While shopping for books, Dominique spent $38 less than 3 times what Roberto
spent. Write an equation to represent the scenario if Dominique spent $10.

The distance from the line [tex]y=\frac{1}{6} x+6[/tex] to the given point (-6,5) is o units .

Distance Formula : the distance between the line ax+by+c=0 and the point (p,q) is given by the formula

[tex]d=\frac{|ap+bq+c|}{\sqrt{a^{2} +b^{2} } }[/tex]

In the given question the equation of line is [tex]y=\frac{1}{6} x+6[/tex]

taking LCM and solving further

[tex]y=\frac{x+36}{6} \\ \\ 6y=x+36\\ \\ x-6y+36=0[/tex] ⇒equation of the line .

Given point (-6,5)

from above values we found that a=1 , b = -6 , c=36, p=-6, q=5.

Substituting the values in distance formula we get

[tex]d=\frac{|1*(-6)-6*5+36}{\sqrt{1^{2} +(-6)^{2} } }[/tex]

[tex]=\frac{|-6-30+36|}{\sqrt{37} }[/tex]

[tex]=\frac{-36+36}{\sqrt{37} }[/tex]

[tex]=0[/tex]

Therefore , the distance from the line [tex]y=\frac{1}{6} x+6[/tex] to the given point (-6,5) is 0 units.

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30x is the value of the given equation .

Algebraic expression multiplication is the operation of multiplying two given expressions made up of variables and constants. An algebraic expression is one that incorporates variables and integer constants.

x = 5

y = 3x

2xy = 2 * 5 * 3x ( plugging in the value )  

       = 30x

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Ricardo will be left with $23.92 after 3 hours of Jet ski riding

Ricardo is on vacation so he went jet skiing

The Jet ski has a rental flat rate of $25

They also charge $17.75 per hour

Ricardo had $102.17

The amount spent in 3 hours is

17.75(3) + 25

= 53.25 + 25

= 78.25

The amount left is

= 102.17 - 78.25

= 23.92

Hence Ricardo has $23.92 left after the Jet ski ride

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The area of the cross section of the planet at the equator is 5. 92 × 10^9 square miles

From the information given, we have the formula for area to be;

A = 3.14r²

Where 'r' is the radius of the shape

The radius of Jupiter = 2 * 5^2 * 11 * 79

This is simplified to = 2 × 25 × 11 × 79 = 43, 450

Substitute into the formula

Area = 3. 14 × (43, 450)²

Area = 3. 14 × 1. 89 × 10^9

Area = 5. 92 × 10^9 square miles

Thus, the area of the cross section of the planet at the equator is 5. 92 × 10^9 square miles

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Answer:

5,928,013,850

Answer:

a₁ = 8 and r = 16

Step-by-step explanation:

the sequence has a common ratio r between consecutive terms and is therefore geometric , that is

r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{2^{7} }{2^3}[/tex] = [tex]2^{(7-3)}[/tex] = [tex]2^{4}[/tex] = 16

r = [tex]\frac{a_{3} }{a_{2} }[/tex] = [tex]\frac{2^{11} }{2^7}[/tex] = [tex]2^{(11-7)}[/tex] = [tex]2^{4}[/tex] = 16

r = [tex]\frac{a_{4} }{a_{3} }[/tex] = [tex]\frac{2^{15} }{2^{11} }[/tex] = [tex]2^{(15-11)}[/tex] = [tex]2^{4}[/tex] = 16

the first term a₁ = 2³ = 8

Answer: 3.82x10^7

Step-by-step explanation:

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ N(\stackrel{x_1}{5}~,~\stackrel{y_1}{-3})\qquad Q(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +5}{2}~~~ ,~~~ \cfrac{ y -3}{2} \right) ~~ = ~~\underset{midpoint}{\stackrel{\textit{\LARGE P}}{(3~~,~~-2)}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{x+5}{2}=3\implies x+5=6\implies \boxed{x=1} \\\\\\ \cfrac{ y -3}{2}=-2\implies y-3=-4\implies \boxed{y=-1}[/tex]

Answer:

LCM = 27,720

Step-by-step explanation:

brainliest please

7 - The geocentric model says that the earth is at the center of the cosmos or universe, and the planets, the sun and the moon, and the stars circles around it. The early heliocentric models consider the sun as the center, and the planets revolve around the sun.

8 - Modele A is the most accurate cause the sun, earth, & moon are in a straight line & in the time and space all the planets are in one straight line.

Answer:

g(x) = |4x+3|

Step-by-step explanation:

g(x) = f(x) - 2

=|4x+3|

Answer:

-30, -32 and -34

Step-by-step explanation:

-30 + -32 + -34 = -96

The sum of finite arithmetic series  8+9+10+. . . . . . +15 is 92

Suppose we are given an arithmetic series:

      a(1) + a(2) + ... + a(n)

Then the sum is:

      S(n) = n/2 (a(1) + a(n))

Where: a(1) = first term

a(n) = nth term

The given series is:

      8+9+10+. . . . . . +15

We need to find n such that a(n) = 15.

