15. Graph f(x) = 0.5 - 2x?. Then find the value
of f(x) when x = 0.

Answer:

-2^2 + 6*2=11

4+12=11

16=11

16-11=4

Step-by-step explanation:

The two expressions are not equivalent.

To simplify the expression (p^2n^1/2)^0 √ p^5n^4, we first need to understand the properties of exponents and radicals.

Recall that any number raised to the power of zero is equal to 1, so (p^2n^1/2)^0 = 1.

Next, we can simplify the radical term by multiplying the exponents inside and outside the radical:

√ p^5n^4 =

(p^5n^4)^(1/2)

= p^(5/2)n^(4/2)

= p^(5/2)n^2

Combining this result with the previous step, we have:

(p^2n^1/2)^0 √ p^5n^4

= 1 * p^(5/2)n^2

= p^(5/2)n^2

This is not equivalent to p^18n^6 √p. In fact, p^(5/2)n^2 cannot be simplified any further without additional information about the expression.  ,

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The graph of the equation 3x + 4y = 0 is a straight line with a negative slope passing through the origin.

The given equation, 3x + 4y = 0, represents a linear graph in the Cartesian coordinate system. Let's analyze its characteristics.

First, note that the equation is in the standard form for a linear equation, which is Ax + By = C, where A, B, and C are constants. In this case, A = 3, B = 4, and C = 0.

To graph this equation, we can rewrite it in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. By isolating y, we have y = (-3/4)x + 0. Since the y-intercept (b) is 0, the line intersects the y-axis at the origin (0,0).

Next, we can examine the slope. The coefficient of x, -3/4, represents the ratio of the change in y (vertical) to the change in x (horizontal) as we move along the line. In this case, the slope is negative, indicating that the line descends from left to right. The magnitude of the slope, 3/4, implies that for every 4 units moved horizontally to the right, the line goes 3 units down vertically.

Therefore, we can conclude that the graph of the equation 3x + 4y = 0 is a straight line passing through the origin (0,0) with a negative slope. It extends indefinitely in both directions, with the line getting steeper as we move to the right.

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The solution set is for the given inequality is (-∞, -2.25]

Here we want to solve the following inequality:

-11 - 8k ≥ 23 - (7 - 4k)

To solve this, we need to isolate the variable k in one side of the equation.

First we can expand the right side so we get:

-11 - 8k ≥ 23 - (7 - 4k)

-11 - 8k ≥ 23 - 7 + 4k

Group like terms:

-11 - 23 + 7  ≥ 4k + 8k

-34 + 7 ≥  12k

-27 ≥  12k

-27/12 ≥  k

-2.25 ≥  k

Then the solution is the set of all values smaller than or equal to -2.25, then the solution set is (-∞, -2.25]

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The value of x in the given equation using laws of exponents is; x = 512

The different laws of exponents include;

1) Product of powers rule.

2) Quotient of powers rule.

3) Power of a power rule.

4) Power of a product rule.

5) Power of a quotient rule.

6) Zero power rule.

7) Negative exponent rule.

We have the equation as;

x^(2/3) = 64

We can write 64 as (∛512)²

This can be further expressed as;

512^(2/3)

Thus, we have;

x^(2/3) = 512^(2/3)

Thus, by identity rule;

x = 512

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Based on the scatterplot, the form of the relationshipbetween fire spread rate and wind speed   can be described as a positive correlation.

As wind speed increases,the fire spread rate also tends   to increase.

b. Direction  -

Based on the given scatterplot,the direction of the relationship between fire spread rate and wind speed appears to   be positive.

As the wind speed   increases,the fire spread rate generally tends to increase as well.

c. Strength  -

The scatterplot suggests a   moderate to strong relationship between fire spread rate and wind speed.

The data points   exhibit a somewhat linear pattern, indicating that there is a noticeable association between these variables.

The firespread rate tends to increase consistently as the wind speed increases, suggesting a relatively strong positive correlation between the two factors.

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Full Question:

Wind and Moisture: To understand how weather and landscape affect the spread of wildfires, an experiment was conducted in a low velocity wind tunnel. A fire was started in pine litter, and the researchers measured the fire spread rate for varying wind speeds and pine litter moisture contents.

Data for fires started in pine litter that had a moisture content of 4% are shown in the table below.

Wind Speed (miles/hour) Fire Spread Rate (feet/minute)

0.76                                         0

1.78                                             2

3.34                                                4

5.38                                       6

8.10                                                8

11.75                                     10

16.70                                    12

A scatterplot of these data is shown here  -

1. Based on the scatterplot, how would you describe the following with regard to the relationship between fire spread rate and wind speed?

a. Form:

b. Direction:

c. Strength:

The mean of the data set is 3.560. The median of the data set is 1.98.

