The variables x and y vary inversely with a constant variation of 6. Find y when x=12.

Answer: [tex]y-\frac{1}{2}=-(x+\frac{1}{2})[/tex]

Step-by-step explanation:

The point-slope form of the equation of the line is:

[tex]y-y_1=m(x-x_1)[/tex]

Where "m" is the slope of the line and [tex](x_1,y_1)[/tex] is a point of the line.

You know the value of the slope and you also know a point of the line, then you need to substitute values into [tex]y-y_1=m(x-x_1)[/tex].

Therefore, you get that the equation of this line in  point-slope form is:

[tex]y-\frac{1}{2}=-1(x-(-\frac{1}{2})\\\\y-\frac{1}{2}=-(x+\frac{1}{2})[/tex]

Answer:

y = -x

Step-by-step explanation:

Given in the question,

co-ordinate(-1/2 , 1/2)

gradient of the line = -1

Standard equation form of a straight line

here y1 = 1/2

        x1 = -1/2

        m = -1

Plug values in the equation

y - 1/2 = -1(x + 1/2)

y -1/2 = -x - 1/2

y = -x

It’ll be (5,4) because it’s on the same Y line (aka 4) just like (1,2) and (5,2).

The coordinates of the fourth vertex of the rectangle are (5, 4).

A rectangle is a closed two-dimensional figure with four sides. The opposite sides of a rectangle are equal and parallel to each other and all the angles of a rectangle are equal to 90°.

Given that, three vertices of a rectangle are located at (1,4), (1,2), and (5,2).

The intersection point of diagonals of rectangle is midpoint of each diagonal.

Let the fourth coordinate be (x, y). By the above property we get

Now, the midpoint of (1, 4) and (5, 2) is

[(1+5)/2, (4+2)/2] =(3, 3)

Thus, (3, 3) =[(x+1)/2, (y+2)/2]

3=(x+1)/2, 3=(y+2)/2

6=x+1, 6=y+2

x=5, y=4

Therefore, the coordinates of the fourth vertex of the rectangle are (5, 4).

Learn more about a rectangle here:

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Answer:

The root of the polynomial is 3

Step-by-step explanation:

To find the root of the polynomial x(x-2)(x+3)=18

We can use a graphing utility and the system of equations.

We can have the equations;

y = x(x-2)(x+3) ......(i)

Therefore, from the initial equation;

y = 18 ..................... (ii)

We can then plot the graph using the equations, and the x-coordinate of the point of intersection will be the root of the equation.

From the graph, the x-coordinate is 3, since the intersection point is (3,18).

Therefore; the root of the equation is 3.

Answer:

70 points

Step-by-step explanation:

Let n represent Noah's score, m as Maya's score, and c as Claire's score.

n=20

m=30

c=?

Let's try make an equation for this problem. The mean score for the three of them is 40, so the following equation is possible:

n+m+c/3=40

Now replace the variable with their values and continue to simplify.

20+30+c/3=40

Multiply both sides by 3.

20+30+c=120

Add 20 and 30 together.

50+c=120

Subtract 50 from 120 to find c.

c=70

Claire's score is 70 points.

Final answer:

To find Claire's score, calculate the total points based on the mean score and then subtract the scores of Noah and Maya. This calculation reveals that Claire's score was 70 points.

Explanation:

The question asks for the score of Claire based on the mean score of Noah, Maya, and Claire combined. Noah scored 20 points, Maya scored 30 points, and the mean score for all three players was 40 points.

To find Claire's score, we first calculate the total points scored by all three. The mean score is the total points divided by the number of scores, which in this case is 3. Therefore, we multiply the mean score (40 points) by 3 to get the total points.

Mean score × number of players = Total points

40 × 3 = 120 points

Next, we subtract Noah's and Maya's scores from the total to find Claire's score.

Total points - Noah's score - Maya's score = Claire's score

120 points - 20 points - 30 points = 70 points

Therefore, Claire's score was 70 points.

