Gina opened a bank account with $40. She plans to add $20 per week to the account and not make any withdrawals. After how many weeks will Gina have exactly $700 in her account, excluding interest?

1. EG = HJ (Given)

2. EG = EF + FG, HJ = HF + FJ (Seg. Add. Prop.)

3. EF + FG = HF + FJ (Subst. Prop.)

4. EF =  FJ (Given)

5. FG = HF (Subtraction Prop.)

It's challenging to demonstrate that FG equals HF as these may represent different elements or variables in different mathematics or physics contexts. At its simplest, FG seems to represent the gravitational force between two masses, and HF would need to represent the same force to hold true.

The equation given seems to pertain to gravitational forces where FG represents the gravitational force between two masses, electron and proton.

Given that FG = GMM where G is the gravitational constant (6.67×10-¹1 N·m²/kg²), m and M represent the masses of the electron and proton, to prove that FG=HF, it implies that HF represents the same gravitational pull.

However, without more detailed context or information, I can't further demonstrate or prove that FG does equal HF as these terms may refer to different elements or variables in different contexts of mathematics or physics problems.

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The given sequence is an arithmetic sequence with a common difference of -5. The explicit formula for the sequence is A_n = 2 + (n-1)*-5. Using this formula, the 13th term of the sequence is -58.

The given sequence is 2, -3, -8, -13, -18. We find that the common difference of the sequence is -5 because each term subtracts 5 from the previous term. This is an arithmetic sequence. The explicit formula for an arithmetic sequence is given by A_n = A_1 + (n-1)*d where A_n is the nth term, A_1 is the first term, d is the common difference and n is the position in the sequence. So in this case, our formula becomes A_n = 2 + (n-1)*-5.

Now let's find the 13th term in the sequence. Substituting n=13 into the formula we get: A_13 = 2 + (13-1)*-5 = 2 - 60 = -58. Therefore, the 13th term of the sequence is -58.

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63 People came on the third day

Hi there!

So there was a public pool opened for summer and a total of 246 people came swimming over the first 3 days. On the first day 79 came to swim and on the second day 104 came to swim. To find how much people swam on the third day, we need to add 104 + 79 and subtract the answer with 246.

104 + 79 = 183

246 - 183 = 63

63 people came to swim on the third day.

Hope this helped!~

Answer: G(x) = 3|x + 2| - 8

Step-by-step explanation:

"a" represents the vertical stretch (or shrink)

"h" represents the x-coordinate of the vertex

"k" represents the y-coordinate of the vertex

F(x) = 3|x - 2| - 5

G(x) = 3(x - 2 + 4| - 5 - 3

       = 3|x + 2| - 8

Answer:

g(x)=3 lx+2l-8

:)

Answer:

D. (1, 5, 2)

Step-by-step explanation:

It is convenient to let a graphing calculator do this. See the attachment.

Answer:

D.(1,5,2)

Step-by-step explanation:

Lets write the augmented matrix by writing the coefficients of all the variables

3      -4    -5      -27              Row 1

5        2     -2      11               Row 2

5       -4      4      -7               Row 3

WE need to get

1   0   0

0   1    0

0   0   1  then last column will be the value of x , y , z

To get identity matrix we use row operations

(R1=R1/3)

1      -4/3    -5/3      -9              Row 1

5        2        -2      11               Row 2

5       -4        4      -7               Row 3

Subtract row 1 multiplied by 5 from row 2 (R2=R2−(5)R1)

1      -4/3      -5/3      -9              Row 1

0     26/3      19/3     56              Row 2

5       -4             4      -7               Row 3

Subtract row 1 multiplied by 5 from row 3 (R3=R3−(5)R1)

1      -4/3      -5/3      -9              Row 1

0     26/3      19/3     56              Row 2

0      8/3       37/3    38               Row 3

Multiply row 2 by 326 (R2=(3/26)R2)

1      -4/3      -5/3        -9              Row 1

0     1       19/26    84/13              Row 2

0      8/3       37/3    38               Row 3

Add row 2 multiplied by 4/3 to row 1 (R1=R1+(4/3)R2)

1      0        -9/13     -5/13              Row 1

0     1       19/26    84/13              Row 2

0      8/3       37/3    38               Row 3

Subtract row 2 multiplied by 8/3 from row 3 (R3=R3−(8/3)R2)

1      0        -9/13     -5/13              Row 1

0     1       19/26    84/13              Row 2

0    0       135/13    270/13           Row 3

Multiply row 3 by 13/135 (R3=(13/135)R3)

1      0        -9/13     -5/13              Row 1

0     1       19/26    84/13              Row 2

0    0          1         2                    Row 3

Add row 3 multiplied by 9/13 to row 1 (R1=R1+(9/13)R3)

 1      0       0            1                  Row 1

0     1       19/26    84/13              Row 2

0    0          1         2                    Row 3

Subtract row 3 multiplied by 19/26 from row 2 (R2=R2−(19/26)R3)

 1      0       0            1                  Row 1

0     1          0          5                 Row 2

0    0          1         2                    Row 3

From the above matrix we can say that x=1 , y=5 and z= 2

To find the equation of a line perpendicular to a given line, find the negative reciprocal of the slope and use the point-slope form of a line.

To find the equation of a line that is perpendicular to the given line and passes through the given point, we first need to determine the slope of the given line. The given line has a slope of -1/5, which is the negative reciprocal of the slope we want for the perpendicular line. The negative reciprocal of -1/5 is 5/1 or 5. Now we have the slope of the perpendicular line and a point it passes through (-2, 7), we can use the point-slope form of a line to find the equation: y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point.

Substituting the values, we get: y - 7 = 5(x - (-2))
y - 7 = 5(x + 2)
y - 7 = 5x + 10
y = 5x + 10 + 7
y = 5x + 17

Therefore, the equation of the line that is perpendicular to the given line and passes through the given point (-2, 7) is y = 5x + 17. Option B is the correct answer.

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The correct answer is B. y=5x+17.

To write the equation of a line that is perpendicular to the given line y-3=-1/5(x+2) and that passes through the point (-2, 7), first, we need to find the slope of the given line and then determine the slope of the perpendicular line, which will be the negative reciprocal of the given line's slope. The slope of the given line is -1/5, so the slope of the line perpendicular to it will be 5 (since the negative reciprocal of -1/5 is 5).

Next, we use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point through which the line passes. Plugging in our slope of 5 and the point (-2, 7), the equation becomes:

y - 7 = 5(x - (-2))

Expand and simplify to solve for y:

y - 7 = 5x + 10

y = 5x + 17

The correct answer is B. y=5x+17.

Answer:

3.3 hours.

Step-by-step explanation:

We have been given that a scientist is testing a new antibiotic by applying the antibiotic to a colony of 10,000 bacteria. The number of bacteria decreases by 75% every two hours.

Since number of bacteria is decreasing exponentially, so we will use exponential decay function.

[tex]y=a*b^x[/tex], where,

a= Initial value,

b = For decay b is in form (1-r), where r is rate in decimal form.

Let us convert our given rate in decimal form.

[tex]75\%=\frac{75}{100}=0.75[/tex]

As number of bacteria is decreasing every 2 hours, so number of bacteria decreased in 1 hour will be x/2.

Upon substituting our given values in above formula we will get,

[tex]y=10,000(1-0.75)^{\frac{x}{2}}[/tex]

To find the number of hours it will take to for the bacteria colony to decrease to 1000, we will substitute y = 1,000 in our equation.

[tex]1,000=10,000(0.25)^{\frac{x}{2}}[/tex]

Let us divide both sides of our equation by 10,000.

[tex]\frac{1,000}{10,000}=\frac{10,000(0.25)^{\frac{x}{2}}}{10,000}[/tex]

[tex]0.1=(0.25)^{\frac{x}{2}}[/tex]  

Let us take natural log of both sides of our equation.

[tex]ln(0.1)=ln((0.25)^{\frac{x}{2}})[/tex]

[tex]ln(0.1)=\frac{x}{2}*ln(0.25)[/tex]

[tex]-2.302585=\frac{x}{2}*-1.386294[/tex]

[tex]x=\frac{-2.302585}{-1.386294}*2[/tex]

[tex]x=1.660964*2[/tex]

[tex]x=3.3219\approx 3.3[/tex]

Therefore, it will take 3.3 hours  for the bacteria colony to decrease to 1000.

Final answer:

It will take 4 hours for the bacteria colony to decrease from 10,000 to 1,000, considering a 75% decrease every two hours.

Explanation:

To find out how many hours it will take for the bacteria colony to decrease from 10,000 to 1,000 with a 75% decrease every two hours, we can use the formula for exponential decay: [tex]N = N0(1 - r)^t[/tex], where N is the final amount, N0 is the initial amount, r is the rate of decrease (expressed as a decimal), and t is the time in units of the rate's period (in this case, every two hours).

