7 = 11

Ratio = 2 : 5

Numbers = 2x & 5x

[tex]2x + 5x = 21 \\ 7x = 21 \\ x = 21 \div 7 \\ x = 3[/tex]

Numbers :-

2x = 2 × 3 = 6

5x = 5 × 3 = 15.

The numbers are 6 & 15.

9514 1404 393

Answer:

Step-by-step explanation:

Let w represent the length of the wire. Then the height of attachment is (w-1). The Pythagorean theorem tells us a relevant relation is ...

  5² +(w -1)² = w²

  w² -2w +26 = w² . . . . . . . eliminate parentheses, collect terms

  26 = 2w . . . . . . . . . . . . add 2w

  13 = w . . . . . . . . . . . . divide by 2

The length of the wire is 13 feet.

__

(a) When h = 0, the equation is ...

  0 = -16t^2 +8t +8

Dividing by -8 puts this into standard form:

  2t^2 -t -1 = 0

Factoring, we get ...

  (2t +1)(t -1) = 0

The positive value of t that makes a factor zero is t = 1.

It will take 1 second for the gymnast to reach the ground.

__

(b) When h = 8, the equation is ...

  8 = -16t^2 +8t +8

Subtract 8 and divide by 8 to get ...

  0 = -2t^2 +t

  0 = t(1 -2t) . . . . factor out t

Values of t that make the factors zero are ...

  t = 0

  t = 1/2

The gymnast will be 8 feet above the ground at the start of the dismount, and 1/2 second later.

Answer:

888888

Step-by-step explanation:

Answer: The last option is the answer

3(3 root 3)-3(3 root 2)

Using the Factor Theorem, it is found that the function is given by:

[tex]f(x) = 0.0409(x^3 + x^2 - 77x - 330)[/tex]

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

From the graph, the zeroes are [tex]x_1 = -8, x_2 = -3, x_3 = 10[/tex], hence:

[tex]f(x) = a(x + 8)(x + 3)(x - 10)[/tex]

[tex]f(x) = a(x^2 + 11x + 33)(x - 10)[/tex]

[tex]f(x) = a(x^3 + x^2 - 77x - 330)[/tex]

From the y-intercept, that is, when [tex]x = 0, y = -13.5[/tex], we find a.

[tex]f(x) = a(x^3 + x^2 - 77x - 330)[/tex]

[tex]-330a = -13.5[/tex]

[tex]330a = 13.5[/tex]

[tex]a = \frac{13.5}{330}[/tex]

[tex]a = 0.0409[/tex]

Hence:

[tex]f(x) = 0.0409(x^3 + x^2 - 77x - 330)[/tex]

To learn more about the Factor Theorem, you can take a look at https://brainly.com/question/24380382

Answer:

first guy is wrong

Step-by-step explanation:

my teacher said it's wrong, when I find out the right answer ill put it here

Answer:

0.915

Step-by-step explanation: