Fast forward a few years and suppose you need to get your car repaired. You see the ads above and decide to write an equation to represent the total cost at each repair shop x=number of hours for repair y= total cost Mike's Repair Shop: y = 100 + 65x Amy's Auto Repair: y = 40 + 80X. 1. Use the substitution or elimination method to find the point of intersection. Show your work below. 2. At what point do the two lines intersect? What is the meaning of the point of intersection in the context of this problem? * 3. If it takes 3 hours to fix your car, which company is the cheapest and what is the associated cost? Show your work below​

[tex](\stackrel{x_1}{6}~,~\stackrel{y_1}{24})\qquad \stackrel{origin}{(\stackrel{x_2}{0}~,~\stackrel{y_2}{0})} ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{0}-\stackrel{y1}{24}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{6}}}\implies \cfrac{-24}{-6}\implies 4[/tex]

Answer:

h = 2[tex]\sqrt{3}[/tex]

b = 3[tex]\sqrt{2}[/tex]

Step-by-step explanation:

to find 'h' we can use the ratio of sides in a 30-60-90° triangle which, respectively, is 1 : [tex]\sqrt{3}[/tex] : 2

so we can set up this proportion:

h/2 = 1/[tex]\sqrt{3}[/tex]

cross-multiply:

h = 2[tex]\sqrt{3}[/tex]

to find 'b' we can use the ratio of sides in a 45-45-90° triangle which, respectively, is 1 : 1 : [tex]\sqrt{2}[/tex]

we can set up this proportion:

3/b = 1/[tex]\sqrt{2}[/tex]

cross-multiply:

b = 3[tex]\sqrt{2}[/tex]

sinθ is equal to the division of the opposite side of the reference angle (θ) by the hypotenuse.

the cosine of an angle in a right triangle equals the adjacent side divided by the hypotenuse

tan30 = h/2

[tex]tan30 = \frac{1}{ \sqrt{3} } [/tex]

1/sqrt3 = h/2

[tex]h = \frac{2}{ \sqrt{3} } [/tex]

sin45 = 3/b

[tex]sin45 = \frac{1}{ \sqrt{2} } [/tex]

1/sqrt2 = 3/b

b/sqrt2 =3

[tex]b = 3 \sqrt{2} [/tex]

∠ABD and ∠EBC are complementary by the definition of complementary angles.

Given that in a figure, BD ⊥ BC ; ∠ABD ≅ ∠DBE.

We need to prove ∠ABD and ∠EBC are complementary.

BD ⊥ BC = given

∠DBC = 90° by the definition of perpendiculars.

∠ABD ≅ ∠DBE = given

∴ ∠ABD = ∠DBE by the definition of congruence.

Using the angles addition postulate,

∠EBC + ∠DBE = 90°

Now, replace ∠DBE by ∠ABD, we get,

∠EBC + ∠ABD = 90°

Hence ∠ABD and ∠EBC are complementary by the definition of complementary angles.

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The complete question is given below.

Answer:

a = 43/8

Step-by-step explanation:

8a-48+5+8a-43=0

16a-86=0

a=86/16

a=43/8

Ans

427

Step-by-step explanation:

divide 366 by 6 then multiply by 7.

2x^2 - x = 10

=> 2x^2 - x - 10 = 0

=> 2x^2 - (5 - 4)x - 10 = 0

=> 2x^2 - 5x + 4x - 10 = 0

=> x(2x - 5) + 2(2x - 5) = 0

=> (2x - 5)(x + 2) = 0

Either, Or,

2x - 5 = 0 x + 2 = 0

=> 2x = 5 => x = - 2

=> x = 5/2

Answer:

[tex]x1 = \frac{5}{2} \: \: and \: x2 = - 2[/tex]

Step-by-step explanation:

So, our equation is:

2x² - x - 10 = 0

The numbers before x are a, b, and c

We must first find the discriminant which is equal to b² - 4*a*c

D = b² - 4 * a * c

Be careful here, b is -1 because we have minus before x and c is -10

D = (-1)² - 4*2*-10

D = 1 + 80

D = 81

Now we need to find the roots of the equation, since D is greater than 0, the roots are equal to (-b ± sqrt(D)) / 2*a

[tex]x1 = \frac{ -( - 1) + \sqrt{81} }{2 \times 2} = \frac{1 + 9}{4} = \frac{10}{4} = \frac{5}{2} [/tex]

and for x2 we will put minus:

[tex]x2 = \frac{ - ( - 1) - \sqrt{81} }{2 \times 2} = \frac{1 - 9}{4} = \frac{ - 8}{4} = -2 [/tex]

Answer:

They are not equivalent

Step-by-step explanation:

[tex]{ \tt{ - 9h - 4.5 \equiv - 0.75(12h - 4.5)}} \\ \\ { \tt{ - 9h - 4.5≠( - 9h + 3.375)}}[/tex]

Answer:

No, they are not equivalent.

Step-by-step explanation:

So in order to solve this question, you need to set the equations equal to each other. -9h-4.5=-0.75(12h-4.5)

Let's work on the left side first, only because it's going to take more work and because we need to solve it in order to continue the process. So you first are going to want to use the distributive property. Multiply 12h and -4.5 by -0.75. 12h*-0.75=-9h. -4.5*-0.75=3.375. so now your equation looks like -9h-4.5=-9h+3.375

So just looking at it, it seems as if these equations are not equivalent, just parallel.

Hope this helps!

Answer:

Step-by-step explanation:

The filling speed is 30 hours or:

The draining speed is 34 hours or:

If both lines are open simultaneously, the filling speed is:

If the tank is 1/5 full, then we need to fill the 4/5 of level and it will take:

Answer:

30

Step-by-step explanation:

30 can be divided by 5, 6, and 10

Answer:

[tex]approxmatly \: = 6[/tex]

Answer:

√ [37]

Step-by-step explanation:

I'll be calling the first point, A,

being A(-4,1) ; B(2,0)

For the distance: d(A,B) = √(xB - xA)² + (yB - yA)² ⇔

⇔ d(A,B) = √(2+4)² + (0-1)² = √6² + 1² = √36 + 1 = √37

Use the given formula:

Sqrt((5–4)^2 + (-3-2)^2)

Sqrt(9^2 +-5^2)

Sqrt(81 + 25)

Sqrt(106)

Answer is A. Sqrt106

Solution:

Draw the two legs of the right triangle (Refer to image). According to the image, point R shows a right angle. This means that:

Now, let's use Pythagoras theorem to find JK.

Option A is correct.

Answer:

It contains 3 pints of fruit juice.

Step-by-step explanation:

A pint is 16 ounces.

48 ounces divided by 16 ounces equals 3, giving us 3 pints.

I hope this helps.

Answer:

Check the image below the explanation.

Step-by-step explanation:

Answer:

164,340

Step-by-step explanation:

120n + 160,500

120(32) + 160,500

3842 + 160,500

164,340

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the surface area, we need to find the area of all the squares and triangles available.

Solution:

Now, multiply the area of the triangle by 4.

Now, let's find the area of the square.

Now, add the area of the triangles and the squares.

Hence, the surface area of the pyramid is 63 cm².

The formula for slope is:  m  =  (y2 - y1) / (x2 - x1)   --->   m  =  (b - b) / (-a - a)  =  0/(-2a)  =  0

Answer:

Step-by-step explanation:

Perimeter equation:

We have:

Simplify the first equation and solve by substitution:

Find the value of l:

The equation is

And

And

L=7+2=9ft

Using it's formula, it is found that the geometric mean between 6 and 12 is of 8.4853.

The geometric mean between n numbers is given by the nth root of the product of the numbers.

In this problem, there are 2 numbers, 6 and 12, hence the geometric mean is given by:

[tex]M_g = \sqrt{6 \times 12} = \sqrt{72} = 8.4853[/tex]

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Answer:

5

Step-by-step explanation:

-6+2n=3n-(6+5)

-6+2n=3n-11

-6+2n-3n=-11

-6-n=-11

n=-6-(-11)

n=-6+11

n=5

Answer:

x=−3

Step-by-step explanation:

Move all terms that don't contain

x to the right side and solve.

hope this helps !

Answer:

P = 2x + 150

Step-by-step explanation:

P = 2x + 150

Answer:

Step-by-step explanation:

QR is the corresponding side to ST since ΔPQR ~ ΔVST, considering the order of vertices.

Since the scale factor is 2/5, the ratio of corresponding sides is:

Answer:

[tex]a_{n}[/tex] = - 4n + 6

Step-by-step explanation:

There is a common difference between consecutive terms of the sequence

- 2 - 2 = - 6 - (- 2) = - 10 - (- 6) = - 14 - (- 10) = - 4

This indicates the sequence is arithmetic with explicit formula

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 2 and d = - 4 , then

[tex]a_{n}[/tex] = 2 - 4(n - 1) = 2 - 4n + 4 = - 4n + 6

Answer:

(5,2i) or (5,2)

Step-by-step explanation:

In the Argand Diagram, the imaginary value acts as the y-axis and the real value acts as the x-axis

(5, 2i) or (5,2)

Answer:

x = -2  ||   y = -3

Step-by-step explanation:

5x - 2y = -4

x + 2y = -8

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

5x - 2y = -4

5x = -4 + 2y

x = (-4 + 2y)/5

x + 2y = -8

x = -8 - 2y

Solving simultaneously:

-8 - 2y  =   (-4 + 2y)/5

5(-8 - 2y) = -4 + 2y

-40 - 10y = -4 + 2y

-40 + 4 = 2y + 10y

-36 = 12y

y = -3

if y is -3 then x is:

x = -8 - 2y

x = -8 - 2(-3)

x = -2

Step-by-step explanation:

Let the two consecutive natural numbers be x and x+1

Now, according to the problem

x+(x+1)=23

⇒ 2x+1=23

⇒ 2x=23−1

⇒ 2x=22

⇒ x=22÷2=11

The one number is 11

The next number is x+1=11+1=12

Hence the numbers are 11 and 12.

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