A box is in the shape of a right rectangular prism made from cardboard has dimensions of 18 inches, by 12 inches, by 8 inches, as shown in the diagram below. find the volume of the box and show your calculations and use appropriate units

If wasps had eaten 20 apples then, 50 rotten apples were there and the rest of the apples were quality apples in the ratio of 4: 10: 20 respectively.

This is a problem from simple mathematical equations. We can solve this problem by following a few steps.

Let's consider x as the highest common factor of apples eaten by wasps, rotten and quality apples.

So, the number of apples eaten by wasps is, 4 × x = 4x

The number of rotten apples is, 10 × x = 10x

The number of quality apples is, 20 × x = 20x

As, we all know HCF of the numbers × ratio of numbers = The numbers

So, 4x = 20 as per the question.

Therefore, x = 5.

Now, we can write that the HCF is 5.

So, the number of rotten apples ≡ HCF × 10 = 5× 10 = 50.

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Answer:

45g = 40.5°

45g = 40° 30′ 0″

Let's begin by identifying key information given to us:

Numbers of apples = 35

Number of oranges = 30

Total number of fruits = 65

The ratio of apples to oranges is given by:

Answer:

sama sma tayi

Step-by-step explanation:

3×3()56(7)

(x-2) is not a factor of f([tex]x[/tex]) = [tex]3x^{4}-3x^{3}-9x^{2} +5x-2[/tex].

Remainder Theorem is an approach of Euclidean division of polynomials. According to this theorem, if we divide a polynomial P(x) by a factor ( x – a) that isn't essentially an element of the polynomial, you will find a smaller polynomial along with a remainder.

The Remainder Theorem: If (x-a) is a factor of the f(x) then f(a) = 0

Here,

f([tex]x[/tex]) = [tex]3x^{4}-3x^{3}-9x^{2} +5x-2[/tex]

substitute a = 2

[tex]f(2)=3(2^{4}) -3(2) ^{3}-9(2)^{2}+5(2)-2[/tex]

      = 48-24-36+10-2

      = 32-36

f(2)  = -4

f(2) [tex]\neq 0[/tex]

Hence, (x-2) is not a factor of f([tex]x[/tex]) = [tex]3x^{4}-3x^{3}-9x^{2} +5x-2[/tex].

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The expressions which is equivalent to 2x + 3 would be 4x + 6.

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions. To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.

We need to find the expressions which is equivalent to 2x + 3

Thus, we will Use the Distribute Property of Multiplication by multiplying the number outside the parenthesis with the numbers inside.

Let the expression be multiplying by 2 then;

2(2x + 3)

4x + 6

Hence, we can say that the expressions which is equivalent to 2x + 3 would be 4x + 6.

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The coordinates of  Point O that is on MN and divides it such that MO:NO is 2:1 is; (10, 10)

We are given a line segment as MN with its' endpoint coordinates as;

M(4,14) and N(13,8)

Now, point O divides MN such that MO:NO is 2:1.

Now, the formula for the coordinate of the point that divides a line segment in the ratio a:b is;

(x, y) = (ax₂ + bx₁)/(a + b), (ay₂ + by₁)/(a + b)

Since point O is the point that divides the line segment in the ratio 2:1, we have;

O(x, y) = (2*13 + 1*4)/(2 + 1), (2*8 + 1*14)/(2 + 1)

O(x, y) = (30/3), (30/3)

O(x, y) = (10, 10)

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The value of the variable x is 2 and length of the segment AB = 25 and length of segment BC is 14.

If a Line segment AC is given in a plane and B is some point between the points A and C on the line segment AC. Then two segments of the line segment ac are formed that are AB and BC. and length of AC is equal to the sum of lengths of AB and BC.

Then AC = AB +BC

Given that  B is point on the line segment AC

Length of AB line = 9x+7

Length of BC = -3x +20

Length of AC = 39

Using segment addition postulate,

we have AC = AB +BC

⇒ 39 = 9x+7 + (-3x) +20

⇒ 39 = 9x -3x +7+20

⇒39 = 6x +27

⇒ 39-27 = 6x

⇒ 12 = 6x

⇒ 2 = x

∴ Length of AB will be = 9(2) +7 = 25

∴ Length of BC will be = -3x + 20 = -3(2) +20 = 14

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The complete question is mentioned in the picture below:

The Inequality notation of the given equation 10+3x>-16 is x > -2

What is Inequality notation?

