A ramp goes from a doorway of a building to the ground. The end of the ramp connected to the doorway is 1 foot above the ground. The distance along the ramp to the building is 5 feet. What is the angle of elevation of the ramp to the nearest degree?
A. 11°
B. 0°
C. 12°
D. 1°

Answer:

m = 20.2; n = 10.4

Step-by-step explanation:

\(\left \bigg \{ { \big {3m + n = 71} \atop \big {2m - n = 30}} \right.; => \left \bigg \{ { \big {3m + n -3m= 71-3m} \atop \big {2m - n-2m = 30-2m}} \right.; => \left \bigg \{ { \big { n = 71-3m} \atop \big { - n = 30-2m}} \right. ; => \\\\=> \left \bigg \{ { \big { n = 71-3m} \atop \big { - n \times (-1) = (30-2m)\times (-1)}} \right.; =>\left \bigg \{ { \big { n = 71-3m} \atop \big { n = -30+2m}} \right..\)

-30 + 2m = 71 - 3m

-30 + 2m + 30 = 71 - 3m + 30

2m = 101 - 3m

2m + 3m = 101 - 3m + 3m

5m = 101

5m ÷ 5 = 101 ÷ 5

m = 20.2

n = 71 - 3m = 71 - 3 × 20.2 = 10.4

Answer:

x = ± 6

Step-by-step explanation:

1: Subtract both sides by -54

\(-1.5x^2=-54\)

2: Divide both sides by -1.5

\(x^2=36\)

3: Take both sides to the 1/2 power

\(x= 6, -6\)

Answer:

its 11

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

The reduced model and complete are the two models that can be used to determine test the hypothesis. The best way to determine which model fits the data set is to determine the F-test. The Full model is unrestricted model whereas reduced model is restricted model. F-test determines which model to choose for hypothesis testing for better and accurate results.

Answer:

x = -4, 7

Step-by-step explanation:

We are given the graph of the function f(x), and we want to find the values that make the statement f(x) = 0.

f(x) = 0 means that there are certain values that make the value of f(x) (which can be considered as y) equal to 0.

We can look to the graph to help us - we should look at where y is equal to 0, which is the x-axis.

On the x-axis, we can see that the function passes through both -4 and 7 (the graph goes up by 1) on that line.

This means that when either -4 or 7 are substituted into the function (i.e. when they are equal to x), they will make the function equal 0.

So,  it means that x = -4, 7.

Answer:

B. SAS

Step-by-step explanation:

Two sides of ∆DEF (DE and DF) are proportional to two corresponding sides of ∆ABC (AB and AC), and also their included angles (<D and <A) are equal to each other.

Therefore, based on the SAS criterion, both triangles are proven to be similar to each other.

Both triangles satisfy the SAD Criterion, and hence, they can be proven to be similar to each other.

Answer:

UH

Step-by-step explanation:

25

Answer:

23/28   (82.1%)

Step-by-step explanation:

See attached Venn Diagram

23 out of 28  play basketball or baseball

The chocolate bar costs 9 cents. The little girl is missing 10 cents and the little boy is missing 1 cent, so together they are missing 11 cents.

Cost is a monetary measure of the amount of resources, such as time or money, that must be expended to produce a product or service. It is a fundamental factor of economic production, as it is necessary to make products and services available to consumers. Cost can be determined in a variety of ways and can be linked to economic theory through the concept of opportunity cost. In business, cost is a major factor in decisions related to production, pricing, and marketing. Cost is also a factor in accounting and budgeting, as it is necessary to track and report the costs of organizational operations.

The chocolate bar costs 9 cents. The little girl is missing 10 cents and the little boy is missing 1 cent, so together they are missing 11 cents. If the chocolate bar cost 9 cents, that would leave 1 cent for them to split.

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Answer:

3m+20>35

Explanation

m stands for months 3 every m

+ the 20 he starts with will be grater than >35

Answer:

Step-by-step explanation:

Here is a more detailed explanation:

We are given two linear functions, f(x) and g(x), and their values for x = 1 and x = 4:

x   f(x)   g(x)

1    3      5

4    9      20

To find the value of a + b at the point of intersection (a, b) of the two functions, we need to first find the equations of the two functions. To do this, we need to find the slope and y-intercept of each function.

For f(x), the slope is (9 - 3) / (4 - 1) = 2, and using the point (1, 3) we can find the y-intercept as:

y - 3 = 2(x - 1)

y - 3 = 2x - 2

y = 2x + 1

So the equation of f(x) is y = 2x + 1.

