Two men, 400 feet apart, observe a balloon between them; it is in the same vertical plane as they are. The respective angles of elevation of the balloon are observed by the men to be 75°20' and 49°30'. Find x rounded to the nearest whole number.

Your answer should be

-1

Don't forget to MARK BRAINLIEST!! <3 :)

Final answer:

To prove that the diagonals of a square are congruent and perpendicular, label the vertices of a square on a coordinate grid and calculate the slopes and lengths using the slope formula and distance formula respectively. The diagonals have slopes of +1 and -1, proving they are perpendicular, and they have equal lengths, proving they are congruent.

Explanation:

To prove that the diagonals of a square are congruent and perpendicular, we place a square with its vertices on a coordinate grid and label each vertex with variables.

Let's consider a unit square where c = 1 for simplicity, which means the length of each side is 1 unit. Place the square so that one vertex is at the origin (0,0), and label the vertices A(0,0), B(1,0), C(1,1), and D(0,1).

The diagonal AC will have endpoints at A(0,0) and C(1,1), and diagonal BD will have endpoints at B(1,0) and D(0,1). The slope of diagonal AC is (1 - 0)/(1 - 0) = 1, and the slope of diagonal BD is (1 - 0)/(0 - 1) = -1. Since the product of their slopes is -1 (1 * -1 = -1), this proves that they are perpendicular to each other.

To show they are congruent, we calculate their lengths using the distance formula: the distance between two points (x1,y1) and (x2,y2) is √[(x2 - x1)² + (y2 - y1)²]. Applying this to AC and BD reveals both lengths to be √[(1-0)² + (1-0)²] = √[1 + 1] = √2, proving the diagonals are congruent.

The possible range of [tex]\dfrac{8}{3}-5mx[/tex] is:

                   (-9,-3) i.e. [tex]-9<\dfrac{8}{3}-5mx<-3[/tex]

We are given a set of inequalities of the form:

[tex]9<15mx-8<27[/tex]

Now when we divide all of the inequality by 3 we get that:

[tex]\dfrac{9}{3}<\dfrac{15mx}{3}-\dfrac{8}{3}<\dfrac{27}{3}\\\\i.e.\\\\3<5mx-\dfrac{8}{3}<9[/tex]

Now when we multiply the inequality by -1 then the sign of the inequality gets interchanged.

i.e.

[tex]-3>-(5mx-\dfrac{8}{3})>-9\\\\i.e.\\\\-3>\dfrac{8}{3}-5mx>-9[/tex]

i.e.

[tex]-9<\dfrac{8}{3}-5mx<-3[/tex]

Hence, the possible range of [tex]\dfrac{8}{3}-5mx[/tex] is:

    (-9,-3) i.e. between -9 and -3 with -9 and -3 excluded from the range.

Answer:

9 square inches.

Step-by-step explanation:

We have been given that a rectangle has a length of the [tex]\sqrt[3]{81}[/tex] inches and a width of [tex]3^{\frac{2}{3}}[/tex] power inches. We are asked to find the area of given rectangle.

We know that area of rectangle in length times width of rectangle.

[tex]\text{Area of rectangle}=\sqrt[3]{81}\times 3^{\frac{2}{3}}[/tex]

We can write 81 as [tex]3^4[/tex] as:

[tex]\text{Area of rectangle}=\sqrt[3]{3^4}\times 3^{\frac{2}{3}}[/tex]

Using exponent rule [tex]\sqrt[n]{a^m}=a^{\frac{m}{n}}[/tex], we can write [tex]\sqrt[3]{3^4}=3^{\frac{4}{3}}[/tex].

[tex]\text{Area of rectangle}=3^{\frac{4}{3}}\times 3^{\frac{2}{3}}[/tex]

Using exponent rule [tex]a^b\cdot a^c=a^{b+c}[/tex], we will get:

[tex]\text{Area of rectangle}=3^{\frac{4}{3}+\frac{2}{3}}[/tex]

[tex]\text{Area of rectangle}=3^{\frac{4+2}{3}}[/tex]

[tex]\text{Area of rectangle}=3^{\frac{6}{3}}[/tex]

[tex]\text{Area of rectangle}=3^{2}[/tex]

[tex]\text{Area of rectangle}=9[/tex]

Therefore, the area of given rectangle is 9 square inches.

5 different meats

3 different cheeses

3 different breads

5x3x3 = 15*3 = 45

 there are 45 choices

The sandwich shop offers a total of 45 different sandwich combinations based on the given options of meats, cheeses, and breads. Each sandwich consists of one type of each category.

The question asked is related to the concept of combinations in mathematics. It gives a variety of choices for making a sandwich - 5 types of meats, 3 types of cheeses, and 3 types of breads. Assuming that each sandwich will have one meat, one cheese, and one type of bread, we can calculate the total combinations by multiplying the number of options in each category together. Combinations are used when the order of selection does not matter.

So, the total number of sandwich combinations would be 5 (meats) * 3 (cheeses) * 3 (breads) = 45 different sandwich choices.

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a $9 fee plus $4 oper ride

let T = total cost

X= number of rides

T=9.00+4.00X

Answer:

Option B is correct.

[tex]3x^2+4x+2[/tex].

Step-by-step explanation:

We are asked to find the quotient obtained by dividing the expression [tex](3x^3+10x^2+10x+4)[/tex] by the expression [tex](x+2)[/tex]

We can also write this expression as i.e. we are asked to find the value of the expression:

[tex]\dfrac{3x^3+10x^2+10x+4}{x+2}[/tex]

We can write the expression on the numerator as:

[tex]3x^3+10x^2+10x+4=(3x^2+4x+2)(x+2)[/tex]

Hence,

[tex]\dfrac{3x^3+10x^2+10x+4}{x+2}=\dfrac{(3x^2+4x+2)(x+2)}{x+2}[/tex].

Hence,

[tex]\dfrac{3x^3+10x^2+10x+4}{x+2}=3x^2+4x+2[/tex].

Hence, option B is correct.

Hence, the quotient is:

[tex]3x^2+4x+2[/tex].

Final answer:

To use normal distribution for calculating confidence intervals for proportion p, both np and nq must be greater than or equal to 5.

Explanation:

In order to use a normal distribution to calculate confidence intervals for a population proportion p, the conditions on np and nq need to be such that both np ≥ 5 and nq ≥ 5. These conditions are necessary because they ensure that the shape of the binomial distribution is similar to that of a normal distribution, which allows for the approximation of the binomial distribution by the normal distribution. When performing a hypothesis test of a single population proportion, it is imperative that the sample data meet these conditions to ensure a valid test. Therefore, the correct answer to the question is d. np and nq must be > 5.

Answer:  The answer is 0.5 and 5.

Step-by-step explanation: The given equation of the line is

[tex]2(y+1)=10x+3.[/tex]

We are to find the y-intercept and the slope of the given line.

We know that the slope-intercept form of a line is given by

y = mx + c, where, 'm' is the slope and 'c' is the y-intercept of the line.

We have

[tex]2(y+1)=10x+3\\\\\Rightarrow 2y+2=10x+3\\\\\Rightarrow 2y=10x+3-2\\\\\Rightarrow 2y=10x+1\\\\\Rightarrow y=5x+0.5.[/tex]

Therefore, c = 0.5 and m = 5.

Thus, the y-intercept of the line is 0.5 and the slope is 5.

3-1 = 2

 2 is greater than 1/4

 so > is the answer

Answer: 12.496

Step-by-step explanation:

The formula to find the sum of geometric progression is given by :-

[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]

Given : The first term : [tex]a_1=10[/tex]

Common ratio = [tex]r=\dfrac{1}{5}=0.2[/tex]

Then , the sum of first five terms of a geometric series is given by :-

[tex]S_5=\dfrac{10(1-(0.2)^5)}{1-0.2}=12.496[/tex]

Hence, the sum of the first five terms of given geometric series =12.496

area = 1/2 x b x h

1/2 x 8 x 3 = 12

area is 12 square yards

Simply multiply the number outside the brackets with each one inside it..

3 [ 1 5 -5 6 0 0 ]
3 x 1 = 3
3 x 5 = 15
3 x -5 = -15
3 x 6 = 18
3 x 0 = 0
3 x 0 = 0
[ 3 15 -15 18 0 0 ]

[ 3 15 ]
[ -15 18 ]
[ 0 0]

The answer is B and I hope I explained this well for you.

I think it is c or D but it should be C

hope that help

[I don't think it did lol ]

BMK

Answer:

The slope of the line that is perpendicular to the line whose equation is 2x + y = 4 is   [tex]\frac{1}{2}[/tex].

Step-by-step explanation:

Given : Equation is 2x + y = 4.

To find : What is the slope of the line that is perpendicular to the line.

Formula used : equation of line y =  m[tex]m_{1}[/tex] x + c.

Solution : We have 2x + y = 4.

Rearranging the equation :  y = - 2x + 4.

On comparing   m[tex]m_{1}[/tex] = - 2.

Condition for  slope of the line that is perpendicular to the line :

      m[tex]m_{1}[/tex] × m[tex]m_{2}[/tex] = -1 .

So,       -2 × m[tex]m_{2}[/tex] = -1 .

On dividing by 2 both we get ,

  m[tex]m_{2}[/tex] = [tex]\frac{1}{2}[/tex].

Therefore, The slope of the line that is perpendicular to the line whose equation is 2x + y = 4 is   [tex]\frac{1}{2}[/tex].

opposite angles are identical so if angle 1 = 130

 than angle 3 is also 130 degrees

Answer:

Angle 3

Step-by-step explanation:

we know that

[tex]m<1=m<3[/tex] -----> by vertical angles

we have

[tex]m<1=130\°[/tex]

therefore

[tex]m<3=130\°[/tex]

An odd function, by definition, is a function that is symmetric about the origin.

An even function, by definition, is a function that is symmetric with respect to the y-axis.

Since the question says that f(x) is an odd function, it has rotational symmetry about the origin. First option is correct.

ANSWER: symmetric about the origin.

Answer:It has rotational symmetry about the origin.

Step-by-step explanation:

An odd function : is a function that is symmetric about the origin.

An even function : is a function that is symmetric with respect to the y-axis.

Since , f(x) is an odd function, it has rotational symmetry about the origin.

its meaning that its graph remains unchanged after rotation of 180 degrees about the origin.

Therefore, It has rotational symmetry about the origin.

The angle of depression represents the angle from a horizontal layout to a lower surface. The distance between the two stadiums is 3115.1 meters

The given parameters have been illustrated using the attached image of triangles.

The stadiums are represented with A and B.

First, calculate distance BO using:

[tex]\tan T =\frac{BO}{TO}[/tex]

Where:

[tex]\angle T = 90 -75.2 = 14.8[/tex]

[tex]TO = 1100[/tex]

So, we have:

[tex]\tan(14.8^o) = \frac{BO}{1100}[/tex]

Make BO the subject

[tex]BO = 1100 * \tan(14.8^o)[/tex]

[tex]BO = 1100 * 0.2642[/tex]

[tex]BO = 290.62[/tex]

Next, calculate distance AO using:

[tex]\tan T =\frac{AO}{TO}[/tex]

But in this case:

[tex]\angle T = 90 -17.9 = 72.1[/tex]

[tex]TO = 1100[/tex]

So, we have:

[tex]\tan(72.1^o) = \frac{AO}{1100}[/tex]

Make AO the subject

[tex]AO = 1100 * \tan(72.1^o)[/tex]

[tex]AO = 1100 * 3.0961[/tex]

[tex]AO = 3405.71[/tex]

The distance AB between the 2 stadiums is:

[tex]AB = AO - BO[/tex]

[tex]AB = 3405.71-290.61[/tex]

[tex]AB = 3115.1[/tex]

Hence, the distance between the 2 stadiums is 3115.1 meters.

Read more about angles of depression at:

https://brainly.com/question/13697260

Answer:

The graph of polar equation is symmetric about the x-axis.

Step-by-step explanation:

The given polar equation is

[tex]r=-5-5\cos \theta[/tex]

If [tex](r,\theta)[/tex] and [tex](r,-\theta)[/tex] lie on the graph then the graph of polar equation is symmetric about the x-axis.

Substitute [tex]\theta=-\theta[/tex] in the given equation.

[tex]r=-5-5\cos (-\theta)[/tex]

Cosine is an even function.

[tex]r=-5-5\cos \theta[/tex]                   [tex][\cos (-\theta)=\cos (\theta)][/tex]

Point [tex](r,-\theta)[/tex] lies on the graph, therefore the graph of polar equation is symmetric about the x-axis.