Alexis put $2000 in savings account. After 4 years, she had $2543 in the account. What rate of interest did she earn?

Answer:

$9.00

Step-by-step explanation:

4x + 12 = 48   - First, subtract 12 from both sides.

4x = 36           - Then, divide each side by 4 to get x by itself.

x = 9                - After getting x by itself, we see that x = 9, so one ticket will

                         cost $9.00

For this case we have the following equation:

[tex]4x + 12 = 48[/tex]

Where the variable "x" represents the cost of a performance ticket.

Clear "x" of the equation to know the cost of a ticket.

Subtracting 12 on both sides of the equation:

[tex]4x = 48-12\\4x = 36[/tex]

Dividing between 4 on both sides of the equation:

[tex]x = \frac {36} {4}\\x = 9[/tex]

So, the cost of a ticket is $ 9.00

Answer:

Option C

Answer:

6

Step-by-step explanation:

10-7=3

2*3=6

Answer:

6

Step-by-step explanation:

Order of operations

PEMDAS

Parenthesis

Exponent

Multiply

Divide

Add

Subtract

[tex]2(10-b)[/tex]

[tex]2(10-7)[/tex]

First, do parenthesis.

[tex]2(10-7)[/tex]

[tex]10-7=3[/tex]

[tex]2(3)[/tex]

Then, multiply to find the answer.

[tex]2*3=6[/tex]

6 is the correct answer.

Answer:

m = -6

Step-by-step explanation:

Put this given equation into slope-intercept form:

y−15=−6(x+7)  becomes y - 15 = -6x - 42.

Adding 15 to both sides results in y = -6x - 27,

and so the slope is -6.  The y-intercept is -27, or (0, -27).

Answer:

slope m = -6

Step-by-step explanation:

y−15=−6(x+7)

y =−6(x+7) + 15

y =−6x +7(-6) + 15

y =−6x -42 + 15

y =−6x - 27

THis is in slope intercept form where slope m = -6

Answer:

Part 1) The diameter is [tex]D=6\ units[/tex]   and the radius is equal to [tex]r=3\ units[/tex]

Part 2) The center of the circle is (1+6i)

Part 3) The point (1+9i) lies on the circle

Part 4) The point (2-i) does not lies on the circle

Step-by-step explanation:

Part 1) Show me how you would determine the length of the diameter and radius.

we have that

The circle has a diameter with end points: (4 + 6i) and (-2 + 6i)

we know that

The distance between the end points is equal to the diameter

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

(4 + 6i) ----> (4,6)

(-2 + 6i) ---> (-2,6)

substitute the values

[tex]d=\sqrt{(6-6)^{2}+(-2-4)^{2}}[/tex]    

[tex]d=\sqrt{(0)^{2}+(-6)^{2}}[/tex]    

[tex]d=6\ units[/tex]    

therefore

The diameter is [tex]D=6\ units[/tex]    

The radius is equal to [tex]r=6/2=3\ units[/tex]    ---> the radius is half the diameter

Part 2) Show me how you would determine the center of the circle

we know that

The center of the circle is equal to the midpoint between the endpoints of the diameter

The circle has a diameter with end points: (4 + 6i) and (-2 + 6i)

The formula to calculate the midpoint between two points is equal to

[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]

substitute

[tex]M(\frac{4-2}{2},\frac{6+6}{2})[/tex]

[tex]M(1,6})[/tex]

therefore

(1,6) ----> (1+6i)

The center of the circle is (1+6i)

Part 3) Determine, mathematically, if (1+9i) lies on the circle. Show how you proved it mathematically

Find the equation of the circle

[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]

we have

The center is (1+6i) -----> (1,6)

r=3 units

substitute

[tex](x-1)^{2}+(y-6)^{2}=3^{2}[/tex]

[tex](x-1)^{2}+(y-6)^{2}=9[/tex]

Verify if the point (1+9i) lies on the circle

Remember that

If a point lies on the circle, then the point must satisfy the equation of the circle

Substitute the value of x and the value of y in the equation and then compare the results

we have

the point (1+9i) -----> (1,9)

[tex](1-1)^{2}+(9-6)^{2}=9[/tex]

[tex](0)^{2}+(3)^{2}=9[/tex]

[tex]9=9[/tex] -----> is true

therefore

The point (1+9i) lies on the circle

Part 4) Determine, mathematically, if (2-i) lies on the circle. Show how you proved it mathematically

The equation of the circle is equal to

[tex](x-1)^{2}+(y-6)^{2}=9[/tex]

Verify if the point (2-i) lies on the circle

Remember that

If a point lies on the circle, then the point must satisfy the equation of the circle

Substitute the value of x and the value of y in the equation and then compare the results

we have

the point (2-i) -----> (2,-1)

[tex](2-1)^{2}+(-1-6)^{2}=9[/tex]

[tex](1)^{2}+(-7)^{2}=9[/tex]

[tex]50=9[/tex] -----> is not true

therefore

The point (2-i) does not lies on the circle

To determine the length of the diameter and radius, use the distance formula. The center of the circle can be found by finding the midpoint of the diameter's end points. To determine if a point lies on the circle, use the distance formula to compare the distance between the point and the center to the radius.

1. Determining the length of the diameter and radius:

To find the length of the diameter, we can use the distance formula. The distance between two complex numbers (a + bi) and (c + di) is given by the formula √((c-a)^2 + (d-b)^2). In this case, the two end points of the diameter are (4 + 6i) and (-2 + 6i). Using the formula, the distance is √((-2-4)^2 + (6-6)^2) = √((-6)^2 + 0) = √(36) = 6.

The radius of a circle is half the length of the diameter. Therefore, the radius of this circle is 6/2 = 3.

2. Determining the center of the circle:

The center of the circle is the midpoint between the two end points of the diameter. To find the midpoint, we can take the average of the x-coordinates and the average of the y-coordinates. In this case, the x-coordinates of the end points are 4 and -2, and the y-coordinates are 6. Taking the averages, the x-coordinate of the center is (4 + (-2))/2 = 1 and the y-coordinate of the center is (6 + 6)/2 = 6. Therefore, the center of the circle is the complex number 1 + 6i.

3. Determining if (1 + 9i) lies on the circle:

To determine if a point lies on the circle, we can check if the distance between the center of the circle and the point is equal to the radius. Using the distance formula again, the distance between the center (1 + 6i) and the point (1 + 9i) is √((1-1)^2 + (9-6)^2) = √(0 + 9) = √(9) = 3. Since the distance is equal to the radius, we can conclude that (1 + 9i) does lie on the circle.

4. Determining if (2 - i) lies on the circle:

Using the same process, we find that the distance between the center (1 + 6i) and the point (2 - i) is √((2-1)^2 + (-1-6)^2) = √(1 + 49) = √(50). Since √(50) is not equal to the radius (3), we can conclude that (2 - i) does not lie on the circle.

Answer:

1.5

Step-by-step explanation:

m=80-65/84-74

=15/10

1.5

*Since this is an application problem, we can use decimals.*

Answer:

The slope of the line is 1.5

Step-by-step explanation:

To know the slope of a line we can have the equation or to know points of the line. In this case from the graph we have to points (84,80) and (74,65). Having this and using the equation to calculate the slope, we have:

[tex]m=\frac{y2-y1}{x2-x1} \\[/tex]

Defining:

[tex](x1=84,y1=80)[/tex] and [tex](x2=74,y2=65)[/tex]

Now using the equation:

[tex]m=\frac{65-80}{74-84}[/tex]

[tex]m=\frac{-15}{-10} \\m=\frac{15}{10} =1.5[/tex]

The slope of the line is 1.5

The probability of getting heads on a coin toss is 1/2

The probability of getting an even number rolling a number cube is 1/2 ( 3 even numbers out of 6 total numbers).

To find the probability of both happening, multiply each probability by each other:

1/2 x 1/2 = 1/4

Answer:

The system of linear equations 8x - 3y = 10 and 16x - 6y = 22 has no solution is correct.

Step-by-step explanation:

1) The system of linear equations 6x - 5y = 8 and 12x - 10y = 16 has no solution.

Solve these linear equations simultaneously

Step 1 : Find y in terms of x from any one equation

6x - 5y = 8

y = 8 - 6x

        -5

Step 2 : Substitute y in terms of x from step 1 in the second equation.

