Under his cell phone plan, Gabriel pays a flat cost of $52.50 per month and $5 per gigabyte. He wants to keep his bill under $75 per month. Write and solve an inequality which can be used to determine 9, the number of gigabytes Gabriel can use while staying within his budget.

X is 55 after rearranging the equation given

x(t) = [tex]c_1e^1^4^t+c_2e^-^t[/tex]  , y(t) = [tex]2c_1e^1^4^t-c_2e^-^t[/tex]   is the general solution of the sytem of differention eqution dx/dt = 4x+ 5y , dy/dt = 10x + 9y .

given  dx/dt = 4x+ 5y  and dy/dt = 10x + 9y

X'(t) = [tex]\left[\begin{array}{ccc}4&5\\10&9\end{array}\right][/tex]  X

where X = [tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex]

so A = [tex]\left[\begin{array}{ccc}4&5\\10&9\end{array}\right][/tex]

now we need to find eigen value of the matrix and the corresponding eigen vector.

| A- λI | = 0

so after equation the value to zero

λ = 14 and λ = -1

now for the  λ = 14 corresponding eigen vector = [tex]\left[\begin{array}{ccc}1\\2\\\end{array}\right][/tex]

for λ = -1 corresponding eigen vector =  [tex]\left[\begin{array}{ccc}1\\-1\\\end{array}\right][/tex]

So general equation is given by:

X(t) = [tex]c_1e^1^4^t[/tex]  [tex]\left[\begin{array}{ccc}1\\2\\\end{array}\right][/tex]  +  [tex]c_2e^-^t[/tex]   [tex]\left[\begin{array}{ccc}1\\-1\\\end{array}\right][/tex]

after solving this

x(t) = [tex]c_1e^1^4^t+c_2e^-^t[/tex]

y(t) = [tex]2c_1e^1^4^t-c_2e^-^t[/tex]

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Answer:

The area of the dog pen is 522 [tex]ft^2[/tex].    (feet squared)

The perimeter of the dog pen is 94 feet

Step-by-step explanation:

Area

Here is the formula for the area of a rectangle.

[tex]A=lw[/tex]

We are given

[tex]l=29\\w=18[/tex]

Lets evaluate [tex]A[/tex].

[tex]A=29*18\\A=522[/tex]

Perimeter

Here is the formula for the perimeter of a rectangle.

[tex]P=2w+2l[/tex]

We are given

[tex]l=29\\w=18[/tex]

Lets evaluate [tex]P[/tex].

[tex]P=2l+2w\\P=(2*29)+(2*18)\\P=58+(2*18)\\P=58+36\\P=94[/tex]

Rotation is the process of turning a figure a specific amount around a point. When we dilate a figure, we increase or decrease its size.

The circular movement of an item about a primary axis is referred to as rotation or spin. A revolving object in two dimensions only has one conceivable central axis and can revolve either clockwise or counterclockwise. There are many conceivable central axes and rotating orientations for a three-dimensional object.

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size.

On a coordinate plane, forms can be rotated and dilated in addition to translated and reflected. When a shape is rotated, the new shape is consistent with the old. When you dilate a shape, the resulting shape is similar to the original.

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Answer:

#1 multiply

#2 divide

#3 subtract

#4 subtract

#5 divide

Answer:

m = 2

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

We see the y increase by 4 and the x increase by 2, so the slope is

m = 4/2 = 2

So, m = 2

Answer:

  a.  y = 2.5x

  b.  markup: $30; retail price: $42

  c.  75%

  d.  y = 0.75x

Step-by-step explanation:

You want equations relating markup, retail price, and sale price on a phone that costs $12, is marked up 250%, then put on sale for $31.50.

The problem statement tells you the markup is 250% of the cost. You could write the equation as ...

  y = (250%)x

Or you can simplify it to a decimal number:

  y = 2.5x

The markup amount is ...

  y = 2.5(12) = 30

The markup amount is $30.

That is added to the cost to get the retail price:

  retail = $12 +30 = $42

The retail price of the phone is $42.

The sale price as a percent of the retail price is ...

  percent = (sale price)/(retail price) × 100%

  percent = 31.50/42 × 100% = 75%

The sale price is 75% of the retail price.

As in part (a), we could write this as ...

  y = (75%)x

or, in decimal, as ...

  y = 0.75x

<95141404393>

^answer:^

~10 cubic feet~

^step by step explanation:^

first, calculate the volume of the front “panel” of the shape. (5 cubic centimeters because 5 times 3 is 15 and 15 times 1/3 is 5. 5 times 2 is 10.

