A shooting star forms a right triangle with the Earth and the Sun, as shown below:

A right triangle is shown with the vertices labeled Earth, Sun, and Shooting Star. The angle formed by the Sun is labeled x deg

A scientist measures the angle x and the distance y between the Sun and the shooting star. Using complete sentences, explain how the scientist can use only these two measurements to calculate the distance between the Earth and the Sun. (10 points)

Answer:

x=0

Step-by-step explanation:

a vertical line is x= whatever the x-term is

Answer:

g(x) = f(2) at x = 4

Step-by-step explanation:

Assuming that you meant g(x) = 2x - 3:

Set f(2) = g(x) and solve the resulting equation for x:

f(2) = 3(2) - 1 = g(x) = 2x - 3.

Thus,   6 - 1 = 2x - 3.

Adding 3 to both sides and simplifying the result, we get:

8 = 2x, or x = 4.

g(x) = f(2) at x = 4.

Step-by-step explanation:

5x-30=3x

5x-3x=30

2x=30

Divide by 2 for 2x and 30

x=15

Check answer subsituition method:

5x-30=3x

5(15)-30=3(15)

75-30=45

45=45

Answer: x=15 ( choice 3)

We simply have to solve a quadratic equation [tex]ax^2+bx+c=0[/tex] using the quadratic formula

[tex]x_{1,2} = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

In your case, [tex]a=b=1,\ c=-42[/tex]. So, the formula becomes

[tex]x_{1,2} = \dfrac{-1\pm\sqrt{1+168}}{2} = \dfrac{-1\pm 13}{2}[/tex]

So, if we choose the two signs, we have

[tex]x_1 = \dfrac{-1-13}{2}=-7,\quad x_2 = \dfrac{-1+13}{2}=6[/tex]

Answer:

x = -7, x = 6

Step-by-step explanation:

f(x) = x² + x − 42

You can use the quadratic formula to find the roots (x-intercepts), or, if it's "factorable", you can use the AC method.

Here, a = 1, b = 1, and c = -42.

The product a times c is -42.

Factors of ac that add up to b are +7 and -6.

So the quadratic factors to:

f(x) = (x + 7) (x − 6)

To find the x-intercepts, we set this equal to 0:

0 = (x + 7) (x − 6)

x + 7 = 0, x − 6 = 0

x = -7, x = 6

Answer:

A)

Step-by-step explanation:

 Since we are given the function, we can simply plug in the x as 9. So we get 50(0.952)9. Solving this, we get 450(.952) and this is about 428. SO our answer is a) about 428 feral cats.

There will be 428 feral cats in 9 years.

We can substitute the given number in the function to find the required value here, years are represented by x. Therefore, we must substitute the value of x = 9 in the function to find the population of feral cats in 9 years.

The function is given as:

f(x) = 50(0.952)x.

We have to find the number of feral cats in 9 years. Therefore, the value of x is 9.

Now, we can substitute the value of x in the function. This can be done as follows:

f(x) = 50(0.952)x

f(9) = 50(0.952)*9

f(9) = 50(8.568)

f(9) = 428.4

f(9) ≈ 428

We have found the number of feral cats in 9 years. The number of feral cats that will be alive after 9 years is found to be 428.

Therefore, we have found that there will be 428 feral cats in 9 years. The correct answer is option A.

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Answer with explanation:

 →The equation of line which we have to write in slope intercept form is:

  3 x -2 y=6

The equation of line in slope Intercept form is given as:

       y = m x +c

Where, m=Slope of line

c=Y- intercept

Slope Intercept form of line can be as follows :

   [tex]\Rightarrow 3 x-2 y=6\\\\\Rightarrow \text{Adding 2y on both sides}\\\\\Rightarrow 3 x-2 y+2 y=2 y+6\\\\\Rightarrow 3 x= 2 y+6\\\\\text{Dividing both sides by 3}\\\\\Rightarrow x=\frac{2y}{3}+\frac{6}{3}\\\\\Rightarrow x=\frac{2y}{3}+2[/tex]

Answer:

y = three-halves x minus 3

y = one-eighth x minus three-fourths

Step-by-step explanation:

Hello There!

Consecutive Angles In Parallelograms Are "Supplementary"

"Supplementary Angles" Are Angles That Have A Sum of 180 Degrees  

Answer:

Step-by-step explanation:

Are "Supplementary

Answer:

17 liters

Step-by-step explanation:

0.5 and above will make 1, 0.4 and below makes it the same

ANSWER

The amplitude is 2 and the maximum value is 2.

EXPLANATION

The given function is

[tex]f(t) = 2 \sin(t) [/tex]

This function is of the form:

[tex]f(t) = a\sin(bt) [/tex]

The amplitude of this function is

[tex] |a| [/tex]

Hence the amplitude is

[tex] |2| = 2[/tex]

Since the amplitude is 2, and there is no vertical shift, it means the function is bounded by

y=-2 and y=2.

The maximum value is :

2

Answer: 4x^3+2x^2-12x+8

I am sorry it takes to long to type in the equation of this problem step by step. I only can just give you an answer.

Answer:

(x - 3)² + (y - 8)² = 4

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (3, 8) and r = 2

(x - 3)² + (y - 8)² = 4 ← equation of circle

The equation of a circle with center (3, 8) and radius 2 will be given as

[tex]( x -3 )^2 + ( y -8 )^2 = 4[/tex].

Equation of circle is given as,

[tex]( x -a )^2 + ( y -b )^2 = r^2[/tex]

where,

(a,b) are the coordinates of the center of the circle in form (x, y),

r is the radius of the circle.

Now, the equation of a circle with center (3, 8) and radius 2.

Given to us,

a = 3,

b = 8,

r = 2.

substituting the values,

[tex]( x -a )^2 + ( y -b )^2 = r^2[/tex]

[tex]( x -3 )^2 + ( y -8 )^2 = 2^2[/tex]

[tex]( x -3 )^2 + ( y -8 )^2 = 4[/tex]

Hence, the equation of a circle with center (3, 8) and radius 2 will be given as  [tex]( x -3 )^2 + ( y -8 )^2 = 4[/tex].

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Answer:

Step-by-step explanation:

[tex]12a=\bold{(3)}(4)\bold{(a)}\\\\9a^2=\bold{(3)}(3)\bold{(a)}(a)\\\\GCF(12a,\ 9a^2)=\bold{(3)(a)}=3a[/tex]

Answer:

Allison = $0.27

Brianna = $1.89

Step-by-step explanation:

The total cookies that the three girls have are:

Allison's cookies + Brianna's Cookies

= 9+15

=24

There is a total of 24 cookies which has to be divided between the 3.

So

Each girl gets 24/3 = 8 cookies.

Since Celeste had no cookies she will have to pay for the 8 cookies.

Allison had 9, she will give one to Celeste

Brianna had 15 out of which she will use 8 for her self and 7 will be given to Celeste.

Celeste is paying 2.16 for 8 cookies.

Price of one cookie = 2.16/8

=$0.27

So, amount that will be given to Allison = 0.27 * 1 = $0.27

Amount that will be given to Brianna = 0.27 * 7 = $1.89

Each person gets 8 cookies. Allison and Brianna each receive $1.08 of Celeste's $2.16.

To find the fair way to divide Celeste's money, we first need to determine how many cookies each person gets when the total number of cookies is divided equally among them.

Total number of cookies = Allison's cookies + Brianna's cookies

Total number of cookies = 9 cookies + 15 cookies

Total number of cookies = 24 cookies

Now, we'll divide the total number of cookies by the number of people (3) to find out how many cookies each person gets:

Number of cookies per person = Total number of cookies / Number of people

Number of cookies per person = 24 cookies / 3

Number of cookies per person = 8 cookies

So each person will get 8 cookies.

Now, since Celeste forgot to bring treats, Allison and Brianna agreed to divide Celeste's money equally between them. To do this fairly, they'll each receive half of Celeste's money.

Celeste's money = $2.16

Now, we'll find out how much each person gets from Celeste's money:

Amount per person = Celeste's money / Number of people

Amount per person = $2.16 / 2

Amount per person = $1.08

So each person will receive $1.08 from Celeste's money.

In summary:

- Each person will get 8 cookies.

