Marvin is factoring the expression 54a^4+16ab^3 completely. What is the result

To solve this problem, we need to use the formula for the area of a rectangle, which is length times width. We can set up the formula as follows:

Area = length * width

Since we know that the width is 7 greater than ⅔ the length, we can represent the width as follows:

width = ⅔ * length + 7

We can substitute this expression for the width in the area formula to get the following:

Area = length * (⅔ * length + 7)

We are given that the area of the rectangle must be 172, so we can set up the following equation:

172 = length * (⅔ * length + 7)

To solve for the length of the rectangle, we can first distribute the length on the right-hand side of the equation, like this:

172 = length * ⅔ * length + 7 * length

We can then combine like terms on the right-hand side of the equation to get the following:

172 = ⅔ * length^2 + 7 * length

To solve for the length, we can use the quadratic formula, which is as follows:

length = (-b +/- sqrt(b^2 - 4ac)) / 2a

In this case, a = ⅔, b = 7, and c = -172. Plugging these values into the quadratic formula, we get the following:

length = (-7 +/- sqrt(49 - 4 * ⅔ * -172)) / 2 * ⅔

Simplifying this expression, we get the following:

length = (-7 +/- sqrt(49 + 576)) / ⅓

We can further simplify this expression by calculating the value of the square root, like this:

length = (-7 +/- sqrt(625)) / ⅓

Simplifying again, we get the following:

length = (-7 +/- 25) / ⅓

To find the final value of the length, we need to calculate the two possible values of the square root, which are 25 and -25. Plugging these values into the equation for the length, we get the following:

length = (-7 + 25) / ⅓ = 18 / ⅓ = 6

length = (-7 - 25) / ⅓ = -32 / ⅓ = -10

Since the length of a rectangle must be positive, we can discard the negative value and only consider the value of 6. This means that the length of the rectangle is 6, and the width is ⅔ * 6 + 7 = 11. Therefore, the dimensions of the rectangle are 6 by 11.

Answer:13 is a prime number

Step-by-step explanation:

Answer:

b) 13

Step-by-step explanation:

Now we have to,

→ find prime number from the options.

Generally we know that,

→ 2 is the only even prime number.

→ Other all prime numbers are odd.

Then the prime number is,

→ 13

(Because, it is the only odd number given)

Hence, the option (b) is correct.

Answer:

1/6

Step-by-step explanation:

A (6,1)

B (12,2)

slope = (2-1)/(12-6)

1/6

we are allowed to change the vertical axis on a line chart.

suppose we have a large range of value needed to plot along the vertical and horizontal axis, but the current line chart cannot meet this demand. in such cases, we can customize the scales to provide more vertical and horizontal spaces.

dramatic slopes are the steep slopes of a straight line calculated by vertical and horizontal coordinate of two points laying on it. By changing the vertical axis as well as the horizontal axis we can plot a graph of a straight line more properly and finally more dramatic slope is visible there.

hence, we can change the scale values on a line chart to meet the requirement of the plot.

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Clark will have $5820.80 in his account when he turns 22.

With an example, what is compound interest?

The interest you earn on interest is known as compound interest. Simple math may be used to demonstrate this: if you have $100 and it generates 5% interest annually, you will have $105 at the end of the first year. You will wind up with $110.25 at the conclusion of the second year.

Clark reportedly placed $5000 at a constant 3.8% interest rate when he was 18 years old.

Using the compound interest calculation, we can calculate how much Clark will make when he turns 22.

[tex]A=P . e^{rT}[/tex]

A= Amount after T years.

P= Principal amount.

e= Mathematical constant e.

r= Interest rate (in decimal form).

T=  Time in years.

Let's decimalize the interest rate we've been given.

3.8 percent = 3.8/100 = 0.038

When we enter our provided values into the formula above, we will obtain,

[tex]A=5000 * e^{0.038(22-18)} \\A=5000*e^{0.038(4)}\\A=5000*e^{0.152}\\A=5000*1.1641\\A=5820.80[/tex]

Clark will therefore have $5820.80 in his account when he turns 22.

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Here is the two column proof:

    Statement                                        Reason                                              

===================================================

    Statement                                        Reason                                              

The area of the figure is 84.139 square ft

From the question, we have the following parameters that can be used in our computation:

Shapes = Rectangle and Semicircle

For the rectangle, we have

Length = 5 ft and Width = 14 feet

For the circle, we have

Diameter = 14 ft - 4 ft - 4 ft

Evaluate

Diameter = 6 feet

Start by calculating the radius of the semicircle

So, we have the following representation

radius = Diameter/2

This gives

radius = 6/2

Evaluate

radius = 3

The area of the shape is then calculated as

Area = Length * WIdth + πr²/2

So, we have

Area = 5 * 14 + 3.142 * 3²/2

Evaluate

Area = 84.139

Hence, the area is 84.139 square ft

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The following equation are perpendicular to each other .

The equation of a line in slope intercept form can be represented as follows:

y = mx + b

where

Therefore, perpendicular lines have slopes that are the opposite of the reciprocal of each other.

Hence,

The equation perpendicular to y = 1 / 3 x + 4 is  y = -3x - 4.

The equation perpendicular to y = 2 / 5 x - 7 is  y = - 5 / 2 x + 7.

The equation perpendicular to y = - 5 / 2 x + 8 is  y = 2 / 5 x - 6.

The equation perpendicular to y = -2x + 6 is  y = 1 / 2 x + 3.

The equation perpendicular to y = 7 / 5 x - 9 is  y = - 5 / 7 x - 11.

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Answer:

3 hr

Step-by-step explanation:

750 ml  /  (250 ml/hr) = 3 hr

Answer:

To solve this inequality, we need to isolate the x-variable on one side of the equation. To do this, we can add 38 to both sides of the equation to get the following:

-200 - 12x - 38 = 38

-200 - 12x = 76

Next, we can divide both sides of the equation by -12 to get the following:

-200 - 12x = 76

x = -17

Finally, we can use the value of x to determine how long it will take the explorer to reach an elevation deeper than -200 feet. Since the explorer moves at a rate of -12 feet per minute, it will take her 17 minutes to reach this depth.

The value of the given equation 3 2/3x = 2 2/5 is 36/55.

A mixed number is one that combines a whole number and a legal fraction. A number that contains both an integer (whole number) and a correct fraction is known as a mixed number or mixed fraction.

Pretzels, peanuts, Cheerios, and of course, rice and corn Chex are all included in this mix, which is why it is called a mix. Mixed numbers are those that contain both an integer and a fraction.

A mixed fraction is a fraction that is represented by both its quotient and remainder. For instance, 2 1/3 is a mixed fraction, where 2 is the quotient and 1 is the remainder. Therefore, a mixed fraction is a combination of a whole number and a proper fraction.

3 2/3x= 2 2/5

11/3 x=12/5

55x=36

x=36/55

Therefore, the value of the given equation 3 2/3x = 2 2/5 is 36/55.

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Answer: 1.06

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Answer: c = 7

Step-by-step explanation:

180 = 86 + 31 + 9c
180 = 117 + 9c
63 = 9c
7 = c

Answer:

  c = 7°

Step-by-step explanation:

You want the value of c given that angles in a triangle are marked 86°, 31°, and 9c.

The angle sum theorem tells you the sum of angles in a triangle is 180°. Using given angle values, this means ...

  86° +31° +9c = 180°

  117° +9c = 180° . . . . collect terms

  9c = 63° . . . . . . . subtract 117°

  c = 7° . . . . . . . . divide by 9

The value of c is 7°.

Answer:

y = 10.5x - 8.25

Step-by-step explanation:

m = (44.25 - 12.75)/(5 - 2) = 10.5

y = mx + b

y = 10.5x + b

12.75 = 10.5 × 2 + b

b = -8.25

y = 10.5x - 8.25

Answer:

C. 7°F

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

2x + 1 ≥ 0

2x ≥ -1

2/2 x ≥ -1/2

x ≥ -1/2

√(2x+1)² = (4-1)²

2x + 1 = 3²

2x = 9 - 1

2x = 8

2/2 x = 8/2

x = 4

We follow the inclusive rule, The answer to the question is (A) that is

if y>=10 and y <=50

In mathematics, an interval is expressed in numerical terms. All the numbers between two specific integers are referred to as an interval. All actual values between those two are included in this range. Any form of number you may imagine is a real number.

The intervals used are:

(a , b) , All the numbers between a & b without including them.

[a, b] , All the numbers between a & b including them.

y lies in [10,50].

And since it means that it includes 10 and 50 and all the numbers between them.

The final answer is (A) that is if y>1=10 and y <=50.

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Triangle ΔPMO and  ΔNMO are congruent, therefore  ΔPMO ≅ ΔNMO.

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of the angles of a triangle is always 180°

Given that,

MO bisects ∠PMN and OM bisects ∠PON.

1.

MO bisects ∠PMN,

Reason : It is given condition.

2.

∠PMO ≅ ∠NMO

Reason : The image is symmetrical, therefore ∠PMO ≅ ∠NMO.

3.

MO = MO

Reason : In triangle, PMO and NMO the side MO is common,

Therefore, MO = MO

4.

OM bisects ∠PON.

Reason : It is given condition.

5.

∠POM =  ∠NOM

Reason : The image is symmetrical, therefore  ∠POM =  ∠NOM.

6.

ΔPMO ≅ ΔNMO

Reason : The figure is symmetric, and triangle ΔPMO and  ΔNMO are congurent.

