if y varies directly as x and y=8 when x=2, find y when x=6

Answer:16x-4. You add all the numbers with common terms first, such as all the xs together. Then you add all the numbers without an x in front and tada!

Step-by-step explanation:Above

To show that 3/5 and 6/10 are equivalent using a number line, mark both fractions on the number line using tenths. As 3/5 is equal to 6/10, both fractions will land on the same point, confirming their equivalence.

The question is asking us to show that 3/5 and 6/10 are equivalent using a number line. First, let's understand that these are both fractions and are representations of the same value. To show this equivalence on a number line, start by drawing a line and marking it in increments from 0 to 1. You can choose to have 10 ticks, therefore each tick will represent 0.1.

Mark 3/5 on your number line by counting 6 ticks/tenths (because 3/5 is equal to 6/10 when the denominator is 10) from zero. Now, also mark 6/10 on the number line by counting 6 tenths from zero. You will find that both the fractions 3/5 and 6/10 land on the same point on the number line, thus showing they are equivalent.

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Mark both fractions on the number line with tenths to demonstrate that 3/5 and 6/10 are equivalent. Because 3/5 equals 6/10, both fractions will settle on the same point, proving their similarity.

The question asks us to use a number line to demonstrate that 3/5 and 6/10 are comparable. To begin, recognize that these are both fractions and represent the same amount. To demonstrate this equivalency on a number line, draw a line and mark it in increments of 0 to 1. You have the option of having 10 ticks, in which case each tick represents 0.1.

Mark 3/5 on your number line by counting 6 ticks/tenths from zero (since 3/5 equals 6/10 when the denominator is 10). Mark 6/10 on the number line as well by counting 6 tenths from zero. Both the fractions 3/5 and 6/10 land on the same point on the number line, indicating that they are comparable.

Answer:

x = 10

Step-by-step explanation:

An equilateral triangle has 3 congruent sides.

Let each side have length s.

P = 60 cm

P = 3s

3s = 60 cm

s = 20 cm

Each side has length 20 cm.

Draw an equilateral triangle with a horizontal side on the bottom. From the top vertex, drop a vertical segment to the horizontal side. This segment is the altitude. The altitude is the perpendicular bisector of the horizontal side of the triangle. Now you have two small congruent triangles, one on each side. One angle at the horizontal side is 60 degrees. The other is 90 degrees. The top angle is 30 degrees. Half of the bottom side of the original equilateral triangle has length 10 cm. The hypotenuse is 20 cm. The altitude is the third side.

10^2 + 20^2 = altitude^2

altitude^2 = 20^2 - 10^2

altitude^2 = 400 - 100

altitude^2 = 300

altitude^2 = 100 * 3

altitude = sqrt(100) * sqrt(3)

altitude = 10sqrt(3)

altitude = x * sqrt(3)

x = 10

Answer:

360 screws

Step-by-step explanation:

First we need to determine how many screws she needs for the 2 decks

We will determine the number of screws for 1 deck

1 deck uses 25 pieces of wood

25 pieces of wood * 8 screws/ piece of wood = 200

200 screws per deck

She is building 2 decks

2 * 200 = 400

400 screws for the 2 decks

She has 40 screws

400 screws she needs - 40 screws she has = 360 screws she still needs

Answer:

168km

Step-by-step explanation:

132/11=12km per litre

12*14=168km

Adam can cover [tex]\boxed{{\mathbf{168 km}}}[/tex]  with [tex]14{\text{ liters}}[/tex]  of fuel.

Further explanation:

The direct relationship is the relationship between two quantities in which one quantity decreases then the other quantity also decreases and vice versa. The examples are supply function and speed distance function.

The direct relationship of the variables [tex]a{\text{ and }}b[/tex]  as

[tex]\frac{{{a_1}}}{{{a_2}}}=\frac{{{b_1}}}{{{b_2}}}[/tex]                   ......(1)

Here, [tex]{a_1},{a_2}[/tex]  are the quantities of the variable [tex]a[/tex]  and [tex]{b_1},{b_2}[/tex]  are the quantities of the variable [tex]b[/tex]  

Given:

Adam covered the distance [tex]132{\text{km}}[/tex]  by car with 11 liters of fuel.

Step by step explanation:

Step 1:

The provided data can be written in the table form as,

It can be seen that data is direct relationship.

Here, [tex]{a_1}=132,{a_2}=a,{b_1}=11{\text{ and }}{{\text{b}}_2}=14[/tex]

Step 2:

Now put the values [tex]{a_1}=132,{a_2}=a,{b_1}=11{\text{ and }}{{\text{b}}_2}=14[/tex] in equation (1) to get the value of [tex]a[/tex] .

[tex]\begin{gathered}\frac{{{a_1}}}{{{a_2}}}=\frac{{{b_1}}}{{{b_2}}}\hfill\\\frac{{132}}{a}=\frac{{11}}{{14}}\hfill\\\end{gathered}[/tex]

Now calculate the further equation by the cross multiplication method.

[tex]\begin{aligned}\frac{{132}}{a}&=\frac{{11}}{{14}}\\132\times14&=11a\\1848&=11a\\a&=168\\\end{aligned}[/tex]

Thus, Adam can cover [tex]168{\text{ km}}[/tex]  distance with [tex]14{\text{ liters}}[/tex]  of fuel.

Learn more:  

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Comparing quantities

Keywords: Adam, car, fuel, distance, direct relationship, speed, positive relationship, increase, decrease, equation, cross multiplication method, variables, quantity, substitute.

Answer:

4, 4452 scooters were sold

Step-by-step explanation:

Add the number of scooters sold in the previous 3 years.

725 + 679 + 696 = 2100

If In year 4, the store sold 112% of the total number of scooters sold during the previous three years combined, then we have:

2100 (1 + 1.12) = 4452

In Year 4, 4452 scooters were sold

Answer:

2352

Step-by-step explanation:

We are given that:

The number of scooters sold at a store during a three-year period

Year 1-725

Year 2-679

Year 3-696

In year 4,the store sold 112% of the total number of scooters sold during the previous three years combined.

Total scooters sold in previous three years=725+679+696

                                                                       = 2100

the number of scooters sold in year 4=112% of 2100

                                                               = [tex]\dfrac{112}{100}\times 2100[/tex]

                                                               =2352

Answer:

2

Step-by-step explanation:

8% is the same thing as multiplying something by 0.08.

25 x 0.08 = 2

Hope this helps :)

Answer:

8 is 2 percent of 25

Step-by-step explanation:

we can prove this as

=[tex]\frac{25}{100}[/tex]×8

=[tex]\frac{2oo}{100}[/tex]

=2

hence proved

The question is about solving the equation 4/3x+2=5x and identifying the corresponding graph. There appears to be a mix-up with unrelated information about proportions and graphing the equation y = 9 + 3x. The correct approach to solve the equation was described, but without graphical context, a specific graph cannot be identified.

The student asked which graph represents the solution for the equation 4/3x+2=5x. To solve this equation algebraically, we need to isolate the variable x. However, it seems that the information provided in the question does not directly relate to the solution of the given equation. Instead, there is a mix-up with an example of setting up a proportion, finding the slope of a line, and graphing the equation y = 9 + 3x.

For the equation 4/3x+2=5x, we would solve for x by first combining like terms or using inverse operations to get all x terms on one side and constants on the other. The correct approach would be to subtract 4/3x from both sides of the equation and subtract 2 from both sides, which simplifies to 0 = 5x - 4/3x - 2, giving us a single-variable linear equation that can be solved for x. However, without a clear graph or further context, this explanation cannot indicate which specific graph represents the solution to the original equation.

Answer:

8

Step-by-step explanation:

Read a little bit at a time.

Equation

Solution

Answer:

x=8

Step-by-step explanation:

4x+30 =70-x

Add x to each side

4x+x+30 =70-x+x

4x+x +30 =70

5x +30 = 70

Subtract 30 from each side

5x +30 -30 =70-30

5x = 40

Divide each side by 5

5x/5 = 40/5

x = 8

Answer:

This winds up being a 4% decrease.

Step-by-step explanation:

For an example, we will take an object that costs $100. If we mark it up by 60%, the new cost will be $160.

Now we want to take the cost of $160, and subtract 40%. First we need to find 40% of $160. We can do that by multiplying them together.

$160*40% = $64

Now we will subtract that from the cost of the item after the increase.

$160 - $64 = $96.

Even though the percent decrease was less, the order in which we do it causes this to be an overall decrease

The net effect of a 60 percent increase followed by a 40 percent decrease is a 4 percent decrease from the initial value.

The student is asking about the net effect of a 60 percent increase followed by a 40 percent decrease on a value. To solve this, one would typically express these percentages as factors; an increase of 60% would be represented as multiplying by 1.60 (100% original + 60% increase), and a decrease of 40% as multiplying by 0.60 (100% original - 40% decrease). If we call the initial value 'x', then after the increase, the value becomes 1.60x.

Then, applying the 40 percent decrease, we multiply by 0.60: 1.60x * 0.60 = 0.96x. Thus, the net effect of a 60 percent increase followed by a 40 percent decrease results in a 4 percent decrease of the initial value.

Answer:

Either 130 or 131 would be acceptable.

Step-by-step explanation:

When we estimate, we do not use exact values.

66.17 is close to 66

44.98 is close to 45

20.15 is close to 20

Add the estimates together: 66+ 45+ 20 = 131

We could also estimate 66.17 to 65 which would give us an estimate of 130

Answer: The total cost would be $ 131.

Step-by-step explanation:

Since we have given that

Amount for bought clothes = $ 66.17

Amount for books = $ 44.98

Amount for meal = $ 20.15

First we add all the amount to get the total cost.

Total cost is given by

$ 66.17 + $ 44.98 + $ 20.15 = $ 131.30 So, the good estimate of $ 131.30 is

$ 130.

Hence, the total cost would be $ 131.

Answer:

I would say associative property of multiplcation

Step-by-step explanation:

Your just switching the parenthesis to a different set of numbers you arent changing the order of the numbers and they have multiplying signs inside the parenthesis

Answer:

10 2/15 hours

Step-by-step explanation:

If we have a candle that is 11 2/5 inches tall

It burns 1 1/8 inches per hour.  We need to divide to see how long the candle will last

11 2/5 ÷ 1 1/8

I will convert the mixed numbers to improper fractions

11 2/5 = (5*11+2)/5 = 57/5

1 1/8 = (8*1+1)/8 = 9/8

57/5 ÷ 9/8

Copy dot flip

57/5 * 8/9

456/45

Now we change it back to a mixed number

45 goes into 456  10 times with 6 left over

10 6/45

This simplifies to 10 2/15

Answer:

21 girls

Step-by-step explanation:

Boys: girls

5:7

Multiply each number by 3

15: 21

There will be 15 boys and 21 girls

Answer:

81/16

Step-by-step explanation:

We have [(3^2 * 5^0) / 4]^2

= [ ( 9 * 1) / 4]^2

= (9/4)^2

= 81/16

Answer:

81/16

Step-by-step explanation:

3 to the power of 2 multiplied by 5 to the power of 0 whole over 4, the whole squared

[(3^2 * 5^0)/4]^2

According to PEMDAS, we work the inside parentheses first

3^2 * 5^0

3^2 = 9

5^0 = 1

9*1 =9

[(3^2 * 5^0)/4]^2

[9/4]^2

I will break this up into parts

9^2/4^2

9^2 =81

4^2 =16

81/16

Answer:

well what you do is times it

Step-by-step explanation:

so 14 x 12 and its 168 and 168 x 5 is 840 so its 840 c

can i get brainlyest

your welcome

These lines are perpendicular since their slopes are negative reciprocals. If you multiply a slope times its negative reciprocal, the result is always -1. ... Let's prove that perpendicular lines have negative reciprocal slopes, AND that negative reciprocal slopes imply perpendicular lines.

Answer:

1.12

Step-by-step explanation:

1.6 x 0.7

Answer:

=0

Step-by-step explanation:

Answer:

Step-by-step explanation:

1

Answer:

54.56

Step-by-step explanation:

The number after the point is not 5 or higher

Answer:

The fraction 22/7 is sometimes used as an estimate of is "pi."

Yes, it is a repeating fraction.

Step-by-step explanation:

22 divided by 7 is 3.142857142857143... going on into infinity. It is an estimate of pi, and does repeat every 6 decimal numbers.

Answer:

Federico

Step-by-step explanation:

11/10 is a mixed number, that means it is larger than the whole, which in this case is the money for the school trip, since the numerator is larger than the denominator, and Luis and Marisa both have numerators smaller than the denominator, that makes 11/10 the largest.

Answer:Federico

Step-by-step explanation:

Answer: My expected value would be of $10

Step-by-step explanation The way you can determine the expected value is by thinking about the lowest price and how much you paid. I think I would get $10 because They wouldn't make it very easy to get a big prize like $100. Pleas mark this brainliest and I will be glad to help you anytime.

The expected value of buying a ticket in this raffle is -$0.348, meaning you're expected to lose about 35 cents per ticket. Thus, in terms of expected financial return, this game is not favorable to play.

The expected value, in probability theory, is the average result of an experiment repeated many times. In this case, to calculate the expected value of the game, we will multiply each outcome by the probability of that outcome, and then sum these values. The outcomes here are $100, $50, $10, and -$1 (the cost of the ticket), and the respective probabilities are 1/250, 1/250, 1/250, and 247/250 (the probability of not winning anything).

Here's the calculation: ($100 x (1/250)) + ($50 x (1/250)) + ($10 x (1/250)) + (-$1 x 247/250) = $0.40 + $0.20 + $0.04 - $0.988 = -$0.348. That indicates that, on average, for each ticket you buy, you're expected to lose about $0.35. Therefore, in terms of pure expected value, it's not a favorable game to play. However, decisions to participate in games like this often consider more than just expected financial return, such as the thrill of participation or the opportunity to support a charitable cause.

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Answer:

96 sqrt(210)

Step-by-step explanation:

6√3 • 8√14 • √10 • √2

We multiply what is outside the square roots with what is outside the square roots  and what is inside the square roots with what is inside the square roots

6*8 = 48

3*14*10*2 = 840

6√3 • 8√14 • √10 • √2

48 sqrt(840)

48 sqrt( 4*210)

sqrt(a*b) = sqrt(a) sqrt(b)

48 sqrt(4) sqrt(210)

48 *2 sqrt(210)

96 sqrt(210)

210 is 3*7 *5*2  which are all primes, so we cannot simplify the sqrt (210)

Answer:

7.5 litres.

Step-by-step explanation:

Volume of water lost in 1 month = 2.5 * 10^-4 * 3 * 10^5

= 2.5 * 3 * 10^(-4+5)

= 7.5 * 10^1

= 7.5 litres (answer)

Answer:

The answer is 7.5 times 10 to the power of 1

Step-by-step explanation:

Answer:

Her guinea pig is 210 millimeters longer than her fish

Step-by-step explanation:

1.Convert centimeters into millimeters

2.Subtract 40 from 250

3.You have the answer!

I hope this was helpful

Answer:

The length of the ladder is 14.5 ft

Step-by-step explanation:

For a right triangle

sinx = opposite / hypotenuse

Since we know the angle and the opposite side, we can calculate the hypotenuse

sin 64 = 13/ hypotenuse

Multiply each side by the hypotenuse

hypotenuse * sin 64 = 13

Divide by sin 64

hypotenuse = 13/sin 64

hypotenuse=14.4638

Rounding to the nearest tenth

14.5

The problem asks for the length of the ladder that forms a triangle with the house. The length of the ladder, which represents the hypotenuse of the triangle, can be calculated using the sine function and the given angle of 64 degrees and the opposite side of 13 feet. The calculated length of the ladder, rounded to the nearest tenth of a foot, is 14.2 feet.

The subject of this question falls under the branch of Mathematics, specifically trigonometry. The problem statement defines a right-angled triangle with a 64-degree angle, a known opposite side (13 ft), and we are asked to find the hypotenuse or the length of the ladder.

To find the length of the ladder, we will use the sine function which in a right triangle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. In mathematical form, Sin(θ) = Opposite / Hypotenuse. To find the hypotenuse, we will rearrange the formula to Hypotenuse = Opposite / Sin(θ).

Substituting the known values: Hypotenuse = 13 ft / Sin(64 degrees). Therefore, the length of the ladder is approximately 14.2 feet rounding to the nearest tenth.

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Answer:

1/6

Step-by-step explanation:

[tex]\frac{1}{3} * \frac{50}{100}  = \frac{50}{300} = \frac{1}{6}[/tex]