The area of a square is given by the formula A=s, where s is the length of the side. What is the area of the square shown? ​

Answer:

The height is 3791 ft.

Step-by-step explanation:

You need to make a drawing. Start with a vertical segment, 2 inches long, on the left side of the page. Label the top point A and the bottom point B. At the bottom endpoint, draw a longer horizontal segment, 4 inches long, to the right. Label the bottom right endpoint C. Connect A and C with a segment. Angle C is the original angle of elevation. On the bottom horizontal side, approximately 1 inch to the left of C, draw point D. Connect D and A with a segment. DA = 1000 ft. m<C = 34.8°. m<ABD = 40.4°. We are looking for AB, the height of the volcano.

We can work on triangle ADC.

m<C = 34.8°

Angles ADB and ADC are a linear pair, so m<ADC = 180° - 40.4° = 139.6°

m<DAC + m<ADC + m<C = 180°

m<DAC + 139.6° + 34.8° = 180°

m<DAC = 5.6°

Using the law of sines, we can find AC.

[tex] \dfrac{\sin A}{a} = \dfrac{\sin B}{b} [/tex]

[tex]\dfrac{\sin 5.6^\circ}{1000} = \dfrac{\sin 139.6^\circ}{AC}[/tex]

[tex]AC = \dfrac{1000\sin 139.6^\circ}{\sin 5.6^\circ}[/tex]

[tex] AC = 6642~ft [/tex]

Now we use triangle ABC. AC = hypotenuse. AB = opposite leg. <C is known angle.

[tex] \sin C = \dfrac{opp}{hyp} [/tex]

[tex]\sin 34.8^\circ = \dfrac{AB}{6642~ft}[/tex]

[tex]AB = 6642~ft \times \sin 34.8^\circ[/tex]

[tex] AB = 3791~ft [/tex]

Answer: The height is 3791 ft.

Given:

The two endpoints are (4,5) and (4,-3).

To find:

The line segment between the given endpoints and the length of the line segment.

Solution:

Plot the given point and connect them by and straight line segment as shown in the below graph.

The distance between (4,5) and (4,-3) is

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]d=\sqrt{(4-4)^2+(-3-5)^2}[/tex]

[tex]d=\sqrt{(0)^2+(-8)^2}[/tex]

[tex]d=\sqrt{0+64}[/tex]

[tex]d=\sqrt{64}[/tex]

[tex]d=8[/tex]

Therefore, the length of the line segment is 8 units.

Final Answer: [tex]f = \frac{ax}{2} + \frac{3b}{2}[/tex]

Steps/Reasons/Explanation:

We will be trying to rewrite the equation. To do this we will move [tex]2f[/tex] to the left. Then, we will move [tex]ax + 3b[/tex] to the right.

Question: Solve for [tex]f[/tex]: [tex]ax + 3b = 2f[/tex].

Step 1: Rewrite the equation.

[tex]2f = ax + 3b[/tex]

Step 2: Divide each term by [tex]2[/tex] and simplify.

[tex]\frac{2f}{2} = \frac{ax}{2} + \frac{3b}{2}[/tex]

Step 3: Cancel out the common factor of [tex]2[/tex].

[tex]\frac{Cancel 2 f}{Cancel 2} = \frac{ax}{2} + \frac{3b}{2}[/tex]

Step 4: Divide [tex]f[/tex] by [tex]1[/tex].

[tex]f = \frac{ax}{2} + \frac{3b}{2}[/tex]

~I hope I helped you :)~

Answer:

It is clear that both equations are identical. Hence, the solution to the system of equations would contain infinitely many solutions.

Step-by-step explanation:

Given the system of equations

y = -4x + 2

y = -4x + 2

It is clear that both equations are identical. We know that when the system of equations is identical, then the system of equations will have infinitely many solutions.

Hence the given system of equations would contain infinitely many solutions.

solving the system of equations

[tex]\begin{bmatrix}y=-4x+2\\ y=-4x+2\end{bmatrix}[/tex]

Substitute y = -4x+2

[tex]\begin{bmatrix}-4x+2=-4x+2\end{bmatrix}[/tex]

For y = -4x+2

Express y in terms of x

[tex]y=-4x+2[/tex]

Thus, the solution to the system of equations would be:

[tex]y=-4x+2,\:x=x[/tex]

It is clear that x = x is true no matter what. Hence, the solution to the system of equations would contain infinitely many solutions.

Answer:

50,373 feet

Step-by-step explanation:

tan 15° = 13500 / x

.268 = 13500 / x

x = 50,373

Answer:

Step-by-step explanation:

Given formula:

Solving for n:

[tex]S = 180(n - 2) \\ S = 180n - 360 \\ 180n =( S + 360) \\ n = \frac{(S+ 360)}{180} [/tex]

where, n =number of sides of polygon

S =sum of the degree measures of the interior angles of the polygon

Answer:

change/original price X 100

22/88 X 100 = 25%

Answer:

C

Step-by-step explanation:

The x coordinate of the rest stop:

1/2 × (the sum of the x coordinates of the highschool and the stadium)

= 1/2 × (3+7)

= 1/2 × 10

= 5

The y coordinate of the rest stop:

- Same thing i did for the x coordinate, but use the y coordinates.

1/2 × (the sum of the y coordinates of the highschool and the stadium)

= 1/2 × (4 + 1)

= 1/2 × 5

=5/2

So the coordinate of the rest stop would be (5, 5/2).

Next for the distance, i used the pythagoras theory so it's like this:

a^2 + b^2 = c^2

Here you plot the highschool and the stadium on the coodinate plane, then connect the two dots to make a right triangle. The height of the triangle will be 3, and the base would be 4. So a=3, b=4 in the equation.

3^2 + 4^2 = c^2

9 + 16 + c^2

25 + c^2

c = 5

(Note that this isn't the real answer cuz at the end of the question it said that one UNIT equals 6.4 MILES.)

So the final answer is 5 × 6.4, which is 32. The answer is C.

Answer:

The co-ordinates of B (1,3 )

Step-by-step explanation:

Step(i):-

Given A( 3,4) and C( -9, -2)

Given  'B' partition AC such that

B divides AC in the ratio is 1:5 internally

Section formula

       [tex](\frac{mx_{2}+nx_{1} }{m+n} ,\frac{my_{2}_+ny_{1} }{m+n} )[/tex]

Step(ii):-

Given points are

     A( 3,4) and C( -9, -2) and ratio 1 : 5

(x₁ , y₁) = ( 3,4)     and (x₂, y₂) = (-9,-2)

m:n = 1 : 5

The co-ordinates of B

           = [tex](\frac{1(-9)+5(3) }{1+5} ,\frac{1(-2)+5(4) }{1+5} )[/tex]

         =  [tex](\frac{6}{6} , \frac{18}{6} )[/tex]

       = (1 , 3)

Final answer:-

The co-ordinates of B (1,3 )

Answer:

B

Step-by-step explanation:

i did the same test

Answer:

264 miles

Step-by-step explanation:

Let's convert 3 hours and 40 minutes into hours first.

Recall that 1 hour = 60 minutes.

Therefore 40 minutes = 40/60 hours = 2/3 hours.

The car travelled 3 and 2/3 hours in total.

Recall that distance = speed times time.

The car has travelled 72 x 3 2/3 miles = 264 miles.

Answer:

3611/12

Step-by-step explanation:

Answer:

one-solution

Step-by-step explanation:

(x + 2y = 6)2

2x - 3y = 26

2x + 4y = 12

2x - 3y = 26

7y = -14

y = -2

x + 2(-2) = 6

x + -4 = 6

x = 10

Answer:

Step-by-step explanation:

It is two lines, if they intersect there is one solution, if parallel- no solution, if  same lines- infinitely many solutions

Lets put them in slope-intercept form and compare:

As we see the lines have different slopes, so they intersect which means one solution only.

Answer in fraction form: x = 55/4

Answer in decimal form: x = 13.75

Both forms are equivalent, but they say it in a slightly different way.

===========================================================

Work Shown:

AC/QY = CD/YW

(x+5)/15 = 5/4

4(x+5) = 15*5

4x+20 = 75

4x = 75-20

4x = 55

x = 55/4

x = 13.75

------------

Explanations:

Answer:

$5.60

Step-by-step explanation:

So each pound equals to $1.75 which means that we need to multiply by 3.2 because we're trying to find the number of money we'll spend on a certain amount of coffee. So if we multiply, we get 5.6. Though in context with the problem, it should be $5.60.

