The length of an aquarium, which has the form of a rectangular solid, is equal to 5 decimeters, and the width is 4/5 the length. When you put 40 liters of water into the aquarium, it was full to 2/3 its volume. What part of the length makes up the height of the aquarium? (1 liter is equal by volume to 1 decimeter^3)

f(x) + n - move the graph n units up

f(x) - n - move the graph n units down

n · f(x) - stretch by n in the y-direction

1/n · f(x) - compress by n in the y-direction

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First:

[tex]A)\ y=x^2\\\\B)\ y=x^2-4\\\\C)\ y=x^2-2\\\\D)\ y=x^2+2\\\\E)\ y=x^2+4[/tex]

Second:

[tex]A)\ y=x^2\\\\K)\ y=4x^2\\\\L)\ y=2x^2\\\\M)\ y=\dfrac{1}{2}x^2\\\\N)\ y=\dfrac{1}{4}x^2[/tex]

Answer:

a^2+4a-2

Step-by-step explanation:

f(x)= x^2+2x-5

f(a+1) = (a+1)^2 + 2(a+1) -5

        = a^2 + 2a + 1 + 2a +2 -5

       =a^2+4a -2

Answer:

11 + 7i

Step-by-step explanation:

(1 + 2i)(5 - 3i)

= 1(5 - 3i) + 2i(5 - 3i)

= 5 - 3i + 10i - 6i^2  

Note i^2 = -1 So we have:-

5 + 7i + 6  

= 11 + 7i  (answer).

The expression (1+2i) times (5-3i) simplifies to -1 + 7i by using the distributive property for multiplication over addition and remembering that i squared equals -1.

The expression (1+2i) times (5-3i) is a function of two complex numbers. To simplify this, you would use the distributive property for multiplication over addition.

The first step is to distribute each component of the first number against each component of the second number. (1 * 5 + 2i * -3i) + (1 * -3i + 2i * 5)

Next, we perform the multiplications and simplify, bearing in mind that i squared is -1. This gives us (5 - 6) + (-3i + 10i)

So the simplified expression is -1 + 7i.

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Answer:

Mean of resulting data = 7 times mean of original data=7a

Step-by-step explanation:

Given that all values in a data set are multiplied by 7. to find the mean of the new set.

Let {x1,x2....xn} be the original data set.

The mean of this data set a= [tex]\frac{x1+x2+...+xn}{n}[/tex]

Now multiply all values by 7

New data set

= {7x1, 7x2...7xn}

Sum of these = 7(x1+x2+..+xn) = 7 times sum of original data set

No of element = n for both the sets

Hence new mean = 7 * mean of original set.=7a

in other words, if the mean of the values in a data set is a. If each of the values in the data set were multiplied by 7, new mean would be 7a.

Answer:

It’s 7a

Step-by-step explanation:

ANSWER:

To prove that opposite sides of a parallelogram are congruent, we have to prove that the quadrilateral is a parallelogram.

The ways to prove that a quadrilateral is a parallelogram include:

- a quadrilateral with parallel opposite sides

- a quadrilateral with congruent opposite angles

- a quadrilateral with diagonals that bisect each other

Answer:

alternate interior angles of congruent

opposite sides are parallel

Step-by-step explanation:

ap3x

Answer:

Function: y= $4.25x + $50; After 6 hours: $25.50

Step-by-step explanation:

Answer:

Joe would make $75.50 after 6 hours.

Step-by-step explanation:

A function for this would be m = 50 + 4.25t. The $50 is the one time thing. We must multiply the tips by 6. 4.25 * 6 = 25.50. 50 + 25.50 is 75.50.

Answer:

56/79=.7088

The answer is 70.9%

Answer:

70.9%

Step-by-step explanation:

Hope this helps

Probably the third answer is right. If you divide the 9x-6y=12 by 3, it gives you the exact same equation as the 3x-2y=4. They're the same, so they'd overlap.

