Which function will produce the same graph as the function shown below?

y=(x+1)(x-3)

a. y+3=x(x-1)
b. y-3=(x-1)^2
c. y=x^2+2x+3
d. y=x^2-2x-3 Which function will produce the same graph as the function shown below?

y=(x+1)(x-3)

a. y+3=x(x-1)
b. y-3=(x-1)^2
c. y=x^2+2x+3
d. y=x^2-2x-3

Final answer:

The equation 4x - 6y = 14 can be written in general form as 4x - 6y - 14 = 0, which is option (a). This is the standard general form for a linear equation.

Explanation:

The equation given, 4x - 6y = 14, needs to be written in the general form. The general form of a linear equation is Ax + By + C = 0, where A, B, and C are constants. To rewrite the given equation in general form, we simply need to move all terms to one side of the equation. So the general form of the given equation is:

4x - 6y - 14 = 0.

This matches option (a) from the choices provided. It is important to note that a linear equation represents a straight line when graphed on the coordinate plane. The general form is helpful for various applications, including determining the x and y-intercepts.

The percent of change from the original amount of $90 to the new amount of $84.50 is approximately a 6.11% decrease.

To calculate the percent of change, we need to determine the difference between the original and new amounts, then divide that difference by the original amount and multiply by 100 to get the percentage. In this case, the original amount is $90, and the new amount is $84.50. The difference between these two amounts is $90 - $84.50 = $5.50. We then take this change and divide it by the original amount: $5.50 / $90. Finally, to get the percent change, we multiply by 100:

($5.50 / $90)  times 100 = 6.11%

The percent of change from the original amount of $90 to the new amount of $84.50 is approximately 6.11% decrease.

The value of log₆ 5 as a logarithm of base 4 is,

⇒ log₄ 5 / log₄ 6

We have to given that;

Logarithmic function is,

⇒ log₆ 5

Now, WE can write in as a logarithm of base 4 as;

Since, WE know that;

⇒ logₐ b = logₓ b / logₓ a

Hence, By above rule we get;

⇒ log₆ 5

⇒ log₄ 5 / log₄ 6

Thus, The value of log₆ 5 as a logarithm of base 4 is,

⇒ log₄ 5 / log₄ 6

Learn more about logarithmic equations here:

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Answer:

idiot

Step-by-step explanation:

its b a c i think

To find the third term, substitute n = 3 into the formula A(n) = 4 + (n-1)(-5).

The sequence A(n) is defined as 4 plus the product of (n-1) and -5. To find the third term, substitute n = 3 into the formula: A(3) = 4 + (3-1)(-5) = 4 + 2(-5) = 4 - 10 = -6.

To find the fifth term, substitute n = 5 into the formula: A(5) = 4 + (5-1)(-5) = 4 + 4(-5) = 4 - 20 = -16.

To find the tenth term, substitute n = 10 into the formula: A(10) = 4 + (10-1)(-5) = 4 + 9(-5) = 4 - 45 = -41.

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Answer:

D. y = 6x

Step-by-step explanation:

In order to conclude which pair is a real solution to one of these equations, we need to evaluate the point in each equation.

Let:

[tex](x,y)=(2,12)[/tex]

So, this pair will be a solution if when evaluating the value of x=2 in the function the result is y=12.

For A.

[tex]y(x)=\frac{1}{5}x \\\\y(2)=\frac{2}{5} =0.4\neq12[/tex]

This pair is not a solution to this equation.

For B.

[tex]y(x)=\frac{1}{2}x\\\\y(2)=\frac{2}{2} =1 \neq 12[/tex]

This pair is not a solution to this equation.

For C.

[tex]y(x)=2x\\\\y(2)=2*2=4 \neq 12[/tex]

This pair is not a solution to this equation.

For D.

[tex]y(x)=6x\\\\y(2)=6*2=12[/tex]

This pair is a solution to this equation.

Answer:

D) 9 years

Step-by-step explanation:

The slope-intercept form equation for the word problem is [tex]\( y = \frac{3}{4}x + 1 \).[/tex]

Let's consider a word problem where a local gym charges a $1 sign-up fee and $3 for every hour of use. If we let [tex]\( x \)[/tex] represent the number of hours a member uses the gym and [tex]\( y \)[/tex] represent the total cost, we can write an equation in slope-intercept form.

The slope-intercept form of a linear equation is given by [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope of the line and [tex]\( b \)[/tex] is the y-intercept.

In this scenario, the slope [tex]\( m \)[/tex] is the cost per hour, which is $3. The y-intercept [tex]\( b \)[/tex] is the initial sign-up fee, which is $1.

Therefore, the equation representing the total cost [tex]\( y \)[/tex] as a function of the number of hours [tex]\( x \)[/tex] used at the gym is:

[tex]\[ y = 3x + 1 \][/tex]

However, to make the equation more precise and to express the cost per hour as a fraction, we can write $3 as [tex]\( \frac{3}{1} \)[/tex] and then multiply both the numerator and the denominator by 4 to get [tex]\( \frac{3 \times 4}{1 \times 4} = \frac{12}{4} \)[/tex]. Simplifying the fraction [tex]\( \frac{12}{4} \)[/tex] gives us [tex]\( \frac{3}{4} \)[/tex]per hour.

Thus, the final slope-intercept form equation for the word problem is:

[tex]\[ y = \frac{3}{4}x + 1 \][/tex]

Final answer:

To find Sc, which represents the complement of set S, we need to determine the elements that are in the universal set but not in S. Sc represents the set of all rational numbers that are not integers.

Explanation:

To find Sc, which represents the complement of set S, we need to determine the elements that are in the universal set but not in S. The universal set, in this case, is the set of rational numbers, which includes all numbers that can be expressed as a quotient or fraction. Set S is the set of integers, which includes the whole numbers and their negatives.

So, to find the complement of S, we need to consider all rational numbers that are not integers. This includes numbers with decimals or fractions that are not whole numbers. For example, 4.5, -3.2, and 1/2 would be in the complement of S.

Therefore, Sc represents the set of all rational numbers that are not integers.

The circumference of a unit circle is calculated using the formula C = 2πr. For a unit circle, where the radius (r) is 1, the circumference (C) is 2π, approximately 6.2832.

The Circumference of a Unit Circle

In mathematics, the circumference of a circle is the distance around its perimeter. For a unit circle, which is a circle with a radius of 1, the formula to calculate circumference is given by C = 2πr, where r is the radius.

Since the radius of a unit circle is 1, substituting in the formula gives us:

C = 2π(1) = 2π

Thus, the circumference of a unit circle is 2π, which is approximately 6.2832 when using the value of π ≈ 3.1416.

The ratio of the length to the width of the largest stamp ever issued by China, having dimensions of 210mm long and 65mm wide, is approximately 3.23:1 after dividing the length by the width.

To answer the question about the ratio of the length to the width of the largest stamp ever issued by China, we need to follow a few simple steps. First, we have the dimensions of the stamp: 210mm long and 65mm wide.

Step 1: Identify the numbers given. In this case, the length of the stamp is 210mm, and the width is 65mm.

Step 2: To find the ratio of length to width, we need to divide the length by the width. So, 210 divided by 65 gives us approximately 3.23 (rounded to two decimal places).

Therefore, the ratio of the length to the width of the largest stamp ever issued by China, in simplest form, is approximately 3.23:1.

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