A blimp is 1100 meters high in the air and measures the angles of depression to two stadiums to the west of the blimp. If those measurements are 75.2° and 17.9°, how far apart are the two stadiums?

Answer:

[tex]f(x) = x^{2}\cdot (x^{2}+9)\cdot (x^{3}+2\cdot x)[/tex] is an odd function.

Step-by-step explanation:

Let be [tex]f(x) = x^{2}\cdot (x^{2}+9)\cdot (x^{3}+2\cdot x)[/tex], by Algebra this expression can be rewritten as:

[tex]f(x) = x^{3}\cdot (x^{2}+9)\cdot (x^{2}+2)[/tex]

Where [tex]x^{2} + 9[/tex] and [tex]x^{2}+ 2[/tex] are even functions, because they satisfy the condition that [tex]g(x) = g(-x)[/tex], whereas [tex]x^{3}[/tex] is an odd function, as the condition of [tex]h(-x) = - h(x)[/tex] is observed. Then, the overall function is odd.

Answer:

14)  answer is 4

15) proved

Step-by-step explanation:

x=7-4√3 , √x +1/√x

√(7-4√3) +1/√7-4√3)=

8-4√x/√(7-4√3)= 4 ( use calculator)

Answer:

I think it should be (C)

Answer:

B

Step-by-step explanation:

The fastest way to solve this would to plug in a number for x such as 1 in both equations to find which 2 are equivalent.

When you plug 1 into the top equation it equals 3.5, so now we need to find the correct equation below that equals 3.5 when 1 is plugged in for x.

When you plug 1 into equation B you are also left with 3.5.

Answer:

x= -8 , y = 5

x= 25/4 , y = 1/4

Step-by-step explanation:

substitute first eqn into the second eqn:

(7 - 3y)^2 -y^2 = 39

49 - 42y + 9y^2 - y^2 = 39

8y^2 - 42y +10 =0

4y^2 - 21y + 5 = 0

(4y-1) (y-5) = 0

y= 1/4 , 5

when y=1/4

x = 7- 3/4

=25/4

when y= 5

x = 7- 15

= -8

The required solution of the given simultaneous equations are x = -8, 25/4 and y = 5, 1/4.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
x = 7 – 3y - - - - -(1)
x² - y² = 39 - - - - (2)

Put x from equation 1 in equation 2

(7 - 3y)² -y² = 39

49 - 42y + 9y² - y² = 39

8y² - 42y +10 =0

4y² - 21y + 5 = 0

(4y-1) (y-5) = 0

y= 1/4 , 5

Substitute this values in the equation 1,
x = -8 and 25/4

Learn more about simultaneous equations here:

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Answer:

8

Step-by-step explanation:

total: 28 water attractions

pools: p

game areas: p + 2

water slides: 50% of 28 = 14

14 + p + p + 2 = 28

2p = 12

p = 6

game areas:

p + 2 = 6 + 2 = 8

Answer:

Step-by-step explanation:

Area of a rectangle = Length * Width

Given parameters

Area A = 8x2 – 10x – 12

Length of the rectangle = 4x+3

Required

Width of the rectangle.

Substituting the given parameters into the formula

8x2 – 10x – 12  = (4x+3)*width

width = 8x2 – 10x – 12 /4x+3

S

Factorizing the numerator

8x² – 10x – 12

= 2(4x²-5x-6)

= 2(4x²-8x+3x-6)

= 2(4x(x-2)+3(x-2))

= 2(4x+3)(x-2)

Width = 2(4x+3)(x-2)/4x+3

Width = 2(x-2)

Width = 2x-4

Hence the width of the rectangle is 2x-4

Answer:

4.6225

Step-by-step explanation: It would be too long to get an exact

Answer:

Step-by-step explanation:

Area of square = 18.49 square yards

side² = 18.49

side = √18.49

side = 4.3 yards

Answer: 2x2−3x−8

Step-by-step explanation:

Answer:

The probability that the sample proportion of households spending more than $125 a week is between 0.36 and 0.42 is 0.3115

Step-by-step explanation:

From the question, we can deduce the following;

n = 75

p = 0.35

where q = 1-p = 1-0.35 = 0.65

To compute the probability that the sample proportion of households spending more than $125 a week is between 0.36 and 0.42, we start by calculating the standard deviation of sample proportion.

Mathematically;

Standard deviation of sample proportion = √pq/n

SD = √(0.35)(0.65)/75 = 0.055 which is approximately 0.06

Let’s now compute the z-scores

For 0.36, we have ; (0.36-0.35)/0.06 = 0.01/0.06 = 0.17

For 0.42, we have; (0.42-0.35)/0.06 = 0.07/0.06 = 1.17

So the probability we want to calculate is :

P(0.17<z<1.17) = P(z<1.17) - P(z < 0.17) = 0.8790 - 0.5675 = 0.3115

Answer:

x = 2

Step-by-step explanation:

Probability that the marble comes to rest in the shaded region is equal to the ratio of the shaded area to the total area.

Probability 'P' = [tex]\frac{A'}{A}[/tex]

Area of the shaded region (A')= (x + 1)(x + 2)

Total area of the figure (A) = (2x + 1)(3x + 2)

P = [tex]\frac{(x+1)(x+2)}{(2x+1)(3x+2)}=\frac{3}{10}[/tex]

10(x + 1)(x + 2) = 3(2x + 1)(3x + 2)

10(x² + 3x + 2) = 3(6x² + 7x + 2)

10x² + 30x + 20 = 18x² + 21x + 6

(18x² - 10x²) + (21x - 30x) + (6 - 20) = 0

8x² - 9x - 14 = 0

x = [tex]\frac{9\pm\sqrt{(-9)^2-4(8)(-14)} }{2(8)}[/tex]

x = [tex]\frac{9\pm \sqrt{81+448}}{16}[/tex]

x = [tex]\frac{9\pm 23}{16}[/tex]

x = -[tex]\frac{7}{8}, 2[/tex]

Therefore, positive value of x = 2 will be the answer.

Answer:

The 2 values that makes the function equal to 18 is 3 and -6

Step-by-step explanation:

First you can convert the quadratic equation from standard form to root form

Step 1: Substitute f(g) = 18

Step 2: Move 18 to the other side to create

0 = g² + 3g - 18

Step 3: Now we rearrange equation from standard form into root form

Step 4: Find what adds to 3 and multiples to -18

-3 and 6 adds to 3 and multiples to -18

Step 5: Now we substitute -3 and 6 into the root equation

0 = (g-3)(g+6)

Step 6: Set the brackets to 0 and solve

g - 3 = 0

g = 3

g + 6 = 0

g = -6

Answer:

59.5 feet

Step-by-step explanation:

The second tree is 59.5 feet tall.

Two trees are growing in a clearing.

The first tree is 17 feet tall and casts a 10-foot shadow.

The second tree casts a 35-foot shadow.

Let x be the tall is the second tree.

Then,

The ratio of the height of the tree is;

[tex]\rm \dfrac{17}{10} = \dfrac{x}{35}\\\\17 \times 35 = x \times 10\\\\595 = 10x\\\\x = \dfrac{595}{10}\\\\x = 59.5 \ feet[/tex]

Hence, the second tree is 59.5 feet tall.

To know more about Ratio click the link given below.

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Answer:

21

Step-by-step explanation:

4[tex]\frac{1}{5}[/tex] = [tex]\frac{21}{5}[/tex]

5 × [tex]\frac{21}{5}[/tex] = (5×21)/5

[tex]\frac{105}{5}[/tex] = 21

Answer:

a) m∠BPD = 120°

b) m∠BC + m∠AD = 120°

Step-by-step explanation:

a) To solve for question a, we make use of a theorem called the intersecting chord theorem. This states that:

The measure of the angle formed by two chords that intersect inside a circle is the average of the measures of the intercepted arcs.

The Interior angle =( The larger exterior arc + The smaller exterior arcs) ÷ 2

The larger exterior arc (m∠BD) = 170°

The small exterior arc (m∠CA) = 70°

m∠BPD = m∠BD + m∠CA/2

m∠BPD = 170° + 70°/2

= 240°/2

= 120°

b) We are to find m∠BC + m∠AD

The sum of exterior angles in a circle = 360°

360° = m∠BD + m∠CA + m∠BC + m∠AD

360° = 170° + 70° + m∠BC + m∠AD

360° = 240 + m∠BC + m∠AD

360 - 240° = m∠BC + m∠AD

Thererefore,

m∠BC + m∠AD = 120°

Answer:

1. m∠BPD = 120°

2. m∠BC + m∠AD = 120°

Answer:

The correct option is;

y < x - 2, and y > x + 1

Step-by-step explanation:

The given graph of inequalities is made up of parallel lines. Therefore, the slope of the inequalities are equal

By examination of the graph, the common slope = (Increase in y-value)/(Corresponding increase in x-value) = (0 - 1)/(-1 - 0) = 1

Therefore, the slope = 1

We note that the there are three different colored regions, therefore, the different colored regions opposite to each inequalities should be the areas of interest

The y-intercept for the upper bounding linear inequality, (y >) is 1

The y-intercept for the lower bounding linear inequality, (y <) is -2

The two inequalities are y > x + 1 and y < x - 2

The correct option is y < x - 2, and y > x + 1.

The system of linear inequalities is represented by  the graph is y> x-2 and y < x + 1

Inequalities is an expression that shows the non equal comparison of two or more variables and numbers.

Given that:

The system of linear inequalities is represented by  the graph is y> x-2 and y < x + 1

Find out more on linear inequalities at: https://brainly.com/question/21103162

Answer:

42

Step-by-step explanation:

If the scale factor is 2/7 divide 12 by 2 which is 6. 6 is 1/7 and if Figure a is 7/7

multiply 6 by 7 to get x. That would be 42.

Answer:

42

Step-by-step explanation:

Since the scale factor is [tex]\frac{2}{7}[/tex], we know that the bigger shape went to the smaller shape.

If we know that the smaller shape's side, 12, is [tex]\frac{2}{7}[/tex] of the bigger one, we can make the equation

[tex]\frac{2}{7}x = 12[/tex].

To solve for x, we can divide both sides by  [tex]\frac{2}{7}[/tex].

[tex]x = 12\div{\frac{2}{7}}[/tex]

We can multiply by the reciprocal:

[tex]\frac{12}{1} \cdot \frac{7}{2} = \frac{84}{2} = 42[/tex]

Hope this helped!

The statements that can be used to describe the reasoning used to determine if Kelsey’s inequality is correct include:

It should be noted that the inequality symbol is incorrect because she can spend up to and including $65.

Based on the information given, the correct expression that can be used to solve the question should be:

65 - (5.50b + 7.5)

In conclusion, the correct options are B and C.

Read related link on:

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Answer:

B and C

Step-by-step explanation:

Answer:

3 - b=12

4- b=14.1

Step-by-step explanation:

Area of the bookshelf=864 square inches

the book shelf is a rectangular prism

if we have height=4b, width=3b, length=b

then the area=length * width

A=(l*w)*2 ( we have 2 shelves)

864=(b*3b)*2

864=6b²

b²=864/6=144

b=√144= 12 inches

4- to cover the sides :

(height * length)*2   ( we have 2 sides)

(4b*b)×2=1600

8b²=1600

b²=1600/8=200

b=√200=14.1

Answer:

Question #3:  b = 12 in

Question #4:  b = 14.1 in

Step-by-step explanation:

Please see in the image attached the actual proportions that the furniture manufacturer uses to build the furniture in question:

Height = 4 b

Width = 3 b

Depth = b

So for question #3, given that the customer wants a total surface of the shaded shelves to be 864 [tex]in^2[/tex]

we can write that one wants twice the area of each rectangle of width 3 b and depth b to total 864:

[tex]2\,(3b\,*\,b)=864\\6 b^2=864\\b^2=864/6\\b^2=144\\b=12\,\,in[/tex]

Question # 4:

The total lateral surface to be covered by the silk is 1600 [tex]in^2[/tex], therefore if we consider the surface of each lateral plank as:

Area of each lateral plank :

[tex](4b)\,(b) = 4\,b^2[/tex]

Then twice these is: [tex]8\, b^2[/tex]

So we can solve for be requesting that these total surface equal the amount of silk:

[tex]8\,b^2=1600\\b^2=1600/8\\b^2=200\\b=\sqrt{200} \\b\approx 14.1421\,\,in[/tex]

which rounded to the nearest tenth of an inch gives:

[tex]b\approx 14.1\,\,in[/tex]

if [tex] x\times e=x[/tex] for all x, then e is the Multiplicative Identity.

is this enough for you to get the answer?

Answer:

FALSE.

Step-by-step explanation:

1 is the multiplicative identity of the set of rationals.

Answer:

117.79

Step-by-step explanation:

Answer:

x = 7.5

Step-by-step explanation:

Step 1: Create a fraction with the known sides

[tex]\frac{x}{10}[/tex]

Step 2: Set the fraction equal to the scale factor

[tex]\frac{x}{10}=\frac{0.75}{1}[/tex]

Cross multiple to solve for x

[tex]x = 7.5[/tex]

Therefore x is equal to 7.5

Answer:

7.5

Step-by-step explanation:

did it on khan

Answer:

Step-by-step explanation:

a=3400t+600, we put in 21,000 for a. Because we have to find 't' when 'a' is 21,000.

which will give us  21,000 = 3400t+600.

Then,Subtract 600 to both sides to get 20,400 = 3400t

Divide both sides by 3,400 and you get 6 = t.

The ans is 6 minutes. The plane will take 6 min to reach the altitude 21,000 feet

Range: 71.9

Spread out above the median

The range is the biggest number minus the smallest number. This makes sense. The range here is 81.3 - 9.4 = 71.9.

Next, see the two middle groups? You can see the median, 45.5. Does the left or right side seem more spread out? It's the right side. 34.7 is closer to 45.5 than 63.6 is to 45.5.

