12. Solve the systems of linear equations using the substitution method.
x=y - 2
4y = x + 23

Answer:

  y = 5x

Step-by-step explanation:

The revenue (y) is 5 dollars for each car washed. The number of cars washed is x, so the revenue equation is ...

  y = 5x

_____

Additional comment

At the end of the exercise of writing revenue and cost and profit equations, you will find that the break-even number of cars is the ratio of fixed cost (start-up cost in this case) to the profit contribution of each car (per-car charge in this case). That is, it will take 75/5 = 15 cars to break even. Each additional car will contribute a positive profit.

Answer:

Equation INCLUDING the setup cost:   y = 5x - 75

Equation EXCLUDING the setup cost:   y = 5x

Step-by-step explanation:

It spent a total of $75 to set up the car wash.

It is charging $5 per car.

y = amount collected in $

x = number of cars washed

=> We can make an equation INCLUDING the setup cost and EXCLUDING the setup cost.

=> INCLUDING the setup cost.

=> y = 5x - 75

=> I subtracted 75 from 5x because they spent a total of $75 to set up the car wash.

=> I wrote 5x because they get $5 for each car so if they wash 10 cars they get 5 * 10 = $50.

An EXAMPLE  from the above equation:

y = 5x -75

=> y = 5*14 - 75

=> y = 70 - 75

=> y = -5

=> This means that if they wash 14 cars, they still have a debt of 5 dollars.

An equation EXCLUDING the setup cost will look like:

=> y = 5x

I wrote this because, they didn't spend any money so they will get 5 dollars per car. How many cars they wash, the answer will be 'number of cars x 5'.

An EXAMPLE from the above equation is:

=> y = 5x

=> y = 5 * 14

=> y = $70

=> This means that if they wash 14 cars, they get $70.

Answer:

The corresponding point is (-8, -6).

Step-by-step explanation:

Given that

(-6,-6) lies on the graph of [tex]f(x)[/tex]

A function is represented in the form:

[tex]y = f(x)[/tex]

i.e. (-6,-6) means value of x = -6 is put and value y came out as -6.

[tex]f(-6) = -6[/tex]

Now, we have to find the corresponding point on [tex]f(\frac{3}{4}x)[/tex].

We know the value of [tex]f(-6)[/tex]

Let us find the value of x where [tex]\frac{3}{4}x[/tex] becomes equal to -6

[tex]\dfrac{3}{4}x=-6\\\Rightarrow 3x=-24\\ \Rightarrow x =-8[/tex]

So, let us put value of [tex]x = -8[/tex] in [tex]f(\frac{3}{4}x)[/tex]:

[tex]f(\frac{3}{4}\times (-8))\\\Rightarrow f(3\times (-2))\\\Rightarrow f(-6) = -6[/tex](as per given statement)

So, the corresponding point is (-8, -6).

Exact Area = 98pi  

Approximate Area = 307.8760800518 (use calculator stored version of pi)

Approximate Area = 307.72 (using pi = 3.14)

Units are in square millimeters

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

Explanation:

In 60 seconds, the hand sweeps out a full circle of radius 14. The area of this circle is

A = pi*r^2 = pi*14^2 = 196pi

Half of this is what the hand sweeps out in 30 seconds, so A/2 = (196pi)/2 = 98pi is the exact area it sweeps out. Your calculator would then show 98pi = 307.8760800518 approximately

If instead you use pi = 3.14, then the approximate area is 98*3.14 = 307.72

Answer:

0.6

Step-by-step explanation:

0.6-0.45=0.15

The value of y from the given equation is 0.60.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is 0.15=y-0.45.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Here, 0.15=y-0.45

y=0.15+0.45

y=0.60

Therefore, the value of y is 0.60.

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Answer:

P = 0,88          or       P  =  88 %

Step-by-step explanation:

The probability of having a married couple in nonadjacent desks is the total number of probabilities minus the probabilities of having them in adjacent places divide by total number of outcomes

The total possibilities (outcomes) of 9 elements in a row is:

P(₉) = 9!