A mathematical statement known as an inequality expresses the relationship between two quantities while indicating that they are not completely equal. The four symbols used to represent inequality are. ≥, >,<, and ≤.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare the two values in inequality. Less than (or less than and equal to), greater than (and greater than or equal to), and also not equal to signs are used in place of the equal sign.

Consider the above equation.

-10 +3x > -16

Add 10 on both sides.

= -10+3x+10> -16+10

= 3x> -6

Divide by 3 to equation into both sides.

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

=  x > -2

Inequality notation is x > -2

Interval Notation: [−2,∞)

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The division of (4+5i) / (2-4i) is performed by multiplying the numerator and denominator by 2+4i and the result of the given expression is (-3/5) + (13/10) i

The given expression is

(4+5i) / (2-4i)

Here we have to divide the given complex number

First multiply both numerator and denominator by 2+4i

(4+5i) / (2-4i) × (2+4i) / (2+4i)

= [tex]\frac{(4+5i)(2+4i)}{(2-4i)(2+4i)}[/tex]

Multiply the terms in the numerator and denominator.

= [tex]\frac{8+16i+10i-20}{2^2+4^2}[/tex]

= (-12+26i) / 20

= (-12/20) + (26/20)i

Divide both numerator and denominator by common terms

= (-3/5) + (13/10)i

Hence, the division of (4+5i) / (2-4i) is performed by multiplying the numerator and denominator by 2+4i and the result of the given expression is (-3/5) + (13/10)i

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       A mathematical statement indicating an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.

|x+1/3| < 3/2.

Consider the center of the group of numbers that fulfill 2|x+1/3|3 to be x = -1/3.

The maximum value of this set is obtained by adding 3/2 to this -1/3:

-1/3 + 3/2, or -2/6 + 9/6, or 7/6.

The bottom limit of this solution set is obtained by subtracting 3/2 from this and then -1/3:

-1/3 - 3/2, or -2/6 - 9/6, or - 11/6.

The answer range is (7/6, -11/6).

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Answer: Look at step by step

Step-by-step explanation:

(ax + b)(ax + b) = [tex]a^{2}[/tex] [tex]x^{2}[/tex]+ 2abx + [tex]b^{2}[/tex]

Substitute g into x

[tex]a^{2}[/tex] = 7

a = [tex]\sqrt{7}[/tex]

2ab = -3

b = -3 / (2 x [tex]\sqrt{7}[/tex])

[tex]b^{2}[/tex] = 9 / (4 x 7) = 9/28

So the term to be added to make a perfect square is 9/28

When factorized would get ([tex]\sqrt{7}[/tex]x - 3/2[tex]\sqrt{7}[/tex])([tex]\sqrt{7}[/tex]x - 3/2[tex]\sqrt{7}[/tex])

If this doesn't help, maybe it is best you ask your teacher instead of listening to a random person on the internet. Hope this helps though

The pair of vertical angles are

There are four angles made by the intersection of two lines. Those are ∠1, ∠2, ∠3 and ∠4

Vertical angles are the each of opposite angles formed when two lines meet each other at a point. So whenever two lines intersect each other four angles are formed and each set of opposite angles are called vertical angles

Here, two lines intersect each other and ∠1, ∠2, ∠3 and ∠4 are formed.

∠1,∠3 and ∠2,∠4 are the opposite angles

So the vertical angles are ∠1,∠3 and ∠2,∠4

Hence, the pair of vertical angles are

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For the given function g(x) , the values at given points :

a. g(9) = 2

b. g(0) = -2.5

c. g(3) = -1

d. g(17) = 6

A function is a set of rules that assigns each element of a set a unique element of another set.

If f is a function and f(x) = x+2, then if we have to find value of at x= 1 ,put 1 in place of x,

Then f(1 ) = 1+2 =3

Given that a function g is such that

g(x) = (x -5)/2

This the values of the function g at given points:

a. g(9) = (9-5)/2 = 4/2 = 2

b. g(0) = (0-5)/2 = -5/2 = -2.5

c. g(3) = (3-5)/2 = -2/2 = -1

d. g(17 ) =  (17-5)/2 = 12/2 = 6

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Answer: 13 and 5= coeeficients, x and y = variables,  -2 and 3 =constants

Step-by-step explanation:

The statements that are true about the quadratic function and its graph include the following:

In Mathematics, the graph of any quadratic function or equation always forms a parabola because it is a u-shaped curve. For the given quadratic function, the graph is a upward parabola because the coefficient of x² is positive i.e when the value of "a" is greater than zero.