16x - 6y = 22

16x - 6 (8 - 6x) = 22

              -5

80x - 48 + 36x = 22 x -5

94x = 43

x = 0.457

This statement is incorrect as it does have a solution.

2) The system of linear equations 7x + 2y = 6 and 14x + 4y = 16 has an infinite number of solutions.

Solve these linear equations simultaneously

Step 1 : Find y in terms of x from any one equation

7x + 2y = 6

y = 6 - 7x

        2

Step 2 : Substitute y in terms of x from step 1 in the second equation.

14x + 4y = 16

14x + 4(6 - 7x) = 16

              2

14x + 12 - 14x = 16

0 ≠ 4

This statement is not true as there are no solutions.

3) The system of linear equations 8x - 3y = 10 and 16x - 6y = 22 has no solution.

Solve these linear equations simultaneously

Step 1 : Find x in terms of y from any one equation

8x - 3y = 10

x = 10 + 3y

        8

Step 2 : Substitute x in terms of y from step 1 in the second equation.

16x - 6y = 22

16(10 + 3y) - 6y = 22

       8

20 + 6y - 6y = 2

0 ≠ -18

This statement is true because there are no solutions

4) The system of linear equations 9x + 6y = 14 and 18x + 12y = 26 has an infinite number of solutions.

Solve these linear equations simultaneously

Step 1 : Find x in terms of y from any one equation

9x + 6y = 14

x = 14 - 6y

        9

Step 2 : Substitute x in terms of y from step 1 in the second equation.

18x + 12y = 26

18 (14 - 6y) + 12y = 26

        9

8 - 12y + 12y = 26

0 ≠ 18

This statement is incorrect because there are no solutions. It does not have infinite number of solutions.

!!

Answer:

Step-by-step explanation:

The true statement is the third one, because that system of equations has no solutions. This is because those lines are parallel, see image attached.

We can demonstrate this by solving the system:

[tex]\left \{ {{8x-3y=10} \atop {16x-6y=22}} \right.[/tex]

If we multiply the first equation by -2, we would have

[tex]\left \{ {{-16x+6y=-20} \atop {16x-6y=22}} \right\\0x+0y=2\\0=2[/tex]

When this happens, means that the system has no solution, that is, the lines that represents those linear equations, are parallel.

Therefore, the right answer is the third option.

Answer:

1.) 8 = 8

2.) -12 = -12

3.) -3y² = -3y²

4.) 6x² + 36x = 6x(x + 6)

5.) 7x - 14x² = 7x(1 - 2x)

~

Answer:

77 inches

Step-by-step explanation:

1 foot=12 inches so what you have to do is 12x6=72 and since he is 6 foot 5 inches you add 5 to get 77.

Please mark brainliest and have a great day!

Answer:

3.10 * 72

Step-by-step explanation:

To find 310% of 72

Of means multiply and is means equal

310% * 72 = answer

Change to decimal form

3.10 * 72 = answer

223.20

Answer: (3.10)(72) is the correct answer

Step-by-step explanation:

Answer:A

Step-by-step explanation:

Y varies directly as x

Y = kx

When y = 2.5, x = 5

Substitute the value of y and x

2.5 = k * 5

Make k the subject of the formula

k = 2.5/5

k = 1/2

:. The equation connectin y and x is

Y = 1/2x

When x = 10

Y = 1/2*10

Y = 10/2

Y = 5

Answer:

B) [tex](x^2 - 5x + 13) +(x^2 + 3x - 6)\\[/tex]

Step-by-step explanation:

Let's simplify the given options and find the correct answer.

The given expression is [tex]2x^2 - 2x + 7[/tex]

Let's take the option A and simplify.

[tex]-(4x + 12) + (2x^2 - 6x + 5)[/tex]

Distributing the negative sign and simplify.

[tex]-4x - 12 + 2x^2 -6x + 5[/tex]

Simplify the like terms.

[tex]2x^2 -10x - 7[/tex]

Which is not equal to the given expression.

Let's take the option B and simplify.