[tex]\dfrac{sin\theta + cos\theta}{sin\theta-cos\theta}+\dfrac{sin\theta-cos\theta}{sin\theta+cos\theta}=\dfrac{2sec^2\theta}{tan^2\theta-1}[/tex]

From Left side:

[tex]\dfrac{sin\theta + cos\theta}{sin\theta-cos\theta}\bigg(\dfrac{sin\theta+cos\theta}{sin\theta+cos\theta}\bigg)+\dfrac{sin\theta-cos\theta}{sin\theta+cos\theta}\bigg(\dfrac{sin\theta-cos\theta}{sin\theta-cos\theta}\bigg)[/tex]

[tex]\dfrac{sin^2\theta+2cos\thetasin\theta+cos^2\theta}{sin^2\theta-cos^2\theta}+\dfrac{sin^2\theta-2cos\thetasin\theta+cos^2\theta}{sin^2\theta-cos^2\theta}[/tex]

NOTE: sin²θ + cos²θ = 1

[tex]\dfrac{1 + 2cos\theta sin\theta}{sin^2\theta-cos^2\theta}+\dfrac{1-2cos\theta sin\theta}{sin^2\theta-cos^2\theta}[/tex]

[tex]\dfrac{1 + 2cos\theta sin\theta+1-2cos\theta sin\theta}{sin^2\theta-cos^2\theta}[/tex]

[tex]\dfrac{2}{sin^2\theta-cos^2\theta}[/tex]

[tex]\dfrac{2}{\bigg(sin^2\theta-cos^2\theta\bigg)\bigg(\dfrac{cos^2\theta}{cos^2\theta}\bigg)}[/tex]

[tex]\dfrac{2sec^2\theta}{\dfrac{sin^2\theta}{cos^2\theta}-\dfrac{cos^2\theta}{cos^2\theta}}[/tex]

[tex]\dfrac{2sec^2\theta}{tan^2\theta-1}[/tex]

Left side = Right side so proof is complete

Answer:

\dfrac{sin\theta + cos\theta}{sin\theta-cos\theta}+\dfrac{sin\theta-cos\theta}{sin\theta+cos\theta}=\dfrac{2sec^2\theta}{tan^2\theta-1}

From Left side:

\dfrac{sin\theta + cos\theta}{sin\theta-cos\theta}\bigg(\dfrac{sin\theta+cos\theta}{sin\theta+cos\theta}\bigg)+\dfrac{sin\theta-cos\theta}{sin\theta+cos\theta}\bigg(\dfrac{sin\theta-cos\theta}{sin\theta-cos\theta}\bigg)

\dfrac{sin^2\theta+2cos\thetasin\theta+cos^2\theta}{sin^2\theta-cos^2\theta}+\dfrac{sin^2\theta-2cos\thetasin\theta+cos^2\theta}{sin^2\theta-cos^2\theta}

NOTE: sin²θ + cos²θ = 1

\dfrac{1 + 2cos\theta sin\theta}{sin^2\theta-cos^2\theta}+\dfrac{1-2cos\theta sin\theta}{sin^2\theta-cos^2\theta}

\dfrac{1 + 2cos\theta sin\theta+1-2cos\theta sin\theta}{sin^2\theta-cos^2\theta}

\dfrac{2}{sin^2\theta-cos^2\theta}

\dfrac{2}{\bigg(sin^2\theta-cos^2\theta\bigg)\bigg(\dfrac{cos^2\theta}{cos^2\theta}\bigg)}

\dfrac{2sec^2\theta}{\dfrac{sin^2\theta}{cos^2\theta}-\dfrac{cos^2\theta}{cos^2\theta}}

\dfrac{2sec^2\theta}{tan^2\theta-1}

Left side = Right side so proof is complete

Step-by-step explanation:

Answer: SAS, Triangle JKN and LKM are congruent by SAS

Step-by-step explanation: Vertical angles are equal, so the triangles are congruent by SAS.

The given triangles congruent by SAS congruency . Option D is correct.

The angles opposite each other when two lines cross are called vertically opposite angles.

Considering Δ JKN and Δ LKM

                         JK     =        LK     (given)

                          ∠JKN  =     ∠LKM (vertically opposite angles)

                         KN        =     KM   (given)

So Δ JKN and Δ LKM are congruent by SAS congruency .

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Answer:

4+y

Step-by-step explanation:

4 · y

4 + y

4y

(4)(y)

All of these are multiplication except 4+y

Final answer:

The solution to the system of equations is (-6, 8), found by substituting x = -6 into the first equation and simplifying to find the value of y.

