1 pts
Write the equation of a line through (2, -3), perpendicular to y= xy=
O y=-3x-3
Oy=3x-3
O y=-3x+3
O y=3x+3

Answer:

A.) 96 ft/sec

Step-by-step explanation:

to find the average speed of the watermelon's fall in 6 seconds, substitute 6 as t in the equation and then divide by 6: \(y = \frac{16(6)^{2} }{6} = 96 ft/sec\)

At a price of $3, the total revenue will be the greatest, and the company will sell 3 units at that price.

To find the total revenue at each price, we can multiply the price by the corresponding quantity.

Price        Quantity          Total Revenue

$6                0                      $0

$5                 1                       $5

$4                 2                       $8

$3                 3                        $9

$2                 4                         $8

$1                  5                          $5

To find the price at which total revenue is the greatest, we look for the highest value in the Total Revenue column.

In this case, the highest total revenue is $9, which occurs when the price is $3.

At a price of $3, the company will sell 3 units (as indicated in the Quantity column).

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Answer:

2.8 Miles

Step-by-step explanation:

You subract 5.8 from 8.6 to get the answer.

Using translation concepts, the image of the kite after the reflection over the line y = x is given on the graph at the end of the answer.

Transformations in the graph of a function involve operations such as multiplication/division or sum/subtraction, either in the domain of the function, involving values of x, or the range, involving values of y.

Examples of transformations are as follows:

The rule for a reflection over the line y = x is given by:

(x,y) -> (y,x).

The vertices of the kite are given as follows:

S(-6,5), R(-5,6), P(-5,4), Q(1,5).

After the reflection, the vertices of the image are given as follows:

S'(5,-6), R'(6,-5), P'(4,-5), Q'(5,1).

The image of the kite after the reflection over the line y = x is given on the graph at the end of the answer, with the vertices labeled.

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Hope it helps :)

\(x + 4y = 9 \\

-x - 2y = 3 \\ eliminate \: one \: variable \: by \\ adding \: the \: equations \\ 2y = 12 \\ divide \: both \: sides \\ y = 6 \\ substitute \: the \: value \: of \: y \\ \: into \: equation \: ...2 \\ - x - 2(6) = 3 \\ solve \: the \: equation \\ - x - 12 = 3 \\ - x = 3 + 12 \\ - x = 15 \\ x = - 15 \\ SOLUTION \\ x = - 15 \\ y = 6 \\ Hope \: it \: helps :)\)

Here using the correct order of operations that is PEMDAS, we get the value to be 13.

PEDMAS can be summed up as a mathematical acronym that lists the various arithmetic operations in order of greatest to least practical use.

The letters stand for:

P stands for parentheses.

Exponents are shown as E.

D stands for division.

The letter M stands for multiplication.

A stand for addition.

S stands for subtraction.

Now in the given question,

15 - (4-3)2

First the parentheses

15 - (1)2

Next is exponents.

15 - 2

At last, after subtracting, we get:

13

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The bench costs $375, and the garden table costs $295. Together, they amount to $670, with the table being $80 cheaper than the bench.

Let the cost of the bench be x. Then the cost of the garden table is x-80. The sum of the costs of both items is $670. So we have the equation: x + (x-80) = $670.

Simplifying this, we get 2x - 80 = $670  + 80 2x = $750  x = $375. So the cost of the bench is $375. The garden table costs $375 - $80 = $295. A garden table and a bench cost $670 combined.

The garden table costs $80 less than the bench. To find the cost of the bench, we can use algebraic equations. Let the cost of the bench be x. Then, the cost of the garden table is x - 80.

The sum of both costs is $670. Using this information, we can form an equation: x + (x - 80) = $670. Simplifying, we get 2x - 80 = $670 + 80. Solving for x, we get x = $375.

Therefore, the cost of the bench is $375, and the cost of the garden table is $295.

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Answer:7

Step-by-step explanation:

This question is on the ukmt junior maths challenge which I'm doing now, out of the options given I got 7, because 2+4+6+5+(5×20)+(7×7)= 166, (then dividing that by the number of numbers to get the mean) so 166÷31= 5.354.....

Also the 3 has a recurring symbol above it

The 7 is times seven so uh yeah<3

The smallest possible value of 'q' is 7 and this can be determined by using the hit and trial method and mean formula.

Given :

The following steps can be used in order to determine the smallest possible value of q:

Step 1 - The formula of the mean can be used in order to determine the smallest possible value of q.

Step 2 - The mean of all the numbers is given by:

\(\rm \dfrac{2+4+6+5+5p+7q}{6+p+q}=5.3\)

\(\rm \dfrac{21 + 5p + 7 q}{6+p+q} = 5.3\)

Step 3 - So, by the hit and trial method, the value of q can be determined.

Therefore, the value of 'q' is 7.

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Step-by-step explanation:

To eliminate x in the system of equations:

1. Multiply Equation 1 by 9 and multiply Equation 2 by -4, this gives:

Equation 1: 36x -54y = 90

Equation 2: -36x - 8y = -28

2. Add the two equations together to eliminate x:

(36x - 54y) + (-36x - 8y) = 90 - 28

Simplifying, we get:

-62y = 62

3. Solve for y:

y = -1

4. Substitute y = -1 into one of the original equations, say Equation 1:

4x - 6(-1) = 10

Simplifying, we get:

4x + 6 = 10

5. Solve for x:

4x = 4

x = 1

Therefore, the solution to the system of equations is x = 1 and y = -1. We can check that these values are correct by substituting them back into the original equations and verifying that they satisfy both equations.

Answer:

x = 56.31%

Step-by-step explanation:

to find x, use \(tan^{-1}\)

\(tan^{-1}\) x = \(\frac{opposite}{adjacent}\)

\(tan^{-1}\) x = \(\frac{15}{10}\)

\(tan^{-1}\) x = 1.5

x = 56.3099

56.3099 = 56.31

The probability that you win is 6%, and the two choices are dependent events option (B) is correct.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

It is given that:

A standard deck of playing cards contains 52 total cards, 13 of which are "spades".

The probability of the first draw:

Probability = favorable outcomes/total outcomes

First draw: 1/4

For the second draw:

Second draw = 12/51

The probability that you win = (1/4)(12/51) = 3/51

In percent:

= (3/51)x100

= 5.88 = 6%

Thus, the probability that you win is 6%, and the two choices are dependent on events option (B) is correct.

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Answer:

3. complementary 4&5. neither 6. supplementary

Step-by-step explanation:

comp angles add up to 90⁰

supp angles add up to 180⁰

The given system of equations has no solution.

Given that a system of equations, 12x + 36y = −3 and −12x − 36y = 0, we need to solve it,

We know for a system of equations =

a₁x + b₁y = c₁ and a₂x + b₂y = c₂

If a₁ / a₂ = b₁ / b₂ = c₁ / c₂ then the system has infinite solutions.

If a₁ / a₂ = b₁ / b₂ ≠ c₁ / c₂ then the system has no solutions.

If a₁ / a₂ ≠ b₁ / b₂ then the system has a unique solution.

comparing the coefficients given,

-12/12 = -1

-36/36 = -1

-3/0 = -3

We get here the condition of a₁ / a₂ ≠ b₁ / b₂, which means that the system has no solution.

Hence the given system of equations has no solution.

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The area inside the polar curve R = 2cos(3θ) for three full rotations is 6π.

The polar curve R = 2cos(3θ) is symmetric about the x-axis, with three petals that extend from θ = 0 to θ = π/3, π to 4π/3, and 5π/3 to 2π. To find the area inside the curve, we need to integrate the expression for the area element in polar coordinates over the desired region:

dA = (1/2) \(R^{2}\) dθ

The limits of integration for θ are from α = -6π to β = 6π, since we want to find the total area inside the curve for three full rotations. Thus, the integral for the area is:

A = ∫(β=6π, α=-6π) (1/2) \(R^{2}\)dθ

= ∫(β=6π, α=-6π) (1/2) (2cos(3θ))^2 dθ

= 2∫(β=6π/3, α=-6π/3) cos^2(3θ) d(3θ) (using the identity cos^2(3θ) = (1 +    cos(6θ))/2)

= ∫(β=6π/3, α=-6π/3) (1/2 + (1/2)cos(6θ)) d(3θ)

= (1/2)θ + (1/12)sin(6θ) ∣(β=6π/3, α=-6π/3)

= (1/2)(6π - (-6π)) + (1/12)(sin(36π) - sin(-36π))

= 6π

Correct Question :

Find The Area Inside R=2cos(3θ) (Tip: Use Α=−6π And Β=6π )

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The range of data set 1 is 4

The range of data set 2 is 4.

A line plot is a graph that is made up of a number line and check marks above the number line. The check mark above the number represents the frequency of the number in the data set. For example, if the number 3 on the number line has 2 checkmarks above it, it means 3 has a frequency of 2.

The range is the difference between the highest number in a dataset and the smallest number in the dataset. Range is a measure of variation.

Range = highest number - lowest number

The range of data set 1 = 7 - 3 =  4

The range of data set 2 : 7 - 3 =  4

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Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

When you want to find out what the slope is, you have to remember what the formula is first....

\(m=\frac{y}{x} =\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

so in this case -3 would be the \(y_{2}\) because it's the y in the ordered pair and it's the second one. Then one of the 5's would be \(x_{2}\) and 9 would be \(y_{1}\) and then the other 5 would be \(x_{1}\).

now if we plug it in

\(\frac{-3-9}{5-5} =\frac{-12}{0}\)

now we can tell that we can't divide by zero so the slope would be unidentified and that's it.

The BEST answer from the choices provided is Option (A) -2.

The simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).

