a rectangular prism is 12 inches long, 6 inches wide and 10 inches tall. what is the length of it's longest diagonal?

Answer:

4x^2+19x-47

Step-by-step explanation:

(4x^2+8x+15)+(x^2-x-27)-(x-5)(x-7)

=(4x^2+8x+15)+(x^2-x-27)-x^2+7x+5x-35

=(4x^2+x^2-x^2) + (8x-x+7x+5x) + (15-27-35)

= 4x^2+19x-47

Hope this helps!

The given expression after simplifying 4x^2+19x-47.

We have given the following expression

[tex](4x^2+8x+15)+(x^2-x-27)-(x-5)(x-7)[/tex]

An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

[tex]=(4x^2+8x+15)+(x^2-x-27)-x^2+7x+5x-35[/tex]

[tex]=(4x^2+x^2-x^2) + (8x-x+7x+5x) + (15-27-35)[/tex]

[tex]= 4x^2+19x-47[/tex]

The given expression after simplifying 4x^2+19x-47.

To learn more about the expression visit:

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Answer:

[tex]A = 34\frac{1}{3}[/tex]

[tex]B = 72\frac{2}{3}[/tex]

[tex]C = 73[/tex]

Step-by-step explanation:

Given

Shape: Triangle

[tex]B = 4 + 2A[/tex]

[tex]C = 3A - 30[/tex]

Required

Solve for A, B and C

Since the shape is a triangle,

[tex]A + B +C = 180[/tex]

Substitute [tex]B = 4 + 2A[/tex] and [tex]C = 3A - 30[/tex] in [tex]A + B +C = 180[/tex]

[tex]A + 4 + 2A + 3A - 30 = 180[/tex]

Collect Like Terms

[tex]A + 2A + 3A = 180 + 30 - 4[/tex]

[tex]6A = 206[/tex]

Solve for A

[tex]A = 206/6[/tex]

[tex]A = 34\frac{1}{3}[/tex]

Substitute [tex]A = 34\frac{1}{3}[/tex] in [tex]B = 4 + 2A[/tex]

[tex]B = 4 + 2 * 34\frac{1}{3}[/tex]

[tex]B = 4 + 2 * \frac{103}{3}[/tex]

[tex]B = 4 + \frac{206}{3}[/tex]

[tex]B = \frac{12 + 206}{3}[/tex]

[tex]B = \frac{218}{3}[/tex]

[tex]B = 72\frac{2}{3}[/tex]

Substitute [tex]A = 34\frac{1}{3}[/tex] in [tex]C = 3A - 30[/tex]

[tex]C = 3 * 34\frac{1}{3} - 30[/tex]

[tex]C = 3 * \frac{103}{3} - 30[/tex]

[tex]C = 103 - 30[/tex]

[tex]C = 73[/tex]

Answer:

25%

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

400*.25=100

400-100=300

Hope this helps!!

Step-by-step explanation:

y+6 = (1/3)(x -9)

y+6 = x/3 - 9/3

y=x/3 -3 -6

y = x/3 -9

Answer:

See Explanation

Step-by-step explanation:

[tex] \sec \: x - cos \: x = \sin \: x \tan \: x \\ \\ LHS = \sec \: x - cos \: x \\ \\ = \frac{1}{ \cos x} - cos \: x \\ \\ = \frac{1 - { \cos x}^{2} }{ \cos x} \\ \\ = \frac{ { \sin x}^{2} }{ \cos x} \\ \\ = \frac{ \sin \: x \times \sin x}{ \cos x} \\ \\ = \sin x \: tan x \\ \\ = RHS \\ \\ thus \: proved \\ [/tex]

The answer fam is.......... "b.up"

Answer:

i think a,c,e

Step-by-step explanation:

Answer:5

Step-by-step explanation:

Answer:

Before her donation, Marie owned 35 comic books.

Step-by-step explanation:

Marie donated 40% of her comic books to a school, that is, Marie donated 40 comic books per 100 comic books she owned. We can write it as a ratio: the ratio of donated comic books to total comic books is 100:40. If she donated 14 comic books, the number of comic books she owned before her donation were:

14 donated cb × (100 total cb/40 donated cb) = 35 total cb

Answer:

A power function is a function with a single term that is the product of a real number, a coefficient, and a variable raised to a fixed real number.

Answer:

a) The mean cost of the 25 trips is:

$12.35.

b) The standard deviation of the cost of the 25 trips is:

$52.50

Step-by-step explanation:

a) Data and Calculations:

Initial fee (fixed) = $2.55

Variable (additional) charge = $1.75 per mile

Equation = 2.55 + 1.75(miles)

Trips = 25

Mean distance for first 25 rides = 5.6 miles

Standard deviation = 1.2 miles

Mean cost of the 25 trips = 2.55 + 1.75 (5.6) = $12.35

Total cost = $308.75 (25 * 12.35) based on mean cost

Standard deviation of the cost of the 25 trips:

Total standard deviation for the 25 trips = 30 miles (1.2 * 25)

= $52.50 (1.2 * 25 * $1.75)

Answer:

690 km will take it.for good condition

Step-by-step explanation:

mark me BRAINLIEST

Answer:

It is C, in my opinion. Have a nice day. :)

Step-by-step explanation:

Answer:

a =

✔ 310

b =

✔ 250

c =

✔ 60

d =

✔ 60/250

e =

✔ 24%

Step-by-step explanation:

Answer:

x = 5 + 5y/4

Step-by-step explanation:

I think its like this: 4x - 5y = 20

Add 5y to both sides: 4x = 20 + 5y

Divide both sides by 4: x = 20/4 + 5y/4

Simplify: x = 5 + 5y/4

I'm pretty sure it is like this

Hope this helps!

Answer:

[tex]\frac{2}{3} x + \frac{1}{3} - \frac{1}{3} x = \frac{1}{3} ( x - 1)\\\\ \\\frac{4}{3}x - \frac{4}{3} - \frac{2}{3} = \frac{4}{3} ( x - 1)\\\\( \frac{1}{3} x + \frac{2}{3} ) + ( -\frac{2}{3}x - \frac{4}{3}) = -\frac{1}{3} ( x + 2)\\\\(\frac{2}{3}x + \frac{1}{3} ) + (\frac{2}{3} x - \frac{2}{3} ) = \frac{1}{3} ( 4x - 1 )[/tex]

Step-by-step explanation:

Simplify each equation by combining like terms, and then factoring

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

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

= [tex]\frac{1}{3}[/tex] ( x + 1)

[tex]\frac{4}{3}x - \frac{4}{3} - \frac{2}{3}[/tex]

= [tex]\frac{4}{3}x - \frac{6}{3}[/tex]

= [tex]\frac{4}{3}[/tex] ( x - 1 )

[tex]\ ( \frac{1}{3} x + \frac{2}{3} ) + ( -\frac{2}{3}x - \frac{4}{3})[/tex]

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

=[tex]- \frac{1}{3} x[/tex] ( x + 2)

[tex]\ (\frac{2}{3}x + \frac{1}{3} ) + (\frac{2}{3} x - \frac{2}{3} )[/tex]

= [tex]\ \frac{4}{3}x - \frac{1}{3}[/tex]

= [tex]\(\frac{1}{3}[/tex] ( 4x - 1)

Answer:

Step-by-step explanation:

[tex]1)\frac{2}{3}x + \frac{1}{3}-\frac{1}{3}x = \frac{2}{3}x-\frac{1}{3}x +\frac{1}{3}\\\\\\=\frac{(2-1)}{3}x+\frac{1}{3}\\\\\\=\frac{1}{3}x+\frac{1}{3}\\\\\\=\frac{1}{3}(x+1)[/tex]

[tex]2) \frac{4}{3}x-\frac{2}{3}-\frac{2}{3}=\frac{4}{3}x + \frac{(-2-2)}{3}\\\\\\[/tex]

                    [tex]=\frac{4}{3}x -\frac{4}{3}\\\\\\=\frac{4}{3}(x-1)[/tex]

[tex]3) (\frac{1}{3}x+\frac{2}{3})+(\frac{-2}{3}x-\frac{4}{3})=\frac{1}{3}x-\frac{2}{3}x+\frac{2}{3}-\frac{4}{3}[/tex]

                                     [tex]= \frac{-1}{3}x-\frac{2}{3}\\\\\\=\frac{-1}{3}(x+2)\\[/tex]

4) [tex](\frac{2}{3}x +\frac{1}{3})+(\frac{2}{3}x-\frac{2}{3})=\frac{2}{3}x+\frac{2}{3}x+\frac{1}{3}-\frac{2}{3}[/tex]

                                    [tex]=\frac{4}{3}x-\frac{1}{3}\\\\\\=\frac{1}{3}(4x-1)[/tex]

Answer:

55.25

Step-by-step explanation:

85 X 0.35 = 29.75

85 - 29.75 = 55.25

Answer: 29.75

My Explanation:

85 divided by 10 = 8.5 (10%)

8.5 x 4 = 34.0 (40%)

8.5 divided by 2 = 4.25 (5%)

34 - 4.25 = 29.75 (35!)

Hope this helped!

Answer:

169

Step-by-step explanation:

9 + 10 × 2 × 8

9 + ( 10 × 2 × 8)

9 + (20×8)

9 + 160

169

Answer:

ok

Step-by-step explanation:

Answer: x = 13/2

Step-by-step explanation:

Distribute: 4(x - 2) = 18

4x - 8 = 18

Add 8 to both sides

4x - 8 + 8 = 18 + 8

Simplify:

4x = 26

Divide both sides of the equation by the same term

4x = 26

4x/4 and 26/4

Cancel term that are both in the numerator and denominator

Divide the numbers

X = 13/2

Answer:  see below

Step-by-step explanation:

I'm not sure exactly what you are asking for but here is what the box plot tells you:

Minimum is 17 items.

Q1 (Lower Quartile) is 22 items. So, 25% of the customers bought 22 items.

Q2 (Median) is 32 items. So, 50% of the customers bought 32 items.

Q3 (Upper Quartile) is 35 items, So, 75% of the customers bought 35 items.

Maximum is 62 items.

The data is "heavier" on the right so it is skewed left.

Range is 62 - 17 = 45

IQR (Interquartile range) is Q3 - Q1 = 35 - 22 = 13

Answer:

Angle: 22.5 deg, Complement: 67.5 deg, Supplement: 157.5 deg

Step-by-step explanation:

22.5 is 1/3 of 67.5

so compliment is 67.5.

Supplement is just adding another angle so I chose 7.

I did 22.5 x 7 = 157.5

Another example would be:

Angle: 10 deg, Complement: 30 (because 10 x 3), Supplement: 70 (because 10 x 7)

Hope this helps :)

Answer: See attachment

Step-by-step explanation:

The journal entry for Dilbert has-been prepared and attached. The journal entry shows the transaction that was done by Dilbert on a March 1st.

Check the attachment for the entry.

Answer:

3.75

Step-by-step explanation:

you can search this up going like 75% of 15 and it will give the answer before you hit enter

Answer:

grew by 6

Step-by-step explanation:

Answer:

Expectation is equal to 4.75

Variance is equal to 3.02

Step-by-step explanation:

Consider the attached image.

Let [tex]x_i[/tex] denotes each of the outcome.

Expectation [tex]=E(X)[/tex] = ∑[tex]x_if(x_i)[/tex]

[tex]=1(\frac{1}{12}) +2(\frac{1}{12}) +3(\frac{1}{12}) +4(\frac{1}{12}) +5(\frac{1}{12}) +6(\frac{7}{12})[/tex]

[tex]=\frac{1}{12}+\frac{2}{12}+\frac{3}{12}+\frac{4}{12}+\frac{5}{12}+\frac{42}{12}\\\\=\frac{57}{12}\\\\=4.75[/tex]

[tex]E(X^2)=[/tex] ∑ [tex]x_i^2f(x_i)[/tex]

[tex]=1^2(\frac{1}{12}) +2^2(\frac{1}{12}) +3^2(\frac{1}{12}) +4^2(\frac{1}{12}) +5^2(\frac{1}{12}) +6^2(\frac{7}{12})[/tex]

[tex]=(\frac{1}{12}) +4(\frac{1}{12}) +9(\frac{1}{12}) +16(\frac{1}{12}) +25(\frac{1}{12}) +36(\frac{7}{12})\\\\=\frac{307}{12}[/tex]

Variance  [tex]=E(X^2)-[E(X)]^2[/tex]

[tex]=(\frac{307}{12})-(\frac{57}{12})^2\\\\ =\frac{307}{12}-\frac{3249}{144}\\\\ =\frac{3684-3249}{144}\\\\ =\frac{435}{144}\\\\ =3.02[/tex]

false false false false false

Answer:

no the first on is true and the last one is false

Step-by-step explanation:

Answer:

2 & 5

Step-by-step explanation:

Answer:

It's 1 and 4

Step-by-step explanation:

Because the arrow is going to the left so that means x is less than -4 and those equations show that

Answer:

C. 60

Step-by-step explanation:

They all have a multiple f 60.