If y varies directly with x and
y = 48 when x = 6, find y if x = 3.
First, find the direct variation equation.
y = [? ]x

Answer:

50

Step-by-step explanation:

I did this by inspection because {7, 24, 25} is a common trio, but ill just break it down for you.

Let the hypotenuse be x

Then [tex]14^2+48^2=50^2[/tex]

2500 = [tex]x^2[/tex]

x=50 or -50 (not applicable because you cannot have a negative length).

So the hypotenuse is 50.

Note: Common trios such as {3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {8, 15, 17} are worth remembering as you can often multiply them in such questions. Such as in this question, {7, 24, 25} times 2 is {14, 48, 50}.

Hope you have a nice day!

The first line is perpendicular, the second line is not perpendicular and not parallel , the third line is parallel to the above line and the forth line not parallel or perpendicular to the line.

The slope of the line  is been given as −3x+5y=−15

Then [tex]y= \frac{3}{5x} -3[/tex], hence the slope is [tex]\frac{3}{5}[/tex]

the slope is [tex]y= \frac{5}{-3x} +5\\\\\frac{5}{-3}[/tex]

this means that the line is perpendicular to the given line

[tex]y= \frac{3}{-5x} +15\\\\\frac{3}{-5}[/tex]

This means that the line is not perpendicular and not parallel

[tex]y= \frac{3}{5x} +15\\\\\frac{3}{5}[/tex]

This means that the line is parallel to the above line.

[tex]y= \frac{-3}{5x} +3\\\\\frac{-3}{5}[/tex]

This means that the line is not parallel or perpendicular to the line

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Answer:

b = 1

Step-by-step explanation:

since the point (1, 4 ) lies on the line then it satisfies the equation , that is

3(1) + b = 4

3 + b = 4 ( subtract 3 from both sides )

b = 1

The cost of electricity consumed by the TV per month is $4.968.

In the question, we are given that a TV set consumes 120W of electric power when switched on. It is kept on for a daily average of 6 hours per day. The number of days in the month is given to be 30 days. The cost per unit of electricity is 23 cents per kWh.

We are asked to find the cost of electricity the TV consumes in the month.

The daily energy consumed by the TV = Power*Daily time = 120*6 Wh = 720 Wh.

The monthly energy consumed by the TV = Daily energy*Number of days in the month = 720*30 Wh = 21600 Wh = 21600/1000 kWh = 21.6 kWh.

Hence, the total cost of electricity the TV consumes = Monthly energy*Per unit cost = 21.6*23 cents = 496.8 cents = $496.8/100 = $4.968.

Therefore, the cost of electricity consumed by the TV per month is $4.968.

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Answer:

AC = 9

Step-by-step explanation:

Set the negative value into absolute as length cannot be negative.

⇒ AC = AB + BC

⇒ AC = |-5| + 4

Formula: |-a| = a

⇒ AC = 5 + 4

⇒ AC = 9

Answer: I think the length is 9 units

Step-by-step explanation:

The type of data that would be best displayed in a box plot is the number of votes received by each of four candidate.

A box plot is used to study the distribution and level of a set of scores. The scores are distributed into 4 groups. Each group has a value of 25%

The whiskers represent the minimum and maximum scores.  On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.

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The solution to the inequality y > x + 3 and y < -x + 2 is the dark green region shown in the graph.

An equation is an expression that shows the relationship between two or more numbers and variables.

Inequality shows the non equal comparison of two or more numbers and variables.

Given the inequality y > x + 3 and y < -x + 2.

The solution to the inequality y > x + 3 and y < -x + 2 is the dark green region shown in the graph.

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Image vertices are  mathematically given as:

Generally, Multiplying the vertices by a scale factor of four is required in order for us to locate the picture vertices for dilation with center (0, 0).

In conclusion,, the image vertices are :

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Step-by-step explanation:

the ans is 19 a6 x5 y3

93-12-62×a2xy×a2x×a2x3y2

ans. 19 a6 x5 y3 add all the spuare and cube

Answer:

[tex]31a^2x(3y-4-2x^2y^2)[/tex]

Step-by-step explanation:

So the given equation is : 93a²xy - 124a²x - 62a²x³y². In this form you'll notice they all have a, and specifically a^2, and they also have x, but we only factor out x^1 since the first variable only has a degree of 1. So this gives us the equation: [tex]a^2x(93y-124-62x^2y^2)[/tex]. Now if we look at the coefficients you'll notice that they have a GCF of 31. So we can factor that out to. This gives you the equation: [tex]31a^2x(3y-4-2x^2y^2)[/tex] Which is your completely factored equation. You could also technically group 2xy^2 and 3y to get: [tex]31a^2x(y(3-2xy)-4)[/tex], although I'm not sure if that's considered "simplifying it"

I think the answer is D

☆...hope this helps...☆

_♡_mashi_♡_

The equation connecting L, m, A is L = [tex]\frac{1.8m}{A}[/tex]

Variation is a mathematical relationship that shows how a certain variable behaves when other variables depending on it increase or decrease.

The types of variation are: Direct, indirect, joint and partial.

Analysis:

L ∝ [tex]\frac{m}{A}[/tex]

introducing a constant K to replace the proportionality sign,

L = [tex]\frac{Km}{A}[/tex]

when L = 18, m = 0.4, A = 0.4

18 = [tex]\frac{K(4)}{0.4}[/tex]

4K = 0.4 x 18

k = 1.8

Therefore the equation connecting the three variables is,

L = [tex]\frac{1.8m}{A}[/tex]

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Answer:

1/18

Step-by-step explanation:

P(Orange AND Red)

= P(Orange socks)*P(Red shirt)

= 1/3*1/6

= 1/18

Probabilities that can be estimated from long-run relative frequencies of events are called objective probabilities.

In contrast to intuition or guessing, objective probability refers to the chances or odds that an event will occur based on the examination of certain measurements. Each metric is based on factual observation, a documented observation, or a long history of data collection.

Instead of being dependent on anecdotes, firsthand knowledge, or hunches, the objective probability is based on statistics, experiments, and mathematical measures. Using objective probability is crucial in the realm of finance to prevent making irrational investment decisions.

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Answer:

Width = 3y - 3

Step-by-step explanation:

P = 2l + 2w

12x - 4y - 4 = 2(6x - 5y + 1) + 2w

12x - 4y - 4 = (12x - 10y + 2) + 2w

6y - 6 = 2w

w = 3y - 3

Using the median concept, it is found that the interquartile range of Sara's daily miles is of 21 miles.

The ordered data-set is given as follows:

65, 72, 86, 88, 91, 93, 97

There are 7 elements, hence the median is the 4th element, of 88. Then:

Since the quartiles are the medians of each half, the have that:

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The probability shows that when one name is drawn from the jar, the country that has the best chance of having a name drawn is Great Britain.

It should be noted that Great Britain has won 6 golds in the 1500 meters Olympics and the next placed country is Kenya. In this case, the country that has the best chance of having a name drawn is Great Britain.

Note that New Zealand has 3 gold medals while Australia has 2 gold medals. Also, the Olympics has taken place 29 times.

The probability that the winners will be from either New Zealand or Australia will be:

= 3/29 + 2/29

= 5/29

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Answer

A. Great Britain

B. 3/29+2/29=5/29

please give me the brainliest.

The scatter plot is shown in the attached picture, and the line of best is also shown.

Scatter plots are graphs representing individual data points and are labeled with quantitative values on both the co-ordinate axes, meaning that there is only one projection on the x-axis and one on the y-axis for each point.

We have the data shown in the table.

We can plot the data on the coordinate plane such as:

(x, y) = (54, 92), (46, 80) and so on

We can find the equation of best fit:

[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2} \\\\\\\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]

y = mx + c

Thus, the scatter plot is shown in the attached picture, and the line of best is also shown.

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Answer:

Mean: 29.5;    Median: 26;    Modes: 25, 26

Step-by-step explanation:

Add 10+12+25+25+26+26+30+31+33+34+47+55 = 354

Then divide it by 12      354/12 = 29.5

Mode are numbers that appear most often which in this case are 2 numbers, 25 and 26.

Answer: a = 18

Step-by-step explanation:

The pythagorean theorem says that the sum of the square of the two legs of a triangle is equal to the square of the hypotenuse.

The two legs are 80 and a, and the hypotenuse is 82 which gives us

80² + a² = 82²

a² = 324

a = 18.

Answer:

18

Step-by-step explanation:

a² + b² = c²

a² + 80² = 82²

a² + 6400 = 6724

a² = 324

a = √324

a = 18

The product of the two factors (t - sa) (9t + 6sa) is 9t² - 3tsa - 6s²a²

The product of two factors of an expression results in a quadratic or polynomial expression depending on the degree to which their power is being raised.

From the information given, we have:

= (t - sa) (9t +6sa)

= 9t² + 6tsa - 9tsa - 6(sa)²

= 9t² - 3tsa - 6s²a²

Therefore, we can conclude that the product of the two factors (t - sa) (9t + 6sa) is 9t² - 3tsa - 6s²a².