Answer:

[tex]\frac{dy}{dx}[/tex] = 8(2x + 3)³

Step-by-step explanation:

Differentiate using the chain rule

Given

y = f(g(x)) , then

[tex]\frac{dy}{dx}[/tex] = f'(g(x)) × g'(x)

Here

f(x) = [tex](2x+3)^{4}[/tex] ⇒ f'(x) = 4(2x + 3)³

g(x) = 2x + 3 ⇒ g'(x) = 2

Thus

[tex]\frac{dy}{dx}[/tex] = 4(2x + 3)³ × 2

    = 8(2x + 3)³

Answer:

y = 15

x = 43

Step-by-step explanation:

this is giving us a system of equations because we know two things:

x + y = 58

x - y = 28

take the second equation and format it where you have simplified it for one variable:

x = 28 + y

(we did this by adding y to both sides)

now substitute this new value of x into the first equation:

28 + y + y = 58

simplify this to get 2y = 30

divide both sides by 2: y = 15

now substitute your new value of y into the second equation:

x = 28 + 15

x = 43

Answer:

y = 45 + 0.15x

Step-by-step explanation:

$45 is the initial cost

0.15 is the cost for each mile

we dont know the miles so miles is x, unknown

Answer:

I think it's the y-function. Are there any choices to choose from?

Step-by-step explanation:

Answer:

They increase at the same rate

Step-by-step explanation:

If you look at linear function p, the equation is y=3x-6

Answer:

a) 900

b) 9,000

Step-by-step explanation:

Answer:

Step-by-step explanation:

A. a=100. an=999

an=a+n-1.d

Therefore answer will be 900.

B. 9000.

Answer:

0

Step-by-step explanation:

Answer:

a = −1 or a = 7

Step-by-step explanation:

Let's solve your equation step-by-step.

( a − 7 ) ( a + 1 ) = 0

Step 1: Simplify both sides of the equation.

a^2 − 6a − 7 = 0

Step 2: Factor left side of equation.

( a + 1 ) ( a − 7 ) = 0

Step 3: Set factors equal to 0.

a + 1 = 0 or a − 7 = 0

a = −1 or a = 7

Answer:

The perimeter of square will be 18 units

Step-by-step explanation:

We are given that the coordinates of three vertices of a square A (-2 1/2 , 1 1/2), B (-2 1/2 -3), and C (2,1 1/2 )

When point D is placed on this perimeter.

We have to find the perimeter of the square.

First we have to find the side of square by using the distance formula

Distance formula

[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Coordinates of A=(-5/2,3/2)

Coordinates of B=(-5/2,-3)

Length of side AB=[tex]\sqrt{(-5/2+5/2)^2+(-3-3/2)^2}[/tex]

Length of side AB=[tex]\sqrt{0+(-9/2)^2}[/tex]

Length of side AB=9/2 units

Now, the perimeter of square=4 (side)

Using the formula

Perimeter of square=4(9/2)=18 units

Answer: a. Lin's tank hold 20 cups and Elena's tank hold 20 gallons; I know this because gallons are greater than cups.

Step-by-step explanation:

Gallons are greater than cups so the fish tank that will hold 20 gallons would have to be the bigger one which in this case is Elena's.

With cups being lesser in quantity than gallons, the fish tank that will hold 20 cups of water will definitely have to be the smaller one which in the case is Lina's.

Answer: x=9 1/3

Step-by-step explanation:

-5=-3x-33

-5+33=-3x

28=-3x

3x=-28

x=28/3

x=9 1/3

Answer: X=-28/3

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

−5=−3(x+11)

−5=(−3)(x)+(−3)(11)(Distribute)

−5=−3x+−33

−5=−3x−33

Step 2: Flip the equation.

−3x−33=−5

Step 3: Add 33 to both sides.

−3x−33+33=−5+33

−3x=28

Step 4: Divide both sides by -3.

-3x/-3= 28/-3

X=-28/3

have a nice day :)

Answer:

-7/3

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define

y = -7/3x + 5

Step 2: Break Function

Identify Parts

Slope m = -7/3

y-intercept b = 5

Answer:

-2

Step-by-step explanation:

f(x) = –x– 5

f(x) = -(-3)– 5

f(x) = 3– 5

f(x) = -2

Answer:

Answer is -2 because - * - = + 3-5=-2

Answer:

1410

Step-by-step explanation:

they said they would spend 3000 more than last year. it said this years budget is 4410.