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:

Answer: 1st 3rd and 5th trust me

A) 4.17 is equivalent to 4.17 x 100

C) The product has a positive exponent.

E) The E in the product is the indicator that the solution is in scientific notation.

Given that,

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Answer: (-12,-6)

Step-by-step explanation:

If we already have two points of the line, we can find its slope ([tex]m[/tex]), its intersection with the y-axis ([tex]b[/tex]), hence its equation:

Point 1: [tex](x_{1},y_{1})=(3,0)[/tex]

Point 2: [tex](x_{2},y_{2})=(-2,-2)[/tex]

Slope equation:

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{-2-0}{-2-3}[/tex]

[tex]m=\frac{2}{5}[/tex] This is the slope of the line

Now, the equation of the line is:

[tex]y=mx+b[/tex]

We already know the slope, now we have to find [tex]b[/tex] with any of the given points. Let's choose Point 1: [tex](x_{1},y_{1})=(3,0)[/tex]

[tex]0=\frac{2}{5}(3)+b[/tex]

Isolating [tex]b[/tex]:

[tex]b=-\frac{6}{5}[/tex]

Then, the equation of the line is:

[tex]y=\frac{2}{5} x-\frac{6}{5}[/tex]

With this equation we can find which point is a solution. Let's begin with the first point (-12,-6):

[tex]-6=\frac{2}{5} (-12)-\frac{6}{5}[/tex]

[tex]-6=-\frac{24}{5} -\frac{6}{5}[/tex]

[tex]-6=-6[/tex] Since both sides of the equation are equal, (-12,-6) is the point that fulfills the solution of the equation.

Answer:

the answer would be 90

Step-by-step explanation:

first you multiply 8 until you get 48, which would be 6 times, then do the same thing for 7 (7x6), which would be 42 and just add it all together and you get 90

The chess player played a total of 56 games.

To find the total number of games the chess player played, we need to determine the ratio of wins and losses. The ratio of wins to losses is given as 8:7. This means for every 8 wins, there are 7 losses. Since the player won a total of 48 games, we can set up the following proportion:

8/7 = 48/x

Cross-multiplying, we get 8x = 7 * 48. Solving for x, we find that the player played a total of 56 games.

Answer:

[tex]20.83[/tex]

Step-by-step explanation:

[tex]12 \times x = 250 \\ 12x = 250 \\ \frac{12x}{12} = \frac{250}{12} \\ x = 20.83[/tex]

hope this helps

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good luck! have a nice day!

The equivalent value of the equation is A = 12 x 20.833 = 250

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the first number be p

Let the second number be q

Now , A = pq

when the value of p = 12

And , when the value of q

On simplifying the equation , we get

250 = 12 x q

So , the left hand side of the equation is equated to the right hand side by the value of 12 x q

250 = 12 x q

Divide by 12 on both sides , we get

q = 250/12

On simplifying , we get

q = 20.833

Therefore , the value of q = 20.833

Hence , the expression is A = 12 x 20.833 = 250

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Answer:

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

Answer:

4725

Step-by-step explanation:

25-10=15

15^2=225

10*45*10=4500

225+4500=4725

Answer:

6 complex numbers

There are 6 solutions to the polynomial over the complex number system.

The given equation is 3[tex]x^{6}[/tex]-x³-4x²+5x+52=0.

The Fundamental Theorem of Algebra states that every polynomial of degree one or greater has at least one root in the complex number system. A further theorem, in some cases referred to as the Linear Factorization Theorem, states that a polynomial of degree n has exactly n linear factors, and each can be written in the form (x - c), where c is a root. These n complex roots are counted with multiplicity.

In polynomials, the number of roots or highest power is equal to the degree of the polynomial.

Here, 3[tex]x^{6}[/tex]-x³-4x²+5x+52=0.

We can see that the polynomial is a sixth-degree polynomial.

Therefore, there are 6 solutions to the polynomial over the complex number system.

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I'm not sure, but I know that it is longer than 5

Answer:

5.5-6ish sorry its hard to tell

Happy Holidays!

Answer:

$ 9.99  almost  $ 10 she would save every week.

Step-by-step explanation:

Weekly Salary = $ 628

Tax deduction= $149.8

Superannuation Fund = 4.5 % of $ 628= $28.26

Mortgage = 8 % of 628= $ 50.24

Income after deductions = $ 628- $ 149.8 - $ 28.26- $ 50.24=  $ 399.7

10 % of $ 399.7 = $ 39.97 almost $ 40

In one week  she would save $39.97/4= $ 9.99 = $ 10

Final answer:

It will take Alex 4 minutes to type 176 words at his current typing speed of 44 words per minute.

Explanation:

The question asks how long it would take for Alex to type 176 words if he can type 44 words in one minute. To find the answer, we utilize a simple rate calculation by dividing the total number of words (176) by Alex's typing speed (44 words per minute).

176 words ÷ 44 words/minute = 4 minutes

Therefore, it will take Alex exactly 4 minutes to type 176 words at the rate of 44 words per minute.

Answer:

50.4

Step-by-step explanation:

First, add the values. You will get 756. The you divide the sum by the number of data values, which is 15. You will end up with 50.4

Answer: 50.4

Step-by-step explanation: The mean of a data set is equal to the sum of the set of numbers divided by how many number are in the set.

So to find the mean of the data set shown here, let's begin by adding the numbers.

12 + 16 + 22+ 23 + 34 + 44 + 46 + 47 + 48 + 64 + 67 + 73 + 83 + 88 + 89 = 756

756 will be divided by how many numbers are in the set which is 15 which gives us 50.4.

50.4 is already rounded to the nearest tenth.

Answer:

x^2-9x+4

Step-by-step explanation:

(-5x^2-9x-6)+(6x^2+10)

-5x^2+6x^2-9x-6+10

x^2-9x+4

Answer:

x^2 - 9x + 4.

Step-by-step explanation:

(-5x²-9x-6)+(6x²+10)​

= -5x² - 9x - 6 + 6x² + 10 ​

=  -5x² + 6x² - 9x  - 6  + 10 ​

= x^2 - 9x + 4.

Answer:

i think 10.30 according to my calculation

Answer:

10.30

Step-by-step explanation:

Answer:

No idea what the other person who answered was trying to say since it has to be 1 answer but i think its multiplication because to get 1/5 to be 1 so x you multiply by 5 and it matches because to get 6 to be 30 you multiply by 5 and to get 5 to be 25 you multiply by 5

ANSWER A

Step-by-step explanation:

Answer:

Step-by-step explanation:

5y + 6y + 7y = 18y......any numbers that add(or subtract) to equal 18, stick them before the y....

or it could be : 10y + 10y - 2y = 18y or 5y + 10y + 3y or 30y - 20y + 8y....I could go on forever...lol

Answer:

1.  [tex]1200 \ kg/m^3[/tex]

2.

a)

35 cm = 0.35 meters

11 dm = 1.1 meters

15 mm = 0.015 meters

b)

Volume = 0.005775 cubic meters

Mass = 15.5925 kilograms

Step-by-step explanation:

1.

We know

Density = Mass/Volume

Given

Mass = 90 kg

Volume = 0.075 cubic meters

The SI unit for density is kilograms per cubic meters. Our dimensions are just that, so we just need to plug in the numbers into the formula and get our answer. Shown below:

Density = [tex]\frac{90}{0.075}=1200 \ kg/m^3[/tex]

The Density of asphalt block = [tex]1200 \ kg/m^3[/tex]

2.

a)

We need to express 35cm, 11dm, and 15mm in meters

We know

100 cm = 1 meters, so

35 cm = 35/100 = 0.35 meters

We know 1 dm = 0.1 meters, so

11 dm * 0.1 = 1.1 meters

We know, 1mm = 0.001 meters, so

15 mm * 0.001 = 0.015 meters

b)

Volume of the Slab is length * width * height, in meters, that would be:

Volume = 0.35 * 1.1 * 0.015 = 0.005775 cubic meters

THe mass would be found by the formula:

Density = Mass/Volume

2700 = Mass/0.005775

Mass = 0.005775 * 2700 =  15.5925 kilograms

Answer:

Step-by-step explanation:

[tex]x+5+2x=x+15\qquad\text{combine like terms}\\\\(x+2x)+5=x+15\\\\3x+5=x+15\qquad\text{subtract 5 from both sides}\\\\3x+5-5=x+15-5\\\\3x=x+10\qquad\text{subtract}\ x\ \text{from both sides}\\\\3x-x=x-x+10\\\\2x=10\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{10}{2}\\\\x=5[/tex]

Answer:

g(f(x)) = -x - 18

Step-by-step explanation:

2x - 6( (x + 6) / (2) )

2x - 3( x + 6)

2x - 3x - 18

-x - 18

Answer:

AAS I just answered this question and I got it right.

Final answer:

Given W=N, S=T, and WA=NO, no congruence theorems (SSS, SAS, ASA, AAS) demonstrate that triangles WAS and NOT are congruent, so the triangles are not congruent.

Explanation:

The student is asking which postulate or theorem supports the conclusion that triangle WAS is not congruent to triangle NOT. Given that W = N, S = T, and WA = NO, we can determine that the two triangles are not congruent. The four options provided are abbreviations for congruence theorems in geometry: Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), and Angle-Angle-Side (AAS).

However, none of these congruence theorems apply here because those would be used to prove congruence, not the lack thereof. In this case, if we look at the information given, we see that we have two pairs of sides and one pair of angles that are congruent. But the postulated congruent angles, A in triangle WAS and O in triangle NOT, are not included between the sides of the triangles that are known to be congruent. Therefore, none of the listed congruence postulates or theorems (SSS, SAS, ASA, AAS) can be used to conclude that the triangles are congruent. As a result, it can be concluded that the triangles are not congruent without needing to invoke a specific congruence theorem.

Answer:

8 Liters of 20% acid and 7 Liters of 50% acid

Step-by-step explanation:

Let we mix "x" liters of 20% acid, and

"y" liters of 50% acid

Total is 15 liters, so we can write:

x + y = 15

or x = 15 - y

Then,

We mix x liters of 20% (20/100=0.2) and y liters of 50% (50/100=0.5) acid solution to make 15 liters of 34% (34/100=0.34) solution, we can write:

0.2x + 0.5y = 0.34(15)

This becomes:

[tex]0.2x + 0.5y = 5.1[/tex]

We replace x with what we got in 1st equation and solve for y:

[tex]0.2x + 0.5y = 5.1\\0.2(15-y) + 0.5y = 5.1\\3-0.2y+0.5y=5.1\\0.3y=5.1-3\\0.3y=2.1\\y=\frac{2.1}{0.3}\\y=7[/tex]

We know x = 15 - y, so

x = 15 - 7

x = 8

So, we use 8 Liters of 20% acid and 7 Liters of 50% acid

Final answer:

To find out how many liters of each acid solution (20% and 50%) a chemist needs to mix to get 15 liters of a 34% acid solution, a system of equations using the volumes and concentrations is set up and solved to determine the exact volumes needed.

Explanation:

To solve the problem of mixing a 20% acid solution with a 50% acid solution to get 15 liters of a 34% acid solution, we can set up a system of equations based on the volumes and concentrations. Let's define x as the number of liters of the 20% solution and y as the number of liters of the 50% solution. The first equation is based on the total volume: x + y = 15. The second equation is based on the total amount of pure acid: 0.20x + 0.50y = 0.34 × 15. Solving this system gives us the volumes needed for each solution.

Steps to Solve the System of Equations:

Write the two equations:
x + y = 15 (the volume equation)
0.20x + 0.50y = 5.1 (the acid equation, since 0.34 × 15 = 5.1)

Solve one of the equations for x or y. For instance:
x = 15 - y

Substitute into the second equation and solve for y:
0.20(15 - y) + 0.50y = 5.1

Solve for y, which represents the volume of the 50% solution:

Substitute the value of y back into any of the original equations to solve for x, which represents the volume of the 20% solution:

By following these steps, the chemist can determine precisely how many liters of each acid solution must be used to obtain the final mixture.

3 - 0.3y = 5.1

y = 7 liters

x = 8 liters

Answer:

She gets a raise of 91 cents per hour. So that means each hour, she makes $13.91

Kelli's raise per hour is $13.91.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Kelli makes $13 an hour working at the bakery,

and her boss gave her a 7% raise.

That means,

Kelli's raise per hour = 13 + 13 x 7/100

= $13.91

Therefore, $13.91 raise per hour.

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Answer:

2.75 or 2 3/4

Step-by-step explanation:

Divide the total cost by the price of each ribbon.

$1.54 ÷ $0.56/yard = 2.75 yards

If the answer needs to be in mixed fractional form, convert 0.75 to a fraction.

3/4 = 0.75

The fraction form of 2.75 is 2 3/4.

Therefore Olivia bought 2 3/4 yards of ribbon.

A customer will pay $225.5 for one rug.

Step-by-step explanation:

Given,

Purchase price of rug = $82.00

Mark up = 150%

Amount of mark up = 150% of purchase price

Amount of mark up = [tex]\frac{150}{100}*82[/tex]

Amount of mark up = 1.5*82 = $123

Price of rug after mark up = Purchase price + Mark up

Price of rug after mark up = 82+123 = $205

Sales tax = 10%

Amount of sales tax = 10% of price after markup

Amount of sales tax = [tex]\frac{10}{100}*205=\$20.5[/tex]

Selling price = Price after markup + Amount of sales tax

Selling price = 205+20.5 = $225.5

A customer will pay $225.5 for one rug.

Keywords: percentage, markup

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Answer:

Step-by-step explanation:

P(x)=  x³ - x² - 18

Q(x) = P(2x-1)

       = (2x-1)³ - (2x-1)² -18

       = (2x)³ - 3*(2x)² * 1 + 3*2x* 1² - 1³ - [ (2x)² - 2*2x*1 + 1 ] - 18

=8x³ - 12x² + 6x - 1 - [4x² - 4x +1 ] - 18

= 8x³ - 12x² + 6x - 1 - 4x² + 4x - 1  - 18

= 8x³ - 16x² + 10x - 20

Hint : (a-b)³ = a³-3a²b+3ab²-b³

(a-b)² = a² -2ab + b²

The farmer's hog pen, with length of 12 meters and a width of 11 meters, is 32 square meters larger than the goat pen which has a length and width of 10 meters.

First, let's establish the dimensions of both pens. For the goat pen, given that the farmer used 20 meters of fencing and one side was provided by the barn, the fence was distributed between two sides. If we assume these two sides to be equal (maximizing the area), each side would be 10 meters long.

On the other hand, the hog pen had 24 meters of fence distributed between two sides, with the length being 2 meters more than the goat pen and the width being 1 meter more than the goat pen. So, the length of the hog pen is 12 meters and width is 11 meters.

To find the difference in areas, we subtract the area of the goat pen from the hog pen. The area of a rectangle is calculated by multiplying the length by the width. For the goat pen, the area is 10m * 10m = 100m² and for the hog pen, the area is 12m * 11m = 132m². Thus, the area of the hog pen is 32m² larger than the goat pen.

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Answer:

Step-by-step explanation:

No, unless the function decides to follow a different pattern. See more explanation below.

Step-by-step explanation:

He is wrong, the table doesn't tell us what happens at x=6.

It does tell us the following:

1) When x=-4, f(x)=6.

2) When x=-2, f(x)=3.

3) When x=0, f(x)=-1.

4) When x=2, f(x)=-4.

So maybe he got it the x and f(x) value switched in his brain.

Because according to 1) x=-4 when f(x)=6.

If the points keep having x increase while y decreases, then every x>2 will have a y less than -4 correspond to it.

Rob's determination that the function X = 6 when f(x) = -4 appears to be correct based on the provided data.

An equation is a mathematical statement that shows that two expressions are equal.

It typically includes variables, constants, and mathematical operations and is used to solve for unknown values.

Rob seems to be correct. If you look at the table of values:

x | f(x)

-4 | 6

-2 | 3

0 | -1

2 | -4

When x = 6,

we find that the function f(x) = -4 (as indicated in the last row of the table).

So, Rob's determination that X = 6 when f(x) = -4 appears to be correct based on the provided data.

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Answer:

s=2

Step-by-step explanation:

-5s-(-6s)+8=3+7

-5s+6s+8=10

s+8=10

s=10-8

s=2

The word problem would be translated as s + 8 = 10.

The solution is: s = 2

First, let's translate the statement given to form an algebraic equation, then solve for the unknown variable.

Therefore, the equation would be:

s + 8 = 10

s + 8 - 8 = 10 - 8

s = 2

Therefore, the word problem would be translated as s + 8 = 10.

The solution is: s = 2

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Answer:

2700 degrees.

Step-by-step explanation:

The external angles add up to 360 degrees

So 1 external angle in a regular 17-gon = 360/17

= 21.176 degrees

The internal angle = 180 - 21.176

= 158.824 degrees

Sum of internal angles = 158.824 * 17

= 2700 degrees.

Answer:

Step-by-step explanation:

Every closed curve called a polygon can be separated into a specific number of triangles.  Then, because the sum of the interior angles of a triangle is 180, you take the number of triangles and multiply by 180 to get the sum of the interior angles of the n-gon.  To find the number of triangles that exist within an n-gon, subtract 2 from the number of sides.  If our figure is a 17-sided polygon, then the number of triangles within it is 17 - 2 = 15.  15 triangles, each with a sum of 180 for its angles.  15 * 180 = 2700.

Each central angle is 360 divided by 17 to get 21°10'35"

Each interior angle is 2700 divided by 17 to get 158°49'24"