Answer:

Step-by-step explanation:

Some foundation pieces:

Floor is 30 ft^2

tiles are 3w

Equation:

30=(3w)*10

3=3w

1=w

Now that you know that w has to 1 you can write the formula 30=(3w)×10

Answer:

it's A&B

Step-by-step explanation:

Answer:

[tex]\large \boxed{\mathrm{\bold{A.} } \ \frac{2}{x^4-y^4} \cdot \frac{1}{x^4 +y^4}} \\\\\\ \large \boxed{\mathrm{\bold{B.} } \ \frac{2}{(x^4)^2 -(y^4)^2 } }[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{2}{x^8-y^8 }[/tex]

Factor the denominator.

[tex]\displaystyle \frac{2}{(x^4)^2 -(y^4)^2 }[/tex]

[tex]\displaystyle \frac{2}{(x^4-y^4)^2 }[/tex]

[tex]\displaystyle \frac{2}{(x^4-y^4)(x^4 +y^4) }[/tex]

Split the fraction into two fractions.

[tex]\displaystyle \frac{2}{x^4-y^4} \cdot \frac{1}{x^4 +y^4}[/tex]

Answer:

The correct answer is option C.  490 units ²

Step-by-step explanation:

Area of cuboid = 2(lb + bh + lh)

From the figure we can see that a rectangular prism.

To find the surface area of prism

Here l = 14 units

b = 7 units and h = 7 units

Surface area = 2((14 * 7) + (7 * 7) + (14 * 7))

= 490 units ²

Answer:

490 units squared

Step-by-step explanation:

Answer:

Option B

Step-by-step explanation:

Step-by-step explanation:

We have the function [tex]g(x)=ax^2 +d[/tex]  then, by definition:

If  [tex]0 <a <1[/tex] then the graph is compressed vertically by a factor a.

If  [tex]|a| > 1[/tex] then the graph is stretched vertically by a factor a

If [tex]a <0[/tex]  then the graph is reflected on the x axis.

If [tex]d> 0[/tex] the graph moves vertically upwards d units.

If [tex]d <0[/tex] the graph moves vertically down  d units.

We know that:

[tex]a > 1[/tex] then the graph is stretched vertically by a factor a

and

[tex]d <0[/tex] the graph moves vertically down  d units

The searched graph is stretched vertically and its vertex is displaced downwards

The answer is option B

Answer:

$59.4

Step-by-step explanation:

The original price of the shoes was £60 before the 10% discount was applied, resulting in a final price of £54.

1. First, let's denote the original price of the shoes as [tex]\( x \)[/tex] pounds.

2. Since Nathalie bought the shoes during the sale, she received a 10% discount.

3. Therefore, she paid 90% of the original price after the discount. This can be represented as [tex]\( 0.90x \)[/tex].

4. According to the given information, Nathalie paid £54 for the shoes. So, we can set up the equation:

[tex]\[ 0.90x = 54 \][/tex]

5. To find the original price [tex](\( x \))[/tex], we need to isolate it by dividing both sides of the equation by 0.90:

[tex]\[ x = \frac{54}{0.90} \][/tex]

6. Solving the equation gives us:

[tex]\[ x = 60 \][/tex]

7. Hence, the original price of the shoes was £60 before the 10% discount was applied.

The complete question is here:

In a sale, normal prices are reduced by 10% Nathalie bought a pair of shoes in the sale for £54. What was the original price of the shoes?

Answer:

[tex]\$412.64[/tex]

Step-by-step explanation:

we know that

The formula to calculate continuously compounded interest is equal to

[tex]A=P(e)^{rt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

[tex]t=9\ years\\ P=\$315\\ r=0.03[/tex]  

substitute in the formula above  

[tex]A=\$315(e)^{0.03*9}=\$412.64[/tex]

Answer: $412.64

Step-by-step explanation: you’re welcome :)

Answer:

Step-by-step explanation:

According to southeastern.edu,

The first statement is true for the sample "those surveyed" the population but not necessarily the entire population. Statistic.

The second statement implies that the soccer team is the population. All members of the population are surveyed. Parameter.

The third statement states that a sample of 100 of all swimming teams are surveyed. Statistic.

The fourth statement implies that the population is all members of the golf team, and that all members of the population are surveyed. Parameter.

Answer:

[tex]\frac{2c}{3x^2c}+ \frac{36x^3c}{3x^2c} +\frac{24x^2}{3x^2c} [\tex]

Step-by-step explanation:

We need to find sum of 2 / 3x^2 +12x and 8 / c

So, solving:

[tex](\frac{2}{3x^2} + 12 x ) +\frac{8}{c}[/tex]

Taking LCM of 3x^2 and 1 i.e. 3x^2

[tex]=(\frac{2 + 12 x(3x^2)}{3x^2} ) +\frac{8}{c}\\=(\frac{2 + 36x^3}{3x^2} ) +\frac{8}{c}\\=\frac{2 + 36x^3}{3x^2} +\frac{8}{c}\\LCM \,\, 36x^2 c\\=\frac{(2 + 36x^3)c + 8(3x^2)}{3x^2c}\\=\frac{2c + 36x^3c + 24x^2}{3x^2c}\\= \frac{2c}{3x^2c}+ \frac{36x^3c}{3x^2c} +\frac{24x^2}{3x^2c}[/tex]

Row A:   x = 3

y = 2x - 3

y = 2(3) - 3 = 3      This is correct

Row B: x = 5

y = 2x - 3

y = 2(5) - 3 = 7        This is correct

Row C: x = 7

y = 2x - 3

y = 2(7) - 3 = 11      this is correct

Row D: x = 10

y = 2x - 3

y = 2(10) - 3 = 17  THIS IS INCORRECT, SO ROW D

Answer:

Road D

Step-by-step explanation:

In the commutative property, order does not matter for addition and multiplication. However, this is not true when it comes to subtraction and division problems, where order does matter.

The commutative property states that:

a + b = b + a (addition)

a × b = b × a (multiplication)

However, this does not apply to:

a - b ≠ b - a (subtraction)

a ÷ b ≠ b ÷ a (division)

In subtraction and division, the order of the operands matters, and changing the order can result in different values.

Answer:

[tex]\dfrac{9}{64}[/tex]

Step-by-step explanation:

There are 12 face cards in a deck of standard playing cards and 20 even numbered cards, in total 32 cards.

1. The probabilty that the first drawn card is face card is

[tex]p_1=\dfrac{12}{32}=\dfrac{3}{8}.[/tex]

2. The probabilty that the second drawn card is an even numbered card (even numbered cards are 6, 8, 10 - 12 in total, odd numbered cards are 7, 9 - 8 in total) is

[tex]p_2=\dfrac{12}{32}=\dfrac{3}{8}.[/tex]

3. The probability that the first drawn card is a face card and the second drawn card is an even numbered card is

[tex]p_1\cdot p_2=\dfrac{3}{8}\cdot \dfrac{3}{8}=\dfrac{9}{64}.[/tex]

In matrix from, the system is

[tex]\dfrac{\mathrm d}{\mathrm dt}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}3&-1&-1\\1&1&-1\\1&-1&1\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}[/tex]

The coefficient matrix has eigenvalues [tex]\lambda[/tex] such that

[tex]\begin{vmatrix}3-\lambda&-1&-1\\1&1-\lambda&-1\\1&-1&1-\lambda\end{vmatrix}=-(\lambda-2)^2(\lambda-1)=0\implies\lambda=2_{(2)},\lambda=1[/tex]

(where the subscript denotes multiplicity of the eigenvalue).

[tex]\lambda=2[/tex]:

[tex]\begin{bmatrix}1&-1&-1\\1&-1&-1\\1&-1&-1\end{bmatrix}\vec\eta_1=\vec0[/tex]

[tex]\implies\eta_{1,1}-\eta_{1,2}-\eta_{1,3}=0\implies\eta_{1,1}=\eta_{1,2}+\eta_{1,3}[/tex]

By picking [tex]\eta_{1,1}=1[/tex], we can then set [tex]\eta_{1,2}=1[/tex] and [tex]\eta_{1,3}=0[/tex], and vice versa, to find two corresponding eigenvectors,

[tex]\vec\eta_1=\begin{bmatrix}1\\1\\0\end{bmatrix},\vec\eta_2=\begin{bmatrix}1\\0\\1\end{bmatrix}[/tex]

[tex]\lambda=1[/tex]:

[tex]\begin{bmatrix}2&-1&-1\\1&0&-1\\1&-1&0\end{bmatrix}\vec\eta_3=\vec0[/tex]

[tex]\implies2\eta_{3,1}-\eta_{3,2}-\eta_{3,3}=0\implies2\eta_{3,1}=\eta_{3,2}+\eta_{3,3}[/tex]

We obtain [tex]\vec\eta_3[/tex] independent of [tex]\vec\eta_1,\vec\eta_2[/tex] by picking [tex]\eta_{3,2}=\eta_{3,3}=1[/tex], so that the third corresponding eigenvector is

[tex]\vec\eta_3=\begin{bmatrix}1\\1\\1\end{bmatrix}[/tex]

Then the general solution to this system is

[tex]\begin{bmatrix}x\\y\\z\end{bmatrix}=C_1e^{2t}\vec\eta_1+C_2te^{2t}\vec\eta_2+C_3e^t\vec\eta_3[/tex]

[tex]\begin{cases}x=C_1e^{2t}+C_2te^{2t}+C_3e^t\\y=C_1e^{2t}+C_3e^t\\z=C_2te^{2t}+C_3e^t\end{cases}[/tex]

To find the general solution of the given system of differential equations, we can solve each equation separately and obtain the general solution for x(t), y(t), and z(t).

The given system of differential equations is:

dx/dt = 3x - y - z

dy/dt = x + y - z

dz/dt = x - y + z

To find the general solution, we can treat each equation separately.

For dx/dt = 3x - y - z, we can rewrite it as:

dx / (3x - y - z) = dt

Integrating both sides gives us:

ln|3x - y - z| = t + C1, where C1 is the constant of integration.

Exponentiating both sides gives us:

|3x - y - z| = e^(t+C1)

Since |3x - y - z| is always positive, we can remove the absolute value signs:

3x - y - z = e^(t+C1)

Now, we can solve the remaining two equations in a similar manner to find y(t) and z(t).

By solving the three equations, we can obtain the general solution for x(t), y(t), and z(t).

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(I think) you just divide the length of the bead string the the inches of the beads

(Which equals 4.4 so when simplified is 4)

Answer:

1/8.

Step-by-step explanation:

The probability of of a head (and a tail) in one toss of a coin  being obtained is 1/2.

Each toss is independent of the others so we multiply the probabilities.

So Prob(Head - tail - head) = 1/2*1/2*1/2 = 1/8.

Answer:

1/8.

Step-by-step explanation:

Answer:

The possible shapes of the playground should be: parallelogram, rectangle, and kite because all of these shapes have 2 pairs of equal sides, and also the question didn't specify if the sides are opposite to each other or not so kite is also a possible option.

The quadrilaterals that describe the shape of a playground with these dimensions will be Rectangle.

A  rectangle is a quadrilateral with four sides and the two opposite sides are equal and parallel the two sides are also perpendicular to each other.

It is given in the question that a playground has two sides that each measure 70 feet and two sides that each measure 50 feet.

So it is clear that the two sides are equal and parallel to the shape of the playground will be rectangular.

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5 out of 20 people said that they like the new packaging of Toasty Toasts.

Answer:

No

Step-by-step explanation:

If its a square garden then that means all 4 sides are 12 meters so 12 times 4 equals 48. This meaning you need 48 meters of wire to wire the entire fence garden.

Answer:

no

Step-by-step explanation:

if the garden is to be fence on all 4 sides then the total length of wire needed is 48 meters as 12*4=48 so since 19<48 it will not be enough  

Answer:

50x.2 is the correct expression. :)

Step-by-step explanation:

50x.2 =10

So you would get a $10 discount off of a $50 video game.

Hope this helps! If you don't mind, please mark as brainliest! Thx :)

Answer:

0.80($50)

Step-by-step explanation:

1.00 times the $50 cost is the initial price of the video.

(1.00 - 0.20) times $50 is the discounted price.

0.80($50) is the desired expression.

Next time, please be sure to share the answer choices.  Thanks.

ANSWER

D.

[tex] {x}^{6} - x + \sqrt{6} [/tex]

EXPLANATION

A trinomial is a simplified polynomial with three terms.

The first option is not a polynomial because of the presence of √x.

The second option is not a trinomial because it has only two terms.

The third option is not a polynomial because of the presence of

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

The last option:

[tex] {x}^{6} - x + \sqrt{6} [/tex]

This is trinomial because it has three terms and cannot be simplified further.

There is not fractional exponent.

Answer:

x^8 - x + √6

Step-by-step explanation:

The fourth expression is a trinomial (a polynomial with three terms).  The term √6 is acceptable because it's a constant; it's the coefficient of x^0.

Answer:

Option B. Quadratic

Step-by-step explanation:

In a regression model, the value of [tex]r ^ 2[/tex] tells us how accurately the model fits the data.

That closer the value of [tex]r ^ 2[/tex] of 1 is,  better is the model.

This can be used to compare what type of model is most convenient to use in some cases.

In this problem the attached table shows a comparison of the value of [tex]r ^ 2[/tex] for 3 models

Linear

Quadratic

Exponential

Note that the value of [tex]r ^ 2[/tex] that is closest to 1 is that which corresponds to the quadratic model.

[tex]r ^ 2 = 0.89[/tex]

Therefore the function that best fits the points is the quadratic

Answer:

108

Step-by-step explanation:

36÷4= 9

9 is the unit rate

5×9=45

Natasha has 45 sweets

3×9= 27

Richard has 27 sweets

36+ 45+ 27= 108

All together they have 108 sweets

In total, there are 108 sweets. This answer is derived by finding the value of one part of the ratio and then multiplying this by the sum of all parts of the ratio.

The question is about the distribution of sweets among Sarah, Natasha and Richard in the ratio 4:5:3. You have been given that Sarah, represented by the first term of the ratio, gets 36 sweets. To find how many sweets there are altogether, we first need to determine the value of one part of the ratio.

In this case, if 4 parts are equivalent to 36 sweets, then one part is equivalent to 36 divided by 4 which equals 9 sweets.

Now, to find the total sweets, we need to sum all parts of the ratio which is 4 parts for Sarah, 5 parts for Natasha and 3 parts for Richard. Total parts = 4 + 5 + 3 = 12. This total is then multiplied by the value of one part of the ratio. Here, total sweets = 12 parts * 9 sweets = 108 sweets.

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The sides of the box are 12in by 12in by 30in.

The interior diagonal =[12^2+12^2+30^2]0.5

=[144+144+900]^0.5

=1188^0.5

The final answer is 34.47in.

My deepest apology if this is not what you meant.

= 34.47in.

Answer:

34.47

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The graph of the parent function f(x)=x is the straight line that passes trough the origin and is the bisector of first and third coordinate quadrants (red line in attached diagram).

The graph of the function g(x)=1/3x-5 is the straight line that passes through the point (0,-5) and is less steep (because the slope 1/3 is less than the slope 1). This line is blue line in attached diagram.

So, correct option is option A

Answer:

t/8 + t/7 = 1

Step-by-step explanation:

Given in the question that,

time require for Jose to paint the house = 7 hours

time require for Brandon to paint the house = 8 hours

Suppose t means Full house painted.

7 hours----t

1 hour ---- t/7

8 hours----t

1 hour ---- t/8

t/8 + t/7 = 1 (in one hour)

(7t + 8t)/8(7) = 1

15t/56 = 1

15t = 56

t = 56/15

t = 3.73 hours

Answer:

4(a + b)^2

p = 6/5 or 1.2

Step-by-step explanation:

Question One

z = a^2 + b^2

y = ab

4z = 4*a^2 + 4*b^2

8y = 8*ab

=================

4z + 8y = 4a^2 + 8ab + 4b^2

4z + 8y = 4(a^2 + 2ab + b^2)

4z + 8y = 4(a + b)^2

Question Two

2(p + 1) + 8(p - 1) = 5p

2p + 2 + 8p - 8 = 5p

2p + 8p + 2 - 8 = 5p

10*p - 6 = 5p

10*p = 5p + 6

10p - 5p = 6

5p = 6

p = 6/5 or 1.2

Answer:

She started with 26 boxes.

Step-by-step explanation:

She started with x boxes. Then she bought 8 more boxes. Now she had x + 8 boxes. Then half the boxes were destroyed, so she has the other half of the boxes. Half of the boxes is (x + 8)/2. She has now 17 boxes, so (x + 8)/2 = 17.

(x + 8)/2 = 17

Multiply both sides by 2.

x + 8 = 34

Subtract 8 from both sides.

x = 26

She started with 26 boxes.