*1/2
*4 to 4
*2:1
*8/4

1. An equation that finds the number of car washes for which the costs of Plan A and Plan B are the same is 12n = 16 + 8n.

2. The solution of the equation shows that the number of car washes for which the cost of each plan is the same is 4.

Equations are mathematical statements claiming that two or more mathematical expressions are equal or equivalent when solved.

Equations use numbers, constants, variables, and the equation symbol (=) to depict the equality of the mathematical expressions.

                                 Plan A     Plan B

Cost per cash wash  $12           $8

Fixed cost                  $0           $16

Mathematical Expressions for the Carwash Plans:

Let Plan A = 0 + 12n

Let Plan B = 16 + 8n

The number of car washes when the two plans' costs are equal can be derived by equating the two mathematical expressions above:

12n = 16 + 8n

12n - 8n = 16

4n = 16

n = 4

= 4 car washes

Check:

Plan A = 0 + 12n

= 12(4)

= 48

= $48

Plan B = 16 + 8n

= 16 + 8(4)

= 16 + 32

= 48

= $48

Thus, solving the equation, we can conclude that choosing Plan B will take 4 car washes to equal the cost of Plan A.

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Answer: x=5

Step-by-step explanation:

4x-3=17 Add three to both sides

4x=20 Divide both side by 4 to isolate x

x=5

Las expresiones algebraicas que completan la tabla son 200+x, 2(200+x), 650+ 2(200+x),  y -5, y+ 10, y+8, 75- y

El lenguaje algebraico es simbólico es decir se expresa mediante consonantes o vocales, el lenguaje algebraico nos permite expresar de manera sencilla y practica el valor desconocido de una determinada cantidad.

A partir de la información dada es decir  "x" naranjas y "Y" que es la edad de José vamos a expresar las respuestas en lenguaje algebraico.  Para esto se debe relacionar la x o y con el valor dado y el signo matemático correspondiente:                                                

Luis tiene 200 naranjas mas que Soraya  =  200+x

Susana tiene el doble de Luis  = 2(200+x)

Juan tiene 650 naranjas mas que susana   = 650+ 2(200+x)

Considerando que Y es la edad de José

Los años que tenia hace 5 años = y -5

Los años que tendrá en 10 años  = y+ 10

Los años que tendrá dentro de 8 años = y+8

Los años que faltan para que cumpla 75 años = 75- y

Podemos concluir que el lenguaje algebraico nos permite representar de manera practica un valor desconocido y de igual manera obtener respuestas practicas y sencillas a partir de variables.

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Answer:

36.2/4=length of each sandwich piece

The answer choice which must be a factor of the polynomial in discuss is; (x - 1).

It follows from the vertex form equation of a parabola; f(x) = a ( x - h )² + k where the vertex of the parabola is; (h, k).

Therefore, the equation of the parabola in discuss is;

f(x) = a (x - 3.5)² + 3.

Recall that the x coordinates of the vertex, h is given by; h = (p + q) / 2

where p and q are the zeroes of the quadratic function.

Therefore, since one of the zeroes is given as; 6 ( from (6, 0) ); it follows that the second zero can be determined as follows;

3.5 = ( 6 + q ) / 2

7 = 6 + q

q = 1

Therefore, since the second zero is; 1. It follows that the associated factor as required is; ( x - 1 ).

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Answer: 12

Step-by-step explanation:

       1 2  

   5 ⟌ 6 0  

     - 5    

       1 0  

     - 1 0  

         0  

The intercepts of x-axis for the given polynomial function is (1. 0)

The intercepts of y-axis for the given polynomial function is (0, -3) and the graph is attached below:

A function of a set X to a set Y in mathematics assigns to each element of X exactly one element of Y. The domain in a function is the set X, and the codomain of the function is the set Y.

The first known attempt to define function can be found in the writings of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. The concept of a function was codified in terms of set theory at the end of the nineteenth century, which substantially expanded its realms of applicability.

Given function is,

f(x)=x³+2x²-3

The graph of the polynomial function is plotted below:

The intercepts of x-axis for the given polynomial function is (1. 0)

The intercepts of y-axis for the given polynomial function is (0, -3)

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Step-by-step explanation:

divide 15 by 2 to get the radius which is 7.5

then 7.5² = 56.25 x3.15=177.1875 round and its A=177.188

if this is incorrect someone else correct me

Answer:

[tex]\dfrac{27}{20}[/tex]

Step-by-step explanation:

First, convert both numbers into fractions:

[tex]\dfrac{15}{1} \div \left(\dfrac{10}{3}\right)^2[/tex]

Then, apply the exponent of the second fraction in parentheses to its numerator and denominator.

[tex]\dfrac{15}{1} \div \left(\dfrac{10^2}{3^2}\right)[/tex]

[tex]\dfrac{15}{1} \div \dfrac{100}{9}[/tex]

Finally, multiply the first fraction by the reciprocal of the second fraction.

(Skip, Flip, Multiply)

[tex]\dfrac{15}{1} \times \dfrac{9}{100}[/tex]

[tex]\dfrac{135}{100}[/tex]

And simplify.

[tex]\dfrac{135 \div 5}{100 \div 5}[/tex]

[tex]\dfrac{27}{20}[/tex]

Answer:

Step-by-step explanation:

6(6p-9)-10p-6(6p-9)-10p

36p-54-10p-36p+54-10p

36p-36p-54+54-10p= -10p

For the initial fee, Bob charges less than Ginny.

A unit rate means a rate for one of something.

Given that Ginny charges by uses the function f(x)=60x+80 where x represents the number of hours of labour.

Ginny initial charge = $80

Bob initial charge =$60

Hence, For the initial fee, Bob charges less than Ginny.

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The investment amount is $37263.09.

Interest that compounded continuously to the principal amount. This interest rate provides exponential growth to period of time.

Formula of continuous compound interest rate;

P(t) = P₀ [tex]e^{rt}[/tex] , where P₀ is the principal amount, r is the interest rate and t is the time period.

Given that the Alang is going to invest with the continuous compound interest rate 5.7%.

Using the formula of continuous compound interest rate,

P(t) = P₀ [tex]e^{rt}[/tex]

P(t) = $113000 x    [tex]e^{(5.7)(5)}[/tex]

P(t) = $37263.09

Therefore, the investment amount is $37263.09.

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The domain and the range of the function are given as follows:

The domain of a function is the set containing all the values assumed by the input of a function, hence on the graph it is given by the values of x for which the function is defined.

The range of a function is the set containing all the values assumed by the output of a function, hence on the graph it is given by the values of y which the function assumes.

In this problem, the horizontal line is given as follows:

y = -3.

Hence the lone value assumed by output is of 3, meaning that the range is given as follows:

{3}.

In {} notation because it is a single element, not an interval.

The values of x, that is, the values of the horizontal axis assumed by the function are between -3 and 3, hence the domain is given by the following interval:

[-3, 3].

Which is a closed interval due to the closed circle.

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If Lianne has some dimes and nickels with a total value of $4.60. The number of dimes she has is 4 more than 3 times the number of nickels then 0.15 Nickels does Lianne has.

Two or more expressions with an Equal sign is called as Equation.

Given,

Lianne has some dimes and nickels with a total value of $4.60.

The number of dimes she has is 4 more than 3 times the number of nickels.

We need to find number of nickels

From the given information

N+D=4.60

D=3N+4

N+3N+4=4.60

4N=4.60-4

4N=0.6

Divide both sides by 4

N=0.15

Hence, 0.15 Nickels does Lianne has.

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Answer:172 cm²

Step-by-step explanation:

when we use the formula, and we can  solve out is like 172.05 and round to tenth and will have the answer

Formula is 1/2 × p × a  

Answer:

t = 11.7

Step-by-step explanation:

                  r

A = P (1 + -------)^(nt)

                  n

A = 5000 = (2500 × 2)

P = 2500

n = 2

t = ?

                               0.06

5000 = 2500 (1 + ----------)^(2)(t)

                                 2

                               0.06

5000 = 2500 (1 + ----------)^(2)(t)

÷2500  ÷2500         2

             0.06

2 = (1 + ----------)^(2)(t)

               2

                               0.06

log₁₀ 2 = log₁₀ (1 + ----------)^(2)(t)

                                 2

                                                              0.06

log₁₀ 2                          = 2t × log₁₀ (1 + ----------)

                                                                 2

                 0.06                                  0.06

÷ log₁₀ (1 + ----------)        ÷ log₁₀ (1 + ----------)  

                    2                                     2

            log₁₀ 2

-----------------------------   =   2t

                0.06

log₁₀ (1 + -------- )

                 2

                  log₁₀ 2

(1/2)  -----------------------------   =   2t (1/2)

                  0.06

   log₁₀ (1 + -------- )

                     2

(1/2) 23.44977225  =   2t (1/2)

       11.72488613 = t

        11.7 ≈ t

I hope this helps!

Hence, the  decimal equivalent of students who passed the test is [tex]0.33[/tex].

What is the decimal values?

Decimals are a set of numbers lying between integers on a number line.

Here given that,

Three out of nine students passed the SHSAT test.

So,

[tex]\frac{3}{9}=0.33[/tex]

Hence, the  decimal equivalent of students who passed the test is [tex]0.33[/tex].

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Answer: 29000

Step-by-step explanation:

12000 + 2500 = 14500

14500 * 2 = 29000

Answer: Radio

Step-by-step explanation:

An electromagnet wave with a wavelength of 100m is a Radio. These signals are invisible to the human eye, humans are only able to detect visible light.

The time period of the loan was 1 year.

a) The first term of the sequence is; ³¹/₆

b) The term to term rule is; aₙ = ³¹/₆ + (n - 1)²/₆

c) The next three terms are; ³⁷/₆, ³⁹/₆, ⁴¹/₆

d) The 10th term in the sequence is; a₁₀ = ⁴⁹/₆

The first term of the sequence is given by the expression;

2 ÷ ¹²/₃₁ = ³¹/₆

The second term of the sequence is given by the expression;

3 ÷ ⁶/₁₁ = ³³/₆

The third term of the sequence is given by the expression;

5 ÷ ⁶/₇ = ³⁵/₆

These are the first three terms of a sequence and so the sequence is;

³¹/₆, ³³/₆, ³⁵/₆,....

d = ³³/₆ - ³¹/₆ = ²/₆

Thus, term to term rule is given by the nth term of an arithmetic progression;

aₙ = ³¹/₆ + (n - 1)²/₆

The next three terms are; ³⁷/₆, ³⁹/₆, ⁴¹/₆

The 10th term in the sequence is;

a₁₀ = ³¹/₆ + (10 - 1)²/₆

a₁₀ = ³¹/₆ + ¹⁸/₆

a₁₀ = ⁴⁹/₆

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The slope of C and D in the picture shows that ΔPQR is a Right Triangle.

What is slope of line?

Slope of line is defined as the angle of line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂).

If the product of slopes of any two sides is equal to -1, then those two sides are perpendicular

Given,

The vertices of △PQR are at P(-2,5), Q(-1,1), and R(7,3).

Slope of PQ = (y₂ - y₁)/(x₂ -x₁ )

                    = (1 - 5)/(- 1 - (-2)

                    = -4/1

                    = - 4

Slope of QR = (y₂ - y₁)/(x₂ -x₁ )

                    = 3 -  1/7 - ( -1)

                    = - 1 / 4

The product of Slope of PQ and QR is  - 1. It means lines PQ and QR is perpendicular to each other consequently △PQR is a right triangle.

Therefore,The slope of C and D in the picture shows that ΔPQR is a Right Triangle.

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The time it takes for the projectile to reach its maximum height would be 0.77 s. The time it takes for the projectile to hit the ground is 2.67 s.

The horizontal range ∆x would be 20.3 m.

To determine the time it takes for the projectile to reach its maximum height, we can use the formula:

t = (vi sin(θ)) / g

where t is the time, vi is the initial velocity, θ is the angle of launch, and g is the acceleration of gravity.

In this case, the initial velocity has a horizontal component of 7.5 m/s, so we can assume that the initial velocity is 7.5 m/s and the angle of launch is 90 degrees (since the projectile is launched horizontally). Therefore, the time it takes for the projectile to reach its maximum height would be:

t = (7.5 m/s × sin(90)) / 9.8 m/s2 = 0.77 s

To determine the time it takes for the projectile to hit the ground, we can use the formula:

t = (2 ∆y) / (vi sin(θ))

where t is the time, ∆y is the maximum height, vi is the initial velocity, and θ is the angle of launch.

Since we know that the projectile rises to a maximum height of ∆y above the end of the cannon's barrel, the initial velocity has a horizontal component of 7.5 m/s and the angle of launch is 90 degrees, we can calculate the time it takes for the projectile to hit the ground as follows:

t = (2 ∆y) / (7.5 m/s x sin(90)) = (2 ∆y) / 7.5 m/s = 2.67 s

To determine the horizontal range ∆x of the shot, we can use the formula:

∆x = (vi × t) cos(θ)

where ∆x is the horizontal range, vi is the initial velocity, t is the time, and θ is the angle of launch.

In this case, we know that the initial velocity has a horizontal component of 7.5 m/s, the time it takes for the projectile to hit the ground is 2.67 s, and the angle of launch is 90 degrees.

Therefore, the horizontal range ∆x would be:

∆x = (7.5 m/s × 2.67 s) × cos(90) = 20.3 m.

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Owen went to Best Buy to purchase a new laptop. He put a down payment of $200 and will pay $75 each month until he pays it off. Use the

formula p= 200 + 75c to identify which statement below is false.

The ‘p’ is represented as the dependent variable [true]

The ‘c’ represents the number of months [true]

The independent variable is 75 [FALSE]

The ‘c’ is represented as the independent variable [true]

Constant of variation for the direct function is y = [tex]\frac{2 x}5}[/tex]

Direct variation in mathematics is the general form of formula  y = k x  where x and y are variables (numbers that change) and k is a constant

Convert to slope intercept form

2x -5y =0

Add 5y to both sides

2x-5y +5y =5y

2x=5y

divide both sides by 5

[tex]\frac{2x}{5}[/tex]  =[tex]\frac{5y}{5}[/tex]

Cross multiply to solve for y

5(2x) =5(5y)

y = [tex]\frac{2 x}5}[/tex]

Therefore, the constant of variation y = [tex]\frac{2 x}5}[/tex]

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Answer:

22 people

Step-by-step explanation:

First, let's convert the percentage into a decimal so we can multiply the two.

55% = 0.55

Next, we'll multiply 40 times 0.55. This is so we can find the amount of people who said yes. (55% of people said yes.)

0.55*40 = 22

22 people said yes.

The slope calculations she can use to correctly show that △PQR is a right triangle are

From the question, we have the following ordered pairs that can be used in our computation:

The vertices of △PQR are at P(-2,5), Q(-1,1), and R(7,3).

This means that

P = (-2,5),

Q = (-1,1)

R = (7,3).

The slope of the points are calculated using

slope = (y₂ - y₁)/(x₂ - x₁)

So, we have

Slope of PQ = (y₂ - y₁)/(x₂ - x₁) = (1 - 5)/(-1 - (-2)) = -4

Also, we have

Slope of QR = (y₂ - y₁)/(x₂ - x₁) = (3 - 1)/(7 - (-1)) = 2/8 = 1/4

Hence, the equations are (a) and (d)

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The total number of buttons they have is 4033.

A system having more than two equations is known as a system of equations.

Given that, Sebastian and Zoey had 3068 buttons, Sebastian and Valeria had 2103 buttons, and Valeria has half as many buttons as Zoey.

The equations corresponding to the statements are:

S + Z = 3068         (1)

S + V = 2103          (2)

V = Z/2                   (3)

Subtract equation (2) from equation (1):

Z - V = 965

Substitute V = Z/2 into the above equation:

Z - Z/2 = 965

Z/2 = 965

Z = 1930

Substitute Z = 1930 into equation (3):

V = 1930/2

V = 965

Substitute V = 965 into equation (2):

S + 965 = 2103

S = 1138

The total number of buttons is:
S + V + Z

= 1138 + 965 + 1930

= 4033

Hence, the total number of buttons they have is 4033.

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Answer:7

Step-by-step explanation:

What it is asking you is what multiplied by it self gets you to 49. the answer would be 7 because 7*7=49

Answer:

GM = 18

Step-by-step explanation:

JK = KL = 2

GJ = LM =7

GM = 7+2+2+7 = 18!

So the answer it is 18.