Therefore, ΔPMO ≅ ΔNMO.

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Answer:

angle b

Step-by-step explanation:

let's assume the triangle is a right angle triangle . either angle a or c can be equal to 60 degree

Answer:

100000000000000000000000000000000000000000000000000

Step-by-step explanation:

Answer:

The slope of a line parallel to the line with slope m=3/4 is also m=3/4. Parallel lines have the same slope.

Both the coordinate points are plotted on the graph. The cartesian graph is attached with the answer.

Given are the two coordinates to be plotted on a Cartesian plan -

(5, 4) , (3, 4).

The two given coordinate points are (5, 4) , (3, 4).

Refer to the graph attached. It shows both the points plotted.

Therefore, both the coordinate points are plotted on the cartesian graph.

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a. Correlation coefficient, r. =0.76751

b. Linear regression line y=6.5071+1.3929x

c. mean amount of sugar when temp. is 1.7

  then y=8.87503

A correlation coefficient is a statistical indicator of how well changes in one variable's value predict changes in another. When two variables are positively linked, the value either rises or falls together.

According to linear regression, sales are predicted to equal 168 + 23 advertising when using advertising as the predictor variable. This means that if spending on advertising is increased by one million euros, sales should grow by 23 million euros, and if no advertising was done, sales should be 168 million euros.

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Max can draw Rectangles of side lengths which are the integral divisors of 24 that can be (2,12) or (3,8) or (4,6) etc.

You can calculate a rectangle's area if you know its length and width. However, because these two amounts are distinct, you can't do a reverse computation to find both of them if you only know the area. You can find both of them in the specific case where they are equal, which gives the shape of a square, and you can compute one if you know the other. If you are aware of the rectangle's perimeter as well, you can utilize that knowledge to determine two potential length and width numbers.

Area of a Rectangle = Length × Breadth

Area= 24 square centimeters

So, Side Lengths or Breadth of the Rectangle can be the divisors of 24.

Lengths and Breadths can be (2,12) or (3,8) or (4,6) etc.

Max can draw Rectangles of side lengths which are the integral divisors of 24 that can be (2,12) or (3,8) or (4,6) etc.

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According to the Pythagorean theorem, The Answer is Yes the third side is greater than 1 foot.

A right triangle is one that has an interior angle of 90 degrees. The hypotenuse, which is also the side of the right triangle that faces the right angle, is its longest side. The height and base make up the two arms of the right angle.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

p=1 foot

b=1 foot

[tex]h^{2} = p ^{2} + b ^{2}[/tex]

[tex]h=\sqrt {1^{2}+1^{2}}\\=\sqrt 2\\=1.41\\[/tex]

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The equation that calculates the number of scoops of ice cream that can be purchased is 0.20x = 5, and the number of scoops that can be purchased is 25.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

The definition of an equation is algebra is a mathematical assertion that shows the equality of two mathematical equations.

For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

So, we know that 1 scoop of ice cream is $0.20.

Anna wants to purchase scoops for $5.00.

Let, the number of scoops is x.

Now, form the equation as follows:

0.20x = 5

x = 5/0.20

x = 25

Therefore, the equation that calculates the number of scoops of ice cream that can be purchased is 0.20x = 5, and the number of scoops that can be purchased is 25.

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Answer:

Below

Step-by-step explanation:

x - y = 8     find slope of this line , parallel slope is the same

 re-arrange the given line equation to y = mx + b form (m= slope)

y = (1) x-8    has slope = 1

Answer:

no

Step-by-step explanation:

If the triangles are similar, then the ratios of the lengths of corresponding sides must be equal.

3/4 must equal 5/6 which must equal 6/7

3/4 = 0.75

5/6 = 0.8333...

6/7 = 0.857142...

None of the ratios are equal, so the triangles are not similar.

The expression representing the situation is (r+6).

An expression in maths is a sentence with a minimum of two numbers or variables and at least one maths operation.

Given that, Conrad has 6 more marbles than Rory and r represents the number of marbles that Rory has,

We see, Conrad has more marble than Rory and Rory has r marbles,

Mathematical can be represented as,

c = r+6

Hence, The expression representing the situation is (r+6).

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For a given t-value is 1.67 in an upper-tailed test , the interval below that contains the p-value is 0.05487.. So, the correct option is option (d) .

Values are given as,

test- statistic , t-value = 1.67

degree of freedom = 21

Using upper tailed test,

Using EXCEL function to find the p-value:

Function : =T.DIST.RT (t-value , deg -freedom)

Settings : =T.DIST.RT (1.67 , 21) = 0.05487

We used only positive value to find the upper tailed p-value .

lower tailed p-value ,

Settings : =T.DIST.RT ( - 1.67 , 21) = 0.94516

So, 0.05 < p-value < 0.95.. The interval value of p-value for upper tailed test is 0.005..

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