Explanation:

The solution to the system of equations y= -1/3x+6 and x = -6 can be found by substituting the value of x from the second equation into the first equation. Here's how it's done:

Substitute x into the first equation: y = -1/3(-6) + 6.

Simplify the equation: y = 2 + 6.

Add the numbers to find the value of y: y = 8.

Therefore, the solution to the system of equations is the point (-6, 8).

Calculate total area:

12 x 10 = 120 square feet

Convert square feet to square meters:

1 square foot = 0.0929 square meters

120 x 0.0929 = 11.1484 square meters

Total cost = 11.1484 x 25 = $278.71

Answer: 43.59

Step-by-step explanation:

The hundredth place is two points after the decimal, so it is where the 8 is.

When the number to the right of it is 5 or higher you round it up.

Answer:

43.59

Step-by-step explanation:

  tens  ones . tenths  hundredths  thousandths

 4            3       5           8                        6

We want to round the 8   so we look at the 6.  

Since 6>=5  we round the 8 up

43.59

Answer:

the blue and the pink

Step-by-step explanation:

Answer:

In a 28 day month 20 dollars and 30 cents

Step-by-step explanation:

1+2+3+4+5+6+7......

Answer*5=Cents

If cents equal to or greater than 100 than = dollar

$30 money you would have if for a month you were given a nickel on day one, two nickels on day two, three nickels on day three, and so on.

The arithmetic series is a series in which the numbers are in the order of some common difference. The difference between any two consecutive numbers is constant.

[tex]a_n = a_1 + (n -1)d[/tex]

you would be using a be using the [tex]a_n = a_1 + (n -1)d[/tex] meaning that it's the previous entry plus the different process.

[tex]a_n = a_1 + (n -1)d[/tex]

[tex]a_{30} = .05 + (30-1).05[/tex]

[tex]a_{30}[/tex] = $29.10

Thus, $30 money you would have if for a month you were given a nickel on day one, two nickels on day two, three nickels on day three, and so on.

Learn more about arithmetic series:

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Answer:

$45.61

Step-by-step explanation:

1) On the first day of the month, John counted his money and found he had $28.35

2) He has received an additional $17.26

so

to find the total money he has now sum the two quantities

$28.35 + $17.26 = $45.61

therefore

the answer is

$45.61

Final answer:

The square root of -9 is not -3 but 3i, indicating the need for complex numbers to describe the square root of negative numbers, with 'i' denoting the imaginary unit.

Explanation:

The value of the square root of -9 is not -3 because the square root operation defined for real numbers does not apply to negative numbers in the same way. Instead, when dealing with the square root of a negative number, we enter the realm of complex numbers.

A complex number is a combination of a real part and an imaginary part. The square root of -1 is defined as i, the imaginary unit. Therefore, the square root of -9 is correctly expressed as 3i, not -3. This is a critical distinction because the result provides a basis for complex arithmetic, expanding the scope of mathematical operations into the complex plane.

Complex numbers and imaginary numbers are fundamental in various fields of science and engineering, particularly in situations involving quadratic equations with no real roots or in the analysis of electrical circuits. Recognizing the utility of the imaginary unit, i, allows for solving equations that otherwise would not have solutions within the set of real numbers.

Answer:

<A = 30

<B = 150

Step-by-step explanation:

Answer:

The correct option is C.

Step-by-step explanation:

The vertices of ABCD are A(2,-3), B(8,-6), C(14,-3), and D(8,0).

Distance formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The length of sides are

[tex]AB=\sqrt{(8-2)^2+(-6+3)^2}=\sqrt{36+9}=\sqrt{45}[/tex]

[tex]BC=\sqrt{(14-8)^2+(-3+6)^2}=\sqrt{36+9}=\sqrt{45}[/tex]

[tex]CD=\sqrt{(8-14)^2+(0-3)^2}=\sqrt{36+9}=\sqrt{45}[/tex]

[tex]AD=\sqrt{(8-2)^2+(0+3)^2}=\sqrt{36+9}=\sqrt{45}[/tex]

Since length of all sides are equation therefore the given parallelogram cannot be a rectangle.

Slope formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Slope of AB is

[tex]m_1=\frac{-6-(-3)}{8-2}=\frac{-3}{6}=\frac{-1}{2}[/tex]

Slope of BC is

[tex]m_2=\frac{-3-(-6)}{14-8}=\frac{3}{6}=\frac{1}{2}[/tex]

Since the slopes of two consecutive sides are not opposite reciprocals, therefore the given parallelogram is a rhombus. Option C is correct.

