marcus borrows $3,000 from his local credit union, to be repaid with 3.5% simple interest over 4 years. What are the principal, interest rate, and time in this situation?

Answer: b

Step-by-step explanation:

It's a line, so the formula will be y = mx + b.

        [tex]-3=1(-7)+b\\7-3=b\\b=4[/tex]

So, the function would be y = x + 4. Plug the values of the coordinate in to find the missing value:

[tex]y=x+4=-1+4=3[/tex]

The zeros, the polynomial x³-5x²+8x-6 are 3, (1-i) and (1+i) and factors are

(x-3)(x²-2x+2)

Zeros of a polynomial can be defined as the points where the polynomial becomes zero as a whole.

Given a polynomial (x³-5x²+8x-6)

x³-5x²+8x-6 = (x-3)(x²-2x+2)

(x²-2x+2) can't be factorized and will have imaginary roots,

Hence, The zeros, the polynomial x³-5x²+8x-6 are 3, (1-i) and (1+i) and factors are (x-3)(x²-2x+2)

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Answer:

240?

Step-by-step explanation:

Answer:

That is a line. Here's two points that pass through the line:

Literally just graph a line that passes through those two points.

The probability that every even number appears at least once before the first occurrence of an odd is 1/20.

Given:

A fair 6-sided die is repeatedly rolled until an odd number appears.

There are 6! ways to order the 6 numbers and 3!(3!) ways to order the evens in the first three spots and the odds in the next three spots.

so the probability = 3!*3! / 6!

= 3!*3! / 6*5*4*3!

= 3*2*1 / 6*5*4

= 6*1 / 30*4

= 6/120

= 1/20

Therefore the probability that every even number appears at least once before the first occurrence of an odd is 1/20.

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The table that represents g(x) is

x         g(x)

1           1

2          5

3          9

The correct option (4)

A function is defined as a relationship between a collection of inputs with one output each. In simple terms, a function is a relationship between inputs, with each input corresponding to exactly one output. Every function has a domain and a codomain or range. A function is commonly denoted by f(x), where x is the input.

From the given information, we have that

f(x) = 3x - 4 and

g(x) = f(2x)

Then,

g(x) = f(2x) becomes

g(x) = f(2x) = 3(2x) -4

g(x) = 6x - 4

Now, we'll plug x numbers ranging from 1 to 3 into the equation.

When x = 1

g(x) = 6x - 4 becomes

g(x) = 6(1) - 4

g(x) = 6 - 4

g(x) = 2

When x = 2

g(x) = 6x - 4 becomes

g(x) = 6(2) - 4

g(x) = 12 - 4

g(x) = 8

When x = 3

g(x) = 6x - 4 becomes

g(x) = 6(3) - 4

g(x) = 18 - 4

g(x) = 14

Hence, the table that represents g(x) is

x         g(x)

1          2

2          8

3          14

Therefore option (4) is correct.

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Answer:

Rs. 4000

Step-by-step explanation:

Profit = 80% = 180% of original price

Therefore, [tex]\frac{180}{100}x=7200\\ 180x=720000\\x=4000[/tex]

Answer:

9000

Step-by-step explanation:

80 percent *9000 =

(80:100)*9000 =

(80*9000):100 =

720000:100 = 7200

Answer:12 1/2

Step-by-step explanation:

Answer:

24√2

Step-by-step explanation:

[tex]2 \sqrt{50} + 3 \sqrt{72} - \sqrt{32} [/tex]

[tex]2 \sqrt{25 \times 2} + 3 \sqrt{36 \times 2} - \sqrt{16 \times 2} [/tex]

[tex]2 \sqrt{25} \sqrt{2} + 3 \sqrt{36} \sqrt{2} - \sqrt{16} \sqrt{2} [/tex]

[tex]2(5 \sqrt{2} ) + 3(6 \sqrt{2} ) - 4 \sqrt{2} [/tex]

[tex]10 \sqrt{2} + 1 8\sqrt{2} - 4 \sqrt{2} [/tex]

[tex]24 \sqrt{2} [/tex]

Answer:

Step-by-step explanation:

As we see the two expressions are equal in value

Answer:

log3 1/3 = logb 1/b

(Both expressions are equal)

Step-by-step explanation:

Now we have to,

→ find the expression with greater value.

Then the greatest value is,

→ log3 1/3 = logb 1/b

→ log3 3^(-1) = logb b^(-1)

→ -1 = -1

→ [ LHS = RHS ]

Hence, both have same value.

Each share of the tech company cost is $1 and 18 more shares can Josh buy with the remainder of his savings.

Given:

Josh spends of his savings to buy 48 4/5 shares in a cech company. He has $18 left.

Let x be the total savings

4/5 x = 48

x = 48*5/4

= 240/4

= $60

= 4/5*60

= 240/5

= $48.

Part A:

The cost of each share of the tech company = 48/48

= $1

Part B :

He has 18 so he can buy =18*1

= 18 shares .

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If the system of equations, A·x + B·y = C and P·x + Q·y = R has infinitely many solutions, then the relationship between the values, A, B, C, P, Q, and R is; A/P = B/Q = C/R

A system of linear equations can have no solutions, only one solution or infinitely many solutions.

Part of the question that appear missing is presented as follows;

The system of equations in the question is;

If the system has infinitely many solutions, then the equations (1) and (2) represent the same equation, such that equation (1) can be obtained directly from equation (2) and vice versa

This indicates that equation (1) is a multiple of equation (2)

Let the common factor be c, we have;

A = c·P

B = c·Q

C = c·R

Which gives;

A/P = B/Q = C/R = c

The relationship between the coefficient is that; A/P = B/Q = C/R

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The amount that Vince will be able to spend on the bike, given the amount deposited in the savings account, is $410. 29

The amount that Vince would have to spend on the bike is the future value of the amount he deposited in the savings account.

This future value is found by the formula:

= Amount deposited x ( 1 + rate) ^ number of years

= 300 x ( 1 + 11%) ³

= 300 x 1. 11 ³

= 300 x 1. 367631

= $410. 2893

= $410. 29

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Answer: \frac{2x^3-3x^2+5}{x-4}

Step-by-step explanation:

The correct option regarding the end behavior of p(x)=-9x^9+6x^6-3x^3+1 is given as follows:

B. As x -> -∞, f(x) -> ∞ and as x -> ∞, f(x) -> -∞.

The end behavior of a polynomial function is obtained by the limits of the function as x approaches infinity, meaning that only the term with the highest exponent is considered.

These limits are divided into two tails, as follows:

The function for this problem is defined as follows:

p(x)=-9x^9+6x^6-3x^3+1.

Hence the term with the highest exponent is:

-9x^9.

At the left tail of the graph, the end behavior is given as follows:

lim x -> -∞ f(x) =lim x -> -∞ -9x^9 = -9(-∞)^9 = -9 x (-∞) = ∞.

At the right tail of the graph, the end behavior is given as follows:

lim x -> ∞ f(x) =lim x -> ∞ -9x^9 = -9(∞)^9 = -9 x (∞) = -∞.

Hence option B is correct.

The problem is given by the image shown at the end of the answer.

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The possible values of k that forms a triangle with an area of 1.5 square units are 1 and 2/3

A triangle is a three sided polygon.

The equation of the parabola is; y = 0.5•(x - 3)•(x + k)

The area of the triangle = 1.5 square units

A x-intercept of the equation, y = 0.5•(x - 3)•(x + k) is x = 3.

The area of a triangle, A, is found from the equation

A = 0.5 × Base length × Height

When x = 3, the height of the triangle is therefore;

A = 1.5 = 0.5 × 3 × Height

Height = 1.5 ÷ (0.5 × 3) = 1

Similarly, when the height is 3, the base length is 1

The y-intercept has a value of y = 0.5•(0 - 3)•(0 + k) = -1.5•k

Area of triangle = 0.5 × 1.5•k × k = 1.5

k = 1

When the x-intercept is 3, we have;

0.5 × 1.5•k × 3 = 1.5

k = 1/(1.5) = 2/3

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If the Area= Length × Width

Then, The width of the rectangle is (x -1).

We know that area of rectangle is the number of unit square within the boundary of the rectangle.

The formula of area of rectangle is:

    Area = Length × width

⇒ Width = Length / Area

Given that,  

(x⁴ +4x³ + 3x² -4x -4) / (x³ + 5x² + 8x + 4 ) = Width   ----------------- (1)

Let's simply the expression :

Note that: x=1 is a zero of the numerator since the sum of the coefficient is zero.

So, (x-1) is a factor:

Putting the values in equation (1)

(x⁴ +4x³ + 3x² -4x -4) = (x-1)  (x³ + 5x² + 8x + 4 )

(x⁴ +4x³ + 3x² -4x -4) / (x³ + 5x² + 8x + 4 ) = (x-1)

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Answer:

D on Edge 23

Step-by-step explanation:

because i said so

The smallest number of instances at which the acceleration of the plane could equal zero on the open interval 0 < c < 6 is t= 25 to t= 30.

By the mean value theorem, somewhere between t = 0 and t = 15 , v'(t) = 0, because v(15)-v(0)/15-0 = 0. Also somewhere between t=25 and t=30, v'(t) = 0, because v(30) - v(25) / 30 - 25 = 0. This means a(t) = 0 for at least two values of t.

f(t) = 6+cos(t/10)+3sin(7t/40)

a(t) = f'(t) = 1/10 sin (t/10) + 21/40 cos (7t/40)

f'(23) = -.408 miles/min²

Average Velocity = 5.916 miles per minute

Average Speed is characterized as the adjustment of position or displacement of the object (∆x) partitioned when the time interval (∆t) in which the displacement happens. The average speed can be a positive or negative sign on the indication of the displacement of the object.

The total distance that the plane flies in 40 min is 229 miles.

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Answer:

No

Step-by-step explanation:

listen to guy above he opened my eyes

The information in the word problem indicates that the initial total number of marbles that were given to the three of them at the beginning of the game was 40 marbles

A word problem consists of describing a situation as well as providing the necessary information to a question verbally that is to be solved by by calculations mathematically.

The initial number of marbles Brea had = 10

The number of marbles Brea had at the end = 0

Let A represent the number of marbles given to Abby, let B represent the number of marbles given to Brea and let C represent the number of marbles given to Cleo, we get;

The number of marbles Abby gave Brea and Cleo = B + C

The number of marbles Brea gave Abby and Cleo = (A - (B + C)) + 2·C

The number of marbles Brea gave Abby and Cleo = All her marbles = 2·B

Therefore;

20 = (A - (B + C)) + 2·C = (A - (10 + C)) + 2·C

20 = A - 10 + C

A + C = 20 + 10 = 30

A + B + C = A + 10 + C = A + C + 10 = 30 + 10 = 40

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Using the substitution method, the solution is: x = 31, y = -5.

To solve a system of equations by substitution, rewrite one of the equations in terms of one of the variables, then substitute its value into the other equation and solve.

Given the system:

x - 3y = 16 --> eqn. 1

4x - y = 9 ---> eqn. 2

Rewrite equation 1:

x = 16 + 3y

Substitute the value of x into eqn. 2:

4(16 + 3y) - y = 9

64 + 12y - y = 9

64 + 11y = 9

11y = 9 - 64

11y = -55

y = -5

Substitute the value of y into eqn. 1:

x - 3(-5) = 16

x + 15 = 16

x = 16 - 15

x = 1

The solution is: x = 1, y = -5

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Answer:

10%

Step-by-step explanation:

percent = part/whole × 100%

percent = 3/30 × 100%

percent = 0.1 × 100%

percent = 10%

Answer: 10%

Answer: 10%

Step-by-step explanation:

10% of 30 is the 30 divided by 10, which is 3

Answer:

40:60: 90

Step-by-step explanation:

interior angles of a triangle add up to 180 so...

2/9 * 180 = 40

(i got the 9 by adding the ratio)

The value of the expression -15x+14y as calculated from the given equations is 12.

The pair of simultaneous equations are given as

-9x+8y=3............................1

6x-6y=-3

Now we will solve these equation by elimination method.

6x-6y=-3

or, 2x-2y=-3.......................2

Now multiplying equation 2 by 4 and adding to equation 1 we get:

-9x+8y=3

8x - 8y = -12

or, -x = -9

or, x = 9

Now we use this value of x to find the value of y

-9x + 8y = 3

or , -81 -3 = -8y

or, y = 10.5  

Hence the value of the expression -15x+14y is

=-15(9) + (14)(10.5)

=12

The theory of linear systems serves as the foundation for the field of linear algebra, which is used in most branches of modern mathematics. Computing techniques for obtaining the solutions, which are essential to the disciplines of engineering, physics, chemistry, computer science, and economics are included in numerical linear algebra.