Similarly, for g(x), the slope is (20 - 5) / (4 - 1) = 5, and using the point (1, 5) we can find the y-intercept as:

y - 5 = 5(x - 1)

y - 5 = 5x - 5

y = 5x

So the equation of g(x) is y = 5x.

To find the point of intersection of the two functions, we can set their equations equal to each other and solve for x:

2x + 1 = 5x

3x = 1

x = 1/3

Substituting this value of x back into either equation, we can find the corresponding value of y:

y = 2(1/3) + 1 = 7/3

So the point of intersection is (1/3, 7/3).

Therefore, a + b = 1/3 + 7/3 = 8/3. This is approximately equal to 2.67. The answer closest to this value is -1, so the correct answer is (b) -1.

Answer:

\(Area = x^2- 25\)

\(Area =9x^2 +24x + 16\)

\(Length = (3x -2)\)

\(Speed = \left(y^2-3y+1\right)\)

\(Product = 3m^3 + 6m^2 - 6m\)

Step-by-step explanation:

Solving (1):

\(Length = (x + 5)\)

\(Width = (x - 5)\)

Required

Calculate Area

\(Area = Length * Width\)

\(Area = (x + 5) * (x - 5)\)

\(Area = x^2 + 5x - 5x - 25\)

\(Area = x^2- 25\)

Solving (2):

Given

\(Length = (3x + 4)\)

Required: Calculate Area

\(Area =Length * Length\)

\(Area =(3x + 4) * (3x + 4)\)

\(Area =9x^2 + 12x + 12x + 16\)

\(Area =9x^2 +24x + 16\)

Solving (3):

\(Area = 3x^2 + 7x - 6\)

\(Width = x + 3\)

Required: Calculate Length

\(Area = Length * Width\)

\(Length = \frac{Area}{Width}\)

\(Length = \frac{3x^2 + 7x - 6}{x + 3}\)

Factorize the numerator

\(Length = \frac{3x^2 + 9x -2x - 6}{x + 3}\)

\(Length = \frac{3x(x + 3) -2(x + 3)}{x + 3}\)

\(Length = \frac{(3x -2) (x + 3)}{x + 3}\)

Divide by x + 3

\(Length = (3x -2)\)

Solving (4):

\(Distance = (2y^3 - 7y^2 + 5y -1)\)

\(Time = 2y - 1\)

Required: Determine the average speed

This is calculated as:

\(Speed = \frac{Distance}{Time}\)

\(Speed = \frac{2y^3 - 7y^2 + 5y -1}{2y - 1}\)

Factorize the numerator

\(Speed = \frac{\left(2y-1\right)\left(y^2-3y+1\right)}{2y - 1}\)

\(Speed = \left(y^2-3y+1\right)\)

Solving (5):

Multiply \((m^2 + 2m - 2)\) by sum of \((m + 3)\) and \((2m - 3)\)

First, calculate the sum:

\(Sum = m + 3 + 2m - 3\)

\(Sum = m + 2m+3 - 3\)

\(Sum = 3m\)

Then, the product

\(Product = (m^2 + 2m - 2)(3m)\)

\(Product = 3m^3 + 6m^2 - 6m\)

Answer:

Step-by-step explanation:

Solving (1):

Required

Calculate Area

Solving (2):

Given

Required: Calculate Area

Solving (3):

Required: Calculate Length

Factorize the numerator

Divide by x + 3

Solving (4):

Required: Determine the average speed

This is calculated as:

Factorize the numerator

Solving (5):

Multiply  by sum of  and  

First, calculate the sum:

Then, the product

Answer:

38.8

Step-by-step explanation:

Because 6 is 5 and higher so it rounds up

Answer:

38.8

Step-by-step explanation:

in 38.765 the number 7 is in the tenths place so you if the number to the right of it is 5or bigger you turn the 7 into an 8

Step-by-step explanation:

150 is base pay

5 is pay per shoe

The distance between the two ship based on the angle of depression is 42 meters.

The distance of each ship can be calculated thus:

TanX = opposite / Adjacent

The first ship:

Tan53 = distance/ 82

distance= 108.82 meters

The second ship:

Tan39 = distance/ 82

distance= 66.40 meters

The Difference between the ships are :

Therefore, the distance between the two ships is 42 meters.

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Answer:

0.30

Step-by-step explanation:

Probability of stopping at first signal = 0.36 ;

P(stop 1) = P(x) = 0.36

Probability of stopping at second signal = 0.54;

P(stop 2) = P(y) = 0.54

Probability of stopping at atleast one of the two signals:

P(x U y) = 0.6

Stopping at both signals :

P(xny) = p(x) + p(y) - p(xUy)

P(xny) = 0.36 + 0.54 - 0.6

P(xny) = 0.3

Stopping at x but not y

P(x n y') = P(x) - P(xny) = 0.36 - 0.3 = 0.06

Stopping at y but not x

P(y n x') = P(y) - P(xny) = 0.54 - 0.3 = 0.24

Probability of stopping at exactly 1 signal :

P(x n y') or P(y n x') = 0.06 + 0.24 = 0.30

Both angle K and angle L must be acute angles, measuring less than 90 degrees, in order to satisfy the conditions of the given triangle.

In triangle JKL, if angle J is less than 90 degrees, then angle K and angle L are both acute angles.

An acute angle is defined as an angle that measures less than 90 degrees. Since angle J is given to be less than 90 degrees, it is an acute angle.

In a triangle, the sum of the interior angles is always 180 degrees. Therefore, if angle J is less than 90 degrees, the sum of angles K and L must be greater than 90 degrees in order to satisfy the condition that the angles of a triangle add up to 180 degrees.

Hence, both angle K and angle L must be acute angles, measuring less than 90 degrees, in order to satisfy the conditions of the given triangle.

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Answer:

Step-by-step explanation:

the degree of a polynomial determines 1:1 the number of solutions.

a quadratic equation (degree 2) has 2 solutions.

the general solution is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = -4

b = -4

c = -1

so,

x = (4 ± sqrt((-4)² - 4×-4×-1))/(2×-4)

when we look at the square root

16 - 16

we see that it is 0.

the square root of 0 is 0, and there is no difference between -0 and +0.

so, we get only one (real) solution : 4/-8 = -1/2

but : formally, there are still 2 solutions (as this is a quadratic equation). they are just identical.

so, I am not sure what your teacher wants to see in this case as answer.

my answer would be 2 real identical solutions. did this help?

The angles of the triangle are 125 degrees, 20 degrees, and 35 degrees.

A triangle is a closed geometric shape with three sides, three angles, and three line segments. Three non-collinear points are joined by line segments to create the simplest polygon, which has three non-collinear points.

Triangles can be categorized according to the size of their sides and angles. Triangles can be categorized as equilateral (all sides are equal in length), isosceles (both sides are equal in length), or scalene based on their sides (all sides are different in length). Triangles can be categorized as acute (all angles are less than 90 degrees), obtuse (one angle is greater than 90 degrees), or right (one angle is greater than 90 degrees) (one angle is exactly 90 degrees).

In any triangle, the sum of the three interior angles is always 180 degrees. Therefore, we can write:

a + b + c = 180

Substituting the given values, we get:

(6x-1) + 20 + (x+14) = 180

Simplifying and solving for x, we get:

7x + 33 = 180

7x = 147

x = 21

Now that we have the value of x, we can substitute it back into the expressions for the angles to find their values:

angle a = (6x-1) = (6*21-1) = 125 degrees

angle b = 20 degrees

angle c = (x+14) = (21+14) = 35 degrees

Therefore, the angles of the triangle are 125 degrees, 20 degrees, and 35 degrees.

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Note that the Polynomial Expression for to represent the total surface area of the two drums is: 4πrh + 4hr².

A polynomial expression is any expression that consists of variables, constants, and exponents and is combined using mathematical operators such as addition, subtraction, multiplication, and division.

According to the number of terms in the expression, polynomial expressions are classed as monomials, binomials, or trinomials.

Given that the total surface area of one cylinder is:

2πrh + 2πr²,

The total surface area of two drums will therefore be:

(2πrh + 2πr²) * 2

⇒ 4πrh + 4hr²

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Answer: To find A and B such that g(x) = f(x) is bijective, we need to ensure that g(x) satisfies the conditions for a bijective function, namely, that it is both injective and surjective.

To show that g(x) is injective, we need to show that for any distinct x1, x2 in A, g(x1) ≠ g(x2). We can do this by assuming that g(x1) = g(x2) and then showing that it leads to a contradiction.

So, let's assume that g(x1) = g(x2). Then, we have:

f(x1) = f(x2)

x1(x1-1) = x2(x2-1)

x1^2 - x1 = x2^2 - x2

x1^2 - x2^2 - x1 + x2 = 0

(x1 - x2)(x1 + x2 - 1) = 0

Since x1 and x2 are distinct, we must have x1 + x2 = 1.

