The angle of elevation from a sailboat to a point on a lighthouse is 30* as shown in the drawing. What is x, the angle of depression? A. 15*B. 30*C. 60*D. 150*

The evaluation of the statements with regards to the graph of a function are;

A function maps an input value to an output based on a definition or rule.

First part of the statement;

The graph of a non-vertical straight line has a range of values for the slope, m, of 0 ≤ m < ∞

The equation of a straight line function is of the form; y = m·x + c

Therefore;

The graph of a non-vertical straight line can be represented by the equation, y = m·x + c, where y has possible values of; -∞ < y < ∞, which indicates that as x increases or decreases, y increases (or decreases), such that each value of x maps unto only one value of y, which indicates that the graph is a function. The statement is therefore true.

Second part of the statement.

The graph of the quadratic function; y = a·x² + b·x + c has a shape of a parabola, therefore, the statement, the graph of a function is not always a straight line is true also.

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Answer:

\(P(F/E) = 0.6\)

Step-by-step explanation:

If we are given two dependent events \(A\) and \(B\) such that their chances of occurrence or the probabilities of the events are: \(P(A)\) and \(P(B)\).

Then the conditional probability that the event \(B\) will occur given that \(A\) has already occurred is given by the following formula:

\(P(B/A) = \dfrac{P(A \cap B)}{P(A)}\)

Here the two events given are \(E\) and \(F\).

\(P(E\ and\ F)\ or\ P(E\cup F) = 0.3\)

and \(P(E) = 0.5\)

As per the above formula that we have already discussed, the formula can be written as:

\(P(F/E) = \dfrac{P(E \cap F)}{P(E)}\\\Rightarrow P(F/E) = \dfrac{0.3}{0.5}\\\Rightarrow P(F/E) = \dfrac{3}{5}\\\Rightarrow \bold{P(F/E) = 0.6}\)

Answer:

FALSE

Step-by-step explanation:

<E in ∆AED ≅ <E in ∆CEB.

Both are 90°.

Side ED ≅ Side EB

Side AD ≅ Side CB.

Thus, two sides (ED and AD) and a non-included angle (<E) of ∆AED are congruent to corresponding two sides (EB and CB) and a non-included angle (<E) of ∆CEB. Therefore, by A-S-S Congruence Theorem, both triangles are congruent to each other not by SSS.

Answer:

no bc they r swapped and 40 is higher

Step-by-step explanation:

k

Each decreasing portion of the graph indicates the ball has been thrown upward and is traveling toward the ground.  

A graph can be defined as a type of chart that is used to graphically represent data on both the horizontal and vertical lines of a Cartesian coordinate i.e x-axis and y-axis.

By critically observing the graph attached in the image below, we can infer and logically deduce that each decreasing portion of the graph indicates the ball has been thrown upward and is traveling toward the ground.

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dont cheat please (-99.99%)

Step-by-step explanation:

just here for points

Answer: 9 bottles in each box and they bought 2, 4 & 5 boxes respectively.

Step-by-step explanation:

As it is clearly mentioned at the start of question that store only sells 'boxes' of juice bottles so all three of them bought perfect boxes.

So we'll find out how many boxes they'd have bought.

The largest possible divisor of 18, 36 and 45 is 9 so each box contains 9 juice bottles and guys purchased 2, 4 and 5 boxes respectively.

If you've still not understood, you can ask me for more detailed answer :)

Answer:

the answer is Y

Step-by-step explanation:

The greatest common factor (GCF) of two polynomial expressions is y.

The greatest common factor (GCF) of two polynomial expressions is the polynomial with the largest set of factors that is a factor of both polynomials.

To find the GCF of y2(y + 1) and y(y + 2), we can factor each polynomial:

y2(y + 1) = y(y)(y + 1)

y(y + 2) = y(y + 2)

The only factor that both polynomials have in common is y, so the GCF is y.

Here is the solution in more detail:

Factor each polynomial.

y2(y + 1) = y(y)(y + 1)

y(y + 2) = y(y + 2)

Find the factors that are common to both polynomials.

