Which graph shows a triangle and its reflection image across the x-axis?

One of the factors of 54xy + 45x + 18y + 15 is b) 6y + 5.

The GCF of two or more than two numbers is the highest number that divides the given two numbers completely.

We also know that distributive property states a(b + c) = ab + ac.

Given,

54xy + 45x + 18y + 15.

= 54xy + 18y + 45x + 15.

= 18y(3x + 1) + 15(3x + 1).

= (3x + 1)(18y + 15).

= (3x + 1)(3)(6y + 5).

So, a factor of 54xy + 45x + 18y + 15 is (6y + 5).

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Answer:

it should be CAB and GEF

Step-by-step explanation

Answer:

2

Step-by-step explanation:

Oscar needs to pack only one type of cd in each box and he must pack the same number of cd's in each box.

To solve this problem we would need to find the greatest common factor of the numbers given; the numbers that we have are 14, 12, 8.

First we are going to find the factors of all these three numbers:

14 = 1 x 2 x 7

12 = 1 x 2 x 2 x 3

8 = 1 x 2 x 2 x 2

The common factors of these three numbers are bolded:

14 = 1 x 2 x 7

12 = 1 x 2 x 2 x 3

8 = 1 x 2 x 2 x 2

We can see that the common factors are 1 and 2. The biggest of them is 2.

Therefore, the greatest number of cd's Oscar can pack in each box is 2

Since 2 is common to them all, hence the greatest number of cds oscar can pack in each box is 2 CDs

Given the number of cars needed to ship 14 rock CDs, 12 classical CDs, and 8 pop CDs

In order to get the greatest number of cds oscar can pack in each box, we will have to calculate the GCF of each value as shown:

The prime factors of each value is as shown

14 = 2 * 7

12 = 3 * 2 * 2

8 = 2 * 2 * 2

From the factors, we can see that only 2 is common to them all, hence the greatest number of CDs oscar can pack in each box is 2 CDs

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Answer:

true

Step-by-step explanation:

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7x10^-5 as a decimal is 0.00007, achieved by multiplying 7 by 0.00001, which represents 10^-5.

To convert 7x10^-5 into decimal form, you can use the concept that a negative exponent indicates the inverse. This means that 10^-5 is the same as 1/10^5 or 1 divided by 100,000. Thus, to find 7x10^-5 in decimal form, you multiply 7 by 0.00001.

Here's the calculation:

7 x 0.00001 = 0.00007

Therefore, 7x10^-5 in decimal form is 0.00007.

Answer:

It’s true

Step-by-step explanation: just took the test

Answer:  [tex]\dfrac{8}{9}[/tex]

Step-by-step explanation:

Given : Marty has saved $72. He spent $8 on a video rental.

i.e. The amount of money he saved = $72

The amount of money he spent on video rental = $8

Now, the amount of money he had left = [tex]\$72-\$8=\$64[/tex]

Thus , the ratio that represent what portion of his savings he has left :-

[tex]\dfrac{64}{72}=\dfrac{8}{9}[/tex]

Hence, the ratio that represent what portion of his savings he has left :-

[tex]=\dfrac{8}{9}[/tex]

Answer:

Option D - $6312.38

Step-by-step explanation:

Given : If you were to place $5,000 in a savings account that pays 6% interest compounded continuously.

To find : How much money will you have after 4 years?

Solution :

Using compound interest formula,

[tex]A=P(1+r)^t[/tex]

Where A is the amount,

P is the principle P=$5000  

r is the rate r=6%=0.06

t is the time t= 4 years

Substitute the value,

[tex]A=P(1+r)^t[/tex]

[tex]A=(5000)(1+0.06)^4[/tex]

[tex]A=(5000)(1.06)^4[/tex]

[tex]A=5000\times 1.262[/tex]

[tex]A=6312.38[/tex]

The money he have after 4 years is $6312.38

Therefore, Option D is correct.

Answer:

A. $6,356.25

Step-by-step explanation:

To calculate the amount of money you will have after 4 years in a savings account with continuous compounding, we can use the formula:

A = P * e^(rt)

Where:

A = the amount of money accumulated after t years

P = the initial principal amount (in this case, $5,000)

e = the base of the natural logarithm (approximately 2.71828)

r = the annual interest rate (in decimal form, so 6% becomes 0.06)

t = the number of years (in this case, 4)

Plugging in the values, we get:

A = 5000 * e^(0.06 * 4)

Using a calculator, we can evaluate this expression:

A ≈ 5000 * 2.71828^(0.24)

A ≈ 5000 * 1.276281

A ≈ 6381.405

Rounding to the nearest cent, the amount of money you will have after 4 years is approximately $6,381.41.

Therefore, the closest answer option is A. $6,356.25.

Answer:

A term at position n can be expressed as \[2*3^{n-1}\]

Step-by-step explanation:

The given geometric sequence is 2, 6, 18, 54, …

Starting term = 2

Second term = 6

So second term is 3 times the first term.

Similarly, Third term = 18

This is 3 times the second term, that is , 3 * 6

Fourth term is is 54.

This is 3 times the third term, that is , 3 * 18

Generalizing, a term in the sequence can be expressed as \[2*3^{n-1}\]

where n represents the position of the term in the sequence.

Answer:

b = 2A/have a nice day :)

The required simplified solution for b for the given expression is b=2A/h.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression,
A = bh/2

Isolate the variable B, and multiply both sides by 2/h,
2A/h = b

So
b = 2A/h

Thus, the required simplified solution for b for the given expression is b=2A/h.

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The coordinates of the midpoint of the diagonals of a rectangle are found by averaging the x-coordinates and the y-coordinates of the endpoints of the diagonals. Because of the properties of a rectangle, the midpoint will be the same for both diagonals, confirming that the diagonals bisect each other. The midpoint's coordinates are ((x1+x2)/2, (y1+y2)/2).

To find the coordinates of the midpoint of the diagonals of a rectangle, you must first know the coordinates of the rectangle's vertices. Suppose the rectangle has vertices at (x1, y1), (x1, y2), (x2, y1), and (x2, y2). Without loss of generality, let (x1, y1) and (x2, y2) be the endpoints of one diagonal and (x1, y2) and (x2, y1) be the endpoints of the other diagonal.

The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) can be found by averaging each of the x-coordinates and the y-coordinates of the endpoints. Thus, the midpoint M1 has coordinates ((x1+x2)/2, (y1+y2)/2). Similarly, the midpoint M2 for the other diagonal has coordinates ((x1+x2)/2, (y2+y1)/2). Because of the properties of a rectangle, these midpoints will be the same, confirming that the diagonals bisect each other.

Therefore, the coordinates of the midpoint of the diagonals of a rectangle are ((x1+x2)/2, (y1+y2)/2).

Final answer:

To find the hypotenuse of a right triangle, apply the Pythagorean theorem: a² + b² = c². After squaring the lengths of the two other sides and adding them together, take the square root of the sum to get the length of the hypotenuse, which is approximately 10.3 units in the example provided.

Explanation:

To find the hypotenuse of a right triangle, you can use the Pythagorean theorem, which states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). This can be written as the equation a² + b² = c². To solve for the hypotenuse, you would rearrange the equation to c = √(a² + b²).

For example, if the legs of a right triangle measure 9 and 5 units:

Thus, the hypotenuse would measure approximately 10.3 units, where we use three significant figures for precision in measurement.

The maximum volume of the box is:

              1000 cm³

Let x be the length of the square base

and h be the height(h) of the box.

As we know that the length(l) and width(w) of the box is same( since the base is in the shape of square)

As we know that the surface area of box is given by:

[tex]Surface\ Area=2(lw+wh+hl)\\\\\\i.e.\\\\\\Surface\ Area=2(x^2+xh+xh)\\\\\\Surface\ Area=2(x^2+2hx)[/tex]

We are given surface area of box=600 cm²

Hence,

[tex]2(x^2+2hx)=600\\\\i.e.\\\\x^2+2xh=300\\\\i.e.\\\\h=\dfrac{150}{x}-\dfrac{x}{2}[/tex]

The volume of box is given by:

[tex]Volume(V)=l\times w\times h\\\\\\Volume=x^2h\\\\\\Volume=x^2(\dfrac{150}{x}-\dfrac{x}{2})[/tex]

Hence,

[tex]V=150x-\dfrac{x^3}{2}[/tex]

Now, for maxima or minima we have derivative equal to zero.

[tex]i.e.\\\\\\\dfrac{dV}{dx}=0\\\\\\i.e.\\\\\dfrac{d}{dx}(150x-\dfrac{x^3}{2})=0\\\\\\i.e.\\\\\\150-\dfrac{3x^2}{2}=0\\\\\\i.e.\\\\\\150=\dfrac{3}{2}x^2\\\\\\x^2=100\\\\\\i.e.\\\\\\x=\pm 10[/tex]

Now,

[tex]\dfrac{d^2V}{dx^2}=\dfrac{-6x}{2}\\\\\\=-3x[/tex]

Now, as we know if for a given x

[tex]\dfrac{d^2V}{dx^2}<0[/tex]

then that x is a point of maxima.

Hence, when we put x=10 we get:  [tex]\dfrac{d^2V}{dx^2}<0[/tex]

Hence, x=10 is a point of maxima

Also, the value of V at x=10 is:

[tex]V=150\times 10-\dfrac{(10)^3}{2}\\\\\\V=1500-\dfrac{1000}{2}\\\\\\V=1500-500\\\\V=1000\ cubic\ cm.[/tex]

       Hence, the maximum volume of the box is:

                     1000 cm³

To find the bigger number in the given ratio of 3:6 with a sum of 63, simplify the ratio to 1:2, assign a variable to the smaller number, and solve for the larger one. The bigger number is found to be 42.

To find the bigger number when two numbers are in a ratio of 3:6 and their sum is 63, first simplify the ratio to its lowest terms. The ratio 3:6 simplifies to 1:2, since both terms can be divided by 3. Let's assign the variable x to the smaller number, which corresponds to the '1' part of the ratio. Therefore, the bigger number is twice the smaller one, so it can be represented as 2x.

The sum of the two numbers is given by the equation x + 2x = 63. Combine like terms to get 3x = 63. Dividing both sides by 3 gives x = 21. Since 2x represents the bigger number, we have 2x = 2  imes 21 = 42.

Hence, the bigger number in this ratio is 42.

Answer:

it will be D

Step-by-step explanation: