Winston pays $8 for a burger, an order of fries, and a soft drink. Tia buys 2 burgers and a soft drink for $10.50. George buys 2 orders of fries, a burger, and 2 soft drinks for $12. Let x, y, and z represent the cost of a burger, an order of fries, and a soft drink, respectively. If A is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, A-1, and the solution matrix, X, of the system of equations.

Answers

Answer 1

Answer:

[tex]A^{-1}=\left[\begin{array}{ccc}2&0&-1\\3&-1&-1\\-4&1&2\end{array}\right][/tex]

X = 4

Step-by-step explanation:

* At first lets revise how to find the inverse of 3 × 3 matrix

- To find the inverse of a 3 x 3 matrix,

# first calculate the determinant of the matrix.

- If the determinant is 0, the matrix has no inverse.

# Second, transpose the matrix by rewriting the first row as the first

  column, the middle row as the middle column, and the third row

  as the third column.

# Third, Find the determinant of each of the 2 x 2 minor matrices,

- To find the right minor matrix for each term, first highlight the row

  and column of the term you begin with. This should include five

  terms of the matrix. The remaining four terms make up the  

  minor matrix.

- Find the determinant of each minor matrix by cross-multiplying

 the diagonals and subtracting

# Fourth, create the matrix of cofactors.

- Place the results of the previous step into a new matrix of

 co-factors by aligning each minor matrix determinant with the

 corresponding position in the original matrix

- When assigning signs, the first element of the first row keeps its

 original sign. The second element is reversed. The third element

 keeps its original sign. Continue on with the rest of the matrix

- The final result of this step is called the Adj matrix of the original

# The inverse matrix = 1/determinant  × Adj matrix

* Now lets find the matrix A from the story problem

∵ x, y, and z represent the cost of a burger, an order of fries, and

  a soft drink

- Order of Winston: x + y + z = 8

- Order of Tia: 2x + z = 10.50

- Order of George: x + 2y + 2z = 12

* Lets make the matrix A

# [tex]A=\left[\begin{array}{ccc}1&1&1\\2&0&1\\1&2&2\end{array}\right][/tex]

# Determinant of A = 1(0×2 - 1×2) - 1(2×2 - 1×1) + 1(2×2 - 0×1)

∴ Determinant of A = 1(-2) - 1(3) + 1(4) = -2 - 3 + 4 = -1

* Lets transposed A

# [tex]A^{T}=\left[\begin{array}{ccc}1&2&1\\1&0&2\\1&1&2\end{array}\right][/tex]

* Lets find the minor matrix for each term

- The 1st row

# (0×2 - 2×1) = -2 , (1×2 - 2×1) = 0 , (1×1 - 0×1) = 1

- The 2nd row

# (2×2 - 1×1) = 3 , (1×2 - 1×1) = 1 , (1×1 - 2×1) = -1

- The 3rd row

# (2×2 - 1×0) = 4 , (1×2 - 1×1) = 1 , (1×0 - 2×1) = -2

* Lets Make Adj A

# [tex]AdjA=\left[\begin{array}{ccc}-2&0&1\\3&1&-1\\4&1&-2\end{array}\right] *\left[\begin{array}{ccc}+&-&+\\-&+&-\\+&-&+\end{array}\right]=\left[\begin{array}{ccc}-2&0&1\\-3&1&1\\4&-1&-2\end{array}\right][/tex]

* Lets write inverse of A

# [tex]A^{-1}=\frac{1}{-1}\left[\begin{array}{ccc}-2&0&1\\-3&1&1\\4&-1&-2\end{array}\right]=\left[\begin{array}{ccc}2&0&-1\\3&-1&-1\\-4&1&2\end{array}\right][/tex]

* Now lets find the solution matrix for X

# [tex]A_{x}=\left[\begin{array}{ccc}8&1&1\\10.5&0&1\\12&2&2\end{array}\right][/tex]

∴ Ax = 8(0×2 - 1×2) - 1(10.5×2 - 1×12) + 1(10.5×2 - 0×12)

∴ Ax = -16 - 9 + 21 = -4

* Lets find the value of X

∵ X = Ax/A

∴ X = -4/-1 = 4

Answer 2

The costs: burger ($3), fries ($1.50), and soft drink ($3.50). We used the inverse matrix A⁻¹ to solve the system Aˣ=b.

