Evaluate the following
expression using x = 5:
3(3x + 5)

The natural values of n for which the difference (2-2n) - (5n-27) is positive are 1, 2, 3, and 4.

To find the natural values of n for which the difference (2-2n) - (5n-27) is positive, we need to simplify the expression and then solve for n.

(2-2n) - (5n-27) = 2 - 2n - 5n + 27

= -7n + 29

So, we need to find the natural numbers n for which -7n + 29 > 0.

To do this, we can solve for n as follows

-7n + 29 > 0

-7n > -29

n < 29/7

Since n is a natural number, it must be an integer greater than or equal to 1. Therefore, the natural values of n for which the difference (2-2n) - (5n-27) is positive are 1, 2, 3, and 4.

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Answer:

Step-by-step explanation:

From the question the two angles that's

\(\angle\) ZXY and \(\angle\) WXZ are complementary since they lie on a right angle

Complementary angles are angles that add up to 90°

Let m \(\angle\) WXZ be x

To find m \(\angle\) WXZ add up the two angles and equate them to 180° to find the angle

So we have

\(\angle\) WXZ + \(\angle\) ZXY = 90

x + 26 = 90

x = 90 - 26

x = 64°

So we have the final answer as

Hope this helps you

Answer:

1. 3

2. 1/9

3. 9/2

4. 1

Step-by-step explanation:

hope this helps

Answer:

1. 3

2. 1/9

3. 9/2

4. 1

Answer:

-34x+29

Step-by-step explanation:

\(7(5-x)-3(9x+2)=7.5-7x-3.9x-3.2=35-7x-27x-6\\=-34x+29\)

The amount that Victoria will have in one year if she invests $20 at 7.2% simple interest is $21.44.

The simple interest system does not compound the interest.

This statement implies that interest is not computed on the accumulated interest.  Periodically, the interest is computed on the principal, using the following simple interest formula:

Simple interest = Principal x Rate x Time

Simple interest rate = 7.2% per year

Investment = $20

Investment period = 1 year

Amount in account after 1 year = P + (P x R x T)

= $20 + ($20 x 7.2% x 1)

= $20 + $1.44

= $21.44

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Answer:

Step-by-step explanation:

This is a positive parabola so it opens upwards. The equation for the directrix of this parabola is y = k - p. k is the second number in the vertex of the parabola which is (0, 0), but we need to solve for p.

The form that the parabola is currently in is

\(y=a(x-h)^2+k\) so that means that \(a=\frac{1}{8}\). We can use that to solve for p in the formula

\(p=\frac{1}{4a}\) so

\(p=\frac{1}{4(\frac{1}{8}) }\) which simplifies to

\(p=\frac{1}{\frac{1}{2} }\) which gives us that

p = 2. Now to find the directrix:

y = k - p becomes

y = 0 - 2 so

y = -2, choice A.

Option second \(\rm (w-2.5)(w+2.5)\) and option fourth  \(\rm (-4v-9)(-4v+9)\)  are the products that result in a difference in squares

It is required to identify which products result in a difference of squares.

Polynomial is the combination of variables and constants in a systematic manner with "n" number of power in ascending or descending order.

We know that:

\(\rm (a^2-b^2)=(a+b)(a-b)\)

In option first:

\(\\\rm= (5z+3)(-5z-3)\\\rm =-(5z+3)(5z+3)\\\rm =-(5z+3)^2\)

It is not the difference between squares.

In option second:

\(\rm = (w-2.5)(w+2.5)\\\rm = (w^2-2.5^2)\) By using \(\rm (a^2-b^2)=(a+b)(a-b)\)

It is the difference between squares.

Similarly, in option third:

\(\rm = (8g+1)(8g+1)\\\rm = (8g+1)^2\)

It is not the difference between squares.

Similarly, in option forth:

\(\rm = (-4v-9)(-4v+9)\\\rm = (4v+9)(4v-9)\\\rm = (4v)^2-9^2\)

It is the difference between squares.

Similarly, in option fifth:

\(\rm = (6y+7)(7y-6)\\\rm = 42y^2+13y-42\)

It is not the difference between squares.

Similarly, in option sixth:

\(\rm = (p-5)(p-5)\\\rm = (p-5)^2\)

It is also not the difference between squares.

Thus, option 2 and option 4 are correct.

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Answer:

\(x = 5\), \(y = -2\)

Step-by-step explanation:

\(2x + 5y = 0\)

\(3x - 4y = 23\)

By using substitution:

\(2x + 5y = 0\)

\(2x = -5y\)

\(x = -\frac{5}{2}y\)

\(3x - 4y = 23\)

\(3 (-\frac{5}{2} y) - 4y = 23\)

\(-\frac{23}{2} y = 23\)

\(y = -2\)

\(x = -\frac{5}{2} y\)

\(x = -\frac{5}{2} (-2)\)

\(x = 5\)

Answer:

2 units ^2

Step-by-step explanation:

A = 1/2 (2) (2)

A = 4/2 = 2

According to the given information the formula for f(x) in term of x is  f(x) = (4/5)x - 4.

A function is a relationship between a number of inputs and outcomes. Simply described, a function is an association between inputs where each input is linked to exactly one output. There is a range, codomain, as well as domain for every function. A function is commonly referred to as f(x), where x is in fact the input.

When looking at a graph, we use a procedure known as the Vertical Line Test to determine whether a function is indeed a function. Simply drawing a vertical line will reveal if the graph is a function if it touches it once.

4x - 5y = 20

Subtracting 4x from both sides

-5y = -4x + 20

Dividing 5 from the both sides

y = (4/5)x - 4

The formula for f(x) in terms of x is:

f(x) = (4/5)x - 4

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Answer: -13

hope it helps

The linear equation is y = (1/7)*x + 11/7.

The general linear equation is:

y = a*x + b

Where a is the slope.

Here we know that a = (1/7), then the line is:

y = (1/7)*x + b

We also know that the line contains the point (-4, 1), this means that when x = -4, we must have y = 1.

Replacing that, we get:

1 = (1/7)*(-4) + b

1 + 4/7 = b

7/7 + 4/7 = b

11/7 = b

So the linear equation is:

y = (1/7)*x + 11/7.

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The equation of the linear function of the line is: y = 1/7x + 11/7.

A linear function equation is modelled as, y = mx + b, where m is the slope and b is the y-intercept.

Slope (m) = 1/7, and the line passes through (-4, 1), therefore, substitute (x, y) = (-4, 1) and m = 1/7 into y = mx + b:

1 = 1/7(-4) + b

1 = -4/7 + b

1 + 4/7 = b

11/7 = b

b = 11/7

Plug in the values of m and b into y = mx + b:

y = 1/7x + 11/7

The equation of the linear function is: y = 1/7x + 11/7

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Answer:

m < 1 = 18°

Step-by-step explanation:

If <ABD = 72°, and m < 2 is three times the measure of m < 1, then:

Let < ABC = m < 1 =  x

     < CBD = m < 2 = 3x

We can set up the following formula, since the sum of the measures of angles < 1 and < 2 is equal to <ABD (72°):

m < 1 + m < 2 = < ABD

x + 3x = 72°

Add like terms:

4x = 72°

Divide both sides by 4 to solve for x:

\(\frac{4x}{4} = \frac{72}{4}\)

x = 18

Since x = 18, and m < 1 = x , then m < 1 = 18°.

And since m < 2 = 3x, then m < 2 = 3(18°) = 54°.

Let's check to see whether we derived the correct answers by plugging in the values of m < 1 and m < 2 into the established formula:

m < 1 + m < 2 = < ABD

18° + 54° = 72°

72° = 72° (True statement).

