You have 8 gallons of lemonade to sell. You use cone-shaped cups that are 9 centimeters in diameter and 12 centimeters tall. Each customer uses one paper cup. How many paper cups will you need if you sell all of the lemonade? (1 gal ≈ 3785 cm3)

Answer:

y = - 17

Step-by-step explanation:

[tex]y = 1 - 2x[/tex]

When x = 9

[tex]y = 1 - 2(9)[/tex]

[tex]y = 1 - 18[/tex]

[tex]y = - 17[/tex]

Therefore, given equation y = 1 - 2x; when x = 9, y = - 17

Degree of polynomials:

[tex]6x^2 = 2\\\\18x^3+5ab-6y = 3\\\\4x^3y +3x^2-xy-4 = 4\\[/tex]

Least to greatest based on degree:

[tex]6x^2[/tex]

[tex]18x^3+5ab-6y[/tex]

[tex]4x^3y +3x^2-xy-4[/tex]

Solution:

The degree of the polynomial is the highest degree of any of the terms

Know that the degree of a constant is zero

Option I

[tex]6x^2[/tex]

Here the highest degree is 2 ( x power 2)

In this case, degree of polynomial is 2

Option II

[tex]18x^3+5ab-6y[/tex]

To find the degree of the polynomial, add up the exponents of each term and select the highest sum.

[tex]Degree\ of\ 18x^3 = 3[/tex]

[tex]Degree\ of\ 5ab = 5a^1b^1 = 1+1 = 2[/tex]

[tex]Degree\ of\ 6y = 6y^1 = 1[/tex]

Thus the highest degree is 3

Option III

[tex]8a^{-5}[/tex]

This is not a polynomial

A polynomial does not contain variables raised to negative

Option IV

[tex]4x^3y +3x^2-xy-4[/tex]

To find the degree of the polynomial, add up the exponents of each term and select the highest sum.

[tex]Degree\ of\ 4x^3y = 4x^3y^1=3+1 = 4\\\\Degree\ of\ 3x^2 = 2\\\\Degree\ of\ xy = x^1y^1 = 1+1 = 2\\\\Degree\ of\ 4 = 0[/tex]

Thus highest degree is 4

Then organize the expressions from least to greatest based on their degree

Least to greatest based on degree:

[tex]6x^2[/tex]

[tex]18x^3+5ab-6y[/tex]

[tex]4x^3y +3x^2-xy-4[/tex]

Answer: B

Step-by-step explanation: you multiply 25 x 13 + 150

Answer:

42 miles

Step-by-step explanation

Distance = Speed * Time

X=12mph*3.5h

X=42 miles

Distance he can travel is 42 miles.

Step-by-step explanation:

⇒ Distance = 12 × 7/2 = 42 miles

Yo sup??

m3 and m6 for a supplementary pair therefore

m3+m6=180

122+m6=180

m6=58

Hope this helps

The required measure of the angle m∠6 is given as 58 degrees. Option B is correct.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

Here,
For the bisection of parallel line by transversal line,
Corresponding angles always have an equal measure,
So, ∠2 = ∠6

Now,
∠2 + ∠3 = 180

∠6 + 122 = 180
∠6 = 58°

Thus, the required measure of the angle m∠6 is given as 58 degrees. Option B is correct.

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Answer:

7.25

Explanation:

14.5×½=7.25

Therefore the inequality is x≤11

and maximum I can withdraw 11 bills.

Step-by-step explanation:

Given ,

Current balance $320

Minimum balance $100

I could spent =$(320-100) = $220

Let the number of bills be x.

Total amount of x bills = $20x

According to the problem,

20x≤ 220

⇔x ≤ [tex]\frac{220}{20}[/tex]

⇔x≤11

Therefore the inequality is x≤11

and maximum I can withdraw 11 bills.

QT = 36

Step-by-step explanation:

Step 1 :

Lines RT and SV are the diagonals of the parallelogram RSTV.

Step 2 :

The diagonals of a parallelogram bisect each other . (Properties of a parallelogram)

Step 3 :

Given that the diagonals RT and SV intersect at Q, we have QT = RQ.

=> 5 x + 1 = 3 x + 15

=> 5 x - 3 x = 15 -1

=> 2 x = 14

= > x = 7

Step 4:

QT = 3 x + 15

=> QT = 3 * 7 + 15

=> QT =  21 + 15 = 36

Applying the properties of the diagonal of a parallelogram, the length of QT = 36 units.

Therefore,

RQ = QT

5x + 1 = 3x + 15

5x - 3x = -1 + 15

2x = 14

x = 7

QT = 3x + 15

QT = 3(7) + 15

QT = 36

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Final answer:

To determine the number of charms for the bracelet to cost the same at both jewelry shops, we set up a system of equations and solved it using substitution. We found that Hana will need to add 2 charms, resulting in a total cost of $96 for the bracelet at either shop.