Let's define the system of equations based on the given information:

Burger + Fries + Soft Drink = $82 Burgers + Soft Drink = $10.502 Fries + Burger + 2 Soft Drinks = $12

This can be written as:

x + y + z = 82x + 0y + z = 10.50x + 2y + 2z = 12

In matrix form, this is:

A * X = B

Where:

[tex]A = \left[\begin{array}{ccc}1&1&1\\2&0&1\\1&2&2\end{array}\right][/tex]

[tex]X = \left[\begin{array}{c}x\\y\\z\end{array}\right][/tex]

[tex]B = \left[\begin{array}{c}8\\10.5\\12\end{array}\right][/tex]

The inverse matrix A-1 is found using matrix inversion methods. Let's denote A⁻¹:

[tex]A^{-1} = \left[\begin{array}{ccc}[2&-2.5&0.5\\-1&1.5&-0.5\\0&0&1\end{array}\right][/tex]

The solution matrix X is:

X = A⁻¹ * B

After performing matrix multiplication:

[tex]X = \left[\begin{array}{ccc}[2&-2.5&0.5\\-1&1.5&-0.5\\0&0&1\end{array}\right] * \left[\begin{array}{c}8\\10.5\\12\end{array}\right] = \left[\begin{array}{c}3\\1.5\\3.5\end{array}\right][/tex]

Therefore, the cost of a burger is $3, an order of fries is $1.50, and a soft drink is $3.50.


Related Questions

The expression 4x^2 represents

(4x)(4x)

(4)(x)(x)

(4)(x)(2)

Answers

The answer is (4)(x)(x) because it’s 4 times 2 x’s

Answer:

(4)(x)(x)

Step-by-step explanation:

The square ONLY effects the x

What is the product? 6(x^2-1) times 6x-1 over 6(x+1)

Answers

(36x^3-36x-1)/6x+6 or 6x^2-6x+(-1/6x+6)

For this case we must find the product of the following expression:

[tex]6 (x ^ 2-1) * \frac {6 (x-1)} {6 (x + 1)}[/tex]

We can rewrite [tex]x ^ 2-1[/tex] as:

[tex](x + 1) (x-1)[/tex], then:

[tex]6 (x + 1) (x-1) * \frac {6 (x-1)} {6 (x + 1)} =[/tex]

Canceling similar terms of the numerator and denominator:

[tex](x-1) * 6 (x-1) =\\6 (x-1) ^ 2[/tex]

ANswer:

[tex]6 (x-1) ^ 2[/tex]

Which polynomial function has x intercepts -1,0, and 2 and passes through the point (1,-6)?

Answers

Answer:

f(x) = [tex]3x^3 - 3x^2 - 6x[/tex]

Step-by-step explanation:

Which polynomial function has x intercepts -1,0, and 2 and passes through the point (1,-6)?

There are 3 distinct and real roots given in the question, which means that the  function must be a third degree polynomial. The roots are -1, 0, and 2. This means that f(x) = 0 at these points. The general form of the cubic equation is given by:

f(x) = ax^3 + bx^2 + cx + d; where a, b, c, and d are arbitrary constants.

From the given data:

f(-1)=0 implies a*(-1)^3 + b*(-1)^2 + c(-1) + d = -a + b - c + d = 0. (Equation 1).

f(0)=0 implies a*(0)^3 + b*(0)^2 + c(0) + d = 0a + 0b + 0c + d = 0. (Equation 2).

f(2)=0 implies a*(2)^3 + b*(2)^2 + c(2) + d = 8a + 4b + 2c + d = 0. (Equation 3).

f(1)=0 implies a*(1)^3 + b*(1)^2 + c(1) + d = a + b + c + d = -6. (Equation 4).

