Dante is standing at horizontal ground level with the base of the Empire State Building in New York City. The angle formed by the ground and the line segment from his position to the top of the building is 48.4°. The height of the Empire State Building is 1,472 feet. Find his distance from the Empire State Building to the nearest foot.

A. 7.65 ft
B. 1, 968 ft
C. 1,307 ft
D. 2, 217 ft

Answer:

k = 2

Step-by-step explanation:

If the roots are real and equal then the condition for the discriminant is

b² - 4ac = 0

For 2x² - (k + 2)x + k = 0 ← in standard form

with a = 2, b = - (k + 2) and c = k, then

(- (k + 2))² - (4 × 2 × k ) = 0

k² + 4k + 4 - 8k = 0

k² - 4k + 4 = 0

(k - 2)² = 0

Equate factor to zero and solve for k

(k - 2)² = 0 ⇒ k - 2 = 0 ⇒ k = 2

Answer:

Step-by-step explanation:

A quadratic equation has two equal real roots if a discriminant is equal 0.

[tex]ax^2+bx+c=0[/tex]

Discriminant [tex]b^2-4ac[/tex]

We have the equation

[tex]2x^2-(k+2)x+k=0\to a=2,\ b=-(k+2),\ c=k[/tex]

Substitute:

[tex]b^2-4ac=\bigg(-(k+2)\bigg)^2-4(2)(k)\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\=k^2+2(k)(2)+2^2-8k=k^2+4k+4-8k=k^2-4k+4\\\\b^2-4ac=0\iff k^2-4k+4=0\\\\k^2-2k-2k+4=0\\\\k(k-2)-2(k-2)=0\\\\(k-2)(k-2)=0\\\\(k-2)^2=0\iff k-2=0\qquad\text{add 2 to both sides}\\\\k=2[/tex]

Find the answer in the attachment.

The hyperbola's equation is x² / 3600 - y² / 121 = 1, centered at the origin (0,0). Its vertices are at (60,0), (-60,0) on the x-axis, and (0,11), (0,-11) on the y-axis.

To find the equation of the hyperbola, we need to determine its center and the distances from the center to the vertices along the x and y axes. The general equation of a hyperbola centered at (h, k) is given by:

(x - h)² / a² - (y - k)² / b² = 1

Where (h, k) is the center of the hyperbola, and 'a' and 'b' are the distances from the center to the vertices along the x and y axes, respectively.

In this case, since the hyperbola is symmetric along the x and y axes, the center is at the origin (0, 0). Also, we know the distance from the center to the vertices along the x-axis is 60 units (60 and -60) and along the y-axis is 11 units (11 and -11).

So, a = 60 and b = 11.

Now we can plug these values into the equation:

x² / (60)² - y² / (11)² = 1

Simplifying further:

x² / 3600 - y² / 121 = 1

And that's the equation of the hyperbola.

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Answer:

x+6

Step-by-step explanation:

Let's see if the numerator is factorable.

Since the coefficient of x^2 is 1 (a=1), all you have to do is find two numbers that multiply to be -6  (c) and add up to be 5 (b).

Those numbers are 6 and -1.

So the factored form of the numerator is (x+6)(x-1)

So when you divide (x+6)(x-1) by (x-1) you get (x+6) because (x-1)/(x-1)=1 for number x except x=1 (since that would lead to division by 0).

Anyways, this is what I'm saying:

[tex]\frac{(x+6)(x-1)}{(x-1)}=\frac{(x+6)\xout{(x-1)}}{\xout{(x-1)}}[/tex]

[tex]x+6[/tex]

Answer:

[tex]-8 < x < 8[/tex]

Step-by-step explanation:

Your compound inequality will include two inequalities.

These are:

x > -8

x < 8

Put your lowest number first, ensuring that your sign is pointed in the correct direction.

[tex]-8 < x[/tex]

Next, enter your higher number, again making sure that your sign is pointing in the correct direction.

[tex]-8 < x < 8[/tex]

Answer:

-8 < r < 8

Step-by-step explanation:

Let r = real number

Greater than  >

r>-8

less than  <

r <8

We want a compound inequality so we combine these

-8 < r < 8

To find (f/g)(x) with f(x) = 6x + 2 and g(x) = x - 7, one must divide f(x) by g(x). The domain restriction occurs because division by zero is not defined, so we exclude the x value that makes g(x) zero, which is x = 7.

To perform the indicated operation (f/g)(x) with the given functions f(x) = 6x + 2 and g(x) = x - 7, we need to divide the function f(x) by the function g(x). This operation is equivalent to finding the quotient of the two functions, which is expressed as:

(f/g)(x) = f(x)/g(x) = (6x + 2)/(x - 7)

The domain restriction occurs when the denominator, g(x), is equal to zero since division by zero is undefined. So we must find the value of x for which g(x) = 0. Since g(x) = x - 7, setting this equal to zero gives us:

x - 7 = 0 → x = 7

Therefore, the domain of the function (f/g)(x) is all real numbers except for x = 7, because at x = 7 the function is undefined. The domain of (f/g)(x) can be expressed as ℜ - {7}, where ℜ represents the set of all real numbers.

Answer:

B

Step-by-step explanation:

Given

(5 + 7i) + (- 2 + 6i ) ← remove parenthesis and collect like terms

= 5 + 7i - 2 + 6i

= 3 + 13i → B

The sum of the complex number is 3 + 13i.

Option B is the correct answer.

We have,

To find the sum of the complex numbers (5+7i) and (-2+6i), you can simply add the real parts together and add the imaginary parts together separately.

Real part: 5 + (-2) = 3

Imaginary part: 7i + 6i = 13i

Combining the real and imaginary parts, we get:

Sum = 3 + 13i

Therefore,

The sum of the complex number is 3 + 13i.

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Answer:

She has 9 5 cent stamps and 6 7 cent stamps.

Step-by-step explanation:

Let the number of five cent stamps be represented by F and the number of seven cent stamps be represented by S.

The difference between the number of five cent and seven cent stamps is 3

F-S=3

The sum of the collection from each type of stamp is 87 cents

5F+7S=87

Let us solve the equations simultaneously.

F-S=3

5F+7S=87

Using substitution method,

F= 3+S

5(3+S)+7S=87

15+5S+7S=87

12S=87-15

12S=72

S=6

F=3+S

=3+6=9

Therefore the number of five cent stamps is 9 and seven cent stamps is 6.

Answer:

Number of 5 cent stamps = 9

Number of 7 cent stamps = 6

Step-by-step explanation:

We are given that Bianca has a stamp collection of 5 cent stamps and 7 cent stamps in which there are 3 less 7 cent stamps as 5 cent stamps.

If the total face value of stamps is 87 cents, we are to find the number of stamps of each value.

Assuming [tex]t[/tex] to be the number of 5 cent stamps and [tex]s[/tex] to be the 7 cent stamps so we can write it as:

[tex]0.05t+0.07s=0.87[/tex] --- (1)

[tex]s=t-3[/tex] --- (2)

Substituting this value of [tex]s[/tex] from (2) in (1):

[tex]0.05t+0.07(t-3)=0.87[/tex]

[tex]0.05s+0.07t-0.21=0.87[/tex]

[tex]0.12t=1.08[/tex]

[tex]t=9[/tex]

Number of 5 cent stamps = 9

Number of 7 cent stamps = 9 - 3 = 6

Answer:

110

Step-by-step explanation:

He said he had atleast 1 of each. Hope it helps.

The smallest possible total weight of Tom's toys​ is:

                          210 grams

It is given that:

Tom has 8 toys each toy weighs either 20 grams or 40 grams or 50 grams.

Also, he  has a different number of toys (at least one) of each weight.

Now, the smallest possible weight of Tom's toy is such that:

He has one toy of 50 grams , one of 40 grams and the other's are of smallest weight i.e. 20 grams.

This means he has 6 toys of 20 grams.

One of 40 grams.

One of 50 grams.

Hence,

Total weight= 20×6+40+50

i.e.

Total weight= 120+90

i.e.

Total weight= 210 grams.

Answer:

h=7

Step-by-step explanation:

[tex]h+(-3)=4[/tex]

may be rewritten as

[tex]h-3=4[/tex]

as adding a negative is the same as subtracting a positive.

To solve, add 3 to both sides.

[tex]h-3=4\\h=7[/tex]

Answer:

h=7

Step-by-step explanation:

1) Add three to both sides

2) You should get h=7

Answer:

Speed of the boat in still water = 6.125 miles/hour

Step-by-step explanation:

We are given that a boat travels 33 miles downstream in 4 hours and the return trip takes the boat 7 hours.

We are to find the speed of the boat in the still water.

Assuming [tex]S_b[/tex] to be the speed of the boat in still water and [tex]S_w[/tex] to be the speed of the water.

The speeds of the boat add up when the boat and water travel in the same direction.

[tex]Speed = \frac{distance}{time}[/tex]

[tex]S_b+S_w=\frac{d}{t_1}=\frac{33 miles}{4 hours} [/tex]

And the speed of the water is subtracted from the speed of the boat when the boat is moving upstream.

[tex]S_b-S_w=\frac{d}{t_2}=\frac{33 miles}{7 hours} [/tex]

Adding the two equations to get:

   [tex]S_b+S_w=\frac{d}{t_1}[/tex]

+  [tex]S_b-S_w=\frac{d}{t_2} [/tex]

___________________________

[tex]2S_b=\frac{d}{t_1} +\frac{d}{t_2}[/tex]

Solving this equation for [tex]S_b[/tex] and substituting the given values for [tex]d,t_1, t_2[/tex]:

[tex]S_b=\frac{(t_1+t_2)d}{2t_1t_2}[/tex]

[tex]S_b=\frac{(4 hour + 7hour)33 mi}{2(4hour)(7hour)}[/tex]

[tex]S_b=\frac{(11 hour)(33mi)}{56hour^2}[/tex]

[tex]S_b=6.125 mi/hr[/tex]

Therefore, the speed of the boat in still water is 6.125 miles/hour.

Answer:

[tex]6.48\frac{mi}{h}[/tex]

Step-by-step explanation:

Let' call "b" the speed of the boat and "c" the speed of the river.

We know that:

[tex]V=\frac{d}{t}[/tex]

Where "V" is the speed, "d" is the distance and "t" is the time.

Then:

[tex]d=V*t[/tex]

We know that distance traveled downstream is 33 miles and the time is 4 hours. Then, we set up the folllowing equation:

[tex]4(b+c)=33[/tex]

For the return trip:

 [tex]7(b-c)=33[/tex]  (Remember that in the return trip the speed of the river is opposite to the boat)

By solving thr system of equations, we get:

- Make both equations equal to each other and solve for "c".

[tex]4(b+c)=7(b-c)\\\\4b+4c=7b-7c\\\\4c+7c=7b-4b\\\\11c=3b\\\\c=\frac{3b}{11}[/tex]

- Substitute "c" into any original equation and solve for "b":

[tex]4b+\frac{3b}{11} =33\\\\4b+\frac{12b}{11}=33\\\\\frac{56b}{11}=33\\\\b=6.48\frac{mi}{h}[/tex]

ANSWER

C) 4x-3y=-12

EXPLANATION

The intercept form of a straight line is given by:

[tex] \frac{x}{x - intercept} + \frac{y}{y - intercept} = 1[/tex]

From the the x-intercept is -3 and the y-intercept is 4.

This is because each box is one unit each.

We substitute the intercepts to get:

[tex] \frac{x}{ - 3} + \frac{y}{4} = 1[/tex]

We now multiply through by -12 to get

[tex] - 12 \times \frac{x}{ - 3} + - 12 \times \frac{y}{4} = 1 \times - 12[/tex]

[tex]4x - 3y = -12[/tex]

The correct choice is C.

Answer:

=70$

Step-by-step explanation:

The total in her account at day zero =85$

Lunch for five days= 3$×5

=15$

Total in her account= Initial amount - Expenditure on lunch

=85$-15$

=70$

The balance in Latesha's Lunch Account after having lunch for five day=70$

Answer:

a)120

b)6.67%

Step-by-step explanation:

Given:

No. of digits given= 6

Digits given= 1,2,3,5,8,9

Number to be formed should be 3-digits, as we have to choose 3 digits from given 6-digits so the no. of combinations will be

6P3= 6!/3!

      = 6*5*4*3*2*1/3*2*1

      =6*5*4

      =120

Now finding the probability that both the first digit and the last digit of the three-digit number are even numbers:

As the first and last digits can only be even

then the form of number can be

a)2n8 or

b)8n2

where n can be 1,3,5 or 9

4*2=8

so there can be 8 three-digit numbers with both the first digit and the last digit even numbers

And probability = 8/120

                          = 0.0667

                          =6.67%

The probability that both the first digit and the last digit of the three-digit number are even numbers is 6.67% !

1.

[tex]6\cdot5\cdot4=120[/tex]

2.

[tex]|\Omega|=120\\|A|=2\cdot4\cdot1=8\\\\P(A)=\dfrac{8}{120}=\dfrac{1}{15}\approx6.7\%[/tex]

Answer:

corresponding

Step-by-step explanation:

Answer:

Corresponding

Step-by-step explanation:

I like to call corresponding angles, the copy and paste angles because you can copy and paste the top intersection over the bottom intersection; the angles that lay down on top of each other are the corresponding angles. 1 and 5 do this.

Answer:

Option B

Step-by-step explanation:

we know that

To find the reciprocal of a fraction, flip the fraction.

Remember that

A number multiplied by its reciprocal is equal to 1

In this problem we have

[tex]\frac{10b}{2b+8}[/tex]

Flip the fraction

[tex]\frac{2b+8}{10b}[/tex] -----> reciprocal

therefore

The reciprocal is

The quantity 2 multiplied by b plus 8 end of quantity divided by the quantity 10 multiplied by b end of quantity.

[tex]\bf \begin{array}{ccll} \$&hour\\ \cline{1-2} 5.5&1\\ x&3\frac{1}{3} \end{array}\implies \cfrac{5.5}{x}=\cfrac{1}{3\frac{1}{3}}\implies \cfrac{5.5}{x}=\cfrac{1}{\frac{3\cdot 3+1}{3}}\implies \cfrac{5.5}{x}=\cfrac{1}{\frac{10}{3}}\implies \cfrac{5.5}{x}=\cfrac{\frac{1}{1}}{\frac{10}{3}} \\\\\\ \cfrac{5.5}{x}=\cfrac{1}{1}\cdot \cfrac{3}{10}\implies \cfrac{5.5}{x}=\cfrac{3}{10}\implies 55=3x\implies \stackrel{\textit{about 18 bucks and 33 cents}}{\cfrac{55}{3}=x\implies 18\frac{1}{3}=x}[/tex]

Answer:

$18.3

Step-by-step explanation:

If you are paid $5.50/hour for mowing yards, and you take 3 1/3 hours to mow a yard, you should earn $18.3.

3 1/3 hours

$5.50 and hour

$5.50 x 3 = $16.5

$5.50 / 3 = $1.8

$16.5 + $1.8 = $18.3

Therefore, you are owed $18.3.

Answer:

Assume that [tex]a[/tex] and [tex]p[/tex] are constants. The slope of the line will be equal to

Step-by-step explanation:

Rewrite the expression of the line to express [tex]y[/tex] in terms of [tex]x[/tex] and the constants.

Substract [tex]x\cdot \cos{(a)}[/tex] from both sides of the equation:

[tex]y \sin{(a)} = p - x\cos{(a)}[/tex].

In case [tex]\sin{a} \ne 0[/tex], divide both sides with [tex]\sin{a}[/tex]:

[tex]\displaystyle y = - \frac{\cos{(a)}}{\sin{(a)}}\cdot x+ \frac{p}{\sin{(a)}}[/tex].

Take the first derivative of both sides with respect to [tex]x[/tex]. [tex]\frac{p}{\sin{(a)}}[/tex] is a constant, so its first derivative will be zero.

[tex]\displaystyle \frac{dy}{dx} = - \frac{\cos{(a)}}{\sin{(a)}}[/tex].

[tex]\displaystyle \frac{dy}{dx}[/tex] is the slope of this line. The slope of this line is therefore

[tex]\displaystyle - \frac{\cos{(a)}}{\sin{(a)}} = -\cot{(a)}[/tex].

In case [tex]\sin{a} = 0[/tex], the equation of this line becomes:

[tex]y \sin{(a)} = p - x\cos{(a)}[/tex].

[tex]x\cos{(a)} = p[/tex].

[tex]\displaystyle x = \frac{p}{\cos{(a)}}[/tex],

which is the equation of a vertical line that goes through the point [tex]\displaystyle \left(0, \frac{p}{\cos{(a)}}\right)[/tex]. The slope of this line will be infinity.

Answer:

[tex]\frac{147}{100}[/tex]

Step-by-step explanation:

This is the answer because 147 ÷ 100 = 1.47

Answer:

Option B. g(x) is greater

Step-by-step explanation:

step 1

Find the value of f(x) when the value of x is equal to 3

we have

f(x)=2x-1

substitute the value of x=3

f(3)=2(3)-1=5

step 2

Find the value of g(x) when the value of x is equal to 3

Observing the graph

when x=3

g(3)=7

step 3

Compare the values

f(x)=5

g(x)=7

so

g(x) > f(x)

g(x) is greater

Answer:

Correct option is:

B. g(x) is greater

Step-by-step explanation:

Firstly, we find the value of f(x) when x=3

f(x)=2x-1

substitute the value of x=3

f(3)=2×3-1=5

On observing the graph, we see that g(x)=7 when x=3

Now, on Comparing the values of f(x) and g(x) when x=3

f(3)=5

g(3)=7

so, g(x) > f(x) when x=3

So, Correct option is:

B. g(x) is greater

Answer:

Step-by-step explanation:

There are 3 ways to find the other x intercept.

1) Polynomial Long Division.

Divide x^2 - 3x + 2 by the binomial x - 2, because by the Factor Theorem if a is a root of a polynomial then x - a is a factor of said polynomial.

2) Just solving for x when y = 0, by using the quadratic formula.

[tex]x^2 - 3x + 2 = 0\\x_{12} = \frac{3 \pm \sqrt{9 - 4(1)(2)}}{2} = \frac{3 \pm 1}{2} = 2, 1[/tex].

So the other x - intercept is at (1, 0)

3) Using Vietta's Theorem regarding the solutions of a quadratic

Namely, the sum of the solutions of a quadratic equation is equal to the quotient between the negative coefficient of the linear term divided by the coefficient of the quadratic term.

[tex]x_1 + x_2 = \frac{-b}{a}[/tex]

And the product between the solutions of a quadratic equation is just the quotient between the constant term and the coefficient of the quadratic term.

[tex]x_1 \cdot x_2 = \frac{c}{a}[/tex]

These relations between the solutions give us a brief idea of what the solutions should be like.

there's a scale factor of two!

five times two is ten.

hope this helps! :) xx

Answer:

Step-by-step explanation:

We only need two points to plot the graph of each equation.

[tex]y=-3x+2\\\\for\ x=0\to y=-3(0)+2=0+2=2\to(0,\ 2)\\for\ x=1\to y=-3(1)+3=-3+2=-1\to(1,\ -1)\\\\y=5x+28\\\\for\ x=-4\to y=5(-4)+28=-20+28=8\to(-4,\ 8)\\for\ x=-6\to y=5(-6)+28=-30+28=-2\to(-6,\ -2)[/tex]

Look at the picture.

Read the coordinates of the intersection of the line (solution).

Answer:

regular

Step-by-step explanation:

1. look at table

Answer:

The correct option is A)

P(Win|Regular)=0.76

P(Win|Prevent )=0.58

You are more likely to win by playing regular defense.

Step-by-step explanation:

Consider the provided table.

We need to find which strategy is better.

If team play regular defense then they win 38 matches out of 50.

[tex]Probability=\frac{\text{Favorable outcomes}}{\text{Total number of outcomes}}[/tex]

[tex]P(Win|Regular)=\frac{38}{50}[/tex]

[tex]P(Win|Regular)=0.76[/tex]

If team play prevent defense then they win 29 matches out of 50.

Thus, the probability of win is:

[tex]P(Win|Prevent )=\frac{29}{50}[/tex]

[tex]P(Win|Prevent )=0.58[/tex]

Since, 0.76 is greater than 0.58

That means the probability of winning the game by playing regular defense is more as compare to playing prevent defense.

Hence, the conclusion is: You are more likely to win by playing regular defense.

Thus, the correct option is A)

P(Win|Regular)=0.76

P(Win|Prevent )=0.58

You are more likely to win by playing regular defense.

Answer:

B) 28.53 unit²

Step-by-step explanation:

The diagonal AD divides the quadrilateral in two triangles:

Area of Quadrilateral will be equal to the sum of Areas of both triangles.

i.e.

Area of ABCD = Area of ABD + Area of ACD

Area of Triangle ABD:

Area of a triangle is given as:

[tex]Area = \frac{1}{2} \times base \times height[/tex]

Base = AB = 2.89

Height = AD = 8.6

Using these values, we get:

[tex]Area = \frac{1}{2} \times 2.89 \times 8.6 = 12.43[/tex]

Thus, Area of Triangle ABD is 12.43 square units

Area of Triangle ACD:

Base = AC = 4.3

Height = CD = 7.58

Using the values in formula of area, we get:

[tex]Area = \frac{1}{2} \times 4.3 \times 7.58 = 16.30[/tex]

Thus, Area of Triangle ACD is 16.30 square units

Area of Quadrilateral ABCD:

The Area of the quadrilateral will be = 12.43 + 16.30 = 28.73 units²

None of the option gives the exact answer, however, option B gives the closest most answer. So I'll go with option B) 28.53 unit²

For this case we must represent the following expression algebraically, in addition to indicating its result:

"2 plus 9"

So, we have:

[tex]2 + 9 =[/tex]

By law of the signs of the sum, we have that equal signs are added and the same sign is placed:

[tex]2 + 9 = 11[/tex]

ANswer:

11

Answer:

x = - 15

Step-by-step explanation:

The equation is  [tex]\frac{5}{x}=\frac{4}{x+3}[/tex]

We now cross mulitply and do algebra to figure the value of x (shown below):

[tex]\frac{5}{x}=\frac{4}{x+3}\\5(x+3)=4(x)\\5x+15=4x\\5x-4x=-15\\x=-15[/tex]

Hence x = -15

Answer:

D

Step-by-step explanation:

[tex]\bf \sqrt{3x^2}\cdot \sqrt{4x}\implies \sqrt{3x^2\cdot 4x}\implies \sqrt{12x^2x}\implies \sqrt{4\cdot 3\cdot x^2x} \\\\\\ \sqrt{2^2\cdot 3\cdot x^2x}\implies 2x\sqrt{3x}[/tex]

ANSWER

[tex]{(x + 10)}^{2} + {(y + 6)}^{2} = 121[/tex]

EXPLANATION

The equation of the circle in general form is given as:

[tex] {x}^{2} + {y}^{2} + 20x + 12y + 15 = 0[/tex]

To obtain the standard form, we need to complete the squares.

We rearrange the terms to obtain:

[tex] {x}^{2} + 20x + {y}^{2} + 12y = - 15 [/tex]

Add the square of half the coefficient of the linear terms to both sides to get:

[tex]{x}^{2} + 20x +100 + {y}^{2} + 12y + 36 = - 15 + 100 + 36[/tex]

Factor the perfect square trinomial and simplify the RHS.

[tex]{(x + 10)}^{2} + {(y + 6)}^{2} = 121[/tex]

This is the equation of the circle in standard form.

Answer:

0.00008 ÷ 640,000,000 means

8*10^-5 ÷ 6.4*10^8

so let's collect to simplify the operation

(8÷6.4)*(10^-12) -5-7=-12

then the answer becomes 1.25×10^-14 that is B

Answer:

option C

Step-by-step explanation:

Evaluate 0.00008 ÷ 640,000,000.

0.00008 can be written in standard notation

Move the decimal point to the end

so it becomes  [tex]8 \cdot 10^{-5}[/tex]

for 640,000,000 , remove all the zeros and write it in standard form

[tex]64 \cdot 10^7[/tex]

Now we divide both

[tex]\frac{8 \cdot 10^{-5}}{64 \cdot 10^7}[/tex]

Apply exponential property

a^m divide by a^n  is a^ m-n

[tex]\frac{8}{64} =0.125[/tex]

[tex]\frac{10^{-5}}{10^7}=10^{-12}[/tex]

[tex]0.125 \cdot 10^{-12}= 1.25 \cdot 10^{-13}[/tex]