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Answer:

a

Step-by-step explanation:

go it right on a mastery test

The vertex U' is located at (-4, -5)

The vertices are given as:

U = (-4, 5)

V = (-6, 2)

The rule of transformation is given as:

Reflection across the x-axis

This is represented as:

(x, y) => (x, -y)

So, we have:

U' = (-4, -5)

Hence, the vertex U' is located at (-4, -5)

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Complete question

Quadrilateral UVWX is reflected over the x-axis to form quadrilateral U′V′W′X′. If vertex U is located at (-4, 5) and vertex V is located at (-6, 2), then vertex U′ is located at

Answer:

50

Step-by-step explanation:

[tex]\sqrt{-64}[/tex] and [tex]\sqrt{-16}[/tex] can be expressed in complex form, with [tex]\sqrt{-1}[/tex] = i

[tex]\sqrt{-64}[/tex] = [tex]\sqrt{64(-1)}[/tex] = [tex]\sqrt{64}[/tex] × [tex]\sqrt{-1}[/tex] = 8i

[tex]\sqrt{-16}[/tex] = [tex]\sqrt{16(-1)}[/tex] = [tex]\sqrt{16}[/tex] × [tex]\sqrt{-1}[/tex] = 4i

the factors can then be expressed as

(6 + 8i)(3 - 4i) ← expand using FOIL

= 18 - 24i + 24i - 32i² [ i² = ([tex]\sqrt{-1}[/tex] )² = - 1 ]

= 18 - 24i + 24i + 32 ← collect like terms

= 18 + 32 + 0

= 50

Answer:

x = 3

Step-by-step explanation:

1) Divide both sides by -2.

[tex]6^x=\frac{-432}{-2}[/tex]

2) Two negatives make a positive.

[tex]6^x=\frac{432}{2}[/tex]

3) Simplify [tex]\frac{432}{2}[/tex] to 216.

[tex]6^x=216[/tex]

4) Convert both sides to the same base.

[tex]6^x=6^3[/tex]

5)  Cancel the base of 6 on both sides.

x = 3

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathbf{-2(6)^x = -432}[/tex]

[tex]\huge\textbf{DIVIDE -2 to BOTH SIDES:}[/tex]

[tex]\mathbf{\dfrac{-2(6^x)}{-2} = \dfrac{-432}{-2}}[/tex]

[tex]\huge\textbf{SIMPLIFY IT!}[/tex]

[tex]\mathbf{6^x = 216}[/tex]

[tex]\huge\textbf{Solve for the current exponent:}[/tex]

[tex]\mathbf{6^x = 216}[/tex]

[tex]\huge\textbf{Log them:}[/tex]

[tex]\mathbf{Log \ 6^x = log = 216}[/tex]

[tex]\huge\textbf{Take the log to both of the sides:}[/tex]

[tex]\mathbf{x \times log (6) = log(216)}[/tex]

[tex]\huge\textbf{Convert it:}[/tex]

[tex]\mathbf{x = \dfrac{log(216)}{log(6)}}[/tex]

[tex]\huge\textbf{SIMPLIFY IT!}[/tex]

[tex]\mathbf{x = 3}[/tex]

[tex]\huge\textbf{Answer:}[/tex]

[tex]\huge\boxed{\mathsf{x = 3}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The largest possible volume of the given box is; 96.28 ft³

Let b be the length and the width of the base (length and width are the same since the base is square).

Let h be the height of the box.

The surface area of the box is;

S = b² + 4bh

We are given S = 100 ft². Thus;

b² + 4bh = 100

h = (100 - b²)/4b

Volume of the box in terms of b will be;

V(b) = b²h = b² * (100 - b²)/4b

V(b) = 25b - b³/4

The volume is maximum when dV/db = 0. Thus;

dV/db = 25 - 3b²/4

25 - 3b²/4 = 0

√(100/3) = b

b = 5.77 ft

Thus;

h = (100 - (√(100/3)²)/4(5.77)

h = 2.8885 ft

Thus;

Largest volume = [√(100/3)]² * 2.8885

Largest Volume = 96.28 ft³

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Answer:

-84.

Step-by-step explanation:

n * -5 = 420

n = 420/ -5 = -84.

Answer:

- 84

Step-by-step explanation:

let the other integer be x , then

- 5 × x = 420

- 5x = 420 ( divide both sides by - 5 )

x = 420 ÷ - 5 = - 84

[0.3105, 0.3695] expect to buy a new car next year.

These are the answer choices -

A) [0.3074, 0.3726]

B) [0.3105, 0.3695]

C) [0.3140, 0.3660]

D) [0.3392, 0.3408]

It is given that a sample of 1,400 American households was asked if they planned to buy a new car next year. Of the respondents, 34% indicated they planned to buy a new car next year.

For large random samples, a confidence interval for a population proportion is given by

[tex]sample proportion[/tex] ± [tex]z * \frac{\sqrt{sample proportion (1 - sample proportion)} }{n}[/tex]

where z* is a multiplier number that comes from the normal curve and determines the level of confidence (see Table 9.1 for some common multiplier numbers).

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The transformations which map f(x) to g(x) according to the equation are; Translation of f(x) 2 units to the left and 3 units upwards.

The equation given in the task content is as follows;

It therefore follows that the transformations which would produce function g(x) from f(x) involves a 2 units translation to the left and a 3 units translation upward.

Remarks:

The complete question requires that the transformations from f(x) to g(x) be identified.

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x= 8 , -3

Given:

x² - 5x -24 =0

x² - 8x  + 3x -24=0

x(x-8) + 3(x- 8)=0

(x-8)(x+3)=0

x= 8 , -3

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