P(₉) = 9*8*7*6*5*4*3*2*1

P(₉) = 362880

And the outcomes in which they are adjacent to each other is:

We consider them as one unit them we in this situation have 8 elements

P(₈) = 8!

P(₈) = 8*7*6*5*4*3*2*1

P(₈) = 40320

Then the probability that the married couple will have nonadjacent desks is:

P = P(₉)  -  P(₈) / P(₉)

P =  362880 - 40320 / 362880

P = 322560/ 362880

P = 0,88          or       P  =  88 %

Hello!

Answer:

[tex]\huge\boxed{59.04 units}[/tex]

To solve, we will need to use Right-Triangle Trigonometry:

Begin by solving for angles ∠S and ∠R using tangent (tan = opp/adj)

tan ∠S = a / (1/2b)

tan ∠S = 3√5 / 14

tan ∠S ≈ 0.479

arctan 0.479  = m∠S (inverse)

m∠S and m∠R ≈ 25.6°

Use cosine to solve for the hypotenuse, or the missing side-length:

cos ∠S = 14 / x

x · cos (25.6) = 14

x  = 14 / cos(25.6)

x ≈ 15.52

Both triangles are congruent, so we can go ahead and find the perimeter of the figure:

RS + RQ + QS = 28 + 15.52 + 15.52 = 59.04 units.

Hope this helped you! :)

Answer:

[tex]\large \boxed{\mathrm{59.05 \ units}}[/tex]

Step-by-step explanation:

Take one small triangle, solve for hypotenuse.

[tex]\frac{b}{2} =\frac{28}{2} =14[/tex]

Use Pythagorean theorem.

[tex]c=\sqrt{(3\sqrt{5})^2 +14^2 }[/tex]

[tex]c= 15.524175...[/tex]

Add the hypotenuse twice because there are two triangles, then add to the length of b to find the perimeter.

[tex]15.524175...+15.524175...+28[/tex]

[tex]59.048349...[/tex]

A = (-7,-6)

B = (8,-9)

Find the slope of line AB

m = (y2-y1)/(x2-x1)

m = (-9-(-6))/(8-(-7))

m = (-9+6)/(8+7)

m = -3/15

m = -1/5

The slope of line AB is -1/5.

Flip the fraction and the sign to go from -1/5 to +5/1 = 5. The perpendicular slope is 5.

Let m = 5.

Use the coordinates of point C (2,12) along with the perpendicular slope to get

y - y1 = m(x - x1)

y - 12 = 5(x - 2)

y - 12 = 5x - 10

y = 5x - 10+12

y = 5x + 2

Lastly, convert this to standard form

y = 5x + 2

5x+2 = y

5x+2-y = 0

5x-y = -2

Choice A is the closest match, but the -56 should be -2 instead. It seems like your teacher made a typo somewhere.

Answer:

5x - y = -2.

Step-by-step explanation:

The equation of this altitude line has a slope = -1/m where m is the slope of line AB . It will also pass through the point C.

The slope of line AB = (-9 - (-6)) / (8 - (-7))

= -3/15

= -1/5

So the slope  of the required line = -1 / -1/5 = 5.

Using the point C and the point-slope form of a line:

y - y1 = m(x - x1)

y - 12 =  5(x - 2)

y - 5x = -10 + 12

y - 5x = 2

5x - y = -2.

Answer:

[tex]C=(x-32)\times\frac{5}{9}[/tex]

Step-by-step explanation:

The formula to convert the temperature in Fahrenheit to degrees Celsius is:

[tex]C=(F-32)\times\frac{5}{9}[/tex]

Here,

C = temperature in degrees Celsius

F = temperature in Fahrenheit

Suppose the boiling point for silver is x Fahrenheit, then then the temperature in degrees Celsius will be:

[tex]C=(x-32)\times\frac{5}{9}[/tex]

THIS IS THE COMPLETE QUESTION BELOW;

young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly. He started at 909090 kilograms and gained weight at a constant rate. After 888 months, he weighed 138138138 kilograms. Let W(t)W(t)W, left parenthesis, t, right parenthesis denote the sumo wrestler's weight WWW (measured in kilograms) as a function of time ttt (measured in months). Write the function's formula.

Answer:

W=6t+90

Step-by-step explanation:

We know that a linear equation in slope takes the form

y= mx+ c

where

m is the slope

c is the y-coordinate of the y-intercept

Let us denote W as the sumo weight in kg then

t as the time in months

Then forming a linear equation from this knowing t is a dependent variable then

W(t)= mt+90

But here we know that is our slope, W was given as 138kg and t is 8 months.

We we substitute this values in the equation we have

138= 8m+90

8m= 138-90

8m=48

m=6kg/month

Therefore, the function formula is W(t)= 6t+90

Answer:

11/50 is the simplified form of the given expression.

Step-by-step explanation:

22/100

We will cancel the values by the table of 2

11/50 is the simplified form of the given expression.

Hope it will help you :)

Answer:

D

Step-by-step explanation:

Both are exponential decay.

Answer:

Step-by-step explanation:

f(0) = 24,  f(1) = 6 and f(2) = 0 means f(x) > 0 in (0,2)

and f(0) > f(1) > f(2) means f is decreasing in (0,2)

g(0) = 15 and g(2) = 0 means g(x) > 0 in (0,2)

and g(0) > g(2) means g is decreasing in (0,2)

Answer:

none of above .

Step-by-step explanation:

because the unit of area is always in square forms.

[tex]8(9)+18[/tex]

$=8\cdot9+2\cdot9$

$=(8+2)\cdot9$

Answer:

please mark my answer brainliest

Step-by-step explanation:

- 2a -12

Answer:

Step-by-step explanation:

The diagonal ^2= 13^2+7^2

=169+49=218

diagonal = V218

the lengh of the square=l

l^2+l^2= 218

2l^2=218

l^2= 218/2= 109

l= ✓109

Answer:  see proof below

Step-by-step explanation:

Use the following when solving the proof...

Double Angle Identity: cos2A = 1 - 2sin²B

Pythagorean Identity: cos²A + sin²A = 1

note that A can be replaced with B

Proof from LHS → RHS

Given:                            cos²A + sin²A · cos2B

Double Angle Identity: cos²A + sin²A(1 - 2sin²B)

Distribute:                      cos²A + sin²A - 2sin²A·sin²B

Pythagorean Identity:                        1 - 2sin²A·sin²B

Pythagorean Identity:   cos²B + sin²B - 2sin²A·sin²B

Factor:                           cos²A + sin²B(1 - 2sin²A)

Double Angle Identity: cos²B + sin²B · cos2A

cos²B + sin²B · cos2A = cos²B + sin²B · cos2A  [tex]\checkmark[/tex]

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Hi my lil bunny!

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

[tex]2x-3x+5=18[/tex]

Step 1: Simplify both sides of the equation.

[tex]2x-3x+5=18\\2x + -3x + 5 = 18[/tex]

[tex]( 2x + -3x ) + ( 5) = 18[/tex] (Combine Like Terms)

[tex]-x + 5 = 18\\-x + 5 = 18[/tex]

Step 2: Subtract 5 from both sides.

[tex]-x + 5 - 5 = 18 - 5 \\-x = 13[/tex]

Step 3: Divide both sides by -1.

[tex]\frac{-x}{-1} = \frac{13}{-1} \\x = -13[/tex]

Answer : [tex]\boxed {x = -13}[/tex]

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Have a great day/night!

❀*May*❀

Answer:

Step-by-step explanation:

[tex] \mathsf{2x - 3x + 5 = 18}[/tex]

Collect like terms

[tex] \mathsf{ - x + 5 = 18}[/tex]

Move constant to R.H.S and change it's sign

[tex] \mathsf{ - x = 18 - 5} [/tex]

Calculate the difference

[tex] - x = 13[/tex]

Change the signs on both sides of the equation

[tex] \mathsf{x = - 13}[/tex]

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

[tex] \blue{ \mathsf{verification}}[/tex]

[tex] \mathsf{LHS \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: RHS}[/tex]

[tex] \mathsf{2x - 3x + 5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 18}[/tex]

[tex] \mathsf{ = 2 \times ( - 13) - 3 \times ( - 13) + 5}[/tex]

[tex] \mathsf{ - 26 + 39 + 5}[/tex]

[tex] \mathsf{ = 13 + 5}[/tex]

[tex] = 18[/tex]

Thus, LHS = RHS

hope I helped!

Best regards!

Answer:

[tex]\frac{\pi }{10}[/tex] radians

Step-by-step explanation:

To convert degrees into radians, multiply the degrees with [tex]\frac{\pi}{180}[/tex].

If you have 18 degrees:

[tex]18*\frac{\pi}{180} = \frac{\pi }{10}[/tex]

Answer:

420 cubic inches is the answer

Answer:

420 cubic inches

Step-by-step explanation:

Volume of rectangular pyramid

= 1/3*lbh

= 1/3 * 10*9*14

= 10*3*14

= 420 cubic inches

Answer:

19958.1

step-by-step explanation:

HOPE I HELPED

PLS MARK BRAINLIEST

DESPERATELY TRYING TO LEVEL UP

      ✌ -ZYLYNN JADE ARDENNE

JUST A RANDOM GIRL WANTING TO HELP PEOPLE!

                                     PEACE!

Answer:

B

Step-by-step explanation:

The greatest prime factor between 1 and 30 is 29. Remember that a prime number is a number whose only 2 factors is 1 and the number itself. To find out which number is a multiple of 29, all we have to do is divide it by 29, and if the quotient is a whole number then we have found our answer.

A: 1593 / 29 ≈ 54.93

B: 1247 / 29 = 43

We don't need to check C and D because we know that B is the answer.

1247 has the greatest prime factor between 1 and 30

The factor of a number that divides another number perfectly without leaving any remainder.  

For example, the factors of 12 are 1,2,3,4,6 and 12

A prime factor is a number that a prime number

A prime number is a number that can be divided only by 1 and that number

Prime numbers between 1 and 30 are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29

The greatest prime factor between 1 and 30 is 29

To determine which number has the greatest prime factor, divide each of the numbers in the options by 29.

1593 / 29 = 54.9 (29 is not a prime factor of 1593)

1247/29 = 43 (29 is a prime factor of 1247)

1311 / 29 = 45.2  (29 is not a prime factor of 1311)

943 / 29 = 32.5  (29 is not a prime factor of 943)

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Answer/Step-by-step explanation:

1. <B is an inscribed angle intercepting arc CA.

Therefore, m<B = ½*128 (inscribed angle theorem)

m<B = 64°

x = 180 - (m<B + m<A) (sum of angles in a triangle)

x = 180 - (64 + 43)

x = 180 - 107 = 73°

2. [tex] KH*HI = JH*HG [/tex] (intersecting chords theorem)

[tex] 10*x = 14*5 [/tex]

Solve for x

[tex] 10x = 70 [/tex]

[tex] \frac{10x}{10} = \frac{70}{10} [/tex]

[tex] x = 7 [/tex]

Answer:

Im pretty sure they stay the same. But that might just be me

Answer:

AandB=80miles

Total=240miles

Step-by-step explanation:

Draw the figure first indicating the figures then find the distance each degrees then find the total

The distance ship travels from A to B is 273.2 miles and total distance covered by ship is  707.82 miles.

The law of sines specifies how many sides there are in a triangle and how their individual sine angles are equal. The sine law, sine rule, and sine formula are additional names for the sine law.

The side or unknown angle of an oblique triangle is found using the law of sine. Any triangle that is not a right triangle is referred to as an oblique triangle. At least two angles and their corresponding side measurements should be used at once for the sine law to function.

Given distance from C to A = 100 miles north

From B to A ship travels 60° east of north,

and From B to C 45° west of south,

the figure for problem is attached,

from figure we can  calculate the angles of A, B and C

so ∠A makes supplementary with 60°

∠A + 60° = 180°

∠A = 120°

for ∠B we need to draw an imaginary perpendicular on the line extending from A, we get

∠B + 45° + 30° = 90° (30° is angle of imaginary right triangle)

∠B = 90 - 75 = 15°

and ∠C can be found by,

∠A + ∠B + ∠C = 180°

∠C = 180 - 15 - 120

∠C = 45°

now use sine formula for triangles,

sinA/a = sinB/b = sinC/c

where A, B and C are angles of triangle and a, b and c are length of opposite side of angle A, B and C respectively.

a = BC, b = AC, and c = AB

so

sinA/BC = sinB/AC = sinC/AB

we have AC = 100 miles

substitute the values

sinC/AB = sinB/AC

sin(45)/AB = sin(15)/100

AB = 100/(√2sin(15))

AB = 100/0.3659

AB = 273.298 miles

and sinA/BC = sinB/AC

BC = AC sinA/sinB

BC = 100(sin 120/sin15)

BC = 100(0.866/0.2588)

BC = 100 x 3.3462

BC = 334.62 miles

total distance = AB + BC + AC

total distance = 334.62 + 273.2 + 100

total distance =  707.82 miles

Hence the distance from A to B is 273.2 miles and total distance is 707.82 miles.

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Answer:

The rectangular prism is 30 times larger than the cube.

Step-by-step explanation:

The Cube has a length of 2, a width of 2, and a height of 2.

Volume = length times width times height     or V=lwh

2 x 2 x 2= 8

The Rectangular prism has a length of 10, a width of 6, and a height of 4.

10 x 6 x 4= 240

240 divided by eight is 30.

Answer:

30 times larger than the cube.

Step-by-step explanation:

Answer:

The probability that a randomly selected person gets incorrect result is 2.2 × 10⁻⁴

Step-by-step explanation:

The parameters given are;

The accuracy of the test for a person who has the respiratory synctial virus = 97%

The accuracy of the test for a person who does not have the respiratory synctial virus = 99%

We have;

a = TP =

b = FP

c = FN

d = TN

a/(a + c) = 0.97

d/(d + b) = 0.99

a/(a + b) = 0.97*0.0055/(0.97*0.0055 + (1 - 0.99)*(1-0.0055))

PPV = 0.349 = 34.9%

Therefore, we have;

a/(a + c) = 0.97 and

a/(a + b)  =  0.349

0.97(a + c) =0.349(a + b)

(0.97 - 0.349)a = 0.349·b - 0.97·c

a = (0.349·b - 0.97·c)0.621

b × (1 - 0.0055) = (1 - 0.97)×(1 - 0.0055)

b = 1 - 0.97 = 0.03

Similarly,

c = 1 - 0.99 = 0.01

The proportion of the population that have false positive and false negative = 0.03 + 0.01 = 0.04 = 4%

The probability that a randomly selected person gets incorrect result = 0.04×0.0055 = 0.00022.

Answer:

0.01011

Step-by-step explanation:

Answer:

Yes they are of the same size since they have the same number and standard unit of measurement (i.e 24 inches).

Each person measures the circumference of the circle.

Step-by-step explanation:

Given that :

Priya, Han, and Mai each measured one of the circular objects from earlier.

Priya says that the bike wheel is 24 inches.

Han says that the yo-yo trick is 24 inches.

Mai says that the glow necklace is 24 inches.

Do you think that all these circles are the same size?

Yes they are of the same size since they have the same number and standard unit of measurement (i.e 24 inches).

What part of the circle did each person measure?

Each person measures the circumference of the circle.

The circumference also known as the perimeter of the circle is denoted by :

C = 2π r

The circumference of a circle is the distance round the edges of the circle.

Given that C = 24

24 = 2π r

r = 24/(2π)

r = 3.8 inches

This confirms the claim that all the circle are of the same size since they possess the same radius.

