Factorise 6p^2-5pq-6q^2

Answer:

9yb

Step-by-step explanation:

The exact value of cos(θ + π/6) when sin θ = 1/4 and θ is in quadrant II is (-√(45) - 1)/8, found by using the Pythagorean identity and the angle sum identity.

To find the exact value of cos(θ + π/6) when sin θ = 1/4 and θ is in quadrant II, we can use trigonometric identities and properties of angles. First, we use the Pythagorean identity to find cos θ. Since θ is in the second quadrant, cos θ is negative and solving for cos θ gives cos θ = -√(1 - sin² θ) = -√(1 - (1/4)²) = -√(15)/4.

Next, we apply the angle sum identity for cosine, which is cos(α + β) = cos α cos β - sin α sin β. Using this identity, we find:

cos(θ + π/6) = cos θ cos(π/6) - sin θ sin(π/6) = (-√(15)/4)(√(3)/2) - (1/4)(1/2) = -√(45)/8 - 1/8 = (-√(45) - 1) / 8.

Martha earns $6.50 per hour, so for 1.5 hours, she will earn $9.75; for 2.5 hours, she will earn $16.25; and for 3.5 hours, she will earn $22.75. We simply multiply her hourly wage by the number of hours to find the total earnings for each duration.

If Martha earns $6.50 per hour for babysitting, we can find out how much she will earn for different numbers of hours by multiplying her hourly rate by the number of hours worked.

As a result:

The graph touches the x-axis at (–2.5, 0). The answer is the second option The graph touches the x-axis at (–2.5, 0)

The given function is f(x) = 4x² + 20x + 25

The table of values for the function from -1 to -4 is

x          -1     -2   -3    -4

f(x)       9      1   1      9

The graph of the function is attached below

From the graph, we can observe that the graph touches the x-axis at the point (-2.5, 0)

Hence, the graph touches the x-axis at (–2.5, 0). The answer is the second option The graph touches the x-axis at (–2.5, 0).

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Answer:

Step-by-step explanation:

Answer:

5/8

Step-by-step explanation:

Answer:

Step-by-step explanation:

It said free points

The correct statement is (a), 'There is a correlation of 0.54 between the social intelligence of a 6-year old and his weight.' Correlation values range from -1 to +1, and units or nominal variables can't be used.

The correct statement among the given options is (a) 'There is a correlation of 0.54 between the social intelligence of a 6-year old and his weight.' In a correlation, the value ranges from -1 to +1 where -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 indicates no correlation. The other statements, (b), (c), (d) and (e), are blunders because the correlation value (r) in (d) exceeds +1 which is impossible, the units in (b) and (c) are incorrectly applied as correlation doesn't have physical units, and in (e), gender is a nominal variable for which correlation cannot be calculated.

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I just had the same question and the answer was 5.7. Hope this helps somebody

The account value after 18 years with an initial deposit of $6,000 and a change in interest rate and compounding periods is approximately $15,526 when rounded to the nearest dollar.

To calculate the value of the account after 18 years with a change in the interest rate and compounding periods, we need to use the compound interest formula separately for the two different periods and rates.

First, we compound the original $6,000 at 5.25% semiannually for 10 years:

A = P(1 + r/n)(nt)

A = $6,000(1 + 0.0525/2)(2*10) = $6,000(1.02625)20 = $9,984.21 (rounded)

Now, we take the amount after 10 years and compound it at 5.4% quarterly for the remaining 8 years:

A = P(1 + r/n)(nt)

A = $9,984.21(1 + 0.054/4)(4*8) = $9,984.21(1.0135)32 = $15,526.14 (rounded)

So, after 18 years, the value of the account would be $15,526 (rounded to the nearest dollar).

The issue was inconsistent units - converting everything to cm squared, the appropriate number of 20 by 30 cm tiles to cover an area of 10.95m squared is 183.

The problem here involves area measurement and conversions. The area of the outdoor space is given in square meters (m²), while the area of the tiles is given in square centimeters (cm²). Therefore, the first step here is to convert all measurements to the same unit.

Since 1 meter is equal to 100 centimeters, we can convert the area of the outdoor space to square centimeters by squaring 100 (which equals to 10,000) and then multiplying it by the area in square meters. That gives us 109,500 cm².

Next, to find the area of a single tile we multiply its length by its width, which is 20 cm by 30 cm, giving us 600 cm². The number of tiles needed will be the total area divided by the area of one tile. So, 109,500 cm² divided by 600 cm² equals to about 182.5.

Since we cannot have a half tile, we round up that number to 183 tiles. Therefore, the correct answer is 183 tiles.

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As they are lined out, the amounts must correlate horizontally, so the compacts should be longer than the rest, the mid-size behind it, and the trucks half-way between the compacts and the mid-size.

It is defined as the data representation in visual way, and it makes the appearance of the data simpler.

As we can see in the graph:

Total of 40 compact cars, 4 of 10 each.

Total of 30 mid-size, 3 of 10 each.

And Total of 20 trucks,

However, they all appear to have the same start and end points in the graph, with the mid-sizes being longer than the compacts and the trucks being considerably larger than the others above it, virtually implying that the amounts for all are identical for that period.

Thus, as they are lined out, the amounts must correlate horizontally, so the compacts should be longer than the rest, the mid-size behind it, and the trucks half-way between the compacts and the mid-size.

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Move all terms not containing  y  to the right side of the equation. You should get y=6.21

The equation 4y + 12x = 0 in slope-intercept form is y = -3x. The slope (m) is -3, and since there is no constant term, the y-intercept (b) is 0.

The equation provided, 4y + 12x = 0, can be converted into slope-intercept form, which is represented by y = mx + b. The slope, m, indicates the steepness of the line, while the y-intercept, b, denotes the y-value when x equals zero or where the line crosses the y-axis. Let's rearrange the equation step-by-step:

Here, the slope (m) is -3, indicating a decrease in y by 3 units for every increase of 1 unit in x. The equation does not have a b term, thereby indicating that the y-intercept (b) is 0. Hence, the slope-intercept form of the equation is y = -3x + 0, which can be simplified to y = -3x.