The only factor that both polynomials have in common is y.

The GCF is the polynomial with the largest set of factors that is a factor of both polynomials.

The GCF is y.

Therefore, the GCF of y2(y + 1) and y(y + 2) is y.

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x = number of radio ads

y = number of TV ads

x and y are nonnegative whole numbers (0,1,2,3,...) which means that both \(\text{x} \ge 0\) and \(\text{y} \ge 0\)

x+y = total number of ads purchased

This total must be 60 or more due to the phrasing "they plan to purchase at least 60 total ads". We will form the inequality \(\text{x}+\text{y} \ge 60\) and that solves to \(\text{y} \ge -\text{x}+60\)

-------------------

1 radio ad costs $400, so x of them will cost 400x dollars.

1200y = cost of all the TV ads

400x+1200y = total cost

This total cost must be $68,000 or smaller to keep under budget.

We arrive at \(400\text{x}+1200\text{y} \le 68000\) which is the same as \(\text{x}+3\text{y} \le 170\) and solves to \(\text{y} \le -\frac{1}{3}\text{x}+170\)

Another inequality is \(\text{y} \ge 3\text{x}\) because we want at least 3 times as many TV ads compared to radio.

-------------------

Let's recap so far.

We have this system of inequalities

\(\begin{cases}\text{x}+\text{y} \ge 60\\400\text{x}+1200\text{y} \le 68000\\\text{y} \ge 3\text{x}\\\text{x} \ge 0\\\text{y} \ge 0\end{cases}\)

which is equivalent to this system

\(\begin{cases}\text{y} \ge -\text{x}+60\\\text{y} \le -\frac{1}{3}\text{x}+170\\\text{y} \ge 3\text{x}\\\text{x} \ge 0\\\text{y} \ge 0\end{cases}\)

The idea from here is to plot each boundary line associated with those inequalities shown above.

For instance, the boundary equation for \(\text{y} \ge -\text{x}+60\) would be \(\text{y} = -\text{x}+60\)

Desmos is useful to quickly plot such an equation. Plot the other equations \(\text{y} = -\frac{1}{3}\text{x}+170\) and \(\text{y} = 3\text{x}\) on the same xy grid.

We'll then shade above the line y = -x+60 because of the "greater than" symbol associated with this corresponding inequality. The same goes for y = 3x. The other inequality has "less than" to mean we shade below that boundary.

The shaded region is inside a triangle which forms the 3 vertices we need.

The vertex points are:

Refer to the diagram below. Each corner point is a result of solving a system of exactly two equations. For instance, solve this system

\(\begin{cases}\text{y} = -\frac{1}{3}\text{x}+170\\\text{y} = 3\text{x}\end{cases}\)

and the solution is the point (17,51) meaning x = 17 and y = 51. Use substitution to solve.

-------------------

We're then given the info that "It is estimated that each radio ad will be heard by 1900 listeners" and also "each TV ad will be seen by 14500 people".

1 radio ad = 1900 people

x radio ads = 1900x people

1 TV ad = 14500 people

y TV ads = 14500y people

1900x+14500y = total people reached by both types of ads combined

The goal is to max out how many people are reached.

To find when 1900x+14500y is maxed out, we plug each of those corner points into that expression.

Let's try (5,55)

1900x+14500y

1900*5+14500*55

807000

This means purchasing 5 radio and 55 TV ads will reach 807,000 total people. This is an estimate.

Now try (15,45)

1900x+14500y

1900*15+14500*45

681000

The number has gone down from its previous value (807000), which means it's not a good idea to go for this corner point compared to the first one mentioned.

The last one to check is the corner (17,51)

1900x+14500y

1900*17+14500*51

771800

This result isn't larger than 807000, so the first corner point is the best one to go for. It makes 1900x+14500y as large as possible while keeping within the constraints set up with the inequalities.

As given by the question

There are given that 4<6, so 204<216.