Recall that in an arithmetic sequence:

      a(n) = a(1) + (n -1) . d

where d = difference between 2 consecutive terms.

Substituting a(1) = 8, and  d = 9 - 8 =1 into the formula:

a(n) = 8 + (n -1) . 1

15 = 7 + n

n = 8

Substitute n = 8 into the sum formula:

S(n) = n/2 (a(1) + a(n))

S(8) = 8/2 . (8 + 15)

        = 4 . 23 = 92  

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Answer:

Step-by-step explanation

Height for time = 8 seconds

h = -4.9t^2 + 259t + 423

h = -4.9(8)^2 + 259(8) + 423

h = -313.6 + 2072 + 423

h = 2181.4 meters at 8 seconds

Heoght for time = 0 seconds

h = -4.9t^2 + 259t +423

h = -4.9(0)^2 + 259(0) + 423

h = 0 + 0 + 423

h = 423 meters at 0 seconds

The values of the variable x, y and z are x = 4; y = 3 and z = 25.

Now, as per the given question, the three equations are given below;

x = 2y - 2  .......eq 1

z = 5x + 3y - 4    .........eq 2

3y = 9       ...............eq 3

From equation , calculate y.

3y = 9

y = 9/3 = 3.

Substitute the value of y in eq 1.

x = 2y - 2

x = 2×3 - 2

x = 6 - 2

x = 4

Now, put the value of x and y in equation 2.

z = 5x + 3y - 4

z = 5×4 + 3×3 - 4

z = 20 + 9 - 4

z = 25

Thus, the values of the three variables are;

x = 4; y = 3 and z = 25.

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The value of the expression 13 + (2^2 x 7) - 10 is 31

The expression is given as

13 + (2^2 x 7) - 10

Evaluate the exponent

So, we have

13 + (2^2 x 7) - 10 = 13 + (4 x 7) - 10

Evaluate the product

So, we have

13 + (2^2 x 7) - 10 = 13 + 28 - 10

Evaluate the sum

So, we have

13 + (2^2 x 7) - 10 = 41 - 10

Evaluate the difference

So, we have

13 + (2^2 x 7) - 10 = 31

Hence, the value of the expression 13 + (2^2 x 7) - 10 is 31

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The equation that represents the linear relationship between the x- values and y-values in the table is y = 6x - 5 .

What is a linear equation?

An algebraic equation of the form y=mx+b is referred to as a linear equation. m is the slope, and b is the y-intercept, and all that is involved is a constant and a first-order (linear) term. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

The equation y = 6x - 5  can represent the linear relationship between the x- values and y-values because it satisfies all the given values for x and y.

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Sum of the two separate equations.

The values satisfies the equation is 2430.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

Given that,

Equations for the two separate days :

125a +65 s = 1,200 - - - Friday

140a +50s = 1,230 - - - Saturday

Because, Inputting the solution, satisfied the equation:

a = 7 ; s = 5

265a+115s=2430

265(7) + 115(5) = 2430

1855 + 575 = 2430.

Therefore, The values satisfies the equation is 2430.

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Answer:

-59

Step-by-step explanation:

use pemdas

1+10-70

11-70

-59

Answer: y = -4x + 3

Step-by-step explanation:

Line touches at point 3 on the y axis

Goes up 4 and left by 1

If Edgar is a high school senior who has great grades and just received a notification that he was awarded a few scholarships in the amounts of $4,500, $7,500, and $750 while his expected tuition with books and fees is $25,000, then the amount of money Edgar will need to pay for the rest of his education bill is equal to $12,250.

The amount of money Edgar will need to pay can be determined by the subtraction of the total tuition with books and fees from the total amount of scholarships awarded to Edgar.

The total amount of scholarships awarded to Edgar can be determined by the sum of all of the scholarships.

Total amount of scholarships = 4500 + 7500 + 750

Total amount of scholarships = $12,750

Now the amount that Edgar will need to pay for the rest of his education bill can be determined by subtraction.

Amount to be paid by Edgar =  Tuition with books and fees - Total amount of scholarships

Amount to be paid by Edgar  = 25,000 - 12750

Amount to be paid by Edgar = $12,250

Hence, the amount of money Edgar will need to pay for the rest of his education bill is calculated to be $12,250.

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The solutions of the given equation 11/3x - 1/3 = -4/x² are x = -1 and x = 12

In this question, we have been given an equation.

11/3x - 1/3 = -4/x²

We need to solve given equation.

⇒ 11/3x - 1/3 = -4/x²

⇒ (33 - 3x)/9x = -4/x²

⇒(33 - 3x)/9 = -4/x

⇒ x(33 - 3x) = -36

⇒ -3x² + 33x + 36 = 0

⇒ x² - 11x - 12 = 0

⇒ x² - 12x + x - 12 = 0

⇒ x(x - 12) + 1(x - 12) = 0

⇒ (x - 12)(x + 1) = 0

⇒ x - 12 = 0           or       x + 1 = 0

⇒ x = 12           or          x = -1

Now we need to check above solutions.