- Each person will receive $1.08 from Celeste's money.

Answer:

1. 5(4 + 6) + 1-0

2. 9(9b + 2)

3. 40

4. Nine plus r multiplied by four over five and then added to eight w.

5. The quotient is [tex]\frac{45}{d}[/tex]

Step-by-step explanation:

Answer:

125.6 square inches of plastic is needed

Step-by-step explanation:

To make 10 plastic beach balls each with a radius of 2 inches, the company would need approximately 502.4 square inches of plastic.

To determine the amount of plastic needed to make 10 beach balls, we first calculate the surface area of one beach ball. The formula for the surface area of a sphere is 4πr². Given the radius of 2 inches, we plug this into the formula:

A = 4πr² = 4 × 3.14 × (2 inches)² = 4 × 3.14 × 4 square inches = 50.24 square inches.
Since this is for one beach ball, we need to multiply this amount by 10, to account for the total plastic needed for 10 beach balls:

Total surface area for 10 beach balls = 50.24 square inches × 10 = 502.4 square inches.

Therefore, the company would need approximately 502.4 square inches of plastic to make 10 beach balls, rounding to the nearest tenth.

Answer:

1.26 x [tex]10^{7}[/tex]

Step-by-step explanation:

For this case we must find the quotient of the following expression:

[tex]\frac {48 * j ^ 5 * k ^ 2} {- 3 * j ^ 3 * k} =[/tex]

We have to:

[tex]\frac {48} {- 3} = - 16[/tex]

By definition of power properties we have:

[tex]\frac {a ^ m} {a ^ n} = a ^ {m-n}[/tex]

So so:

[tex]\frac {48 * j ^ 5 * k ^ 2} {- 3 * j ^ 3 * k} = - 16 * j ^ {5-3} * k^{2-1}=-16*j^2*k[/tex]

Answer:

Option A

Answer:

B. 75°

Step-by-step explanation:

When lines that are parallel are crossed by a transversal , angles in matching corners are equal and called corresponding angles

To get the value of the angle;

180°-105°= 75°.................sum of angles on a straight line

This angle corresponds to angle y because of the parallel lines DE and XY

Answer:D

Step-by-step explanation:

Answer:

(k + 7)(3k - 8)

Step-by-step explanation:

To factor the quadratic

Consider the factors of the product of the k² term and the constant term which sum to give the coefficient of the k- term

product = 3 × - 56 = - 168 and sum = + 13

The factors are + 21 and - 8

Use these factors to split the k- term

3k² + 21k - 8k - 56 ( factor the first/second and third/fourth terms )

= 3k(k + 7) - 8(k + 7) ← factor out (k + 7)

= (k + 7)(3k - 8)

well if 18 out of 25 like it, then the remaining 7 doesn't like it, namely 7 out of 25.

if we take 25 to be the 100%, what is 7 off of if in percentage?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 25&100\\ 7&x \end{array}\implies \cfrac{25}{7}=\cfrac{100}{x}\implies 25x=700\implies x=\cfrac{700}{25}\implies x=28[/tex]

Answer:

AB² = VAC²-BC²

= V8²-6²

= V64-36 = V28

AB = V7×4 = 2V7 = 5.29

Answer:

The value 1.8 represent the club's total number of members today or the present number of members

Step-by-step explanation:

Given an exponential function;

[tex]y=ab^{x}[/tex]

b is the base or the growth factor

a is the initial value, that is the value of y when x = 0

We have been given the exponential function;

[tex]y=1.8(1.02)^{12t}[/tex]

The value 1.8 simply represents the initial value of y. Plug in t = 0 in the equation;

[tex]y=1.8(1.02)^{12(0)}=1.8[/tex]

Therefore, the value 1.8 represent the club's total number of members today or the present number of members

The answer is:

The correct option is:

B) 83 feet

To solve the problem, we need to use the following trigonometric identity:

[tex]Tan(\alpha)=\frac{Opposite}{Adjacent}[/tex]

Which, translated to our problem, will be:

[tex]Tan(\alpha)=\frac{Height}{Base}[/tex]

We are given two triangles, and we know their height and their angles between their hypothenuse and their bases.

So,

For the first triangle, we have:

[tex]height=60ft\\\alpha=64\°[/tex]

So, using the trigometric identity of the tangent, we have:

[tex]Tan(\alpha)=\frac{Height}{Base}\\\\Tan(64\°)=\frac{60ft}{Base}\\\\Base=\frac{60ft}{Tan(64\°)}=\frac{60ft}{2.05}=29.27ft[/tex]

Therefore, we have that the base of the first triangle is equal to 29.27 feet.

For the second triangle, we have:

[tex]height=60ft\\\alpha=48\°[/tex]

So, using the trigometric identity of the tangent, we have:

[tex]Tan(\alpha)=\frac{Height}{Base}\\\\Tan(48\°)=\frac{60ft}{Base}\\\\Base=\frac{60ft}{Tan(48\°)}=\frac{60ft}{1.11}=54.05ft[/tex]

Therefore, we have that the base of the second triangle is equal to 54.05  feet.

Now, to calculate the horizontal distance between the two trees (x), we need to use the following formula with the obtained values of both triangles:

[tex]HorizontalDistance=FirstTriangleBase+SecondTriangleBase\\\\HorizontalDistance=29.27ft+54.05=83.29ft[/tex]

Hence, we have that the distance between the two trees rounded to the nearest foot is 83 feet.

Have a nice day!

Step-by-step explanation:

First, reflect over line k:

(2, 5) → (-5, -2)

Then, reflect over the x-axis:

(-5, -2) → (-5, 2)

Answer: C. would be your option

Step-by-step explanation:

Answer:

3x – 5 < –10 or 3x – 5 > 10

Answer choice C on Edge

[tex]

x-4+5=2 \\

x+5=6 \\

\boxed{x=1}

[/tex]

Hope this helps.

r3t40

i^223 = -i

i^82 = -1

i^113 = i

i^48 = 1

Match each complex number with its equivalent by using the complex plane, polar coordinates, complex conjugates, and Euler's equation.

Matching each complex number with its equivalent expression involves understanding the complex plane, complex conjugates, and Euler's formula. A complex number z is represented by z = a + ib, where a is the real part and b is the imaginary part. Converting this to polar form involves finding the magnitude r and the angle θ, where r = (a² + b²)½ and θ = tan⁻¹(b/a). Euler's formula, z = r exp(iθ), can be used to express the complex number in terms of its magnitude and angle: z = r cos(θ) + ir sin(θ). The complex conjugate of z is z* = a - ib, and it is found by changing the sign of the imaginary part.

Answer:iuhihi

Step-by-step explanation:

nvjfuy

The surface area of the pyramid is 160ft^2

To find the surface area of a pyramid, we need to calculate the sum of the areas of all its faces. A pyramid has 4 triangular faces and 1 square base. The formula for the surface area of a pyramid is: Surface Area = Base Area + (0.5 × Perimeter of Base × Slant Height). In this case, the base side of the pyramid is 8ft and the slant height is 6ft.

First, we calculate the perimeter of the square base, which is 4 times the length of the base side: Perimeter = 4 × 8ft = 32ft.

The base area of the pyramid is found by squaring the length of one side of the base: Base Area = (8ft)^2 = 64ft^2.

Now we can substitute the values into the formula: Surface Area = 64ft^2 + (0.5 × 32ft × 6ft) = 64ft^2 + 96ft^2 = 160ft^2.

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The surface area of a pyramid with an 8 ft side length and a 10 ft slant height is 224 square ft. Hence, option A is correct.

To find the surface area of a pyramid with a square base, we need to calculate both the base area and the lateral surface area.

The side length of the square base is 8 ft, so the base area is:

The slant height of the pyramid is 10 ft, and the side length of the base is 8 ft. Each triangular face of the pyramid has a height (slant height) and base equal to the side of the square base. The area of one triangular face is:

Since a square-based pyramid has 4 triangular faces, the total lateral surface area is:

Adding the base area and the lateral surface area gives the total surface area:

Therefore, the total surface area of the pyramid is (Option A) 224 square ft.

Complete Question:

What is the surface area of the pyramid with slant height 10 ft and base 8 ft ?

A. 224ft

B. 460ft

C. 112 ft

D. 336ft