Find the length of side x in simplest radical form with a rational denominator

[tex]3x-\dfrac{1}{5}(10x+5)=6\qquad\text{use distributive property}\\\\3x-\left(\dfrac{1}{5}\right)(10x)-\left(\dfrac{1}{5}\right)(5)=6\\\\3x-2x-1=6\qquad\text{add 1 to both sides}\\\\\boxed{x=7}[/tex]

Answer:

80 miles per gallon

hope it helps

Step-by-step explanation:

to find the miles per gallon you would have to divide the miles driven (16,282) by gallons used (203) to find how many miles per gallon wasted

16,282 ÷ 203 = 80.2

80.2 rounded to the nearest 10 = 80 miles per gallon

Answer:9.5*3+6*2

Step-by-step explanation:

You multiply each price by the number that they want to buy

Answer:

terminating decimal

Step-by-step explanation:

Terminating decimals stop,  non terminating decimals go on forever.

4/25  

Multiply the top and bottom by 4

4/25*4/4 = 16/100

.16

This is a terminating decimal

Answer:

Step-by-step explanation: If you are trying to figure out how many gallons the whole family uses, the answer is 99 gallons.The reason is is because it says 2.2 gallons a minute and it takes 9 minutes for a shower. So you multiply 9 by 2.2 which would give you 19.8. Then you multiply it by 5 isnce it says 5 people take a shower.

Answer:

99 gallons

Step-by-step explanation:

Let as assume we need to find how many gallons of water does the family use for showering every morning.

It is given that every minute 2.2 gallons of water flows from a shower.

Total number of family members = 5

Average time of shower = 9 minutes per person every morning.

Total time of shower = [tex]9\times 5=45[/tex] minutes

1 minute = 2.2 gallons

45 minute = 2.2 × 45  gallons

45 minute = 99 gallons

Therefore, in every morning 99 gallons of water was used by the family

Final answer:

To find the size of a cube that David can cover with 169 quarts of paint, set up a proportion and solve for the edge length, David can cover a cube with an edge length of approximately 5.31 feet using 169 quarts of paint.

Explanation:

To find the size of a cube that David can cover with 169 quarts of paint, we need to use the direct proportion between the amount of paint and the surface area of the cube. Let x be the edge length of the cube. The surface area of a cube is given by[tex]6x^2[/tex]can set up the proportion:

[tex]16 quarts / 2 feet^2 = 169 quarts / (6x^2)[/tex]

Cross-multiplying and then solving for x, we get:

[tex]x^2 = (2^2 * 169) / 16[/tex]

[tex]x^2 = 28.1875[/tex]

x = sqrt(28.1875)

x ≈ 5.31 feet

Therefore, David can cover a cube with an edge length of approximately 5.31 feet using 169 quarts of paint.

Answer:

x = number of text messages sent

0.2x+40=50

0.2x = 10

5(0.2x) = 5(10)

x = 50

Therefore, 50 text messages would have to be sent or received in order for the plans to cost the same each month.

Step-by-step explanation:

Answer:

Correct choice is D

Step-by-step explanation:

Plot points (12, 16), (13, 18), (13, 10), (14, 16), (15, 9), (15, 8), (16, 17), (17, 23) on the coordinate plane. On this coordinate plane x represents age in years and y represents texting speed in words per minute.

Option A is false. Consider points A(12,16) and C(13,10). For these points x-coordinates increases, but y-coordinates decreases. Therefore, as age increases, texting speed doesn't increase.

Option B is false. Consider points A(12,16) and B(13,18). For these points both x-coordinates and y-coordinates increases. Therefore, as age increases, texting speed increases too.

Option C is false. Consider points C(13,10) and F(15,8). For these points y-coordinates decreases, but x-coordinates increases. Therefore, as texting speed decreases, age increases.

Option D is true, there is no clear relationship between age and texting speed.

Answer:

The Answer is D. No, there is no clear relationship between age and texting speed.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Make circles. 4 circles. Then divide the beads to your circles. The one's you have leftover is your remainder. Hope that helps.

Answer:

3

Step-by-step explanation:

x÷4 is the expression

Evaluate when x=12

12÷4

12/4

3

He subtracted instead of dividing.

12-4 = 8          12/4 =3

Answer: w = 9 cm,   L = 23 cm

Step-by-step explanation:

P (Perimeter)  = 2L(length) + 2w(width)

A (Area) = L (length) x w (width)

Use the formulas above to create a system of equations, then solve using the substitution method.

P = 2L + 2w

64 = 2L + 2w

32 = L + w

32 - w = L    ←←←   use this to substitute for L in the Area equation

                              A = L · w

                          207 = (32 - w)w

                          207 = 32w - w²

      w² - 32w + 207 = 0

         (w - 23)(w - 9) = 0

     w - 23 = 0            w - 9 = 0

           w₁ = 23                w₂ = 9

Now, solve for L:

      L₁ = 32 - w₁                      L₂ = 32 - w₂

         = 32 - 23                           = 32 - 9

          = 9                                    = 23

We have 2 sets of solutions (w₁ , L₁) and (w₂ , L₂)

                                              (23, 9)  and  (9, 23)

Notice that they are the same values but in reverse order.  These are the dimensions of the rectangle.  We generally consider width (w) to have the smaller value. So, w = 9 and L = 23

Answer:

Jack is 6 and Mom is 30

Step-by-step explanation:

J = Jacks age

M = Mom's age

5J = M

In 6 years, so add 6 to the age

3(J+6) = (M+6)

We have a system of 2 equations and 2 unknowns

Lets simplify the 2nd equation

3(J+6) = (M+6)

3J + 18 = M+6

Substituting M =5J

3J + 18 = 5J +6

Subtract 3J from each side

3J-3J + 18 = 5J-3J +6

18 = 2J+6

Subtract 6 from each side

18-6 = 2J+6-6

12 = 2J

Divide each side by 2

12/2 = 2J/2

6=J

Jack is 6

We still need to find Mom's age

M = 5J

     = 5*6

    =30

Mom is 30

Answer:23

Step-by-step explanation:

92/4

Answer:

32.5%

Step-by-step explanation:

The percentage decrease of available credit in Dylan's account is 30%. This was found by subtracting the new available credit from the original, dividing the difference by the original available credit, and multiplying by 100.

To calculate the percentage decrease of the available credit in Dylan's account, we need to first determine the amount of credit that has been used. The original available credit was $650.00, and it has decreased to $455.00 after some purchases. The difference between the two amounts is $650.00 - $455.00 = $195.00. This value represents the decrease in available credit.

Next, we calculate the percentage decrease by dividing the decrease by the original amount and multiplying by 100. So, the percentage decrease = ($195.00 / $650.00) × 100 = 30%.

Answer:

I would say that the answer is a. because I would go with the lowest one knowing that if I roll anything other than six, I lose this game is designed for you to nearly lose, so I would go with the lowest choice which is a. since i have a lower chance at winning.  

Step-by-step explanation: please mark this brainliest and I will be glad to help anytime.

Answer:

As per the statement:

The internal dimension of a cylindrical container has a base area of 20 cm2 and a height of 10 cm.

Volume(V) of a cylinder is given by:

[tex]V =A \cdot h[/tex]

where

A is the area of the base cylinder and

h is the height of the cylinder

Substitute the value A = 20 cm square and h = 10 cm we have;

[tex]V=20 \cdot 10[/tex]

Simplify:

V = 200 cubic cm

Therefore, the internal volume of the container is 200 cubic cm

Answer:

200 cm³

Step-by-step explanation:

In question we have given the area and height of the internal dimension of a cylindrical container.We have to find volume of the container.

From question statement ,we observe that

Area=20 cm² and   Height=10 cm

The  formula to find volume is :

Volume= Area×Height

putting the values of area and height in above formula,we get

Volume= 20 cm²×10 cm

Volume= 200 cm³

Hence, The internal volume of the container is 200 cm³.

Answer:

Corresponding Parts of Congruent Figures. The word corresponding refers to parts that match between two congruent triangles. You can identify corresponding angles and corresponding sides. First, name the corresponding angles.

Step-by-step explanation:

In geometry, two figures are congruent if they have the same size and shape. To verify congruence, all corresponding sides and angles of two figures must match in size and measure. For instance, given two triangles ABC and DEF, they would be congruent if their corresponding sides and angles were equal.

In geometric terms, two figures are congruent if they have the same size and shape. This means all corresponding sides and angles of the two figures are equal. In order to determine if two shapes are congruent, you need to match each part of one shape with a corresponding part on the other and see if they are of the same size and angle.

For instance, if you have two triangles ABC and DEF, these triangles would be congruent (often written as △ABC≅△DEF) if the sides AB=DE, BC=EF, and AC=DF and angles ∠A=∠D, ∠B=∠E and ∠C=∠F. This is the principle of corresponding parts of congruent figures being congruent.

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Answer:

a. 9.34 billions of pounds.

b. 14.37 billions of pounds.

Step-by-step explanation:

We have been given that cheese production in a country is currently growing at a rate of 4% per year. the equation [tex]y=8.3*(1.04)^{x}[/tex] models the cheese production in the country from 2003 to 2009. In this equation l, y is the amount of cheese produced in billions of pounds and x represents the number of years after 2003.

a. To find the total cheese production in the country in 2006 we will substitute x= 3 in our given equation as 2006-2003=3.

[tex]y=8.3*(1.04)^{3}[/tex]

[tex]y=8.3*1.124864[/tex]  

[tex]y=9.3363712[/tex]

Therefore, the cheese production in year 2006 will be 9.34 billions of pounds.

b. To find the total cheese production in the country in 2017 we will substitute x= 14 in our given equation as 2017-2003=14.

[tex]y=8.3*(1.04)^{14}[/tex]

[tex]y=8.3*1.7316764476028035[/tex]

[tex]y=14.37291451510326905[/tex]

Therefore, the cheese production in year 2017 will be 14.37 billions of pounds.

Answer:

Given the equation: [tex]y = 8.3(1.04)^x[/tex]        ......[1]

where

y is the amount of cheese produced in billions of pounds and

x represents the number of years after 2003

Since, this equation models the cheese production in the country from 2003 to 2009.

(a)

we have to find the total cheese production in the country in 2006.

Substitute x = 3 years(i.e, 2003 -2006) in [1] to solve for y;

[tex]y = 8.3(1.04)^{3}[/tex]

Simplify:

y = $9.3363712

Therefore, the total cheese production in the country in 2006 is, $9.34.

(b)

we use  the equation to predict the total amount of cheese produced in the country in 2017.

We have x = 14 years.

Substitute in [1] we get;

[tex]y = 8.3(1.04)^{14}[/tex]

Simplify:

y = $14.3729145151

Therefore, the estimate total amount of cheese produced in the country in 2017 is, $14.37

Answer:

[tex]\frac{1}{25}[/tex]

Step-by-step explanation:

using the rule of exponents

• [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex], then

[tex]5^{-2}[/tex] = [tex]\frac{1}{5^{2} }[/tex] = [tex]\frac{1}{25}[/tex]

Answer:

Area = 20.52 cm^2 and Perimeter = 28.68 cm.

Step-by-step explanation:

Use Pythagoras theorem to find the base of the triangle.

a^2 = 6^2 - 3^2 =  27

a = sqrt27

b^2 = 9^2 - 3^2 =  72

b = sqrt72

Base = sqrt27 + sqrt72

= 13.68

So Area = 0.5 * 13.68 * 3

= 20.52 cm^2   (answer)

Perimeter = 9 + 6 + 13.68

= 28.68  ( answer).

The standard form of quadratic equation for given points is x² - 3 x + 2 =0.

The standard form of quadratic equation is given by ax² + bx + c = 0.

where a , b , c are the constant .

Given,

The value of a, b, c as 1 , -3, 2 respectively.

Putting the value a, b, c in the standard form

we get  x² - 3 x + 2 =0.

So, The standard form of quadratic equation for given points is x² - 3 x + 2 =0.

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Answer:

120 dollars

Step-by-step explanation:

6 hours per day, for 2 days, leads to a total of 12 hours (2*6 = 12)

If it takes 2 gallons of gas to run the boat for 1 hour, then it will take 24 gallons to run for 12 hours. We can see this if we have the ratio below

2 gallons: 1 hour

12*(2 gallons): 12*(1 hour) .... multiply both sides by 12

24 gallons: 12 hours

Now multiply this gallon count (24) by the cost per gallon ($5) and we get to 5*24 = 120

Answer can you show use the graph then i would be able to answer it

Answer:

y = -2x+28

Step-by-step explanation:

We have the slope and a point, so we can use the point slope form to make a line

y-y1 = m(x-x1)

y-12 = -2(x-8)

Distribute the -2

y-12 = -2x+16

Add 12 to each side

y-12+12 = -2x+16+12

y = -2x+28

This is the slope intercept form of the line

Answer:

Use the slope-intercept form to find the slope and y-intercept.Slope:  

2

Y-Intercept:  

0

Any line can be graphed using two points. Select two  

x

values, and plug them into the equation to find the corresponding  

y

values.x

y

0

0

1

2

Graph the line using the slope and the y-intercept, or the points.

Slope:  

2

Y-Intercept:  

0

x

y

0

0

1

2

Step-by-step explanation:

Answer:

arithmetic

Step-by-step explanation:

It is  arithmetic because the terms go up by 15 . That is the common difference is 15.

Answer:

it is an arithmetic sequence

Step-by-step explanation:

general formula of arithmetic progression is

an=a1+(n-1)d

we are given

a1=1

a2=16

we can find d

d=a2-a1=16-1=15

d=a3-a2=31-16=15

d=a4-a3=46-31=15

as we can see that there is a common difference d =15 between successive terms  of the this sequence

hence it is a arithmetic sequence