the sum of four times a number and six divided by the number squared

The dimensions of the mold are a length and width of 3 inches and a height of 7 inches.

The volume of a rectangular prism is the space that it contains. We know that the volume of any prism is calculated by multiplying its base area by its height.

Given :

Let's assume that the length and the width of the "box" is x.

It is said that the height is 4 inches greater, so the height is x+4.

The volume of the mold is:

V = (x)(x)(x +4)

V = x²(x +4 ) using the Distributive Property.

V = x³ + 4x²

Since from the question we have Volume = 63 cubic inches

The equation we have is,

63 = x³ + 4x²

Subtracting 63 from both sides of the equation,

x³ + 4x²- 63 = 0

The cubic equation can be written as,

(x−3)(x²+7x+21) = 0

The solution of the quadratic equation (x²+7x+21) is,

x = -b ±√(b² - 4ac) / 2a

a = 1 , b =7 and c = 21

Substituting the values in the formula,

x = -7 ±√(7² - 4(1(21)) / 2(1)

x = -7 ±√-35 / 2

Hence,there are no real solutions to the quadratic equation.

There is only one real solution to the equation x = 3.

Therefore, the length and width of the rectangular prism are 3 inches and the height is x+4 = 3+4 = 7 inches.

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Answer:

Step-by-step explanation:

Answer:1 1/12

Step-by-step explanation: 3/4+1/3=13/12=1 1/12

Answer:

0.375

Step-by-step explanation:

-3x+14-11+11x

-3x+11x = 8x

14-11 = 3

8x=3

÷8 on both sides

No, it is not feasible to produce any two structuring elements that is not always congruent with one another. This is because equilateral triangles have no internal angles.

This is further explained below.

Generally, In the field of geometry, a triangle is said to be equilateral if all three of its sides have the same length.

In the well-known geometry of Euclidean, an equilateral triangle is also an equiangular triangle. This means that all three of the triangle's interior angles are equivalent to each other and are each 60 degrees.

No, it is not possible to create any two equilateral triangles that are not always congruent with one another.

In conclusion, The logic for this is that while each angle in an equilateral triangle is 60 degrees, the sides of the triangle cannot always be identical.

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The amount in pounds of sliced ham he can buy is 083 pounds.

It costs $3.50 per pound of sliced ham at the deli and Weylan spent $2.90.

The number of pounds of sliced ham he bought can be calculated as follows:

Hence,

3.50 dollars = 1 pounds of sliced ham

2.90 dollars = ?

cross multiply

amount of pounds he bought = 2.90 × 1 / 3.50

amount of pounds he bought = 2.90 / 3.50

amount of pounds he bought = 0.82857142857

amount of pounds he bought = 0.83 pounds

Therefore, the amount of pounds bought to the nearest hundredth is 0.83 pounds.

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Answer:its 2

Step-by-step explanation:

Answer: c=1

Step-by-step explanation:

Move the variable to the left side

2c+8−10c=0

Subtract the terms

−8c+8=0

Move the constant to the right side

−8c=0−8

Subtract the terms

−8c=−8

Divide both sides

−8c  = −8

−8       -8

Simplify

Soyala travelled for 3 hours with a speed of 25 mph and 5 hours with a speed of 15 mph

We know that Distance = Rate x Time. The distance traveled to the library is assumed to be same as the distance traveled on the way to home from the library. Let t be the time it took to travel to the library after which (8 - t) = the time it took to travel back home. We can write following two equations using the formula for distance:

d = 25t ---------> (1)

d = 15(8 - t) = 120 - 15t -----------> (2)

Since the distance d is equal for both trips, let's set the two expressions of time t equal to each other.

25t = 120 - 15t

40t = 120

t = 3 hours

Therefore, Soyala travelled for 3 hours at 25 mph and for 8 - 3 = 5 hours at 15 mph. Each rate will yield a distance traveled of 125 miles.

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Regarding the scales to plot the points on the table, we have that:

To find the ideal scales, we have to verify which are the extrema values of each variable, that is, the minimum and maximum value of each x and y.

