A candy box is made from a piece of cardboard that measures by inches. Squares of equal size will be cut out of each corner. The sides will then be folded up to form a rectangular box. What size square should be cut from each corner to obtain maximum​ volume?.

In this equation the solution for x in terms of a and b is 8.

What is equation?

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.

Sol- As per the question given that- ax-3= bx+5------(equation 1)

Let ax=3-----(equation 2)

And bx =5------(equation 3)

On adding equation(1)and (2) we get

(ax)+(bx)= 3+5

(ax)+(bx)=8

x(a+b)+y(a+b)=8

(x+y)+(a+b)=8

1×(a+b)=8

Thus

a+b=8

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If I'm not mistaken, the answer is 43.17

The graph of the equation is attached to the solution.

We can graph the equation of the line by finding the x and y intercept of the line.

We know that the equation is in the slope intercept form.

Hence, we can write the y-intercept of the line as 2.

The coordinates of the point will be (0,2).

To find the x - intercept, we can put y = 0

0 = 2x + 2

-2 = 2x

x = -2/2 = -1

x = -1

The coordinates of the point will be (-1,0).

We can find another point on the line.

Let x = 1

y = 2(1) + 2

y = 2 + 2

y = 4

The coordinates of the point will be (1,4).

We can plot these points on the graph and get our graph.

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Solution:

Given that;

To find the amount in 5 years, we will apply the compound interest formula below

Substitute the values of the variables into the formula above

Hence, the answer is B

Answer:

Step-by-step explanation:

(4x + 50)° = 150°

4x = 150° - 50°

4x = 100°

x = 100° / 4 = 25°

Using the information of the factors f ( x ) are

The term function as used n math refers to a relation consisting of variables. the variables are of two major types which include

The given function is substituted in the several equations given but the equations that yielded the desirable result of f ( x ) = 0 are:

Therefore they are the correct choice

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The coordinates of the rotated triangle will be (2, - 2) , (3, -8) , (7, 0)

Function translation takes a function (and its graph) and, by adding and subtraction, moves the graph around the plane without changing its shape.

Given is a triangle coordinate on x - y plane.

The rule (x, y) → (- x, - y) represents the rotation of a figure by 180 °.

Now, initially the coordinates of the triangle are -

(-2, 2) , (-3, 8) , (-7, 0)

After transforming the graph by the rotation of 180°, the new coordinates will be -

(2, - 2) , (3, -8) , (7, 0)

Plot the coordinates on the graph and you will get the rotated image.

Therefore, the coordinates of the rotated triangle will be (2, - 2) , (3, -8) , (7, 0).

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The coordinates of the point C on the line AB such that AC is 2/3 the length of AB is (3,6) .

In the question ,

it is given that

the coordinates of the end points of A and B is A(-1,2) and B(5,8) .

also AC = 2/3(AB)

So , AC/AB = 2/3

and given that point C is on the line AB , hence AC+CB=AC

2+CB=3

So , CB=1

hence AC/CB = 2/1

so , the point C divides the line AB in the ration 2:1 .

and we have the coordinates of end points ,

that is x₁[tex]=[/tex] -1 , y₁=2 and x₂=5 , y₂ = 8 and the ratio m=2 and n=1 .

Substituting the above values in the section formula ,

which states that the coordinate of point C will be

((m*x₂+n*x₁)/(m+n)  ,  (m*y₂+n*y₁)/(m+n))

= ((2*5+1*(-1))/(2+1) , (2*8+1*2)/(2+1))

= ((10-1)/3 , (16+2)/3)

= (9/3 , 18/3)

= (3,6)

Therefore , The coordinates of the point C on AB such that AC is 2/3 the length of AB is (3,6) .

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Solution

For this case we can do the following:

tan x = 35/30

And we can solve for x and we got:

And rounded to the nearest degree is:

49º

Average speed is 35.56 mph.

Calculating average speed involves dividing the whole distance travelled by the total time it took to cover that distance. Speed is the rate of movement of something at a specific time. Average speed refers to the average speed during the course of a journey.

We have to find the average speed of the whole journey.

First we have to find total distance for whole journey and then total time for whole journey.

Total distance for whole journey = 30 miles + 50 miles = 80 miles

Time for 30 miles = distance/speed = 30/40 = 3/4 hrs  = 0.75 hrs

Total time = 1.5 + 0.75 hrs = 2.25 hrs

Average speed =  total distance/ total time

= 80/2.25

= 35.56 mph.