It is useful to approximate a system of nonlinear equations by a linear system when developing a mathematical model or computer simulation of a relatively complex system.

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Answer:

Step-by-step explanation:

A*X = B

A=2x2 matrix

B= 2x1 matrix

X= 2x1 matrix of   [x1;x2]

1(x1) +3(x2) = 18

0(x1) + 1(x2) = 7

so you can probably see that x2 has to be 7, from that 2nd equation

1(x1) + 3(7) = 18

x1= -3

X = [ -3 ; 7 ]

does this make sense??

The height of the school is 8.5 m.

For a project in his Geometry class, Jacob uses a mirror on the ground to measure the height of his school building.

To find out how tall is the school:

An image is always formed at the back of a mirror. Thus, the appropriate option is -8.75 m. The flagpole is 8.75 m tall.

Let the angle of depression from Madelyn's point of view be represented by θ. Then applying the required trigonometric function, we have;

Tan θ = [tex]\frac{opposite}{adjacent}[/tex]

         = [tex]\frac{1.65}{1.7}[/tex]

Tan θ = 0.9706

θ = [tex]Tan^{-1} 0.9706[/tex]

 = [tex]44.2^{o}[/tex]

θ = [tex]44.2^{o}[/tex]

Let the height of the flag be represented by h. And for a given mirror, the angle of incidence is equal to that of reflection. Then;

Tan θ = [tex]\frac{opposite}{adjacent}[/tex]

        = [tex]\frac{h}{8.75}[/tex]

0.9706 = [tex]\frac{h}{8.75}[/tex]

h = 0.9706 x 8.75

 = 8.49275

h = 8.5 m

Since the image is formed at the back of the mirror, then the flagpole is 8.5 m.

Hence the answer is the height of the school is 8.5 m.

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The two triangles ΔABC and ΔDEC are similar as the triangles follow the angle-angle axiom of similarity .

In the given triangles ΔABC and ΔDEC

In ΔABC

∠ABC = 21°

∠BAC = 36°

∠ACB = 180° - (36+21)°

or, ∠ACB = 180° - (57)° = 123°

In ΔDEC

∠CDE = 36°

∠DCE = 123°

∠CED = 21°

Therefore we can see that the two triangles are similar as all the angles are equal.

Hence the ΔABC and ΔDEC has 3 congruent angles by the angle sum property and the triangles are similar by angle-angle-angle axiom of similarity.

Two triangles are considered to be similar if their corresponding sides and angles match. Alternatively, comparable triangles may have the same shape but vary in size. The triangles are also congruent if the lengths of their respective sides are the same.

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Answer:

d) {(-2,0), (-1,0), (1,0), (2,0)}

Step-by-step explanation:

We know that,

→ A set function has different x values.

Then the set function will be,

a) {(1,0), (1,1), (2,2), (2,2)}

→ The x values underlined are repeated.

Hence, it is not a set function.

b) {(0,0), (1,1), (1,1), (3,3)}

→ The x values underlined are repeated.

Hence, it is not a set function.

c) {(0,-2), (0,-1), (0,1), (0,2)}

→ The x values underlined are repeated.

Hence, it is not a set function.

d) {(-2,0), (-1,0), (1,0), (2,0)}

→ There are no repeated values for x.

Hence, it is a set function.

A student skipped the step  (1 minute / 60 seconds).

The time in seconds divided by 3,600 results in the time in hours.

Given:

A student skipped a step when he tried to convert 720 seconds into hours, and he got the following incorrect result;

720 seconds (1 hour / 60 minutes) = 12 hours.

In order to convert the seconds to hours:

First, we should convert the seconds to minutes.

And the rate of conversion is 1 minute per 60 seconds.

720 / 60 = 12 minutes.

Now, converting minutes to hours.

And the rate of conversion is 60 minutes per hour.

12/60 = 1/5 hours.

Therefore, student skipped the step where rate of conversion is (1 minute / 60 seconds).

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