Bret has a fish tank that holds 320 liquid ounces of water. On average, the water evaporates from the tank at a rate of 3.84 ounces per day. Bret went on vacation for 2 weeks, and asked a friend to feed his fish. The fish tank was full of water when Bret left. To the nearest hundredth, how many liquid ounces of water were left in the tank when Bret returned from his vacation?

Answer:

x² + 2x + [3\x - 1]

Step-by-step explanation:

Since the divisor is in the form of x - c, use what is called Synthetic Division. Remember, in this formula, -c gives you the OPPOSITE terms of what they really are, so do not forget it. Anyway, here is how it is done:

1| 1 1 -2 3

↓ 1 2 0

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

1 2 0 3 → x² + 2x + [3\x - 1]

You start by placing the c in the top left corner, then list all the coefficients of your dividend [x² + 5x - 36]. You bring down the original term closest to c then begin your multiplication. Now depending on what symbol your result is tells you whether the next step is to subtract or add, then you continue this process starting with multiplication all the way up until you reach the end. Now, when the last term is 0, that means you have no remainder, which in this case is a 3, so what you is set the divisor underneath the remainder of 3. Finally, your quotient is one degree less than your dividend, so that 1 in your quotient can be an x², 2 becomes 2x, and the remainder of 3 is set over the divisor, giving you the other factor of x² + 2x + [3\x - 1].

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Answer:

Part 1) The system is solved using elimination

The cost  per can of grape juice is [tex]\$1.19[/tex] and the cost per can of apple juice is [tex]\$1.49[/tex]

Part 2) The system is solved using substitution

The cost  per can of grape juice is [tex]\$1.19[/tex] and the cost per can of apple juice is [tex]\$1.49[/tex]

Part 3) The system is solved by graphing

The graph in the attached figure

Step-by-step explanation:

Part 1) Solve the system by elimination

Let

x----> the cost per can of grape juice

y----> the cost per can of apple juice

we know that

[tex]6x+4y=13.10[/tex] -----> equation A

[tex]4x+6y=13.10+0.60[/tex]

[tex]4x+6y=13.70[/tex]  -----> equation B

Solve the system by elimination

Multiply the equation A by -6 both sides

[tex]-36x-24y=-78.6[/tex] -------> equation C

Multiply the equation B by 4 both sides

[tex]16x+24y=54.8[/tex] -------> equation D

Adds equation C and equation D

[tex]-36x-24y=-78.6\\16x+24y=54.8\\----------\\-36x+16x=-78.6+54.5\\-20x=-23.8\\x=1.19[/tex]

Substitute the value of x in the equation A

[tex]6(1.19)+4y=13.10[/tex]

[tex]4y=5.96[/tex]

[tex]y=1.49[/tex]

therefore

The cost  per can of grape juice is [tex]\$1.19[/tex]

The cost per can of apple juice is [tex]\$1.49[/tex]

Part 2) Solve the system by substitution

Let

x----> the cost per can of grape juice

y----> the cost per can of apple juice

we know that

[tex]6x+4y=13.10[/tex]    

[tex]4y=-6x+13.10[/tex]

[tex]y=-1.5x+3.275[/tex] -----> equation A

[tex]4x+6y=13.10+0.60[/tex]

[tex]4x+6y=13.70[/tex]  

[tex]6y=-4x+13.70[/tex]

[tex]y=-(4/6)x+13.70/6[/tex]

[tex]y=--0.67x+2.28[/tex] -----> equation B

Substitute equation B in equation A and solve for x

[tex]-0.67x+2.28=-1.5x+3.275[/tex]

[tex]1.5x-0.67x=3.275-2.28[/tex]

[tex]0.83x=0.995[/tex]

[tex]x=1.19[/tex]

Find the value of y

Substitute the value of x in the equation A

[tex]y=-1.5(1.19)+3.275=1.49[/tex]

therefore

The cost  per can of grape juice is [tex]\$1.19[/tex]

The cost per can of apple juice is [tex]\$1.49[/tex]

Part 3) Solve the system by graphing

we have

[tex]y=-1.5x+3.275[/tex] -----> equation A

[tex]y=-(4/6)x+13.70/6[/tex] -----> equation B

Remember that

The solution of the system of equations is equal to the intersection point both lines

The solution is the point [tex](1.19,1.49)[/tex]

see the attached figure

therefore

The cost  per can of grape juice is [tex]\$1.19[/tex]

The cost per can of apple juice is [tex]\$1.49[/tex]

there would be 12 combinations

Answer:

12

Step-by-step explanation:

We are given that tent hold 2,3,5,6 or 12 people.