But this is impossible, since x1 and x2 are both real numbers, and the sum of two real numbers cannot equal 1 unless one of them is complex. Therefore, our assumption that g(x1) = g(x2) must be false, and g(x) is injective.

To show that g(x) is surjective, we need to show that for any y in B, there exists at least one x in A such that g(x) = y. In other words, we need to find an expression for x in terms of y.

So, let's solve the equation f(x) = y for x:

x(x-1) = y

x^2 - x - y = 0

Using the quadratic formula, we get:

x = (1 ± √(1 + 4y))/2

Since we want to define g(x) on R, we need to ensure that the expression under the square root is non-negative. This means that 1 + 4y ≥ 0, or y ≥ -1/4.

Therefore, we can define A = [-1/4, ∞) and B = [0, ∞), and g(x) = f(x) is a bijective function from A to B.

Step-by-step explanation:

\(a = \frac{3}{4} \)

Therefore,

\( {a}^{2} = ( { \frac{3}{4} })^{2} \\ \: \: = \frac{ {3}^{2} }{ {4}^{2} } \\ = \frac{9}{16} \)

Solution:

Given:

\(a = \dfrac{3}{4}\)

Square both sides of the given equation:

\(a = \dfrac{3}{4}\)

\(\rightarrow (a)^{2} = \text{\huge{[}}\dfrac{3}{4}\text{\huge{]}}^{2}\)

Simplify the equation:

\(\rightarrow a^{2} = \text{\huge{[}}\dfrac{3}{4}\text{\huge{]}}\text{\huge{[}}\dfrac{3}{4}\text{\huge{]}}\)

\(\rightarrow a^{2} = \text{\huge{[}}\dfrac{3^{2} }{4^{2} }\text{\huge{]}}\)

\(\rightarrow \boxed{a^{2} =\dfrac{9 }{16 }}\)

Answer:

27,000 feet

Step-by-step explanation:

Let \(x\) be the actual length of the pipeline, in feet.

Set up the following proportion:

\(\displaystyle\\\frac{1}{2,000}=\frac{13.5}{x}\)

Cross-multiplying yields \(x=13.5\cdot 2,000=\boxed{27,000\text{ ft}}\)

Answer:

 26s - 45

Step-by-step explanation:

Where the daily growth factor is 1.15 and the starting height in inches is 7.

a. Given by, the function that calculates the height of the beanstalk in relation to the time since Gregory planted it.

\(f(t) = 7(1.15)^t\)

where the daily growth factor is 1.15 and the starting height in inches is 7.

B). The following ratios can be calculated using the formula from section (a):

f(1)/f(0) = (71.15¹)/(71.15⁰) = 1.15

f(2)/f(1) = (71.15²)/(71.15¹ = 1.15

f(1)/f(1) = (71.15¹)/(71.15¹) = 1

\(f(9.56)/f(8.56) = (71.15^{9.56})/(71.15^{8.56})\) ≈ 1.15

\(f(8.56)/f(8.55) = (71.15^{8.56})/(71.15^{8.55})\) ≈ 1.15

c. For the any value of z, we have:

\(f(z+1)/f(z) = (71.15^{(z+1)})/(71.15^z)\) = 1.15

and

\(f(z)/f(z-1) = (71.15^z)/(71.15^{(z-1)})\) = 1.15

For question 6:

a. As a increases throughout the function's domain, f(z) [Select an answer]

Since the base of the exponential function is less than 1 (0.69 < 1), as x increases, f(x) will approach 0.

b. The 1-unit growth factor of f is

The 1-unit growth factor for f is 0.69, since f(x+1)/f(x) = 0.69.

c. The -unit growth factor of f is

The 1/2-unit growth factor for f is (0.69)¹/₂, since f(x+1/2)/f(x) = (0.69)¹/₂.

d. The 6-unit growth factor of f is

The 6-unit growth factor for f is (0.69)⁶, since f(x+6)/f(x) = (0.69)⁶.

e. The 6-unit percent change of  f is

The 6-unit percent change for f is ((0.69)^6 - 1) * 100%, which is approximately -38.77%.

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Answer:

The range is -2,2,-4

Step-by-step explanation:

hope this helps

Answer:

7 and 1/4

Step-by-step explanation:

Answer:

The answer is 7 1/4 or 29/4

Step-by-step explanation: