Estimate how long it would take an investment of £100 to double with a compound interest rate of 3%. Then use your answer to see exactly what the answer would be after that many years. T = 72/3 = 24 So it would take approximately 24 years to double an investment at a 3% compound interest rate.

Answer:

x = 4

y = 12

Step-by-step explanation:

Replace all occurrences of y with 3x in each equation.

7x = 28

y = 3x

Divide each term in 7x = 28 by 7 and simplify.

x = 4

y = 3x

Replace all occurrences of x with 4 in each equation.

y = 12

x = 4

The solution to the system is the complete set of ordered pairs that are valid solutions.

(4,12)

The result can be shown in multiple forms.

Point Form:

(4,12)

Equation Form:

x = 4,y = 12

Hope I helped <3

It can express as tan (θ) =  -√(sec² (θ) - 1).

A quadrant is defined as an area contained by the x and y axes, which there are four quadrants in a graph.

We have to express tan(θ) in terms of sec(θ) for θ in Quadrant II.

As per the trigonometry identity, we know that

sec² (θ) - tan² (θ) = 1

tan² (θ) = sec² (θ) - 1

Apply the square root property to both sides, and we get

tan (θ) = ± √(sec² (θ) - 1)

Since θ in Quadrant II, so we take a negative value

tan (θ) =  -√(sec² (θ) - 1)

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Answer:

y=6

Step-by-step explanation:

right!!

option C again correct if I'm wrong

An arithmetic sequence has a constant difference between each consecutive pair of terms. This is similar to the linear functions that have the form y=mx+b. A geometric sequence has a constant ratio between each pair of consecutive terms. This would create the effect of a constant multiplier.

Step-by-step explanation:

With bodmas rule

first should be solve divide

so 2^6/2^3=2^3

6^3*2^3=1728

The net yardage the Bobcats football coach logged over four plays of game is  19.8x - 11.1y

The net yardage is calculated using the addition and subtraction operation as follows

For the gains the calculation is as follows

= Gain 25x yards + Gain 0.9y yards.

= 25x + 0.9y

For the lose the calculation is as follows

= Lose 12y yards + Lose 5.2x yards.

= 5.2x + 12y

the net yardage is solved as follows

net yardage = gains - loses

net yardage = (25x + 0.9y) - (5.2x + 12y)

removing the parenthesis and rearranging

net yardage = 25x + 0.9y - 5.2x - 12y

net yardage = 25x - 5.2x + 0.9y - 12y

net yardage = 19.8x - 11.1y

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Answer:

y = 2/5x + 10 (1st box)

y = -1/2x + 1/2 (2nd box)

y = 3/2x - 11/2 (3rd box)

y = 4/3 x - 7/3 (4th box)

y = 3/4x - 10 (5th box)

Step-by-step explanation:

The y-intercept represents the number of snapper fish in the area in 2004, which is the year that t = 0.

An area can be represented by the given formula:

[tex]F = 1500(1.02)^t[/tex]

where t represents the number of years since 2004.

The y-intercept of this equation is the point where the graph of the equation crosses the y-axis. In other words, it is the value of F when t is equal to 0.

Plugging in t = 0 into the equation above gives us:

F = 1500(1.02)⁰

= 1500(1)

= 1500

So the y-intercept of this equation is 1500.

Thus, the y-intercept reflects the amount of snapper fish caught in the area in 2004, the year t = 0.

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The derivative of the function h(x) = 1 - x^2 sin^-1(x) -x^2-x is h'(x) = - x^2/(sqrt(1-x^2)) - 2x - 1.

What is derivative ?

The derivative of a function is a measure of how much the output of the function changes with respect to the change in its input. It is represented by the symbol "d/dx" or "∂/∂x" and it is a fundamental concept in calculus.

First, we will apply the chain rule to the term -x^2 sin^-1(x)

Let u = sin^-1(x)

du/dx = 1/(sqrt(1-x^2))

so, -x^2sin^-1(x) = -x^2u

then dh/du = -x^2

then dh/dx = -x^2 * (du/dx) = -x^2/(sqrt(1-x^2))

Next, we will differentiate the rest of the function ,

h(x) = 1 - x^2sin^-1(x) - x^2 - x

h'(x) = - x^2/(sqrt(1-x^2)) - 2x - 1

So, the derivative of the function h(x) = 1 - x^2 sin^-1(x) -x^2-x is h'(x) = - x^2/(sqrt(1-x^2)) - 2x - 1.

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Everybody votes in a direct democracy to select a place for  the yearbook signing party.

Rules, institutions, and procedures known as "direct democracy" allow members of the public to vote directly on proposed constitutional amendments, laws, treaties, or policy decisions. Referendum and initiatives are the two most significant examples of direct democracy that are addressed in this primer.

Given:

It's the end of the school year, and your class of 250 students must decide the best place for the yearbook signing party.

To select the place:

They vote in direct democracy.

Because they have only 250 people.

And 250 people can have direct say.

Number of people is less.

So, selecting representatives would be not fair.

Therefore, everybody votes in a direct democracy.

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Answer:

16 gallons of gas are needed to travel 300 miles

Step-by-step explanation:

75x4=300

4x4=16

The equation with the same solutions are; 2.3·p - 10.1 = 6.5·p - 4 - 0.01·p

The properties of equality can be used to rewrite the equations in

simplified form.

Two equations that have the same solution as the given equation are;

2.3p-10.1=6.49.p-4

230.p-1010=650.p-400-p

Reasons:

The given equation is; 2.3·p - 10.1 = 6.5·p - 4 - 0.01·p

Simplifying the above equation by collecting like terms gives;

2.3·p - 10.1 = 6.5·p - 0.01·p - 4 = 6.49·p - 4

2.3·p - 10.1 = 6.49·p - 4

Multiplication property of equality:

Both sides of an equation will remain equal, when both sides are

multiplied by the same amount.

Multiplying both sides of the original equation by 100 gives the same

solution as follows;

100 × (2.3·p - 10.1) = 100 × (6.5·p - 4 - 0.01·p)

230·p - 1010 = 650·p - 400 - p

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Answer:

B-2.3p – 10.1 = 6.49p – 4 and C- 230p – 1010 = 650p – 400 – p

Step-by-step explanation:

The four statemen that describes the relationship of the model

A model refers to images, objects variables meant to depict a relation

In the model provided the relationship existing between the models is that the mass are equal hence there will be an equality sign to balance the relationship in the left and right hand side

examining the model shows that

3 cylinders = 1 cylinder + 1 cube

3 cylinders - 1 cylinder = 1 cube

2 cylinders = 1 cube

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Answer:

The answer is C

Step-by-step explanation:

Answer:

See Below

Step-by-step explanation:

Answer:

Line: Solid

Shade: Above

m = -4/5

b = 2

(0,2) - True -Yes

(3,4) - True - Yes

(-2,-2) - False - No

Step-by-step explanation:

Given:

4x + 5y ≥ 10

Questions:

Line: Solid or Dashed?

Shade: Above or Below?

m= [?]

b= [?]

Are these points solution:

Solve:

Inequalities that use '< or >' symbols are plotted with a dashed line. Due to that dashed line means the solution doesn't include the line itself.

< = Less than

> = Greater than

Inequalities that use '≤ or ≥' symbols are plotted with a solid line. Due to that solid line means the solution does includes the line itself

≤ = Less than or equal to

≥ = Greater than or equal to

Therefore, based on the given, the line is solid. Which also means the solution does includes the line itself.

We also know that the given info with the inequalities of "≥".

"≥" Means greater than or equal to which means shade above. If it was "≤ " which means less than or equal to you have to shade below.

To find the m and b we first have to know that;

y = mx + b

m = Slope

b = y-intercept

To find the Slope(m) and b(y-intercept) we first have to put 4x + 5y ≥ 10 in  slope-intercept form.

4x + 5y ≥ 10

4x-4x + 5y ≥ 10-4x {Subtract 4x from both sides}

5y ≥ -4x + 10

5y ≥ -4x + 10 {Divided all by 5}

5y/5  ≥ -4x/5 + 10/5

y =-4/5x+2

Hence, now we know that;

m = -4/5

b = 2

To see if the following points {(0,2) (3,4) (-2,-2)} are solutions for 4x + 5y ≥ 10

All we have to do is to substitute it in.