The mean of a data set refers to the average of the data distribution which is achieved by the sum of all the data set divided by the number of values in the data set.

The missing data for the first 5 countries are as follows:

Country          CO2 emission (metric tons per capita)

Aruba               8.41

Afghanistan     0.29

Angola              1.29

Albania              1.98

Andorra             5.83

The mean of the data set is computed as:

\(\mathbf{Mean \ \bar {x} = \dfrac{8.41+0.29+1.29+1.98+5.83}{5}}\)

\(\mathbf{Mean \ \bar {x} =3.560}\)

To determine the median of the data set, we first rearrange the data set from the highest to the lowest:

= 8.41, 5.83, 1.98, 1.29, 0.29

The median value is 1.98

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On expanding the expression, we get -

{x³ - 2x²y + xy² - x²y + 2xy² - y³}

Given is the expression as -

(x - y) (x² - 2xy + y²)

The given expression is -

(x - y) (x² - 2xy + y²)

x {x² - 2xy + y²} - y {x² - 2xy + y²}

x³ - 2x²y + xy² - x²y + 2xy² - y³

Therefore, on expanding the expression, we get -

{x³ - 2x²y + xy² - x²y + 2xy² - y³}

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Answer

\(\pink\sf{y=-1}\)

Step-by-step explanation

I'm assuming that this exercise is asking us to simplify the equation \(\sf{y=0.5(6)-4}\).

We know that 0.5 (6) means 0.5 multiplied by 6. That is the same as 6 divided by 2, which is 3:

\(\sf{y=3-4}\)

And now we just simplify the last part:

\(\sf{y=-1}\)

∴ answer: y = -1

Clare paid 50% more than Priya.

So, she paid as much as Priya paid, PLUS 50% of what Priya paid.

Priya paid $5.

50% of $5 is $2.50.

5 + 2.50 = 7.50

Clare paid $7.50.

Hope this helps! :)

Answer:

The number of pies baked in the two years = ( k + 145) pies

Step-by-step explanation:

Here, we are interested in writing an expression for the total number of pies baked in the two years.

Last year, the number of pies baked = 145

This year the number of pies baked = k

Thus, the total number of pies baked in the two years will be ( k + 145) pies

Therefore, the answer is A. {5, 5√3, 10}.

The set of values {5, 5√3, 10} could be the side lengths of a 30-60-90 triangle.

In a 30-60-90 triangle, the sides are in a specific ratio. The ratio is 1 : √3 : 2, where the shortest side (opposite the 30-degree angle) has length x, the side opposite the 60-degree angle has length x√3, and the hypotenuse (opposite the 90-degree angle) has length 2x.

Let's check if the given set of values satisfies this ratio:

   If x= 5, then the side opposite the 60-degree angle should be 5√3, and the hypotenuse should be 10. These values match the ratio, so the set {5, 5√3, 10} could be the side lengths of a 30-60-90 triangle.

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Answer:

this is an equation of closure property of rational numbers under addition

Step-by-step explanation:

this is the meaning of it

for every a and b belongs to q then a+b belongs to q

Answer:

Step-by-step explanation:

r = 6cm

so area = 6²π

The expression can be written as x ≤ 3 + y ≤ 12 ≥ 6. which is an inequality.

A mathematical operator that expresses the inequal comparison between different numbers or different variables and numbers. There are various types of inequalities such as greater than >, less than <, greater than or equal ≥ and less than or equal ≤

Frank participates in exercise program at least 6 hours in each week.

He spends at most 12 hours on weight training

y denotes the time in hours that he spends on weight training.

Frank spends at most 3 hours doing cardiovascular works

x denotes the time in hours that he spends doing cardiovascular works

The expression that can represent the above statement.

can be written as

x ≤ 3 and y≤ 12

x ≤ 3 + y ≤ 12 ≥ 6

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Answer:

The factors of the expression \(f(x)= 3x^{2} + 4x + 1\) are (3x + 1)(x + 1).

Step-by-step explanation:

The expression is:

\(f(x)= 3x^{2} + 4x + 1\)

Factorize the expression as follows:

\(f(x)= 3x^{2} + 4x + 1\)

       \(=3x^{2}+3x+x+ 1\\\\=3x(x+1)+1(x+1)\\\\=(3x+1)(x+1)\)

Thus, the factors of the expression \(f(x)= 3x^{2} + 4x + 1\) are (3x + 1)(x + 1).

Answer: It shows correct if this is the model your looking for

Step-by-step explanation:

Answer:

32 students

Step-by-step explanation:

24 divided by .75 is 32

Based on the information given, there'll be 32 students.

Let the total number of students be represented by x.

From the information, it was stated that 75% of the students are boys and that there are 24 boys. Therefore, the total number of students will be:

75% × x = 24

0.75x = 24

x = 24/0.75

x = 32

There are 32 students.

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The notation "t(x)" represents the statement t is a function of x

The notation is given as:

t(x) = ....

The above notation is a function notation, and it used to relate one element  to another

For instance:

f(x) means f is a function of x

Similarly, "t(x)" represents the statement t is a function of x

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Answer:

5

Step-by-step explanation:

a minus times by another minus makes a positive, so it is basically 1 x 5

Answer:

5

Step-by-step explanation:

Since the you are multiplying 2 minuses together they will cancel each other out to form a positive number. However if you have an example like this

-6 × 7

Then the answer will be -42 because there is only one negative

Therefore, B's share is Rs. 30,000 and C's share is Rs. 40,000.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The equals sign indicates that the two expressions are equal, and the goal of solving the equation is to find the value of x that makes this statement true. Equations can be solved using various algebraic techniques, such as simplifying and rearranging the expressions, applying operations to both sides of the equation, and factoring or expanding expressions. Solving an equation involves finding the values of the variables that make the equation true.

Here,

Let the total sum of money be x.

Then, according to the given ratio, A's share is 2/9 of the total sum, so we have:

2/9 * x = 20000

Multiplying both sides by 9/2, we get:

x = 90000

Now, we can find the shares of B and C as follows:

B's share = 3/9 * 90000 = 30000

C's share = 4/9 * 90000 = 40000

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The system of equations where the combination of the candies gives you a total of 22 points are:

x + y = 9

2x + 3y = 22

To create the equations, we shall first define the variables:

x = the number of purple candies

y = the number of yellow candies

Next, we shall use the given information that purple candies are worth 2 points and yellow candies are worth 3 points.

Then, we would make sure that the total number of candies selected is 9.

The first equation represents the total number of candies selected:

x + y = 9

The second equation represents the total number of points obtained:

2x + 3y = 22

Therefore, the system of equations is:

x + y = 9

2x + 3y = 22

This is a system of linear equations.

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Answer:

675

Step-by-step explanation:

675 is decreased by 3% and then increased by 3%. Hence, no change occurred.

Answer:

x = 4

Step-by-step explanation:

using the rule of exponents

• \(a^{-m}\) = \(\frac{1}{a^{m} }\) , then

\(4^{-x}\) = \(\frac{1}{4^{x} }\)

and 256 = \(4^{4}\)

then

\(\frac{1}{4^{x} }\) = \(\frac{1}{4^{4} }\)

so

\(4^{x}\) = \(4^{4}\)

since bases on both sides are equal, bot 4 then equate exponents

x = 4

Answer:

the answer is A

Step-by-step explanation: it is A because 45 percent of $166 is $47.7 and if you subtract it from 166 it turns out to be $118.3

Answer: 3274 cookies

Step-by-step explanation:

She sold : 2016 ÷ 8 = 252 ( bags )

The remaining cookies : 12 × 252 = 3024 ( cookies )

She baked : 3024 + 250 = 3274 ( cookies )

Answer:

10

Step-by-step explanation:

Every time you multiply by 10 you move the decimal point one digit to the right. So if you multiply 1.62 by 10 you move the decimal point one digit to the right so it becomes 16.2.

So the answer is 10

Answer:

The answer is 10

Step-by-step explanation:

Every time you multiply by a power of 10 that does not have a negative exponent, the decimal point moves to the right.

How many times, you might wonder. It all just depends on how many zeroes there are. If there's one 0, (10) then the decimal point just moves one over, if were multiplying by 100 then 2 places over, 1000 three places over, and so on.

1.62 * 10 = 16.2, since the decimal point moved one to the right.

10 is therefore the answer, but if you wanted to you could check the other answers as well.

1.62 * 100 = 162

1.62 * 1000 = 1620

Therefore, the answer is 10. Please mark brainliest if possible. Have a nice day.

Answer:

-6

Step-by-step explanation:

If x=3 and y=6, 4x-3y=-6 because 4x with x=3 makes the first number 12. 3y with y=6 makes the result 18, so now the equation is 12-18. 12-18=-6, so 4x-3y with x=3 and y=6 will equal -6.

Hopefully the answer and explanation helps!

Answer:

-6

Step-by-step explanation:

All you have to do is plug in the numbers. So it should look like 4(3) - 3(6). Now all you have to do is solve. 4 x 3 = 12. 3 x 6 = 18. Now subtract. 12 - 18 = -6

Answer:

\(6\sqrt{3}\)

Step-by-step explanation:

because of the 90-60-30 theorem

which \(6*\sqrt{3}=6\sqrt{3}\)