Answer:

7.25

Step-by-step explanation:

We know that 7 equals to 7.0. We also know that 1/4=0.25. So we can add the two together and we get 7.25

A basketball priced at $35.00 with a 40% discount would cost $21.00 after the discount.

The final price of the basketball can be calculated by first identifying the amount being discounted from the original price. A 40% discount of a $35.00 basketball means you take 40% of 35. Here's how:

0.40 (40% converted to decimal) times $35.00 equals $14.00.

This $14.00 is the discount from the original price. Now, subtract this discount from the original price of the basketball to get the final price: $35.00 - $14.00 equals $21.00.

So, the final cost of the basketball after a 40% discount is $21.00.

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Answer: There are 20 white lights.

Step-by-step explanation:

Given : There is a string of green and white lights strung around a mirror for every 6 green lights there are 4 white lights.

i.e. Ratio of green lights to white lights = 6:4

i.e.

[tex]\dfrac{\text{Number of green lights}}{\text{Number of white lights}}=\dfrac{6}{4}\\\\\Rightarrow\ \dfrac{30}{\text{Number of white lights}}=\dfrac{6}{4}\\\\\Rightarrow\ \text{Number of white lights}=\dfrac{4\times30}{6}=20[/tex]

Hence, there are 20 white lights.

Answer: It would be $4.38

Step-by-step explanation: If you divide the $5 by .8 it will give you what 1/8 of it would be then you multiply it by 7 to get the 7/8 of it.

Answer:

y=[tex]6x+ \frac{1}{2}[/tex]

Step-by-step explanation:

m=6

yint=1/2

y=mx+b

when x=0 y=1/2

1/2=6(0)+b

b=1/2

y=[tex]6x+ \frac{1}{2}[/tex]

The equation of the line in slope-intercept form is y = 6x + 1/2, where the slope is 6 and the y-intercept is 1/2. The slope of 6 means that for every increase of 1 in the x-axis, the y-axis will increase by 6.

The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope and b is the y-intercept.

Given that the slope is 6 and the y-intercept is 1/2, the equation of the line is y = 6x + 1/2.

The slope of 6 means that for every increase of 1 in the x-axis, the y-axis will increase by 6.

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Step-by-step explanation:

Percentage by which the gas tank of the car is full = 40%

Amount of gas in the gas tank = 8 gallons

capacity of the gas tank = x gallons

40% * x = 8

(40/100) * x = 8

4x/10 = 8

4x = 8 * 10

4x = 80

x = 80/4

Answer   = 20 gallons

Answer:

y = abs (x-5) -4

Step-by-step explanation:

We are shifting the absolute value function

f(x) = |x| to

g(x) =  | x +h| + k

where  h is a shift left if h >  0

                               right if h < 0

 and  k is a shift up if k> 0

                           down if k< 0

Since the graph is shifted down and to the right

k is <0 and h < 0

where k = -4 and h=-5

Answer:

y = 0.5

Step-by-step explanation:

plug in x = 4 into the second equation

4 - 4y = 2

Simplify

-4y = -2

y = 0.5

The distance between -57 and 13 on a number line is 70 units.

The distance between -57 and 13 on a number line is 70 units.

To find this distance, we subtract -57 from 13:

13 - (-57) = 13 + 57 = 70.

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The distance between -57 and 13 on a number line is 70 units.

A number line is a visual representation of real numbers arranged in order along a straight line. It extends infinitely in both directions, with zero at the center. Positive numbers are to the right, and negative numbers are to the left. Integers, fractions, and decimals are located at corresponding points.

The number line aids in understanding numerical relationships, performing arithmetic operations, and visualizing the concept of magnitude and direction in mathematics. It's a fundamental tool for teaching and learning mathematical concepts. The distance between -57 and 13 on a number line is 70 units.

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Answer:

1) 2/25 = 0.08

2) 23/50 = 0.46 = 46%

3) 14/20 = 0.7 = 70%

4) 90% = 0.9

Answer:

1) 2/25 = 0.08%

2) 23/50 = 46%

3) 14/20 = 70%

4) 90% = 0.9