Find k, the constant of proportionality, for the data in this table. Then write an equation for the relationship.

They equation needs to be in the form y=kx

K=

Equation:

There are 6 balloons in small bouquet and 21 balloons in large bouquet.

Step-by-step explanation:

Let,

Number of balloons in small balloon bouquet = x

Number of balloons in large balloon bouquet = y

According to given statement;

2x+3y=75    Eqn 1

2x+y=33      Eqn 2

Subtracting Eqn 2 from Eqn 1

[tex](2x+3y)-(2x+y)=75-33\\2x+3y-2x-y=42\\2y=42[/tex]

Dividing both sides by 2

[tex]\frac{2y}{2}=\frac{42}{2}\\y=21[/tex]

Putting y=21 in Eqn 2

[tex]2x+21=33\\2x=33-21\\2x=12[/tex]

Dividing both sides by 2

[tex]\frac{2x}{2}=\frac{12}{2}\\x=6[/tex]

There are 6 balloons in small bouquet and 21 balloons in large bouquet.

Keywords: linear equation, subtraction

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Final answer:

In solving the system of linear equations, we determined that a small balloon bouquet contains 6 balloons and a large balloon bouquet contains 21 balloons.

Explanation:

Solving a System of Equations

Let's denote the number of balloons in a small bouquet as s and in a large bouquet as l. The given problem provides us with two equations based on the information about the graduation party and Father's Day celebration:

For the graduation party: 2s + 3l = 75

For the Father's Day celebration: 2s + l = 33

Now we solve this system of linear equations to find the values of s and l. Subtracting the second equation from the first gives us:

2s + 3l - (2s + l) = 75 - 33

Which simplifies to:

2l = 42

Dividing by 2 gives us:

l = 21

Now we can plug in the value of l into any of the original equations to find the value of s. Let's use the Father's Day equation:

2s + 21 = 33

Subtracting 21 from both sides gives us:

2s = 12

Finally, dividing by 2 gives us:

s = 6

Therefore, a small balloon bouquet contains 6 balloons and a large balloon bouquet contains 21 balloons.

Answer:

Equation: y = 15x.

:)

Answer:

y = 15x

Step-by-step explanation:

The question asked,  what equation shows the line through the data points.  And it stated the equation needed to be in the form y = kx

Where

y represents the vertical axis

x represents the horizontal axis

k = constant

K is the constant interval and can be use to get the next points

y = kx

viewing the most visible points from the graph , let use the point where total saved is 90(y axis) and the time in weeks (x axis) is 6, the constant K can be gotten.

y = 90

x = 6

y = kx

90 = 6k

divide both sides by 6

k = 90/6

k = 15

Therefore,

y = 15x

Answer: $4

Step-by-step explanation:

2d + 14 = 22

subtract 14

2d = 8

divide by 2

d = $4

each bag of Doritos costs $4

Elizabeth spent a total of $8 on 2 large bags of Doritos after spending $14 on soda, which means each bag costs $4.

To determine the price of each bag of Doritos, we need to subtract the amount spent on soda from the total amount spent. Elizabeth spent $14 on soda and had a total of $22 in expenses. So, the money spent on Doritos is the difference between the total amount and the soda amount.

Amount spent on Doritos = Total amount - Amount spent on soda

Amount spent on Doritos = $22 - $14

Amount spent on Doritos = $8

Since Elizabeth bought 2 large bags of Doritos, we can find the price per bag by dividing the total amount spent on Doritos by 2.

Price per bag of Doritos = Total spent on Doritos / Number of bags

Price per bag of Doritos = $8 / 2

Price per bag of Doritos = $4 per bag

Therefore, each large bag of Doritos costs $4.

Answer:n=10, 5n=50

Step-by-step explanation:

an=50

n=50/a

n=50/5=10

5n=5×10=50

Answer:

Step-by-step explanation:

an = 50

a +(n-1)d = 50

5 + (n-1)*3 = 50

(n-1)*3 = 50 - 5 = 45

n-1 = 45/3

n-1 = 15

n=15+1 = 16

n = 16

Answer:

-4, -0.5, 1

that's the answer

Answer:-4, -0.5, 1

Step-by-step explanation:

Answer:   Hence the dimension of triangle are 15, 15 and 23.