To simplify the expression √([2m5z6]/[xy]), we can break it down step by step:

Simplify the numerator:

√(2m5z6) = √(2) * √(m) * √(5) * √(z) * √(6)

= √2m√5z√6

Simplify the denominator:

√(xy) = √(x) * √(y)

Combine the numerator and denominator:

√([2m5z6]/[xy]) = (√2m√5z√6) / (√x√y)

Thus, the simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).

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Answer:

yes u can but i dont know how to show u becuase i cant move them round

Step-by-step explanation:

The equation of the line in fully simplified slope intercept form is y = -5x + 8.

From the graph:

Take any two points:

suppose (1,3) and (2,-2)

slope m = y2 - y1 / x2 - x1

= -2 - 3 / 2 - 1

= -5/1

= -5

substitute m and (1,3) in y = mx + c

3 = -5*1 + c

3 = -5 + c

c = 3+5

c = 8

y = mx+c

y = -5x + 8.

Therefore the equation of the line in fully simplified slope intercept form is y = -5x + 8.

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Answer:

7, 2, -3, -8

Step-by-step explanation:

y = -5x + 2  Substitute in -1 for x

y = -5(-1) + 2

y = 5 + 2

y = 7

y = -5x + 2  Substitute in 0 for x

y = -5(0) + 2

y = 0 + 2

y = 2

y = -5 + 2 substitutes in 1 for x

y = -5(1) + 2

y = -5 + 2

y = -3

y = -5x + 2  Substitute in 2 for x

y = -5(2) + 2

y = -10 + 2

y = -8

Helping in the name of Jesus.

Answer:

942 square millimeters.

Step-by-step explanation:

The formula for the surface area of a cylinder is:

S = 2πr^2 + 2πrh

where S is the surface area, r is the radius, and h is the height.

Substituting the given values, we get:

S = 2 x 3.14 x 10^2 + 2 x 3.14 x 10 x 5

S = 628 + 314

S = 942

Therefore, the surface area of the cylinder is 942 square millimeters.

\( = \: \: \: \sqrt[4]{ {x}^{3} + 15 \sqrt{x} + 75 \sqrt[4]{x} + 125 } \)

hope it helps

see the attachment

Answer:

x = 27 , ∠ EAF = 27°

Step-by-step explanation:

∠ GAF = 90° , then

∠ GAC + ∠ CAF = ∠ GAF , that is

x + 63 = 90 ( subtract 63 from both sides )

x = 27

∠ DAE = 90°

since CD is a straight angle of 180° , then

∠ CAE = 90° , so

∠ CAF + ∠ EAF = ∠ CAE , that is

63° + ∠ EAF = 90° ( subtract 63° from both sides )

∠ EAF = 27°

Answer:

33.33%

Step-by-step explanation:

% increase : new value - old value/old value * 100%

                   1200 - 900/900 * 100% (to make it easier, cut the zeros the best                  

                   you can)

                   300/ 9

                   = 33.33 or 33 1/3%

Answer:

Belinda threw the ball 2.31 meters farther than Lorraine.

Step-by-step explanation:

To find how many meters farther Belinda threw the ball, we subtract Belinda's distance from Lorraine's distance.

We have that:

Lorraine threw a football 9.89 meters.

Belinda threw the football 12.20 meters.

12.20 - 9.89 = 2.31

Belinda threw the ball 2.31 meters farther than Lorraine.

\(\quad \huge \quad \quad \boxed{ \tt \:Answer }\)

\(\qquad \tt \rightarrow \: f(0) = -2\)

____________________________________

\( \large \tt Solution \: : \)

\(\qquad \tt \rightarrow \: 2 {x}^{2} - 3y = 6\)

\(\qquad \tt \rightarrow \: 3y + 6 = 2 {x}^{2} \)

\(\qquad \tt \rightarrow \: 3y = 2 {x}^{2} - 6\)

\(\qquad \tt \rightarrow \: y = \cfrac{2 {x}^{2} - 6 }{3} \)

\(\qquad \tt \rightarrow \: y = \cfrac{2 {}^{} }{3} {x}^{2} - 2\)

[ here, y can be replaced with f(x) because y is a function of x ]

\(\qquad \tt \rightarrow \: f(x) = \cfrac{2 {}^{} }{3} {x}^{2} - 2\)

\( \large\textsf{Find f(0):} \)

\(\qquad \tt \rightarrow \: f(0) = \cfrac{2 {}^{} }{3} {(0)}^{2} - 2\)

\(\qquad \tt \rightarrow \: f(0) = 0 - 2\)

\(\qquad \tt \rightarrow \: f(0) = - 2\)

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

below

Step-by-step explanation:

This is isosceles because you have TWO equal sides

Equilateral has THREE equal sides

Answer: no

Step-by-step explanation: 2 is not less than 1

Answer:

No because if you plug in f with 2 it is saying 2 is less than 1 which is not true so it would be

No