An aquarium has 12 equal size tanks of fish on display. All together, the tanks hold 643. 8 gallons of water. How much water can each tank hold?.

Answer:

  ±{1, 2, 3, 6, 9, 18}

Step-by-step explanation:

You want the possible rational zeros of f(x)= x^3-6x^2+6x-18.

The rational root theorem tells you the possible rational zeros are of the form ...

  ±{divisors of the constant term} / {divisors of the leading coefficient}

Here, the leading coefficient is 1, so its only divisor is 1.

The constant term is 18, and its divisors are 1, 2, 3, 6, 9, 18.

The possible rational roots are ±{1, 2, 3, 6, 9, 18}.

__

Additional comment

A graph shows the only real root is between 5 and 6, so none of the roots are rational.

Answer:

  19 units

Step-by-step explanation:

You have midline LM marked as 6x+1 and parallel baseline IJ marked as -6x+56 in triangle IJK. You want to know the length of LM.

The midline of a triangle is half the length of the parallel base:

  LM = 1/2(IJ)

  6x +1 = 1/2(-6x +56) . . . . . substitute expressions

  6x +1 = -3x +28 . . . . . . . simplify

  9x = 27 . . . . . . . . . . . . sdd 3x-1

  x = 3

Now, we can find LM:

  6x +1 = 6(3) +1 = 19

The measure of LM is 19 units.

The inverse of the function g(x) = ∛(2x + 4) is equal to: D. g(x)⁻¹ = 1/2(x³) - 2.

The domain of the function shown in the graph is: B. [-2, 1].

In Mathematics, an inverse function can be defined as a type of function that is obtained by reversing (undoing) the operation of a given function (f(x)).

In order to determine the inverse of the given function, we would interchange input value (x) and the output value (y) as follows:

g(x) = ∛(2x + 4)

x = ∛(2y + 4)

Next, we would take the cube root of both sides of the function;

x³ = 2y + 4

2y = x³ - 4

y = (x³ - 4)/2

y = x³/2 - 2

g(x)⁻¹ = 1/2(x³) - 2

In Mathematics, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right as follows;

Domain = [-2, 1].

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Answer:

$84.50

Step-by-step explanation:

Add the amounts:

$63.48 + $52.02 = $115.50

Two $100 bills add to $200.

To find the change, subtract the total cost from the amount of money handed over.

$200 - $115.50 = $84.50

Molly should give him $84.50. Thus option B is the correct answer.

The change given must be equal to the balance left after deducting the price of the goods from the total money received.

In this case,  

Price of goods = Price of DVD player + Price of five DVDs

                         = $63.48 + $52.02

                         =$115.50

Total Money Received = 2 x $100 = $200

Therefore, Change = Total Money Received - Price of goods

                                = $200 - $115.50

                                = $84.50

Answer:

  (x, y) = (4 7/9, 1 2/3)

Step-by-step explanation:

You want to solve this system of equations using the elimination method.

First of all, take a look at the coefficients of the variables:

  x: 3 and 3. Subtracting one from the other will eliminate x

  y: 4 and -2. Adding twice the second to the first will eliminate y.

The easiest elimination is accomplished by subtracting the second equation from the first:

  (3x +4y) -(3x -2y) = (21) -(11)

  6y = 10 . . . . . . . . . . simplify

  y = 10/6 = 5/3 = 1 2/3 . . . . divide by the coefficient of y

Substitute for y to find x.

  3x +4(5/3) = 21

  x +20/9 = 7 . . . . . . divide by 3

  x = 7 -(2 2/9) = 4 7/9

The solution is (x, y) = (4 7/9, 1 2/3).

__

Additional comment

A graphing calculator confirms this solution.

Answer:

Soft tacos are $1.25 each, while double deckers are $2.5 each.

(I didn't have time for a step by step explanation at the moment)

Sorry

The solution to the given inequality 2(2.1z + 4.5) < 21.6 to solve for the unknown value of z is z < 3

Inequality refers to a statement that is of two quantities in which one is specifically less than (or greater than) another.

The symbols of inequality includes;

2(2.1z + 4.5) < 21.6

open parenthesis

4.2z + 9 < 21.6

substract 9 from both sides

4.2z < 21.6 - 9

4.2z < 12.6

divide both sides by 4.2

z < 12.6 / 4.2

z < 3

Hence, z < 3 satisfies the value of z in the inequality 2(2.1z + 4.5) < 21.6

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Answer:

103.98cm

Step-by-step explanation:

14 + 14 = 28

20 + 20 = 40

(14(3.14)) / 2+ 14 = 35.98cm

40 + 28 + 35.98 = 103.98cm

At 55 seconds , both the plane A and plane B will have same altitude.

According to the question,

The altitude of plane A = 1500m

The altitude of plane B = 1115m

Altitude plane A gained = 19m/s

Altitude plane B gained = 26m/s

Let "x" be the number of second

Let the equation of plan A and plane B is

a(x) = m₁ x + 1500

b(x) = m₂ x + 1115

We know how fast they are gaining altitude. The are the m values

m₁ = 19

m₂ = 26

So, now we have

a(x) = 19 x + 1500

b(x) = 26 x + 1115

So , to have same altitude ,

a(x) = b(x)

=> 19 x + 1500 = 26 x + 1115

Solving for x,

=> 26x-19x = 1500 - 1115

=> 17x = 385

=> x = 55 seconds

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1. Which equation represents a line that has a slope of 2 and passes through the origin?

A y=2x

B. y=x+2

C. y x

D. y=-x

2. A regular jeepney ride costs $12.00 for the first 4 km, and each additional km adds P1.50 to the fare. Which of the following can be used to compute a regular fare (F), in pesos, for a 6-km nde?

A. F = 12(7)

B. F=12(7)+1.50

C.=12(150)+7

D.=12+2(1.50)

3. A regular jeepney ride costs P12.00 for the first 4 km, and each additional km adds P1.50 to the fare. How much is the regular fare for a 6-km ride?

A. P15

B. P13.50

C. P14.50

D. P16

4.Which equation represents a vertical line?

A. y =2x

B. x = 2

C. y = 3

D. y = -x​

Ummi's quotients in this situation represent the unit rates of the advertisement

You will not be able to draw a straight line through the points

From the question, we have the following quotients parameters that can be used in our computation:

2.90/10 = 0.29/1 3.48/12 = 0.29.1 4.48/16 = 0.28.1

These can be rewritten as

2.90/10 = 0.29/1

3.48/12 = 0.29/1

4.48/16 = 0.28/1

The quotients mean that

Unit rate = Total amount spent/Number of adverts

So, the quotient expressions represent the unit rate

Recall that

2.90/10 = 0.29/1

3.48/12 = 0.29/1

4.48/16 = 0.28/1

The values of the quotients are not equal

This means that it is not possible to draw a straight line through the points

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The print is 35.41 cm tall.

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

The original painting is 120 cm wide and 85 cm tall.

and, the print is 50 cm wide.

let the print is x cm tall

So, x/ 50 = 85 / 120

120x = 4250

x= 35.41 cm

Hence, the print is 35.41 cm tall.

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Answer: This is where the answer is undefined

Step-by-step explanation:

Edge 2022 :)

Answer: 5th option

Step-by-step explanation:

edge 2023

Answer: 6:11

Step-by-step explanation:

Find the total by 6 + 5 =11

He bought 6 videotapes so ratio is 6:11

The 3 to the power of three halves equal to square root of 27 sqrt(27).

What is the square root?

A square root of a number x is a number y such that y² = x; in other words, a number y whose square is x. For example, 4 and −4 are square roots of 16, because 4² = ² = 16.

A square root is a number that can be multiplied by itself to give the original number.

3 to the power of 3/2 is equal to the square root of 3 to the power of 3, which is equal to the square root of 27. The square root of 27 is approximately 3.872983346207417.

To calculate this value, you can use a calculator or you can use the following formula:

3^(3/2) = sqrt(3^3) = sqrt(27) = 3.872983346207417

Hence, the 3 to the power of three halves equal to square root of 27 sqrt(27).