Step-by-step explanation:

Alright, lets get started.

Please refer the diagram attached.

Suppose two congruent sides of triangle are : x

Suppose the base of the triangle : y

As per question, the base of the triangle is seven less than two times the congruent sides lengths.

So,

[tex]y = 2x-7[/tex]  .......................(1)

Now the perimeter of triangle is given as : 53

It means

[tex]x+x+y=53[/tex]

[tex]2x+y=53[/tex]  .......................(2)

Plugging the value of y from equation (1) in equation (2)

[tex]2x+2x-7=53[/tex]

[tex]4x-7=53[/tex]

[tex]4x=60[/tex]

[tex]x=15[/tex]

Plugging the value of x in equation (1)

[tex]y=2\times (15)-7[/tex]

[tex]y=23[/tex]

Hence the dimension of triangle are 15, 15 and 23.    :   Answer

Hope it will help :)

By using the fact of supplement angles of congruent angles are congruent, we proved that ∠2 ≅ ∠3

Step-by-step explanation:

The supplementary angles are:

∵ ∠1 and ∠2 are supplementary

∴ m∠1 + m∠2 = 180° ⇒ (1)

∵ ∠3 and ∠4 are supplementary

∴ m∠3 + m∠4 = 180° ⇒ (2)

We can equate the left hand sides of (1) and (2) because the right hand sides are equal

∴ m∠1 + m∠2 = m∠3 + m∠4 ⇒ (3)

∵ ∠1 ≅ ∠4

∴ m∠1 = m∠4

- Substitute m∠4 by m∠1 in (3)

∴ m∠1 + m∠2 = m∠3 + m∠1

- Subtract m∠1 from both sides

∴ m∠2 = m∠3

∴ ∠2 ≅ ∠3

By using the fact of supplement angles of congruent angles are congruent, we proved that ∠2 ≅ ∠3

Learn more:

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Answer:

discriminant=D=0

Step-by-step explanation:

given, 9x^2-18x+9=0...............(1)

equ (1) divided by 9

x^2-2x+1=0

discriminant=D=b^2-4ac

where, b=-2, a=1, c=1

D=(-2)^2-[tex]4\times 1\times 1[/tex]

D=4-4=0

D=0

hence discriminant=D=0  answer

Answer:

Paul. He has made 60 pizzas after 9 days.

Step-by-step explanation:

Paul makes 12 pizzas the first day and 6 pizzas each day after that.

So, after 9 days Paul will make total [12 + (9 - 1)6] = 60 pizzas.

Now, Cindy makes 16 pizzas the first day and 4 pizzas each day after that.

So, after 9 days Cindy will make total [16 + (9 - 1)4] = 48 pizzas.

Therefore, after 9 days Paul will make more pizzas and the number is 60 pizzas. (Answer)

Answer:

B

Step-by-step explanation:

Answer:

C) Y = -45

Step-by-step explanation:

Y/9 + 5 = 0

Y/9 = -5

y = -5 * 9

Y= -45

Answer:

The two numbers are 10 and 7.

Step-by-step explanation:

Given:

The two numbers whose difference is three, when the larger number is decreased by three times the smaller number the result is -11.

Now, find the two numbers.

Let the larger number be [tex]x[/tex].

Let the smaller number be [tex]y[/tex].

As given, the two numbers whose difference is three:

[tex]x-y=3[/tex]

[tex]x=3+y[/tex]

So, the value of [tex]x=3+y[/tex].

According to question:

[tex]x-3y=-11[/tex]

Putting the value of [tex]x[/tex] we get:

[tex]3+y-3y=-11[/tex]

[tex]3-2y=-11[/tex]

Moving variables on one side and the number on the other we get:

[tex]3+11=2y[/tex]

[tex]14=2y[/tex]

Dividing both sides by 2 we get:

[tex]7=y[/tex]

The smaller number = 7.