Equation 2 shows that d = 0. So rest of the equations become:

-a + b - c = 0;

8a + 4b + 2c = 0;  (Divide 2 on both sides of the equation to simplify).

a + b + c = -6

This system of equation can be solved using the Gaussian Elimination Method. Converting the system into the augmented matrix form:

• 1 1 1 | -6  

• -1 1 -1 | 0

• 4 2 1 | 0

Adding row 1 into row 3:

• 1 1 1 | -6  

• 0 2 0 | -6

• 4 2 1 | 0

Dividing row 2 with 2 and multiplying row 1 with -4 and add it into row 3:

• 1 1        1 | -6

• 0 1       0 | -3

• 0 -2 -3 | 24

Multiplying row 2 with 2 and add it into row 3:

• 1 1       1 | -6

• 0 1       0 | -3

• 0 0 -3 | 18

It can be seen that when this updated augmented matrix is converted into a system, it comes out to be:

• a + b + c = -6

• b  = -3

• -3c = 18 (This implies that c = -6.)

Put c = -6 and b = -3 in equation 1:

• a + (-3) + (-6) = -6

• a = -6 + 3 + 6

• a = 3.

So f(x) = [tex]3x^3 - 3x^2 - 6x[/tex] (All conditions are being satisfied)!!!

The half-life of silicon-32 is 710 years. If 30 grams is present now, how much will be present in 300 years? Round answer to three decimal places. Using A(t)=A0e^(ln(0.5)/T)t

Answers

Final answer:

Using the provided radioactive decay formula and the half-life information for Silicon-32, we can predict there will be approximately 21.978 grams of Silicon-32 remaining after a 300 year period.

Explanation:

The question refers to the concept of half-life in physics, particularly in relation to radioactive substances. In this case, we're dealing with silicon-32, which has a half-life of 710 years. This means in 710 years, half of the silicon-32 will have decayed.

Given that the half-life of silicon-32 is 710 years, and we're examining a span of 300 years, let's use the decay formula A(t)=A0e^(ln(0.5)/T)t . Here, A0 is the initial quantity of the substance (30 grams in this case), T is the half-life (710 years), and t is the time elapsed (300 years).

Plugging these values into the formula gives us:

A(300) = 30e^(ln(0.5)/710)*300

Calculating this, we find that the amount of Silicon-32 remaining after 300 years would be approximately 21.978 grams, rounded to three decimal places.

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A right cylinder has a radius of 2 units and height of 5 units. What is the volume of the cylinder? Round to the nearest tenth. ____ cubic units

Answers

Hi,

The volume of the cylinder is :

V = π × r^2 × h

V = 3,142 × (2)^2 × 5

V = 62, 8319 cm^3

π : Pi => 3,142

r : radius of the cylinder (2 units).

h : height of the cylinder (5 units).

The base of the cylinder is a circle , so to calculate the area we have to use the formula : area = π × r^2. And to find the volume , we have to multiply the area by the height.

•It was nice to help you, Bellalocc!

Given that the two figures are similar, what scale factor can be used to find the missing length x?
A. 1/4
B. 5/16
C. 6/16
D. 4

Answers

Answer:

A

Step-by-step explanation:

4/16 = 1/4

Answer: The correct option is

(D) 4.

Step-by-step explanation:  Given that the two triangles in the figure are similar.

We are to find the scale factor that can be used to find the missing length x.

From the figure, we note that

two pairs of corresponding lengths of the sides of the given triangles are (4, 16) and (6, x).

And, the scale factor is given by

[tex]S=\dfrac{\textup{length of a side of dilated triangle}}{\textup{length of the corresponding side of the original trinagle}}\\\\\\\Rightarrow S=\dfrac{16}{4}\\\\\Rightarrow S=4.[/tex]

Also, we get

[tex]S=\dfrac{x}{6}\\\\\\\Rightarrow 4=\dfrac{x}{6}\\\\\Rightarrow x=24.[/tex]

Therefore, the missing length x is 24 units and the scale factor is 4.

Option (D) is CORRECT.

Please help anyone and explain?

Answers

Answer:

a) 47 people (count each leaf)

b) 66 - 1 = 65 (max - min)

c) 4 (occurs the most)

Find the area of the trapezoid.

A) 18 cm2

B) 22.5 cm2

C) 27 cm2

D) 45 cm2

Answers

Answer:

22.5

Step-by-step explanation:

the formula is A=a+b

2h

Answer:

I think the answer will be B or C

Step-by-step explanation:

It might be wrong but do the best you can

A chemist is using 388 milliliters of a solution of acid and water. If 19.7% of the solution is acid, how many milliliters of acid are there? Round your answer to the nearest tenth.

Answers

____________________________________________________

Answer:

Your answer would be 76.4.

____________________________________________________

Step-by-step explanation:

First, lets take out some key information in the question:

------------------------

Key information:

388 milliliters

19.7%

------------------------

With the information above, it will make it easier to find the answer for your question.

To find the answer to your question, we would need to find how much is 19.7% of 388 millimeters

Therefore, we would need to multiply 388 and 19.7% to get our answer.

In order for this to work, we would need to move the decimal places to times to the left from 19.7; 19.7 will turn to .197. After you move the decimal place, we can now multiply.

[tex]388 * .197=76.436[/tex]

In the question, it asks that we need to round to the nearest tenth, so that's the place right after the decimal place.

The 3 is not a big enoug hnumber to change the number before it, so we would keep the tenth place the same.

It would be rounded up as 76.4

76.4 would be your FINAL answer. There are 76.4 milliliters of acid

____________________________________________________

Help me Again for 46 points ill go higher I have over 900+ points to spend also with my alt acc so please help me

Answers

For the first question there is no mode because none of the numbers are the same. Mode means the popular number.

Answer: There is no mode.

For the second question , the answer is 3. Median means the middle number.

Answer:

5. ○ There is no mode.

6. ○ 3

Step-by-step explanation:

6. Median means the "midst" term [greatest to least (or vice versa)]:

5, 3,5, 3, 2,3, 2,2

5. Mode means "Most Often". We do not see any replicas in the data chart, therefore there is no mode.

I am joyous to assist you anytime.

A riverfront business offers raft trips. The capacity of each raft is 4 people. Suppose 29 adults and 22 children would like to raft. If each raft is filled to capacity, how many people will be aboard the last raft?​

Answers

Answer:

People left for last raft is 3

Step-by-step explanation:

Total Number of person on a raft = 4

Number of adults would like to raft = 29

Number of children would like to raft = 22

Total Number of would like to raft = 29 + 22 = 51

Number of people left for last raft = remainder of division of 51 and 4

When 51 divided by 4,

we get

Quotient = 12

Remainder = 3

Therefore, People left for last raft is 3

y = 2x + 3 2y = 4x + 6 The system of equations has _____ solution(s).
A. no
B. one
C. infinite

Answers

Answer:

C. infinite

Step-by-step explanation:

We want to solve the system:

First equation: [tex]y=2x+3[/tex]

Second equation: [tex]2y=4x+6[/tex]

Multiply the first equation by 2.

This gives us:

Third equation: [tex]2y=4x+6[/tex]

Subtract the third equation to obtain;

[tex]2y-2y=4x-4x+6-6[/tex]

[tex]0=0[/tex]

This implies that, the solution is all real numbers.

