If semantics D=2x² X -
a trinomial in standard form.
Ox²-3x - 15
2
6x²-3x - 15
O3x²-3x + 15
O-2x² + x + 15
15find an expression that equals semantics-1D as

When the the light's angle is 20° from perpendicular to the wall, and the light is rotating at an angular speed of one rotation in 2 seconds the rate the light projected onto the wall is moving is approximately 60.48 feet/s

Angular speed, ω, is the angle, θ, in radians rotated by a rotating object per second. The unit of angular speed is radians per second, rad/s.

Mathematically;

[tex]\omega = \dfrac{\Delta \theta}{\Delta t}[/tex]

Where;

Δt = The time the object rotates through an angle of Δθ

The distance of the light from the wall, x = 17 feet

Time it takes the light to complete one rotation = 2 seconds

Angle the light makes with the perpendicular wall = 20°

[tex]tan(\theta) = \dfrac{y}{x}[/tex]

The distance the light has moved along the wall, y = x × tan(θ)

Therefore;

The y = 17 × tan(θ)

The angular velocity of the light, ω = θ/t

Therefore, θ = ω × t = ω·t

Which gives; y = 17 × tan(ω·t)

[tex]\omega = \dfrac{2\cdot \pi}{2}\ rad/s = \pi \ rad/s[/tex]

Therefore; x = 17 × tan(·t)

[tex]\dfrac{dy}{dt} = \dfrac{d}{dt} \left(17\times tan(\omega\cdot t)\right) = 17\cdot \omega\cdot sec^2(\omega \cdot t)[/tex]

ω = π rad/s (constant)

ω·t = θ

Therefore;

[tex]\dfrac{dy}{dt}= 17\cdot \omega\cdot sec^2(\theta)[/tex]

Rate the light is moving along the wall, dy/dt when θ = 20°, is therefore;

[tex]\dfrac{dy}{dt}= 17\times \pi\cdot sec^2(20^{\circ}) \approx 60.48[/tex]

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The circumference of the circle is 25.1 inches.

The length of the arc ACB is 4.2 inches.

The circumference of a circle is the perimeter of the circle.

Therefore,

circumference of a circle = 2πr

where

Hence,

circumference of a circle = 2 × 3.14 × 4

circumference of a circle = 8 × 3.14

circumference of a circle = 25.1 inches

The length of the arc ACB can be found as follows:

length of arc = ∅/ 360 × 2πr

length of the arc = 60 / 360 ×  2 × 3.14 × 4

length of the arc = 60 / 360 ×  25.12

length of the arc = 1507.2 / 360

length of the arc = 4.18666666667

length of the arc = 4.2 inches

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If P= (2, 7) and Q= (2, -3), then for triangle to be isosceles coordinate of R must be 2

Let coordinates

P = (2, 7) and Q = (2, -3)

PR = QR

(X-2)^2 +(Y-7)^2 = (X-2)^2 + {Y-(-3)}^2

(Y-7) = {Y - (-3)}^2. or y - 7 = ±(Y

or Y^2 - 14Y + 49 = Y^2 + 6Y + 9

20Y = 40

Y=2

coordinates of R if triangle PQR is isosceles ;

Hence any point R on the line Y = 2 will make PQR a isosceles triangle

with PR = QR.

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The percent that Desmond average speed increase is 25%.

From the information, with his old trainer, Desmond averaged a pace of 24 MPH and with his new trainer, he rode at an average speed of 30 MPH.

It should be noted that the percentage increase in speed will be:

= Change in speed / Initial speed × 100

= (30 - 24) / 24 × 100

= 6/24 × 100

= 25%

The percentage is 25%.

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The image of point (2,0) after the transformation involving the dilation and the rotation is given as follows:

(0, -1).

The first transformation applied to the point is a dilation, which multiplies the coordinates of the point by the scale factor.

The point has these following coordinates:

(2,0).

The scale factor of the dilation is:

k = 1/2 = 0.5.

Then each coordinate of the point is multiplied by 0.5, hence:

Hence the coordinates are:

(1,0).

The rule for a rotation of 270º clockwise around the origin is:

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

Then:

Thus the coordinates of the image are given as follows:

(0, -1).

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Answer: (f+g)(x) = 6x²- 4x + 6

Step-by-step explanation:

We add f(x) and g(x) together, (4x²-5x+8) + (2x²+x-2)

Add like terms together, (4x²+2x²) + (-5x+x) +(8-2)

We are left with (f+g)(x) = 6x²- 4x + 6

if we take 25 to be the 100%, what is 100 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 25 & 100\\ 100& x \end{array} \implies \cfrac{25}{100}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{1}{4}=\cfrac{100}{x}\implies x=400[/tex]

Answer:

25

Step-by-step explanation:

25/100=.25x100=25

Answer:

6 and - 18

Step-by-step explanation:

let the 2 integers be a and b , then

a + b = - 12 → (1)

[tex]\frac{a}{b}[/tex] = - 3 → (2)

multiply both sides by b ( b ≠ 0 )

a = - 3b

substitute a = - 3b into (1)

- 3b + b = - 12

- 2b = - 12 ( divide both sides by - 2 )

b = 6

substitute b = 6 into (1) and solve for a

a + 6 = - 12 ( subtract 6 from both sides )

a = - 18

the two integers are - 18 and 6

The solution to the inequality given as 2x+5y<1 has the coordinates of (-10, 4)

From the question, we have the following inequality that can be used in our computation:

2x+5y<1

Solving further, we need to collect the like terms

Since there are no like terms in the expression, it remains unchanged

So, the inequality becomes

2x + 5y < 1

Subtract 5y from both sides of the inequality

This gives

2x < 1 - 5y

Divide both sides by 2

The expression becomes

x < 1/2 - 5/2y

Evaluate

x < 0.5 - 2.5y

At this point, we assume any value for y and then solve for x

Assume that the value of y is 4

So, we have the following representation

x < 0.5 - 2.5 * 4

Evaluate the products

x < -9.5

This means that x is less than -9.5 when y is 4

-10 is less than -9.5

So, we have

x = -10 and y = 4

Express as ordered pairs (i.e. coordinates)

(x, y) = (-10, 4)

Hence, the coordinates of the solution is (-10, 4)

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The y-intercept of the graph as shown is 2.

The equation of a line can be represented as follows:

y = mx + b

where

The y-intercept is the point where the graph intersects the y-axis. In other words, it is the value of y when x = 0 .

Therefore, let's trace the value of y when x  = 0 on the graph.

Hence, when x = 0, y = 2

Therefore,

b =  y-intercept = 2

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Answer:b=2b

b=−2b

b=−3b

b=3b

Step-by-step explanation: because I tought myself i know

Answer:

A. REFLECTION

Please guys do some research i know you're not that stu p id-_-

The number of ways that there are to get dealt exactly a single pair is; 6,589,440 ways

The combination in probability selection is defined as a method where we count the number of ways a certain number of objects can be arranged in "n" different ways. If the number of different objects are "n", then it means that the number of ways that we can select "r" number of different objects is expressed as:

nCr = n!/(r!(n - r)!)

The total number of cards that we have in a deck of cards = 52.

There total number of different cards are 13 in number and this tells us that we can possibly have a pair of any one of the 13 cards. There are also 4 cards of the same rank and this means that the number of ways of selecting two cards of the same rank is; 4C2 = 6 ways

After selecting a card for the pair, we have 48 different cards as an option for the third card. Thereafter, we will have a total of 44 cards as an option for the fourth card and then 40 cards will be an option for the fifth card (due to the fact that none of the cards can be of same rank except for the pair of cards).

Therefore, the total number of ways that we can deal with exactly a single pair can be expressed as:

Number of ways = number of ways for the pair × number of ways for the third card × number of ways for the fourth card × number of ways for the fifth card

Plugging in the relevant values gives;

Number of ways = (13 × 6) × 48 × 44 × 40

= 6,589,440 ways

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The correct equation to representing the temperature y, in degrees Fahrenheit, at x hours after sunset will be;

⇒ y = - 4°x + 0°

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

At 2 hours before sunset, the temperature is 0°F.

And,  At 2 hours after sunset, the temperature is −4°F.

Now,

Let the temperature in degrees Fahrenheit = y

So, We can formulate;

⇒ y = - 4°x + 0°

Thus, The correct equation to representing the temperature y, in degrees Fahrenheit, at x hours after sunset will be;

⇒ y = - 4°x + 0°

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The value of WV is 9x - 10

A line segment can be defined as the part of a straight line which is bound by two distinct end points, and is known to be made up of every point on the line that between its endpoints.

From the information given, we can say that WY is a line with V as its midpoint with segments WV and VY.

We have;

This is represented as;

WV + VY = WY

Then;

WV = WY - VY

substitute the values

WV = 5x + 19 - (29 - 4x)

expand the bracket

WV = 5x + 19 - 29 + 4x

collect like terms

WV = 9x - 10

Hence, the value is  9x - 10

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Answer:

x+5

Step-by-step explanation:

there are no like terms

The measure of angle B is x, while the measure of angle A is 2·x. The 70° measure of angle C and the angle sum property of the interior angles of a triangle indicates that angle B is [tex]36.\overline 6^{\circ}[/tex] and angle A is [tex]73.\overline 3^{\circ}[/tex]

The interior angles of a triangle are the angles formed by the sides sides of the triangle.

The question can be solved by making use of the known properties of a triangle.

The angle sum property of the interior angles in a triangle gives;

The sum of the interior angles of a triangle is 180°

Therefore; x + 2·x + 70 = 180

3·x = 180° - 70° = 110°

[tex]x = \dfrac{110^{\circ}}{3} = 36\frac{2}{3} ^{\circ}[/tex]

The measure of angle A is 2·x

Which gives;

[tex]A = 2 \times 36\frac{2}{3} ^{\circ} = 73\frac{1}{3} ^{\circ} = 73.\overline 3^{\circ}[/tex]

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The scatter plot that displays the relationship between the bench press and squat weights for this sample is given by the second image at the end of the answer.

From the scatter plot, it can be taken that the relationship is that the variables have a positive association, as when the bench press weight increases, so does the squat weight. The relationship, however, is not strong, as the scatter plot is not 100% increasing.

The scatter plot is built inserting all the points of the table in a graph, which are in the following input-output format:

(bench press weight, squat weight).

From the table given by the first image at the end of the answer, the points are listed as follows:

(95, 141), (111, 208), (113, 100), (125, 218), (135, 284), (145, 275), (165, 338), (180, 338), (140, 420), (196, 420), (95, 141), (111, 208).

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The number of pounds of grapes sold is 17 pounds and the number of pounds of apples sold is 47 pounds.

According to the question,

We have the following information:

Cost of 1 pound of grapes = $3.75

Cost of 1 pound of apples = $4

Total cost made by selling = $251.75

And the weight of the apples and grapes sold = 64

Now, let's take the weight of grapes to be x pounds and the weight of apples to be y pounds.

So, we have:

x+y = 64

x = 64-y ....(1)

3.75x+4y = 251.75

Putting the value of x in this equation:

3.75(64-y)+4y = 251.75

3.75*64-3.75y+4y = 251.75

240+0.25y = 251.75

0.25y = 251.75-240

0.25y = 11.75

y = 11.75/0.25

y = 47 pounds

Now, putting this value of y in equation 1:

x = 64-y

x = 64-47

x = 17 pounds

Hence, the number of pounds of grapes sold is 17 pounds and the number of pounds of apples sold is 47 pounds.

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Answer:

20 mph

Step-by-step explanation:

If it took the car originally 12 minutes to travel the road with an average speed of 60 mph. Than you would just divide the average speed by three because it is taking 3 times the amount of time than it would originally.
36/12=3
60/3=20
20 mph

The time taken is obtained as 3 years.

We know that radioactivity has to do with the fact that a substances does disintegrate gradually over a period of time.

Let us recall the formula;

N/No = (1/2)^t/t1/2

N = The mass of radioactive atoms at time t

No = The mass of radioactive atoms initially present

t = time taken

t/12 = half life of the radioactive nucleus

Then;

32/50 = (1/2)^t/28

0.64 =  (1/2)^t/28

log 0.64 = t/28 log0.5

t/28 = log(0.64/0.5)

t = 28 * log(0.64/0.5)

t = 3 years

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If from a population of 50 bank accounts, we want to take a random sample of four accounts in order to learn about the population. The number of  different random samples of four accounts that are possible is 230,300.

Given data:

Number of population of bank account = 50

Random sample = 4 accounts

Now let find the different random samples of four account that are possible

Different random sample = 50! / (50 -4)! × 4!

Different random sample = 50! / 46! × 4!

Different random sample = 230,300

Therefore the different random samples is 230,300.

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[tex]\framebox{w=$\dfrac{25}{3}$}[/tex]

Flip the equation:

[tex]\frac{6}{5} w=10[/tex]

Multiply both sides by [tex]\frac{5}{6}[/tex]:

[tex](\frac{5}{6} )\times(\frac{6}{5} w)=(\frac{5}{6} )\times(10)[/tex]

[tex]w=\frac{25}{3}[/tex]

The expressions are:

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

15 x squared minus 18 end quantity over 6.

= 15x² - 18 / 6

= 3(5x² - 6)/ 6

= (5x² - 6)/ 2

and, 5 x squared minus 18 end quantity over 2

= 5x² - 18/2

and, 5 x squared minus 6 end quantity over 2

= 5x² -6 /2

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We got x = 16.54 by using Pythagorean theorem .

What is the Pythagorean theorem in plain English?

angle of semicircle is always be 90° .

   18² = 7.1² + x²

    324 = 50.41 + x²

     x² = 324 - 50.41

          = 273.59

    x = √ 273.59

    x = 16.54

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Answer:

I'm not sure if its right but I got

6/9

Step-by-step explanation:

What I did was:

I took the 2 points:

(-4,4) and (5,-2)

Then did rise over run

Which left me with 6/9

The inequality as per the question is x ≥ 9 and y > 3 and the diagram according to this is attached below.

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare the two values. Less than (or less than and equal to), larger than (or greater or equal to), or not similar to signs are used in place of the equal sign in between.

As per the given information in the question.,

x ≥ 9 and,

y > 3

The equation is,

650 x + 1400 y ≤ 1

[tex]\frac{x/15000}{650}+\frac{y/15000}{1400} \leq 1[/tex]

x/23.07 + y/10.71 ≤ 1

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