Hope that helped,

-sirswagger21

Answer:

I am not good at word problems but I think I found some good examples

Step-by-step explanation:

Durain beans cost $9 per pound and they sold 11 pounds.

Multiply the cost by the amount sold: 9 x 11 = $99

Subtract that from the total sold:

196 - 99 = $97

Now divide the amount left by the cost per pound for Ice cream beans:

97 / 10 = 9.7 pounds.

Zoologists are studying two newly discovered species of insects in a previously unexplored section of rain forest. They estimate the current population of insect A to be 1.3 million and the current population of insect B to be 2.1 million. As development is encroaching on the section of rain forest where these insects live, the zoologists estimate the populations of insect A to be reducing at a rate of 3.8% and insect B to be reducing at a rate of 4.6%.

If P represents the population of each species of insect in millions, and t represents the elapsed time in years, then which of the following systems of equations can be used to determine how long it will be before the populations of the two species are equal?

Answer:

the  system of equation that  can be used to determine how long it will be before the populations of the two species are equal is :

[tex]\begin{cases} {\mathtt{P = 1.3 e^{-0.038 \ t}} & \\ \mathtt{P = 2.1 \ e^{-0.046 \ t}} & \end{cases}[/tex]

Step-by-step explanation:

Given that :

the current population of insect A to be 1.3 million

the current population of insect B to be 2.1 million.

As development is encroaching on the section of rain forest where these insects live, the zoologists estimate the populations of insect A to be reducing at a rate of 3.8% and insect B to be reducing at a rate of 4.6%.

The equation that can be used to determine how long it will be before the populations of the two species are equal is an equation for exponential decay, which can be represented as follows:

[tex]\mathtt{y = pe^{-rt}}[/tex]

where;

P represents the population of each species of insect in millions

t represents the elapsed time in years

r is the rate of decrease

So, we can have:

[tex]\mathtt{p_1 = 1.3 }[/tex] in million   and  [tex]\mathtt{p_2 = 2.1}[/tex] in million

Also for rate of decrease;

[tex]\mathtt{r_1 = 0.038}[/tex]     and [tex]\mathtt{r_2 = 0.046}[/tex]

Therefore;

the exponential decay for Population of insect A can now be:

[tex]\mathtt{P = 1.3 e^{-0.038 \ t}}[/tex]

the exponential decay for Population of insect B can now be:

[tex]\mathtt{P = 2.1 \ e^{-0.046 \ t}}[/tex]

Hence, the  system of equation that  can be used to determine how long it will be before the populations of the two species are equal is :

[tex]\begin{cases} {\mathtt{P = 1.3 e^{-0.038 \ t}} & \\ \mathtt{P = 2.1 \ e^{-0.046 \ t}} & \end{cases}[/tex]

Answer:

A!

Step-by-step explanation:

Plato

Answer:

D. 9%, 440.36 million

Step-by-step explanation:

w = 221(1.09)t

9%, 440.36 million

Answer:

Step-by-step explanation:

The figure above is a rectangle

Area of a rectangle = length × width

From the question

The total length of the rectangle = 3x

The total width of the rectangle = 4x + 5

So the area of the figure is

A = 3x( 4x + 5)

Expand

We have the final answer as

Hope this helps you

[tex](-3+5,10-7)=(2,3)[/tex]

Pregunta completa:

En una empresa trabajan 60 personas. Usan gafas el 16% de los hombres y el 20% de las mujeres. Si el numero total de personas que usan gafas es 11. ¿Cuantos hombres y mujeres hay en la empresa?

Responder:

Hombres = 25

Mujeres = 35

Explicación paso a paso:

Dado lo siguiente:

Número de personas que trabajan en la empresa = 60

Porcentaje de hombres que usan anteojos = 16%

Porcentaje de mujeres que usan anteojos = 20%

Número total de personas que usan anteojos = 11

Suponga, Número de hombres en la empresa = m

Número de mujeres = número total - número de hombres = 60 - m

Por lo tanto,

16% de los hombres = 0,16 m

20% de mujeres = 0,2 (60 - m) = 12 - 0,2 m

Por lo tanto,

0,16 m + 12 - 0,2 m = 11

- 0,04 m = 11 - 12

-0,04 m = - 1

m = 1 / 0.04 = 25

Por tanto, Número de hombres en la empresa = m = 25

Número de mujeres en la empresa = (60 - m) = (60 - 25) = 35 mujeres

Hey there! I'm happy to help!

When building equations, the word "is" means "equals".

First, we have the sum of a number and six. You can use any letter to represent the number. I will use n.

(n+6)

We see that this is multiplied by 5. We can just put the 5 next to the parentheses. This shows multiplication.

5(n+6)

Is 48

5(n+6)=48

Have a wonderful day! :D