a water barrel that had 4 gallons of water is being filled with water at a rate of 4 gallons per minute . write a function

Answer:

The inequality is: 5<c<19

Length of third side "c" can have values greater than 5 but less than 19

Solution:

Given that,

Length of two sides of triangle are 7 inches and 12 inches respectively

Let the length of third side be "c"

The Triangle Inequality Theorem, states that, the sum of the lengths of any two sides of a triangle is greater than the length of the third side

So we get a inequality as:

Case 1:

Sum of length of two sides of triangle > length of third side

Rewrite,

Case 2:

Let 12 inches be the length of third side

Sum of sides of length 7 and c > 12

Therefore from case 1 and case 2,

Which can be combined,

Therefore the possible values of "c" are:

"c" can have values greater than 5 but less than 19

Answer:

the rate of change from 4 to 8 is 4

Step-by-step explanation:

you can find this by subtracting the first number from the secone number and if the two numbers were in a diffrent order being 8 and 4 the answer would still be 4 because when you subtract 8 from 4 you ger-4 but with rate of change you always use the absolute value

hope this helped

The steps for the geometry sequence with the help of two terms of the sequence, make a system of equation and solve them to find common ratio and first term.

Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.

It can be given as,

[tex]a_n=a_1r^{n-1}[/tex]

Here, a₁ is the first term of the sequence and r is the common ratio.

The fourth term and sixth term given in for the geometric sequence are 3 and 3/16. For the fourth term,

[tex]a_4=a_1r^{4-1}\\3=a_1r^3[/tex]             ...1

For the sixth term,

[tex]a_6=a_1r^{6-1}\\\dfrac{3}{16}=a_1r^5[/tex]           ....2

On solving, we get,  a₁=192 and r=1/4. Thus, the geometric sequence can be given as,

[tex]a_n=a_1r^{n-1}\\a_n=192\times\dfrac{1}{4}^{n-1}[/tex]

Hence, the steps for the geometry sequence with the help of two terms of the sequence, make a system of equation and solve them to find common ratio and first term.

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Answer:

72.

Step-by-step explanation:

2 x{15 plus[24-(1.5 x2)]}

Using PEDMAS:

= 2 x {15 + [24-(3)]}

= 2 x (15 + 21)

= 2 x 36

= 72.

A rhombus is a quadrilateral whose all sides are of equal length. The measure of the ∠QPR is 42°.

A rhombus is a quadrilateral whose all sides are of equal length, and the opposite are parallel to each other.

The diagonals of a rhombus intersect each other at 90°. Therefore, the measure of ∠QTR can be written as,

∠QTR = 90°

(6y+6) = 90°

6y = 90 - 6

6y = 84

y = 14

Also, the diagonals of the rhombus divide the angle into two equal angles, therefore,

∠QPR = ∠SPR

∠QPR = 3y

∠QPR = 3(14)

∠QPR = 42°

Hence, the measure of the ∠QPR is 42°.

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Step-by-step explanation:

[tex] = 1 - ( \frac{1}{6} + \frac{1}{5} )[/tex]

[tex] = 1 - ( \frac{5}{30} + \frac{6}{30} )[/tex]

[tex] = 1 - \frac{11}{30} [/tex]

[tex] = \frac{30}{30} - \frac{11}{30} [/tex]

[tex] = \frac{19}{30} [/tex]

So, he keeps [tex] \frac{19}{30}[/tex]

Answer:

Sanjeev kept 19/30 of his cake.

Step-by-step explanation:

So, if Sanjeev ate 1/6 of the cake there will be 5/6 of the cake left over.

He gave 1/5 of this 5/6 to his friend.

He did not give 1/5 of the entire cake, he gave 1/5 of the remainder of his cake, which was 5/6.

To solve this, we must first convert both fractions to the same denominator.

1/5 and 5/6 becomes 6/30 and 25/30

He gave away 6/30 of this 25/30

It is now clear that we must take away how much he gave away from the remainder of the cake.

25/30 subtract 6/30 becomes 19/30

We cannot simplify this.

Therefore, Sanjeev kept 19/30 of his cake.

Answer:

Your first answer is correct.

Second question: 300 ft.

Step-by-step explanation:

2nd problem, create a proportion.

[tex]\frac{220}{x}=\frac{305}{416} \\305x = 91520\\\frac{305x}{305}= \frac{91520}{305} \\x=300[/tex]

AnsweB i think

Step-by-step explanation:

[tex]\bf Blue \ Color \ Line : y = x^2[/tex]

When added all together:

[tex]\bf Black \ color \ Line: y=-\left(x+2\right)^{2}-10[/tex]    =  Final answer.

Answer:

Yes, it is correct.

Step-by-step explanation:

7x≥20x-39

39≥13x

x≤39/13

x≤3

Step-by-step explanation:

we assume day and night are equally long.

and the mouse will start at night of day 1.

then, on day 2, it will first retreat 2 meters (during daylight) and then advance 14 meters (at night).

so, on every full day, the mouse will effectively advance 12 meters (-2 + 14 = 12).

with a starting value of 14 (the first night).

so, we are getting an arithmetic sequence

an = an-1 + c

c = 12 in our case.

a1 = 14

a2 = a1 + 12 = 14+12 = 26

a3 = a2 + 12 = a1 + 12 + 12 = 14 + 2×12 = 38

an = a1 + (n-1)×12 = 14 + 12(n-1)

at what n will it reach 86 ?

86 = 14 + 12(n-1) = 14 + 12n - 12 = 2 + 12n

84 = 12n

n = 7

so, on the 7th day the mouse will reach the surface (if we truly count the first starting night day 1 - this is up to your teacher, but I would).

Answer:

y = 12 mm

Step-by-step explanation:

Volume of a rectangular prism: length × width × height

V = L×W×H

Substitute the values above and solve for y:

2,016 = 14 × 12 × y

2,016 = 168y

2,016/168 = 1395v/168

12 = y

Final answer: 12 mm

Hope this helps!

Answer:

46.77 cm

Step-by-step explanation:

Perimeter of the semicircle = Circumference + 2r

Answer:

each friend will get 5/4 or 1.25 cups of lemonade

Step-by-step explanation:

5 divide by 4 since there are 4 friends.

so 5/4 of the lemonade will be shared by each friend.

Step-by-step explanation:

each friend would get 1.25 cups each

Answer:

No there are 180 degrees on a line

Step-by-step explanation:

180

115-

065

65°

The value of y in the given question will be y = -2x  +  26.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

The value of y will be calculated as:-

Given the equation :-

4y  -  2x  =  12

y =  x / 2 + 12

Now for two perpendicular lines, the product of the intercepts is -1

m₁  x  m₂  = -1

So the new intercept will be

m₂ = -1 / m₁ = -1 / 1 / 2 = -2

So new equation will be

y  =  -2x  +  c

2 = -2  x  12  +  c

c  =  26

So the equation will be:-

y =  -2x  +  26

Therefore the value of y in the given question will be y = -2x  +  26.

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Answer:

0.333333...

Step-by-step explanation:

2/6 = 1/3 = 0.33333...

You can divide on paper or on a calculator 2÷6 or 1÷3 to find this. If you are allowed to use a calculator and your calculator has F>D and D>F buttons they are for converting decimals and fractions back and forth. On paper, you are doing like a long division calculation. Put 2 inside the little dividing frame and put 6 on the outside. Or 1 inside and 3 outside. See image.

The root of the polynomial function f(x) = 3x⁵ - 2x² + 7x is 0

The polynomial function is given as:

f(x) = 3x⁵ - 2x² + 7x

Set the function to 0

3x⁵ - 2x² + 7x = 0

Factor out x

x(3x⁴ - 2x + 7) = 0

Divide both sides by (3x⁴ - 2x + 7)

x = 0

Hence, the root of the equation is 0

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Answer:

B

Step-by-step explanation:

cause math

Answer:

  60 gallons

Step-by-step explanation:

The amount of 10% solution he should add can be found by writing an equation for the total amount of chocolate in the mix.

__

Let x represent the amount of 10% solution that Augustus needs to add to the 30 gallons of 25% solution. The amount of chocolate in the resulting 15% mix is ...

  0.10x +0.25(30) = 0.15(x +30) . . . . gallons of chocolate in the mix

  0.10(30) = 0.05x . . . . . . . . subtract 0.10x +0.15(30)

  60 = x . . . . . . . . . . . . divide by 0.05

Augustus should add 60 gallons of the 10% solution to make a 15% mixture.

Answer:

[tex]A = 256[/tex]

Step-by-step explanation:

Since the hexagon is regular, we know that all of the side lengths are equal. We can find the length of the sides by solving for [tex]l[/tex] in the formula for the area of a hexagon:

[tex]A = \frac{3\sqrt{3}}{2}l^2\\384\sqrt{3} = \frac{3\sqrt{3}}{2}l^2\\384 = \frac{3}{2}l^2\\256 = l^2\\16 = l[/tex]

Now that we have the side length, we can find the area of the square:

[tex]A = l^2\\A = 16^2\\A = 256[/tex]

Answer:

256 in²

Step-by-step explanation:

Area of a Hexagon (To find side length)

Area of square

Answer:

y < 1 and y > x

Step-by-step explanation:

Let's find each equation without any inequalities first.

We have a dotted line at y = 1

Now, a dotted line represents exclusivity, and hence; it should not include the = sign

Therefore, the answer is y < 1 and y > x

Answer:

-81/-9

both minus will be cut so

81/9

9

Step-by-step explanation:

the answer is 9

(a) 12 boys play basketball

(b) See figure 2 below

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

Explanation:

Part (a)

You are on the right track so far when you wrote the partial table.

There are 15 girls in the class, and 8 girls that play basketball. That must mean 15-8 = 7 girls do not play basketball.

Focusing on the first row only, we'll have 7 go in the second column and 15 go in the third column. The first row is filled out entirely.

There are 32 students and 15 girls. This means there are 32-15 = 17 boys. We'll write 17 at the end of the second row.

The other missing value of this row is 17-5 = 12 to represent the number of boys who play basketball. This is because of the 5 boys that don't play basketball.

To fill out the missing items in the third row, add the columns straight down.

We have 8+12 = 20 basketball players and 7+5 = 12 people who do not play basketball. Notice how 20+12 = 32 along the bottom row to help confirm the correct values.

Check out figure 1 to see the entire two-way frequency table.

We see that there are 12 boys that play basketball.

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

Part (b)

The previous part detailed how to set up the two-way frequency table.

For this part, we'll be creating the two-way relative frequency table. The keyword "relative" means that we'll divide each item by the grand total 32.

For instance, in the first row & first column we have 8/32 = 0.25; do the same with the other values. Do not round. The reason for this is because each decimal item is a terminal decimal, meaning the digits stop at some point. If your teacher instructs you to round, then be sure to follow those instructions of course.

Check out figure 2 so you can see the two-way relative frequency table.

A result like 0.25 in the first row & first column tells us that 25% of the class is a girl and plays basketball.

Answer:

2210

Step-by-step explanation:

390 =15%

390*3 = 130=5%

130*17=2210

Answer:

f

Step-by-step explanation:

your welcome