a soccer player has made 3 of his last 24 shots on goal, or 12.5%. How many consecutive goals does he need to raise his shots-on-goal average to at least 20%?

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 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:

69 420 911

Step-by-step explanation:

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 answer is: only one pair of sides is parallel a.k.a b

Answer:

The statement satisfied the  expression 10 + x 12 = 12x + 10 is

Option (e) i.e commutative - multiplication and Option (a) i.e commutative - addition .

Step-by-step explanation:

Commutative Property

Let a, b be two numbers thus they satisfied the commutative property

i.e a + b = b + a

As given the expression.

10 + x ×12 = 12x + 10

First apply the Option (e) i.e Commutative - multiplication.

Thus expression becomes

10 + 12x = 12x + 10

Now apply the Option (a) i.e Commutative - addition.

Therefore the statement satisfied the  expression 10 + x 12 = 12x + 10 is

Option (e) i.e commutative - multiplication and Option (a) i.e commutative - addition .

Answer:

Should be f(x) = x^3 + 3x^2 − x − 3  because this is written in standard form.

Step-by-step explanation:

the solution to the equation [tex]\(0.6(r - 0.2) = 1.8\) is \(r \approx 3.2\).[/tex]

To solve the equation 0.6(r - 0.2) = 1.8, we first distribute the 0.6 to the terms inside the parentheses:

0.6r - 0.6(0.2) = 1.8

0.6r - 0.12 = 1.8

Next, we add 0.12 to both sides of the equation to isolate 0.6r:

0.6r - 0.12 + 0.12 = 1.8 + 0.12

0.6r = 1.92

Now, to solve for r, we divide both sides of the equation by 0.6:

[tex]\[ \frac{0.6r}{0.6} = \frac{1.92}{0.6} \][/tex]

[tex]\[ r = \frac{1.92}{0.6} \][/tex]

[tex]\[ r \approx 3.2 \][/tex]

So, the solution to the equation [tex]\(0.6(r - 0.2) = 1.8\) is \(r \approx 3.2\).[/tex]

The probable question maybe:

solve the equation 0.6(r - 0.2) = 1.8

Answer:

A and C

Step-by-step explanation:

A.between 8 and 10 years of age

C.between 10 and 12 years of age

To have a greater percent increase than private investigators between 2006 to 2016, there must be approximately 760,945 police officers in 2016. This is found by applying the formula for percentage increase and adjusting it to find the required final number.

The percent increase of private investigators from 2006 to 2016 is found by subtracting the initial number from the final number, then dividing by the initial number and multiplying by 100%. This formula gives us (61000 - 52000) / 52000 * 100 = 17.3%, rounded to the nearest tenth of a percent.

To have a greater increase in police officers than that of private investigators, the percent increase must be more than 17.3%. To find the required number of police officers in 2016, we first express 17.3% as a decimal, which is 0.173. Then we use the formula for percentage increase, which is (final number - initial number) / initial number = percentage increase. By rearranging the formula, we get the required final number = (initial number * percentage increase) + initial number. Substituting the given figures, we have (648982 * 0.173) + 648982 = 760945, rounded to the nearest whole number.

Therefore, there must be approximately 760,945 police officers in 2016 to have a greater percent increase than that of the private investigators.

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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]

Answer:

idiot

Step-by-step explanation:

its b a c i think

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.

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.

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.