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12: This one if fairy simple: all you need is a line that is not parallel to the line provided, and combined with it, it will provide a solution that's on that line. For example:

y = 2x

x - y = 10

13: Just find two lines that cross (6, -4).

You can use point-slope form:

y - y1 = m(x-x1)

y + 4 = m(x - 6)

then choose two equations with different m's

y = 2(x-6) - 4

y = 3(x-6) - 4

14:

Line one has a slope of two and an intercept at y=0 so it is y = 2x

Line two has a slope of one and an intercept at y=-1 so it is y = x - 1

To find the solution of the system, substitute y:

2x = x - 1

x = -1

Then plug back in:

y = 2 * -1 = -2

So the solution is: (-1, -2)

The approximate percentage of women with platelet count between 3 and 4.1 is 350

We should know that platelet deals the cells that are found in our body which assemble together when they discover bad blood in the cells.

The range of women is given as 3-4.1

The average of the women is [tex]\frac{3+4.1}{2}=\frac{7.1}{2}[/tex]

Simplifying the expression we have

= 3.5

The appromimate percentage is 3.1*100=350 women

In conclusion the approximate percentage of women with blood platelet is 350 women

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Answer:

93.2° (nearest tenth)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Sine Rule} \\\\\\$\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c} $\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}[/tex]

From inspection of the given triangle:

Substitute the values into the sine rule to find the measure of angle C:

[tex]\implies \dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]

[tex]\implies \dfrac{\sin 38^{\circ}}{9}=\dfrac{\sin C}{11}[/tex]

[tex]\implies \sin C=\dfrac{11\sin 38^{\circ}}{9}[/tex]

[tex]\implies C=\sin ^{-1} \left(\dfrac{11\sin 38^{\circ}}{9}\right)[/tex]

[tex]\implies C=48.80523914...^{\circ}[/tex]

Interior angles of a triangle sum to 180°.

[tex]\implies A+B+C=180^{\circ}[/tex]

[tex]\implies A+38^{\circ}+48.80523914...^{\circ}=180^{\circ}[/tex]

[tex]\implies A=93.19476086...^{\circ}[/tex]

Therefore, the size of angle A is 93.2° (nearest tenth).

The best estimate of the average change in mood rating linked with an additional hour spent playing sports is 1.5 points, according to the presented linear function.

Modeling a linear function involves:

y = mx + b

The slope, or m, measures how quickly y changes when x changes by one.

The value of y at x = 0 is represented by the y-intercept, or b.

In the given problem

The amount of time they invested in sports is x.

Their mood score is y.

The required equation is ,

y =1.5 + 5

Given that the slope is m = 1.5, the best estimate of the average change in mood rating resulting from an extra hour spent playing sports is 1.5 points.

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The values of x and y for fig. 1) is 5/4 and 4/7, for fig. 2) x = 15, y = 4 and for fig. 3) x = 3 and y = 2

Thales's Theorem or Basic Proportionality Theorem states that if a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio.

Given are three figures of triangles,

Figure 1)

5/x+5 = 8/10

50 = 40+8x

x = 5/4

y = 7/7+y = 8/10

70 = 56 +8y

y = 4/7

Figure 2)

12/12+y = 18/18+6

12/12+y = 18/24

48 = 36 +3y

y = 4

12/4 = x/5

x = 15

Figure 3)

y/4 = 1.5/3

y = 2

x/6 = 1.5/3

x = 3

Hence, the values of x and y for fig. 1) is 5/4 and 4/7, for fig. 2) x = 15, y = 4 and for fig. 3) x = 3 and y = 2

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Answer:

Step-by-step explanation:

The slope of a line is defined as the change in y-coordinate divided by the change in x-coordinate between two points on the line. In this case, the change in y-coordinate between the two points is -11 - (-1) = -10, and the change in x-coordinate is 0 since both points have the same x-coordinate. Therefore, the slope of the line that passes through the points (-8, -1) and (-8, -11) is -10/0, which is undefined.

255 biology and 192 sociology textbooks were sold in a week.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

While the graph of a linear equation with two variables, x and y, creates a straight line, the graph of a linear equation with just one variable, x, forms a vertical line that is parallel to the y-axis.

Step 1:

Let x be the number of biology textbooks and y be number of sociology textbooks.

x + y = 447 ------(1)

x - y = 63 ------(2)

Step 2:

Adding (1) and (2), we get

2x = 510

x = 255

Step 3:

Subtracting (1) from (2), we get

2y = 384

y = 192

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Answer:

5.2

Step-by-step explanation:

Construct an altitude. Using the Pythagorean theorem, the height is [tex]\sqrt{6^2-3^2} \approx 5.2[/tex]

The solution to the expression 2 1/2 + 3 1/5 x 5 5/8 is 223/2

fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

2 1/2 + 3 1/5 x 5 5/8 can be solved by converting all the mixed fraction to improper fraction

2 1/2 = 5/2

3 1/5 = 16/5

5 5/8 = 45/8

which reduces it to

5/2 + 45/8 x 16/5

using BODMAS we taking care of the multiplication section first

45/8 x 16/5 = 18

5/2 + 18

18 can be writen as a fraction which is 36/2

5/2 + 36/2 = 41/2

in conclusion the simplified form of the expression is 41/2

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Using the table we find the constant of proportionality  is 15/8

The ratio that establishes a proportionate link between any two given values is referred to as the constant of proportionality. There are also other names for the constant of proportionality, such as constant ratio, constant rate, unit rate, constant of variation, and even rate of change.

Here,

Since from the table we have to find the constant of proportionality

So, the values of ounces of milk(x) are

30,45

and the values of amount of truffle(y) are

16,24

So for finding the constant of proportionality We take 2 cases,

a)Taking first values of x & y

x/y=30/16

x/y=15/8

b)Taking secondary values of x & y

x/y=45/24

x/y=15/8

Therefore the constant of proportionality  is 15/8

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The point-slope form with a slope of 5/2 and a point of (4,-7) is 5x-2y=34.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10. Linear equations are classified into three types: point-slope, standard, and slope-intercept.

Here,

The slope of line perpendicular to the line y +6=-2/5(x-1)

m1=5/2

point=(4,-7)

y-y1=m(x-x1)

y+7=5/2(x-4)

2y+14=5x-20

5x-2y=34

The point-slope form for slope given as 5/2 and point as (4,-7) will be 5x-2y=34.

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Answer: 40%

Step-by-step explanation:

Answer:

a. 240pieces

b. 4800+ 10x

Step-by-step explanation:

a. 40÷4=10, 120÷5=24, 10×24=240

b. (240×20)+ (x×10)= 4800+ 10x ===> x is the number of cars

Answer:

[tex]\begin{gathered} \sf - 21 \div (2 - 5) + ( - 14) + 6 \times (8 - 4 \times 3) = \\\sf- 21 \div (2 - 5) + ( - 14) + 6 \times (8 - 12) = \\ \sf- 21 \div( - 3) + ( - 14) + 6 \times ( - 4) = \\ 7 + ( - 14) +( - 24) = \\ \sf 7 - 14 - 24 = \\ \sf - 7 - 24 = \\ \sf \green{ - 31}\end{gathered}[/tex]

When we solve combined calculations, we must first separate into terms when there is an addition or a subtraction.

Then, we solve the operations respecting the hierarchical order of the operations:

If the calculation has grouping signs, they must be solved in the following order:

Merry Christmas and Happy New Year

Answer:

negative 36

Step-by-step explanation:

You will useva method known as BODMAS its a principle of combined operations like the one above in mathematics.

B-brackets

O-Of (multipliction) ;commonly used when fractions are involved

D- division

M- multiplication

A- addition

S- subtraction

Working out:

first we will solve the brackets then rewrite the question with the answer obtained

-2-5=-7

8-4×3= minus 4

new question :

-21÷-7+-14+6×minus 4

Next is division since there is no of

-21÷-7=3

Negative divided by negative equals positive

3+minus 14 +6×minus 4

Now do multiplication 6×minus 4= minus24

3+ minus 14+minus 24=minus 36