We have to find the combinations of tents are possible to sleep 32 all tents are fully occupied and exactly one 12 person tent is used.

If one 12 person tents is used then remaining people=32-12=20

Therefore, 20 people that must be in other tents.

To place 20 persons in combination of 2,3,5 and 6.

20=5+5+5+5

20=5+5+5+2+3

20=6+6+6+2

20=2(10)=2+2+....+2(10 times)

20=5+5+2(5)(5 times add 2)

20=6+6+2(4) (4 times add 2)

20=3+3+3+3+3+3+2

20=3+3+3+3+3+5

20=3+2+6+5+2+2

20=3+3+3+3+6+2

20=3+3+5+5+2+2

20=6+6+3+5

Hence, there are 12 possible combination of tents  to sleep 32  all tents are fully occupied and exactly one 12 person tents is used.

Answer:

d

Step-by-step explanation:

To determine if (1, 2) is a solution to the system

Substitute x = 1, y = 2 into the inequalities and check their validity.

y > 2x → 2 > 2 ← incorrect statement

x + y < 3

1 + 2 < 3 → 3 < 3 ← incorrect statement

(1, 2) is not a solution to either inequality → d

For this case we must build a quotient that multiplied by the divisor, is eliminating the terms of the dividend until you reach the remainder of the division. It must be fulfilled that:

Dividend = Quotient * Divider + Remainder

Answer:

See attached image

Option D

Answer:

It's a 50% chance

Step-by-step explanation:

Answer:

1/3 most likely

Step-by-step explanation:

because you take out one tile and it only has one of each color so there are only three left so 1/3

Answer:

12, 18.

Step-by-step explanation:

2x-5 < 33

2x < 38

x < 38/2

x < 19

Answer:

11,499 cm^3

Step-by-step explanation:

The volume of a sphere is given by the formula  [tex]V=\frac{4}{3}\pi r^3[/tex]

The radius is given as 14, we plug it into the formula and find the volume:

[tex]V=\frac{4}{3}\pi r^3\\V=\frac{4}{3}(\frac{22}{7}) (14)^3\\V=11498.66[/tex]

rounded to nearest integer, the volume is 11,499

Answer:

r=14 cm

V=11499 cubic cm

Step-by-step explanation:

If the radius of the sphere is r cm, then the perimeter of the largest cross section is the circumference of the circle qith radius r. Thus,

[tex]88=2\pi r,\\ \\r=\dfrac{88}{2\pi}=\dfrac{44}{\pi}=\dfrac{44}{\frac{22}{7}}=\dfrac{44}{1}\cdot \dfrac{7}{22}=14\ cm.[/tex]

Thvolume of the sphere can be calculated using formula

[tex]V=\dfrac{4}{3}\pi r^3.[/tex]

Since r=14 cm, we get

[tex]V=\dfrac{4}{3}\cdot \dfrac{22}{7}\cdot 14^3=\dfrac{4\cdot 22\cdot 2\cdot 14^2}{3}=\dfrac{34496}{3}\approx 11499\ cm^3.[/tex]

Answer:

the answers are B, C, and D.

The given item soup can is a cylinder.

The volume of the cylinder is given as :

[tex]V=\pi r^{2} h[/tex]

Here 'h' is the height and 'r' is the radius.

So, the true statements are:

B) The volume is the area of the base times the height - The base of the cylinder is circular and the area of the circle is [tex]\pi r^{2}[/tex], so the volume is the area of base multiplied by height.

C) Given the radius or the diameter, you can calculate the area of the base of a cylinder - Yes as the area is [tex]\pi r^{2}[/tex] where 'r' is the radius.

D) The height of a cylinder is the distance between the 2 parallel bases. Yes this is right.

Answer:

√143 = 11.958

√79+√63 = 16.825

4π = 12.66

Im pretty sure this is correct since I used a calculator. Hope it helps

Answer:

A

Step-by-step explanation:

The type of interest where you earn interest on your savings and even earn interest in the previous years interest is compound interest.

Compound interest is when both the amount saved and the interest already accured earn interest at the next date interest is being paid. Simple interest rate is the interest that is paid only on the amount saved.

To learn more about compound interest, please check: https://brainly.com/question/26367706

Answer:

s     a

6    3

22  1

30  0

Step-by-step explanation:

Download song .50

Download album = 4

Let s = number of songs

a = number of albums

She can spend 15 dollars

.5s +4a =15

If she downloads 6 songs, let s=6

.5(6) +4a = 15

3+4a = 15

Subtract 3 from each side

3-3+4a = 15-3

4a = 12

Divide by 4

4a/4 =12/4

a=3

She can buy 3 albums

If she downloads 1 album, let a=1

.5(s) +4(1) = 15

.5s +4=15

Subtract 4 from each side

.5s +4-4=15-4

.5s = 11

Divide by .5

.5s/.5 = 11/.5

s = 22

She can download 22 songs

If she downloads 30 songs, let s=30

.5(30) +4a = 15

15+4a= 15

Subtract 15 from each side

15-15 +4a = 15-15

4a=0

a=0

Answer:

8 cups

Step-by-step explanation:

The number of cups of Gatorade served to the players during the last game was 8 cups.

To solve the problem, we need to determine how many cups are in half a gallon, given that 1 cup is equal to 1/16 of a gallon.

First, we establish the conversion factor between cups and gallons:

1 cup = 1/16 gallon

Now, we need to find out how many cups are in 1/2 gallon. To do this, we multiply the amount of Gatorade used in the last game by the conversion factor:

Cups served = (1/2 gallon) * (16 cups / 1 gallon)

Performing the multiplication:

Cups served = 1/2 * 16

Cups served = 8 cups

Therefore, 8 cups of Gatorade were served to the players during the last game.

Answer:

20% increase

Step-by-step explanation:

Percent increase = (difference) / original *100 percent

                             = (12-10)/10 * 100percent

                             = 2/10 *100 percent

                             = 1/5 * 100 percent

                              =.2 * 100 percent

                              = 20%

Answer:

Final answer is [tex]80x^2[/tex].

Step-by-step explanation:

Given expression is [tex]\frac{16x^3}{y}\cdot\frac{5y^2}{xy}[/tex].

Now we need to simplify this expression as shown below:

[tex]\frac{16x^3}{y}\cdot\frac{5y^2}{xy}[/tex]

[tex]=\frac{80x^3\cdot y^2}{y\cdot xy}[/tex]

[tex]=\frac{80x^3\cdot y^2}{xy^2}[/tex]

[tex]=\frac{80x^3}{x}[/tex]

[tex]=80x^2[/tex]

Hence final answer is [tex]80x^2[/tex].

Answer:

Step-by-step explanation:

let dwight represent x nd his sister represent y

y+3x2=x

Answer:

I did not know that Dwight Schrute has a sisterrrrr

Step-by-step explanation:

Um just the other dude brainliest

Answer:

B

Step-by-step explanation:

B). RA and NY are perpendicular segments

Answer:

The correct answer option is B. Perpendicular segments.

Step-by-step explanation:

We are given two segments RA and NY and we are to determine whether which of the given answer options describe them the best.

Since the angles ∠RDA and ∠NDY are perpendicular angles and they lines RA and NY intersect each other at point D so the formed segments are also perpendicular.

Therefore, the option which best describes this is B. Perpendicular segments.

1) What are the zeros of the function?

smaller r: -11, larger r: -14

2) What is the vertex of the parabola

Vertex: (-12.5, 3)

1. Zeros:

The zeros of the function occur when G(r) = 0. So we need to solve the equation:

-(r + 11)(r + 14) = 0

Since the product of two factors is zero when one or both factors are zero, we can set each factor equal to zero and solve for r:

r + 11 = 0 --> r = -11 (smaller r)

r + 14 = 0 --> r = -14 (larger r)

2. Vertex:

The function is given in factored form, which makes finding the vertex a bit easier. The vertex of a parabola in factored form is exactly between the two zeros.

Therefore, the x-coordinate of the vertex is:

(smaller r + larger r) / 2 = (-11 - 14) / 2 = -12.5

To find the y-coordinate (i.e., the function's value at the vertex), we can plug the x-coordinate of the vertex back into the function (G(r)). However, since the function is multiplied by -1, it might be easier to use one of the original zeros (say, r = -11).

G(-11) = -(-11 + 11)(-11 + 14) = 3 (notice how the negative sign cancels out)

Answer:

Step-by-step explanation:

The log is basically saying: 13/5 to what exponent gives you 50 000/3.

and the exponent is approximated at 10.17378.

Answer:

14

Step-by-step explanation:

Mean = (5+10+10+20+20+5+20+20+15+15)÷10

= 140÷10

= 14

Answer:

After 7.5 seconds and a height of 0

Step-by-step explanation:

The time taken for the bolt to hit the elevator is 3 seconds, at a height of 60 feet.

Given that the elevator height is h(t)=20t while the bolt height is given by h(t)=-16t² + 200.

At the point when the bolt hit the elevator, they would be at the same height, hence:

-16t² + 200 = 20t

16t² + 20t - 200 = 0

t = -4.2 or t = 3

Therefore the time taken for the bolt to hit the elevator is 3 seconds, the height is:

h(3) = 20(3) = 60 feet

The time taken for the bolt to hit the elevator is 3 seconds, at a height of 60 feet.

Find out more at: https://brainly.com/question/11600459

Answer:

Thus, the fourth answer choice is the correct one

Step-by-step explanation:

Let's check this, using the Pythagorean Theorem:

"Yes, the distance from (0, 0) to (2, square root 6 ) is 3 units."

Does 2² + (√6)² = 3²?

Does 4 + 6 = 9?  NO.   .

Answer:

x = 12 or A

Step-by-step explanation:

Tangents from an exterior point to the circumference of a circle are equal

Since one of the tangents = 17, the other one must as well

x + 5 = 17            Subtract 5 from both sides.

x + 5-5 = 17-5

x = 12

The answer is A

Answer:

y=26

Step-by-step explanation:

We just subsitiute.

y=8(4)-6

8*4=32

y=32-6

y=26

The equation of a circle is written as (x-h)^2 +(y-k)^2 = r^2

h and K are the center points of the circle and r is the radius.

replace the letters with the provided center and radius:

(x- (-7))^2 + (y- (-3))^2 = 2^2

Simplify:

(x+7)^2 + (y+3)^2 = 4

The probability of drawing the number 14 is 1/10 (because there are 10 different numbers to pick from). The probability of drawing a number less than 12 is 8/10 (or 4/5 simplified). Multiply the fractions: 1/10 *4/5 = 4/50. Simplify to 2/25. The probability of drawing 14 and then a number less than 12 is 2/25.

Answer:

The correct answer is option B.

Step-by-step explanation:

The given rational expression is:

[tex]\frac{x^2-4}{x^2+5x+6}[/tex]

Factor the numerator and the denominator:

[tex]\frac{x^2-2^2}{x^2+2x+3x+6}[/tex]

Factor the numerator using difference of two squares and the denominator using factorization by grouping.

[tex]\frac{(x-2)}{x(x+2)+3(x+2)}[/tex]

[tex]\frac{(x-2)(x+2)}{(x+2)(x+3)}[/tex]

This function is defined if and only if the denominator is not zero.

That is: (x+3)(x+2)≠0.

x≠-2,x≠-3

We simplify now to obtain:

[tex]\frac{x-2}{x+3}[/tex]

The correct choice is the second option.

Option B is correct.

I just took the semester review.

Congruent is the same size and same shape. When a ray bisects an angle, the two newly created angles will be congruent, since the ray went right in the middle of the first angle (so in this case, ABC and DBC will be congruent)

Answer: C) ∠ABC & ∠DBC

Step-by-step explanation:

When a ray bisect an angle , then it divided the original angle into two congruent angles.

We are given that Ray BC bisects angle ABD.

Then, Ray BC divides ∠ABD into two congruent angles.

From the picture, The angle formed by it : ∠ABC & ∠DBC

So  ∠ABC & ∠DBC must be congruent.

Hence, the pair of angles must be congruent : ∠ABC & ∠DBC

Answer: 33.5 tons

Direct conversion formula: 1 Tons (metric) / 2204.5855379189 = 1 Pounds

Opposite conversion: 67000 Pounds to Tons (metric)

Each person in the Vale family will drink a total of 339.5 ounces of water over the course of 7 days.

The student is asking how much water in ounces each person in the Vale family will drink over the span of 7 days if each person drinks 48.5 ounces of water daily.

To find the total amount of water consumed by one person in 7 days, we multiply the daily intake by the number of days:

48.5 ounces/day imes 7 days = 339.5 ounces

So, each person will drink a total of 339.5 ounces of water in 7 days.