From the table, the minimum and maximum values of X are given as follows:

This is a small range of values, hence the horizontal scale should be of 1.

From the same table, second column, the minimum and maximum values of Y are given as follows:

This is a large range of values, hence an ideal vertical scale is of 200, as then the number of traces would be almost the same as the number of traces of x.

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Answer:

[tex](1)\;\;\;\text{Slope }= \dfrac{3}{5}\\[/tex]

(2) Equation of line in slope-intercept form is
[tex]y = \dfrac{3}{5}x + 3[/tex]

(3) Equation of line in standard form is:
[tex]5y - 3x = 15[/tex]

Step-by-step explanation:

Equation of a line in slope-intercept form is
y = mx + b

where m = slope and b = y-intercept

Slope = [tex]\dfrac{y2 - y1}{x2-x1}[/tex]

where (x1, y1) and (x2, y2) are two points on the line.

y2 - y1 is known as the rise
x2 - x1 is known as the run
Slope is also defined as rise/run

We are given x-intercept = -5.
The ex-intercept is the point at which the line crosses the x-axis. At this point the y-value = 0.

So we get one of the points (-5, 0)

We are given y-intercept = 3
The y-intercept is the point at which the line crosses the y-axis. At this point the x-value is 0

So another point on the line is (0, 3)

Knowing this we can compute rise and run
rise = y2 - y1 = 3 - 0 = 3

run = x2 - x1 = 0 - (-5) = 0+5 = 5

[tex](1)\;\;\;\text{Slope = $\dfrac{3}{5}$}[/tex]

(2) Equation is
y = mx + b where m = slope and b = y-intercept
Slope = 3/5 from (1) and y-intercept = 3

So equation of line in slope-intercept form is
[tex]y = \dfrac{3}{5}x + 3[/tex]

(3) Equation in standard form
In (2) subtract (3/5)x from both sides.

[tex]y - \dfrac{3}{5}x = 3[/tex]

We can multiply both sides by 5 to get
[tex]5(y - \dfrac{3}{5}x )= 5 \times 3\\\\= 5y - 3x = 15[/tex]

To find the scale factor, we just have to divide

The slope of the parallel line to line MN -6

From the question, the line is given as

Line MN

Also, we have the slope of line MN to be

Slope of MN = -6

As a general rule in linear functions and parallel lines

The slopes of parallel lines are equal

This means that any line that is parallel to the line MN and the line MN would have the same slope of -6

Hence, the slope of the line segments that are parallel to line MN is -6

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The postulate that could be used is the: linear pair postulate.

If two angles share a common side and also a common vertex lie on a straight line, they both form a special angle relationship that is called the linear pair.

Based on the linear pair postulate, it is proven that angles that form a linear pair add up to 180 degrees and are therefore regarded as supplementary.

Angle CAD and angle CAB have a common side, side CA, and a common vertex, angle A. They are also on the straight line, line AB.

Thus, it can be proved that the angles CAB and CAD are supplementary based on the linear pair postulate.

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IN THE ATTACHED PICTURE YOU CAN SEE THE YELLOW VERTICAL LINE TOUCHED THE GRAPH ONCE IT MEANS THE GRAPH ABOVE IS A FUNCTION.

THEREFORE THE LAST OPTION IS THE SOLUTION. THE GRAPH IS A FUNCTION BECAUSE IT PASSES THE VERTICAL LINE TEST .

HOPE THIS HELPS

Answer:

0.325 as a fraction is expressed as 13/40

Step-by-step explanation:

What is a fraction ?

A fraction is a portion of any quantity out of a whole. It consists of a numerator and a denominator.

To convert a decimal number into a fraction, we write the given number as the numerator and place 1 in the denominator right below the decimal point followed by the number of zeros required accordingly. Then, this fraction can be simplified.

In this case, 0.325 has three numbers after the decimal, so, we place 1000 in the denominator and remove the decimal point.

⇒ 325/1000

After reducing this fraction we get,

⇒ (325 ÷ 25) / (1000 ÷ 25) = 13/40

So, 0.325 as a fraction is 13/40.

(Hi fyi this answer took a lot of time & effort to make sure it was accurate, precise and to the point to be produced, so if you could opt this answer as the brainliest it would mean the world to me,)

Stay positive and Take care,

A fellow mate,

Cheers !

Answer:

Formula for slope is given as (y2-y1)÷(x2-x1) or (y1-y2)÷(x1-x2).

Slope of line = (14-8)÷(7-10)

                     = 6÷(-3)

                     = -2

Answer:

$569.80

Step-by-step explanation:

She worked $12.95 per hour for 6 hours of overtime, meaning we would multiply $12.95 by 6 which is equal to $77.70, since she worked for 38 hours that week, we would multiply $12.95 by 38 which is $492.10, so now we add how much she earned for the total. Her overtime pay was $77.70 + her regular pay was $492.10 which adds up to $569.80

Answer:

I believe you have a 25% of spinning an A

Step-by-step explanation:

If there are two possible A's to land on and there are 8 different choices,

2/8 = 1/4 and 1/4 is equal to 25%

So the probability would be "not likely"

Hope this helps! Please have an amazing day! :)

Answer:

1 7/8 inches is 1.875 in decimal form.

Answer:

slope = 0

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (7, - 6 ) and (x₂, y₂ ) = (6, - 6 )

m = [tex]\frac{-6-(-6)}{6-7}[/tex] = [tex]\frac{-6+6}{-1}[/tex] = [tex]\frac{0}{-1}[/tex] = 0

Step-by-step explanation:

a probability is always

desired cases / totally possible cases

25 students in total.

13 are female. therefore, 25-13 = 12 students are male.

15 students have an A.

10 students are female and have an A.

therefore, 15-10 = 5 male students have an A.

"given that a student is female".

this reduces our totally possible cases to 13.

so, the probability that a female student has an A is

10/13 = 0.769230769...

Answer: 10 cm

Step-by-step explanation: because i am alwauys right about your mom

In standard deviation, 120  is the percentile of this class.

Why is there a standard deviation?

Test statistic (z) = (weekly study time - average study time)/standard deviation

weekly study time = 2.3 hours

average study time =  .5 hours

standard deviation = 1.5 hours

z = (2.3 - 0.5)/1.5

   = 1.8/1.5 = 1.2 (to 2 decimal places)

Cumulative area of the test statistic is 1.2

Percentile = 1.2×100 = 120

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Answer:  The difference in temperature is 45.9F.

Answer:

2nd one

Step-by-step explanation:

Hope I helped!

Since y is directly proportional to x then the value of y is 8

In a proportional relationship, one variable is always equal to the constant value of the other.

It is clear that y increases in proportion to x by applying the direct proportionality formula, y = kx.

Given y is directly proportional to x.

Therefore y = kx

now at x = 20 , y = 16/5

∴16/5 = 20 k

or, k = 16 /100

Now at x = 50 ,

Y = 16 /100 × 50

or, y = 8

Therefore that value of y is 8.

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The relationship will be a solid line.

How many $4 meals you may purchase with a $100 school lunch card and how much money is still on the card.

Given that the slope is common and linear, the connection will be a solid line. The balance on the card will drop by $5 each time you purchase lunch.

Let x be the amount of lunches you purchase.

Let the balance on the card be = y.

Equation then becomes:

y= 105-4x

when x=1

y = 105 - 4(1) = 101

when x= 2

y= 105 - 4(2) = 97

when x=3

y= 105 - 4(3) = 93

We can see that the decline is gradual and same.

On the graph that is provided, you can also observe that a straight line is created.

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Step-by-step explanation:

in 3-dimensional math we have 3 dimensions, and not just 2.

we have

forwards - backwards

left- right

up- down

so, we have there x, y and z.

and the equations typically are

z = ax + by

or even more general

cz = ax + by

or more complex functions of x and y.

z = f(x, y).

I am not sure what else you could mean with that question.

Given:

The function is,

Replace x by -x in the given function,

It is observed that, when the x is replace by -x the function end up with exactly opposite of the given function.

Thus, the given function is odd.