[tex](x^2 - 5x + 13) +(x^2 + 3x - 6)\\[/tex]

Simplify the like terms, we get

[tex]x^2 + x^2 -5x +3x +13 -6[/tex]

[tex]2x^2 -2x +7[/tex]

Which is equal to the given expression [tex]2x^2 -2x +7[/tex]

Therefore, the answer is B) [tex](x^2 - 5x + 13) +(x^2 + 3x - 6)\\[/tex]

Answer: 12

Step-by-step explanation:

Triangle JKL is dilated by a scale factor of 1.5 to get triangle XYZ. You can find this out by dividing 9 by 6, which will give you 1.5. To get the answer, you multiply 8 by 1.5 to get 12

ANSWER

EXPLANATION

We have that ΔJKL is similar to ΔXYZ.

The corresponding sides will therefore

be in the same proportion.

This implies that,

[tex] \frac{XY}{JK} = \frac{YZ}{KL} [/tex]

From the diagram,XY=9, JK=6, KL=8, and YZ=x.

We plug in the known values into the formula to get:

[tex] \frac{9}{6} = \frac{x}{8} [/tex]

Multiply both sides by 8

[tex] \frac{9}{6} \times 8=\frac{x}{8} \times 8[/tex]

[tex]12 = x[/tex]

The correct answer is B.

Answer:

10°

Step-by-step explanation:

i did it in my brain maybe not the best but can help u 75°(180°-115°)+4k+5°+6k+10°=180

Answer:

k=10

Step-by-step explanation:

The measure of the exterior angle is equal to the sum of the opposite interior angles

115 = 4k+5 + (6k+10)

Combine like terms

115 = 10k +15

Subtract 15 from each side

115-15 =10k+15-15

100 = 10k

Divide by 10

100/10= 10k/10

10 =k

Answer:

A

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (1, 1)

m = [tex]\frac{1-3}{1-0}[/tex] = - 2

note the line crosses the y- axis at (0, 3) ⇒ c = 3

y = - 2x + 3  → A

Answer:

6 + 0.7 + 0.04 + 0.001 = 6.741

6 x 1 + 0.1 x 7 + 0.01 x 4 + 0.001 x 1 = 6.741

[tex]x- 13 =25\\x=38[/tex]

Answer:

[tex]x = 38[/tex]

Step-by-step explanation:

We have the following equation

[tex]x- 13 =25[/tex]

We must solve the equation for the variable x

Add 13 on both sides of the equation

[tex]x- 13 +13 =25+ 13[/tex]

[tex]x=25+ 13[/tex]

[tex]x=38[/tex]

So the solution to the equation is [tex]x = 38[/tex]

Answer:

8^5

Step-by-step explanation:

Answer:

The first answer :)

Step-by-step explanation:

That is because N represents the amount of hours that the other person studied.

Answer:

The equation is y = 15(2)^x , the graph is X

Step-by-step explanation:

* Lets talk about the exponential graph

- The form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

 b ≠ 1, and x is any real number

- It has a constant base b

- It has a variable exponent x

- The constant a is the beginning value

* Lets solve the problem

- The sample containing 15 cells

∴ a = 15

- The cells double with each cycle ⇒ means × 2 each cycle

∴ b = 2

- x is the number of cycles

- y is the number of cells

∴ The equation is y = 15(2)^x

- From the graphs the answer could be X or Y

* To know which one substitute the values of x to find the value of y

# Figure X

∵ y = 15(2)^x

∵ x = 0

∴ y = 15(2)^0

∵ (2)^0 = 1 ⇒ any number to the power of 0 = 1 except the zero

∴ y = 15(1) = 15

∵ x = 1

∴ y = 15(2)^1 = 15(2) 30

- The graph has y = 30 when x = 1

# In the Figure Y the value of y not equal 30 at x = 1

∴ The answer is graph X

* The equation is y = 15(2)^x , the graph is X

Final answer:

The number of cells after each cycle of mitosis can be represented by an exponential growth model with the equation N = 15 × 2ⁿ. Graphically, this will be a rapidly ascending curve, starting with 15 cells at cycle 0 and doubling each cycle.

Explanation:

The question is asking us to determine the number of cells after each cycle of mitosis given an initial count of 15 cells. When a cell undergoes mitosis, it produces two genetically identical daughter cells, effectively doubling the number of cells with each cycle. To represent the number of cells after each cycle, we will need to use an exponential growth model as each cell division results in doubling the number of cells present.