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Answer:

23

Step-by-step explanation:

2(3)^2 + 5

2(9)+5

18+5

23

The equation of the line passing through point (-10,1) and parallel to

y = -1/5x+9 is y = -1/5 x -1

The slope of a line is a number that describes both the direction and the steepness of the line.

Given that, Line v has an equation of y = -1/5x+9. Line w includes the point (-10,1) and is parallel to line v.

The standard equation of a line is: y = mx+c

Where, m is the slope and c is the constant,

We know that when two lines are parallel, their slopes are equal.

Therefore, slope of line v = slope of the line w = -1/5

Finding the constant c, for line w,

Since, the line is passing through point (-10,1), then,

1 = -1/5x-10+c

c = 1-2

c = -1

Hence, the equation of line w is y = -1/5 x -1

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Answer:

7:20 A.M.

Step-by-step explanation:

5+35+10=50 mins

So she has to leave 50 mins before 8:10 A.M.

which is 7:20 A.M.

Answer:

2.5 is the original height

Step-by-step explanation:

Hope this helps! :)

The domain and the range of a function are the possible input and output values of the function.

The domain of the function is: [0,20]

The range of the function is: [0,200]

From the graph of the function (See attachment), we have the following observations

The x-coordinates of the graph is from 0 to 20

The y-coordinates is from 0 to 200

The x-coordinates represent the domain, while the y-coordinates represent the range.

Hence, the domain of the function is: [0,20] while the range of the function is: [0,200]

Use the equation formula to find the area of a circle

The radius is given on the question, replace this value on the equation and find the area.

The area of the circle is 201.06 mm^2

The functions are arranged from narrowest to widest as follows

A function with a narrower graph has a smaller range of values for its independent variable (typically the x-axis). Here are some ways to identify functions with narrower graphs:

The coefficient of the polynomial, when the coefficient is greater the graph is narrower. The magnitude used here are the absolute values since the sign takes care of whether the graph face up or down.

Considering this we have that

|4| is the narrowest

|-2x| is wide

|1/4| is the widest

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Answer: yes. a function

Step-by-step explanation:

every x input (x,y) has only one y output

Answer:

72 I think

Step-by-step explanation:

Answer:

113.1 cm³

Step-by-step explanation:

diameter = 2 X radius

Volume of sphere = (4/3) X π X r ³

= (4/3) π (3)³

= 36π

= 113.1 cm³ to nearest tenth

Refer to the attachment

The minimum speed the driver could have been going is equal to 38.02 mph.

Given the following data:

To calculate the minimum speed the driver could have been going:

First of all, we would determine the mean of the skid marks as follows:

\(Mean = \frac{86+93+88+90}{4} \\\\Mean = \frac{357}{4}\)

Mean = 89.25.

For the minimum speed:

\(Minimum\; peed = \sqrt{30 \times 89.25 \times 0.6 \times 0.9} \\\\Minimum\; peed = \sqrt{1445.85}\)

Minimum speed = 38.02 mph.

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The solution is, a. Climate change takes place at a constant rate over time.

Climate is the long-term weather pattern in a region, typically averaged over 30 years. More rigorously, it is the mean and variability of meteorological variables over a time spanning from months to millions of years.

here, we have,

A climate can be define as the average state of the everyday weather condition which remain probably stable for a period of 30 years. It is measured by various parameters like atmospheric pressure, temperature and humidity.

so,

On the basis of the above description, a.Climate change takes place at a constant rate over time. is the correct option.

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Answer:

10k+15/5

Step-by-step explanation:

Note that the pool is in the shape of square with each of its four sides measuring 'x' units.

(a)

So the total length of the rectangular system is given by,

Thus, the total length of the rectangle is (x+20) units.

(b)

Similarly the total width of the rectangular system is given by,

Thus, the total width of the rectangle is (x+16) units.

(c)

Consider that the area of the rectangular area is calculated as,

Substitute the values,

Thus, the above expression gives the area of the given rectangle.