Now, putting the value of [tex]y[/tex] in the equation [tex]x-y=3[/tex]:

[tex]x-y=3[/tex]

[tex]x-7=3[/tex]

Adding both sides by 7 we get:

[tex]x=10.[/tex]

The larger number = 10.

Therefore, the two numbers are 10 and 7.

The equivalent expression to the value 16 is 2 × 8.

The equivalent expression to the value 16 is 2 × 8.

This is because 16 can be written as the product of 2 and 8.

Therefore, the expression 2 × 8 is equivalent to the value 16.

Answer:

A real number encompasses all numbers, whether it be irrational (irrational numbers go on forever) like pi or the square root of 5, an integer like a negative, a decimal, a fraction, 0, a whole number, a natural number etc.

Step-by-step explanation:

A real number encompasses all numbers, whether it be irrational (irrational numbers go on forever) like pi or the square root of 5, an integer like a negative, a decimal, a fraction, 0, a whole number, a natural number etc. (This doesn't include imaginary numbers however, like the square root of -1.)

Answer:

Step-by-step explanation:

A real number is a number that can be found on a number line. Numbers we use everyday. Real numbers include : natural numbers, whole numbers, integers, fractions, rational numbers, and irrational numbers. They do not include imaginary numbers, numbers that cannot be quantified, such as square root of -1.

Answer: The answer is below with explanations.

Step-by-step explanation:

In the binomial expansion of (x+y)^10, each term is calculated using the binomial coefficient formula. The expansion is [tex]x^10 + 10x^9y + 45x^8y^2 + 120x^7y^3 + 210x^6y^4 + 252x^5y^5 + 210x^4y^6 + 120x^3y^7 + 45x^2y^8 + 10xy^9 + y^10[/tex].

To expand the expression (x+y)^10 using the binomial theorem, we need to find the coefficients of each term. The general formula for the binomial expansion is: [tex](a+b)^n = C(n,0)a^n*b^0 + C(n,1)a^(n-1)*b^1 + ... + C(n,n)a^0*b^n[/tex], where C(n,k) represents the binomial coefficient. In this case, a=x, b=y, and n=10. Using the binomial coefficient formula, we can find the coefficients for each term:

[tex]C(10,0)*x^10*y^0 + C(10,1)*x^9*y^1 + C(10,2)*x^8*y^2 + ... + C(10,10)*x^0*y^10[/tex].

By calculating the binomial coefficients, the binomial expansion of (x+y)^10 is:

[tex]x^10 + 10x^9y + 45x^8y^2 + 120x^7y^3 + 210x^6y^4 + 252x^5y^5 + 210x^4y^6 + 120x^3y^7 + 45x^2y^8 + 10xy^9 + y^10[/tex].

The value of the solution to the system of equations are, (10, - 20)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

System of equations are,

y = -5x + 30  .. (i)

x = 10

Now, We can find the solution as;

Plug x = 10 in equation (i);

y = - 5x + 30

y = - 5 × 10 + 30

y = - 50 + 30

y = - 20

Thus, The value of the solution to the system of equations are, (10, - 20)

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Answer:

4m

Step-by-step explanation:

since it is not multiplication, there would be no power.

think of it as 2m + 1m + 1m

The answer is 4m

I hope this helped! If so, please mark brainliest!

Answer:

y=5/4x-5

Step-by-step explanation:

Perpendicular means negative reciprocal of the slope.

y-y1=m(x-x1)

y-(-5)=5/4(x-0)

y+5=5/4(x)

y+5=5/4x

y=5/4x-5

Answer:

x = 3

Step-by-step explanation:

Since all 3 sides of the triangle are congruent then the triangle is equilateral

The 3 angles are congruent and equal to 60°, thus

25x - 15 = 60 ( add 15 to both sides )

25x = 75 ( divide both sides by 25 )

x = 3

Answer:

The interest rate is 8% simple interest.

Step-by-step explanation:

Let the investment of $555 is getting r% simple interest for 6 years to become the balance of $821.4.

