You invest $5,000 in a savings account that earns 6% interest each year.
A. How much money do you have in your savings account after the first year?
















B. How much money do you have in your savings account after the second year?

The length of chord CD is 5 unit.

The line segment connecting any two locations on a circle's circumference is referred to as the chord of the circle. It should be emphasised that the diameter is the circle's longest chord, which runs through its centre.

We have,

As, the distance to both chords are 5.70 unit.

and,  both chords are 90 degrees from the line then the chords are identical.

As, the length of Chord AB = 5 unit then the length of chord CD =5.

Thus, the length of chord CD is 5 unit.

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the answer on APEX is 6

Answer:

First question, x= 10^10.

Second question is 10!. or 362880

Step-by-step explanation:

First Question:

Simple logx has a base of 10, i.e log10 x,

the question will be 10 = log10 x,

when taking the base "10" from the right side to the left, the number on the left side becomes the power of the base, in this case 10 from the right will be base and 10 from the left will power and log will vanish.

x=10^10.

Another example with different numbers

Y=logx if Y= 12, What is x?

The base is ten when not given,so:

12=logx

10^12=x

Second Question;

simple multiplication just multiply the numbers.

10! is pronounced as 10 factorial,

5! will be 5x4x3x2x1=120

Answer:

option (d) is correct.

[tex]f(x+1) = 2x^2+4x+5[/tex]

Step-by-step explanation:

Given : [tex]f(x) = 2x^2 + 3[/tex]

We have to choose out of given option which represent f(x + 1)

Consider the given function [tex]f(x) = 2x^2 + 3[/tex]

Since we have to find f( x + 1 ) , replace x by x + 1 in the given function f(x) , we have,

[tex]f(x+1) = 2(x+1)^2+3[/tex]

Using algebraic identity, [tex](a+b)^2=a^2+b^2+2ab[/tex] , we have,

[tex]f(x+1) = 2(x^2+1+2x)+3[/tex]

Simplify the expression by multiplying 2 with each term in bracket, we have,

[tex]f(x+1) = 2x^2+2+4x+ 3[/tex]

Simplify , we have,

[tex]f(x+1) = 2x^2+4x+5[/tex]

Thus, option (d) is correct.

Answer:

m∠3=115°.

Step-by-step explanation:

It is given from the figure that line q is parallel to s and r is the transversal.

Since, m∠6 and m∠8 forms a linear pair as they are on the straight line r, therefore using the linear pair property, we have

m∠6+m∠8=180°

⇒[tex]2x-5+x+5=180^{\circ}[/tex]

⇒[tex]3x=180^{\circ}[/tex]

⇒[tex]x=60^{\circ}[/tex]

Thus, the measure of ∠6 is [tex]2x-5=2(60)-5=120-5=115^{\circ}[/tex]

Now, m∠3=m∠6=115° as both m∠3 and m∠6 forms the alternate interior angle pair.

Therefore, the measure of m∠3=115°.

D. Y=-(3+x^2)

A. Y=2x-x^2

Answer:

The answers are a) y=2x-x^2 and d) y=-(3+x^2) and in the attached file are the graphs.

Step-by-step explanation:

Quadratic equations are those where the exponent of the unknown term is squared, that is, the unknown is elevated to exponent 2. They have the general form of a trinomial:

ax2 + bx + c = 0

where a, b and c are real numbers and are called coefficients. Thus, a is the coefficient of x2, b is the term or coefficient of x and c is the independent term.

Answer:

This is a square inscribed in a circle.

Step-by-step explanation:

Final answer:

The dimensions of each corral should be 40 meters by 10 meters.

Explanation:

To find the dimensions of the rectangular corrals, we can set up an equation using the perimeter and area of the enclosed space. Let's call the length of one corral x and the width y. The perimeter of the two corrals is 2x + 2y, which equals 100 meters. The area of the enclosed space is xy, which equals 350 square meters.

Using these equations, we can solve for x and y. Rearranging the perimeter equation, we get x = 50 - y. Substituting this into the area equation, we have (50 - y)y = 350.

Simplifying the equation, we get y^2 - 50y + 350 = 0. This is a quadratic equation that can be factored as (y - 35)(y - 10) = 0. Therefore, the possible values for y are 35 and 10.

Since we are looking for positive values for the dimensions, we choose the values y = 10 and x = 50 - y = 50 - 10 = 40. Therefore, the dimensions of each corral should be 40 meters by 10 meters.

To find the dimensions of the rectangular corrals, we can set up a system of equations. By solving the system of equations, we find that the dimensions of the rectangular corrals can be either 25 meters by 14 meters or 7 meters by 50 meters to obtain a total area of 350 square meters.

To find the dimensions of the rectangular corrals, we can set up a system of equations. Let x represent the width of one corral and y represent the length. Since the rancher wants to enclose a total of 350 square meters, we have the equation xy = 350. The perimeter of each corral is 2x + y, so the total amount of fencing used would be 4x + 2y.

Given that the total fencing available is 100 meters, we can set up the equation 4x + 2y = 100. Now we can solve the system of equations:

By substituting the value of y from the first equation into the second equation, we can solve for x. After finding the value of x, we can substitute it back into the first equation to find the corresponding value of y. The solutions will give us the dimensions of the rectangular corrals.

Let's solve the system of equations:

The solutions for x are x = 25 and x = 7. Plugging these values back into the equation xy = 350, we find that the corresponding values for y are y = 14 and y = 50, respectively. Therefore, the dimensions of the rectangular corrals can be either 25 meters by 14 meters or 7 meters by 50 meters to obtain a total area of 350 square meters.

Answer:

I took the test its 1

Step-by-step explanation:

Final answer:

The expected value of the game to the player is $3.68. If played 1000 times, the player would expect to lose $320.

Explanation:

Expected value for the game:

Expected Loss in 1000 Games:

Therefore, you can expect to lose an average of $210.50 if you play this game 1000 times.

There are 8 quarters and 14 dimes.

Let there are x quarters.

and y dimes.

Also as we know,

1 quarter= 0.25 dollar

Hence, x quarter= $ 0.25x

and 1 dime= $ 0.10

Hence,  y dimes= $ 0.10y

This means that:

                 0.25x+0.10y=3.40

Also, in non-decimal form it could be written as:

                  25x+10y=340

This means that:

                       x+y=22

Now on solving it graphically we see what is the point of intersection of the two lines or system of linear equations.

We get the point of intersection as: (8,14)

i.e. x=8 and y=14

Hence, there are 8 quarters.

and 14 dimes.

The interest earned on a deposit of $1,295 at a 7% annual rate for 180 days is approximately $44.70.

To compute the amount of interest earned we can use the simple interest formula:

Interest = Principal × Rate × Time

Since simple interest does not complicate by itself, and the time is less than a year, we'll adjust the time and rate accordingly.

First, we express the annual interest rate as a decimal by dividing the percentage by 100:

Rate = 7% / 100 = 0.07

Next, we convert the time period of 180 days into years, considering there are 365 days in a year:

Time = 180 days / 365 days/year = 0.49315 years (approximately)

Now, let's plug the values into the simple interest formula:

Interest = $1,295 × 0.07 × 0.49315

Calculating the interest:

Interest = $44.70

Answer:

C. t = –4h + 21

Step-by-step explanation:

We know that when h = 0, t = 21°F. Replacing h = 0 in  equation A and D we get:

A.

t = 21h + 4

t = 21(0) + 4

t = 4

D.

t = –21h + 4

t = –21(0) + 4

t = 4

So, none of them are correct.

The temperature drops 4 degrees every hour, this means that for h = 1 then t = 21 - 4 = 17. Replacing h = 1 in  equation B and C we get:

B.

t = 4h + 21

t = 4(1) + 21

t = 25

C.

t = –4h + 21

t = –4(1) + 21

t = 17

In consequence, C is the correct option.

The points that are solutions to the system of inequalities x + y 5 + 2 y > 2 below are (5, 2),  (3, 6), (1, 1). Options B, C, A, and D. For is mathematically given as

Generally, inequalities are simply defined as  the relationship between two non-equal expressions using a symbol like "not equal to," "greater than," or "less than."

In conclusion, The points (5, 2), and (2, 5), (1, 1) are the ones that are the solutions to the system of inequalities x + y 5 + 2 y > 2 below (3, 6).

For (5, 2),

5 + 2* 5 + 2 *2 > 2

19>2

For  (2, 5)

2 + 5* 5 + 2*5 > 2

37>2

For (3, 6).

3 + 6*5 + 2*6 > 2

45>2

For (1, 1)

1 + 1* 5 + 2*1 > 2

8>2

For (1, -1)

1 + -1* 5 + 2 *-1 > 2

-6<2

For (2, -5)

2 + -5* 5 + 2*-5 > 2

−33<2

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Answer: The correct option are A, B and D.

Explanation:

The law of sine states that,

[tex]\frac{\sin A}{a} =\frac{\sin B}{b}=\frac{\sin C}{c} [/tex]

Where A, B, C are interior angles of the triangle and a, b, c are sides opposite these angles respectively as shown in below figure.

Since we need the combination of two angles and one side or two sides and one angle.

The Law of sine is useful for AAS and SSA type problems.

Reason for correct option:

In  option A three sides are known but no angle is not given, therefore the SSS problem can not be solved by Law of sine and the option A is correct.

In option B a side is known and two inclined angle on that line are known. But to use Law of sine we want the line and angle which in not inclined on that line, therefore the ASA problem can not be solved by Law of sine and the option B is correct.

In option D two sides and their inclined angle is known. But to use Law of sine we want the side and angle which in not inclined on that line, therefore the SAS problem can not be solved by Law of sine and the option D is correct.

Reason for incorrect option:

In option C, the two consecutive angles are given and a side which makes the second angle with base side, therefore the first angle is opposite to the given side, so the law of sine can be used for AAS problems.

Therefore, option C is incorrect.

To solve the equation, let’s translate the given information into an algebraic equation. The solution to the equation is x = -18.

To solve the equation, let’s translate the given information into an algebraic equation. Let the number be represented by 'x'. The quotient of the number and 3 is x/3. The problem states that four less than the quotient of a number and 3 is -10, so we can write the equation as:

x/3 - 4 = -10

To solve for x, we can start by adding 4 to both sides:

x/3 = -6

Next, we can multiply both sides of the equation by 3 to isolate x:

x = -18

Therefore, the solution to the equation is x = -18.

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