For the given conditional statement, determine which of the following option(s) has a truth value of true. Select all that apply.
If a polygon is regular, then it has congruent angles and congruent sides.

conditional
converse
inverse
contrapositive

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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9.1 has 2 significant digits so to have 1 you need to round it to a whole number,

in 1 significant digit would be 9

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: [tex]p(x)= 13x-20[/tex]

Step-by-step explanation:

Given: The revenue for mowing x lawns is [tex]r(x) = 18x[/tex] .

Becca's cost for gas and the mower rental is c(x) = 5x + 20

The profit from mowing x lawns is given by :-

[tex]p(x)=(r-c)(x)[/tex]

The above  function can be written as

[tex]p(x)=(r-c)(x)=r(x)-c(x)\\\\\Rightarrow p(x)= 18x-(5x+20)\\\\\Rightarrow p(x)= 18x-5x-20\\\\\Rightarrow p(x)= 13x-20[/tex]

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.

Answer:

96

Step-by-step explanation:

All you gotta do is multiply 7 by a high number like say 80 you wont get 672 just keep on multiplying it by higher numbers till you get 672 i hope i helped

To find the product of the expression (a-3/7) divided by (3-a/21), multiply (a-3/7) by the reciprocal of (3-a/21), yielding the simplified expression ((21a - 9)/ (21a - 7)) valid for all values of 'a' except when 'a' equals 8/3.

The student is asking for the product of the expression (a-3/7) divided by (3-a/21). To simplify this expression, we need to apply the division of fractions rule, which states that to divide by a fraction, you multiply by its reciprocal. The reciprocal of (3-a/21) is (21/(3a-1)). So our new expression is (a-3/7) × (21/(3a-1)).

We can multiply the numerators and denominators separately: (a-3/7) × 21 = (a× 21 - 3× 3) and 7 × (3a-1) = 21a-7. Simplified, we get ((21a - 9)/ (21a - 7)) as the product.

However, we should also check if the expression is defined for all values of 'a' as there may be values for which the denominator becomes zero. Specifically, we need 'a' to not be such that (3a-1) equals 7, which simplifies to a = 8/3. So for all values of 'a' except when 'a' equals 8/3, the product of the given expression is ((21a - 9)/ (21a - 7)).

Answer:

213 euros per month

Step-by-step explanation:

1dollar = 0.7306euros

thus $3,500 dollars can be found by a rule of three

dollar             euro

1             ⇒  0.7306

3500     ⇒        x

we find x as follows:

[tex]x=\frac{0.7306*3500}{1} = 2,557.1[/tex] euros

She will pay 2,557.1  euros per year.

Dividing between the 12 months of the year:

[tex]\frac{2,557.1}{12}=213.1[/tex]

Rounding to the nearest whole euro she will pay 213 euros per month.

Answer:

A

Step-by-step explanation:

I just took the test

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

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!

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.

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 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.