On solving the provided question, we can say that - on doing the fraction we have  [tex]\frac{1}{10} ; \frac{1}{100} ; \frac{1}{10000}[/tex]

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

here we have,

0.1 = 1/10

0.01 = 1/100

0.0001 = 1/10000

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A grocer makes a display of cans in which there are 10 rows.

The top row has one can and each lower row has two more cans than the row above it.

We can write it as sequence:

1, 3, 5, 7, . . .

We can observe that it's an arithmetic sequence: 1, 3, 5, 7, . . . , 2n-1

We know that the formula for the sum of n-terms of arithmetic sequence:

S(n) = (n/2)(1 + 2n-1)

Here, Sn = 100

So, (n/2)[1 + 2n-1] = 100

n(1 + 2n + 1)

n(2n) = 200

2n^2 = 200

n^2 = 100

n = 10

Hence, the number of rows = 10

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David's deposit of $220 compounded continuously at a rate of 1.7% will become $260 after 10 years.

Here we have been given that David invested $220.

The interest rate was 1.7%

Since the amount was compounded continuously, there is no fixed date of when it was compounded, the whole process is taken as an exponential distribution.

There were no withdrawals or additional deposits to this, so our Principal is constant. Hence we can write the formula

Amount = Principal X eᵃˣ

where a = rate of interest/100

x = time

Therefore, we can say that

Ampunt after 10 years = 220 X e¹⁰ ˣ ⁰°⁰¹⁷

= $260.76707

rounding off to the nearest 10 dollars we get

= $260

Hence David's deposit of $220 compounded continuously at a rate of 1.7% will become $260 after 10 years.

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The 3 linear equations are

1. y = mx + b

2. ax + by = c

3. x/a + y/b = 1

1. y = mx + b is a linear equation in two variables, x and y. The equation is in the slope-intercept form, where m is the slope of the line and b is the y-intercept.

2. ax + by = c is a linear equation in two variables, x and y. The equation is in the standard form, where a and b are constants and c is the result of the equation.

3. x/a + y/b = 1 is a linear equation in two variables, x and y. The equation is in the general form, where a and b are constants and 1 is the result of the equation.

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Answer:

74,779,038,221

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given

[tex]5^3*7^5+9^8+0+0+0+0+0+0+9^7*5^6[/tex]

We can eliminate all the zeroes.

[tex]5^3*7^5+9^8+9^7*5^6[/tex]

Evaluate each term.

Raise 5 to the power of 3.

[tex]125*7^5+9^8+9^7*5^6[/tex]

Raise 7 to the power of 5.

[tex]125*16807+9^8+9^7*5^6[/tex]

Raise 9 to the power of 8.

[tex]125*16807+43046721+9^7*5^6[/tex]

Raise 9 to the power of 7.

[tex]125*16807+43046721+4782969*5^6[/tex]

Raise 5 to the power of 6.

[tex]125*16807+43046721+4782969*15625[/tex]

Multiply 125 by 16807.

[tex]2100875+43046721+4782969*15625[/tex]

Multiply 4782969 by 15625.

[tex]2100875+43046721+74733890625[/tex]

Add 2100875 and 43046721.

[tex]45147596+74733890625[/tex]

Add 45147596 and 74733890625.

[tex]74779038221[/tex]

A calculator would help but here you go.

Therefore, the multiple of the given equations is 10x^2yz + 6xyz^2, 5x^3y^2 + 14x^3y^3, and -10x^5 + 15x^4 - 30x^3 + 40x^2.

The process of multiplying two or more polynomials together is known as polynomial multiplication. Applying the distributive property to the multiplication of polynomials allows us to conduct polynomial multiplication.

Multiplication in mathematics is essentially just adding a number repeatedly in relation to another number. For instance, if we multiply 2 by 3, then implies that 3 gets multiplied by itself twice, meaning 3 + 3 = 6. Children can multiply numbers easily with the help of this method.

1. (5xy+3yz) * 2xz = 10x^2yz + 6xyz^2

2. (6/7x2y) * (35/6xy + 14/3 xy2) = 5x^3y^2 + 14x^3y^3

3. (2x3-3x2+6x-8) * (-5x2) = -10x^5 + 15x^4 - 30x^3 + 40x^2

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Answer:

It should be 6 because 6x6 is 36

Answer:

Step-by-step explanation:

fractions are division so just divide 36 by 6 and you will get 6 which is your answer

36/6 =

36 : 6 =

6

Coordinate (0,1) of y-intercept implies that a line or curve cross the Y axis

at 1.

The location of a point on the cartesian coordinate plane where a straight line or curve line as well as a plane crosses the Y axis is called Y-intercept. The coordinate of y-intercept is expressed as (0, y). This y value is y-intercept. The X coordinate of y intercept is zero.

In case of an equation of line while writing in slope-intercept form it is denoted by b such as y = mx+ b

in the above equation, b is y-intercept and m is the slope.

The y -intercept given by coordinate (0, 1) defines that a straight-line or curve line cross the Y axis at 1. The x coordinate of y -intercept is always zero because over the Y axis there is no value of X.

The y-intercept can have negative or positive value.

Suppose we have an equation of line 4x + 8y + 10 = 0

                                we will write it in a slope-intercept form

                                     8y = -4x - 10

                                     y = - 4x/8 - 10/8

                                    y = -1/2x - 5/4

In the above equation - 5/4 or -1.25 is the y-intercept that means the line crosses the Y-axis at -1.25

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The data of the rainfall amount in inches to the locations are used to plot the attached line plot created with MS Excel.

A line plot is a graph is the graphical display of data as check marks or points above a number line.

A line plot shows the frequency of the values in the data on the number line, using dots or check marks. The frequency of the data is shown above the specified locations on the graph of a line plot.

The line plot is therefore, indicative of how frequent particular values in the dataset are.

The possible data in the question are presented as follows;

Rainfall Amount; 1/8,[tex]{}[/tex] 3/8,  3/4,  3/4,     1/4,    1 1/4, 1/8,     1/4,    1,     1/8

Location;     [tex]{}[/tex]          1,    2,     3,      4,        5,       6,     7,       8,      9,    10

The frequency of the data in a tabular form are;

Rainfall        [tex]{}[/tex]  Frequency

1/8        [tex]{}[/tex]          3 locations

3/8        [tex]{}[/tex]         1 location

3/4        [tex]{}[/tex]         2 locations

1/4       [tex]{}[/tex]           2 locations

1 1/4       [tex]{}[/tex]         1 location

1        [tex]{}[/tex]              1 location

The above frequency values can be used to create the attached line plot created with MS Excel

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Answer:  sqrt(2)

Step-by-step explanation:

Remember that sec x = 1/cos x.

That means that sec 7pi/4 = 1/cos(7pi/4)

cos(7pi/4) = -cos(7pi/4 - pi)

                 = -cos(3pi/4)

cos(3pi/4) is a special angle which evaluates to -sqrt(2)/2.

Hence, -cos(3pi/4) evaluates to simply sqrt(2)/2

Since cos(7pi/4) is equal to -cos(3pi/4),

cos(7pi/4) is equal to sqrt(2)/2.

Lastly, sec 7pi/4 = 1/cos(7pi/4) , which is the reciprocal of sqrt(2)/2, that is 2/sqrt(2).

Rationalizing the answer 2/sqrt(2) gives sqrt(2)

The polygon presented will have nine sides. This suggests that a nonagon is the necessary polygon.

Divide the number of triangles in the polygon by 180° to determine the sum of its inner angles. Where is the number of sides, the formula for computing the sum of internal angles is (n 2) 180. In a regular polygon, all internal angles are equal.

The following are crucial polygon formulas: A polygon with "n" sides has a total interior angle sum of 180 degrees (n-2) A "n-sided" polygon has [n(n-3)]/2 diagonals. A regular n-sided polygon's internal angles are measured as [(n-2)180°]/n.

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Answer:

90

Step-by-step explanation:

If we know that for every cup, we can take 3 of 1/3-ounce cups, we can use an equation that looks like this:

number of cups × 3 = total 1/3-ounce cups

If there are 30 cups, then we can simply insert 30 into the equation.

30 × 3 = 90

Therefore, you can make 90 1/3-ounce cups from the cereal box.

The height of an acute triangle can be calculated using the Pythagorean Theorem. The formula for this theorem is a2 + b2 = c2, where a and b are the two legs of a right triangle and c is the hypotenuse.

To find the height of an acute triangle, we must first identify the two legs of the triangle. The length of the two legs can be determined by measuring the lengths of the three sides of the triangle. Once we have the lengths of the two legs, we can apply the Pythagorean Theorem to calculate the length of the hypotenuse.

Once the length of the hypotenuse is determined, we can use the formula h2 = c2 - a2 - b2 to calculate the height of the triangle. This formula states that the square of the height of the triangle is equal to the square of the hypotenuse minus the square of the two legs. So, to find the height of an acute triangle, we first measure the lengths of the three sides, then use the Pythagorean Theorem to calculate the hypotenuse, and finally use the formula h2 = c2 - a2 - b2 to calculate the height of the triangle.The height of an acute triangle can be calculated using the Pythagorean Theorem. The formula for this theorem is a2 + b2 = c2, where a and b are the two legs of a right triangle and c is the hypotenuse. To find the height of an acute triangle, we must first identify the two legs of the triangle. The length of the two legs can be determined by measuring the lengths of the three sides of the triangle. Once we have the lengths of the two legs, we can apply the Pythagorean Theorem to calculate the length of the hypotenuse.

Once the length of the hypotenuse is determined, we can use the formula h2 = c2 - a2 - b2 to calculate the height of the triangle. This formula states that the square of the height of the triangle is equal to the square of the hypotenuse minus the square of the two legs. So, to find the height of an acute triangle, we first measure the lengths of the three sides, then use the Pythagorean Theorem to calculate the hypotenuse, and finally use the formula h2 = c2 - a2 - b2 to calculate the height of the triangle.

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Answer:

1/ 0.8 kilograms

2/ 800 grams

Step-by-step explanation:

We know

1/

Baseball bat = 28 ounces

1 kilogram = 35 ounces

To find weight in kg we take

28 / 35 = 0.8 kg

2/

We know

1 kg = 1000 g

0.8 kg = 800 grams

So, the baseball bat weights 0.8kg or 800 grams

The increase was 250% over the original price.

percentage, a relative value indicating hundredth parts of any quantity.

let 'x' represent the original price, then 'x+0.25x' represents the first increase of 25%

six times greater, converted to a percentage:

(x+0.25x)×2×100 a second increase of six-fold

1.25x×2×100

250

The increase was 250% over the original price.

Hence, the increase was 250% over the original price.

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It will take 25 hours for Jenny to fill up the tank.

To solve this problem, we divide the capacity of the tank by the rate at which it is being filled:

500 gallons / 20 gallons/hour = <<500/20=25>>25 hours

Nate's car was filled with 16 gallons of gas.

The concept is used in this is equations. An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. An equation is the set of variables, constants, and mathematical operations like addition, subtraction, multiplication, or division balanced by an equal sign. For example, 3x + 5 = 15. There are different types of equations like linear, quadratic, cubic, etc.

As gas is $2. 09 per gallon at the gas station.

$2. 09 → per gallon

and Nate filled up his car and spent $33. 44.

$33. 44 for fully filled → how many gallons ?

So,

33.44 / 2.09 = 16 gallons.

Therefore, Nate filled 16 gallons gas in his car.

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Consequently, it would take polynomials roughly 690,64 years for the disintegrations to disappear.

A polynomial is a mathematical statement made up of coefficients and uncertainty that exclusively uses additions, subtractions, multiplications, and positive integer powers of variables. A single indeterminate x polynomial is represented by the expression x2 4x + 7. A polynomial is an expression in mathematics that consists of variables (sometimes referred to as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. A polynomial is an algebraic expression made up of coefficients and variables. The only operations that an expression can contain are addition, subtraction, multiplication, and non-negative integer exponents. These expressions are known as polynomials.

The formula for this is Activity = decay constant x atoms.

1238 = 2.64 x 1010 times the decay constant

decay constant is equal to 4.76 x 10-8 min-1.

Currently, the disintegrations are being slowed to 809 disintegrations per minute.

Ln(809) = Ln(2.64 x 1010) - Ln(4.76 x 10-8 x t)

t=3.63x108min = 690.64y

Consequently, it would take roughly 690,64 years for the disintegrations to disappear.

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The trigonometric functions are sin D = 28/53, sin E = 45/53, cos D =45/53, and cos E = 28/53 as fractions.

Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.

The trigonometric functions are given in the question

Apply the sine ratio on the given right triangle

⇒ sin(θ) = Perpendicular/hypotenuse

sin D = EF/DE

sin D = 28/53

sin E = DF/DE ,

sin E = 45/53

Apply the cosine ratio on the given right triangle

⇒ cos(θ) = Base/hypotenuse

cos D = DF/DE

cos D =45/53

cos E = EF/DE

cos E = 28/53

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Therefore , the solution of gross pay problem is 62% is this of her gross wage.

Hannah's take home pay of percentage 785 is 62.8% of her gross wage of 1250. This can be calculated by dividing 785 by 1250 and multiplying the answer by 100.

Here,

62.8% is the same as 0.628.

This can be calculated by dividing 785 by 1250.

To get the answer to the nearest whole percentage, we round up 0.628 to 0.63 which is 63%.

This means that Hannah's take home pay of 785 is 63% of her gross wage of 1250.

63% is the answer to the question: what percentage is Hannah's take home pay of her gross wage? This is correct to the nearest whole percentage.

To summarise, Hannah's take home pay of 785 is 63% of her gross wage of 1250, correct to the nearest whole percentage.

Hannah's take-home pay is 62.8% of her gross wage. This percentage is the result of taxes and other deductions taken by her employer.

Knowing this percentage can help Hannah better understand how much money she is taking home each week and how much money is being withheld from her paychecks.

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