Answer:

The person who answered first is WRONG

Step-by-step explanation:

I did this and these are the answers the teacher gave me:

the circles are NOT the same size

and they are measuring by diameter, radius, and circumfrence

Answer:

m∠C = 102°

Step-by-step explanation:

This is a quadrilateral inscribed in a circle

The sum of opposite angles in a cyclic quadrilateral is equal to 180°

m∠D + m∠B = 180°

m∠B = 180° - m∠D

m∠B = 180° - 80°

m∠B = 100°

We know what m∠B

We have external angles outside the circle.

m∠CDA is opposite m∠B

m∠CDA = 2 × m∠B

m∠CDA = 2 × 100°

m∠CDA = 200°

m∠CDA is the sum of m∠CD and m∠DA

m∠CDA = m∠CD + m∠DA

m∠DA = m∠CDA - m∠CD

m∠DA = 200° - 116°

m∠DA = 84°

m∠DAB is an exterior angle also, hence,

m∠DAB is the sum of m∠DA and m∠AB

m∠DAB = m∠DA + m∠AB

m∠DAB = 84° + 120°

m∠DAB = 204°

Finally we can solve for m∠C

m∠DAB is Opposite m∠C

So, m∠C = 1/2 × m∠DAB

m∠C = 1/2 × 204

m∠C = 102°

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

Explanation:

I'll use x in place of n

Let y = x^2 - 4x + 5

If we complete the square, then,

y = x^2 - 4x + 5

y = (x^2 - 4x) + 5

y = (x^2 - 4x + 4 - 4) + 5

y = (x^2 - 4x + 4) - 4 + 5

y = (x-2)^2 + 1

The quantity (x-2)^2 is never negative as squaring any real number value is never a negative result. Adding on 1 makes the result positive. So y > 0 regardless of whatever x is. Replace x with n, and this shows how n^2 - 4n + 5 is always positive for any integer n.

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

You could also use the quadratic formula to find that x^2 - 4x + 5 = 0 has no real solutions, so there are no x intercepts. Either the graph is entirely above the x axis or it is entirely below the x axis.

Plug in any x value you want, say x = 0, and the result is positive. Meaning that whatever x value you plug in will be positive (as the graph can't cross the x axis to go into negative territory)

Answer:

2(x -2)² = 0

Step-by-step explanation:

2(x² - 4x - 4) = 0

2(x -2)² = 0

x = 2

Answer:

[tex]2(3x-2)(x+2)=6x^2-8x-8[/tex]

The factored form of [tex]6x^2-8x-8=0[/tex] is [tex]2(3x-2)(x+2)=0[/tex]

Step-by-step explanation:

[tex]6x^2-8x-8=0[/tex]

The way the quadratic equation was given, we can't have a factored form in the format: [tex](ax-b)(cx+d)[/tex]

First, divide both sides by 2

[tex]3x^2-4x-4=0[/tex]

Now, it is about thinking. From the equation, we will get something in the format:  [tex](ax-b)(cx+d)[/tex]

Let's expand this: [tex](ax-b)(cx+d) = acx^2+adx-bcx-bd[/tex]

From here, we can give some values for those variables, based on the quadratic equation [tex]3x^2-4x-4=0[/tex]:

[tex](3x-b)(x+d) = 3\cdot 1\cdot x^2+3dx-b\cdot 1 \cdot x-bd= \boxed{3x^2+3dx-bx-bd}[/tex]

Once we want the middle term to be -4 and bd to be 4, we can easily evaluate the other variables.

[tex](3x-2)(x+2) = 3\cdot 1\cdot x^2+3(2)x-(2)\cdot 1 \cdot x-(2)(2)= \boxed{3x^2+6x-4x-4}[/tex]

Therefore,

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

But we are not ready yet!

This is the factored form of [tex]3x^2-4x-4=0[/tex], to get the factored form of the problem equation, just multiply the factored form we got by 2.

[tex]2(3x-2)(x+2)=6x^2-8x-8[/tex]