A function is defined by f(x) = x/4
What is f(-8)?

-2
-1/2
1/2
2​

Therefore, the probability of landing on land would be higher than landing on water, with a ratio of approximately 1:3.

If you were dropped at a completely random spot on the planet, the chances of landing on land would be one in three, or approximately 33.33%. This is because approximately 71% of the Earth's surface is covered by water, while the remaining 29% is land.

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Answer:

Step-by-step explanation:

An exponential function is written as

\(y=a(b)^x\)

where a is the y-intercept

b is the factor of growth

Here, the y intercept is 8 since the point (0,8) indicates when x=0, the function is equal to 8.

So a=8

\(y=8(b)^x\)

To find b, we will use a little of algebraic manipulation

We know that

\(72=8(b)^5\\9=b^5\\9^{1/5} =b\\\)

Which is close to 1.55

Answer:

(0, 12 ) and (4, 0 )

Step-by-step explanation:

the y- intercept is the point on the y- axis where the line crosses.

the x- coordinate of any point on the y- axis is zero

substitute x = 0 into the equation and solve for y

y = - 3(0) + 12 = 0 + 12 = 12 ← y- intercept , then

y- intercept is (0, 12 )

the x- intercept is the point on the x- axis where the line crosses

the y- coordinate of any point on the x- axis is zero

substitute y = 0 into the equation and solve for x

0 = - 3x + 12 ( subtract 12 from both sides )

- 12 = - 3x ( divide both sides by - 3 )

4 = x ← x- intercept , then

x- intercept is (4, 0 )

Answer:

8

Step-by-step explanation:

3(-2)^2+(-2)−2=8

Based on the given information, we can estimate that the total fish population in the section of the Chattahoochee River is around 250 fish (150 divided by 0.60).

To find the approximate population density of fish after one day, we need to know how many fish are added to or removed from the section in a day. Without this information, we cannot accurately calculate the population density.

However, we can assume that the fish population remains relatively stable over the course of one day. In this case, the population density would be approximately 0.28 fish per cubic yard (250 fish divided by 900 cubic yards).

It is important to note that environmentalists count fish populations for a variety of reasons, including to monitor the health of aquatic ecosystems, inform management decisions, and identify potential threats to biodiversity. Understanding population densities and changes over time can help environmentalists make informed decisions about how to protect and conserve fish populations and their habitats.

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Answer:

y= -3x + 7:)

Step-by-step explanation:

Hope this helps!

Answer:

y = - 3x + 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - 3 , thus

y = - 3x + c ← is the partial equation

To find c substitute (4, - 5) into the partial equation

- 5 = - 12 + c ⇒ c = - 5 + 12 = 7

y = - 3x + 7 ← equation of line

Answer:

fx=2x+2

fx-2x=2

Step-by-step explanation:

x(f-2)=2

x=2/f/2✓marks

Answer:

F ( x ) = x^2 + 2

Domain = R

F ( x - h ) = ( x - h )^2 + 2xh + h^2 + 2

Answer:

it is option D because it make supplementry or 180°

Hey there!☺

\(Answer:\boxed{x=\frac{5}{6},-\frac{5}{6}}\)

\(Explanation:\)

\(|x|=\frac{5}{6}\)

To solve for x, simplify both sides of the equation and then isolate the variable:

\(|x|=\frac{5}{6}\\x=\frac{5}{6},-\frac{5}{6}\)

Hope this helps!☺

The given equation's answer is \($z+5=55\left(5^z\right):$\) \($z=-\frac{W_{-1}\left(-\frac{11 \ln (5)}{625}\right)+5 \ln (5)}{\ln (5)}$\), \($z=-\frac{\mathrm{W}_0\left(-\frac{11 \ln (5)}{625}\right)+5 \ln (5)}{\ln (5)}$\)

\($z+5=55\left(5^z\right):$\) \($z=-\frac{W_{-1}\left(-\frac{11 \ln (5)}{625}\right)+5 \ln (5)}{\ln (5)}$\), \($z=-\frac{\mathrm{W}_0\left(-\frac{11 \ln (5)}{625}\right)+5 \ln (5)}{\ln (5)}$\)

\((Decimal: $z=-1.75934 \ldots, z=-4.98187 \ldots$ )\)

\($$z+5=55\left(5^z\right)$$\)

Prepare \($z+5=55\left(5^z\right)$\) Lambert form: \($(z+5) e^{-\ln (5) z}=55$\)

the equation once more using \($(-z-5) \ln (5)=u$\) and \(z=-\frac{u+5 \ln (5)}{\ln (5)}$\)

\($$\left(\left(-\frac{u+5 \ln (5)}{\ln (5)}\right)+5\right) e^{-\ln (5)\left(-\frac{u+5 \ln (5)}{\ln (5)}\right)}=55$$\)

\($$e^{u+5 \ln (5)}\left(-\frac{u+5 \ln (5)}{\ln (5)}+5\right)=55$$\)

Rewrite \($e^{u+5 \ln (5)}\left(-\frac{u+5 \ln (5)}{\ln (5)}+5\right)=55$\)in Lambert form: \($e^u u=-\frac{11 \ln (5)}{625}$\)

Solve \($e^u u=-\frac{11 \ln (5)}{625}: \quad u=\mathrm{W}_{-1}\left(-\frac{11 \ln (5)}{625}\right), u=\mathrm{W}_0\left(-\frac{11 \ln (5)}{625}\right)$$$u=\mathrm{W}_{-1}\left(-\frac{11 \ln (5)}{625}\right), u=\mathrm{w}_0\left(-\frac{11 \ln (5)}{625}\right)$$\)

Substitute back \($u=(-z-5) \ln (5)$\) , solve for z

\($$\begin{aligned}& \text { Solve }(-z-5) \ln (5)=W_{-1}\left(-\frac{11 \ln (5)}{625}\right): \quad z=-\frac{W_{-1}\left(-\frac{11 \ln (5)}{625}\right)+5 \ln (5)}{\ln (5)} \\& \text { Solve }(-z-5) \ln (5)=W_0\left(-\frac{11 \ln (5)}{625}\right): z=-\frac{W_0\left(-\frac{11 \ln (5)}{625}\right)+5 \ln (5)}{\ln (5)} \\& z=-\frac{W_{-1}\left(-\frac{11 \ln (5)}{625}\right)+5 \ln (5)}{\ln (5)}, z=-\frac{W_0\left(-\frac{11 \ln (5)}{625}\right)+5 \ln (5)}{\ln (5)}\end{aligned}$$\)

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The distribution of the number of values in our sample that are below 50 is a binomial distribution with n = 10 and p = 0.5.

The binomial distribution is a probability distribution that describes the number of successes in a sequence of independent trials. In this case, the trials are the values in our sample and the success is a value that is below 50.

The probability of success is 0.5, because the probability of an outcome being below the median is 50%.

The number of values in our sample that are below 50 is a binomial random variable because the trials are independent and the probability of success is the same for each trial.

The mean of the binomial distribution is np = 10 * 0.5 = 5, and the standard deviation is np(1 - p) = 5 * 0.5 * 0.5 = 2.5.

Here are some additional details about the binomial distribution:

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The divergence of F is 2xyi - 15(2²-3x) 4+uy³k and the curl of F is -x²yi - 15u³k.

To find the divergence and curl of the vector field F(x, y, z) = x²yi - (2²-3x) 5+uy³k, we can use vector calculus operations.

The divergence of a vector field measures the rate of outward flow from an infinitesimally small region surrounding a point. It is calculated using the divergence operator (∇·F), which is the dot product of the gradient (∇) with the vector field F. In this case, the divergence of F can be found as follows:

∇·F = (∂/∂x)(x²yi) + (∂/∂y)(- (2²-3x) 5+uy³k) + (∂/∂z)(0)

      = 2xyi - 15(2²-3x) 4+uy³k

The curl of a vector field measures the rotation or circulation of the field around a point. It is calculated using the curl operator (∇×F), which is the cross product of the gradient (∇) with the vector field F. In this case, the curl of F can be found as follows:

∇×F = (∂/∂x)(0) - (∂/∂y)(x²yi) + (∂/∂z)(- (2²-3x) 5+uy³k)

      = 0 - x²yi - 15u³k

Therefore, the divergence of F is 2xyi - 15(2²-3x) 4+uy³k and the curl of F is -x²yi - 15u³k.

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Answer:

14/11

Step-by-step explanation:

cause when u divide you have to switch the second fraction; it's called the reciprocal.

do crossed division and you'll get 14/11.

Answer:

1 1/2

Step-by-step explanation:

1 4/5 ÷ 1 1/5

convert to full fractions:

9/5 ÷ 6/5

9/5 x 5/6 = 45/30 = 1 1/2

The points that represents a viable solution to the system of inequalities include the following:

A. (−10, 170)

B. (80, 90)

C. (250, −50)

In order to determine which points are true and viable with respect to a solution of the given system of inequalities, we would have to test the each of the points by substituting their values into the inequalities as follows;

For points (-10, 170), we have:

x + y ≥ 150

-10 + 170 ≥ 150

160 ≥ 150 (Viable).

1.5x + 3.5y ≤ 600

1.5(-10) + 3.5(170) ≤ 600

-15 + 595 ≤ 600

580 ≤ 600 (Viable).

For points (80, 90), we have:

x + y ≥ 150

80 + 90 ≥ 150

170 ≥ 150 (Viable).

1.5x + 3.5y ≤ 600

1.5(80) + 3.5(90) ≤ 600

120 + 315 ≤ 600

435 ≤ 600 (Viable).

For points (250, -50), we have:

x + y ≥ 150

250 - 50 ≥ 150

200 ≥ 150 (Viable).

1.5x + 3.5y ≤ 600

1.5(250) + 3.5(-50) ≤ 600

375 - 175 ≤ 600

200 ≤ 600 (Viable).

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An angle of rotation is the measure of the amount that a figure is rotated about a fixed point called a point of rotation.

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Answer:

Step-by-step explanation:

since you moved -1 in the x-axis

+1 to reverse it

(-1,5)

and since you moved +6 in the y-axis

-6 to do the reverse

(-1,-1)

Answer:

-3,-1 maybe

Step-by-step explanation:

Answer:

From the attached graph, the x-intercept is (13, 0)

Step-by-step explanation:

The question equation is y = x³ + 11·x² - 312·x

To graph the equation, we find the value of y for a given value of x and we plot the values on a graph as follows;

x,              y

13,            0

14,            532

15,            1170

16,            1920

17,            2788

18,           3780

19,           4902

20,           6160

21,           7560

22,          9108

23,          10810

24,          12672

25,          14700

From the graph, the x-intercept can be found at at x = 13.

The x-intercept can also be obtained by equating the right hand side of the equation to 0 (y = 0 is the x -intercept) as follows;

0 = x³ + 11·x² - 312·x

Therefore, x = 0 is one of the x-intercepts

By dividing by x, we have

x² + 11·x - 312 = 0

By completing the square we have

x² + 11·x + (11/2)² = 312+(11/2)²

(x + 11/2)² = 1369/4

x + 11/2 = ±37/2

x = 37/2 - 11/2 = 13 or x = -37/2 - 11/2 = -24

Which gives the x-intercept as (13, 0).

Answer:

y=1/2*(x-4)^2+13

Step-by-step explanation:

Answer:

y=1/2*(x-4)^2+13

Step-by-step explanation:

Answer:

Question 2: 6x-21

Question 1: -9x+3

Step-by-step explanation:

To copy segment AB, D, The distance between points A and B needs to be identified for the construction.

A segment is a section of a line that is bounded by two unique ends and contains every point on the line between them. A segment is designated after its endpoints, therefore segment AB refers to the section of the line connecting points A and B.

To copy segment AB can be accomplished by utilizing a measuring instrument such as a ruler or tape measure to determine the distance between the two spots. Once the distance is determined, a new point that is the same distance away from point A as point B can be produced.

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The x-intercept of the equation 70x - 12y = 350 is (5, 0).

The x-intercept of an equation is where a line crosses the x-axis. The x-intercept of an equation is the value of x when y equals to zero.

Therefore, let's find the x-intercept of the equation as follows:

70x - 12y = 350

Hence,

12y = 70x - 350

Let's substitute y = 0 in the equation

12(0) = 70x - 350

70x = 350

divide both sides by 70

x = 350 / 70

x = 5

Therefore, the x-intercept is (5, 0)

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Answer:

59

Step-by-step explanation:

it's my lucky number btw =w=

The value of the number expression 42 divided by (15-2 to the 3rd power) or  42 ÷ (15 - 2³) is 6.

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

It is given that:

42 divided by (15-2 to the 3rd power)

Mathematically,

= 42 ÷ (15 - 2³)

After applying the properties of integer exponent:

= 42 ÷ (15 - 8)

Because 2³ = 8

= 42 ÷ 7

After dividing

= 6

Thus, the value of the number expression 42 divided by (15-2 to the 3rd power) or  42 ÷ (15 - 2³) is 6.

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Answer:

(Negative 6) (4) + (negative 6) (two-thirds

According the nature of the roots for the equation -x^2 + 4x - 4 = 0 is real, equal, and rational.

To determine the nature of the roots for the quadratic equation -x^2 + 4x - 4 = 0, we can examine the discriminant, which is the expression under the square root in the quadratic formula.

The discriminant (D) of a quadratic equation of the form ax^2 + bx + c = 0 is given by D = b^2 - 4ac.

In this case, the coefficients are:

a = -1

b = 4

c = -4

Substituting these values into the discriminant formula, we have:

D = (4)^2 - 4(-1)(-4)

= 16 - 16

= 0

Since the discriminant is equal to 0, it indicates that the quadratic equation has real and equal roots.

Therefore, the nature of the roots for the equation -x^2 + 4x - 4 = 0 is real, equal, and rational.

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The expression (4x+8)² is equivalent to 16x²+64x+64 i.e.D.

What are expressions?

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.

e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.

Now,

Given expression is (4x+8)²

=(4x)²+8²+2*4x*8         As ((a+b)²=a²+b²+2ab)

=16x²+64+64x

hence,

          (4x+8)² is equivalent to 16x²+64x+64.

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