Here, N0 = 10,000, N = 1,000, and r = 0.75. Plugging the values into the formula gives [tex]1,000 = 10,000(1 - 0.75)^t.[/tex]Simplifying, we find [tex](1 - 0.75)^t = 0.1.[/tex]

Solving for t, we find that t equals 2 cycles or 4 hours, because the bacteria population decreases by 75% every 2 hours, and it takes 2 cycles for the population to reach 1,000 from 10,000.

To calculate the amount that should be deposited today in an account that earns 3% compounded semiannually to accumulate to $8000 in three years, we can use the compound interest formula.

To calculate the amount that should be deposited today in an account that earns 3% compounded semiannually to accumulate to $8000 in three years, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the future value, P is the principal, r is the interest rate, n is the number of compounding periods per year, and t is the number of years. In this case, the future value (A) is $8000, the interest rate (r) is 3% or 0.03, the number of compounding periods per year (n) is 2 (semiannual compounding), and the number of years (t) is 3. Plugging these values into the formula, we get:

A = P(1 + r/n)^(nt)

$8000 = P(1 + 0.03/2)^(2*3)

$8000 = P(1 + 0.015)^(6)

$8000 = P(1.015)^(6)

To find the value of P, we divide both sides of the equation by (1.015)^6: P = $8000 / (1.015)^6. Using a calculator, we find that P ≈ $7383.42. Therefore, approximately $7383.42 should be deposited today in the account.

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Divide the cost for 3 ounces by 3, to find the cost per ounce:

2.40 / 3 = 0.80

It cost 80 cents per ounce.

Now multiply the cost per ounce by 16 ounces:

16 x 0.80 = 12.80

It will cost $12.80 for one pound.

Answer: If the recipe wants 3/4 cup of pineapple juice for every 6/4 cups of orange juice, 18/4 is 6x more than the recipe so 6/4 must be 6x larger too.

6 x 3/2 = 18/2 or 9 cups of orange juice. Hope this helps :) Please mark brainliest if you can ;)

Answer:

Total wood required for the project will be 9 3/8 feet.

Step-by-step explanation:

As given in the question Quentin has lumber of length = 6 5/8

feet =53/8 feet.

Now Quentin needs more lumber = 2 3/4 feet =11/4 feet or 22/8 feet.

So we can get total wood required by adding these two figures

That is = 53/8 + 22/8

           = (53 +22)/8

           = 75/8

            = 9 3/8 feet

Answer:

[tex]The\ total\ wood\ will\ the\ project\ have\ used\ be\ 9 \frac{3}{8}.[/tex]

Step-by-step explanation:

As given

[tex]Quentin\ has\ 6 \frac{5}{8}\ feet\ of\ lumber\ but\ needs\ another\ 2 \frac{3}{4}\ feet\ to\ complete\ the\ project\ he's\ working\ on.[/tex]

i.e

 [tex]Quentin\ has\ \frac{53}{8}\ feet\ of\ lumber\ but\ needs\ another\ \frac{11}{4}\ feet\ to\ complete\ the\ project\ he's\ working\ on.[/tex]        

 [tex]Total\ wood\ will\ the\ project\ have\ used =\frac{53}{8} + \frac{11}{4}[/tex]

L.C.M of (8,4) = 8

Than

[tex]Total\ wood\ will\ the\ project\ have\ used =\frac{53 + 11\times 2}{8}[/tex]                              

[tex]Total\ wood\ will\ the\ project\ have\ used =\frac{53 + 22}{8}[/tex]       [tex]Total\ wood\ will\ the\ project\ have\ used =\frac{75}{8}[/tex]  

[tex]Total\ wood\ will\ the\ project\ have\ used = 9 \frac{3}{8}[/tex]  

[tex]Therefore\ the\ total\ wood\ will\ the\ project\ have\ used\ be\ 9 \frac{3}{8}.[/tex]

[tex]\bf \begin{cases} x=7\implies &x-7=0\\ x=-3\implies &x+3=0\\ x=2\implies &x-2=0 \end{cases}~\hspace{7em}(x-7)(x+3)(x-2)=\stackrel{y}{0} \\\\\\ (x^2-4x-21)(x-2)=y \\\\\\ x^3-4x^2-21x-2x^2+8x+42=y\implies x^3-6x^2-13x+42=y[/tex]

Answer:

x= -2

Step-by-step explanation:

The distance from one end of the line  to the other is -3x-1.