Substitute x = 12 in given equation.

⇒ 11/3(12) - 1/3 = -4/(12)²

⇒ 1/3 (11/12 - 1) = 1/3(-4/48)

⇒ -1/12 = -1/12

⇒ LHS = RHS

Now substitute x = -1 in given equation.

⇒ 11/3(-1) - 1/3 = -4/(-1)²

⇒ -12/3 = -4/1

⇒ -4 = -4

⇒ LHS = RHS

Therefore, the solutions of the given equation 11/3x - 1/3 = -4/x² are x = -1 and x = 12

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The true statements are as follows:

(6 ×3) ÷ (6 + 3) = 2

4 × 6 ÷ ( 3 × 8 )  = 1

3 × (3× 3) + 6 = 18

6 ÷ (4 - 3) + 8 = 14

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.

+ Addition operation: Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

/ Division operation: Divides left-hand operand by right-hand operand

For example 4/2 = 2

We have the numbers 3, 4, 6, and 8 once in each exercise to make a true.

⇒ (6 ×3) ÷ (6 + 3) = 2

⇒ 4 × 6 ÷ ( 3 × 8 )  = 1

⇒ 3 × (3× 3) + 6 = 18

⇒ 6 ÷ (4 - 3) + 8 = 14

Thus, the required solution is shown above.

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The equation of the line in point-slope form, which passes through the pair of points located at (-1/2 , -1/2) and (-3 , -4), is y + 1/2 = 7/5(x + 1/2).

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Getting the slope of the two points: (-1/2 , -1/2) and (-3 , -4).

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

m = (-4 - -1/2)/(-3 - -1/2)

m = (-7/2)/(-5/2)

m = 7/5

Using the point slope form, plug in the values of the slope and one point to set up the equation.

(y - y1) = m(x - x1)

where m = 7/5 and (x1 , y1) = (-1/2 , -1/2)

(y - -1/2) = 7/5(x - -1/2)

y + 1/2 = 7/5(x + 1/2)

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x less than or equal to 6 is the following is not a way to represent the solution of the inequality.

What is inequality in math?

2(x − 1) ≤ 10

2x - 2 ≤ 10

2x ≤ 10 + 2

2x ≤ 12

x ≤ 6

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10. m∠HIK (2x+15)°, m∠LIJ = (5x-27)°, m∠HIK =

if they are vertice angles then they are equal to each other or

they both add up to 180°

A.

2x+15=5x-27

3x=42

x=14

B.

(2x+15)° + (5x-27)° = 7x-12

7x-12 = 180

7x=192

x = 27 3/7 or 27.43

Answer:

Step-by-step explanation:

[5x+3x-(-2x)]+[-3-8]=9

10x+(-11)=9

10x=20

x=2

There is need of total of 25 boxes of same size for the next lower level.

A sequence can be taken as the set of numbers having a particular order for all the terms or we can say that arrangement of numbers in some order is known as sequence.

Some examples for sequence are :

2,4,6,8,10,12

3,9,27,81,243

The recursive sequence is the sequence in which any term in the sequence can be find with the help of previous term of that sequence.

In a sequence , first term always known as initial term.

and difference between two terms are known as common difference. It is denoted by d.

General form of sequence is :

[tex]a_1,a_2,a_3,----,a_n[/tex]

where , [tex]a_n[/tex] = last term in sequence.

According to question,

The boxes in each of successive levels make a sequence.

Also, number of boxes at level n = [tex]n^2[/tex]

As upto four level the number of boxes are 16.

at level 5 , n = 25

Thus, the total  boxes of equal or same size need for next lower level is 25.

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The complete question is :

Suppose you're stacking boxes in levels which make squares. The numbers of boxes in each successive levels make a sequence. The figure show top four levels as view from top or above.

a. How many boxes of same size would need for next lower level?

b. How many boxes of same size would need to add the 3 levels?

c. Suppose you are stacking 285 boxes. Then, how many total levels will you have?

The solution of the system of equations involving x + 3y = 5 and -2x - 4y = -5 is (-5/2 , 5/2).

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

There are three methods that can be used to solve system of linear equations.

1. Elimination

2. Substitution

3. Graphing

Using substitution method, given two linear equations in x and y,

x + 3y = 5     (equation 1)

-2x - 4y = -5     (equation 2)

Using the first equation, find the value of one variable, lets say x, in terms of the other.

x + 3y = 5     (equation 1)

x = 5 - 3y

Substitute the equation of x to the second equation.

-2x - 4y = -5     (equation 2)

-2(5 - 3y) - 4y = -5

-10 + 6y - 4y = -5

Combining all terms containing the variable y on one side and the constants on the other side of the equality, and solving for y.

-10 + 6y - 4y = -5

6y - 4y = -5 + 10

2y = 5

y = 5/2

Substitute the value of y in the equation of x.

x = 5 - 3y

x = 5 - 3(5/2)

x = 5 - 15/2

x = -5/2

Hence, the solution of the given system of equations is (-5/2 , 5/2).

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