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3 years ago

Marking brainliest if you answer all 3 of them n

Mathematics

1 answer:

slavikrds [6]3 years ago

5 0

1) Equation: y = 5x + 1

Missing Value: 51

2) Equation: y = 4x

Missing Value: 28

3) I have no idea for this one... sorry!

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Solve for x. Leave your answer in simplest radical form

alexandr1967 [171]

Answer:

x = 2√7

using Pythagoras theorem:

7² + ?² = 9²

?² = 81 - 49

? = √32

? = 4√2

For the bottom part:

x² + 2² = (4√2)²

x² + 4 = 32

x² = 28

x = √28

x = 2√7

5 0

2 years ago

Read 2 more answers

You are creating an open top box with a piece of cardboard that is 16 x 30“. What size of square should be cut out of each corne

Arada [10]

Answer:

$\frac{10}{3} \ inches$ of square should be cut out of each corner to create a box with the largest volume.

Step-by-step explanation:

Given: Dimension of cardboard= 16 x 30“.

As per the dimension given, we know Lenght is 30 inches and width is 16 inches. Also the cardboard has 4 corners which should be cut out.

Lets assume the cut out size of each corner be "x".

∴ Size of cardboard after 4 corner will be cut out is:

Length (l)= $30-2x$

Width (w)= $16-2x$

Height (h)= $x$

Now, finding the volume of box after 4 corner been cut out.

Formula; Volume (v)= $l\times w\times h$

Volume(v)= $(30-2x)\times (16-2x)\times x$

Using distributive property of multiplication

⇒ Volume(v)= $4x^{3} -92x^{2} +480x$

Next using differentiative method to find box largest volume, we will have $\frac{dv}{dx}= 0$

$\frac{d (4x^{3} -92x^{2} +480x)}{dx} = \frac{dv}{dx}$

Differentiating the value

⇒ $\frac{dv}{dx} = 12x^{2} -184x+480$

taking out 12 as common in the equation and subtituting the value.

⇒ $0= 12(x^{2} -\frac{46x}{3} +40)$

solving quadratic equation inside the parenthesis.

⇒ $12(x^{2} -12x-\frac{10x}{x} +40)$ =0

Dividing 12 on both side

⇒ $[x(x-12)-\frac{10}{3} (x-12)]$ = 0

We can again take common as (x-12).

⇒ $x(x-12)[x-\frac{10}{3} ]$ =0

∴ $(x-\frac{10}{3} ) (x-12)= 0$

We have two value for x, which is $12 and \frac{10}{3}$

12 is invalid as, w= $(16-2x)= 16-2\times 12$

∴ 24 inches can not be cut out of 16 inches width.

Hence, the cut out size from cardboard is $\frac{10}{3}\ inches$

Now, subtituting the value of x to find volume of the box.

Volume(v)= $(30-2x)\times (16-2x)\times x$

⇒ Volume(v)= $(30-2\times \frac{10}{3} )\times (16-2\times \frac{10}{3})\times \frac{10}{3}$

⇒ Volume(v)= $(30-\frac{20}{3} ) (16-\frac{20}{3}) (\frac{10}{3} )$

∴ Volume(v)= 725.93 inches³

6 0

3 years ago

What is the surface area of the right rectangular prism?<br>center your answer in the box.

Firlakuza [10]

I believe the answer is 22 in^2

3 0

3 years ago

Read 2 more answers

What the domain and range is for the function f(x) = x2 + 4x - 21.

prisoha [69]

Answer:

Step-by-step explanation:

Please use " ^ " to denote exponentiation: f(x) = x^2 + 4x - 21.

This function has a graph which is a parabola that opens up.

Its vertex is found by completing the square:

x² + 4x + 4 - 4 - 21, or

(x + 2)² - 25

Comparing this to the standard equation

(x - h)² + k, we see that h = -2 and k = -25.

Thus, the vertex (and the minimum of this function) is (-2, -25).

Thus, the range is [-25, ∞ ). This being a polynomial function, it has no restrictions on the domain: the domain is (-∞, ∞ )

7 0

3 years ago

(3a+2.5b)^2=9a^2+6.25b^2+*<br> Please help before Thursday

Anon25 [30]

Step-by-step explanation:

We have (x + y)² = (x + y)(x + y) = x² + 2xy + y².

Let x be 3a and y be 2.5b.

Therefore (3a + 2.5b)²

= (3a)² + 2(3a)(2.5b) + (2.5b)²

= 9a² + 15ab + 6.25b².

Hence the '*' sign should be replaced with 15ab.

5 0

3 years ago