The average speed is 35.56 mph.

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Answer:  m=1/5

Step-by-step explanation:

Solution:

Let the score for the seventh test be represented below as

The mean score t be attained after the sevent tests is

The scores from the 6 tests are given below as

To figure out the seventh score, we will do the calculation below

Hence,

The final asnwer is

Plug in the values in the right positions. And simplify.

[tex] = \frac{1}{2} (12 \times \frac{1}{4} ) - \frac{1}{2} \\ = \frac{1}{2} (3) - \frac{1}{2} \\ = \frac{3}{2} - \frac{1}{2} \\ = \frac{2}{2} \\ = 1[/tex]

OPTION C IS THE ANSWER .

Answer: y=x/3 + 4

Step-by-step explanation:

Answer:

y = 4x - 1.5

Step-by-step explanation:

We need to find the slope (m) and the y-intercept (b), if we are writing this in the slop intercept form of a line.

y =mx + b

The slope is the change in y over the change in x.

The two points give us the y's ad x's

The y's are: -1.5 and 2.5

The x's are: 0 and 1

[tex]\frac{-1.5 - 2.5}{0-1}[/tex] = [tex]\frac{-4}{-1}[/tex] = 4  A negative divided by a negative is a positive.

We have the slope.  The slope is the point (0,b).  We are given that point.

(o, -1.5)  The y-intercept is -1.5

y =mx + b

y = 4x - 1.5

When the expression (m²/³ n⁻¹/³)⁵ is rewritten, the equivalent expression is   ∛m¹⁰n⁻⁵

From the question, the expression is given as

(m2/3n-1/3)^5

Rewrite the expression properly

So, we have the following representation

(m²/³ n⁻¹/³)⁵

Express the radicals as roots

So, we have

(m²/³ n⁻¹/³)⁵ = (∛m² ∛n⁻¹)⁵

Remove the brackets in the expression

This is done by multiplying the exponents

So, we have

(m²/³ n⁻¹/³)⁵ = (∛m¹⁰ ∛n⁻⁵)

Combine the roots

(m²/³ n⁻¹/³)⁵ = ∛m¹⁰n⁻⁵

Hence, the equivalent expression is  ∛m¹⁰n⁻⁵

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The required simplified expression is given as ∛[m¹⁰/n⁵].

Given that,
For an expression (m²/³n-¹/³)⁵ we have to deduce the function that the solution only consists of the positive integer exponents.

Here,
Rewriting the given expression,
= (m²/³n-¹/³)⁵
Simplifying the expression,
using the property, (xᵃ)ᵇ = xᵃᵇ
= m¹⁰/³n⁻⁵/³
= [m¹⁰n⁻⁵]¹/³
we imply cube root for the exponent 1/3.
= ∛[m¹⁰n⁻⁵]
= ∛[m¹⁰/n⁵]   (using the property x⁻¹ = 1 / x )

Thus, the required simplified expression is given as ∛[m¹⁰/n⁵].

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Answer:

x-intercept (-2,0)

y-intercept (0,-3)

Step-by-step explanation:

to find the x-intercept we set y=0

so 3x=-6

x=-2

to find the y-intercept we set x=0

so 2y=-6

y=-3

The probability that, before the low fuel light comes on the car will travel is 0.2576

Given,

The average number of miles driven on a full tank of gas before its low fuel light comes on is ( μ )= 320

It follows the standard deviation of ( δ ) = 30

For the normal distribution,

P(X < x) = P( Z < x - μ / δ)

a)

P( X < 330) = P( Z < 330 - 320 / 30)

                   = P( Z < 0.3333)

                   = 0.6306

b)

P( X > 308) = P( Z > 308 - 320 / 30)

                  = P( Z > -0.4)

                  = P( Z < 0.4)

                  = 0.6554

c)

P( 305 < X < 325) = P( X < 325) - P( X < 305)

                             = P( Z < 325 - 320 / 30) - P( Z < 305 - 320 / 30)

                             = P( Z < 0.1667) - P( Z < -0.5)

                             = 0.5662 - ( 1 - 0.6915)

                             = 0.2576

d) P(X = 340) = 0

Since X is a continuous random variable (For normal distribution).

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Answer:

A. [tex]9n - 190 = 5n[/tex]

Step-by-step explanation:

Dora earning 5 dollars per song is represented by [tex]5n[/tex].

