Which of the following is the graph of y = 4x + 2?

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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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.

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:

The correct answer is A. Yes, because there are two pairs of congruent corresponding angles.

Step-by-step explanation:

This is because to prove that two triangles are congruent, you need at least two pairs of corresponding angles.

Also, the degrees 30, 65, and 85 is equal to 180 degrees.

Hope this helps!

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

Answer:

[tex]\angle CBD=105^{\circ}[/tex]

Step-by-step explanation:

We have been given a diagram. We are asked to find the measure of angle CBD using given diagram.

We can see that in triangle ABD two angles measure 60 degree. Using angle sum property of triangle, we can find measure of triangle angle ADB as:

[tex]\angle A+\angle B+\angle D=180^{\circ}[/tex]

[tex]60^{\circ}+60^{\circ}+\angle D=180^{\circ}[/tex]

[tex]120^{\circ}+\angle D=180^{\circ}[/tex]

[tex]120^{\circ}-120^{\circ}+\angle D=180^{\circ}-120^{\circ}[/tex]

[tex]\angle D=60^{\circ}[/tex]

Since all angles of triangle ABD are equal, so it is an equilateral triangle and its all sides will have same measure.

[tex]AB=BD=AD[/tex]

We have been given segment AB is equal to segment BC. Now, we will get:

[tex]AB=BD=AD=BC[/tex]

In triangle BCD sides two sides (BD and BC) are equal, so it is an isosceles triangle.

We know that angles corresponding to equal sides of an isosceles triangle have equal measure, so measure of angle BDC will be equal to angle BCD.

[tex]\angle BDC=\angle BCD=37\frac{1}{2}^{\circ}[/tex]

Now, we will use angle property of triangle to find measure of angle CBD as:

[tex]\angle CBD+\angle BCD+\angle BDC=180^{\circ}[/tex]

[tex]\angle CBD+37\frac{1}{2}^{\circ}+37\frac{1}{2}^{\circ}=180^{\circ}[/tex]

[tex]\angle CBD+\frac{75}{2}^{\circ}+\frac{75}{2}^{\circ}=180^{\circ}[/tex]

[tex]\angle CBD+\frac{150}{2}^{\circ}=180^{\circ}[/tex]

[tex]\angle CBD+\frac{150}{2}^{\circ}-\frac{150}{2}^{\circ}=180^{\circ}-\frac{150}{2}^{\circ}[/tex]

[tex]\angle CBD=\frac{360}{2}^{\circ}-\frac{150}{2}^{\circ}[/tex]

[tex]\angle CBD=\frac{210}{2}^{\circ}[/tex]

[tex]\angle CBD=105^{\circ}[/tex]

Therefore, the measure of angle CBD is 105 degrees.

Steve can completely fill 3 carousels with his 276 slides as each carousel holds up to 75 slides.

Based on the provided data, Steve has 276 slides and each carousel holds up to 75 slides. To find out how many carousels can be completely filled, we have to divide the total number of slides by the number that each carousel holds.

So, the calculation would be: 276 (total slides) divided by 75 (slides each carousel can hold).

276 ÷ 75 equals about 3.68. Since we cannot have a fraction of a carousel, we round the number down to the nearest whole number. Hence, Steve can completely fill 3 carousels with his slides.

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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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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).

Answer:

it should be CAB and GEF

Step-by-step explanation

Answer:

it will be D

Step-by-step explanation:

Answer:

It’s true

Step-by-step explanation: just took the test

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.