A ladder 33.6 feet long reaches to the top of a building when its foot stands 12.6 feet from the
building. How high is the building?

Answer:

A) (1)/(7)

B) 33

Step-by-step explanation:

For (A), the sequence follows in 1 divided by numbers in a consecutive order, therefore after (1)/(6), the next term is (1)/(7)

For(B), the sequence follows in multiples of three but skips one in between

Example: Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36...

In the sequence, 6, 12, 18 and 24 are skipped, meaning that the next number to be skipped is 30, hence 33 is the next number in the sequence.

Because all the numbers in the sequence are odd numbers we can say that the sequence follows in odd consecutive numbers which are multiples of 3.

Answer:

b

Step-by-step explanation:

Answer:

x = 13

Step-by-step explanation:

Add 3x and 4x - 1 together to get 7x-1.  Since the angle on the bottom right is 90 degrees, we can safely assume that the remaining angles add up to 90 degrees.  Add 1 on both sides to get 7x = 91.  Divide 7 on both sides to get 13 as your x value.

To plug in the x value, plug 13 in.  The one on the bottom left should equal to 39 degrees and the one on the top right should equal to 51 degrees.

Conniving these points and connecting them, we get a V- shaped graph that's reflected vertically and shifted 4 units to the left wing.

       To graph the function g( x) = - f( x 4), we need to start with the graph of the function f( x) = | x| and  also apply the given  metamorphoses.  The function f( x) = | x| represents the absolute value function, which is a V- shaped graph symmetric with respect to the y- axis.  

First, we shift the graph of f( x) = | x| horizontally by 4 units to the left by replacing x with( x 4). This results in f( x 4).  Next, we multiply the entire function by-1, which reflects the graph vertically. This gives us- f( x 4).  Combining these  metamorphoses, we've the function g( x) = - f( x 4). To graph g( x), we can  compass a many points and  also draw the graph by connecting them.

Let's start with the original graph of f( x) = | x| and apply the  metamorphoses

For f( x)  x = -3,-2,-1, 0, 1, 2, 3  

f( x) =  3, 2, 1, 0, 1, 2, 3  For

g( x) = - f( x 4)  x = -7,-6,-5,-4,-3,-2,-1  

g( x) = -3,-2,-1, 0,-1,-2,-3

conniving these points and connecting them, we get a V- shaped graph that's reflected vertically and shifted 4 units to the left wing.

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Answer:

  f(x) = 5/6x +21

Step-by-step explanation:

You want the equation of the line with slope 5/6 through point (-18, 6) written using function notation.

Given a slope and a point, it can be useful to write the equation of the line in point-slope form:

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

The line of interest has slope m = 5/6 through point (h, k) = (-18, 6), so its equation can be written as ...

  y -6 = 5/6(x -(-18))

  y = 5/6x +15 +6 . . . . . eliminate parentheses, add 6

  y = 5/6x +21

Function notation gives a name to the relation, and identifies the independent variable. We want to call this f(x), meaning the name of the relation is "f", and the independent variable is "x". Essentially, "f(x)" replaces "y" in the above equation:

  f(x) = 5/6x +21

Answer:

The answer is 18

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

The perimeter of the rectangle =18 in

Step-by-step explanation:

Given, Area of rectangle= 14 in

Length(l) of one side = 7 in

We know,

Area = lxb

or, 14 = 7xb

or, b = 2 in

then the perimeter of the rectangle = 2x(l+b)

= 2x(7+2)

= 2x9

=18in

Answer:

Area = 2x² + x - 6

Step-by-step explanation:

The area of the shaded region is the square area minus the triangle area:

\((3 {x}^{2} - 7x + 12) - ( {x}^{2} - 8x + 18) \\ {3x}^{2} - 7x + 12 - {x}^{2} + 8x - 18 \\ {2x}^{2} + x - 6\)

The vector components and direction of the river and motorboat are;

(a) 12·i

(b) 12·i + 12·√3·j

(c) 24·i + 12·√3·j

(d) 31.7 mi/h

A vector is a quantity or measurement that indicates a magnitude and a direction of the measurement.

The direction the river flows = East

The speed of the river = 12 mi/h

The direction the boater heads = 60° from the shore

Speed of the motor boar = 24 mi/h

The unit vector in the east direction = i

Unit vector in the north direction = j

(a) The velocity of the river, which is 12 mi/h east expressed in vector form is therefore;

(b) The velocity of the motorboat relative to the river, in vector component form is therefore;

Component of the velocity in the east direction = 24 × cos(60°)·i = 12·i

Component in the north direction = 24 × sin(60°)·j = 12·√3·j

The component form of the velocity of the boat is therefore;

(c) The true velocity of the boat is the vector sum of the velocity of the river and the velocity of the boat, therefore;

True velocity of the boat = 12·i + 12·i + 12·√3·j = 24·i + 12·√3·j

(d) The true speed is the magnitude of the velocity of the boat which can be found ads follows;

The (true) direction of the motorboat, θ, can be obtained from the arctangent of the ratio of the velocity component in the northern direction to the velocity in the eastern direction as follows;

The velocity component of the motorboat in the northern direction = 12·√3

The component of the velocity in the eastern direction = 24

Therefore;

tan(θ) = 12·√3/(24)

θ = arctan(12*√3/(24)) ≈ 40.9°, which is about East 40.9° North

The direction from the north, therefore is found as follows;

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The percent profit that Rabi made will be 10.5%

Let's assume that the price of the house is $100.

Since he fixed the marked price of the good to make a profit of 30%, then the price will be:

= $100 + (30% × $100)

= $100 + $30

= $130

Now, there is a discount of 15%, then the selling price of the good will be:

= $130 - (15% × $130)

= $130 - (0.15 × $130)

= $130 - $19.50

= $110.50

Then, the percentage of profit made will be:

= [($110.50 - $100) / $100] × 100%

= $10.50/$100 × 100%

= 10.5%

In conclusion, the percent profit that he makes is 10.5%.

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Answer:

y = 3x + 20

This is an equation, in slope-intercept form, which represents a the placement of a line. The 3 in the equation represents the slope of the line, and the 20 represents the y-intercept.

Answer:

A. The lowercase​ symbol, p, represents the probability of getting a test statistic at least as extreme as the one representing sample data and is needed to test the claim.

Step-by-step explanation:

The conditions  required for testing  of a claim about a population proportion using a formal method of hypothesis​ testing are:

1) The sample observations are a simple random sample.

2) The conditions for a binomial distribution are satisfied

3) The conditions np5 and nq5 are both satisfied. i.e n: p≥ 5and q≥ 5

These conditions are given in th options b,c and d.

Option A is not a condition for testing  of a claim about a population proportion using a formal method of hypothesis​ testing.

Answer:

Step-by-step explanation:

The answer is B

Answer:

The correct answer is a.

Step-by-step explanation:

The sequence is: 2 3 E 4 5 I 6 8 We can notice that there are numbers and letters alternating in the sequence. The numbers are increasing, and the letters seem to be vowels in alphabetical order. So, the next value should be a letter (vowel) after I, which is O. The correct answer is a.

Answer:

C) A = \(3w^{2} - 4w\)

Step-by-step explanation:

First, read through what the question is asking.

Now, read it again, but slowly and take in everything it is saying (Don't read into it too slowly, or else you will over-complicate the problem and get frustrated - told from experience :) )

Alright, 4 less than 3 times the width. So, lets rearrange this and give width a variable (w).

So, the length is equal to:

l = 3w - 4

and the width is equal to:

w = w

The area of a rectangle is A = l * w

Let's plug in the values.

A = (3w - 4) * w

Now, simplify:

A = \(3w^{2} - 4w\)

A = \(3w^{2} - 4w\) is your final answer.

I hope this helps!

The expression of "The difference of -10 and the product of p and q" in algebraic notation is pq + 10

From the question, we have the following parameters that can be used in our computation:

The difference of -10 and the product of p and q

The numbers are given as

p and q

The product of p and q means pq

So, we have the following

The difference of -10 and pq

The difference of -10 and pq means

pq + 10

Hence, the expression is pq + 10

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Answer:

the deli would have to sell 100 hot dogs or 40 burgers

Step-by-step explanation:

The greatest distance that can be filmed by the drone is 6374.5 km. Rounded to the nearest kilometer, 6375 km.

Now, For the greatest distance that can be filmed by a drone with a maximum altitude of 0.12 km, we can use the Pythagorean theorem.

Let's a right triangle with one leg being the radius of the Earth 6378 km and the other leg being the maximum altitude of the drone 0.12 km.

Hence, The hypotenuse of this triangle represents the line of sight from the drone's camera to the horizon.

Hence, By Using the Pythagorean theorem, we can solve for the length of the hypotenuse:

h² = 6378² + 0.12²

h = √40684000.145

h = 6374.5 km

Therefore, The greatest distance that can be filmed by the drone is 6374.5 km. Rounded to the nearest kilometer, 6375 km.

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Incomplete question. Attached is an image of the table.

Step-by-step explanation:

A.

Yes = 35% = \(\frac{280}{800} * 100 =\) 35%.   and No = 65% = \(\frac{520}{800} * 100 =\) 65%

Answer:

a = 18/b²

Step-by-step explanation:

Step 1: Write equation

1/3ab² = 6

Step 2: Solve for a

Answer:

\(Absolute\ Change = -0.766\)

Step-by-step explanation:

Given

\(2008\ CPI = 215.303\)

\(2009\ CPI = 214.537\)

Required

Determine the absolute change

Absolute change is calculated as thus:

\(Absolute\ Change = 2009\ CPI - 2008\ CPI\)

\(Absolute\ Change = 214.537 - 215.303\)

\(Absolute\ Change = -0.766\)

Hence:

The absolute change from 2008 to 2009 is -0.766

The expression 2 - 5(x - 1) is a linear expression

From the question, we have the following parameters that can be used in our computation:

2 - 5(x - 1)

The general rule is that

Using the above as a guide, we have the following:

2 - 5(x - 1) is a linear expression

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Answer:

Figure STOP is congruent to figure S′T′O′P′.

Step-by-step explanation:

I just took the test

Answer:

Figure STOP is congruent to figure S′T′O′P′.

Step-by-step explanation:

Just finished test and got 100%

Answer:

E. 1/3

Step-by-step explanation:

In this sequence, the numbers are descending and are 1/3 of the previous number.

243 / 3 = 81

81 / 3 = 27

9 / 3 = 3

3 / 3 = 1

1 / 3 = 1 / 3 (the next term)

Answer:

Point-Slope: \(y+4=-\frac{1}{2}(x+3)\)

Slope-Intercept: \(y=-\frac{1}{2}x-\frac{11}{2}\)

Step-by-step explanation:

The point-slope formula is \(y-y_{1}=m(x-x_{1} )\). The slope-intercept formula is \(y=mx+b\). Since we are given the point and slope, we can directly plug it into the point-slope formula.

Point-Slope

\(y-(-4)=-\frac{1}{2}(x- (-3))\)

\(y+4=-\frac{1}{2} (x+3)\)

To find the slope-intercept form, we can manipulate the point-slope form to get the slope-intercept form.

Slope-Intercept

\(y+4=-\frac{1}{2}x-\frac{3}{2}\)

\(y=-\frac{1}{2}x-\frac{11}{2}\)

Answer: Point slope form   y+4= -1/2(x+3)  

Slope intercept form: y=-1/2x -11/2

Step-by-step explanation:

(-3,-4) : m= -1/2  

So we know the slope and to write it in point slope form it will be like ,

y- b = m(x-a)   Where b is the y value and a is the x value  and m in this case is the slope .

y- (-4) = -1/2 ( x-(-3)   which reduces to  y+4= -1/2(x+3)

Now to write it in slope intercept form  it will be  like y=mx+b and we kow htat m is the slope but we do not know b the y-intercept. But using the given coordinates we could plot it into the formula and solve for b.

y = mx +b

We  know that y is -4  

We know that m is -1/2  

we know that x is  -3  

so  -4 = -1/2(-3) + B

    -4  = 3/2 + b

   -3/2    -3/2

  b= -11/2  

We know now that the y intercept is -11/2 so we could write  it in slope intercept form.

y= -1/2x - 11/2

Answer:

C

Step-by-step explanation:

The Brainly equation editor is not working for me right now, so I have attached a screenshot of my workings and explanation.

Answer:

87.2

Step-by-step explanation:

49^2+87.2^2=100.02^2

The meaning of \(\( \mathbb{N}=\bigcap \left \{X:X inductive \right \}\) is that the set of natural numbers is the intersection of all inductive sets.

The set of natural numbers is inductive because it satisfies both of these conditions. The set is non-empty because it contains the number 1. And if x is a natural number, then x+1 is also a natural number.

In other words, a set is inductive if it satisfies the following two conditions:

The concept of an inductive set is important in mathematics because it allows us to define the set of natural numbers.

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Given: The quadratic function shown in the figure

To Determine: The correct Statement

Solution:

Statement I: The x-intercept is located at (3, 0)

The x-intercept is the point where the function cut the x-axis. From the given graph, the curve cuts the axis at the point where x = 3. Note that at x-intercept, y = 0

Hence, the coordinate of the x-intercept is (3, 0)

Statement II: The coordinates of the y-intercept are (0, 9)

The y-intercept is the point where the function cuts the y-axis. From the graph given, the curve cuts the y-axis, at the point

y = 9. Note that at y-intercept, x = 0

Hence, the coordinate of the y - intercept is (0, 9)

Statement III: The axis of symmetry is x = 3

The axis of symmetry is the vertical line that divides the graph into two equal parts. The x-coordinate of the vertex is the equation of the axis of asymmetry

From the graph, it can be seen that the axis of symmetry is x = 3. This is as shown below

Hence, Statement I, II, and III are correct, OPTION C