From the top of a 100 foot high pole, an observer measures the angle of depression of a car on the road as 28 degrees. Find, to the nearest hundredth of a foot, the distance from the car to the base of the pole.

Answer:

15.85%

Step-by-step explanation:

Given:

Acres damaged (burned) = 6,500 acres

Acres in total forest = 41,000 acres

Hence the amount of damaged forest as a fraction of the total forest,

= [tex]\frac{6500}{41000}[/tex] = [tex]\frac{13}{82}[/tex]

expressed as percentage = [tex]\frac{13}{82}[/tex] x 100% = 15.85%

Answer:

Answer:

The radius of the polygon is 8.28 cm

Step-by-step explanation:

See the attached document

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

y = mx + b

m - slope

b - y-intercept

We have the slope m = 5 and the point (1, -6). Put them to te equation:

-6 = 5(1) + b

-6 = 5 + b      subtract 5 from both sides

-11 = b

Finally we have the equation of a line:

y = 5x - 11

Answer:

Range = (-∞,0) U (0,∞)

Step-by-step explanation:

The given function is:

f(x) = (x-1)²/x³-2x²+x

We can reduce the denominator:

= (x-1)²/x(x²-2x+1)

we know that a²-2ab+b² = (a-b)²

= (x-1)²/x(x-1)²

= 1/x

The function 1/x is undefined for x = 0.

Hence, its domain lies in (-∞,0) U (0,∞).

Hence x can either be less than or greater than zero.

The function f(x) is greater than zero when x<0.

The function f(x) is less than zero when x>0.

There is no way the function can be zero because the numerator is constant.

Hence the domain of the function lies in the interval:

(-∞,0) U (0,∞)

Answer:

B. x=0,2

Step-by-step explanation:

(x+4)      1

-------- = -----

6x          x

Using cross products

x * (x+4) = 1*6x

Distribute

x^2 +4x = 6x

Subtract 6x from each side

x^2 +4x-6x = 6x-6x

x^2 -2x = 0

Factor out an x

x (x-2) = 0

Using the zero product property

x=0  x-2 =0

x=0  x-2+2 =0+2

x =0   x=2

Answer:

Option C is correct.

Step-by-step explanation:

We need to solve the equation below and find value of x

[tex]\frac{x+4}{6x} =\frac{1}{x}[/tex]

Cross multiply

x(x+4)=6x

x^2+4x=6x

x^2+4x-6x=0

x^2-2x=0

Taking x common

x(x-2)=0

x=0 and x-2 =0

x=0 and x= 2

Verify solutions

putting x=0

x+4/6(0) = 1/0

the solution is undefined.

Putting x = -2

2+4/6(2) = 1/2

2+4/12 = 1/2

6/12=1/2

1/2=1/2

the solution is defined.

The solutions is x=2 as for x=0 the solution is undefined.

So, Option C is correct.

Answer:

2

Step-by-step explanation:

Factors of |6| factors of 8

, , , , , , , , , 1×8

2×4

1×6

2×3

The greatest common factor is 2.

The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share. For example, 12, 20, and 24 have two common factors: 2 and 4. The largest is 4, so we say that the GCF of 12, 20, and 24 is 4. GCF is often used to find common denominators.

Given numbers:

6 and 8

Now to calculate the greatest common factor we have to

6=2*3

4=2*4

Hence, the only common factor is  2.

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Your question asks which pair represents the y-intercept in the equation.

To find the answer in your question, we are going to need to find the key terms in the question.

Key terms:

y-intercept

y = -5x + 6

With the information above, we can find the answer.

We know that the equation is similar to the equation: y= mx + b

We need to find what the y-intercept is in the equation.

When you look at the equation, y = -5x + 6, you would know that the y intercept would be the last number (6). Therefore, 6 would be our y intercept.

But, we need to get the number 6 in the right ordered pair.

An ordered pair is represented as (x,y).

So, we would plug in the 6 in the y spot, since it's the y-intercept. We would plug in 0 to x, since we're only focusing on the y-axis, any number on this would not allow the ordered pair to be on the y-axis.

This means that your ordered pair should be (0,6).

C). (0,6) should be your FINAL answer

The y-intercept of the equation y = -5x + 6, is represented by the ordered pair (0,6). This is established by substituting x=0 in the equation, which results in y = 6. Hence, the line intersects the y-axis at this point on a graph.

In the equation y = -5x + 6, the y-intercept is the value of y when x equals zero. This can be determined by substituting x=0 into the equation. So, let's do this:

Substitute x = 0 into the equation, we get: y = -5*(0) + 6, which simplifies to y = 6. Therefore, the y-intercept is 6, and in an ordered pair it is represented as (0,6).

So, the correct answer is option C: (0,6). This is the point where the line crosses the y-axis on a graph.

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Answer:

f(x) +g(x)  = -1.3 - 1.75x

Step-by-step explanation:

f(x) +g(x) is simply obtained by adding the two given functions, f(x) and g(x). We are given that;

F(x)= 3.7-2x and g(x)= 0.25x-5

f(x) +g(x)  = 3.7-2x + (0.25x-5)

f(x) +g(x)  = 3.7 -5 + 0.25x - 2x

f(x) +g(x)  = -1.3 - 1.75x

Answer:

f(x) +g(x)  = -1.3 - 1.75x

Step-by-step explanation:

Answer:

The correct answer option is 'orthocenter'.

Step-by-step explanation:

The point of concurrency of the altitudes of a triangle is called the 'orthocenter'.

Orthocenter is the point in a triangle where all of the three altitudes of the triangle intersect each other.

Explaining further, a line which is perpendicular to the opposite side and passes from a vertex of a triangle is called the altitude of the triangle.

Therefore, the correct option is D. orthocenter.

Answer:  2.0 seconds & 2.75 seconds

Step-by-step explanation:

[tex]d=\dfrac{s\times r}{3.6}\quad where;\\\\\bullet d=\text{reaction distance (in meters)}\\\bullet s=\text{speed (in km/hr)}\\\bullet r=\text{reaction time (in seconds)}\\\bullet 3.6=\text{needed to convert km/hr into meters/second}\\\\\\\large{\text{When d=20m and s=36}}\\\\20=\dfrac{36}{3.6}\times r\\\\20=10r\\\\\large{\boxed{2=r}}\\\\\\\text{When d=41.25m and s=54}\\\\41.25=\dfrac{54}{3.6}\times r\\\\41.25=15r\\\\\large\boxed{2.75=r}[/tex]

Answer:

10. 65 = x

9. 8 = x

8. 63 = x [it gave you the answer]

7. 0 = x

6. -5 = x

Step-by-step explanation:

#6 uses the Associative Property of Multiplication. #7 uses the Zero Product Property of Multiplication. #8 gave you the answer because x = 1x. For #9, you have to multiply ⅛ by its multiplicative inverse [reciprocal (8)] to get 1. #10 uses the Commutative Property of Multiplication.

**Associative and Commutative are the same thing, EXCEPT Commutative does NOT use grouping symbols. Associative does.

Answer:

its y is less than -7

Step-by-step explanation:

Answer:

y > -7

Step-by-step explanation:

multiply both sides by -1, remember to reverse the inequality when multiplying (or dividing by -1 on both sides

Hence:

-y (-1) >  7(-1) -----> remember to reverse inequality

y > -7 (answer)

Answer:

The solution of the given equation is (5/2, 1/3)

Step-by-step explanation:

It is given an equation,

(2x - 5)(3x - 1) = 0

To find the solution of given equation

(2x - 5)(3x - 1) = 0 means that,

either (2x - 5) = 0 or (3x - 1) = 0

If 2x - 5 = 0

2x = 5

x = 5/2

or 3x - 1 = 0

3x = 3

x = 1/3

Therefore the solution of the given equation is (5/2, 1/3)

ANSWER

[tex]\: x =2 \frac{1}{2} \: or \: x = \frac{1}{3} [/tex]

EXPLANATION

The equation is given in the factored form as:

[tex](2x - 5)(3x - 1) = 0[/tex]

According to zero product principle

[tex]either \: \: (2x - 5) = 0 \: or \: (3x - 1) = 0[/tex]

This implies that,

[tex]either \: \: 2x = 5 \: or \: 3x = 1[/tex]

We divide the first equation by 2 and the second by 3

[tex]either \: \: x = \frac{5}{2} \: or \: x = \frac{1}{3} [/tex]

The solutions are

[tex]\: x =2 \frac{1}{2} \: or \: x = \frac{1}{3} [/tex]

The inverse function is: [tex]\[ y = \ln(x + 4) - 3 \][/tex]

To find the inverse of the function [tex]\( y = e^{x+3} - 4 \)[/tex], we'll first swap the roles of x and y and then solve for y.

1. Start with the original function:

[tex]\[ y = e^{x+3} - 4 \][/tex]

2. Swap x and y:

 [tex]\[ x = e^{y+3} - 4 \][/tex]

3. Solve for y:

[tex]\[ x + 4 = e^{y+3} \] \[ e^{y+3} = x + 4 \][/tex]

4. Take the natural logarithm (ln) of both sides to isolate y:

[tex]\[ \ln(e^{y+3}) = \ln(x + 4) \][/tex]

[tex]\[ y + 3 = \ln(x + 4) \][/tex]

5. Subtract 3 from both sides:

[tex]\[ y = \ln(x + 4) - 3 \][/tex]

Complete question: Find the Inverse y=e^(x+3)-4

Step-by-step answer:

The answer is circled in red on the output of the calculator, attached.  This is how we need to look for when we use a graphing calculator, which says

"linear regression, y=5.10x+9.12"

However, we need to check the answer by looking at least one point on the curve.  Say we use the point (10,60) on the straight line, and compare with y(10) = 5.10*10+9.12 = 60.12, quite close to 60.  The other answer options all give numbers far away from 60 when x=10.

Answer:

The correct option is 2.

Step-by-step explanation:

The given data is

x               y

5              36

9              64

12            72

18            96

26           141

35           189

The general form of regression line is

[tex]y\approx ax+b[/tex]

From the given picture of graphing calculator, it is clear that the equation of regression line is

[tex]y\approx 5.098x+9.118[/tex]

Approx the value of a and b upto tenth.

[tex]y\approx 5.10x+9.12[/tex]

The equation of the line of best fit is y ≈ 5.10x+9.12. Therefore the correct option is 2.

Answer:

y = mx + 5; m < 0

Step-by-step explanation:

The question mentions that the slope of the line is negative and the y-intercept is 5. The general form of the straight line is given by y = mx + c. Since "c" in the equation is the y-intercept, therefore, c = 5. This means that all the straight lines passing from the point (0,5) can be expressed in a general form y = mx + 5. However, the question mentions that the slope is negative and demands the general equation of all the negatively-sloped straight lines passing from (0,5). Therefore, for the condition to be met, m has to be negative. So the correct answer is y = mx + 5, where m is negative.

Answer:

C. 11, 1

Step-by-step explanation:

Plug in your given x-values, then take the absolute values [ALWAYS POSITIVE] of each.

Answer:

D

Step-by-step explanation:

Option A, does 6 and 2 added makes 8? Yes

does 6 and 2 subtracted makes 2? No

Option B, does 6 and 4 added makes 8? No

does 6 and 4 subtracted gives 2? Yes

Option C, does 4 and 4 added gives 8? Yes

does 4 and 4 subtracted gives 2? No

Option D

Does 5 and 3 added give 8? Yes

Does 5 and 3 subtracted give 2? Yes

So we can see, Option D is the correct answer because it satisfies both conditions.

The probability of a student chosen randomly from the class playing basketball or baseball is 0.84.

The probability that a student chosen randomly from the class plays basketball or baseball can be found using the principle of inclusion-exclusion. First, we add the number of students who play basketball (17) and baseball (10) together, which gives us a total of 27 students. However, we have double-counted the 6 students who play both sports, so we subtract that number from the total. Therefore, the number of students who play basketball or baseball is 27 - 6 = 21. The probability is then calculated by dividing the number of students who play basketball or baseball by the total number of students in the class: 21/25 = 0.84.

Answer:

B. (5x - 7)(x+9)

Step-by-step explanation:

5x(x + 9) - 7(x + 9

Factor out the quantity (x+9)

(x+9) (5x-7)

Rearrange the order

(5x - 7)(x+9)

Final answer:

The expression 5x(x + 9) - 7(x + 9) is factored by finding the common term (x + 9) and factoring it out, resulting in the complete factored form (5x - 7)(x + 9), which is Option B.

Explanation:

The expression given is 5x(x + 9) - 7(x + 9). To factor this expression, we look for a common factor in both terms. Here, the common factor is (x + 9). We can use the distributive property, also known as factoring by grouping, to factor out the common factor. Applying this, we get:

(x + 9) is the common factor, so we pull it out in front: (x + 9)(5x - 7).

Thus, the expression in complete factored form is Option B: (5x - 7)(x + 9).

Let's say BB' = a

2^2 + 1^2 = a^2

4 + 1 = a^2

a^2 = 5

a = √5

So the distance of BB' is √5

The distance of BB' is √5.

Learn how to apply the Pythagorean theorem to find the distance between two points using the distance formula. The Pythagorean theorem can be rewritten as d=(((x₂-x ₁)²+(y ₂-y ₁)²) to calculate the separation between any two locations.

Let's say BB' = a

2² + 1² = a²

4 + 1 = a²

a² = 5

a = √5

So the distance of BB' is √5

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Answer:

(x + 5)^2

Step-by-step explanation:

Learn to recognize perfect squares.  x^2+ 10x + 25 is a perfect square of a binomial:  x^2+ 10x + 25 = (x + 5)^2.

The polynomial expression of the equation [tex]x^2+ 10x + 25[/tex] is  [tex]&(x+5)^{2}[/tex].

A polynomial exists defined as an expression that exists composed of variables, constants, and exponents, that are connected utilizing mathematical operations such as addition, subtraction, multiplication, and division (No division operation by a variable).

Given expression [tex]x^2+ 10x + 25[/tex]

Rewrite in the form of [tex]$a^{2}+2 a b+b^{2}$[/tex] :

[tex]$25=5^{2}$[/tex]

[tex]$10 x=2 x \cdot 5$[/tex]

[tex]$$=x^{2}+2 x \cdot 5+5^{2}$$[/tex]

Apply Perfect Square Formula:

The perfect square formula exists described in the formation of two terms such as [tex](a + b)^{2}[/tex]. The expansion of the perfect square formula exists represented as[tex](a + b)^{2} = a^{2} + 2ab + b^{2}[/tex]

[tex]$\quad a^{2}+2 a b+b^{2}=(a+b)^{2}[/tex]

[tex]&x^{2}+2 x \cdot 5+5^{2}=(x+5)^{2} \\[/tex]

[tex]&=(x+5)^{2}[/tex]

The polynomial expression of the equation [tex]x^2+ 10x + 25[/tex] is  [tex]&(x+5)^{2}[/tex].

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Answer:

An exterior angle is supplementary to the adjacent interior angle.

Step-by-step explanation:

An exterior angle of a triangle and its adjacent interior angle form a linear pair. This means they form a straight line, and a straight line has a measure of 180°. Since they combine for a total of 180°, this means they are supplementary.

Option A (y=-2x-3) is the answer.

Step-by-step explanation:

First, you need to multiply the -2 by what is in the parentheses, in order to expand the equation. -2*x is -2x, and -2*4 is -8. This leaves you with -2x-8 on the right side of the equation.

Next, you need to isolate y on the left side of the equation. You can do this by subtracting -5 from both sides. Subtracting a negative causes it to become positive, so you are really just adding 5 to both sides.

This makes it so the y is now alone, and the right side has -2x-8+5. We add together the -8 and 5 to leave us with -3.

This makes the answer y=-2x-3.

Answer:The answer is A. You have to solve for Y .

Step-by-step explanation:

Answer:

y = -⅘x - 4

Step-by-step explanation:

. So your point is an x-intercept. It happens at times. Alright. Now, we have to know that parallel lines have SIMILAR RATE OF CHANGES [SLOPES], so we keep the -⅘. Moving forward, we simply plug the coordinate into the Slope-Intercept Formula, y = mx + b --> 0 = -⅘[-5] + b. From this, we can see that our y-intercept is [0, -4], so our parallel line is y = -⅘x - 4. Do you understand?

Answer:

y = mnp/(m + n)

Step-by-step explanation:

I assume that both capital y and small case y are meant to be the same variable. If not, let me know, and I'll solve it again for small case y.

y/m + y/n = p

Factor y out on the left side.

y(1/m + 1/n) = p

y = p/(1/m + 1/n)

Multiply the right side by (mn)/(mn).

y = pmn/[(1/m + 1/n)mn]

y = pmn/(n + m)

y = mnp/(m + n)

Solve for y:

y/m + y/n = p

yn + ym = pmn

y = pmn / n + m

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Answer:

C

Step-by-step explanation:

The equation of a line is given by

and

slope (m) is given by:

Where (x_1,y_1) are the first set of point in the line and (x_2,y_2) is the second set of point

Let's take 2 points arbitrarily. (0,0) & (25,20)

Let's plug it and find the equation:

Now

C is the correct answer.

The correct option is  (A)0.8x.

                                     slope m = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

the two points are [tex](x_{1} ,y_{1} ) & (x_{2} ,y_{2} )[/tex].

so,  lets take two points (0,0) & (25,20)

lets put the value in equation,

   m = [tex]\frac{20 -0}{25-0} = 0.8\\now \\ y - y_{1} = m(x - x_{1}) \\\\[/tex]

      y - 0 = 0.8 (x-0)

       y = 0.8x

Therefore, the correct option is  (A)0.8x.

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Answer:

Step-by-step explanation:

1250 feet *12 inches per foot : 25 inches

15000 inches : 25 inches

Scale = 600:1 in other words 600 inches of the building represents 1 inch of the model.

If you want the scale to be feet  of building per inch of the model, then don't multiply by 12

1250 feet : 25 inches

25 feet of building: 1 inch of the model.

Answer:

The scale is 1:600

Step-by-step explanation:

To calculate the scale you have to divide the two values of height for this case, but in the same units. So 1250 feet is equal to 15000 inches. Dividing 15000 by 25 is equal to 600, that is the scale. 1:600.

Answer:

depreciation is $3,333.33 per year

Step-by-step explanation:

Initially : date = 2006, worth = $34,500

Finally : date = 2009, worth = $24,500

if we let x = date and y = worth, we end up with two points (coordinates) on the x-y graph

i.e

Initial = Point 1 (2006, 34500)

Final = Point 2 (2009, 24500)

The rate of change is simply the slope, m of the line joining these two points

given by:

m = (34500 - 24500) / (2006-2009)

= 10000 / -3

= -3,333.33

hence the annual rate of depreciation is $3,333.33 per year

Final answer:

The boat's value depreciated by $10,000 over 3 years, resulting in an annual depreciation rate of $3,333.33.

Explanation:

The student's question involves calculating the annual rate of change of the value of a boat from the year it was bought (2006) to the year 2009. To find the rate of change, we need to determine how much the value of the boat depreciated over the given time period and then divide it by the number of years.

The boat depreciated from $34,500 in 2006 to $24,500 in 2009, which is a decrease of $34,500 - $24,500 = $10,000 over the course of 3 years. To find the annual depreciation rate, we divide the total depreciation amount by the number of years: $10,000 ÷ 3 years = $3,333.33 per year. Therefore, the annual rate of depreciation is $3,333.33 per year, rounded to the nearest hundredth if necessary.

Answer:

93 Is the square root