6x + 10 – 2x = 7 + 23

To solve for sinθ when θ is in Quadrant II and cosθ = -2/3, use the Pythagorean identity sin2θ + cos2θ = 1. Since sinθ will be positive in Quadrant II, after calculations, sinθ equals √5/3.

To find the sine value for an angle θ in Quadrant II, where the cosine of θ is given to be cosθ = -2/3, we can use the Pythagorean identity: sin2θ + cos2θ = 1. We already know that cosθ = -2/3, so we can solve for sinθ:

Since we are in Quadrant II, where sine values are positive, we take the positive square root:

So the value of sinθ when cosθ = -2/3 in Quadrant II is √5/3.

The revenue function for Gymnast Clothing is R(x) = 150x, and the profit function is P(x) = 150x - (2750 + 7x + 0.1x^2). To make a profit, they need to produce and sell more than the breakeven number of cleats, which can be calculated by setting the profit function to zero and solving for x.

When Gymnast Clothing sells soccer cleats at $150 per pair, the revenue function (R) would be the number of cleats, x, multiplied by the selling price. Therefore, R(x) = 150x. To find the profit function (P), we subtract the cost function (C(x)) from the revenue function, so P(x) = R(x) - C(x) or P(x) = 150x - (2750 + 7x + 0.1x2). A profit is made when P(x) > 0.

To determine the number of cleats needed to make a profit, we need to find the break-even point where P(x) = 0, and then any number greater than the break-even number of cleats would yield a profit. By setting the profit function equal to zero and solving for x, we can find the minimum number of cleats Gymnast Clothing should manufacture to begin making a profit.

Final answer:

To find the area of the board in square millimeters, convert the dimensions from meters to millimeters and multiply the length by the width to get 900000 square millimeters.

Explanation:

The area of a rectangle is calculated by multiplying its length by its width. The area in square millimeters can be found by first converting the measurements from meters to millimeters. Since 1 meter is equal to 1000 millimeters, we convert the dimensions and then calculate the area.

Length in millimeters: 1.2 meters × 1000 = 1200 millimeters

Width in millimeters: 0.75 meters × 1000 = 750 millimeters

Area in square millimeters: 1200 mm × 750 mm = 900000 square millimeters

The area of the board is 900000 square millimeters.

There are [tex]\rm 6 \frac{1}{4}[/tex] two - third in [tex]\rm 4 \frac{1}{6}[/tex]. Statement A best interprets the quotient.

A fraction number is a number that represents a portion of a larger number, where the larger number might be any integer. It has the shape of a numerator and a denominator.

The shaded part in step 1 is;

[tex]\rm 4 + \frac{1}{6} = 4 \frac{1}{6}[/tex]

Divide the shaded part with the unshaded part as ;

[tex]\rm \frac{4 \frac{1}{6} }{\frac{2}{3}}\\\\ \frac{25}{6} \times \frac{3}{2} \\\\\ \frac{25}{4} \\\\ 6 \frac{1}{4}[/tex]

There are [tex]\rm 6 \frac{1}{4}[/tex] two - third in [tex]\rm 4 \frac{1}{6}[/tex].

Hence, statement A best interprets the quotient.

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Answer: A

Step-by-step explanation:

To clear fractions in the given equation 1/4x-2/5=1/2x+2, multiply each term by the least common denominator (LCD) of the fractions to eliminate the fractions. Simplify the equation and solve for x.

To clear fractions in the given equation 1/4x-2/5=1/2x+2, we can find the least common denominator (LCD) of the fractions. The LCD is the least common multiple (LCM) of the denominators, which in this case is 20. To clear the fractions, we can multiply each term in the equation by 20:

So, the value that can be used to clear fractions in the given equation is x = -48/5.

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Answer:

(1/12) Pi r^3     option C on plato

Step-by-step explanation:

r = radius of the cylinder

V = (1/3)Pi c^2 h for a cone.

and c = r/2 and h = u

so Volume of the cone is (1/3)Pi(1/4)(r^2)r = r = radius of the cylinder

The simplified expression is log (x⁴y²).

Inverse to exponentiation is the logarithm.

The given expression is 4log x + 2log y.

Simplify the expression as follows:

4log x + 2log y

= log x⁴ + log y²

= log (x⁴y²)

Hence, the simplified expression is log (x⁴y²).

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To achieve balance, the momentum on both sides must be equal so that it cancels out. Momentum is simply the product of mass and distance, therefore:

50 pounds * 6 ft = 100 pounds * X

X = 3 ft

Hence B must be placed 3 ft from the pivot.

The equation of the line parallel to y=4x+1 passing through (3,9) is y=4x-3. It has the same slope of 4 but a different y-intercept, showing that the lines are parallel and do not intersect.

To find the equation of the line that contains the point (3,9) and is parallel to the line y=4x+1, we start by noting that parallel lines have the same slope. The given line has a slope of 4, so our new line will also have a slope of 4. The slope-intercept form of a line is given by y = mx + b, where m is the slope and b is the y-intercept.

Since we have a point (3,9) and a slope of 4, we can use the point-slope form to find our new line:

y - y₁ = m(x - x₁)

Plugging in our point and slope, we get:

y - 9 = 4(x - 3)

Expanding this, we have:

y - 9 = 4x - 12

Add 9 to both sides to get it into slope-intercept form:

y = 4x - 3

Therefore, the equation of the line parallel to y=4x+1 that passes through (3,9) in slope-intercept form is y = 4x - 3.

When graphing these two lines, you'll notice they never intersect, as they have the same slope but different y-intercepts, which is a distinctive feature of parallel lines.

To find the equation of a line that is parallel to another line, we need to determine the slope of the given line and then use the point-slope form of a linear equation. The equation of the line parallel to y = 4x + 1 and passing through the point (3,9) is y = 4x - 3. The graph of the lines show that they are parallel.

To find the equation of a line that is parallel to another line, we need to determine the slope of the given line and then use the point-slope form of a linear equation.

The given line y = 4x + 1 has a slope of 4 because it is in the form y = mx + b, where m is the slope. Since the line we want to find is parallel to this line, it will also have a slope of 4.

Using the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is the given point on the line, we can substitute the values (3, 9) and 4 for x1 and m, respectively, to get the equation:

y - 9 = 4(x - 3)

Expanding and rearranging the equation, we get:

y = 4x - 3

The graph of the given line y = 4x + 1 is a straight line with a slope of 4 and a y-intercept of 1. The line we found, y = 4x - 3, is also a straight line with the same slope but a different y-intercept. By plotting the two lines on the same graph, we can visually see that they are parallel.

The ratio of height to wide in the fraction form of the clock is 75/28.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

Height of clock = 75 inches.

Width of clock = 28 inches.

The ratio of height to width = Height of clock / Width of clock

So,

The ratio of height to width = = 75/28.

Hence "The ratio of height to wide in the fraction form of the clock is 75/28".

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Answer:

10 times greater

Step-by-step explanation:

The value of 7 in 750 is 700, while the value of the 7 in 76 is 70. 10 times 70 equals 700.

Hope this helped!

For a one-year investment, the equation is I = x imes 0.05 imes 1.

If Mary Ellen invests x dollars at an interest rate of 5%, we can write an equation that describes the total interest earned on that investment using the simple interest formula. The formula for calculating simple interest is Interest = Principal imes Rate imes Time. Assuming the investment is for 1 year, the equation for the total interest (I) Mary earns would be:

I = x imes 0.05 imes 1

This equation states that the interest Mary earns is equal to the amount of money she invested (x dollars) multiplied by the interest rate (5% or 0.05 as a decimal) and the time the money is invested (1 year).

If Mary Ellen invests $100, the total interest she would earn in one year at a 5% interest rate would be calculated as follows:

I = $100  imes 0.05 imes 1 = $5

The total cost for gas when driving 113 km per day in Europe for a week, with gas at 1.10 euros per liter and a mileage of 39.0 mi/gal, would be approximately $66.19 after converting euros to dollars at the given exchange rate of 1 euro = 1.26 dollars.

To calculate the cost of gas for driving 113 km per day over a week in Europe, where gas costs 1.10 euros per liter and the car has a gas mileage of 39.0 mi/gal, a series of conversions and calculations need to be done:

Step-by-step this would be:

Therefore, if the car is driven 113 km per day in Europe, the total cost for gas over one week, given the parameters listed, would be approximately $66.19 when converted into dollars.

Answer: B.

[tex]a_1=2\\a_n=a_n\times(-5)[/tex]

Step-by-step explanation:

The given geometric sequence : 2, -10, 50, -250

The first term of the sequence : [tex]a_1=2[/tex]

The common ratio between the terms :[tex]r=\dfrac{-10}{2}=-5[/tex]

We know that the recursive formula for geometric progression is given by :-

[tex]a_n=a_{n-1}r[/tex]

Then , the recursive formula for the given geometric progression will be :-

[tex]a_n=a_n\times(-5)[/tex]

Answer:

[tex](2\times 5)\times 1.5[/tex]

Step-by-step explanation:

Since, according to associative property of multiplication,

a(bc) = (ab)c,

Where a, b and c are any real numbers,

Here, the given expression,

2 × ( 5 × 1.5 ),

By applying the associative property of multiplication,

( 2 × 5 ) × 1.5,

Hence, the appropriate expression in the first box is '(2×5)'

And, the appropriate number in the second box is '1.5'.

Answer:

first box is (2 times 5) next box is 1.5

Step-by-step explanation:

i took K12 test :)