This means that the two lines coincide with each other. Therefore there are infinitely many solutions.

graph the equation to solve the system y= -1/2x +3 y= -1/3x +4

Answers

Answer:

the solution is (-6, 6)

Step-by-step explanation:

This system, y= -1/2x +3 y= -1/3x +4, can be quickly solved for x by letting y = y:

y= -1/2x +3    =   y= -1/3x +4.  Then -1/2x + 3 = -1/3x +4.  The fractional coefficients should be enclosed inside parentheses:

(-1/2)x + 3 = (-1/3)x +4

Let's remove the fractional coefficients.  The LCD is (2)(3) = 6.  Multiply all four terms by 6, obtaining:

-3x + 18 = -2x + 24

Combining like terms, we get -6 = x.  

Find y:  substitute -6 for x in either of the given equations:

y= (-1/2)(-6) +3  =  3 + 3 = 6.  So y = 6 when x = -6, and the solution is (-6, 6).

In your piggy bank, you dropped $1.00 on May 1, $1.75 on May 2, $2.50 on May 3 and so on until the last day of May. a) How much did you drop in the piggy bank on May 19? b) What is the total amount in your piggy bank at the end of May? Show all work.

Answers

Answer:

A. $14.5 B. $23.5

Step-by-step explanation:

You are adding .75 cents to your bank account each day so you can do .75 *18 days plus one dollar from day one to get $14.5 dollars on may 19. If you do 30 * .75 you get 22.5 plus a dollar from what you start with to get $23.5 at the end of may in your account. Hope this helped you!!

caleb throws a ball three times for his dog leo. for each throw. leo either catches the ball of misses it. identify the sample space​

Answers

Answer: {MMM ,MCC ,CMC, CCM ,CMM ,MCM ,MMC ,CCC }

Step-by-step explanation:

The sample space of an random experiment is the set of all possible results of that particular experiment.

Let C denotes the event when dog catches the throw and M denotes the event when dog misses the throw.

Given: Caleb throws a ball three times for his dog leo.

Then the sample space for the situation is given by :-

{MMM ,MCC ,CMC, CCM ,CMM ,MCM ,MMC ,CCC }

Point of tangency of an inscribed circle divides a leg of an isosceles triangle into 3 cm and 4 cm line segments (considered from the vertex to the base). Find the perimeter of the triangle.

Answers

Answer:

22

Step-by-step explanation:

Which is the simplified form of the expression?
12n-1/2(6n-4)

Answers
9n-2
9n+2
15n-2
15n-8

Answers

Let's simplify step-by-step.

12n−1/2(6n−4)

Distribute:

=12n+−3n+2

Combine Like Terms:

=12n+−3n+2

=(12n+−3n)+(2)

=9n+2

Answer:

=9n+2

Answer:

9n+2

Step-by-step explanation:

first distribute the -1/2 to 6n-4 from there you will get -3n+2.

second add like terms (12n-3n+2) you will add 12n and -3, this will give you 9n.

after that since you don't have any other like term your answer stays as 9n+2

Calculate the average rate of change over the interval 2

Answers

Answer:

Average rate of change over the interval 2<= x <= 5:

y = 3x + 5:        3

y = 3x^2 + 1:     21

y = 3^x:             78

Step-by-step explanation:

2<= x <= 5

Average rate of change over the interval 2<= x <= 5:

y = 3x + 5

y(5) = 3(5) + 5 = 20

y(2) = 3(2) + 5 = 11

Average rate of change = (20 - 11)/(5-2) = 9/3 = 3

y = 3x^2 + 1

y(5) = 3(5^2) + 1 = 75 + 1 = 76

y(2) = 3(2^2) + 1= 13

Average rate of change = (76 - 13)/(5-2) = 63/3 = 21

y = 3^x

y(5) = 3^5 = 243

y(2) = 3^2 =9

Average rate of change = (243-9)/(5-2) = 234/3 = 78

1. Average rate of change for y = 3x + 5 over 2 <= x <= 5: 3

2. Average rate of change for y = 3x^2 + 1 over 2 <= x <= 5: 21

3. Average rate of change for y = 3^x over 2 <= x <= 5: 78

Matching:

A. Exponential function: ii. Common ratio

B. Quadratic function: iii. No common difference

C. Linear function: i. Common difference

Y-intercepts and Ranges:

1. For y = -2/5 * x + 1:

  - Y-intercept: 1

  - Range: All real numbers (-∞, ∞)

2. For y = -4x^2:

  - Y-intercept: 0

  - Range: [0, ∞)

First, let's calculate the average rate of change for the provided functions over the interval 2 <= x <= 5:

1. For y = 3x + 5:

  - Average rate of change = (f(5) - f(2)) / (5 - 2) = (3(5) + 5 - (3(2) + 5)) / (5 - 2) = (15 + 5 - 6 - 5) / 3 = 9 / 3 = 3

2. For y = 3x^2 + 1:

  - Average rate of change = (f(5) - f(2)) / (5 - 2) = (3(5)^2 + 1 - (3(2)^2 + 1)) / (5 - 2) = (3(25) + 1 - (3(4) + 1)) / 3 = (75 + 1 - 12 - 1) / 3 = 63 / 3 = 21

3. For y = 3^x:

  - Average rate of change = (f(5) - f(2)) / (5 - 2) = (3^5 - 3^2) / (5 - 2) = (243 - 9) / 3 = 234 / 3 = 78

Now, match each type of function to the term that describes its rate of change:

A. Exponential function: ii. Common ratio

B. Quadratic function: iii. No common difference

C. Linear function: i. Common difference

For the next part, we'll find the y-intercepts and ranges for the given functions:

1. For y = -2/5 * x + 1:

  - Y-intercept (where x = 0): y = -2/5 * 0 + 1 = 1

  - Range: Since the coefficient of x is negative, the function is decreasing, and it extends from negative infinity to positive infinity. The range is all real numbers.

2. For y = -4x^2:

  - Y-intercept (where x = 0): y = -4 * 0^2 = 0

  - Range: Since the coefficient of x^2 is negative, the function is concave down and reaches its maximum value at the vertex. The range is [0, ∞) because it never goes below 0.

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Mark Brainliest and show ur work
Which statement is true about the equation fraction 3 over 4z = fraction 1 over 4z − 3 + 5?

It has no solution.
It has one solution
It has two solutions.
It has infinitely many solutions.

Answers

Answer:

It has two solutions

Step-by-step explanation:

The system [tex]\frac{3}{4z}=\frac{1}{4z-3}   + 5[/tex]

If we try to simplify the fractions applying the Lesser Common Factor

We obtain this:

[tex]12z-9=4z+ 5(4z)(4z-3)[/tex]

From this equation, you can see a square term coming up, from where we can say that this system has two solutions

The Louvre museum in France has a glass pyramid in front. The sides measure 114 feet and it reaches a height of 71 feet. How many cubic feet of water could it hold if it were turned into an aquarium​

Answers

The Louvre Museum's glass pyramid could hold approximately 908,448 cubic feet of water if converted into an aquarium.

The Louvre museum's glass pyramid with sides measuring 114 feet and a height of 71 feet can hold water if converted into an aquarium. To calculate the volume to hold water, we use the formula for the volume of a rectangular pyramid: 1/3 * base area * height. Substituting the values, the pyramid could hold approximately 908,448 cubic feet of water.

Don’t understand c help

Answers

Answer:

Soo

Step-by-step explanation:

The mean is all of the numbers added together and divided by how many numbers you have

4+5+6+7+8= 30

You have five numbers that go into that thirty so divide thirty by five.

30÷5= 6

It’s simple to find mean you need to add up all the numbers then divide by how many numbers there are. So 4+5+6+7+8= 30/ 5 =6 so 6 is your answer.

What are the coordinates of the midpoint between (3, -5) and (-7, 2)?

Answers

Answer:

(-2,-3/2)

Step-by-step explanation:

Midpoint formula=(x1+x2/2, y1+y2/2)

So...

(3+-7/2, -5+2/2) =

(-2, -3/2)

Answer:

[tex](-2, -1.5)[/tex]

x-coordinate:-2

y-coordinate:-1.5

Step-by-step explanation:

You need to use this formula to find the coordinates of the midpoint:

[tex]M=(\frac{x_A+x_B}{2},\frac{y_A+y_B}{2})[/tex]

In this case, given the points  (3, -5) and (-7, 2), you can identify that:

[tex]x_A=3\\x_B=-7\\y_A=-5\\y_B=2[/tex]

Therefore, you need to substitute these values into the formula  [tex]M=(\frac{x_A+x_B}{2},\frac{y_A+y_B}{2})[/tex]. Then you get that the coordinates of this midpoint are:

[tex]M=(\frac{3+(-7)}{2},\frac{-5+2}{2})[/tex]

[tex]M=(\frac{3-7}{2},\frac{-5+2}{2})[/tex]

[tex]M=(-2, -1.5)[/tex]


[tex] - 6.2 ^{0.1x} = - 100[/tex]

Answers

Answer:

[tex]x=25.24[/tex]

Step-by-step explanation:

To find the value of [tex]x[/tex], we are solving the exponential equation [tex]-6.2^{0.1x} =-100[/tex] using logarithms.

Let's solve it step-by-step

Step 1. Divide both sides of the equation by -1 to get rid of the negative signs:

[tex]-6.2^{0.1x} =-100[/tex]

[tex]\frac{-6.2^{0.1x}}{-1} =\frac{-100}{-1}[/tex]

[tex]6.2^{0.1x} =100[/tex]

Step 2. Take natural logarithm to bot sides of the equation:

[tex]ln(6.2^{0.1x)}=ln(100)[/tex]

Step 3. Use the power rule for logarithms: [tex]ln(a^{x} )=xln(a)[/tex]

For our equation: [tex]a=6.2[/tex] and [tex]x=0.1x[/tex]

[tex]ln(6.2^{0.1x)}=ln(100)[/tex]

[tex]0.1xln(6.2)=ln(100)[/tex]

Step 4. Divide both sides of the equation by [tex]0.1ln(6.2)[/tex]

[tex]0.1xln(6.2)=ln(100)[/tex]

[tex]\frac{0.1xln(6.2)}{0.1ln(6.2)} =\frac{ln(100)}{0.1ln(6.2)}[/tex]

[tex]x=\frac{ln(100)}{0.1ln(6.2)}[/tex]

[tex]x=25.24[/tex]

We can conclude that the value of x in our exponential equation is approximately 25.24.

Lucia is building a square patio with a side length of n feet. She will cover the floor of the patio with tiles and put a fence around the
perimeter of the patio. The tiles cost $5 per square foot. The fencing costs $3 per foot. She will also buy additional supplies for $25. Let n represent the edge length, in feet, of the patio.

What does the expression 5n^2 + 12n + 25 represent?

A. The total area of the patio.
B. The cost per foot of fencing.
C. The cost per square foot of tiles.
D. The total cost of tiling and fencing the patio.
E. The sum of the area and perimeter of the patio.

Answers

The cost per square foot of tiles

The given expression is the total cost of tiling and fencing the patio , Option D is the correct answer.

What is a square ?

A square is a two-dimensional figure , and a polygon with four sides , All the sides and angles of square is equal .

It is given that

Lucia is building a square patio with a side length of n feet.

She will cover the floor of the patio with tiles and put a fence around the

perimeter of the patio.

The tiles cost $5 per square foot

The fencing costs $3 per foot

She will also buy additional supplies for $25.

Let n represent the edge length, in feet, of the patio.

the expression 5n² + 12n + 25 represent = ?

Area of the patio in square shape will be given by

side * side = n * n =n²

Title cost total = $5 * n²

Title cost total = 5 n²

Perimeter of the patio is given by 4 * side

Perimeter of the patio = 4n

The fencing cost = 3 * 4n = 12n

and the additional cost is $25

The total cost = 5 n² + 12n + 25

Therefore the given expression is the total cost of tiling and fencing the patio , Option D is the correct answer.

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I need help please!!!???):

Answers

Answer:

x>14

Step-by-step explanation:

If Hayden get's $1.5 per pizza, and he wants to earn at least $20, then the equation is:

$1.5*x> $20

x>20/1.5 = 13.3333

Like Hayden cannot deliver 13.333 pizzas, just an integer number, we round it to 14.

Then x>14

If he delivers 14 pizzas, he would be earning: $21, so he needs to deliver at least 14 pizzas to earn at least $20

What is 4/9 written as a decimal?

Answers

Answer: 0.4 repeading

Step-by-step explanation: this is extremely easy all you have to do is divide 4 / 9 which gives you 0.4 repeating or it might look like this

What is the answer to the q

Answers

Answer:

yes

Step-by-step explanation:

the explanation is that a rhombus is a parallelogram in which all sides are equal. Their diagonals bisect each other at right angles.

Final answer:

The derivative of the equation 4q² + 4q − 1 with respect to q is 8q + 4. The differentiation involves using the power rule and dropping out constants, which results in the derivative 8q + 4.

Explanation:

To find the derivative of an equation 4q² + 4q − 1 with respect to q, we use basic differentiation rules. The power rule states that for any term aq^n, the derivative is naq^(n-1). Applying this rule here:

Differentiate 4q²: 2 * 4q = 8q.Differentiate 4q: 4.The constant -1 drops out as its derivative is 0.

So, the derivative of the equation 4q² + 4q − 1 with respect to q is 8q + 4. To check your answer, you can use the same technique as previously learned: apply the differentiation rules systematically and verify if the results are consistent.

3/4-4z+5/4z-1/2+1/2z SIMPLIFY

Answers

Answer:

-2 1/4z +1/4

Step-by-step explanation:

3/4 - 4z +5/4 z- 1/2 + 1/2 z

Put like terms near each other

3/4- 1/2  - 4z +5/4 z+ 1/2 z

We need to get common denominators to combine

First the constant terms

3/4 - 1/2*2/2  

3/4 - 2/4 = 1/4

Then the variable terms

-4z *4/4 +5/4z + 1/2z *2/2

-16z/4 + 5/4z +2/4z

-9/4z

Changing from an improper fraction to a mixed number

-2 1/4 z

-2 1/4z +1/4

At a pizza shop you can choose thick or thin crust, red or white sauce, and toppings of pepperoni, cheese, or vegetarian. How many different combinations are possible for someone who does not care for meat or white sauce?

Answers

Answer: there is 4 options.

Step-by-step explanation:

there is 2 crusts, 2 sauces, and 3 toppings. he doesn't want pepperoni or white sauce so now there is

2 crusts, 1 sauce, and 2 toppings.

2 times 1 times 2 = 4.

The number of different combinations that are possible for someone who does not care for meat or white sauce is 12 combinations.

What is multiplication?

Multiplication is one of the most basic arithmetic operations, where multiplications tell us the number of ways a number is added to another.

The number of crust, sauce, and toppings that are present at the pizza shop is,

Type of crust; Thick or Thin = 2

Type of sauce; Red or White = 2

Type of toppings;  pepperoni, cheese, or vegetarian = 3

Thus, the number of different combinations that are possible for someone who does not care for meat or white sauce can be written as,

Number of combinations = 2 × 2 × 3 = 12 combinations

Hence, the number of different combinations that are possible for someone who does not care for meat or white sauce is 12 combinations.

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Find the area of the figure.
A-56cm^2
B-88cm^2
C-112cm^2
D-384cm^2

Answers

firstly find the area of the square which is sidexside=8x8=64cm^2then find the area of the triangle which is 1/2xbasexhight=1/2x8x6=24cm^2THEN add both areas (64+24)=88cm^2

Answer:

88cm^2

Step-by-step explanation:

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