Now,

On the number line, 4 is less tha6 and 204 is also less than 216

Hence, the given reasoning is correct.

Hubble's constant in units of km/s/million LY is approximately 21.47.

what is  approximately ?

Approximately means close to or nearly, but not exactly. It is used to indicate that a value or number is an estimation or approximation, rather than an exact value. It is often used when a precise value is not necessary or when the exact value is unknown or difficult to determine.

In the given question,

To convert Hubble's constant from km/s/Mpc to km/s/million LY, we need to multiply it by a conversion factor that accounts for the difference in distance units. We can use the fact that 1 Mpc is equal to 3.26 million LY:

1 Mpc = 3.26 million LY

Therefore, to convert Hubble's constant from km/s/Mpc to km/s/million LY, we can use the following conversion factor:

1 Mpc / 3.26 million LY

Multiplying Hubble's constant by this conversion factor gives:

H = 70 km/s/Mpc x (1 Mpc / 3.26 million LY) = 21.47 km/s/million LY

Therefore, Hubble's constant in units of km/s/million LY is approximately 21.47.

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The result of the expression 20 - 6 is 14.

To solve the given expression, 20 - 6, and isolate the variable, we need to clarify whether there is an equation involved. However, in this case, the expression does not contain any variable to isolate, and it is not an equation that needs balancing. It is a straightforward arithmetic expression.

Step 1: Start with the given expression, 20 - 6.

Step 2: Evaluate the subtraction operation: 20 - 6 = 14.

Step 3: The simplified expression is now 14. However, since there is no variable present, there is no need to isolate any variable.

This means that when you subtract 6 from 20, the answer is 14. Remember that isolating a variable and balancing an equation are relevant when dealing with equations that involve variables. In this case, the expression is a simple subtraction operation, yielding a constant value of 14 as the answer.

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Answer:

c

Step-by-step explanation:

assume base 10

-logy = x

\( \frac{1}{ log(y) } = x\)

log base x y = 5 turns into the format x^ 5 = y

implement that to get c

Answer:  C. 5(7x² - 3)

Step-by-step explanation:

Product means multiplication

Difference means subtraction

square means "to the power of 2"

Product of 5 and  _______ -->     5(__)

Difference of 7 ... and 3   -->  7... - 3

7 times the square of x  --->  7x²

Put it together to get: 5(7x^2 - 3)

Answer:

D is the correct answer

Step-by-step explanation:

I got it right

Answer:

tbh im dumb so

Step-by-step explanation:

-2x – (-6x) + 4 = 3x – (-2) +1-(-3)

= -2x + 6x + 4 = 3x + 2 + 1 + 3

= -2x + 6x - 3x = 2 + 1 + 3 - 4

= 4x - 3x = 3 - 1

= x = 2 ANSWER

HOPE THIS HELPS :)

Answer: y=-7

Step-by-step explanation:

Answer: y=-7

Step-by-step explanation:

Answer:

  -8/3

Step-by-step explanation:

You want the slope of the line shown in the graph.

Whether counting grid squares on the graph, or using the slope formula, it is convenient to choose two points on the grid where the line crosses the intersection of grid lines.

It appears, the line passes through grid points (1, 4) and (4, -4). Using the slope formula, we find the slope of the line to be ...

  m = (y2 -y1)/(x2 -x1)

  m = (-4 -4)/(4 -1) = -8/3

The slope of the line is -8/3.

The slope is the ratio of "rise" to "run" for the line. From the two points we see where the line crosses grid intersections, we have a "rise" of -1 from y=4 to y=-4, and a "run" of 3 from x=1 to x=4.

  rise/run = -8/3 = slope of the line

Answer19/40=x/3.6

By cross multiplication

19*3.6=40*x

68.4 =40x

x=68.4/40

x=1.71

x=

Answer: C

Step-by-step explanation:

\(\frac{19}{40} = \frac{x}{3.6}\)     solve by cross product

40x = 68.4   Divide both sides by 40

x =  1.71

The solution of the equation 4x - 3  = 5 is not extraneous .

Extraneous solutions are values that we get when solving equations that aren't really solutions to the equation.

Therefore, let's solve the equation to know whether it is extraneous solution.

Hence,

4x - 3  = 5

add 3 to both sides of the equation

4x - 3 + 3 = 5 + 3

4x = 8

divide both sides of the equation by 4

4x / 4 = 8 / 4

x = 2

Therefore, it is not extraneous solution.

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Answer:

  a.  gradient: 2/7

  b.  y -5 = 2/7(x +3)

Step-by-step explanation:

The gradient of the line is found from the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (7 -5)/(4 -(-3)) = 2/7 . . . gradient of line AB

__

The equation of the line can be written in point-slope form as ...

  y -k = m(x -h) . . . . . . line with gradient m through point (h, k)

Using point 'a' and the above gradient in the equation, the line is described by ...

  y -5 = 2/7(x +3) . . . equation of AB

_____

Additional comment

The equation of the line can be written in several other forms. Eliminating parentheses and adding 5, we get slope-intercept form:

  y = 2/7x +5 6/7

This can be rearranged to standard form

  2x -7y = -41

Dividing by -41 puts the equation in intercept form:

  x/(-41/2) +y/(41/7) = 1

Then your values of m and n are seen to be -41/2 and 41/7, respectively. These are highlighted on the attached graph.

Answer:

19

Step-by-step explanation:

g(x) = x^2 – 2x + 11

Let x=-2

g(-2) = (-2)^2 – 2(-2) + 11

Powers first

         =4 -2(-2) +11

Then multiply

        = 4 +4 +11

Now add

     = 19

The missing reasons for each of the given statements are respectively;

1) Substitution

2) Definition of a Straight angle because a straight angle is 180°.

3) Congruent Angles have equal measures

We are given that;

m∠1 = 90°

m∠1 + m∠2 = m∠5

∠3 ≅ ∠4

Statement 1; 90° + m∠2 + m∠4 = 180°

Reason 1; Substitution

Statement 2; m∠1 + m∠2 + m∠3 = 180°

Reason 2; Definition of a Straight angle because a straight angle is 180°.

Statement 3; m∠3 = m∠4

Reason 3; Congruent Angles have equal measures

Thus, the missing reasons for each of the given statements are respectively;

1) Substitution

2) Definition of a Straight angle because a straight angle is 180°.

3) Congruent Angles have equal measures

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Answer: 6,987,000 pounds fo CO₂ per kWh.

Step-by-step explanation: Quilowatt-hour (kWh) is a unit of energy that measures the amount of energy expended in 1 hour.

The AC uses 850 Watts, which in kW is 850,000 kW

If you leave the AC on for 6 hours, it will consume

850,000(6) = 5,100,000 kWh

Eletricity produces 1.37 pounds of CO₂ per kWh, then in 5,100,000 kWh:

1.37 \(\frac{pounds}{kWh}\).(5,100,000kWh) = 6,987,000 pounds

If you open a window for 6 hours, you would keep 6,987,000 pounds of CO₂ for entering the atmosphere.

To find the number of dimes and quarters, you have 17 dimes and 34 quarters in your pocket , when there are 51 coins in your pocket.

To solve this problem, we can set up a system of equations using the given information. Let's use "d" to represent the number of dimes and "q" to represent the number of quarters.

We know that there are 51 coins in total, so we can write the equation: d + q = 51.

We also know that the total value of the coins is $10.20, which can be expressed as 10d + 25q (since dimes are worth 10 cents and quarters are worth 25 cents). So our second equation is: 10d + 25q = 1020.

To solve this system of equations, we can use substitution or elimination. Let's use substitution:

Rearrange the first equation to solve for d: d = 51 - q.

Substitute this expression for d in the second equation: 10(51 - q) + 25q = 1020.

Simplify and solve for q: 510 - 10q + 25q = 1020.

Combine like terms: 15q = 510.

Divide both sides by 15: q = 34.

Now substitute this value back into the first equation to solve for d: d + 34 = 51.

Subtract 34 from both sides: d = 17.

Therefore, you have 17 dimes and 34 quarters.

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Answer:

4,050 cubic feet

Step-by-step explanation:

The figure is made up of a square pyramid and cube

Therefore:

Volume of the figure = volume of the square pyramid + volume of the cube

✔️Volume of the square pyramid = ⅓*a²h

a = 15 ft

h = 9 ft

Volume of square pyramid = ⅓*15²*9 = 675 ft³

✔️Volume of the cube = s³

s = 15 ft

Volume of the cube = 15³ = 3,375 ft³

✔️Volume of the figure = 675 + 3,375 = 4,050 cubic feet

The answer will be as follows after answering the supplied question equation (8/15)x = (8/15)(34.29) 18.29 books Vineyard Middle School

A math equation is a process that relates two statements by using the equals sign (=) to indicate equivalence. In algebra, an equation is a mathematical statement that shows the equivalence of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on opposite sides of a letter. Frequently, the logo and the software are the same. For example, 2x - 4 = 2.

Let's tackle this problem with algebra.

Let's call the total number of books contributed "x".

According to the issue, Creative Minds Bookstore donated two-fifths of the books to Sunshine Elementary. Sunshine Elementary received (2/5)x books as a result.

That leaves (3/5)x books to be donated to other schools and libraries.

That leaves (7/15)x books available for donation to the library.

Given that the library acquired 16 books, we may conclude:

(7/15)x = 16

Calculating x:

x = (16)(15/7) = 34.29 (rounded to two decimal places) (rounded to two decimal places)

(2/5)x = (2/5)(34.29) 13.72 books at Sunshine Elementary

(1/5)x = (1/5)(34.29) 6.86 books at Lincoln Elementary

(8/15)x = (8/15)(34.29) 18.29 books Vineyard Middle School

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The actual distance represented by 23.7 cm on the map is 355.5 km.

To find the ratio of the amount of money Mabaso has to the amount of money Thabo has and the amount of money Ally has, we can divide each amount by the smallest amount (which is R35) to simplify the ratio.

Mabaso has R140, Thabo has R70, and Ally has R35.

The ratio of Mabaso's money to Thabo's money is:

R140 ÷ R35 = 4

The ratio of Mabaso's money to Ally's money is:

R140 ÷ R35 = 4

Therefore, the ratio of the amount of money Mabaso has to the amount of money Thabo has and to the amount of money Ally has is 4:1:1.

To calculate the percentage discount of a steel table, we need to find the difference between the original price and the discounted price, and then divide it by the original price. Finally, we multiply the result by 100 to get the percentage.

Original price: R750

Discounted price: R600

Discount: R750 - R600 = R150

Percentage discount: (R150 ÷ R750) × 100 = 20%

So, the table has a 20% discount on Black Friday.

To convert 125 grams to kilograms, we divide the amount in grams by 1,000 (since there are 1,000 grams in a kilogram).

125 g ÷ 1,000 = 0.125 kg

Therefore, 125 grams is equal to 0.125 kilograms.

If a green grocer packs 12 apples in a plastic bag and has 285 apples, we divide the total number of apples by the number of apples per bag to determine the number of bags needed.

Number of bags needed: 285 apples ÷ 12 apples/bag = 23.75 bags

Since we can't have a fraction of a bag, we round up to the nearest whole number. Therefore, the green grocer would need 24 bags.

If the scale of a map is 1,500,000 and the measurement on the map is 23.7 cm, we can use the scale to determine the actual distance.

1 cm on the map represents 1,500,000 cm in reality.

23.7 cm on the map represents x cm in reality.

x = 23.7 cm × 1,500,000 cm = 35,550,000 cm

To convert cm to km, we divide by 100,000 (since there are 100,000 cm in a kilometer).

35,550,000 cm ÷ 100,000 = 355.5 km

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