Gary earning 9 dollars a song but paying the $190 fee is represented by [tex]9n - 190[/tex] because the fee from the coffee shop is subtracted from his total earnings.

we get that:

so the answer is x=-6

The expression for the total cost is 75 + 22h

From the information, the plumber charges a flat fee of 75 to visit a home and examine a clogged drain and also charges an additional 22 per hour spent fixing the drain.

Therefore, the amount that will be charged for each hour will be:

= 75 + (22 × h)

= 75 + 22h

where h = number of hours.

For example if the number of hours is 5 hours. This will be:

= 75 + 22h

= 75 + 22(5)

= 75 + 110

= 185

Your information was incomplete but an overview was given.

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We need to know about scaling of measurements to solve the problem. The length of the bird's beak is 5.29 inches.

In the given question we know that the height of the bird in the photo is 3.4 inches and the real height of the bird is 3.75 feet. We know that the length of the beak in the photo is 0.4 inches, we need to find out the real length of the beak. We need to find by how much the measurement of the bird is scaled down to fit in the photo. We need to convert feet to inches first to get the scaling factor, we can then divide the length of the beak given by the scaling factor.

3.75 feet= 3.75x12 =45 inches

scaling factor= 3.4/45=0.0756

real length of beak=0.4/0.0756=5.29 inches

Therefore the length of the beak of the bird is 5.29 inches.

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- 5 < x < 5

Number line:

Using proportions, two ways of writing the fraction of these books that you read is:

4/12 and 1/3.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations, especially multiplication or division.

One example of application of proportions is for relative frequencies, as a relative frequency is given by the number of successes in the sample divided by the sample size.

In the context of this problem, it is found that:

Hence the relative frequency is:

4/12.

12 is divisible by 4, hence the fraction can be simplified as follows:

1/3.

The number of books is missing, and is of 12. (researching the problem on a search engine).

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For the given function

The sum of all angles = 360°

So,

So, the difference between x and y will be:

So, the answer will be:

∠x is 91° smaller than ∠y

The proof of (g/n)/(g/m) isomorphic to g/m from the first isomorphism theorem is as shown below.

Let a group g with normal subgroups m and n. Furthermore, n is a subset of m.

Proof: We have to prove (g/n)/(m/n) ≅ g/m           (1)

g/m and g/n are valid because m and n are normal in g. As normality satisfies the intermediate subgroup condition, n is normal in m. because normality is image-closed m/n is a normal subgroup in g/n. Under the quotient map by n, the normal subgroup m of g is sent to a normal subgroup m/n of g/n. Thus the L.H.S of the statement to prove makes sense.

To describe the isomorphism from the left side to the right side

φ: g/n \to g/m

ψ(gn) = gm

So, a coset of n is taken by the map and it gives the corresponding coset of m. This is well-defined, because if h∈ n, thus h∈ m, hence (gh)m = g(hm) = gm.

The map is a homomorphism. So we observe that it maps the identity element to the identity element, keeps group multiplication preserved, and also preserves the inverse map.

Also, the map is surjective because any coset gm is present as the image of gn under ψ.

Lastly, we need to find the kernel of the map which is given by the set of gn such that gm = m. This is those cosets of n that are in m, and this is the same as the coset space m/n. Thus the kernel of the map is exactly g/m. Thus, the surjective homomorphism ψ: g/n → g/m has kernel m/n. And now by the first isomorphism theorem

(g/n)/(m/n)≅g/m     where ≅ shows isomorphism

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Answer:

4 Eggs are left since he uses 2 eggs per 1 loaf so 2x4=8

Step-by-step explanation:

Answer:

Angles gh, fh,  and jh are perpendicular :)

Step-by-step explanation:

perpendicular is when line touch and they make a 90* angle and the three angles that i have listed all touch and make 90*

Answer:

Trapezoid

Step-by-step explanation:

The area of this parallelogram is its height (half-height of the trapezoid) times its base (sum of the bases of the trapezoid)

Answer:

7

Step-by-step explanation:

Let x be the "integer."  We'll assume it is odd.

The next consecutive odd integer would be x+2.

(2(x+2) - x) =9    [When an integer is subtracted from 2 times the next consecutive odd integer the difference is 9]

(2(x+2) - x) =9

(2x+4) - x) =9

x+4 =9

x = 5

The greater integer is x+2 or 7

Check:

If 5 is subtracted from 2 times the next consecutive odd integer, 7, is the difference 9?

2*7 - 5 = 9?

14 - 5 = 9?

14 - 5 = 9?  YES