The general equation representing the growth of cells through mitosis is given by N = N0 × 2ⁿ, where N is the number of cells after n cycles, N0 is the initial number of cells, and n is the number of cycles of mitosis. For the given initial condition of 15 cells (N0 = 15), the equation becomes N = 15 × 2ⁿ.

The corresponding graph to this equation would show a curve that rises sharply upward, reflecting the exponential increase in the number of cells after each cycle. The graph starts at 15 cells when n = 0 (no cycles have occurred) and doubles with each subsequent cycle.

Answer:

x =5

Step-by-step explanation:

3.1x−16.3=−0.8

Add 16.3 to each side

3.1x−16.3+16.3=−0.8+16.3

3.1x = 15.5

Divide each side by 3.1

3.1x = 15.5/3.1

x =5

Answer: The equation of the circle whose center is at (2, 1) and radius is 3 is [tex](x-2)^2+(y-1)^2=9[/tex]

Step-by-step explanation:

We know that the equation  of a circle having center at (h,k) and radius r is given by :-

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Given : The center of the circle :  (2, 1)

The radius of the circle : 3 units

Then the equation of a circle with center at (2, 1) and radius is 3 is will be :-

[tex](x-2)^2+(y-1)^2=3^2\\\\\Rightarrow\ (x-2)^2+(y-1)^2=9[/tex]

Answer:

12 guest walk

Step-by-step explanation:

Total number of people that went to the party= 24 (let this be represented as y)

Half of the people walk, this means 1/2 × y   ----------- walk, where y=24 people

Hence half of 24= [tex]\frac{24}{2} =12[/tex]

12 people walked.

Answer:

32

Step-by-step explanation:

Plug in 4 for c.

(c³)/2 = (4³)/2

First, solve the parenthesis, then divide. Multiply:

4³ = 4 * 4 * 4 = 16 * 4 = 64

Next, divide:

64/2 = 32

32 is your answer.

~

Answer:

127%

Step-by-step explanation:

All you have to do is multiply both numerator and denominator by 100.

Hello There!

1.27 to a percent would be 127%

"Percent" means "per 100" or "over 100". So, to convert 1.27 to percent we rewrite 1.27 in terms of "per 100" or over 100.

Multiply 1.27 by 100/100. Since 100/100 = 1, we are only multiplying by 1 and not changing the value of our number.

Therefore, we have shown that

1.27 = 127%

Answer:

x-2 dollars is the lunch money

The expression x-2 represents the spending amount on the lunch.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.

Given:

Mahimi has x dollars for food.

She wants to buy lunch and still have $2 left over to buy a snack later.

To find the spending amount on the lunch:

She spent on the lunch,

= $(x - 2).

Therefore, x -2 is the expression.

To learn more about the expression;

brainly.com/question/24242989

#SPJ5

Answer:

The IQR = 4.

Step-by-step explanation:

The median is the middle number so it is 8.

The lower quartile is 6  (the middle number of those less than 8).

In a similar way the upper quartile is 10.

The interquartile range is 10 - 6 = 4.

Final answer:

To find the interquartile range of the data set 5, 6, 7, 8, 9, 10, 11, we calculate Q3 (10) - Q1 (6), which results in an IQR of 4.

Explanation:

The question asks for the interquartile range (IQR) of the data set 5, 6, 7, 8, 9, 10, 11. The IQR is the difference between the third quartile (Q3) and the first quartile (Q1) in a data set, representing the spread of the middle 50 percent of the data.

Step-by-step Calculation

First, arrange the data in ascending order, which has already been done: 5, 6, 7, 8, 9, 10, 11.

To find Q1, calculate the median of the lower half. Here, Q1 is 6 (the median of 5, 6, 7).

To find Q3, calculate the median of the upper half. Here, Q3 is 10 (the median of 9, 10, 11).

Finally, calculate the IQR by subtracting Q1 from Q3: IQR = Q3 - Q1 = 10 - 6 = 4.

Thus, the interquartile range of this data set is 4.

Answer:

x = 3

Step-by-step explanation:

Given

7x - 4 = 2x + 11 ( subtract 2x from both sides )

5x - 4 = 11 ( add 4 to both sides )

5x = 15 ( divide both sides by 5 )

x = 3