Starting with (0,2)

x = 0

y = 2

4(0) + 5(2) ≥ 10

0 + 10 ≥ 10

10≥ 10

True. 10 isn't greater than 10 but- It's equal to 10. ≥ Means greater than or equal to Hence, (0,2) is a solution.

Next we have (3,4)

x = 3

y = 4

4(3) + 5(4)  ≥ 10

12 + 20  ≥ 10

32  ≥ 10

True. 32 is greater than 10 - Hence, (3,4) is a solution.

Finally we have (-2,-2)

x = -2

y = -2

4(-2) + 5(-2)  ≥ 10

-8 + -10  ≥ 10

-18  ≥ 10

False. Although you may probably think 18 is greater than 10 it is not correct. -18 isn't greater than 10 due to that it is negative.

RevyBreeze

The possible arrangements would be:

Combination refers to the various ways that certain objects or numbers can be arranged. If the set already has an order, rearranging its elements, or placing its members in a linear or sequential order.

Given that solar panels use the sun's energy to generate power. A town wants to install 28 solar panels in an array.

The possible arrangements would be:-

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Answer: 3 feet

It says the water is 3 feet deep, is it meant to say diver?

A sequence is a function whose domain is the set of natural numbers or a subset of the natural numbers.

The domain basically can be defined a set of all possible inputs for the function.

The range  is basically the difference between the highest and the lowest numbers of a sequence.

To find the range, first put all the numbers in order. Then subtract the lowest number from the highest. The difference gives you the range of the list.

The domain of a sequence consists of the natural (counting) numbers 1, 2, 3, 4, ...Whereas the range of a sequence consists of the terms of the sequence.

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The given model is exponential.

The formula for an exponential function is f (x) = ax, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.

When b > 0 and b 1, an exponential function has the form f(x) = bx. The base is b, and the exponent is x, just like in any exponential expression. The development of bacteria is an illustration of an exponential function. Some germs multiply by two per hour.

As it is clear from the figure, 1 block has 2 boxes, then 4, 8.

So, it is in the form 2ⁿ.

∴ It is Exponential model.

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Complete question -

The acute angle of a triangle is an angle that measures less than 90°. Hence, in the triangle ABC, an acute angle is any angle that is smaller than 90°.

An angle is the figure created by two rays whose termini coincide. The measure of an angle is the amount of rotation required to bring one ray onto the other. A degree or angle that is less than 90° is said to be acute. This means that the two rays forming the angle can be brought together without making a full rotation.

A right angle is an angle having a measurement of precisely 90°. A right angle is formed when the two rays are perpendicular to each other, meaning they form a 90-degree angle. A right angle is often symbolized with a small square at the angle's vertex.

If an angle measures more than 90°, it is called an obtuse angle. An obtuse angle is formed when the two rays forming the angle can be brought together by making more than one full rotation. Obtuse angles are larger than right angles, but smaller than straight angles (which measure 180°).

It's important to note that the terms "acute," "right," and "obtuse" are not just limited to angles. They can also be used to describe other geometric shapes, such as triangles and circles. In these cases, the definitions may vary slightly, but the basic concept remains the same.

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The Quadratic form is (x² - 1)(x² - 9) = 0 and the value of x is {1, -1, 3, -3}.

What is Quadratic form ?

In mathematics, a polynomial with all terms of degree two is called a quadratic form.

Given, x^4-10x^2+9=0

here, a + b = -10

and, ab = 9

So, a = -1 and b = -9

So, It can be written in Quadratic form as :

(x² - 1)(x² - 9) = 0

Now, we can solve as follows:

       x² - 1 = 0                         and,    x² - 9 = 0

      (x+1)(x-1) = 0                              (x+3)(x-3)=0

         x = ±1                           and, x = ±3

∴ Value of x = {1, -1, 3, -3}

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The domain is the area enclosed by the circle, which is all the points inside the unit circle.

The domain of a function is the set of all possible input values (x, y) for which the function is defined and produces a valid output.

For f(x, y) = ln(25 − x2 − 25y2), the function is defined as long as 25 − x2 − 25y2 > 0. This is because the natural logarithm (ln) is only defined for positive numbers. To find the domain, we can set 25 − x2 − 25y2 > 0 and solve for x and y.

25 − x2 − 25y2 > 0

x2 + 25y2 < 25

x2 / 25 + y2 < 1

This is the equation of a unit circle centered at (0,0) with a radius of 1.

So the domain is the area enclosed by the circle, which is all the points inside the unit circle.

You can graph this on the x-y plane.

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Answer; Five-halves

Step-by-step explanation:

Put triangles on graph

To find the answer you divide the A' to B' by the A to B distance.

So you divide 5/2

Answer:

see explanation

Step-by-step explanation:

using the identity

sin²Θ = 1 - cos²Θ

consider the left side

1 - [tex]\frac{sin^20}{1+cos0}[/tex]

= 1 - [tex]\frac{1-cos^20}{1+cos0}[/tex]

1 - cos²Θ is a difference of squares and factors as (1 - cosΘ)(1 + cosΘ)

= 1 - [tex]\frac{(1-cos0)(1+cos0)}{1+cos0}[/tex] ← cancel (1 + cosΘ) on numerator/ denominator

= 1 - (1 - cosΘ) ← distribute parenthesis by - 1

= 1 - 1 + cosΘ

= cosΘ

= right side

The driver is safer in the inside lane. The equation for fc=mv^2 states that the force of centripetal acceleration increases with velocity, so the faster the driver goes, the greater the force of centripetal acceleration.

This means that in an icy roundabout, it is safer to drive in the inside lane since the inside lane has a lower speed limit and thus a lower force of centripetal acceleration.

The driver is safer in the inside lane of a roundabout when it is icy, as the equation for fc=mv^2 states that the force of centripetal acceleration increases with velocity, so the lower speed inside lane will have a lower force of centripetal acceleration.

The driver is safer in the inside lane. The equation for fc=mv^2 states that the force of centripetal acceleration increases with velocity, so the faster the driver goes, the greater the force of centripetal acceleration.

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The SAS (Side-Angle-Side) Congruence Rule states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.

The SAS (Side-Angle-Side) congruence rule is a method used to determine if two triangles are congruent. This rule states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

To determine if two triangles are congruent using the SAS rule, we must first identify the two sides and the angle in one triangle that are congruent to the two sides and the angle in the other triangle. This means that they must have the same measures in terms of length and angle.

Once we have identified the corresponding sides and angles, we can use the SAS rule to determine if the two triangles are congruent. If the two sides and the angle of one triangle are congruent to the two sides and the angle of another triangle, then the two triangles are congruent.

However, if the two sides and the angle of one triangle are not congruent to the two sides and the angle of another triangle, then the two triangles are not congruent. The SAS rule is a simple and effective way to determine if two triangles are congruent.

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Answer:

7+8=15 that's the total

7\15 or 8\15

Answer: that is it’s simplest form

Step-by-step explanation:

The simplified form of the expression is ∛5/3x

Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given is an expression, [tex]\sqrt[3]{\frac{10x^{5} }{54x^{8} } }[/tex]

Simplifying, we get,

[tex]\sqrt[3]{\frac{10x^{5} }{54x^{8} } }\\= \sqrt[3]{\frac{10x^{3+2} }{2*27x^{3+3+2} } }\\= \frac{x}{3x^{2} } \sqrt[3]{\frac{10x^{2} }{2x^{2} } }\\= \frac{\sqrt[3]{5} }{3x}[/tex]

Hence, the expression is ∛5/3x

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The value of the mathematical statement is (d) 0.9m  - 4.9n - 1

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

A mathematical statement

The mathematical statement is give as

1.4m + 3.7n +1 subtracted from 2.3m−1.2n

When this is represented as an expression

We have the following representation

2.3m−1.2n - (1.4m + 3.7n +1)

Express properly

2.3m − 1.2n - (1.4m + 3.7n + 1)

Open the brackets

So, we have the following representation

2.3m − 1.2n - (1.4m + 3.7n + 1) = 2.3m − 1.2n - 1.4m - 3.7n - 1

Collect the like terms

So, we have the following representation

2.3m − 1.2n - (1.4m + 3.7n + 1) = 2.3m - 1.4m  − 1.2n - 3.7n - 1

Evaluate the like terms

So, we have the following representation

2.3m − 1.2n - (1.4m + 3.7n + 1) = 0.9m  - 4.9n - 1

Hence, the expression is (d) 0.9m  - 4.9n - 1

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