Find the general solution of the given system. dx/dt = 4x+ 5y dy/dt = 10x + 9y
(x(t), y(t)) =

The time duration for the population to exceed 10,000 is approximately 6.6 hours

What is time ?

In mathematics, time is described as a continuing and continuous series of events that take place in chronological order from the past through the present and into the future. The duration of events, the gaps between them, or even the sequencing of occurrences can all be quantified, measured, or compared using time.

the time frame that an activity, process, or state lasts or continues to exist: duration is a non-spatial continuum that is measured in terms of subsequent occurrences from the past, present, and future.

The mathematical symbol used to represent the multiplication process and its subsequent product is the multiplication sign, sometimes referred to as the times sign or the dimension sign.

t = The time duration in hours

The initial population of the cells = 1,000

Therefore, at t = 0, P(0) = 1,000 = P₀ × 1.42^0

∴  P(0) = 1,000 = P₀ × 1 = P₀

P₀ = 1,000

When the population is 10,000, we have;

P(t) = 10,000 = 1,000 × 1.42^t

∴ 1.42^t = 10,000/1,000 = 10

㏒(1.42^t) = ㏒(10) = 1

∴ t × ㏒(1.42) = 1

t = 1/㏒(1.42) = 6.56649071898

∴ The time duration for the population to exceed 10,000, t ≈ 6.6 hours.

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Answer: k = 11

Step-by-step explanation:

[tex]\frac{11}{3k} = \frac{1}{3} \\\\[/tex]

Cross multiply:

[tex]11 * 3 = 1*3k[/tex]

[tex]33 = 3k[/tex]

[tex]k = 11[/tex]

Answer:

45 degree

Step-by-step explanation:

45+45 90 +90 180

All triangles will have 180 degrees angle

So the only boundary point of [0,∞) and (0,∞) is 0 itself. It is in [0,∞), so that set is closed. It is not in (0,∞), so that set is open.

In mathematics, a (real) interval is a set of real numbers that contains all real numbers lying between any two numbers of the set. For example, the set of numbers x satisfying 0 ≤ x ≤ 1 is an interval which contains 0, 1, and all numbers in between. Other examples of intervals are the set of numbers such that 0 < x < 1, the set of all real numbers

the set of nonnegative real numbers, the set of positive real numbers, the empty set, and any singleton (set of one element).

Real intervals play an important role in the theory of integration, because they are the simplest sets whose "length" (or "measure" or "size") is easy to define. The concept of measure can then be extended to more complicated sets of real numbers, leading to the Borel measure and eventually to the Lebesgue measure.

Intervals are central to interval arithmetic, a general numerical computing technique that automatically provides guaranteed enclosures for arbitrary formulas, even in the presence of uncertainties, mathematical approximations, and arithmetic roundoff.

So the only boundary point of [0,∞) and (0,∞) is 0 itself. It is in [0,∞), so that set is closed. It is not in (0,∞), so that set is open.

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The measure of the exterior angle of the triangle is 114 degrees.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

The measure of the exterior angle of the triangle can be found using exterior angle theorem.

Therefore, the exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.

Hence,

24 + 2x + 18 = 3x + 6

2x - 3x = 6 - 18 - 24

-x = -36

divide both sides of the equation by -1

x = 36

Hence,

exterior angle = 3x + 6 = 3(36) + 6 = 108 + 6 = 114 degrees

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Answer:

453

Step-by-step explanation:

To perform long division of 11,778 by 26, we follow these steps:

452

_____

26 ) 11,778

-104

------

157

156

----

21

Therefore, 11,778 divided by 26 is equal to 452 with a remainder of 21.

Hope this helps <3

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Answer:

6 and -13

Step-by-step explanation:

Absolute Values are magnitudes (only positive values) of any values (be it positive or negative.)

Example: |4.5| = 4.5, |-6.7| = 6.7

1. |2x + z| + 2y

= |2(2.1) + (-4.2)| + 2(3)

= |4.2 - 4.2| + 6

= 0 + 6

= 6

2. 4a - |3b + 2c|

= 4(-2) - |3(-3) + 2(2)|

= -8 - |-9 + 4|

= -8 - |-5|

= -8 - 5

= -13

5. The width of the house. = 30 feet

6. The height of the house. = 22.5 feet

7. The height of the first floor. = 12.5 feet

8. The height of the roof. = 10 feet

9. The width of the door. = 5 feet

10. The height of the door. = 7.5 feet

The actual length of each segment is calculated by counting the units in the scale drawing and multiplying by the scale factor

In the problem, the scale factor is  two and a half feet = 2.5 feet

5. The width of the house

number of units from the drawing = 12 units

actual length = number of units from the drawing * scale factor

actual length = 12 * 2.5 = 30 feet

6. The height of the house

number of units from the drawing = 9 units

actual length = 9 * 2.5 = 22.5 feet

7. The height of the first floor

number of units from the drawing = 5 units

actual length = 5 * 2.5 = 12.5 feet

8. The height of the roof

number of units from the drawing = 4 units

actual length = 4 * 2.5 = 10 feet

9. The width of the door.

number of units from the drawing = 2 units

actual length = 2 * 2.5 = 5 feet

10. The height of the door.

number of units from the drawing = 3 units

actual length = 3 * 2.5 = 7.5 feet

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Answer:

The Average Speed is 48mph

Step-by-step explanation:

I've done this problem before, I wish A+'s upon all that read this answer. take care man!

The time it takes for Jesse to complete his trip from New York to Boston is 5 hours.

To calculate the time it takes for Jesse's trip from New York to Boston, we need to use the formula: time = distance / speed.

Given that Jesse traveled from Boston to his grandpa Isaac in New York at an average speed of 35 mph, and the trip took him 6 hours, we can determine the distance using the formula: distance = speed × time.

Distance = 35 mph × 6 hours = 210 miles.

Now, for the return trip from New York to Boston, Jesse and Isaac travel at an average speed of 42 mph. To find the time it takes, we divide the distance by the speed:

Time = 210 miles / 42 mph = 5 hours.

Therefore, Jesse's trip from New York to Boston takes 5 hours time.

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Since the diameter of this circle is 76 inches, a measurement which the circumference of this circle has include the following: C. 238.64 inches.

Mathematically, the circumference of a circle can be calculated by using this mathematical expression:

C = 2πr or C = πD

Where:

Substituting the given parameters into the circumference of a circle formula, we have;

Circumference of circle, C = πD

Circumference of circle, C = 3.14 × 76

Circumference of circle, C = 238.64 inches.

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Complete Question:

The diameter of a circle is 76 inches. Which measurement does the circumference of this circle have?

A. 123.45 inches.

B. 438.65 inches.

C. 238.64 inches.

D. 338.64 inches.

On solving the provided question, we can say that number 12 is the smallest natural number is abundant

Natural numbers are those employed in mathematics for counting and ranking. Cardinal numbers are the ones used for counting, and ordinal numbers are the ones used for organizing. The natural numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11... are the ones to use while counting or sorting them. Integer a sum that consists of integers and zero. not using decimals or fractions. Integers are not fractions or decimals. Although all integers are integers (as are all natural numbers), not all integers are also integers or natural numbers. For instance, the integer -5 is both an integer and a natural number, but it is neither.

number 12 is the smallest natural number is abundant

factor of 12 = 1,2,3,4,6,12,

1~1

2>1

3>1

4>2+1

.............

10> 1+2+5

11>1

therefore, number 12 is the smallest natural number is abundant

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Complete question: A natural number is abundant if it is less than the sum of its proper divisors. What is the smallest abundant number?

The population of a city is increasing at a rate of 4% each year. In 2020, there were. 236,000 people in the city.

Given, In 2015, the population of the town decreased by 10%, so [tex]8250 x 10/100 = 825[/tex]  people left the town, bringing the population down to [tex]8250 - 825 = 7425.[/tex]

From 2015 to 2020, the population increased by 15% so [tex]7425 x 15/100 = 1113.75[/tex] people came back to the town, bringing the population to [tex]7425+1113.75 = 8538.75[/tex]

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According to the Houa's drawing the distance across the river PR is

The length of line PR is calculated using the knowledge of similar triangles

While similar triangles is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent.

Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions

Examining the figure shown, the pair of equivalent sides are

PO and OC, PR and RE,

The solution is worked out using sides PO and OC, PR and RE,

PO / OC = PR / RE

let PR be equal to y such that PO = 140 + y

(140 + y) / 230 = y / 135

cross multiplying

135(140 + y) = 230y

Expanding

18900 + 135y = 230y

collecting like terms

18900 = 230y - 135y

95y = 18900

y = 198.95 feet

Hence PR = 198.95 feet

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Answer:

its 6.11

6.11 ÷ 1 = 6.11

Calculated to 2 decimal places.

6. 1 1

1 6. 1 1

− 6

0 1

− 1

0 1

− 1

0

∠1 and ∠3 are vertical angles and congruent.

What is congruence?

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

What are vertical angles?

The opposing angles form when two lines cross. They are constantly on par. In this illustration, the angles a° and b° are vertical. The term "vertical" refers to the vertex, not up or down, where they cross.

Here,

we have given a diagram and we have to determine which statement is true that satisfies the true conditions.

By applying congruent property. we get

∠1 = ∠3 are vertivally opposite angle.

This is the only condition that satisfy the true condition from given statement.

Hence, ∠1 and ∠3 are vertical angles and congruent.

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The equation a²-4=0, which corresponds to the factorization of a²-4= (a+ 2)(a-2)

Factorization refers to the process of breaking down a mathematical expression into simpler parts that can be multiplied together to give the original expression. For example, factorizing the expression x² + 4x - 12 would give (x - 3)(x + 4) as the factors.

In algebra, factorization is used to simplify expressions and to find the solutions of equations. For example, in the quadratic equation ax² + bx + c = 0, the first step in solving the equation is to factorize the quadratic expression ax² + bx + c. Once this is done, it becomes easier to find the solutions of the equation by setting each factor equal to zero and solving for x.

Factorization can also be used to simplify expressions in other branches of mathematics, such as number theory. For example, the prime factorization of a composite number is the representation of that number as a product of prime numbers.

Given:

The equation a²-4= (a+ 2)(a-2) is a factorization of a quadratic expression. It states that the expression a²-4 can be represented as the product of two binomials, (a+ 2) and (a-2).

This can be visualized as the graph of a parabola, where the x-intercepts of the parabola are -2 and 2. These are the solutions of the equation a²-4=0, which corresponds to the factorization of a²-4= (a+ 2)(a-2)

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Answer:

x = 11.2

Step-by-step explanation:

We know that the second triangle is just a smaller scale of the bigger triangle.

So, first, we take

28 divided by 25 = 1.12

Then we take

10 times 1.12 = 11.2

So, x = 11.2

On solving the provided question we can say that - Height(h) = h; Radius(r) = r; Length(l) = l Volume of cylinder A(V)=Volume of cylinder B(v) => [tex]4\pi R^2H = \pi r^2h[/tex]

One of the most fundamental curved geometric forms is the cylinder, which is often a three-dimensional solid. It is referred to as a prism with a circle as its base in elementary geometry. Several contemporary fields of geometry and topology also define a cylinder as an indefinitely curved surface. A three-dimensional object known as a "cylinder" consists of curving surfaces with circular tops and bottoms. A cylinder is a three-dimensional solid figure that has two bases that are both identical circles joined by a curving surface at the height of the cylinder, which is determined by the distance between the bases from the center. Examples of cylinders are cold beverage cans and toilet paper wicks.

Cylinder A

Height(h) = H; Radius(r) = 2R; Length(l) = L

Cylinder A

Height(h) = h; Radius(r) = r; Length(l) = l

Volume of cylinder A(V)=Volume of cylinder B(v)

[tex]4\pi R^2H = \pi r^2h[/tex]

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When the inverse of a function is itself a function it is called self-inverse.

A mathematical phrase, rule, or law establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

This relationship is commonly symbolized as y = f(x)—which is said “f of x”—and y and x are related such that for every x, there is a unique value of y.

A self-inverse function ‘reverses itself’ to produce the original input.

A function f is self-inverse if it has the property that f(f(x))=x for every x in the domain of f. In other words, f(x)=f−1(x).

For example, 1x and 3−x are self-inverse.

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Answer:

x=7/2

x=3/2

Step-by-step explanation:

Answer: ax^2+bx+c=0

(4x^2+20x+20=0)

Step-by-step explanation:

It may not make sense but...

Add -20 to both sides of the equation.

4x-20x=-20

Add -20 to both sides of the equation.

4x^2-20x+20=-20+20

Simplify the expression.

4x^2+20x+20=0

I hope this was what you were looking for. :) If not I'm still glad to help.

Answer:

11. ∠5 and ∠7 are corresponding angles

12. ∠1 and ∠8 are alternate exterior angles

13. ∠3 and ∠6 are alternate interior angles

14. ∠6 and ∠7 are consecutive interior angles.

15. ∠1 = 58

    ∠2 = 122

    ∠3 = 58

    ∠5 = 122

    ∠6 = 58

    ∠7 = 122

    ∠8 = 58

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On solving the provided question we can say that - surface area of the following figure cuboid will be - 148cm²

An indication of the overall space occupied by an object's surface is its surface area. A three-dimensional shape's surface area is the total amount of space that surrounds it. A three-dimensional shape's entire surface area is known as its surface area. The surface area of a cuboid with six rectangular faces may be calculated by adding the areas of each face. As an alternative, you may use the formula below and name the box's dimensions as follows: Surface (SA) = 2lh + 2lw + 2hw. Surface area is a measurement of the entire amount of space filled by a three-dimensional shape's surface (a three-dimensional shape is a shape that has height, width, and depth).

Total Surface Area = 2(lw + bw + lb)

Total Surface Area = [tex]2(24 + 30 + 20)[/tex]

Total Surface Area = [tex]148cm^2[/tex]

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On solving the provided question we can say that - surface area of the following figure cuboid will be - 148cm²

what is surface area ?

An indication of the overall space occupied by an object's surface is its surface area. A three-dimensional shape's surface area is the total amount of space that surrounds it. A three-dimensional shape's entire surface area is known as its surface area. The surface area of a cuboid with six rectangular faces may be calculated by adding the areas of each face. As an alternative, you may use the formula below and name the box's dimensions as follows: Surface (SA) = 2lh + 2lw + 2hw. Surface area is a measurement of the entire amount of space filled by a three-dimensional shape's surface (a three-dimensional shape is a shape that has height, width, and depth).

Total Surface Area = 2(lw + bw + lb)

Total Surface Area = - 148cm²

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The best estimate for 225% of 50 is (a) greater than O but less than 1. 50

The maximum likelihood method will be used to calculate the point estimate as follows:

T, note the total number of trials.

List the number of accomplishments, S.

MLE = S / T should be used. Your point estimate is the outcome. Prior to explaining a "formal" method of approximation by rounding each number in the calculation to one significant figure, students must first estimate the result of a computation, use a calculator to determine the precise result, then compare the two results. The most accurate estimate is a definite estimate, as it is created by estimating the individual expenses for the various aspects of the project and then combining them into one estimate. Typically, bottom-up estimates are classified under this heading.

The best estimate for 225% of 50 is

= (225*50)/100

= 11250/100

= 112.5

So that, The best estimate for 225% of 50 is (a) greater than O but less than 1. 50

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Answer: x<-2 or -2>x<1 or x>1

(-infinity,-2) U (-2,1) U (1,infinity)

Step-by-step explanation:

Answer:

Surface Area = 2(22 x 15) + 2(12 x 15) + 2(22 x 12)

Surface Area = 660 + 360 + 528

Surface Area = 1,548 inches²

Step-by-step explanation:

The rectangular prism's volume is equal to [tex]$V=9.375 \mathrm{~m}^3$[/tex]. Prism volume (V) is equal to B ×h, where h is the prism's height and B is the area of the base.

1.25 metres in length, 2.5 metres in width, 3 metres in height, and a diagonal length of 4.10030487 metres make up the total surface area. [tex]$\mathrm{S}_{\text {tot }}[/tex]=[tex]28.75 \mathrm{~m}^2$[/tex] , Latitudinally exposed area [tex]$S_{\text {lat }}=22.5 \mathrm{~m}^2$[/tex] , maximum surface area is [tex]$S_{\text {top }}=3.125 \mathrm{~m}^2$[/tex] , surface area of the ground is [tex]$S_{\text {bot }}=3.125 \mathrm{~m}^2$[/tex] so that the volume is [tex]$V=9.375 \mathrm{~m}^3$[/tex]

When determining the volume of a rectangular prism , we multiply its length, width, and height. The base's area multiplied by the height gives the rectangular prism its volume. Length, width, and height are the cubic units that make up a rectangular prism's volume. Any rectangular solid's volume, V, is equal to the sum of its dimensions, height, width, and depth. In terms of the area of the base, we might alternatively express the formula for a rectangular solid's volume. Size times width equals the base's area, B.

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The sum of the greatest common factor (HCF) and least common multiple (LCM) of 3 and 6 is 9.

The H.C.F. defines the highest common factor present in between given two or more numbers, while L.C.M. defines the least common multiple number which is exactly divisible by two or more numbers.

factors of 3 are 1 and 3

factors of 6 are 1, 2, 3, and 6

3 = 1 × 3

6 = 2 × 3

LCM = 2 × 3

LCM = 6

HCF = 3

sum of HCF and LCM of 3 and 6 = 3 + 6

sum of HCF and LCM of 3 and 6 = 9

Therefore, 9 is the sum of the greatest common factor HCF least common multiple LCM of 3 and 6.

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Answer:

35 dimes and 65 nickels

Step-by-step explanation:

We will need use a system of equations to find the total number of nickels and dimes.

Because there are 100 dimes and there are only nickels and dimes, one equation is N + D = 100, where N is the total number of nickels and D is the total number of dimes.

Because a dime is worth $0.10, a nickel is worth $0.05, and the total change in the jar is worth $6.75, the second equation is 0.05N + 0.1D = 6.75

Substitution will be the easiest method to solve:

[tex]0.05N+0.1D=6.75\\N+D=100\\\\N=-D+100\\\\0.05(-D+100)+0.1D=6.75\\-0.05D+5+0.1D=6.75\\0.05D+5=6.75\\0.05D=1.75\\D=35\\\\N+35=100\\N=65[/tex]

Step-by-step explanation:

O c. 4x²√3x expression is equivalent to √48x^5, if x > 0?