So, from the equation of the simple interest we can write

[tex]821.4 = 555(1 + \frac{6r}{100})[/tex]

⇒ [tex](1 + \frac{6r}{100}) = 1.48[/tex]

⇒ [tex]\frac{6r}{100} = 0.48[/tex]

⇒ r = 8%

Therefore, the interest rate is 8% simple interest. ( Answer )

Answer:

The "I" figure is 13 years old. Her brother is 16. Her Sister is 11. Her mother is 47.

Step-by-step explanation:

13+16=29

29+11=40

40+47=87

Answer:

the answer is c, 5 stages

Answer:

[tex]9\ pounds[/tex]

Step-by-step explanation:

Let

x ----> the number of pounds of a DVD player

we know that

The number of pounds of a DVD player multiplied by the cost per pound ($0.55) plus the charge of $6.99 must be equal to $11.94

so

The linear equation that represent this situation is

[tex]0.55x+6.99=11.94[/tex]

solve for x

subtract 6.99 both sides

[tex]0.55x=11.94-6.99[/tex]

[tex]0.55x=4.95[/tex]

divide by 0.55 both sides

[tex]x=9\ pounds[/tex]

Answer:

9x+5m-3

Step-by-step explanation:

3x-10+5m+6x+7

3x+6x+5m-10+7

9x+5m-3

Answer:

12.8

Step-by-step explanation:

Answer:

x=2 and y = 2

Step-by-step explanation:

Im going to use GeoGebra for graphing the 2 lines. I always find it helpful to move y to side of the equation and the rest of the equation to another side. This is the slope intercept equation by the way. We get our equations as y = -2x+6 and y= 2x-2.

You can find that the common point is (2,2) between the lines.

Answer:

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

Step-by-step explanation:

[tex](1+2x^3)^2\\\\\bold{METHOD\ 1:}\\\\(1+2x^3)^2=(1+2x^3)(1+2x^3)\qquad\text{use FOIL}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=(1)(1)+(1)(2x^3)+(2x^3)(1)+(2x^3)(2x^3)\\\\=1+2x^3+2x^3+4x^6\qquad\text{combine like terms}\\\\=1+4x^3+4x^6[/tex]

[tex]\bold{METHOD\ 2:}\\\\\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(1+2x^3)^2=1^2+2(1)(2x^3)+(2x^3)^2\\\\=1+4x^3+2^2(x^3)^2\\\\=1+4x^3+4x^6[/tex]

Answer:

The library is 6 blocks away to the left of Alberto's place

Step-by-step explanation:

There's missing information on this question.

Suppose the point here is to find the distance.

A reflection across the y-axis makes the y-axis as the symmetry axis.

1) Each unit represents one block and they share the same y-coordinate (4).

2) We have to subtract the absolute value of x-coordinate.

So,

[tex]|-3-(3)|=|6|=6[/tex]

The library is 6 blocks away to the left of Alberto's place.

Answer:

AC = 146

Step-by-step explanation:

Given that B  is the midpoint of AC, then

AB = BC, that is

9x + 1 = 6x + 25 ( subtract 6x from both sides )

3x + 1 = 25 ( subtract 1 from both sides )

3x = 24 ( divide both sides by 3 )

x = 8

Hence

AC = AB + BC = 9x + 1 + 6x + 25 = 15x + 26, thus

AC = (15 × 8) + 26 = 120 + 26 = 146

Answer:

146

Step-by-step explanation:

AB = BC (Definition of midpoint) so:

9x+1=6x+25.

Solve it as you would any other algebraic equation  >>>  9x+1=6x+25  >>>  9x+1-1=6x+25-1  >>>  9x=6x+24  >>>  -6x+9x=6x-6x+24  >>>  3x=24  >>>  3x/3=24/3  >>>  x=8

AB=9x+1  >>>  AB=9*8+1  >>>  AB=73

BC=6x+25  >>>  BC=6*8+25  >>>  BC=73

AC=AB+BC  >>>  AC=73+73  >>>  AC=146

Answer:

b

Step-by-step explanation: