Describe how to graph the solution of
y ≤ −x2 + 2x.

see the attached figure to better understand the problem

we know that the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

Let

[tex]A(-3,3)\ B(3,4))\ C(3,-3)[/tex]  

Step 1

Find the distance AB

[tex]A(-3,3)\ B(3,4)[/tex]  

substitute in the formula

[tex]d=\sqrt{(4-3)^{2}+(3+3)^{2}}[/tex]

[tex]d=\sqrt{(1)^{2}+(6)^{2}}[/tex]

[tex]dAB=\sqrt{37}\ units[/tex]

Step 2

Find the distance BC

[tex]B(3,4))\ C(3,-3)[/tex]  

substitute in the formula

[tex]d=\sqrt{(-3-4)^{2}+(3-3)^{2}}[/tex]

[tex]d=\sqrt{(-7)^{2}+(0)^{2}}[/tex]

[tex]dBC=7\ units[/tex]

Step 3

Find the distance AC

[tex]A(-3,3)\ C(3,-3)[/tex]  

substitute in the formula

[tex]d=\sqrt{(-3-3)^{2}+(3+3)^{2}}[/tex]

[tex]d=\sqrt{(-6)^{2}+(6)^{2}}[/tex]

[tex]dAC=\sqrt{72}\ units[/tex]

Step 4

Find the perimeter of the triangle

we know that

the perimeter of the triangle is the sum of the length sides of the triangle

[tex]P=AB+BC+AC[/tex]

substitute the values

[tex]P=\sqrt{37}\ units+7\ units+\sqrt{72}\ units=21.6\ units[/tex]

therefore

the answer is

the perimeter of the triangle is [tex]21.6\ units[/tex]

Answer:

A is the mofluffin answer

Step-by-step explanation:

It increases the amount by 700,000

Answer: y = 3x - 2

Step-by-step explanation:

Equation of a straight line is

y=mx + c

m is the slope and c is the intercept

comparing it with the equation

y=3x - 2

m = slope =3

and c= intercept= -2

Answer:

Option b , c and d are the part of the expression .

Step-by-step explanation:

We are given that the number of pages she has left to read is 276 - 35d

d represents the number of days she has been reading.

276 denotes the total number of pages

35 pages denotes the number of pages read per day

35 d represents the number of pages she has read during d days

276 - 35d represents teh reamining pages

So, Option b , c and d are the part of the expression .

Answer:

Two times the difference of x and seven plus ten

Step-by-step explanation:

The measure of the vertex angle is 72 degrees

The sum of the interior angle of a triangle is 180 degrees. Of the base angles are equal hence;

54 + 54 + x = 180

where

x is the vertex angles

Simplify

108 + x = 180

x = 180 - 108

x = 72 degrees

Hence the measure of the vertex angle is 72 degrees

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To make m the subject of the equation x-2m=p, add 2m to both sides, subtract p, and divide by 2. The result is m as the subject of the equation, represented as the fraction (x - p)/2.

To solve the equation x-2m=p for m as the subject, we want to isolate m on one side of the equation. Here is the step-by-step process:

Now m is the subject of the equation, and it is represented as a fraction as requested.

28 chores he now has left to do.

An arithmetic intelligence operation minus simulates the process of deleting items from either a collection. To subtract is to take something or something from a particular group. The group's total number of items decreased and became lower when people eliminated it. The components of a subtraction issue are the issues dealing with, forces at play, and differences. The negative symbol, or, denotes subtraction.

35 tasks have been assigned to Tom for today.

He accomplished 7 of them this morning.

The remaining days are:

= 35-7

= 28 chores

The remaing chores are 28.

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The argument is valid by the law of detachment.

The statements that are true about the arguments in the question are;

1) Option C; Law of detachment

2) Option B; Law of detachment

1) We are given the premise that;

If two lines are parallel, then the lines do not intersect.

This premise is true because we know from parallel and perpendicular lines property that parallel lines never intersect each other.

With that premise, we are now given a conclusion that; Lines m and n do not intersect.

This kind of condition is known as law of detachment which states that;

If x is true, then y is also true.

Thus, Option C is correct

2) We are given the premise that;

If a quadrilateral is a square, then the quadrilateral has four right angles.

The given premise is true because from the definition of a square, all sides must be equal and all angles must be right angles.

We are now given the conclusion that;

Quadrilateral JKLM has four right angles.

This conclusion is valid because it follows the given premise.

Again like in 1 above, this follows the law of detachment.

Option B is correct

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Answer:

it's 9 grams for apex

Answer:

B

Step-by-step explanation:

edge

Option C is correct, y=4x-6 is the equation of the line that is parallel to the first line and passes through the point (1, –2)

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

A line passes through the origin and has a slope of 4

y=4x is the equation of the line.

We have to find the equation of the line that is parallel to the first line and passes through the point (1, –2)

Slope is 4 as it is parallel.

We have to find the y intercept

-2=4(1)+b

b=-6

So equation is y=4x-6

Hence, Option C is correct, y=4x-6 is the equation of the line that is parallel to the first line and passes through the point (1, –2)

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(1) the area of a rectangle with vertices at ​ (−6, 3) ​, ​ (−3, 6) ​ , (1, 2) , and (−2, −1)

To find area of rectangle we need to find the length and width

Length = distance between (−6, 3)  and (−2, −1)

Distance = [tex]\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]

=  [tex]\sqrt{(-2-(-6))^2 + (-1-3)^2}[/tex]

=  [tex]\sqrt{(4)^2 + (-4)^2}[/tex]=[tex]\sqrt{(16) + 16}[/tex] =[tex]\sqrt{32}[/tex]

width = Distance between (−6, 3) ​, ​ (−3, 6)

Distance = [tex]\sqrt{(-3-(-6))^2 + (6-3)^2}[/tex]

=[tex]\sqrt{3^2+3^2}= \sqrt{18}[/tex]

Area = Length * width = [tex]\sqrt{32} *\sqrt{18} = \sqrt{576}= 24[/tex]

(2)  the area of a triangle with vertices at (0, −2) , ​ (8, −2) ​ , and ​ (9, 1) ​

Area of triangle = [tex]\frac{1}{2} * base * height[/tex]

base  is the distance between (0,-2) and (8,-2)

Distance =  [tex]\sqrt{(8-0)^2 + (-2-(-2))^2}[/tex] = 8

To find out height we take two vertices (8,-2) and (9,1)

Height is the change in y values = 1- (-2) = 3

base = 8  and height = 3

So area of triangle = [tex]\frac{1}{2} * 8 * 3 = 12[/tex]

(3) the perimeter of a polygon with vertices at (−2, 1) , ​ (−2, 4) ​, (2, 7) , ​ (6, 4) ​, and (6, 1) ​

To find perimeter we add  the length of all the sides

Distance between (−2, 1)  and (−2, 4) = [tex]\sqrt{(-2+2)^2 + (4-1)^2}[/tex]= 3

Distance between(−2, 4) ​and (2, 7) = [tex]\sqrt{(2+2)^2 + (7-4)^2}[/tex]= 5

Distance between (2, 7)  and (6, 4) = [tex]\sqrt{(6 - 2)^2 + (4-7)^2}[/tex]= 5

Distance between (6, 4) ​ and (6, 1) ​= [tex]\sqrt{(6 - 6)^2 + (1-4)^2}[/tex]= 3

Distance between  (6, 1) and (−2, 1) ​= [tex]\sqrt{(-2-6)^2 + (1-1)^2}[/tex]= 8

Perimeter = 3 + 5 + 5 + 3 + 8 = 24

(4) four coordinates are (-7,-1) (-6,4) (3,-3) and (4,2)

Length = Distance between  (3,-3) and (4,2) ​= [tex]\sqrt{(4-3)^2 + (2+3)^2}[/tex]= [tex]\sqrt{26}[/tex]

Width = Distance between (-6,4) and (4,2) ​= [tex]\sqrt{(4+6)^2 + (2-4)^2}[/tex]= [tex]\sqrt{104}[/tex]

Perimeter = 2(lenght + width) = 2*( [tex]\sqrt{26}[/tex]+[tex]\sqrt{104}[/tex] )

= 30.6 units

The area of the rectangle is [tex]24\;square\;units[/tex].

1. According to the question, the vertices of the rectagle are at ​ [tex](-6, 3) ;(-3, 6) ;(1, 2)[/tex] , and [tex](-2, -1)[/tex].

The distance between two vertices on the coordinate plane is

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

So,

[tex]Length=D_1\\D_1=\sqrt{(6-3)^2+(-3+6)^2}\\D_1=\sqrt{9+9}\\D_1=3\sqrt 2 units[/tex]

Similarly,

[tex]Width=D_2\\D_2=\sqrt{(-2+6)^2+(-1-3)^2}\\D_2=\sqrt{16+16}\\D_2=16\sqrt 2\;units[/tex]

The area of the rectangle is equals to product of length and width of the rectabgle.

So,

[tex]Area=length\times width\\Area=3\sqrt{2}\times 4\sqrt{2}\\Area=24\;square\;units[/tex]

Hence, the area of the rectangle is [tex]24\;square\;units[/tex].

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A quotient is a quantity that is obtained by dividing two integers. The quotient of the division (2x²+3x-9) ÷ (x+3) is (2x - 3).

A quotient is a quantity that is obtained by dividing two integers. The quotient is a term that is widely used in mathematics to refer to the integer component of a division, as well as a fraction or a ratio.

The quotient of the division (2x²+3x-9) ÷ (x+3) can be found as shown below,

[tex]\dfrac{2x^2+3x-9}{(x+3)}\\\\=\dfrac{2x^2+6x - 3x -9}{(x+3)}\\\\=\dfrac{2x(x+3)-3(x+3)}{(x+3)}\\\\=\dfrac{(2x-3)(x+3)}{(x+3)}\\\\[/tex]

= (2x - 3)

Hence, The quotient of the division (2x²+3x-9) ÷ (x+3) is (2x - 3).

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An equation is formed when two equal expressions. The number of merchandise that you would have to purchase in a year to pay the same amount under both plans is 800.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given that you are choosing between two plans at a discount warehouse.

The cost for x number of merchandise under plan A, which offers an annual membership fee of $120 and you pay 80% of the manufacturer's. Therefore, the cost will be,

Cost = 120 + 0.8x

The cost for x number of merchandise under plan B, which offers an annual membership fee of $40 and you pay 90% of the manufacturer's recommended list price. Therefore, the cost will be,

Cost = 40 + 0.9x

Now, in order to find the number of merchandise that you would have to purchase in a year to pay the same amount under both plans, you need to equate the two equations together. Therefore,

Cost from Plan A = Cost from Plan B

120 + 0.8x = 40 + 0.9x

120 - 40 = 0.9x - 0.8x

80 = 0.1x

x = 80 / 0.1

x = 800

Hence, the number of merchandise that you would have to purchase in a year to pay the same amount under both plans is 800.

Further, the cost for each plan for 800 merchandise can be written as,

PlanA,

Cost = 120 + 0.8(800)

        = $760

Plan B,

Cost = 40 + 0.9(800)

        = $760

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The probability of rolling a 5 exactly three times in ten rolls of a number cube with six sides is 0.034.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.

The probability of rolling a 5 exactly three times in ten rolls of a number cube with six sides is determined in the following steps given below.

[tex]\rm Probability=\dfrac{10}{3}\times \left (\dfrac{1}{3} \right ) ^3\times \left (\dfrac{5}{6} \right ) ^7\\\\Probability= \dfrac{10}{3}\times \dfrac{1}{27} \times \dfrac{78125}{279936}\\\\Probability=0.034[/tex]

Hence, the probability of rolling a 5 exactly three times in ten rolls of a number cube with six sides is 0.034.

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The velocity function of an object moving along the {x} - axis would be -

v{t} = sin(t) + t³ + 2.

The acceleration at any instant of time is called instantaneous acceleration. Mathematically -

a = dv/dt

dv = a dt

∫dv = ∫a dt

Given is the acceleration function as -

a(t) = 3t² + cos(t)

We know that -

a = dv/dt

dv = a dt

∫dv = ∫a dt

v{t} = ∫{3t² + cos(t)} dt

v(t) = sin(t) + t³ + C

Now -

v(0) = 2

sin(0) + 0 + C = 2

C = 2

So, we can write the velocity function as -

v{t} = sin(t) + t³ + 2

Therefore, the velocity function of an object moving along the {x} - axis would be -

v{t} = sin(t) + t³ + 2.

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Final answer:

To find the remainder of 314162 divided by 7, we use modular arithmetic and find that the powers of 314 mod 7 repeat every 3 powers. Since 162 is a multiple of 3, 314162 mod 7 equals 1.

Explanation:

The question asks for the remainder when 314162 is divided by 7. To solve this problem, we can use a concept known as modular arithmetic, which deals with the remainder upon division. The key here is to find a pattern in the powers of 314 modulo 7, because large numbers can be cumbersome to work with directly. A helpful property is that (a×b) mod n = [(a mod n)×(b mod n)] mod n.

Let's consider the powers of 314 mod 7:

3141 mod 7 = 2

3142 mod 7 = (314 × 314) mod 7 = (2 × 2) mod 7 = 4

3143 mod 7 = (3142 × 314) mod 7 = (4 × 2) mod 7 = 1
Since we reached 1 again, the sequence will repeat every 3 powers. Now, 162 is divisible by 3 (162 = 3 × 54). Therefore, we can conclude that 314162 mod 7 will have the same remainder as 3143 mod 7, which is 1.

Answer:

0.34 miles per minute

Step-by-step explanation:

We have to convert 30 feet per second to miles per minute.

1 minute = 60 seconds

Therefore, in one minute = 60 × 30 = 1800 feet

5280 feet = 1 mile

180 feet =  [tex]\frac{1800}{5280}[/tex]

              = 0.3409 ≈ 0.34 mile

Therefore, 0.34 mile per minute.