Counting on the number line we count 6 units.  Setting them equal we get

-3x-1 = 5

Add 1 to each side

-3x-1+1 = 5+1

-3x = 6

Divide each side by -3

-3x/-3 = 6/-3

x = -2

Answer:

The correct option is B.

Step-by-step explanation:

From the given figure it is nices that the length of sides AB, BC and AC are 20, 22 and 35. The line AD is angle bisector.

Let the missing value be x.

The Triangle Angle Bisector Theorem states that the angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.

Since AD is angle bisector, therefore

[tex]\frac{AB}{AC}=\frac{BD}{CD}[/tex]

[tex]\frac{20}{35}=\frac{22-x}{x}[/tex]

[tex]20x=35(22-x)[/tex]

[tex]20x=770-35x[/tex]

Add 35x both sides.

[tex]55x=770[/tex]

Divide both sides by 55.

[tex]x=\frac{770}{55}[/tex]

[tex]x=14[/tex]

Therefore, second option is correct.

Answer:

Write a formula for P(n) in terms of R(n).

R(n) - E(n)

Write a formula for P(n) in terms of n.

20n - [tex]10\sqrt{n}[/tex]

Step-by-step explanation:

Please rate 5 stars and thanks if the answer is right :)

To calculate Scarlett's profit for selling ponchos, subtract her total expenses from her total revenue using the functions provided. For a specific number of ponchos, plug that number into both the revenue and expense functions and subtract the results.

The student's question deals with the calculation of profit for a business venture, specifically for selling batches of designer ponchos. Given the revenue function R(n) = 20n and the expense function E(n) = 10 √{n}, the profit that Scarlett makes from producing and selling a batch of n ponchos can be calculated by subtracting the total expenses from the total revenue, which is P(n) = R(n) - E(n). To find Scarlett's profit for a specific number of ponchos, simply plug the value of n into both functions and perform the subtraction.

For example, if Scarlett wants to calculate the profit for selling 5 ponchos, the revenue would be R(5) = 20(5) = $100, and the expenses would be E(5) = 10√5. Scarlett's total profit for 5 ponchos would then be P(5) = $100 - 10√5.

Answer:

Josue is Write

Step-by-step explanation:

64 x .10 = 6.4 in savings while $10 off is better

Answer is 4:2 (choice B)

AB is 4 units while A'B' is 2 units. The ratio of the sides is simply gluing these two numbers together with a colon symbol in between to get 4:2. We can reduce this to get 2:1, but your teacher has decided not to do this.

Answer:

Option (b) is correct.

The matrix A is [tex]\begin{pmatrix}-3&-14&7&18\\ -13&2&-5&-6\end{pmatrix}[/tex]

Step-by-step explanation:

Given : A matrix form,

[tex]A+\begin{pmatrix}3&9&-1&-8\\ \:16&-2&3&13\end{pmatrix}=\begin{pmatrix}0&-5&6&10\\ \:3&0&-2&7\end{pmatrix}[/tex]

we have to find the value of matrix A

Consider the given matrix form,

[tex]A+\begin{pmatrix}3&9&-1&-8\\ \:16&-2&3&13\end{pmatrix}=\begin{pmatrix}0&-5&6&10\\ \:3&0&-2&7\end{pmatrix}[/tex]

when A + B = C

Then A = C - B

That is

[tex]A=\begin{pmatrix}0&-5&6&10\\ \:3&0&-2&7\end{pmatrix}-\begin{pmatrix}3&9&-1&-8\\ \:16&-2&3&13\end{pmatrix}[/tex]

Subtract the elements in the matching position, we get,

[tex]A=\begin{pmatrix}0-3&\left(-5\right)-9&6-\left(-1\right)&10-\left(-8\right)\\ 3-16&0-\left(-2\right)&\left(-2\right)-3&7-13\end{pmatrix}[/tex]

Simplify, we get,

[tex]A=\begin{pmatrix}-3&-14&7&18\\ -13&2&-5&-6\end{pmatrix}[/tex]

Thus, The matrix A is [tex]\begin{pmatrix}-3&-14&7&18\\ -13&2&-5&-6\end{pmatrix}[/tex]

Parallel lines have the same a slope. Therefore if

k: y = 3x - 6 → slope = 3

and l: y = mx + b

l || k ⇔ m = 3

l: y = 3x + b

We have the point (-6, -7). Put the coordinates to the equation:

-7 = 3(-6) + b

-7 = -18 + b    add 18 to both sides

11 = b → b = 11

Answer:

1987 + 1257 = 3247

Step-by-step explanation:

We are going to use a base number to start from. That number is 1,987 where the thousand is 1, the hundred is 9 and the ten is 8.

Then we are going to add 1,257 which will be 3,247. Thus we will have a new thousand which is 3 (formerly 1), a new hundred which is 2 (formerly 9), and finally, a new ten which is 5 (formerly 7).

1987 + 1257 = 3247 gives you a new thousand, a new hundred and a new ten.

Answer:

Step-by-step explanatcagion:

Problem 1

Answer: Independent

The reason why is because each bag is separate from one another, so one event doesn't affect the other. If we know the result of what we pulled out of one bag, it doesn't change the probability of the other event.

======================================

Problem 2

Answer: Dependent

Assuming you do not put the first card back, then the probability of picking a King on the second draw will be different than if you picked a King on the first draw. With all 52 cards in the deck, the probability of getting a king is 4/52 = 1/13. It changes to 4/51 after we picked out an ace for the first card (and didn't put that first card back).

1 ║ 1               2                  -3               2

                       1                   3               0

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

       1              3                   0              [tex]\boxed{2}[/tex]

⇒ The Remainder is 2

Answer: 15

Step-by-step explanation:

Using synthetic division:

-5  |  1    9     17    -8    50

    |  ↓   -5   -20   15   -35            

       1     4   -3      7     15  ← this is the remainder

Check:

f(x) = x⁴ + 9x³ + 17x² - 8x + 50

f(-5) = (-5)⁴ + 9(-5)³ + 17(-5)² - 8(-5) + 50

      = 625 - 1125 + 425 + 40 + 50

      = 15

Answer:

see explanation

Step-by-step explanation:

the exterior angle of a triangle equals the sum of the 2 opposite interior angles, that is

2x + 4 = x + 60 ( subtract x from both sides )

x + 4 = 60 ( subtract 4 from both sides )

x = 56

exterior angle = 2x + 4 = (2 × 56) + 4 = 112 + 4 = 116°

Answer:

6

Step-by-step explanation:

First, you multiply 2 to the 2nd power, then add 2

Question

2+2^2

Answer:

Step-by-step explanation:

2² = 2*2

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

power first then sum

2 + 2² =

2 + 4 =

6

Answer:

$273.60

Step-by-step explanation:

The cost of stainless steel tubing varies jointly as the length and the diameter of the tubing.

i.e [tex]C\propto L\cdot D[/tex]

i.e [tex]C=k\cdot L\cdot D[/tex]

A 5 foot or 60 inches length with diameter 2 inches costs $48.00, so

[tex]\Rightarrow 48=k\times 60\times 2[/tex]

[tex]\Rightarrow k=\dfrac{48}{60\times 2}=0.4[/tex]

Now the equation becomes,

[tex]C=0.4\cdot L\cdot D[/tex]

So the cost of a 19 foot or 228 inches length with 3 inches diameter is,

[tex]C=0.4\times 228\times 3=\$273.60[/tex]

Answer:

a = 8

Step-by-step explanation:

Put the given information into the function equation and solve for a.

f(x) = a/(x-h) +k . . . . for (h, k) = (4, 2) and (x, y) = (12, 3)

3 = a/(12 -4) +2 . . . . . . . givens substituted in

1 = a/8 . . . . . . subtract 2

8 = a . . . . . . . multiply by 8

Answer:

1.a=2

2.  C  x=2  and x=-3

Step-by-step explanation:

The standard form for the quadratic function is  

ax^2 +bx+c

so  we need to rewrite the function to be in this form

2x^2 -10 = 7x

Subtract 7x from each side

2x^2 -7x-10 = 7x-7x

2x^2 -7x-10 = 0

a =2, b= -7  c=-10

2.  The quadratic formula is

-b ± sqrt(b^2 -4ac)

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

2a

2x^2 + 2x=12

Lest get the equation in proper form

2x^2 + 2x-12 = 12-12

2x^2 +2x-12 =0

a=2  b=2 c=-12

Lets substitute what we know

-2 ± sqrt(2^2 -4(2)(-12))

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

2(2)

-2 ± sqrt(4+96)

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

2(2)

-2 ± sqrt(100)

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

4

-2 ± 10

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

4

-2 + 10               -2-10

-----------   and  --------------

4                             4

8/4   and -12/4

2  and -3