Explanation:

To determine the number of charms Hana can add to her bracelet such that the cost is the same at Dayton Fine Jewelry and Cain Jewelers, we need to set up a system of equations and solve using the substitution method.

System of Equations:

Let x represent the number of charms and y represent the total cost of the bracelet with charms.

Equation for Dayton Fine Jewelry: y = 17x + 62

Equation for Cain Jewelers: y = 18x + 60

Solution Using Substitution:

Hana will need to add 2 charms to her bracelet, and the total cost of the bracelet will be $96 at either jewelry shop.

The original price is $450.

Step-by-step explanation:

Step 1:

Given details, Discount%, D% = 30 and Selling Price, SP = $315

Step 2:

Write down formula for calculating the Original Price

Selling Price (SP) = Original Price (OP) - Discount (D)

Discount (D) = Original Price (OP) * (D%/100)

Step 3:

Substitute given values in the formula

315 = OP - D

D = [tex]OP \times30/100[/tex]

D = 0.3 OP

Step 4:

Substitute value of D in the first formula

315 = OP - 0.3 OP

315 = OP (1 - 0.3) = 0.7 OP

Original Price, OP = 315/0.7 = $450

Step-by-step explanation:

[tex] \frac{r}{32} = \frac{5}{8} =\frac{30}{t} \\ \\ \therefore \: \frac{r}{32} = \frac{5}{8} \\ \\ \therefore \: r = \frac{32 \times 5}{8} \\ \\\therefore \: r = 4 \times 5\\ \\ \huge \orange{ \boxed{\therefore \: r = 20}} \\ \\ \frac{5}{8} =\frac{30}{t} \\ \\ \therefore \: t = \frac{8 \times 30}{5} \\ \\ \therefore \: t = 8 \times 6 \\ \\ \huge \purple{ \boxed{ \therefore \: t = 48}}[/tex]

8th term is 0.30

Step-by-step explanation:

⇒ r = a2/a1 = 216/648 = 1/3

⇒ 8th term =  648 × (1/3)^8-1 = 648 × (1/3)^7 = 648/2187 = 0.30

First, we need to find out how many siblings the students have in total and how many siblings the teachers have in total.

The students: (1 x 4) = 4 + (2 x 7) = 18 + (3 x 5) = 33 + (4 x 2) = 41. The students have a total of 41 siblings.

The teachers: (1 x 3) = 3 + (2 x 2) = 7 + (3 x 4) = 19 + (4 x 5) = 39 + (5 x 3) = 54 + (6 x 1) = 60 + (8 x 1) = 68. The teachers have a total of 68 siblings.

Now that we have this information, we know that the answer is option 1, the students tend to have fewer siblings than the teachers. This is because the students had a total of 41 siblings and the teachers had a total of 68 siblings, and 41 is less than 68 so the students have fewer siblings than the teachers.

I really hope I could help! I put a lot of work into this answer! :D

Answer:

368.94

Step-by-step explanation:

New value =

258 + Percentage increase =

258 + (43% × 258) =

258 + 43% × 258 =

(1 + 43%) × 258 =

(100% + 43%) × 258 =

143% × 258 =

143 ÷ 100 × 258 =

143 × 258 ÷ 100 =

36,894 ÷ 100 =

368.94

To increase 258 by 43% using the multiplier method, multiply 258 by 1.43. The result is 369.14.

To use the multiplier method to increase 258 by 43, you simply need to calculate 258 times the multiplier. The multiplier is 1 plus the rate of increase, which is 43% in this case. So, the multiplier is 1+0.43=1.43.

Here is the calculation:

258 * 1.43 = 369.14

So, 258 increased by 43% is approximately 369.14.

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Answer:

32.24 gallons

Step-by-step explanation:

From the question,Jed’s shower head releases

6.2 gallons = 1 minute

x gallon = 5 mins 12 secs

First convert 12 secs to minutes and add it to 5 mins .

1 minute = 60secs

x minute = 12 secs

x = 12/60

= 0.2 mins + 5 mins

= 5.2 mins

Therefore,

6.2 gallons = 1 minute

x gallons = 5.2 mins

Cross multiply

x = 6.2 x 5.2 /1

= 32.24/1

= 32.24 gallons

Answer: The other answer is wrong. The answer would be about 50 miles per hour or 49.99 mph.

Step-by-step explanation:

The required approximate speed of the car when the skid mark is 10204 feet long is 49.99 miles per hour.

Given that,
The function S(D) =(7/2) √2D can be used to approximate the speed S, in miles per hour, of a car that has left skid marks of length D, in feet, how fast would a car have been traveling if it left a skid mark that is 102.04 feet long is to be determined.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
Given the function of speed,
S(D) =(7/2) √(2D)
Substitute the value of D = 102.04
S(102.04) = (7/2)√(2*102.04)
S(102.04) = 49.99

Thus, the required approximate speed of the car when the skid mark is 10204 feet long is 49.99 miles per hour.

