A rectangular bin, completely filled, holds 1,200 cubic feet of grain. If the bin is 6 feet wide and 10 feet long, how deep is it ?

Let x,y be the two numbers.

Given that one number is 8 greater than another.

Let x be the smaller number ans y be the greater number.

That is y=x+8. Let this be the first equation.

And also given that product of the two numbers is 84.

That is x × y = 84, let us plugin y=x+8 here.

x × (x+8) = 84

x²+ 8x -84 = 0.

x²+12x-4x-84 = 0

x(x+12)-4(x+12) =0

(x-4)(x+12)=0

That is x= 4 or -12.

Hence two positive numbers corresponding to given conditions are 4,12.

And two negative numbers corresponding to given conditions are -12,-4.

Step-by-step explanation:

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Answer:

x=1

y=-1

Step-by-step explanation:

Answer:

x = 1

y = -1

Step-by-step explanation:

[tex]x = 2x - 1 \\ 1 = 2x - x \\ 1 = x \\ x = 1 \\ [/tex]

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

Answer:

A) P ( chicken is small ) = 0.3085,  P ( chicken is medium ) = 0.6621

   P (chicken is large ) = 0.0294

B) C = 3.9233

C) 0.1404

Step-by-step explanation:

A) Probabilities

i) P ( chicken is small )

 P( w ≤ 3.5 ) = Fw ( 3 .5 )

                    = F ( 3.5 - 3.8 / 0.6 )

                    = F ( -0.5 ) = 1 - F( 0.5 ) [∵ F(-x) 1 - F(x) ]

                    = 1 - 0.6915 ( from Table )

                    = 0.3085

ii) P ( chicken is medium )

  P ( 3.5 < w < 4.9 )

  P ( w < 4.9 ) - P ( w < 3.5 )

= Fw ( 4.9 ) - Fw ( 3.5 )

= F ( 4.9 - 3.8 / 0.6 ) - 0.3085

= 0.9706 - 0.3085 = 0.6621  

iii) P (chicken is large )

= P ( w > 4.9 )

= 1 - P ( w < 4.9 )

= 1 - Fw ( 4.9 ) = 1 - 0.9706 = 0.0294

B) Find c

Given:  P( w < c ) = 0.6

Fw ( c ) = 0.6

F ( c - 3.8 / 0.6 ) = 0.6

c - 3.8 / 0.6 = 0.2055 ( from table )

∴C = 3.9233

C) P ( 3 out of 5 = small )

P ( 3 of 5 = small ) = 0.1404

attached below is a detailed solution

Answer:

x = 111

Step-by-step explanation:

180- 82 -29 is 69 and 180-69 is x which x is equal to 111

Answer:

111°

Step-by-step explanation:

By exterior angle theorem:

[tex]x = 82 \degree + 29 \degree \\ = 111 \degree[/tex]

Answer:

x=7

Step-by-step explanation:

Alternate interior angles so they are congruent. So, 13x+5=12x+12. Subtract 12x and get x+5=12. Subtract 5 and you get x=7

Answer:

12

Step-by-step explanation:

Just substitute 3 for n and solve.

Solve the expression [tex]2+(3-1)5\\[/tex]

Use PEMDAS and solve.

(3-1) = 2 so it becomes 2 + (2)5

Then multiply 2 and 5 to get 10.

Then add 2 so you get 12.

[tex]a_{3}[/tex]=12

Answer:

in this tiangle tanA = 8/15

Answer:

equation: y = 4x-12

slope: 4

y-intercept: -12

Step-by-step explanation:

3 points across an x-axis is +1 x-axis difference and +4 y-axis away from origin, so you have to subtract 3 by 1 andsubtract y by 4. until x is 0, you get -12 on y-axis

Answer:

ST = 15

Step-by-step explanation:

Given:

QR = 3x

LM = x + 9

ST = 6x - 3

Required:

ST

Solution:

First, we need to find the value of x by creating an equation.

Based on the trapezoid mid-segment theorem, we have the following equation:

LM = ½(QR + ST)

Substitute

x + 9 = ½(3x + 6x - 3)

x + 9 = ½(9x - 3)

Multiply both sides by 2

2(x + 9) = 9x - 3

2x + 18 = 9x - 3

Collect like terms

2x - 9x = -18 - 3

-7x = -21

Divide both sides by -7

x = -21/-7

x = 3

Find ST:

ST = 6x - 3

Plug in the value of x

ST = 6(3) - 3 = 18 - 3

ST = 15

Answer:

A term is a single mathematical expression. It may be a single number (positive or negative), a single variable ( a letter ), several variables multiplied but never added or subtracted.

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

60 square meters

Step-by-step explanation:

Answer:

See image below:) :)

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

-48/16 = 48/16

-48/16 = -3/1 = -3

Answer:

There was a 45% increase in furniture sales.

Furniture sales rose by 9 percentage points.

Step-by-step explanation:

absolute difference = new - old

29-20= 9 percentage points

absolute difference / initial value = 9/20 = .45 * 100 = 45%

Two statements which are true about furniture sales are  [tex](a)[/tex] There was a [tex]45\%[/tex] increase in furniture sales and  [tex](f)[/tex]  Furniture sales rose by [tex]9[/tex] percentage points.

Percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".

Percentage [tex]=\frac{Obtained\ number}{Total\ number}\ * 100[/tex]

We have,

Sales of furniture in [tex]2015=20\%[/tex]

Sales of furniture in [tex]2016=29\%[/tex],

So,

Change in Percentage [tex]=29-20=9\%[/tex]

i.e.

Sales rise by [tex]9\%[/tex] points,

And,

Increase in Percentage [tex]=\frac{9}{20}\ *100=45\%[/tex]

Hence, we can say that Two statements which are true about furniture sales are [tex](a)[/tex] There was a [tex]45\%[/tex] increase in furniture sales and [tex](f)[/tex] Furniture sales rose by [tex]9[/tex] percentage points.

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Answer:

D

Step-by-step explanation:

you just add it all up 10+6+8

Answer:

volume of the prism=8×6×10

=480 in²

Answer:

The car uses less gas

They use the same amount of gas after [tex]\frac{640}{7}[/tex] miles

Step-by-step explanation:

Given

The table represents the car mileage

[tex]y = -\frac{1}{5}x + 31[/tex] --- The van

First, calculate the car's slope (m)

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

From the table, we have:

[tex](x_1,y_1) = (60,13.5);\ \ (x_2,y_2) = (180,10.5)[/tex]

So, we have:

[tex]m = \frac{10.5 - 13.5}{180 - 60}[/tex]

[tex]m = \frac{-3}{120}[/tex]

[tex]m = -\frac{1}{40}[/tex]

Calculate the equation using:

[tex]y = -\frac{1}{40}(x - 60)+13.5[/tex]

[tex]y = -\frac{1}{40}x + 1.5+13.5[/tex]

[tex]y = -\frac{1}{40}x + 15[/tex]

[tex]m = -\frac{1}{40}[/tex] implies that for every mile traveled, the car uses 1/40 gallon of gas

Also:

[tex]y = -\frac{1}{5}x + 31[/tex] --- The van

By comparison to: [tex]y = mx + b[/tex]

[tex]m = -\frac{1}{5}[/tex]

This implies that for every mile traveled, the van uses 1/5 gallon of gas.

By comparison:

[tex]1/40 < 1/5[/tex]

This means that the car uses less gas

Solving (b): Distance traveled for them to use the same amount of gas.

We have:

[tex]y = -\frac{1}{5}x + 31[/tex] --- The van

[tex]y = -\frac{1}{40}x + 15[/tex] --- The car

Equate both

[tex]-\frac{1}{5}x + 31 =-\frac{1}{40}x + 15[/tex]

Collect like terms

[tex]\frac{1}{40}x -\frac{1}{5}x =-31 + 15[/tex]

[tex]\frac{1}{40}x -\frac{1}{5}x =-16[/tex]

Take LCM

[tex]\frac{x - 8x}{40} = -16[/tex]

[tex]\frac{- 7x}{40} = -16[/tex]

Solve for -7x

[tex]-7x = -640[/tex]

Solve for x

[tex]x = \frac{640}{7}[/tex]

Answer:

50

Step-by-step explanation:

Think of line AE as a transversal. with DE and AB cutting across it. If we draw it out, looking at the picture, we can see that angles A and E correspond, meaning that angle A = angle E = 50

9514 1404 393

Answer:

  k = 2/15

Step-by-step explanation:

We can solve the given equation for k:

  k = s/p . . . . . . divide the given equation by p on both sides

Using the first values from the table (15 pounds, 2 scoops), we have ...

  k = 2/15

The value of k is 2/15.

Answer:

C

Step-by-step explanation:

Try it.

Answer:Its B or C

Step-by-step explanation:I expain it so A is wrong ebcause 3 times 20 is 60 and since x is 14 that measn 14 times 3 is 42 so 60 minus 42 is not 44 but 18.C is wrong becasue 2 times 14 is 28 and 2 times 3 is 6 so if u subract you get 22 and D is worng because 14 minus 3 isnt 22.

Answer:

5 and 3 is vertical. 4 and 6 are vertical. 2 and 1 are supplementary angles.

Answer:

D x is all real numbers

R y ≥ -3

Step-by-step explanation:

The domain is the values that x can take

The domain is all real numbers

The range is the values that y can take

The range is y is greater than or equal to -3

Answer:

173 949 pounds

Step-by-step explanation:

radius of the hemisphere = diameter / 2 = 11 feet

Volume of the hemisphere = (2/3  * radius^3 * pi) = = (2/3 * 11^3 * pi) = 2.787,639881 ft^3

Total weight = volume of the hemisphere * 62.4 = 173,948.728592

9514 1404 393

Answer:

  a) MBE; b) EBY; c) MBY; d) MBE; e) YME; f) XEW; g) EBM, EBY; h) EBY, EBM

Step-by-step explanation:

There are many choices here. We'll use choices that make as much use as possible of the same points and segments.

a) ∠MBE is an acute angle

b) ∠EBY is an obtuse angle

c) ∠MBY is a straight angle

d) ∠MBE is an angle with vertex B

e) ∠YME is an angle with side MY

f) ∠XEW is another name for ∠BER

g) ∠EBM and ∠EBY are adjacent angles

h) ∠EBY and ∠EBM are supplementary angles

__

Additional comments

An acute angle measures less than 90°; an obtuse angle measures more than 90°. A straight angle measures exactly 180°. A linear pair is a pair of adjacent angles that together measure 180°. That is, they are supplementary and combine to make a straight angle. (Supplementary angles only need to have a sum that is 180°. They do not need to be a linear pair. However, in a figure like this, where angle measures are not marked, angles are guaranteed to be supplementary only if they are a linear pair.)

Answer:

is it correct if yes you may follow me for more helps ☺️

Replace f(x) to 5x-3 and g(x) to 3x-3 then subtract f(x) by g(x).

[tex] \large{f(x) - g(x) = (5x - 3) - (3x - 3)}[/tex]

Cancel the brackets, remember that multiplying or expanding the negative symbol will switch the sign. From plus to minus and minus to plus.

[tex] \large{ f(x) - g(x)= 5x - 3 - 3x + 3 }[/tex]

Combine like terms.

[tex] \large{f(x) - g(x) = 2x + 0 \longrightarrow \boxed{2x}}[/tex]

Answer

Answer:

5x-3-(3x-3)

5x-3-3x+3

5x-3x

2x

Answer:

h(t) = -16t2 + 186t + 43

at the ground h = 0

hence;  -16t2 + 186t + 43 = 0  

solving this quadratic equation using the quadratic formula ; a = -16, b = 186, c = 43 ; x = (-b +-(b2 - 4ac)1/2)/2a

gives t = 11.8 seconds to the nearest tenth (note that the negative root has no practical significance)

Step-by-step explanation:

Answer:

335

Step-by-step explanation:

To convert meters to centimeters, move the decimal point two spaces to the right.

Answer:

335

Step-by-step explanation:

a centimeter is one hundredth of a meter so multiply 3.35x100

Answer:

x= 62

first take linear pair angle with any line then once again with x then you're done

Answer:

x value is 62 degree

because they are vertically opposite angles