Next, we would determine the statements about the quadratic function and its graph that are true:

At point (-10, 82), we have:

f(x) = 1/5 x² – 5x + 12

f(x) = x²/5 – 5x + 12

f(-10) = -10²/5 – 5(-10) + 12

f(-10) = 82

At point (20, -8), we have:

f(x) = 1/5 x² – 5x + 12

f(x) = x²/5 – 5x + 12

f(20) = 20²/5 – 5(20) + 12

f(20) = -8

In conclusion, the graph of this quadratic function does not contain the point (0, 0) as shown in the image attached below.

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Complete Question:

Consider the quadratic function f(x) = 1/5 x² – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).

Answer:

130 m

Step-by-step explanation:

See the attached, pleasantly presented, worksheet.

Answer: v = 2

Step-by-step explanation:

1. Distribute the 5 to the items within the parenthesis.

-3v + 5v - 10 = -6

2. Combine V terms and Isolate V from other terms.

2v = 4

3. Divide both sides by 2.

v = 2

Answer:

4 books a day

Step-by-step explanation:

$30 ÷7=4.28

so If you sell 4 books a day you get $30 I'n the end of the week

Using the vertical angle image we get the following answers:

Given the equations are:

42 = 4x-4 and 24 = x+50.

According to vertical angles theorem, when two lines intersect the opposite angles are equal and adjacent angles are supplementary.

we know that,

∠2 = 4x-4 and ∠4 = x+50

a)To Find the value of x:

4x - 4 = x + 50

4x - x = 50 + 4

3x = 54

x = 54/3

x = 18

b) To Find the measure of ∠2:

∠2 = 4×18 - 4 = 72 - 4

= 68

c)  Angles 2 and 3 are supplementary so their sum is 180°.

∠2 + ∠3 = 180

68 + ∠3 = 180

∠3 = 180 - 68

∠3 = 112°

Hence we get the required angles.

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Your question is incomplete. Please find the missing content here:

Using the vertical angle image from problem 1, let ∠2 = 4x-4 and ∠4 = x+50.

A. What is the value of x?

B. What is the measure of ∠2?

C. Find the measure of ∠3.

The rate of change of the function shown in the graph is $0.5 per minute.

What is rate of change?

The rate of change (ROC) measures how quickly a variable alters over a predetermined amount of time. When discussing momentum, the term "rate of change" is frequently used. It is typically defined as the ratio of a change in one variable to a matching change in another; visually, the rate of change is represented by the slope of a line. The Greek letter delta (Δ) is usually come in use to represent the ROC.

As shown in the graph,

The x-axis represents the minute and y-axis represents the cost.

and the cost is function of time.

For each 10 minute the cost increased $5

So, the cost is changing at a rate of $5 per 10 minute

$5 = 10 minutes

diving both side with 10

$0.5 = 1 minute

Therefore, the rate of change of the function shown in the graph is $0.5 per minute.

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Solution

Given the graphs below

For the graph of figure A and B:

Figure A and figure B are congruent.

Hence, yes they are congruent.

The transformation that map figure A onto figure B is to rotate figure A clockwise 90° about the origin.

For the graph of C and D:

Figure C and figure D are congruent.

Hence, yes they are congruent.

The transformation that map figure C onto figure D is reflect figure C over the y-axis

Answer:

solve the following system of equations by using gauss elimination method

Answer:

-5 2

Step-by-step explanation:

Answer:

AS shown in the purse

Step-by-step explanation:

A. The school attendance happens in the sixth week

B. A(13) ≈ 42$

meaning : In the Thirdteenth week. The student attendance rate is 425

C. A(x)=400 =) x = 10

in the tenth week.The student attendance rate is 400

D.in the fourth week the least attendance nce.

E. It has 450 students

The number of attendance increased to 450.

And the area was flat

Answer: 2.5 meters below sea level

Step-by-step explanation:

0.5 + 2 = 2.5

Hope this Helps!

The mean of the 10 sales amounts for store A is $40,000

The  least-squares regression line is

y=-3000+1.2x

where

x represents the sales amounts each day at store A

y represents the sales amounts each day at store B

we have

y=$45,000

substitute the value of y in the linear equation and solve for x

45000=-3000+1.2x

1.2x=48000

x=40000

therefore

The mean of the 10 sales amounts for store A is $40,000

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Check the picture below.

Answer:

[tex] \huge \sf \: x = 30[/tex]

Step-by-step explanation:

x/3 = 10

[tex] \frac{x}{3} = \frac{10}{1} [/tex]

Cross multiply

x = 30