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Answer:

30

Step-by-step explanation:

a right angle is 90 degrees so if it split into two parts and one is 30 degrees and the other is x (an unknown) you could do 90-30 to get 60 but since it is 2x but has to equal 60 it is going to be 30 because 30 times 2 is 60

Answer:

The answer is 30

Step-by-step explanation:

hope this helps!

Answer:

9/2

Step-by-step explanation:

Slope of line=rise/run=

y2-y1/x2-x1

Where

x1=2

x2=0

y1=5

y2= -4

Slope =(-4-5)/(0-2)

Slope=-9/-2

Slope=9/2

Answer:

look at the picture shown

Answer: 18 months or a year and a half

Step-by-step explanation:

2.5 centimeters every 2 months, so...

1.25 centimeters every month.

22.5 ÷ 1.25 = 18

So it will take 18 months to grow 22.5 centimeters of hair

Answer:

Step-by-step explanation:

4 - 2b = 2

collect terms

4 - 2 = 2b

2 = 2b

divide both side by 2

2/2 = 2b/2

b = 1

y

=

−

(

x

−

2

)

2

+

16

is the vertex form

Explanation:

The vertex form of a quadratic function is given by

y

=

a

(

x

−

h

)

2

+

k

where (h, k) is the vertex of the parabola.

when written in vertex form

(h, k) is the vertex of the parabola and x = h is the axis of symmetry

the h represents a horizontal shift (how far left, or right the graph has shifted from x = 0)

the k represents a vertical shift (how far up, or down the graph has shifted from y = 0)

Now let convert this  

y

=

−

x

2

+

4

x

+

12

into vertex form

y

=

−

x

2

+

4

x

+

12

y

−

12

=

−

x

2

+

4

x

y

−

12

=

−

(

x

2

−

4

x

)

y

−

12

=

−

(

x

2

−

4

x

+

4

−

4

)

y

−

12

=

−

(

x

2

−

4

x

+

4

)

+

4

y

−

16

=

−

(

x

2

−

4

x

+

4

)

y

−

16

=

−

(

x

−

2

)

2

y

=

−

(

x

−

2

)

2

+

16

is the vertex form

show the vertex in the figure below

graph{-x^2+4x+12 [-10.06, 15.25, 6.58, 19.25]}   Hope iam right

The function f(x) = x² - 4x - 12 in vertex form is f(x) = (x - 2)² - 16, and the axis of symmetry is x = 2.

To rewrite the function f(x) = x² - 4x - 12 in vertex form and find the axis of symmetry, we need to complete the square. The general vertex form of a quadratic is f(x) = a(x - h)² + k, where (h, k) is the vertex, and the line x = h is the axis of symmetry.

The first step is to factor the coefficient of x², which is 1 in this case, so we can leave it as is. The next step is to rearrange the equation as x² - 4x and then add and subtract the square of half the coefficient of x, which is (4/2)² = 4. Adding and subtracting 4 inside the parentheses gives us:

f(x) = (x² - 4x + 4) - 4 - 12

Now we can rewrite this as:

f(x) = (x - 2)² - 16

This equation is in vertex form, with the vertex at (2, -16), and the axis of symmetry is the line x = 2.

Therefore, the correct option is f(x) = (x - 2)² - 16, with the axis of symmetry being x = 2.

Answer:

In mathematics, compatible numbers are the numbers that are easy to add, subtract, multiply, or divide mentally...For instance, if we have to add 493 and 549, we can make the numbers compatible by rounding them up to the nearest tens or hundreds.

SO YES! :)

Answer:

x = -3

y = 7

Step-by-step explanation:

Answer: 42%

Step-by-step explanation:

Add 0.16 and 0.26, you get 0.42. Covert 0.42 into percentage and you get 42%

The area of the triangle is (5/12)x²

Step-by-step explanation:

Substitute b=(5/6)x and h=x

Area = 1/2[tex]\times[/tex](5/6)x(x)

Area of triangle = (5/12)x²

Answer:

Pie

Step-by-step explanation:

Answer:

pi

Step-by-step explanation:

The expression 3(4x+7)−4(12x−15) simplifies to -36x + 81. First distribute the constants to the terms inside the parentheses, then combine like terms.

In mathematics, to simplify an algebraic expression like 3(4x+7)−4(12x−15), you need to perform the operations in a certain order, respecting the laws of arithmetic. This is often referred to as simplifying the expression using the distributive property.

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Answer:

Step-by-step explanation:

4.75 x [tex]10^{2}[/tex]

Answer:

Step-by-step explanation:

[tex]4.75 x 10^{2}[/tex]

Answer:

it is D. $9.50

Step-by-step explanation:

Answer: The answer is (D) $9.50/9.50 dollars