which graph represents the equation y=3x^2+12x-6

Answer:

Substitute by equation 1 in equation 2:

3x+3x = 180

6x = 180

x = 30

Substitute with the value of x in equation 1 to get y as follows:

3x = 8y-70

3(30) + 70 = 8y

160 = 8y

y = 20

Answer:

30-70-80

Step-by-step explanation:

The dimension of the carpet are 54 inches and 34 inches.

What is mean by Rectangle?

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given,

A rectangular Persians carpet has a perimeter of 176 inches.

Now,

The perimeter of a rectangle is;

P =2W + 2L

In this case;

⇒  176= 2W + 2L

Also, the 2nd sentence says;

⇒ L = W + 20

We can substitute this value of length in the perimeter formula as;

176 = 2W + 2(W+20)

176 = 2W+ 2W + 40

176 = 4W + 40

136 = 4W

34 = W

W = 34

Since, L = W +20

L = 34 + 20

   = 54

Thus, The dimensions are 54 inches and 34 inches.

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The dimensions of the carpet are 54 inches in length and 34 inches in width. This was determined by setting up and solving the perimeter equation for a rectangle, after which we calculated the length by adding 20 to the width.

To determine the dimensions of a rectangular Persian carpet with a perimeter of 176 inches where the length is 20 inches more than the width, first, let's let the width be represented by w inches. The length will then be w + 20 inches. The perimeter of a rectangle is calculated by adding together twice the width and twice the length (P = 2w + 2l).

The formula with the given values will look like this:
176 = 2w + 2(w + 20)

Simplifying this equation gives us the width and subsequently the length:

176 = 2w + 2w + 40

176 = 4w + 40

136 = 4w

w = 34

So, the width of the carpet is 34 inches. To find the length, we add 20 inches to the width:

Length = w + 20 = 34 + 20 = 54 inches

Therefore, the dimensions of the carpet are 54 inches in length and 34 inches in width.

The values of x that satisfy the given equation are -1 and 3

From the question, we are to determine the values of x that satisfy the given equation

The given equation is

25^x = 5^x^2-3

The can be written as

[tex]25^{x} =5^{x^{2} -3}[/tex]

Expressing 25 in index form, we get

[tex]5^{2x} =5^{x^{2}-3 }[/tex]

Now, equate the powers (since the bases are equal)

[tex]2x =x^{2}-3[/tex]

Then, we have that

[tex]x^{2} -2x-3 =0[/tex]

Solve quadratically

Using the factorization method, we get

[tex]x^{2} -2x-3 =0[/tex]

[tex]x^{2} -3x+x-3 =0[/tex]

[tex]x(x-3)+1(x-3)=0[/tex]

[tex](x+1)(x-3) =0[/tex]

∴ x+1 = 0 OR x-3 = 0

x = -1 OR x = 3

Hence, the values of x that satisfy the given equation are -1 and 3.

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Answer:

14

Step-by-step explanation:

Area = 3.14πr^2

We know that the area of the circle is 658. Divide 658 by 3.14 which equals 209.5 ( rounded to the nearest whole number is 210). The square root of 210 is 14.4 and rounding to the nearest whole number is 14.

Final answer:

Square rooting and cube rooting are processes to find a number that, when raised to the second or third power respectively, equals the original number. Square roots are related to squares, and cube roots are related to cubes; both functions are essential in solving various mathematical problems, including equilibrium and Pythagorean Theorem problems.

Explanation:

Finding the square root of a number is the process of determining a number which, when multiplied by itself, gives the original number. For example, the square root of 25 is 5, because 5 squared (5²) is 25. This can be expressed using exponents as x¹⁄₂ = √x.

On the other hand, finding the cube root of a number involves determining a number which, when multiplied by itself twice (or cubed), results in the original number. For instance, the cube root of 27 is 3, since 3 cubed (3³) equals 27. The formula for a simple equilibrium problem that involves cubic roots is a³ = M₁ × P², where you would then find the cube root of the result to solve for 'a'.

Both operations are inverse functions: square rooting is the inverse of squaring, and cube rooting is the inverse of cubing. When dealing with equilibrium problems or Pythagorean Theorem applications, it's important to know how to perform these operations, often requiring a calculator. Make sure you are comfortable with your calculator's functions for these operations, or seek assistance from your instructor if needed.

Answer:

The correct option is B) 3.

Step-by-step explanation:

Consider the provided expression.

(20-14)^2 divided by 12

The above statement can be written as:

[tex]\frac{(20-14)^2}{12}[/tex]

[tex]\frac{(6)^2}{12}[/tex]

[tex]\frac{6\times 6}{12}[/tex]

[tex]\frac{36}{12}[/tex]

3 times 12 is 36,

[tex]3[/tex]

Hence, the simplified form of the provided expression is 3.

Therefore, the correct option is B) 3.

The line x=5 is the vertical line consisting of all points with x-coordinate equal to 5 (see attached graph).

A. Point (0,5) has first coordinate 0 (not 5).

C. Point (0,2) has first coordinate 0 (not 5).

D. Points (0,5) and (0,2) have first coordinates 0 (not 5).

B. Only in this option both points have first coordinates 5.

Answer: correct choice is B

Answer:

sharon=10

Step-by-step explanation:

The present age of Sharon and Brain is 10 years old and 5 years old.

Given,

Sharon is twice as old as brian.

In 5 years the sum of their ages will be 25 years.

We need to find their present ages.

Some of the terms are:

In x years - add x years to the present age

x years ago - Subtract x years with the present age

Before x years - subtract x years to the present age

After x years - add x years to the present age

Find the present age of Sharon and Brain.

Let the present age of:

Sharon - S

Brain - B

Now,

Sharon is twice as old as brian.

We can write this as:

S = 2B ____(1)

In 5 years the sum of their ages will be 25 years.

It can be written as:

(S + 5) + (B + 5) = 25

S + B + 10 = 25

S + B = 25 - 10

S + B = 15 _____(2)

From (1)

We get,

2B + B = 15

3B = 15

B = 5. ______(3)

Putting (3) in (2)

S + 5 = 15

S = 15 - 5

S = 10

We have,

B = 5 and S = 10

Thus the present age of Sharon and Brain is 10 years old and 5 years old.

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The volume of the box is determined by finding the value of x from the perimeter equation, substituting it back into the expressions for length and width, and finally multiplying the dimensions with the height. Calculating these steps, the volume of the box is 1200 cm³.

To find the volume of a box, we multiply its length, width, and height. The student has provided the length as 3x + 2, the width as 2x - 2, and the height as x. We also know the perimeter of the base is 60 centimeters.

First, we calculate the perimeter of the base, which is 2(length + width). Hence, we set up the equation: 2(3x + 2 + 2x - 2) = 60. Simplifying this, we get 2(5x) = 60, therefore x = 6 cm.

Second, we substitute x into the expressions for length and width to get the actual dimensions of the box base: length 3(6) + 2 = 20 cm, and width 2(6) - 2 = 10 cm.

Finally, we calculate the volume of the box as length × width × height = 20 cm × 10 cm × 6 cm = 1200 cm³.

The function g(x) in terms of f(x) that represents a reflection in the y-axis is g(x) = -f(x).

The function g(x) in terms of f(x) that represents a reflection in the y-axis is g(x) = -f(x).

To reflect a point across the y-axis, we change the sign of the x-coordinate. So, to reflect the graph of f(x) across the y-axis, we need to change the sign of f(x). This can be achieved by multiplying f(x) by -1, giving us g(x) = -f(x).

For example, if f(x) = 2x+3, then g(x) = -(2x+3) = -2x-3.

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The function g(x) that represents a reflection in the y-axis is g(x) = -f(x).

The function g(x) in terms of f(x) that represents a reflection in the y-axis is g(x) = -f(x).

To reflect a graph in the y-axis, we replace each x-coordinate with its opposite (negative value) while keeping the y-coordinate unchanged. In this case, since g is the reflection of f in the y-axis, the function g(x) will have the same y-values as f(x), but the x-values will be their negatives.

For example, if f(x) = 2x + 3, then g(x) = -f(x) would be g(x) = -2x - 3, where the graph of g(x) is the reflection of f(x) across the y-axis.

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Answer:

The correct option is B.

Step-by-step explanation:

The slope intercept form of a line is

[tex]y=mx+b[/tex]

where, m is slope and b is y-intercept.

The given equation is

[tex]y=\frac{5}{2}x-10[/tex]

It means the slope of the line is 5/2 and y-intercept is -10.

The slope of two parallel lines is same. So, the slope of required line is 5/2.

The equation of required line is

[tex]y=\frac{5}{2}x+b[/tex]

It is given that the line passes through the point (-6,-29).

[tex](-29)=\frac{5}{2}(-6)+b[/tex]

[tex]-29=-15+b[/tex]

[tex]-29+15=+b[/tex]

[tex]-14=b[/tex]

The y-intercept of required line is -14. So the equation of required line is

[tex]y=\frac{5}{2}x-14[/tex]

Therefore the correct option is B.

Answer:

the answer is  B. y equals five halves x minus 14

Step-by-step explanation:

hope it helps

Answer:

127

Step-by-step explanation:

It gas geometric sequence,

We has a sequence: 1, 2, 4, 8, 16, 32, 64.

It can be solved by two method either sum these digits individually or use formula of sum of geometric sequence

We have formula: [tex]S_n=\frac{a_1(1-r^n)}{(1-r)}[/tex]

Here r = Common Ratio = 2 ÷ 1 = 4÷2 = 2

and a = First term = 1

⇒ [tex]S_n= \frac{1\times(1-2^7)}{(1-2)} \\\Rightarrow S_n=\frac{(1-128)}{-1}\\ \Rightarrow S_n=127[/tex]